## Begin on: Wed Oct 16 01:32:19 CEST 2019 ENUMERATION No. of records: 848 FAMILY (oriented family) : isomorphism classes 1 [ E1b] : 19 (15 non-degenerate) 2 [ E3b] : 109 (90 non-degenerate) 2* [E3*b] : 109 (90 non-degenerate) 2ex [E3*c] : 5 (5 non-degenerate) 2*ex [ E3c] : 5 (5 non-degenerate) 2P [ E2] : 20 (19 non-degenerate) 2Pex [ E1a] : 4 (4 non-degenerate) 3 [ E5a] : 449 (206 non-degenerate) 4 [ E4] : 46 (21 non-degenerate) 4* [ E4*] : 46 (21 non-degenerate) 4P [ E6] : 10 (2 non-degenerate) 5 [ E3a] : 13 (9 non-degenerate) 5* [E3*a] : 13 (9 non-degenerate) 5P [ E5b] : 0 E12.1 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {12, 12}) Quotient :: toric Aut^+ = C12 (small group id <12, 2>) Aut = D24 (small group id <24, 6>) |r| :: 2 Presentation :: [ A, B, A, B, A, B, A, B, A, B, A, B, A, B, A, 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^12, (Z^-1 * A * B^-1 * A^-1 * B)^12 ] Map:: R = (1, 14, 26, 38, 2, 16, 28, 40, 4, 18, 30, 42, 6, 20, 32, 44, 8, 22, 34, 46, 10, 24, 36, 48, 12, 23, 35, 47, 11, 21, 33, 45, 9, 19, 31, 43, 7, 17, 29, 41, 5, 15, 27, 39, 3, 13, 25, 37) L = (1, 25)(2, 26)(3, 27)(4, 28)(5, 29)(6, 30)(7, 31)(8, 32)(9, 33)(10, 34)(11, 35)(12, 36)(13, 37)(14, 38)(15, 39)(16, 40)(17, 41)(18, 42)(19, 43)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48) local type(s) :: { ( 48^48 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 1 e = 24 f = 1 degree seq :: [ 48 ] E12.2 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {12, 12}) Quotient :: toric Aut^+ = C12 (small group id <12, 2>) Aut = D24 (small group id <24, 6>) |r| :: 2 Presentation :: [ S^2, A^2, B^-1 * A, A * Z * A * Z^-1, (S * Z)^2, S * A * S * B, A * Z^6 ] Map:: R = (1, 14, 26, 38, 2, 17, 29, 41, 5, 21, 33, 45, 9, 23, 35, 47, 11, 19, 31, 43, 7, 15, 27, 39, 3, 18, 30, 42, 6, 22, 34, 46, 10, 24, 36, 48, 12, 20, 32, 44, 8, 16, 28, 40, 4, 13, 25, 37) L = (1, 27)(2, 30)(3, 25)(4, 31)(5, 34)(6, 26)(7, 28)(8, 35)(9, 36)(10, 29)(11, 32)(12, 33)(13, 39)(14, 42)(15, 37)(16, 43)(17, 46)(18, 38)(19, 40)(20, 47)(21, 48)(22, 41)(23, 44)(24, 45) local type(s) :: { ( 48^48 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 1 e = 24 f = 1 degree seq :: [ 48 ] E12.3 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {12, 12}) Quotient :: toric Aut^+ = C12 (small group id <12, 2>) Aut = D24 (small group id <24, 6>) |r| :: 2 Presentation :: [ S^2, B^-1 * A, B^3, A * B * A, (A^-1, Z), (S * Z)^2, S * A * S * B, Z^-2 * B * Z^-2 ] Map:: R = (1, 14, 26, 38, 2, 18, 30, 42, 6, 21, 33, 45, 9, 15, 27, 39, 3, 19, 31, 43, 7, 24, 36, 48, 12, 23, 35, 47, 11, 17, 29, 41, 5, 20, 32, 44, 8, 22, 34, 46, 10, 16, 28, 40, 4, 13, 25, 37) L = (1, 27)(2, 31)(3, 29)(4, 33)(5, 25)(6, 36)(7, 32)(8, 26)(9, 35)(10, 30)(11, 28)(12, 34)(13, 41)(14, 44)(15, 37)(16, 47)(17, 39)(18, 46)(19, 38)(20, 43)(21, 40)(22, 48)(23, 45)(24, 42) local type(s) :: { ( 48^48 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 1 e = 24 f = 1 degree seq :: [ 48 ] E12.4 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {12, 12}) Quotient :: toric Aut^+ = C12 (small group id <12, 2>) Aut = D24 (small group id <24, 6>) |r| :: 2 Presentation :: [ S^2, A^-1 * B, B^3, A^3, A * Z * B^-1 * Z^-1, S * A * S * B, A * Z^-1 * B^-1 * Z, (S * Z)^2, Z^-1 * A^-1 * Z^-3 ] Map:: R = (1, 14, 26, 38, 2, 18, 30, 42, 6, 23, 35, 47, 11, 17, 29, 41, 5, 20, 32, 44, 8, 24, 36, 48, 12, 21, 33, 45, 9, 15, 27, 39, 3, 19, 31, 43, 7, 22, 34, 46, 10, 16, 28, 40, 4, 13, 25, 37) L = (1, 27)(2, 31)(3, 29)(4, 33)(5, 25)(6, 34)(7, 32)(8, 26)(9, 35)(10, 36)(11, 28)(12, 30)(13, 41)(14, 44)(15, 37)(16, 47)(17, 39)(18, 48)(19, 38)(20, 43)(21, 40)(22, 42)(23, 45)(24, 46) local type(s) :: { ( 48^48 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 1 e = 24 f = 1 degree seq :: [ 48 ] E12.5 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {12, 12}) Quotient :: toric Aut^+ = C12 (small group id <12, 2>) Aut = D24 (small group id <24, 6>) |r| :: 2 Presentation :: [ S^2, A^-1 * B, Z^-1 * A * Z^-2, (A^-1, Z^-1), S * A * S * B, (S * Z)^2, A^-1 * B^-1 * A^-2 ] Map:: R = (1, 14, 26, 38, 2, 18, 30, 42, 6, 15, 27, 39, 3, 19, 31, 43, 7, 23, 35, 47, 11, 21, 33, 45, 9, 24, 36, 48, 12, 22, 34, 46, 10, 17, 29, 41, 5, 20, 32, 44, 8, 16, 28, 40, 4, 13, 25, 37) L = (1, 27)(2, 31)(3, 33)(4, 30)(5, 25)(6, 35)(7, 36)(8, 26)(9, 29)(10, 28)(11, 34)(12, 32)(13, 41)(14, 44)(15, 37)(16, 46)(17, 45)(18, 40)(19, 38)(20, 48)(21, 39)(22, 47)(23, 42)(24, 43) local type(s) :: { ( 48^48 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 1 e = 24 f = 1 degree seq :: [ 48 ] E12.6 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {12, 12}) Quotient :: toric Aut^+ = C12 (small group id <12, 2>) Aut = D24 (small group id <24, 6>) |r| :: 2 Presentation :: [ S^2, B * A^-1, Z^2 * A^-1, S * B * S * A, (S * Z)^2, A^6, (B^-1 * Z)^12 ] Map:: R = (1, 14, 26, 38, 2, 15, 27, 39, 3, 18, 30, 42, 6, 19, 31, 43, 7, 22, 34, 46, 10, 23, 35, 47, 11, 24, 36, 48, 12, 21, 33, 45, 9, 20, 32, 44, 8, 17, 29, 41, 5, 16, 28, 40, 4, 13, 25, 37) L = (1, 27)(2, 30)(3, 31)(4, 26)(5, 25)(6, 34)(7, 35)(8, 28)(9, 29)(10, 36)(11, 33)(12, 32)(13, 41)(14, 40)(15, 37)(16, 44)(17, 45)(18, 38)(19, 39)(20, 48)(21, 47)(22, 42)(23, 43)(24, 46) local type(s) :: { ( 48^48 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 1 e = 24 f = 1 degree seq :: [ 48 ] E12.7 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {2, 2}) Quotient :: toric Aut^+ = C22 (small group id <22, 2>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ Z^2, S^2, B * A^-1, S * B * S * A, (S * Z)^2, A * Z * A^-1 * Z, A^11 ] Map:: R = (1, 24, 46, 68, 2, 23, 45, 67)(3, 27, 49, 71, 5, 25, 47, 69)(4, 28, 50, 72, 6, 26, 48, 70)(7, 31, 53, 75, 9, 29, 51, 73)(8, 32, 54, 76, 10, 30, 52, 74)(11, 35, 57, 79, 13, 33, 55, 77)(12, 36, 58, 80, 14, 34, 56, 78)(15, 39, 61, 83, 17, 37, 59, 81)(16, 40, 62, 84, 18, 38, 60, 82)(19, 43, 65, 87, 21, 41, 63, 85)(20, 44, 66, 88, 22, 42, 64, 86) L = (1, 47)(2, 49)(3, 51)(4, 45)(5, 53)(6, 46)(7, 55)(8, 48)(9, 57)(10, 50)(11, 59)(12, 52)(13, 61)(14, 54)(15, 63)(16, 56)(17, 65)(18, 58)(19, 64)(20, 60)(21, 66)(22, 62)(23, 70)(24, 72)(25, 67)(26, 74)(27, 68)(28, 76)(29, 69)(30, 78)(31, 71)(32, 80)(33, 73)(34, 82)(35, 75)(36, 84)(37, 77)(38, 86)(39, 79)(40, 88)(41, 81)(42, 85)(43, 83)(44, 87) local type(s) :: { ( 8^8 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 11 e = 44 f = 11 degree seq :: [ 8^11 ] E12.8 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {2, 2}) Quotient :: toric Aut^+ = D22 (small group id <22, 1>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ Z^2, S^2, A^2, B^-1 * A, S * B * S * A, (S * Z)^2, (A * Z)^11 ] Map:: R = (1, 24, 46, 68, 2, 23, 45, 67)(3, 27, 49, 71, 5, 25, 47, 69)(4, 28, 50, 72, 6, 26, 48, 70)(7, 31, 53, 75, 9, 29, 51, 73)(8, 32, 54, 76, 10, 30, 52, 74)(11, 35, 57, 79, 13, 33, 55, 77)(12, 36, 58, 80, 14, 34, 56, 78)(15, 39, 61, 83, 17, 37, 59, 81)(16, 40, 62, 84, 18, 38, 60, 82)(19, 43, 65, 87, 21, 41, 63, 85)(20, 44, 66, 88, 22, 42, 64, 86) L = (1, 47)(2, 48)(3, 45)(4, 46)(5, 51)(6, 52)(7, 49)(8, 50)(9, 55)(10, 56)(11, 53)(12, 54)(13, 59)(14, 60)(15, 57)(16, 58)(17, 63)(18, 64)(19, 61)(20, 62)(21, 66)(22, 65)(23, 69)(24, 70)(25, 67)(26, 68)(27, 73)(28, 74)(29, 71)(30, 72)(31, 77)(32, 78)(33, 75)(34, 76)(35, 81)(36, 82)(37, 79)(38, 80)(39, 85)(40, 86)(41, 83)(42, 84)(43, 88)(44, 87) local type(s) :: { ( 8^8 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 11 e = 44 f = 11 degree seq :: [ 8^11 ] E12.9 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {2, 2}) Quotient :: toric Aut^+ = D22 (small group id <22, 1>) Aut = D44 (small group id <44, 3>) |r| :: 2 Presentation :: [ Z^2, S^2, A^-1 * B^-1, (S * Z)^2, S * A * S * B, A * Z * B^-1 * Z, A^6 * B^-5 ] Map:: non-degenerate R = (1, 24, 46, 68, 2, 23, 45, 67)(3, 28, 50, 72, 6, 25, 47, 69)(4, 27, 49, 71, 5, 26, 48, 70)(7, 32, 54, 76, 10, 29, 51, 73)(8, 31, 53, 75, 9, 30, 52, 74)(11, 36, 58, 80, 14, 33, 55, 77)(12, 35, 57, 79, 13, 34, 56, 78)(15, 40, 62, 84, 18, 37, 59, 81)(16, 39, 61, 83, 17, 38, 60, 82)(19, 44, 66, 88, 22, 41, 63, 85)(20, 43, 65, 87, 21, 42, 64, 86) L = (1, 47)(2, 49)(3, 51)(4, 45)(5, 53)(6, 46)(7, 55)(8, 48)(9, 57)(10, 50)(11, 59)(12, 52)(13, 61)(14, 54)(15, 63)(16, 56)(17, 65)(18, 58)(19, 64)(20, 60)(21, 66)(22, 62)(23, 69)(24, 71)(25, 73)(26, 67)(27, 75)(28, 68)(29, 77)(30, 70)(31, 79)(32, 72)(33, 81)(34, 74)(35, 83)(36, 76)(37, 85)(38, 78)(39, 87)(40, 80)(41, 86)(42, 82)(43, 88)(44, 84) local type(s) :: { ( 8^8 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 11 e = 44 f = 11 degree seq :: [ 8^11 ] E12.10 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {2, 2}) Quotient :: toric Aut^+ = C22 (small group id <22, 2>) Aut = C22 x C2 (small group id <44, 4>) |r| :: 2 Presentation :: [ Z^2, S^2, B^-1 * A^-1, (S * Z)^2, S * B * S * A, A * Z * A^-1 * Z, B * Z * B^-1 * Z, A^6 * B^-5 ] Map:: non-degenerate R = (1, 24, 46, 68, 2, 23, 45, 67)(3, 27, 49, 71, 5, 25, 47, 69)(4, 28, 50, 72, 6, 26, 48, 70)(7, 31, 53, 75, 9, 29, 51, 73)(8, 32, 54, 76, 10, 30, 52, 74)(11, 35, 57, 79, 13, 33, 55, 77)(12, 36, 58, 80, 14, 34, 56, 78)(15, 39, 61, 83, 17, 37, 59, 81)(16, 40, 62, 84, 18, 38, 60, 82)(19, 43, 65, 87, 21, 41, 63, 85)(20, 44, 66, 88, 22, 42, 64, 86) L = (1, 47)(2, 49)(3, 51)(4, 45)(5, 53)(6, 46)(7, 55)(8, 48)(9, 57)(10, 50)(11, 59)(12, 52)(13, 61)(14, 54)(15, 63)(16, 56)(17, 65)(18, 58)(19, 64)(20, 60)(21, 66)(22, 62)(23, 69)(24, 71)(25, 73)(26, 67)(27, 75)(28, 68)(29, 77)(30, 70)(31, 79)(32, 72)(33, 81)(34, 74)(35, 83)(36, 76)(37, 85)(38, 78)(39, 87)(40, 80)(41, 86)(42, 82)(43, 88)(44, 84) local type(s) :: { ( 8^8 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 11 e = 44 f = 11 degree seq :: [ 8^11 ] E12.11 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {13, 13, 13, 13}) Quotient :: dipole Aut^+ = C13 (small group id <13, 1>) Aut = D26 (small group id <26, 1>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y2 * Y1^-1 * Y2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y1^6 * Y2, (Y3^-1 * Y1^-1)^13, (Y3 * Y2^-1)^13 ] Map:: R = (1, 14, 2, 15, 6, 19, 10, 23, 13, 26, 9, 22, 5, 18, 3, 16, 7, 20, 11, 24, 12, 25, 8, 21, 4, 17)(27, 40, 29, 42, 28, 41, 33, 46, 32, 45, 37, 50, 36, 49, 38, 51, 39, 52, 34, 47, 35, 48, 30, 43, 31, 44) L = (1, 27)(2, 28)(3, 29)(4, 30)(5, 31)(6, 32)(7, 33)(8, 34)(9, 35)(10, 36)(11, 37)(12, 38)(13, 39)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52) local type(s) :: { ( 26^26 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 2 e = 26 f = 2 degree seq :: [ 26^2 ] E12.12 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {13, 13, 13, 13}) Quotient :: dipole Aut^+ = C13 (small group id <13, 1>) Aut = D26 (small group id <26, 1>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y1 * Y2^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2 * Y1^-6, (Y3^-1 * Y1^-1)^13, (Y3 * Y2^-1)^13 ] Map:: R = (1, 14, 2, 15, 6, 19, 10, 23, 12, 25, 8, 21, 3, 16, 5, 18, 7, 20, 11, 24, 13, 26, 9, 22, 4, 17)(27, 40, 29, 42, 30, 43, 34, 47, 35, 48, 38, 51, 39, 52, 36, 49, 37, 50, 32, 45, 33, 46, 28, 41, 31, 44) L = (1, 27)(2, 28)(3, 29)(4, 30)(5, 31)(6, 32)(7, 33)(8, 34)(9, 35)(10, 36)(11, 37)(12, 38)(13, 39)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52) local type(s) :: { ( 26^26 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 2 e = 26 f = 2 degree seq :: [ 26^2 ] E12.13 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {13, 13, 13, 13}) Quotient :: dipole Aut^+ = C13 (small group id <13, 1>) Aut = D26 (small group id <26, 1>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y2^-2 * Y1 * Y2^-1, (R * Y1)^2, (R * Y3)^2, Y1^2 * Y2 * Y1^2, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^13, (Y3 * Y2^-1)^13 ] Map:: R = (1, 14, 2, 15, 6, 19, 11, 24, 5, 18, 8, 21, 12, 25, 13, 26, 9, 22, 3, 16, 7, 20, 10, 23, 4, 17)(27, 40, 29, 42, 34, 47, 28, 41, 33, 46, 38, 51, 32, 45, 36, 49, 39, 52, 37, 50, 30, 43, 35, 48, 31, 44) L = (1, 27)(2, 28)(3, 29)(4, 30)(5, 31)(6, 32)(7, 33)(8, 34)(9, 35)(10, 36)(11, 37)(12, 38)(13, 39)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52) local type(s) :: { ( 26^26 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 2 e = 26 f = 2 degree seq :: [ 26^2 ] E12.14 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {13, 13, 13, 13}) Quotient :: dipole Aut^+ = C13 (small group id <13, 1>) Aut = D26 (small group id <26, 1>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y2^-1 * Y1^-1 * Y2^-2, (R * Y3)^2, (R * Y1)^2, (Y2^-1, Y1^-1), Y2^-1 * Y1^4, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^13, (Y3^-1 * Y1^-1)^13 ] Map:: R = (1, 14, 2, 15, 6, 19, 10, 23, 3, 16, 7, 20, 12, 25, 13, 26, 9, 22, 5, 18, 8, 21, 11, 24, 4, 17)(27, 40, 29, 42, 35, 48, 30, 43, 36, 49, 39, 52, 37, 50, 32, 45, 38, 51, 34, 47, 28, 41, 33, 46, 31, 44) L = (1, 27)(2, 28)(3, 29)(4, 30)(5, 31)(6, 32)(7, 33)(8, 34)(9, 35)(10, 36)(11, 37)(12, 38)(13, 39)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52) local type(s) :: { ( 26^26 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 2 e = 26 f = 2 degree seq :: [ 26^2 ] E12.15 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {13, 13, 13, 13}) Quotient :: dipole Aut^+ = C13 (small group id <13, 1>) Aut = D26 (small group id <26, 1>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (R * Y3)^2, (R * Y1)^2, (Y2^-1, Y1^-1), Y1 * Y2^-1 * Y1 * Y2^-1 * Y1, Y1 * Y2 * Y1 * Y2^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^13, (Y3^-1 * Y1^-1)^13 ] Map:: R = (1, 14, 2, 15, 6, 19, 9, 22, 12, 25, 5, 18, 8, 21, 10, 23, 3, 16, 7, 20, 13, 26, 11, 24, 4, 17)(27, 40, 29, 42, 35, 48, 37, 50, 34, 47, 28, 41, 33, 46, 38, 51, 30, 43, 36, 49, 32, 45, 39, 52, 31, 44) L = (1, 27)(2, 28)(3, 29)(4, 30)(5, 31)(6, 32)(7, 33)(8, 34)(9, 35)(10, 36)(11, 37)(12, 38)(13, 39)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52) local type(s) :: { ( 26^26 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 2 e = 26 f = 2 degree seq :: [ 26^2 ] E12.16 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {13, 13, 13, 13}) Quotient :: dipole Aut^+ = C13 (small group id <13, 1>) Aut = D26 (small group id <26, 1>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3, Y1 * Y3^-2, (R * Y1)^2, (R * Y3)^2, Y1^3 * Y3 * Y1^3, Y2^13, (Y3^-1 * Y1^-1)^13 ] Map:: non-degenerate R = (1, 14, 2, 15, 6, 19, 10, 23, 12, 25, 8, 21, 3, 16, 4, 17, 7, 20, 11, 24, 13, 26, 9, 22, 5, 18)(27, 40, 29, 42, 31, 44, 34, 47, 35, 48, 38, 51, 39, 52, 36, 49, 37, 50, 32, 45, 33, 46, 28, 41, 30, 43) L = (1, 30)(2, 33)(3, 27)(4, 28)(5, 29)(6, 37)(7, 32)(8, 31)(9, 34)(10, 39)(11, 36)(12, 35)(13, 38)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52) local type(s) :: { ( 26^26 ) } Outer automorphisms :: reflexible Dual of E12.27 Graph:: bipartite v = 2 e = 26 f = 2 degree seq :: [ 26^2 ] E12.17 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {13, 13, 13, 13}) Quotient :: dipole Aut^+ = C13 (small group id <13, 1>) Aut = D26 (small group id <26, 1>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2, Y3 * Y2, Y3 * Y1^-1 * Y2^-1 * Y3, Y1^-1 * Y3 * Y2^-2, (Y3^-1, Y1^-1), (R * Y1)^2, R * Y2 * R * Y3^-1, Y1 * Y3 * Y1^3, Y1^-1 * Y2^10, (Y1 * Y2)^13 ] Map:: non-degenerate R = (1, 14, 2, 15, 6, 19, 10, 23, 3, 16, 7, 20, 12, 25, 13, 26, 9, 22, 4, 17, 8, 21, 11, 24, 5, 18)(27, 40, 29, 42, 35, 48, 31, 44, 36, 49, 39, 52, 37, 50, 32, 45, 38, 51, 34, 47, 28, 41, 33, 46, 30, 43) L = (1, 30)(2, 34)(3, 27)(4, 33)(5, 35)(6, 37)(7, 28)(8, 38)(9, 29)(10, 31)(11, 39)(12, 32)(13, 36)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52) local type(s) :: { ( 26^26 ) } Outer automorphisms :: reflexible Dual of E12.31 Graph:: bipartite v = 2 e = 26 f = 2 degree seq :: [ 26^2 ] E12.18 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {13, 13, 13, 13}) Quotient :: dipole Aut^+ = C13 (small group id <13, 1>) Aut = D26 (small group id <26, 1>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3, Y1^-1 * Y3 * Y1^-2, (Y3^-1, Y1^-1), (R * Y3)^2, (R * Y1)^2, (Y1, Y2^-1), Y1^-1 * Y2 * Y3^-3, Y3 * Y1 * Y3 * Y2^-2, Y2^13, Y1^-1 * Y2^-2 * Y1^-1 * Y2^-2 * Y1^-1 * Y2^-2 * Y1^-1 * Y2^-2 * Y1^-1 * Y2^-2 * Y1^-1 * Y2^-2 * Y1^-1 * Y3^-1, (Y3 * Y2^-1)^13 ] Map:: non-degenerate R = (1, 14, 2, 15, 6, 19, 4, 17, 8, 21, 12, 25, 11, 24, 9, 22, 13, 26, 10, 23, 3, 16, 7, 20, 5, 18)(27, 40, 29, 42, 35, 48, 34, 47, 28, 41, 33, 46, 39, 52, 38, 51, 32, 45, 31, 44, 36, 49, 37, 50, 30, 43) L = (1, 30)(2, 34)(3, 27)(4, 37)(5, 32)(6, 38)(7, 28)(8, 35)(9, 29)(10, 31)(11, 36)(12, 39)(13, 33)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52) local type(s) :: { ( 26^26 ) } Outer automorphisms :: reflexible Dual of E12.21 Graph:: bipartite v = 2 e = 26 f = 2 degree seq :: [ 26^2 ] E12.19 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {13, 13, 13, 13}) Quotient :: dipole Aut^+ = C13 (small group id <13, 1>) Aut = D26 (small group id <26, 1>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y2^-1, Y2 * Y3, Y2 * Y1^-3, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1^-1), Y2^2 * Y3^-2 * Y1, Y2^13, (Y1^-1 * Y3^-1)^13, (Y3 * Y2^-1)^13 ] Map:: non-degenerate R = (1, 14, 2, 15, 6, 19, 3, 16, 7, 20, 12, 25, 9, 22, 10, 23, 13, 26, 11, 24, 4, 17, 8, 21, 5, 18)(27, 40, 29, 42, 35, 48, 37, 50, 31, 44, 32, 45, 38, 51, 39, 52, 34, 47, 28, 41, 33, 46, 36, 49, 30, 43) L = (1, 30)(2, 34)(3, 27)(4, 36)(5, 37)(6, 31)(7, 28)(8, 39)(9, 29)(10, 33)(11, 35)(12, 32)(13, 38)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52) local type(s) :: { ( 26^26 ) } Outer automorphisms :: reflexible Dual of E12.33 Graph:: bipartite v = 2 e = 26 f = 2 degree seq :: [ 26^2 ] E12.20 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {13, 13, 13, 13}) Quotient :: dipole Aut^+ = C13 (small group id <13, 1>) Aut = D26 (small group id <26, 1>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y2^-1, (R * Y1)^2, R * Y2 * R * Y3^-1, (Y1, Y3^-1), (Y2^-1, Y1^-1), Y2^-2 * Y1^3, Y2 * Y1 * Y2 * Y1 * Y3^-1, Y2^-13, Y2^13, (Y1^-1 * Y3^-1)^13, (Y3 * Y2^-1)^13 ] Map:: non-degenerate R = (1, 14, 2, 15, 6, 19, 9, 22, 12, 25, 4, 17, 8, 21, 10, 23, 3, 16, 7, 20, 11, 24, 13, 26, 5, 18)(27, 40, 29, 42, 35, 48, 39, 52, 34, 47, 28, 41, 33, 46, 38, 51, 31, 44, 36, 49, 32, 45, 37, 50, 30, 43) L = (1, 30)(2, 34)(3, 27)(4, 37)(5, 38)(6, 36)(7, 28)(8, 39)(9, 29)(10, 31)(11, 32)(12, 33)(13, 35)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52) local type(s) :: { ( 26^26 ) } Outer automorphisms :: reflexible Dual of E12.35 Graph:: bipartite v = 2 e = 26 f = 2 degree seq :: [ 26^2 ] E12.21 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {13, 13, 13, 13}) Quotient :: dipole Aut^+ = C13 (small group id <13, 1>) Aut = D26 (small group id <26, 1>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y3^-1, (Y1, Y3^-1), (R * Y1)^2, R * Y2 * R * Y3^-1, (Y2^-1, Y1^-1), Y2^3 * Y1^-2, Y3 * Y1 * Y3 * Y1 * Y2^-1, Y1 * Y2 * Y1^2 * Y3^-1, Y1^-1 * Y2^-5, Y1^13, (Y3 * Y2^-1)^13 ] Map:: non-degenerate R = (1, 14, 2, 15, 6, 19, 11, 24, 10, 23, 3, 16, 7, 20, 12, 25, 4, 17, 8, 21, 9, 22, 13, 26, 5, 18)(27, 40, 29, 42, 35, 48, 32, 45, 38, 51, 31, 44, 36, 49, 34, 47, 28, 41, 33, 46, 39, 52, 37, 50, 30, 43) L = (1, 30)(2, 34)(3, 27)(4, 37)(5, 38)(6, 35)(7, 28)(8, 36)(9, 29)(10, 31)(11, 39)(12, 32)(13, 33)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52) local type(s) :: { ( 26^26 ) } Outer automorphisms :: reflexible Dual of E12.18 Graph:: bipartite v = 2 e = 26 f = 2 degree seq :: [ 26^2 ] E12.22 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {13, 13, 13, 13}) Quotient :: dipole Aut^+ = C13 (small group id <13, 1>) Aut = D26 (small group id <26, 1>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2, Y1^2 * Y3^-1, (R * Y1)^2, R * Y2 * R * Y3^-1, (Y1, Y2^-1), Y1 * Y2^-3 * Y3^3, Y2^7 * Y1, (Y3 * Y2^-1)^13, (Y3^-1 * Y1^-1)^13 ] Map:: non-degenerate R = (1, 14, 2, 15, 4, 17, 6, 19, 9, 22, 10, 23, 13, 26, 11, 24, 12, 25, 7, 20, 8, 21, 3, 16, 5, 18)(27, 40, 29, 42, 33, 46, 37, 50, 36, 49, 32, 45, 28, 41, 31, 44, 34, 47, 38, 51, 39, 52, 35, 48, 30, 43) L = (1, 30)(2, 32)(3, 27)(4, 35)(5, 28)(6, 36)(7, 29)(8, 31)(9, 39)(10, 37)(11, 33)(12, 34)(13, 38)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52) local type(s) :: { ( 26^26 ) } Outer automorphisms :: reflexible Dual of E12.30 Graph:: bipartite v = 2 e = 26 f = 2 degree seq :: [ 26^2 ] E12.23 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {13, 13, 13, 13}) Quotient :: dipole Aut^+ = C13 (small group id <13, 1>) Aut = D26 (small group id <26, 1>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3, Y2 * Y1^-2, (R * Y1)^2, (R * Y3)^2, (Y1, Y3^-1), Y1 * Y2^6, (Y1^-1 * Y3^-1)^13, (Y3 * Y2^-1)^13 ] Map:: non-degenerate R = (1, 14, 2, 15, 3, 16, 6, 19, 7, 20, 10, 23, 11, 24, 12, 25, 13, 26, 8, 21, 9, 22, 4, 17, 5, 18)(27, 40, 29, 42, 33, 46, 37, 50, 39, 52, 35, 48, 31, 44, 28, 41, 32, 45, 36, 49, 38, 51, 34, 47, 30, 43) L = (1, 30)(2, 31)(3, 27)(4, 34)(5, 35)(6, 28)(7, 29)(8, 38)(9, 39)(10, 32)(11, 33)(12, 36)(13, 37)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52) local type(s) :: { ( 26^26 ) } Outer automorphisms :: reflexible Dual of E12.26 Graph:: bipartite v = 2 e = 26 f = 2 degree seq :: [ 26^2 ] E12.24 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {13, 13, 13, 13}) Quotient :: dipole Aut^+ = C13 (small group id <13, 1>) Aut = D26 (small group id <26, 1>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2^-1 * Y3^-1, Y1 * Y3^-1 * Y2^-1, Y2 * Y3^-1 * Y2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y1^2 * Y2 * Y1^2, Y3^5 * 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 ] Map:: non-degenerate R = (1, 14, 2, 15, 8, 21, 12, 25, 6, 19, 4, 17, 10, 23, 13, 26, 7, 20, 3, 16, 9, 22, 11, 24, 5, 18)(27, 40, 29, 42, 30, 43, 28, 41, 35, 48, 36, 49, 34, 47, 37, 50, 39, 52, 38, 51, 31, 44, 33, 46, 32, 45) L = (1, 30)(2, 36)(3, 28)(4, 35)(5, 32)(6, 29)(7, 27)(8, 39)(9, 34)(10, 37)(11, 38)(12, 33)(13, 31)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52) local type(s) :: { ( 26^26 ) } Outer automorphisms :: reflexible Dual of E12.28 Graph:: bipartite v = 2 e = 26 f = 2 degree seq :: [ 26^2 ] E12.25 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {13, 13, 13, 13}) Quotient :: dipole Aut^+ = C13 (small group id <13, 1>) Aut = D26 (small group id <26, 1>) |r| :: 2 Presentation :: [ R^2, Y2^-2 * Y3, Y1 * Y3^-2, Y1^-2 * Y2^-1 * Y1^-1, (R * Y2)^2, (R * Y3)^2, Y2 * Y3 * Y2 * Y1^-1, (R * Y1)^2 ] Map:: non-degenerate R = (1, 14, 2, 15, 8, 21, 6, 19, 11, 24, 13, 26, 7, 20, 4, 17, 10, 23, 12, 25, 3, 16, 9, 22, 5, 18)(27, 40, 29, 42, 30, 43, 37, 50, 28, 41, 35, 48, 36, 49, 39, 52, 34, 47, 31, 44, 38, 51, 33, 46, 32, 45) L = (1, 30)(2, 36)(3, 37)(4, 28)(5, 33)(6, 29)(7, 27)(8, 38)(9, 39)(10, 34)(11, 35)(12, 32)(13, 31)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52) local type(s) :: { ( 26^26 ) } Outer automorphisms :: reflexible Dual of E12.29 Graph:: bipartite v = 2 e = 26 f = 2 degree seq :: [ 26^2 ] E12.26 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {13, 13, 13, 13}) Quotient :: dipole Aut^+ = C13 (small group id <13, 1>) Aut = D26 (small group id <26, 1>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-2, Y1 * Y3^2, Y2 * Y1^-3, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y1^-1 * Y2^-1 * Y3^-1 * Y2^-1, Y2^-1 * Y3^-1 * Y1^2 * Y3^-1 ] Map:: non-degenerate R = (1, 14, 2, 15, 8, 21, 3, 16, 9, 22, 13, 26, 4, 17, 7, 20, 11, 24, 12, 25, 6, 19, 10, 23, 5, 18)(27, 40, 29, 42, 30, 43, 38, 51, 31, 44, 34, 47, 39, 52, 37, 50, 36, 49, 28, 41, 35, 48, 33, 46, 32, 45) L = (1, 30)(2, 33)(3, 38)(4, 31)(5, 39)(6, 29)(7, 27)(8, 37)(9, 32)(10, 35)(11, 28)(12, 34)(13, 36)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52) local type(s) :: { ( 26^26 ) } Outer automorphisms :: reflexible Dual of E12.23 Graph:: bipartite v = 2 e = 26 f = 2 degree seq :: [ 26^2 ] E12.27 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {13, 13, 13, 13}) Quotient :: dipole Aut^+ = C13 (small group id <13, 1>) Aut = D26 (small group id <26, 1>) |r| :: 2 Presentation :: [ R^2, Y2^2 * Y3^-1, Y3^-1 * Y2^-1 * Y1 * Y3^-1, Y2 * Y3^2 * Y1^-1, (Y3, Y1^-1), Y2^-1 * Y3^-1 * Y1^-2, Y3^2 * Y2 * Y1^-1, Y3^-1 * Y1^-1 * Y2^-1 * Y1^-1, Y3 * Y1^-3, (R * Y3)^2, Y3^-1 * Y2^-1 * Y1^-2, (R * Y2)^2, Y3 * Y2 * Y3 * Y1^-1, (R * Y1)^2, Y1^-1 * Y3^-4 ] Map:: non-degenerate R = (1, 14, 2, 15, 8, 21, 4, 17, 10, 23, 6, 19, 11, 24, 13, 26, 3, 16, 9, 22, 7, 20, 12, 25, 5, 18)(27, 40, 29, 42, 30, 43, 38, 51, 37, 50, 28, 41, 35, 48, 36, 49, 31, 44, 39, 52, 34, 47, 33, 46, 32, 45) L = (1, 30)(2, 36)(3, 38)(4, 37)(5, 34)(6, 29)(7, 27)(8, 32)(9, 31)(10, 39)(11, 35)(12, 28)(13, 33)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52) local type(s) :: { ( 26^26 ) } Outer automorphisms :: reflexible Dual of E12.16 Graph:: bipartite v = 2 e = 26 f = 2 degree seq :: [ 26^2 ] E12.28 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {13, 13, 13, 13}) Quotient :: dipole Aut^+ = C13 (small group id <13, 1>) Aut = D26 (small group id <26, 1>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1 * Y2, Y1^-1 * Y3^-2 * Y2^-1, Y3 * Y2 * Y1^-2, Y1^-1 * Y3^-1 * Y2^-1 * Y3^-1, Y2 * Y1^-1 * Y3 * Y1^-1, Y3^-1 * Y1^-3, (R * Y3)^2, (Y3, Y1^-1), (R * Y2)^2, (R * Y1)^2 ] Map:: non-degenerate R = (1, 14, 2, 15, 8, 21, 7, 20, 12, 25, 3, 16, 9, 22, 13, 26, 6, 19, 11, 24, 4, 17, 10, 23, 5, 18)(27, 40, 29, 42, 30, 43, 34, 47, 39, 52, 31, 44, 38, 51, 37, 50, 28, 41, 35, 48, 36, 49, 33, 46, 32, 45) L = (1, 30)(2, 36)(3, 34)(4, 39)(5, 37)(6, 29)(7, 27)(8, 31)(9, 33)(10, 32)(11, 35)(12, 28)(13, 38)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52) local type(s) :: { ( 26^26 ) } Outer automorphisms :: reflexible Dual of E12.24 Graph:: bipartite v = 2 e = 26 f = 2 degree seq :: [ 26^2 ] E12.29 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {13, 13, 13, 13}) Quotient :: dipole Aut^+ = C13 (small group id <13, 1>) Aut = D26 (small group id <26, 1>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1^-2, Y2^2 * Y3^-1, Y3^-3 * Y1^-1, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y3 * Y1^-1 * Y2^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 14, 2, 15, 3, 16, 8, 21, 4, 17, 9, 22, 11, 24, 13, 26, 12, 25, 7, 20, 10, 23, 6, 19, 5, 18)(27, 40, 29, 42, 30, 43, 37, 50, 38, 51, 36, 49, 31, 44, 28, 41, 34, 47, 35, 48, 39, 52, 33, 46, 32, 45) L = (1, 30)(2, 35)(3, 37)(4, 38)(5, 34)(6, 29)(7, 27)(8, 39)(9, 33)(10, 28)(11, 36)(12, 31)(13, 32)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52) local type(s) :: { ( 26^26 ) } Outer automorphisms :: reflexible Dual of E12.25 Graph:: bipartite v = 2 e = 26 f = 2 degree seq :: [ 26^2 ] E12.30 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {13, 13, 13, 13}) Quotient :: dipole Aut^+ = C13 (small group id <13, 1>) Aut = D26 (small group id <26, 1>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^2, Y1 * Y3^-2, Y1^2 * Y2^-1 * Y1, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y1^-1 * Y2^-1 * Y3 * Y2^-1, Y2^-1 * Y3 * Y1 * Y3 * Y1 ] Map:: non-degenerate R = (1, 14, 2, 15, 8, 21, 3, 16, 9, 22, 13, 26, 7, 20, 4, 17, 10, 23, 12, 25, 6, 19, 11, 24, 5, 18)(27, 40, 29, 42, 33, 46, 38, 51, 31, 44, 34, 47, 39, 52, 36, 49, 37, 50, 28, 41, 35, 48, 30, 43, 32, 45) L = (1, 30)(2, 36)(3, 32)(4, 28)(5, 33)(6, 35)(7, 27)(8, 38)(9, 37)(10, 34)(11, 39)(12, 29)(13, 31)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52) local type(s) :: { ( 26^26 ) } Outer automorphisms :: reflexible Dual of E12.22 Graph:: bipartite v = 2 e = 26 f = 2 degree seq :: [ 26^2 ] E12.31 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {13, 13, 13, 13}) Quotient :: dipole Aut^+ = C13 (small group id <13, 1>) Aut = D26 (small group id <26, 1>) |r| :: 2 Presentation :: [ R^2, Y1^2 * Y2, Y2 * Y3 * Y2, Y3^3 * Y1, (R * Y1)^2, (Y1^-1, Y3^-1), (R * Y3)^2, (R * Y2)^2, Y2^-1 * Y3 * Y2^-1 * Y1 * Y3 ] Map:: non-degenerate R = (1, 14, 2, 15, 6, 19, 9, 22, 4, 17, 8, 21, 13, 26, 11, 24, 12, 25, 7, 20, 10, 23, 3, 16, 5, 18)(27, 40, 29, 42, 33, 46, 37, 50, 34, 47, 35, 48, 28, 41, 31, 44, 36, 49, 38, 51, 39, 52, 30, 43, 32, 45) L = (1, 30)(2, 34)(3, 32)(4, 38)(5, 35)(6, 39)(7, 27)(8, 33)(9, 37)(10, 28)(11, 29)(12, 31)(13, 36)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52) local type(s) :: { ( 26^26 ) } Outer automorphisms :: reflexible Dual of E12.17 Graph:: bipartite v = 2 e = 26 f = 2 degree seq :: [ 26^2 ] E12.32 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {13, 13, 13, 13}) Quotient :: dipole Aut^+ = C13 (small group id <13, 1>) Aut = D26 (small group id <26, 1>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1^-2, Y3 * Y2^2, Y2^-1 * Y1^-1 * Y3^-1 * Y1^-1, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y1 * Y3^-3, Y3^-1 * Y1^-1 * Y3^-1 * Y2 * Y3^-1 ] Map:: non-degenerate R = (1, 14, 2, 15, 3, 16, 8, 21, 7, 20, 10, 23, 11, 24, 13, 26, 12, 25, 4, 17, 9, 22, 6, 19, 5, 18)(27, 40, 29, 42, 33, 46, 37, 50, 38, 51, 35, 48, 31, 44, 28, 41, 34, 47, 36, 49, 39, 52, 30, 43, 32, 45) L = (1, 30)(2, 35)(3, 32)(4, 36)(5, 38)(6, 39)(7, 27)(8, 31)(9, 37)(10, 28)(11, 29)(12, 33)(13, 34)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52) local type(s) :: { ( 26^26 ) } Outer automorphisms :: reflexible Dual of E12.34 Graph:: bipartite v = 2 e = 26 f = 2 degree seq :: [ 26^2 ] E12.33 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {13, 13, 13, 13}) Quotient :: dipole Aut^+ = C13 (small group id <13, 1>) Aut = D26 (small group id <26, 1>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^-1 * Y2^-1, Y2 * Y1^-1 * Y3, (R * Y2)^2, Y1 * Y3^3, Y2^2 * Y3^-1 * Y2, (R * Y1)^2, Y1^-2 * Y2^-1 * Y1^-1, (R * Y3)^2 ] Map:: non-degenerate R = (1, 14, 2, 15, 8, 21, 6, 19, 4, 17, 10, 23, 12, 25, 11, 24, 13, 26, 7, 20, 3, 16, 9, 22, 5, 18)(27, 40, 29, 42, 37, 50, 30, 43, 28, 41, 35, 48, 39, 52, 36, 49, 34, 47, 31, 44, 33, 46, 38, 51, 32, 45) L = (1, 30)(2, 36)(3, 28)(4, 39)(5, 32)(6, 37)(7, 27)(8, 38)(9, 34)(10, 33)(11, 35)(12, 29)(13, 31)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52) local type(s) :: { ( 26^26 ) } Outer automorphisms :: reflexible Dual of E12.19 Graph:: bipartite v = 2 e = 26 f = 2 degree seq :: [ 26^2 ] E12.34 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {13, 13, 13, 13}) Quotient :: dipole Aut^+ = C13 (small group id <13, 1>) Aut = D26 (small group id <26, 1>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^-2, Y1^2 * Y2, (R * Y2)^2, Y2^-2 * Y3 * Y2^-1, (R * Y1)^2, Y3^-1 * Y2^-1 * Y3^-1 * Y1^-1, (R * Y3)^2 ] Map:: non-degenerate R = (1, 14, 2, 15, 6, 19, 9, 22, 13, 26, 11, 24, 7, 20, 4, 17, 8, 21, 10, 23, 12, 25, 3, 16, 5, 18)(27, 40, 29, 42, 36, 49, 30, 43, 37, 50, 35, 48, 28, 41, 31, 44, 38, 51, 34, 47, 33, 46, 39, 52, 32, 45) L = (1, 30)(2, 34)(3, 37)(4, 28)(5, 33)(6, 36)(7, 27)(8, 32)(9, 38)(10, 35)(11, 31)(12, 39)(13, 29)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52) local type(s) :: { ( 26^26 ) } Outer automorphisms :: reflexible Dual of E12.32 Graph:: bipartite v = 2 e = 26 f = 2 degree seq :: [ 26^2 ] E12.35 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {13, 13, 13, 13}) Quotient :: dipole Aut^+ = C13 (small group id <13, 1>) Aut = D26 (small group id <26, 1>) |r| :: 2 Presentation :: [ R^2, Y3^2 * Y1, Y1^2 * Y2^-1, Y2^3 * Y3^-1, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y3 * Y2 * Y3 * Y1^-1 ] Map:: non-degenerate R = (1, 14, 2, 15, 3, 16, 8, 21, 10, 23, 12, 25, 4, 17, 7, 20, 9, 22, 11, 24, 13, 26, 6, 19, 5, 18)(27, 40, 29, 42, 36, 49, 30, 43, 35, 48, 39, 52, 31, 44, 28, 41, 34, 47, 38, 51, 33, 46, 37, 50, 32, 45) L = (1, 30)(2, 33)(3, 35)(4, 31)(5, 38)(6, 36)(7, 27)(8, 37)(9, 28)(10, 39)(11, 29)(12, 32)(13, 34)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52) local type(s) :: { ( 26^26 ) } Outer automorphisms :: reflexible Dual of E12.20 Graph:: bipartite v = 2 e = 26 f = 2 degree seq :: [ 26^2 ] E12.36 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 7, 14, 14}) Quotient :: dipole Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1^-1 * Y2^2, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y3 * Y2 * Y3, Y2 * Y1^3, (R * Y2)^2, Y3 * Y1 * Y3 * Y1^-1 ] Map:: non-degenerate R = (1, 15, 2, 16, 7, 21, 6, 20, 3, 17, 8, 22, 5, 19)(4, 18, 9, 23, 13, 27, 12, 26, 10, 24, 14, 28, 11, 25)(29, 43, 31, 45, 30, 44, 36, 50, 35, 49, 33, 47, 34, 48)(32, 46, 38, 52, 37, 51, 42, 56, 41, 55, 39, 53, 40, 54) L = (1, 32)(2, 37)(3, 38)(4, 29)(5, 39)(6, 40)(7, 41)(8, 42)(9, 30)(10, 31)(11, 33)(12, 34)(13, 35)(14, 36)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56) local type(s) :: { ( 28^14 ) } Outer automorphisms :: reflexible Dual of E12.72 Graph:: bipartite v = 4 e = 28 f = 2 degree seq :: [ 14^4 ] E12.37 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 7, 14, 14}) Quotient :: dipole Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1 * Y2^2, (R * Y2)^2, (R * Y3)^2, Y3 * Y2 * Y3 * Y2^-1, Y1^-1 * Y3 * Y1 * Y3, Y2 * Y1^-3, (R * Y1)^2 ] Map:: non-degenerate R = (1, 15, 2, 16, 7, 21, 3, 17, 6, 20, 9, 23, 5, 19)(4, 18, 8, 22, 13, 27, 10, 24, 12, 26, 14, 28, 11, 25)(29, 43, 31, 45, 33, 47, 35, 49, 37, 51, 30, 44, 34, 48)(32, 46, 38, 52, 39, 53, 41, 55, 42, 56, 36, 50, 40, 54) L = (1, 32)(2, 36)(3, 38)(4, 29)(5, 39)(6, 40)(7, 41)(8, 30)(9, 42)(10, 31)(11, 33)(12, 34)(13, 35)(14, 37)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56) local type(s) :: { ( 28^14 ) } Outer automorphisms :: reflexible Dual of E12.71 Graph:: bipartite v = 4 e = 28 f = 2 degree seq :: [ 14^4 ] E12.38 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 7, 14, 14}) Quotient :: dipole Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2^2, Y1 * Y3^-2, Y2^-1 * Y1^3, (R * Y3)^2, (R * Y1)^2, (Y2^-1, Y3^-1), (R * Y2)^2, Y1 * Y3 * Y1 * Y2^-1 * Y3, (Y2^-1 * Y3)^14 ] Map:: non-degenerate R = (1, 15, 2, 16, 8, 22, 3, 17, 6, 20, 10, 24, 5, 19)(4, 18, 9, 23, 12, 26, 11, 25, 13, 27, 14, 28, 7, 21)(29, 43, 31, 45, 33, 47, 36, 50, 38, 52, 30, 44, 34, 48)(32, 46, 39, 53, 35, 49, 40, 54, 42, 56, 37, 51, 41, 55) L = (1, 32)(2, 37)(3, 39)(4, 30)(5, 35)(6, 41)(7, 29)(8, 40)(9, 36)(10, 42)(11, 34)(12, 31)(13, 38)(14, 33)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56) local type(s) :: { ( 28^14 ) } Outer automorphisms :: reflexible Dual of E12.73 Graph:: bipartite v = 4 e = 28 f = 2 degree seq :: [ 14^4 ] E12.39 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 7, 14, 14}) Quotient :: dipole Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1^-2, Y2^-1 * Y3^-2 * Y2^-1, Y2^-1 * Y3^2 * Y1^-1, Y3 * Y2^-1 * Y3 * Y1^-1, (Y3, Y2), (Y3, Y1^-1), Y2^-3 * Y1^-1, (Y3 * Y2)^2, (R * Y3)^2, (R * Y2)^2, (R * 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 * Y2^-1 ] Map:: non-degenerate R = (1, 15, 2, 16, 3, 17, 8, 22, 11, 25, 6, 20, 5, 19)(4, 18, 9, 23, 12, 26, 14, 28, 7, 21, 10, 24, 13, 27)(29, 43, 31, 45, 39, 53, 33, 47, 30, 44, 36, 50, 34, 48)(32, 46, 40, 54, 35, 49, 41, 55, 37, 51, 42, 56, 38, 52) L = (1, 32)(2, 37)(3, 40)(4, 36)(5, 41)(6, 38)(7, 29)(8, 42)(9, 39)(10, 30)(11, 35)(12, 34)(13, 31)(14, 33)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56) local type(s) :: { ( 28^14 ) } Outer automorphisms :: reflexible Dual of E12.74 Graph:: bipartite v = 4 e = 28 f = 2 degree seq :: [ 14^4 ] E12.40 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 7, 14, 14}) Quotient :: dipole Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (Y2, Y1^-1), (Y2 * Y1^-1)^2, (R * Y1)^2, Y1^2 * Y2^-2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^2 * Y1 * Y2^4, (Y3^-1 * Y1^-1)^7, (Y3 * Y2^-1)^14 ] Map:: R = (1, 15, 2, 16, 6, 20, 11, 25, 13, 27, 9, 23, 4, 18)(3, 17, 7, 21, 12, 26, 14, 28, 10, 24, 5, 19, 8, 22)(29, 43, 31, 45, 34, 48, 40, 54, 41, 55, 38, 52, 32, 46, 36, 50, 30, 44, 35, 49, 39, 53, 42, 56, 37, 51, 33, 47) L = (1, 29)(2, 30)(3, 31)(4, 32)(5, 33)(6, 34)(7, 35)(8, 36)(9, 37)(10, 38)(11, 39)(12, 40)(13, 41)(14, 42)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56) 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 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 3 e = 28 f = 3 degree seq :: [ 14^2, 28 ] E12.41 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 7, 14, 14}) Quotient :: dipole Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (Y2^-1, Y1^-1), (Y2^-1 * Y1^-1)^2, (R * Y1)^2, Y2^2 * Y1^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^-6 * Y1, (Y3^-1 * Y1^-1)^7, (Y3 * Y2^-1)^14 ] Map:: R = (1, 15, 2, 16, 6, 20, 11, 25, 14, 28, 9, 23, 4, 18)(3, 17, 7, 21, 5, 19, 8, 22, 12, 26, 13, 27, 10, 24)(29, 43, 31, 45, 37, 51, 41, 55, 39, 53, 36, 50, 30, 44, 35, 49, 32, 46, 38, 52, 42, 56, 40, 54, 34, 48, 33, 47) L = (1, 29)(2, 30)(3, 31)(4, 32)(5, 33)(6, 34)(7, 35)(8, 36)(9, 37)(10, 38)(11, 39)(12, 40)(13, 41)(14, 42)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56) 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 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 3 e = 28 f = 3 degree seq :: [ 14^2, 28 ] E12.42 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 7, 14, 14}) Quotient :: dipole Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y1 * Y2^-2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1^7, (Y3^-1 * Y1^-1)^7, (Y3 * Y2^-1)^14 ] Map:: R = (1, 15, 2, 16, 6, 20, 10, 24, 12, 26, 8, 22, 4, 18)(3, 17, 7, 21, 11, 25, 14, 28, 13, 27, 9, 23, 5, 19)(29, 43, 31, 45, 30, 44, 35, 49, 34, 48, 39, 53, 38, 52, 42, 56, 40, 54, 41, 55, 36, 50, 37, 51, 32, 46, 33, 47) L = (1, 29)(2, 30)(3, 31)(4, 32)(5, 33)(6, 34)(7, 35)(8, 36)(9, 37)(10, 38)(11, 39)(12, 40)(13, 41)(14, 42)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56) 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 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 3 e = 28 f = 3 degree seq :: [ 14^2, 28 ] E12.43 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 7, 14, 14}) Quotient :: dipole Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y2^2 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y1^7, (Y3^-1 * Y1^-1)^7, (Y3 * Y2^-1)^14 ] Map:: R = (1, 15, 2, 16, 6, 20, 10, 24, 13, 27, 9, 23, 4, 18)(3, 17, 5, 19, 7, 21, 11, 25, 14, 28, 12, 26, 8, 22)(29, 43, 31, 45, 32, 46, 36, 50, 37, 51, 40, 54, 41, 55, 42, 56, 38, 52, 39, 53, 34, 48, 35, 49, 30, 44, 33, 47) L = (1, 29)(2, 30)(3, 31)(4, 32)(5, 33)(6, 34)(7, 35)(8, 36)(9, 37)(10, 38)(11, 39)(12, 40)(13, 41)(14, 42)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56) 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 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 3 e = 28 f = 3 degree seq :: [ 14^2, 28 ] E12.44 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 7, 14, 14}) Quotient :: dipole Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (R * Y3)^2, (R * Y1)^2, (Y2^-1, Y1^-1), Y1 * Y2^-1 * Y1 * Y2^-1 * Y1, Y2 * Y1 * Y2^3, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^7, (Y3 * Y2^-1)^14 ] Map:: R = (1, 15, 2, 16, 6, 20, 9, 23, 13, 27, 11, 25, 4, 18)(3, 17, 7, 21, 14, 28, 12, 26, 5, 19, 8, 22, 10, 24)(29, 43, 31, 45, 37, 51, 40, 54, 32, 46, 38, 52, 34, 48, 42, 56, 39, 53, 36, 50, 30, 44, 35, 49, 41, 55, 33, 47) L = (1, 29)(2, 30)(3, 31)(4, 32)(5, 33)(6, 34)(7, 35)(8, 36)(9, 37)(10, 38)(11, 39)(12, 40)(13, 41)(14, 42)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56) 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 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 3 e = 28 f = 3 degree seq :: [ 14^2, 28 ] E12.45 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 7, 14, 14}) Quotient :: dipole Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (R * Y3)^2, (R * Y1)^2, (Y2^-1, Y1^-1), Y2^-4 * Y1, Y1^2 * Y2 * Y1 * Y2, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^7, (Y3 * Y2^-1)^14 ] Map:: R = (1, 15, 2, 16, 6, 20, 13, 27, 9, 23, 11, 25, 4, 18)(3, 17, 7, 21, 12, 26, 5, 19, 8, 22, 14, 28, 10, 24)(29, 43, 31, 45, 37, 51, 36, 50, 30, 44, 35, 49, 39, 53, 42, 56, 34, 48, 40, 54, 32, 46, 38, 52, 41, 55, 33, 47) L = (1, 29)(2, 30)(3, 31)(4, 32)(5, 33)(6, 34)(7, 35)(8, 36)(9, 37)(10, 38)(11, 39)(12, 40)(13, 41)(14, 42)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56) 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 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 3 e = 28 f = 3 degree seq :: [ 14^2, 28 ] E12.46 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 7, 14, 14}) Quotient :: dipole Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1, Y1 * Y2^2 * Y1, Y2^2 * Y1^2, (Y2^-1, Y1^-1), (R * Y3)^2, (Y2^-1 * R)^2, (Y3^-1, Y2^-1), (R * Y1)^2, Y1 * Y2^-6, Y1^7, (Y3^-1 * Y1^-1)^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 ] Map:: non-degenerate R = (1, 15, 2, 16, 6, 20, 11, 25, 14, 28, 9, 23, 4, 18)(3, 17, 7, 21, 5, 19, 8, 22, 12, 26, 13, 27, 10, 24)(29, 43, 31, 45, 37, 51, 41, 55, 39, 53, 36, 50, 30, 44, 35, 49, 32, 46, 38, 52, 42, 56, 40, 54, 34, 48, 33, 47) L = (1, 30)(2, 34)(3, 35)(4, 29)(5, 36)(6, 39)(7, 33)(8, 40)(9, 32)(10, 31)(11, 42)(12, 41)(13, 38)(14, 37)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56) 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 ) } Outer automorphisms :: reflexible Dual of E12.67 Graph:: bipartite v = 3 e = 28 f = 3 degree seq :: [ 14^2, 28 ] E12.47 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 7, 14, 14}) Quotient :: dipole Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1 * Y3^-1, Y1 * Y2^-2, Y1 * Y3^-1 * Y1^2, (R * Y3)^2, (Y2^-1, Y3^-1), (R * Y1)^2, (R * Y2)^2 ] Map:: non-degenerate R = (1, 15, 2, 16, 8, 22, 4, 18, 7, 21, 10, 24, 5, 19)(3, 17, 9, 23, 13, 27, 11, 25, 12, 26, 14, 28, 6, 20)(29, 43, 31, 45, 30, 44, 37, 51, 36, 50, 41, 55, 32, 46, 39, 53, 35, 49, 40, 54, 38, 52, 42, 56, 33, 47, 34, 48) L = (1, 32)(2, 35)(3, 39)(4, 33)(5, 36)(6, 41)(7, 29)(8, 38)(9, 40)(10, 30)(11, 34)(12, 31)(13, 42)(14, 37)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56) 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 ) } Outer automorphisms :: reflexible Dual of E12.70 Graph:: bipartite v = 3 e = 28 f = 3 degree seq :: [ 14^2, 28 ] E12.48 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 7, 14, 14}) Quotient :: dipole Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1 * Y3^-1, Y1 * Y2^2, (Y3, Y2^-1), (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y1^-2 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 15, 2, 16, 8, 22, 7, 21, 4, 18, 9, 23, 5, 19)(3, 17, 6, 20, 10, 24, 13, 27, 11, 25, 14, 28, 12, 26)(29, 43, 31, 45, 33, 47, 40, 54, 37, 51, 42, 56, 32, 46, 39, 53, 35, 49, 41, 55, 36, 50, 38, 52, 30, 44, 34, 48) L = (1, 32)(2, 37)(3, 39)(4, 30)(5, 35)(6, 42)(7, 29)(8, 33)(9, 36)(10, 40)(11, 34)(12, 41)(13, 31)(14, 38)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56) 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 ) } Outer automorphisms :: reflexible Dual of E12.68 Graph:: bipartite v = 3 e = 28 f = 3 degree seq :: [ 14^2, 28 ] E12.49 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 7, 14, 14}) Quotient :: dipole Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ R^2, Y1^2 * Y3^-1, Y2^-1 * Y1 * Y3 * Y2^-1, Y2^-1 * Y3^-2 * Y2^-1, Y3^-1 * Y1^-1 * Y3^-2, (Y2 * Y3)^2, (Y1^-1, Y2^-1), (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y2^10 * Y1^-1 ] Map:: non-degenerate R = (1, 15, 2, 16, 4, 18, 9, 23, 13, 27, 7, 21, 5, 19)(3, 17, 8, 22, 11, 25, 14, 28, 6, 20, 10, 24, 12, 26)(29, 43, 31, 45, 37, 51, 42, 56, 33, 47, 40, 54, 32, 46, 39, 53, 35, 49, 38, 52, 30, 44, 36, 50, 41, 55, 34, 48) L = (1, 32)(2, 37)(3, 39)(4, 41)(5, 30)(6, 40)(7, 29)(8, 42)(9, 35)(10, 31)(11, 34)(12, 36)(13, 33)(14, 38)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56) 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 ) } Outer automorphisms :: reflexible Dual of E12.66 Graph:: bipartite v = 3 e = 28 f = 3 degree seq :: [ 14^2, 28 ] E12.50 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 7, 14, 14}) Quotient :: dipole Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ R^2, Y1^2 * Y3, Y2^-1 * Y3^-2 * Y2^-1, (Y3^-1 * Y2^-1)^2, (R * Y1)^2, Y2^-1 * Y1^-1 * Y3 * Y2^-1, Y3^3 * Y1^-1, (R * Y2)^2, (Y1^-1, Y2^-1), (R * Y3)^2, Y2^10 * Y1 ] Map:: non-degenerate R = (1, 15, 2, 16, 7, 21, 10, 24, 11, 25, 4, 18, 5, 19)(3, 17, 8, 22, 14, 28, 6, 20, 9, 23, 12, 26, 13, 27)(29, 43, 31, 45, 39, 53, 37, 51, 30, 44, 36, 50, 32, 46, 40, 54, 35, 49, 42, 56, 33, 47, 41, 55, 38, 52, 34, 48) L = (1, 32)(2, 33)(3, 40)(4, 38)(5, 39)(6, 36)(7, 29)(8, 41)(9, 42)(10, 30)(11, 35)(12, 34)(13, 37)(14, 31)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56) 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 ) } Outer automorphisms :: reflexible Dual of E12.69 Graph:: bipartite v = 3 e = 28 f = 3 degree seq :: [ 14^2, 28 ] E12.51 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 7, 14, 14}) Quotient :: dipole Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-2, Y2 * Y3^-1 * Y2, Y1 * Y3^3, (Y1^-1 * Y2)^2, (Y1^-1, Y2^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y1 * Y3^3 ] Map:: non-degenerate R = (1, 15, 2, 16, 4, 18, 9, 23, 12, 26, 7, 21, 5, 19)(3, 17, 8, 22, 11, 25, 14, 28, 13, 27, 6, 20, 10, 24)(29, 43, 31, 45, 32, 46, 39, 53, 40, 54, 41, 55, 33, 47, 38, 52, 30, 44, 36, 50, 37, 51, 42, 56, 35, 49, 34, 48) L = (1, 32)(2, 37)(3, 39)(4, 40)(5, 30)(6, 31)(7, 29)(8, 42)(9, 35)(10, 36)(11, 41)(12, 33)(13, 38)(14, 34)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56) 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 ) } Outer automorphisms :: reflexible Dual of E12.55 Graph:: bipartite v = 3 e = 28 f = 3 degree seq :: [ 14^2, 28 ] E12.52 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 7, 14, 14}) Quotient :: dipole Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^2, Y2 * Y3^-1 * Y2, (Y1^-1 * Y2^-1)^2, (R * Y3)^2, Y1 * Y3^-3, (R * Y2)^2, (R * Y1)^2, (Y1^-1, Y2) ] Map:: non-degenerate R = (1, 15, 2, 16, 7, 21, 10, 24, 13, 27, 4, 18, 5, 19)(3, 17, 8, 22, 6, 20, 9, 23, 14, 28, 11, 25, 12, 26)(29, 43, 31, 45, 32, 46, 39, 53, 38, 52, 37, 51, 30, 44, 36, 50, 33, 47, 40, 54, 41, 55, 42, 56, 35, 49, 34, 48) L = (1, 32)(2, 33)(3, 39)(4, 38)(5, 41)(6, 31)(7, 29)(8, 40)(9, 36)(10, 30)(11, 37)(12, 42)(13, 35)(14, 34)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56) 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 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 3 e = 28 f = 3 degree seq :: [ 14^2, 28 ] E12.53 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 7, 14, 14}) Quotient :: dipole Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1, Y2 * Y1^-1 * Y2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y1^7, (Y3^-1 * Y1^-1)^7, (Y3 * Y2^-1)^14 ] Map:: non-degenerate R = (1, 15, 2, 16, 6, 20, 10, 24, 12, 26, 8, 22, 4, 18)(3, 17, 7, 21, 11, 25, 14, 28, 13, 27, 9, 23, 5, 19)(29, 43, 31, 45, 30, 44, 35, 49, 34, 48, 39, 53, 38, 52, 42, 56, 40, 54, 41, 55, 36, 50, 37, 51, 32, 46, 33, 47) L = (1, 30)(2, 34)(3, 35)(4, 29)(5, 31)(6, 38)(7, 39)(8, 32)(9, 33)(10, 40)(11, 42)(12, 36)(13, 37)(14, 41)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56) 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 ) } Outer automorphisms :: reflexible Dual of E12.54 Graph:: bipartite v = 3 e = 28 f = 3 degree seq :: [ 14^2, 28 ] E12.54 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 7, 14, 14}) Quotient :: dipole Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^2, Y2^-2 * Y3, (Y1, Y2), (R * Y1)^2, Y3 * Y1^-3, (R * Y3)^2, (R * Y2)^2 ] Map:: non-degenerate R = (1, 15, 2, 16, 8, 22, 4, 18, 7, 21, 11, 25, 5, 19)(3, 17, 9, 23, 14, 28, 12, 26, 6, 20, 10, 24, 13, 27)(29, 43, 31, 45, 32, 46, 40, 54, 33, 47, 41, 55, 36, 50, 42, 56, 39, 53, 38, 52, 30, 44, 37, 51, 35, 49, 34, 48) L = (1, 32)(2, 35)(3, 40)(4, 33)(5, 36)(6, 31)(7, 29)(8, 39)(9, 34)(10, 37)(11, 30)(12, 41)(13, 42)(14, 38)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56) 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 ) } Outer automorphisms :: reflexible Dual of E12.53 Graph:: bipartite v = 3 e = 28 f = 3 degree seq :: [ 14^2, 28 ] E12.55 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 7, 14, 14}) Quotient :: dipole Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^-2, Y2^2 * Y3^-1, (R * Y3)^2, (Y2^-1, Y1), (R * Y1)^2, Y1^2 * Y3 * Y1, (R * Y2)^2, Y2 * Y1 * Y2 * Y1^2 ] Map:: non-degenerate R = (1, 15, 2, 16, 8, 22, 7, 21, 4, 18, 10, 24, 5, 19)(3, 17, 9, 23, 13, 27, 6, 20, 11, 25, 14, 28, 12, 26)(29, 43, 31, 45, 32, 46, 39, 53, 30, 44, 37, 51, 38, 52, 42, 56, 36, 50, 41, 55, 33, 47, 40, 54, 35, 49, 34, 48) L = (1, 32)(2, 38)(3, 39)(4, 30)(5, 35)(6, 31)(7, 29)(8, 33)(9, 42)(10, 36)(11, 37)(12, 34)(13, 40)(14, 41)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56) 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 ) } Outer automorphisms :: reflexible Dual of E12.51 Graph:: bipartite v = 3 e = 28 f = 3 degree seq :: [ 14^2, 28 ] E12.56 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 7, 14, 14}) Quotient :: dipole Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-2, Y2 * Y3 * Y2, (Y1^-1 * Y2)^2, Y1 * Y3^-3, (R * Y1)^2, (R * Y3)^2, (Y1^-1, Y2^-1), (R * Y2)^2, Y2 * Y1 * Y3^-1 * Y2 * Y3^-1 ] Map:: non-degenerate R = (1, 15, 2, 16, 7, 21, 10, 24, 12, 26, 4, 18, 5, 19)(3, 17, 8, 22, 11, 25, 13, 27, 14, 28, 6, 20, 9, 23)(29, 43, 31, 45, 35, 49, 39, 53, 40, 54, 42, 56, 33, 47, 37, 51, 30, 44, 36, 50, 38, 52, 41, 55, 32, 46, 34, 48) L = (1, 32)(2, 33)(3, 34)(4, 38)(5, 40)(6, 41)(7, 29)(8, 37)(9, 42)(10, 30)(11, 31)(12, 35)(13, 36)(14, 39)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56) 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 ) } Outer automorphisms :: reflexible Dual of E12.63 Graph:: bipartite v = 3 e = 28 f = 3 degree seq :: [ 14^2, 28 ] E12.57 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 7, 14, 14}) Quotient :: dipole Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^2, Y3 * Y2^2, Y1 * Y3^3, (Y1^-1, Y2^-1), (R * Y3)^2, Y1 * Y3^3, (R * Y1)^2, (R * Y2)^2, (Y3 * Y2^-1)^14 ] Map:: non-degenerate R = (1, 15, 2, 16, 4, 18, 9, 23, 13, 27, 7, 21, 5, 19)(3, 17, 8, 22, 6, 20, 10, 24, 14, 28, 12, 26, 11, 25)(29, 43, 31, 45, 35, 49, 40, 54, 37, 51, 38, 52, 30, 44, 36, 50, 33, 47, 39, 53, 41, 55, 42, 56, 32, 46, 34, 48) L = (1, 32)(2, 37)(3, 34)(4, 41)(5, 30)(6, 42)(7, 29)(8, 38)(9, 35)(10, 40)(11, 36)(12, 31)(13, 33)(14, 39)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56) 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 ) } Outer automorphisms :: reflexible Dual of E12.62 Graph:: bipartite v = 3 e = 28 f = 3 degree seq :: [ 14^2, 28 ] E12.58 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 7, 14, 14}) Quotient :: dipole Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1, Y1 * Y2^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1^7, (Y3^-1 * Y1^-1)^7, (Y3 * Y2^-1)^14 ] Map:: non-degenerate R = (1, 15, 2, 16, 6, 20, 10, 24, 13, 27, 9, 23, 4, 18)(3, 17, 5, 19, 7, 21, 11, 25, 14, 28, 12, 26, 8, 22)(29, 43, 31, 45, 32, 46, 36, 50, 37, 51, 40, 54, 41, 55, 42, 56, 38, 52, 39, 53, 34, 48, 35, 49, 30, 44, 33, 47) L = (1, 30)(2, 34)(3, 33)(4, 29)(5, 35)(6, 38)(7, 39)(8, 31)(9, 32)(10, 41)(11, 42)(12, 36)(13, 37)(14, 40)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56) 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 ) } Outer automorphisms :: reflexible Dual of E12.61 Graph:: bipartite v = 3 e = 28 f = 3 degree seq :: [ 14^2, 28 ] E12.59 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 7, 14, 14}) Quotient :: dipole Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^-2, Y3 * Y2^2, (Y1, Y2), (R * Y1)^2, (R * Y2)^2, Y3^-1 * Y1^-3, (R * Y3)^2 ] Map:: non-degenerate R = (1, 15, 2, 16, 8, 22, 7, 21, 4, 18, 10, 24, 5, 19)(3, 17, 9, 23, 14, 28, 13, 27, 6, 20, 11, 25, 12, 26)(29, 43, 31, 45, 35, 49, 41, 55, 33, 47, 40, 54, 36, 50, 42, 56, 38, 52, 39, 53, 30, 44, 37, 51, 32, 46, 34, 48) L = (1, 32)(2, 38)(3, 34)(4, 30)(5, 35)(6, 37)(7, 29)(8, 33)(9, 39)(10, 36)(11, 42)(12, 41)(13, 31)(14, 40)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56) 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 ) } Outer automorphisms :: reflexible Dual of E12.64 Graph:: bipartite v = 3 e = 28 f = 3 degree seq :: [ 14^2, 28 ] E12.60 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 7, 14, 14}) Quotient :: dipole Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^2, Y2^2 * Y3, (Y2^-1, Y1), (R * Y1)^2, Y3^-1 * Y1^3, (R * Y2)^2, (R * Y3)^2, Y2 * Y1 * Y2 * Y1^2 ] Map:: non-degenerate R = (1, 15, 2, 16, 8, 22, 4, 18, 7, 21, 11, 25, 5, 19)(3, 17, 9, 23, 13, 27, 6, 20, 10, 24, 14, 28, 12, 26)(29, 43, 31, 45, 35, 49, 38, 52, 30, 44, 37, 51, 39, 53, 42, 56, 36, 50, 41, 55, 33, 47, 40, 54, 32, 46, 34, 48) L = (1, 32)(2, 35)(3, 34)(4, 33)(5, 36)(6, 40)(7, 29)(8, 39)(9, 38)(10, 31)(11, 30)(12, 41)(13, 42)(14, 37)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56) 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 ) } Outer automorphisms :: reflexible Dual of E12.65 Graph:: bipartite v = 3 e = 28 f = 3 degree seq :: [ 14^2, 28 ] E12.61 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 7, 14, 14}) Quotient :: dipole Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^2, Y1^-1 * Y2^2 * Y1^-1, (Y3^-1, Y2^-1), Y1^-2 * Y3 * Y1^-1, Y2 * Y1 * Y3^-1 * Y2, Y2^-1 * Y3 * Y2^-1 * Y1^-1, (R * Y3)^2, (Y1^-1, Y2), (R * Y1)^2, (R * Y2)^2, Y3 * Y1^-1 * Y2 * Y3 * Y2 ] Map:: non-degenerate R = (1, 15, 2, 16, 8, 22, 4, 18, 7, 21, 11, 25, 5, 19)(3, 17, 9, 23, 14, 28, 12, 26, 13, 27, 6, 20, 10, 24)(29, 43, 31, 45, 36, 50, 42, 56, 35, 49, 41, 55, 33, 47, 38, 52, 30, 44, 37, 51, 32, 46, 40, 54, 39, 53, 34, 48) L = (1, 32)(2, 35)(3, 40)(4, 33)(5, 36)(6, 37)(7, 29)(8, 39)(9, 41)(10, 42)(11, 30)(12, 38)(13, 31)(14, 34)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56) 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 ) } Outer automorphisms :: reflexible Dual of E12.58 Graph:: bipartite v = 3 e = 28 f = 3 degree seq :: [ 14^2, 28 ] E12.62 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 7, 14, 14}) Quotient :: dipole Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^-2, Y2 * Y1^-1 * Y3^-1 * Y2, Y2^-2 * Y1^-2, (Y2 * Y1)^2, Y2^-1 * Y1 * Y3 * Y2^-1, Y3 * Y2^-1 * Y1 * Y2^-1, (R * Y2)^2, Y1^-3 * Y3^-1, (Y2, Y1^-1), (R * Y1)^2, (R * Y3)^2, Y3^-1 * Y1^-1 * Y2^-1 * Y3^-1 * Y2^-1 ] Map:: non-degenerate R = (1, 15, 2, 16, 8, 22, 7, 21, 4, 18, 10, 24, 5, 19)(3, 17, 9, 23, 6, 20, 11, 25, 12, 26, 14, 28, 13, 27)(29, 43, 31, 45, 38, 52, 42, 56, 35, 49, 39, 53, 30, 44, 37, 51, 33, 47, 41, 55, 32, 46, 40, 54, 36, 50, 34, 48) L = (1, 32)(2, 38)(3, 40)(4, 30)(5, 35)(6, 41)(7, 29)(8, 33)(9, 42)(10, 36)(11, 31)(12, 37)(13, 39)(14, 34)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56) 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 ) } Outer automorphisms :: reflexible Dual of E12.57 Graph:: bipartite v = 3 e = 28 f = 3 degree seq :: [ 14^2, 28 ] E12.63 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 7, 14, 14}) Quotient :: dipole Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ R^2, Y1^2 * Y3, Y1 * Y2^-2, (R * Y2)^2, (R * Y3)^2, Y3^3 * Y1^-1, Y2^-1 * Y3^-1 * Y2^-1 * Y1^-1, (R * Y1)^2, (Y3 * Y2^-1)^14 ] Map:: non-degenerate R = (1, 15, 2, 16, 7, 21, 9, 23, 12, 26, 4, 18, 5, 19)(3, 17, 8, 22, 11, 25, 14, 28, 13, 27, 10, 24, 6, 20)(29, 43, 31, 45, 30, 44, 36, 50, 35, 49, 39, 53, 37, 51, 42, 56, 40, 54, 41, 55, 32, 46, 38, 52, 33, 47, 34, 48) L = (1, 32)(2, 33)(3, 38)(4, 37)(5, 40)(6, 41)(7, 29)(8, 34)(9, 30)(10, 42)(11, 31)(12, 35)(13, 39)(14, 36)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56) 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 ) } Outer automorphisms :: reflexible Dual of E12.56 Graph:: bipartite v = 3 e = 28 f = 3 degree seq :: [ 14^2, 28 ] E12.64 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 7, 14, 14}) Quotient :: dipole Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^2, Y1 * Y2^2, (Y2^-1, Y3), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y2 * Y3 * Y2 * Y1^-1, Y1^-1 * Y3^-3, (Y2 * Y3^2)^2 ] Map:: non-degenerate R = (1, 15, 2, 16, 4, 18, 8, 22, 12, 26, 7, 21, 5, 19)(3, 17, 6, 20, 9, 23, 13, 27, 14, 28, 11, 25, 10, 24)(29, 43, 31, 45, 33, 47, 38, 52, 35, 49, 39, 53, 40, 54, 42, 56, 36, 50, 41, 55, 32, 46, 37, 51, 30, 44, 34, 48) L = (1, 32)(2, 36)(3, 37)(4, 40)(5, 30)(6, 41)(7, 29)(8, 35)(9, 42)(10, 34)(11, 31)(12, 33)(13, 39)(14, 38)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56) 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 ) } Outer automorphisms :: reflexible Dual of E12.59 Graph:: bipartite v = 3 e = 28 f = 3 degree seq :: [ 14^2, 28 ] E12.65 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 7, 14, 14}) Quotient :: dipole Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3, (R * Y3)^2, Y2^-1 * Y3 * Y2 * Y1^-1, (Y2^-1 * R)^2, (R * Y1)^2, Y2 * Y3 * Y2^-1 * Y1^-1, Y2 * Y3 * Y2^3, Y2^-1 * Y3^2 * Y1 * Y2^-1, Y1^2 * Y2^-1 * Y3 * Y2^-1, (Y3^-1 * Y1^-1)^7, (Y2^-1 * Y1)^14 ] Map:: non-degenerate R = (1, 15, 2, 16, 6, 20, 9, 23, 13, 27, 11, 25, 4, 18)(3, 17, 7, 21, 14, 28, 12, 26, 5, 19, 8, 22, 10, 24)(29, 43, 31, 45, 37, 51, 40, 54, 32, 46, 38, 52, 34, 48, 42, 56, 39, 53, 36, 50, 30, 44, 35, 49, 41, 55, 33, 47) L = (1, 30)(2, 34)(3, 35)(4, 29)(5, 36)(6, 37)(7, 42)(8, 38)(9, 41)(10, 31)(11, 32)(12, 33)(13, 39)(14, 40)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56) 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 ) } Outer automorphisms :: reflexible Dual of E12.60 Graph:: bipartite v = 3 e = 28 f = 3 degree seq :: [ 14^2, 28 ] E12.66 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 7, 14, 14}) Quotient :: dipole Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^-2, Y3^-1 * Y1^-3, Y1 * Y2 * Y3 * Y2, Y2^-1 * Y3^-1 * Y1^-1 * Y2^-1, (Y1 * Y2^-1)^2, (Y2^-1 * R)^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y2^-1), Y3^-1 * Y1^-1 * Y2^12, 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 ] Map:: non-degenerate R = (1, 15, 2, 16, 8, 22, 7, 21, 4, 18, 10, 24, 5, 19)(3, 17, 9, 23, 14, 28, 13, 27, 12, 26, 6, 20, 11, 25)(29, 43, 31, 45, 36, 50, 42, 56, 32, 46, 40, 54, 33, 47, 39, 53, 30, 44, 37, 51, 35, 49, 41, 55, 38, 52, 34, 48) L = (1, 32)(2, 38)(3, 40)(4, 30)(5, 35)(6, 42)(7, 29)(8, 33)(9, 34)(10, 36)(11, 41)(12, 37)(13, 31)(14, 39)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56) 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 ) } Outer automorphisms :: reflexible Dual of E12.49 Graph:: bipartite v = 3 e = 28 f = 3 degree seq :: [ 14^2, 28 ] E12.67 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 7, 14, 14}) Quotient :: dipole Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^2, Y3 * Y1^-1 * Y2^2, Y2^-2 * Y1^-2, (R * Y3)^2, (Y1^-1, Y2^-1), Y2 * Y3 * Y2 * Y1^-1, (Y2^-1 * R)^2, Y1^-3 * Y3, (R * Y1)^2, Y3 * Y1^-1 * Y2^-1 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 15, 2, 16, 8, 22, 4, 18, 7, 21, 11, 25, 5, 19)(3, 17, 9, 23, 6, 20, 10, 24, 13, 27, 14, 28, 12, 26)(29, 43, 31, 45, 39, 53, 42, 56, 32, 46, 38, 52, 30, 44, 37, 51, 33, 47, 40, 54, 35, 49, 41, 55, 36, 50, 34, 48) L = (1, 32)(2, 35)(3, 38)(4, 33)(5, 36)(6, 42)(7, 29)(8, 39)(9, 41)(10, 40)(11, 30)(12, 34)(13, 31)(14, 37)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56) 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 ) } Outer automorphisms :: reflexible Dual of E12.46 Graph:: bipartite v = 3 e = 28 f = 3 degree seq :: [ 14^2, 28 ] E12.68 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 7, 14, 14}) Quotient :: dipole Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ R^2, Y1^2 * Y3^-1, Y1 * Y2^-2, (Y3, Y2^-1), (R * Y3)^2, (R * Y1)^2, Y1 * Y3^3, (R * Y2)^2 ] Map:: non-degenerate R = (1, 15, 2, 16, 4, 18, 9, 23, 12, 26, 7, 21, 5, 19)(3, 17, 8, 22, 10, 24, 14, 28, 13, 27, 11, 25, 6, 20)(29, 43, 31, 45, 30, 44, 36, 50, 32, 46, 38, 52, 37, 51, 42, 56, 40, 54, 41, 55, 35, 49, 39, 53, 33, 47, 34, 48) L = (1, 32)(2, 37)(3, 38)(4, 40)(5, 30)(6, 36)(7, 29)(8, 42)(9, 35)(10, 41)(11, 31)(12, 33)(13, 34)(14, 39)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56) 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 ) } Outer automorphisms :: reflexible Dual of E12.48 Graph:: bipartite v = 3 e = 28 f = 3 degree seq :: [ 14^2, 28 ] E12.69 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 7, 14, 14}) Quotient :: dipole Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ R^2, Y1^2 * Y3, Y1 * Y2^2, (Y2^-1, Y3^-1), (R * Y1)^2, Y3^3 * Y1^-1, (R * Y3)^2, (R * Y2)^2 ] Map:: non-degenerate R = (1, 15, 2, 16, 7, 21, 9, 23, 12, 26, 4, 18, 5, 19)(3, 17, 6, 20, 8, 22, 13, 27, 14, 28, 10, 24, 11, 25)(29, 43, 31, 45, 33, 47, 39, 53, 32, 46, 38, 52, 40, 54, 42, 56, 37, 51, 41, 55, 35, 49, 36, 50, 30, 44, 34, 48) L = (1, 32)(2, 33)(3, 38)(4, 37)(5, 40)(6, 39)(7, 29)(8, 31)(9, 30)(10, 41)(11, 42)(12, 35)(13, 34)(14, 36)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56) 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 ) } Outer automorphisms :: reflexible Dual of E12.50 Graph:: bipartite v = 3 e = 28 f = 3 degree seq :: [ 14^2, 28 ] E12.70 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 7, 14, 14}) Quotient :: dipole Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3, Y2^-1 * Y3 * Y2 * Y1^-1, (Y2^-1 * R)^2, (R * Y3)^2, (R * Y1)^2, Y2 * Y3 * Y2^-1 * Y1^-1, Y2^-1 * Y3 * Y2^-3, Y1^2 * Y2 * Y3 * Y2, (Y3^-1 * Y1^-1)^7, (Y2^-1 * Y1)^14 ] Map:: non-degenerate R = (1, 15, 2, 16, 6, 20, 13, 27, 9, 23, 11, 25, 4, 18)(3, 17, 7, 21, 12, 26, 5, 19, 8, 22, 14, 28, 10, 24)(29, 43, 31, 45, 37, 51, 36, 50, 30, 44, 35, 49, 39, 53, 42, 56, 34, 48, 40, 54, 32, 46, 38, 52, 41, 55, 33, 47) L = (1, 30)(2, 34)(3, 35)(4, 29)(5, 36)(6, 41)(7, 40)(8, 42)(9, 39)(10, 31)(11, 32)(12, 33)(13, 37)(14, 38)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56) 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 ) } Outer automorphisms :: reflexible Dual of E12.47 Graph:: bipartite v = 3 e = 28 f = 3 degree seq :: [ 14^2, 28 ] E12.71 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 7, 14, 14}) Quotient :: dipole Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1^-1 * Y3 * Y2^-1 * Y1^-1, Y3 * Y2 * Y3 * Y2^-1, Y2 * Y1 * Y3 * Y1, Y2^-1 * Y3 * Y1^-2, Y3 * Y1 * Y3 * Y1^-1, (R * Y2)^2, (R * Y3)^2, Y2^3 * Y1^-1, (R * Y1)^2, Y1^5 * Y2^-1 ] Map:: non-degenerate R = (1, 15, 2, 16, 7, 21, 13, 27, 12, 26, 3, 17, 8, 22, 4, 18, 9, 23, 6, 20, 10, 24, 14, 28, 11, 25, 5, 19)(29, 43, 31, 45, 38, 52, 30, 44, 36, 50, 42, 56, 35, 49, 32, 46, 39, 53, 41, 55, 37, 51, 33, 47, 40, 54, 34, 48) L = (1, 32)(2, 37)(3, 39)(4, 29)(5, 36)(6, 35)(7, 34)(8, 33)(9, 30)(10, 41)(11, 31)(12, 42)(13, 38)(14, 40)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56) local type(s) :: { ( 14^28 ) } Outer automorphisms :: reflexible Dual of E12.37 Graph:: bipartite v = 2 e = 28 f = 4 degree seq :: [ 28^2 ] E12.72 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 7, 14, 14}) Quotient :: dipole Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ R^2, Y3^2, (Y1, Y2^-1), Y1^-2 * Y2 * Y3, Y3 * Y1 * Y3 * Y1^-1, Y2 * Y1^-2 * Y3, Y2 * Y1^-1 * Y3 * Y1^-1, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y1^-1 * Y2^-3, Y1^5 * Y2 ] Map:: non-degenerate R = (1, 15, 2, 16, 7, 21, 13, 27, 11, 25, 6, 20, 10, 24, 4, 18, 9, 23, 3, 17, 8, 22, 14, 28, 12, 26, 5, 19)(29, 43, 31, 45, 39, 53, 33, 47, 37, 51, 41, 55, 40, 54, 32, 46, 35, 49, 42, 56, 38, 52, 30, 44, 36, 50, 34, 48) L = (1, 32)(2, 37)(3, 35)(4, 29)(5, 38)(6, 40)(7, 31)(8, 41)(9, 30)(10, 33)(11, 42)(12, 34)(13, 36)(14, 39)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56) local type(s) :: { ( 14^28 ) } Outer automorphisms :: reflexible Dual of E12.36 Graph:: bipartite v = 2 e = 28 f = 4 degree seq :: [ 28^2 ] E12.73 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 7, 14, 14}) Quotient :: dipole Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3, Y2 * Y1 * Y3^-1 * Y2, Y2 * Y3^-1 * Y2 * Y1, Y3 * Y2^-2 * Y1^-1, (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y3 * Y1^-4, Y2 * Y1^-2 * Y3^-1 * Y1^-2, Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y2, Y1^-1 * Y2^11, Y3^-1 * Y1 * Y2^-1 * Y1 * Y3^-1 * Y1 * Y2^-1 * Y1 * Y3^-1 * Y1 * Y2^-1 * Y1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 15, 2, 16, 6, 20, 12, 26, 9, 23, 4, 18, 8, 22, 14, 28, 10, 24, 3, 17, 7, 21, 13, 27, 11, 25, 5, 19)(29, 43, 31, 45, 37, 51, 33, 47, 38, 52, 40, 54, 39, 53, 42, 56, 34, 48, 41, 55, 36, 50, 30, 44, 35, 49, 32, 46) L = (1, 32)(2, 36)(3, 29)(4, 35)(5, 37)(6, 42)(7, 30)(8, 41)(9, 31)(10, 33)(11, 40)(12, 38)(13, 34)(14, 39)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56) local type(s) :: { ( 14^28 ) } Outer automorphisms :: reflexible Dual of E12.38 Graph:: bipartite v = 2 e = 28 f = 4 degree seq :: [ 28^2 ] E12.74 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 7, 14, 14}) Quotient :: dipole Aut^+ = C14 (small group id <14, 2>) Aut = D28 (small group id <28, 3>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3, Y2 * Y3, Y2 * Y1^-3, Y3 * Y1^-1 * Y2 * Y1, Y3^-1 * Y1^-3, (R * Y3)^2, (R * Y1)^2, Y2^3 * Y3^-1 * Y1^2, Y3^2 * Y1^-1 * Y2 * Y3^-1 * Y1, Y2 * Y1^7 * Y3^-1 * Y1, (Y3 * Y2^-1)^7 ] Map:: non-degenerate R = (1, 15, 2, 16, 6, 20, 3, 17, 7, 21, 12, 26, 9, 23, 13, 27, 10, 24, 14, 28, 11, 25, 4, 18, 8, 22, 5, 19)(29, 43, 31, 45, 37, 51, 42, 56, 36, 50, 30, 44, 35, 49, 41, 55, 39, 53, 33, 47, 34, 48, 40, 54, 38, 52, 32, 46) L = (1, 32)(2, 36)(3, 29)(4, 38)(5, 39)(6, 33)(7, 30)(8, 42)(9, 31)(10, 40)(11, 41)(12, 34)(13, 35)(14, 37)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56) local type(s) :: { ( 14^28 ) } Outer automorphisms :: reflexible Dual of E12.39 Graph:: bipartite v = 2 e = 28 f = 4 degree seq :: [ 28^2 ] E12.75 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 15, 15}) Quotient :: dipole Aut^+ = C15 (small group id <15, 1>) Aut = D30 (small group id <30, 3>) |r| :: 2 Presentation :: [ R^2, Y1^2 * Y2, Y1 * Y2^-2, Y3^3, (Y3, Y2^-1), (Y1^-1, Y3^-1), (R * Y3)^2, (R * Y1)^2, (R * 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 ] Map:: non-degenerate R = (1, 16, 2, 17, 6, 21, 3, 18, 5, 20)(4, 19, 8, 23, 13, 28, 10, 25, 12, 27)(7, 22, 9, 24, 15, 30, 11, 26, 14, 29)(31, 46, 33, 48, 32, 47, 35, 50, 36, 51)(34, 49, 40, 55, 38, 53, 42, 57, 43, 58)(37, 52, 41, 56, 39, 54, 44, 59, 45, 60) L = (1, 34)(2, 38)(3, 40)(4, 37)(5, 42)(6, 43)(7, 31)(8, 39)(9, 32)(10, 41)(11, 33)(12, 44)(13, 45)(14, 35)(15, 36)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60) local type(s) :: { ( 30^10 ) } Outer automorphisms :: reflexible Dual of E12.89 Graph:: bipartite v = 6 e = 30 f = 2 degree seq :: [ 10^6 ] E12.76 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 15, 15}) Quotient :: dipole Aut^+ = C15 (small group id <15, 1>) Aut = D30 (small group id <30, 3>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), Y2^3 * Y1^2, Y1^5, Y1^-1 * Y2 * Y1^-1 * Y2^2 * Y1^-1, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^5, (Y3 * Y2^-1)^15 ] Map:: R = (1, 16, 2, 17, 6, 21, 11, 26, 4, 19)(3, 18, 7, 22, 13, 28, 15, 30, 10, 25)(5, 20, 8, 23, 14, 29, 9, 24, 12, 27)(31, 46, 33, 48, 39, 54, 41, 56, 45, 60, 38, 53, 32, 47, 37, 52, 42, 57, 34, 49, 40, 55, 44, 59, 36, 51, 43, 58, 35, 50) L = (1, 31)(2, 32)(3, 33)(4, 34)(5, 35)(6, 36)(7, 37)(8, 38)(9, 39)(10, 40)(11, 41)(12, 42)(13, 43)(14, 44)(15, 45)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60) local type(s) :: { ( 10, 30, 10, 30, 10, 30, 10, 30, 10, 30 ), ( 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 4 e = 30 f = 4 degree seq :: [ 10^3, 30 ] E12.77 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 15, 15}) Quotient :: dipole Aut^+ = C15 (small group id <15, 1>) Aut = D30 (small group id <30, 3>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (R * Y1)^2, (R * Y3)^2, (Y1, Y2^-1), Y1^2 * Y2^-3, Y1^5, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^5, (Y3 * Y2^-1)^15 ] Map:: R = (1, 16, 2, 17, 6, 21, 11, 26, 4, 19)(3, 18, 7, 22, 14, 29, 13, 28, 10, 25)(5, 20, 8, 23, 9, 24, 15, 30, 12, 27)(31, 46, 33, 48, 39, 54, 36, 51, 44, 59, 42, 57, 34, 49, 40, 55, 38, 53, 32, 47, 37, 52, 45, 60, 41, 56, 43, 58, 35, 50) L = (1, 31)(2, 32)(3, 33)(4, 34)(5, 35)(6, 36)(7, 37)(8, 38)(9, 39)(10, 40)(11, 41)(12, 42)(13, 43)(14, 44)(15, 45)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60) local type(s) :: { ( 10, 30, 10, 30, 10, 30, 10, 30, 10, 30 ), ( 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 4 e = 30 f = 4 degree seq :: [ 10^3, 30 ] E12.78 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 15, 15}) Quotient :: dipole Aut^+ = C15 (small group id <15, 1>) Aut = D30 (small group id <30, 3>) |r| :: 2 Presentation :: [ 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), Y1^5, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^5, (Y3 * Y2^-1)^15 ] Map:: R = (1, 16, 2, 17, 6, 21, 11, 26, 4, 19)(3, 18, 7, 22, 12, 27, 15, 30, 10, 25)(5, 20, 8, 23, 13, 28, 14, 29, 9, 24)(31, 46, 33, 48, 39, 54, 34, 49, 40, 55, 44, 59, 41, 56, 45, 60, 43, 58, 36, 51, 42, 57, 38, 53, 32, 47, 37, 52, 35, 50) L = (1, 31)(2, 32)(3, 33)(4, 34)(5, 35)(6, 36)(7, 37)(8, 38)(9, 39)(10, 40)(11, 41)(12, 42)(13, 43)(14, 44)(15, 45)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60) local type(s) :: { ( 10, 30, 10, 30, 10, 30, 10, 30, 10, 30 ), ( 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 4 e = 30 f = 4 degree seq :: [ 10^3, 30 ] E12.79 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 15, 15}) Quotient :: dipole Aut^+ = C15 (small group id <15, 1>) Aut = D30 (small group id <30, 3>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y2^-2 * Y1 * Y2^-1, (R * Y1)^2, (R * Y3)^2, Y1^5, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^5, (Y3 * Y2^-1)^15 ] Map:: R = (1, 16, 2, 17, 6, 21, 10, 25, 4, 19)(3, 18, 7, 22, 12, 27, 14, 29, 9, 24)(5, 20, 8, 23, 13, 28, 15, 30, 11, 26)(31, 46, 33, 48, 38, 53, 32, 47, 37, 52, 43, 58, 36, 51, 42, 57, 45, 60, 40, 55, 44, 59, 41, 56, 34, 49, 39, 54, 35, 50) L = (1, 31)(2, 32)(3, 33)(4, 34)(5, 35)(6, 36)(7, 37)(8, 38)(9, 39)(10, 40)(11, 41)(12, 42)(13, 43)(14, 44)(15, 45)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60) local type(s) :: { ( 10, 30, 10, 30, 10, 30, 10, 30, 10, 30 ), ( 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 4 e = 30 f = 4 degree seq :: [ 10^3, 30 ] E12.80 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 15, 15}) Quotient :: dipole Aut^+ = C15 (small group id <15, 1>) Aut = D30 (small group id <30, 3>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3, (R * Y1)^2, Y2^-1 * Y3 * Y2 * Y1^-1, (R * Y3)^2, (Y2^-1 * R)^2, Y2 * Y3 * Y2^-1 * Y1^-1, Y1 * Y2^-1 * Y3 * Y2^-2, Y1^5, Y1 * Y2^6, (Y3^-1 * Y1^-1)^5 ] Map:: non-degenerate R = (1, 16, 2, 17, 6, 21, 11, 26, 4, 19)(3, 18, 7, 22, 14, 29, 13, 28, 10, 25)(5, 20, 8, 23, 9, 24, 15, 30, 12, 27)(31, 46, 33, 48, 39, 54, 36, 51, 44, 59, 42, 57, 34, 49, 40, 55, 38, 53, 32, 47, 37, 52, 45, 60, 41, 56, 43, 58, 35, 50) L = (1, 32)(2, 36)(3, 37)(4, 31)(5, 38)(6, 41)(7, 44)(8, 39)(9, 45)(10, 33)(11, 34)(12, 35)(13, 40)(14, 43)(15, 42)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60) local type(s) :: { ( 10, 30, 10, 30, 10, 30, 10, 30, 10, 30 ), ( 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30 ) } Outer automorphisms :: reflexible Dual of E12.87 Graph:: bipartite v = 4 e = 30 f = 4 degree seq :: [ 10^3, 30 ] E12.81 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 15, 15}) Quotient :: dipole Aut^+ = C15 (small group id <15, 1>) Aut = D30 (small group id <30, 3>) |r| :: 2 Presentation :: [ R^2, Y1^2 * Y3^-1, Y1 * Y3^2, Y2 * Y1 * Y2^2, (Y1^-1, Y2^-1), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y3^-1, Y2^-1), Y2^-1 * Y1 * Y2^-1 * Y3^-1 * Y2^-1, 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 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 16, 2, 17, 4, 19, 7, 22, 5, 20)(3, 18, 8, 23, 11, 26, 13, 28, 12, 27)(6, 21, 9, 24, 14, 29, 15, 30, 10, 25)(31, 46, 33, 48, 40, 55, 35, 50, 42, 57, 45, 60, 37, 52, 43, 58, 44, 59, 34, 49, 41, 56, 39, 54, 32, 47, 38, 53, 36, 51) L = (1, 34)(2, 37)(3, 41)(4, 35)(5, 32)(6, 44)(7, 31)(8, 43)(9, 45)(10, 39)(11, 42)(12, 38)(13, 33)(14, 40)(15, 36)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60) local type(s) :: { ( 10, 30, 10, 30, 10, 30, 10, 30, 10, 30 ), ( 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30 ) } Outer automorphisms :: reflexible Dual of E12.88 Graph:: bipartite v = 4 e = 30 f = 4 degree seq :: [ 10^3, 30 ] E12.82 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 15, 15}) Quotient :: dipole Aut^+ = C15 (small group id <15, 1>) Aut = D30 (small group id <30, 3>) |r| :: 2 Presentation :: [ R^2, Y1^2 * Y3, Y1 * Y3^-2, Y2^2 * Y1^-1 * Y2, Y2 * Y1^-1 * Y2^2, (R * Y1)^2, (Y1^-1, Y2^-1), (Y2, Y3^-1), (R * Y3)^2, (R * Y2)^2, 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 ] Map:: non-degenerate R = (1, 16, 2, 17, 7, 22, 4, 19, 5, 20)(3, 18, 8, 23, 12, 27, 10, 25, 11, 26)(6, 21, 9, 24, 15, 30, 13, 28, 14, 29)(31, 46, 33, 48, 39, 54, 32, 47, 38, 53, 45, 60, 37, 52, 42, 57, 43, 58, 34, 49, 40, 55, 44, 59, 35, 50, 41, 56, 36, 51) L = (1, 34)(2, 35)(3, 40)(4, 32)(5, 37)(6, 43)(7, 31)(8, 41)(9, 44)(10, 38)(11, 42)(12, 33)(13, 39)(14, 45)(15, 36)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60) local type(s) :: { ( 10, 30, 10, 30, 10, 30, 10, 30, 10, 30 ), ( 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30 ) } Outer automorphisms :: reflexible Dual of E12.86 Graph:: bipartite v = 4 e = 30 f = 4 degree seq :: [ 10^3, 30 ] E12.83 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 15, 15}) Quotient :: dipole Aut^+ = C15 (small group id <15, 1>) Aut = D30 (small group id <30, 3>) |r| :: 2 Presentation :: [ R^2, Y1^2 * Y3^-1, Y1 * Y3^2, (Y2, Y1^-1), Y2^3 * Y3, (R * Y3)^2, (R * Y1)^2, (Y2^-1 * R)^2, Y2^-1 * Y1 * Y2^-1 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 16, 2, 17, 4, 19, 7, 22, 5, 20)(3, 18, 8, 23, 11, 26, 13, 28, 12, 27)(6, 21, 9, 24, 14, 29, 10, 25, 15, 30)(31, 46, 33, 48, 40, 55, 37, 52, 43, 58, 39, 54, 32, 47, 38, 53, 45, 60, 35, 50, 42, 57, 44, 59, 34, 49, 41, 56, 36, 51) L = (1, 34)(2, 37)(3, 41)(4, 35)(5, 32)(6, 44)(7, 31)(8, 43)(9, 40)(10, 36)(11, 42)(12, 38)(13, 33)(14, 45)(15, 39)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60) local type(s) :: { ( 10, 30, 10, 30, 10, 30, 10, 30, 10, 30 ), ( 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30 ) } Outer automorphisms :: reflexible Dual of E12.85 Graph:: bipartite v = 4 e = 30 f = 4 degree seq :: [ 10^3, 30 ] E12.84 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 15, 15}) Quotient :: dipole Aut^+ = C15 (small group id <15, 1>) Aut = D30 (small group id <30, 3>) |r| :: 2 Presentation :: [ R^2, Y1^2 * Y3, Y1 * Y3^-2, (Y2, Y1^-1), Y2^3 * Y3, (R * Y1)^2, (Y2^-1 * R)^2, (R * Y3)^2, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 ] Map:: non-degenerate R = (1, 16, 2, 17, 7, 22, 4, 19, 5, 20)(3, 18, 8, 23, 13, 28, 11, 26, 12, 27)(6, 21, 9, 24, 10, 25, 14, 29, 15, 30)(31, 46, 33, 48, 40, 55, 37, 52, 43, 58, 45, 60, 35, 50, 42, 57, 39, 54, 32, 47, 38, 53, 44, 59, 34, 49, 41, 56, 36, 51) L = (1, 34)(2, 35)(3, 41)(4, 32)(5, 37)(6, 44)(7, 31)(8, 42)(9, 45)(10, 36)(11, 38)(12, 43)(13, 33)(14, 39)(15, 40)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60) local type(s) :: { ( 10, 30, 10, 30, 10, 30, 10, 30, 10, 30 ), ( 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 4 e = 30 f = 4 degree seq :: [ 10^3, 30 ] E12.85 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 15, 15}) Quotient :: dipole Aut^+ = C15 (small group id <15, 1>) Aut = D30 (small group id <30, 3>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-1, Y2^-3 * Y1^-1, (R * Y1)^2, (Y2^-1 * R)^2, (Y3^-1, Y2^-1), (R * Y3)^2, Y1^5, (Y3^-1 * Y1^-1)^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 ] Map:: non-degenerate R = (1, 16, 2, 17, 6, 21, 11, 26, 4, 19)(3, 18, 7, 22, 12, 27, 15, 30, 10, 25)(5, 20, 8, 23, 13, 28, 14, 29, 9, 24)(31, 46, 33, 48, 39, 54, 34, 49, 40, 55, 44, 59, 41, 56, 45, 60, 43, 58, 36, 51, 42, 57, 38, 53, 32, 47, 37, 52, 35, 50) L = (1, 32)(2, 36)(3, 37)(4, 31)(5, 38)(6, 41)(7, 42)(8, 43)(9, 35)(10, 33)(11, 34)(12, 45)(13, 44)(14, 39)(15, 40)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60) local type(s) :: { ( 10, 30, 10, 30, 10, 30, 10, 30, 10, 30 ), ( 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30 ) } Outer automorphisms :: reflexible Dual of E12.83 Graph:: bipartite v = 4 e = 30 f = 4 degree seq :: [ 10^3, 30 ] E12.86 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 15, 15}) Quotient :: dipole Aut^+ = C15 (small group id <15, 1>) Aut = D30 (small group id <30, 3>) |r| :: 2 Presentation :: [ R^2, Y1^2 * Y3, Y1 * Y3^-2, (Y2, Y1^-1), Y2^-1 * Y3 * Y2^-2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2 ] Map:: non-degenerate R = (1, 16, 2, 17, 7, 22, 4, 19, 5, 20)(3, 18, 8, 23, 13, 28, 11, 26, 12, 27)(6, 21, 9, 24, 15, 30, 10, 25, 14, 29)(31, 46, 33, 48, 40, 55, 34, 49, 41, 56, 39, 54, 32, 47, 38, 53, 44, 59, 35, 50, 42, 57, 45, 60, 37, 52, 43, 58, 36, 51) L = (1, 34)(2, 35)(3, 41)(4, 32)(5, 37)(6, 40)(7, 31)(8, 42)(9, 44)(10, 39)(11, 38)(12, 43)(13, 33)(14, 45)(15, 36)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60) local type(s) :: { ( 10, 30, 10, 30, 10, 30, 10, 30, 10, 30 ), ( 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30 ) } Outer automorphisms :: reflexible Dual of E12.82 Graph:: bipartite v = 4 e = 30 f = 4 degree seq :: [ 10^3, 30 ] E12.87 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 15, 15}) Quotient :: dipole Aut^+ = C15 (small group id <15, 1>) Aut = D30 (small group id <30, 3>) |r| :: 2 Presentation :: [ R^2, Y1^2 * Y3^-1, Y1 * Y3^2, Y2^2 * Y3^-1 * Y2, Y2^-1 * Y3 * Y2^-2, Y2 * Y3^-1 * Y2^2, (R * Y3)^2, (R * Y1)^2, (Y2, Y3), (Y1^-1, Y2^-1), (R * Y2)^2 ] Map:: non-degenerate R = (1, 16, 2, 17, 4, 19, 7, 22, 5, 20)(3, 18, 8, 23, 11, 26, 13, 28, 12, 27)(6, 21, 9, 24, 10, 25, 15, 30, 14, 29)(31, 46, 33, 48, 40, 55, 34, 49, 41, 56, 44, 59, 35, 50, 42, 57, 39, 54, 32, 47, 38, 53, 45, 60, 37, 52, 43, 58, 36, 51) L = (1, 34)(2, 37)(3, 41)(4, 35)(5, 32)(6, 40)(7, 31)(8, 43)(9, 45)(10, 44)(11, 42)(12, 38)(13, 33)(14, 39)(15, 36)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60) local type(s) :: { ( 10, 30, 10, 30, 10, 30, 10, 30, 10, 30 ), ( 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30 ) } Outer automorphisms :: reflexible Dual of E12.80 Graph:: bipartite v = 4 e = 30 f = 4 degree seq :: [ 10^3, 30 ] E12.88 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 15, 15}) Quotient :: dipole Aut^+ = C15 (small group id <15, 1>) Aut = D30 (small group id <30, 3>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3, Y2^-3 * Y3, Y2^-1 * Y3 * Y2 * Y1^-1, (R * Y3)^2, (Y2^-1 * R)^2, (R * Y1)^2, Y1^5, Y1^-1 * Y2^-2 * Y1^2 * Y2^-1, (Y3^-1 * Y1^-1)^5, Y2^2 * Y3 * Y2 * Y3^8 ] Map:: non-degenerate R = (1, 16, 2, 17, 6, 21, 10, 25, 4, 19)(3, 18, 7, 22, 12, 27, 14, 29, 9, 24)(5, 20, 8, 23, 13, 28, 15, 30, 11, 26)(31, 46, 33, 48, 38, 53, 32, 47, 37, 52, 43, 58, 36, 51, 42, 57, 45, 60, 40, 55, 44, 59, 41, 56, 34, 49, 39, 54, 35, 50) L = (1, 32)(2, 36)(3, 37)(4, 31)(5, 38)(6, 40)(7, 42)(8, 43)(9, 33)(10, 34)(11, 35)(12, 44)(13, 45)(14, 39)(15, 41)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60) local type(s) :: { ( 10, 30, 10, 30, 10, 30, 10, 30, 10, 30 ), ( 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30, 10, 30 ) } Outer automorphisms :: reflexible Dual of E12.81 Graph:: bipartite v = 4 e = 30 f = 4 degree seq :: [ 10^3, 30 ] E12.89 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 5, 15, 15}) Quotient :: dipole Aut^+ = C15 (small group id <15, 1>) Aut = D30 (small group id <30, 3>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2^-2, Y3^3, Y2^-1 * Y3^-1 * Y1^-2, (Y2, Y3^-1), Y3 * Y1^2 * Y2, Y2^-1 * Y1^-1 * Y3^-1 * Y1^-1, (Y3^-1, Y1^-1), (R * Y2)^2, Y3 * Y2 * Y1^2, (R * Y1)^2, (R * Y3)^2 ] Map:: non-degenerate R = (1, 16, 2, 17, 8, 23, 13, 28, 14, 29, 4, 19, 10, 25, 6, 21, 3, 18, 9, 24, 7, 22, 11, 26, 15, 30, 12, 27, 5, 20)(31, 46, 33, 48, 32, 47, 39, 54, 38, 53, 37, 52, 43, 58, 41, 56, 44, 59, 45, 60, 34, 49, 42, 57, 40, 55, 35, 50, 36, 51) L = (1, 34)(2, 40)(3, 42)(4, 37)(5, 44)(6, 45)(7, 31)(8, 36)(9, 35)(10, 41)(11, 32)(12, 43)(13, 33)(14, 39)(15, 38)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60) local type(s) :: { ( 10^30 ) } Outer automorphisms :: reflexible Dual of E12.75 Graph:: bipartite v = 2 e = 30 f = 6 degree seq :: [ 30^2 ] E12.90 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 15, 15, 15}) Quotient :: dipole Aut^+ = C15 (small group id <15, 1>) Aut = D30 (small group id <30, 3>) |r| :: 2 Presentation :: [ R^2, Y1^3, Y1 * Y3^-1 * Y2^-1, Y1 * Y2^-1 * Y3^-1, Y2^-1 * Y1^-1 * Y3^-1 * Y1^-1, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y2^3 * Y3^-2, Y3^10, 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, 16, 2, 17, 5, 20)(3, 18, 8, 23, 7, 22)(4, 19, 9, 24, 6, 21)(10, 25, 15, 30, 11, 26)(12, 27, 14, 29, 13, 28)(31, 46, 33, 48, 40, 55, 42, 57, 39, 54, 35, 50, 37, 52, 41, 56, 43, 58, 34, 49, 32, 47, 38, 53, 45, 60, 44, 59, 36, 51) L = (1, 34)(2, 39)(3, 32)(4, 42)(5, 36)(6, 43)(7, 31)(8, 35)(9, 44)(10, 38)(11, 33)(12, 45)(13, 40)(14, 41)(15, 37)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60) local type(s) :: { ( 30^6 ), ( 30^30 ) } Outer automorphisms :: reflexible Dual of E12.95 Graph:: bipartite v = 6 e = 30 f = 2 degree seq :: [ 6^5, 30 ] E12.91 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 15, 15, 15}) Quotient :: dipole Aut^+ = C15 (small group id <15, 1>) Aut = D30 (small group id <30, 3>) |r| :: 2 Presentation :: [ R^2, Y1^3, Y1 * Y3 * Y2, Y1 * Y2 * Y3, (R * Y1)^2, (R * Y3)^2, Y1 * Y2^-1 * Y1 * Y3^-1, (R * Y2)^2, Y2^3 * Y3^-2, Y3^10, (Y3 * Y2^-1)^15 ] Map:: non-degenerate R = (1, 16, 2, 17, 5, 20)(3, 18, 7, 22, 9, 24)(4, 19, 6, 21, 8, 23)(10, 25, 11, 26, 15, 30)(12, 27, 13, 28, 14, 29)(31, 46, 33, 48, 40, 55, 42, 57, 38, 53, 32, 47, 37, 52, 41, 56, 43, 58, 34, 49, 35, 50, 39, 54, 45, 60, 44, 59, 36, 51) L = (1, 34)(2, 36)(3, 35)(4, 42)(5, 38)(6, 43)(7, 31)(8, 44)(9, 32)(10, 39)(11, 33)(12, 45)(13, 40)(14, 41)(15, 37)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60) local type(s) :: { ( 30^6 ), ( 30^30 ) } Outer automorphisms :: reflexible Dual of E12.97 Graph:: bipartite v = 6 e = 30 f = 2 degree seq :: [ 6^5, 30 ] E12.92 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 15, 15, 15}) Quotient :: dipole Aut^+ = C15 (small group id <15, 1>) Aut = D30 (small group id <30, 3>) |r| :: 2 Presentation :: [ R^2, Y1^3, Y2^-2 * Y3^-1 * Y2^-1, Y3^-2 * Y2^-1 * Y1^-1, Y2^-1 * Y3^-2 * Y1^-1, Y3^-1 * Y1^-1 * Y3^-1 * Y2^-1, (Y1^-1, Y3), (Y1, Y2^-1), (R * Y3)^2, (R * Y1)^2, Y3 * Y2^-1 * Y1 * Y2^-1, (R * Y2)^2, Y2 * Y3^-2 * Y1 * Y3^-1 ] Map:: non-degenerate R = (1, 16, 2, 17, 5, 20)(3, 18, 8, 23, 13, 28)(4, 19, 9, 24, 15, 30)(6, 21, 10, 25, 14, 29)(7, 22, 11, 26, 12, 27)(31, 46, 33, 48, 39, 54, 37, 52, 40, 55, 32, 47, 38, 53, 45, 60, 41, 56, 44, 59, 35, 50, 43, 58, 34, 49, 42, 57, 36, 51) L = (1, 34)(2, 39)(3, 42)(4, 44)(5, 45)(6, 43)(7, 31)(8, 37)(9, 36)(10, 33)(11, 32)(12, 35)(13, 41)(14, 38)(15, 40)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60) local type(s) :: { ( 30^6 ), ( 30^30 ) } Outer automorphisms :: reflexible Dual of E12.96 Graph:: bipartite v = 6 e = 30 f = 2 degree seq :: [ 6^5, 30 ] E12.93 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 15, 15, 15}) Quotient :: dipole Aut^+ = C15 (small group id <15, 1>) Aut = D30 (small group id <30, 3>) |r| :: 2 Presentation :: [ R^2, Y1^3, Y3^2 * Y1^-1 * Y2^-1, (Y2^-1, Y1^-1), Y1^-1 * Y3^2 * Y2^-1, (Y3, Y1^-1), Y3 * Y2^2 * Y1^-1, (R * Y2)^2, Y3^-1 * Y2 * Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, Y1 * Y2 * Y1 * Y2 * Y3, Y3^-15 ] Map:: non-degenerate R = (1, 16, 2, 17, 5, 20)(3, 18, 8, 23, 12, 27)(4, 19, 9, 24, 13, 28)(6, 21, 10, 25, 14, 29)(7, 22, 11, 26, 15, 30)(31, 46, 33, 48, 41, 56, 34, 49, 40, 55, 32, 47, 38, 53, 45, 60, 39, 54, 44, 59, 35, 50, 42, 57, 37, 52, 43, 58, 36, 51) L = (1, 34)(2, 39)(3, 40)(4, 38)(5, 43)(6, 41)(7, 31)(8, 44)(9, 42)(10, 45)(11, 32)(12, 36)(13, 33)(14, 37)(15, 35)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60) local type(s) :: { ( 30^6 ), ( 30^30 ) } Outer automorphisms :: reflexible Dual of E12.94 Graph:: bipartite v = 6 e = 30 f = 2 degree seq :: [ 6^5, 30 ] E12.94 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 15, 15, 15}) Quotient :: dipole Aut^+ = C15 (small group id <15, 1>) Aut = D30 (small group id <30, 3>) |r| :: 2 Presentation :: [ R^2, (Y2^-1, Y1^-1), Y2 * Y1 * Y3^2, Y1^-1 * Y3^-1 * Y2 * Y1^-1, Y2^-1 * Y3^-1 * Y1^-1 * Y3^-1, Y1^-2 * Y2 * Y3^-1, Y2 * Y3 * Y2 * Y1^-1, (Y3^-1, Y1^-1), Y2 * Y1^-1 * Y3^-1 * Y1^-1, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y3^-2 * Y2^-1 * Y1^-1, Y3^-2 * Y1 * Y2 * Y3^-1, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y1^-1, Y2^15 ] Map:: non-degenerate R = (1, 16, 2, 17, 8, 23, 13, 28, 6, 21, 11, 26, 7, 22, 12, 27, 14, 29, 4, 19, 10, 25, 3, 18, 9, 24, 15, 30, 5, 20)(31, 46, 33, 48, 42, 57, 43, 58, 35, 50, 40, 55, 37, 52, 38, 53, 45, 60, 34, 49, 41, 56, 32, 47, 39, 54, 44, 59, 36, 51) L = (1, 34)(2, 40)(3, 41)(4, 43)(5, 44)(6, 45)(7, 31)(8, 33)(9, 37)(10, 36)(11, 35)(12, 32)(13, 39)(14, 38)(15, 42)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60) local type(s) :: { ( 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30 ) } Outer automorphisms :: reflexible Dual of E12.93 Graph:: bipartite v = 2 e = 30 f = 6 degree seq :: [ 30^2 ] E12.95 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 15, 15, 15}) Quotient :: dipole Aut^+ = C15 (small group id <15, 1>) Aut = D30 (small group id <30, 3>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2^2, Y1 * Y2^-1 * Y3^-1, Y1 * Y3^-1 * Y2^-1, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y3^-2 * Y2 * Y3^-2 * Y1^-1, Y3^-1 * Y1^-4 * 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 * Y1^-3 ] Map:: non-degenerate R = (1, 16, 2, 17, 8, 23, 11, 26, 15, 30, 12, 27, 7, 22, 3, 18, 6, 21, 4, 19, 9, 24, 14, 29, 13, 28, 10, 25, 5, 20)(31, 46, 33, 48, 35, 50, 37, 52, 40, 55, 42, 57, 43, 58, 45, 60, 44, 59, 41, 56, 39, 54, 38, 53, 34, 49, 32, 47, 36, 51) L = (1, 34)(2, 39)(3, 32)(4, 41)(5, 36)(6, 38)(7, 31)(8, 44)(9, 45)(10, 33)(11, 43)(12, 35)(13, 37)(14, 42)(15, 40)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60) local type(s) :: { ( 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30 ) } Outer automorphisms :: reflexible Dual of E12.90 Graph:: bipartite v = 2 e = 30 f = 6 degree seq :: [ 30^2 ] E12.96 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 15, 15, 15}) Quotient :: dipole Aut^+ = C15 (small group id <15, 1>) Aut = D30 (small group id <30, 3>) |r| :: 2 Presentation :: [ R^2, Y1^2 * Y2^-1, Y3 * Y2^-1 * Y1^-1 * Y3, Y2^-2 * Y3^-1 * Y2^-1, (Y3^-1, Y1^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2^-1 * Y1^-1 * Y3^-3, (Y1^-1 * Y3^-1)^3 ] Map:: non-degenerate R = (1, 16, 2, 17, 3, 18, 8, 23, 11, 26, 15, 30, 7, 22, 10, 25, 13, 28, 4, 19, 9, 24, 12, 27, 14, 29, 6, 21, 5, 20)(31, 46, 33, 48, 41, 56, 37, 52, 43, 58, 39, 54, 44, 59, 35, 50, 32, 47, 38, 53, 45, 60, 40, 55, 34, 49, 42, 57, 36, 51) L = (1, 34)(2, 39)(3, 42)(4, 38)(5, 43)(6, 40)(7, 31)(8, 44)(9, 41)(10, 32)(11, 36)(12, 45)(13, 33)(14, 37)(15, 35)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60) local type(s) :: { ( 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30 ) } Outer automorphisms :: reflexible Dual of E12.92 Graph:: bipartite v = 2 e = 30 f = 6 degree seq :: [ 30^2 ] E12.97 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 15, 15, 15}) Quotient :: dipole Aut^+ = C15 (small group id <15, 1>) Aut = D30 (small group id <30, 3>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2 * Y3^-1, Y1 * Y2^-2, Y1 * Y3^-1 * Y2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y3^-1 * Y1^-1)^3 ] Map:: non-degenerate R = (1, 16, 2, 17, 8, 23, 10, 25, 15, 30, 12, 27, 7, 22, 6, 21, 3, 18, 4, 19, 9, 24, 14, 29, 13, 28, 11, 26, 5, 20)(31, 46, 33, 48, 32, 47, 34, 49, 38, 53, 39, 54, 40, 55, 44, 59, 45, 60, 43, 58, 42, 57, 41, 56, 37, 52, 35, 50, 36, 51) L = (1, 34)(2, 39)(3, 38)(4, 40)(5, 33)(6, 32)(7, 31)(8, 44)(9, 45)(10, 43)(11, 36)(12, 35)(13, 37)(14, 42)(15, 41)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60) local type(s) :: { ( 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30 ) } Outer automorphisms :: reflexible Dual of E12.91 Graph:: bipartite v = 2 e = 30 f = 6 degree seq :: [ 30^2 ] E12.98 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 16, 16}) Quotient :: dipole Aut^+ = C16 (small group id <16, 1>) Aut = D32 (small group id <32, 18>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (R * Y3)^2, (R * Y1)^2, Y1^4, (Y2^-1, Y1^-1), Y2^4 * Y1, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^4, (Y3 * Y2^-1)^16 ] Map:: R = (1, 17, 2, 18, 6, 22, 4, 20)(3, 19, 7, 23, 13, 29, 10, 26)(5, 21, 8, 24, 14, 30, 11, 27)(9, 25, 12, 28, 15, 31, 16, 32)(33, 49, 35, 51, 41, 57, 43, 59, 36, 52, 42, 58, 48, 64, 46, 62, 38, 54, 45, 61, 47, 63, 40, 56, 34, 50, 39, 55, 44, 60, 37, 53) L = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) 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 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 5 e = 32 f = 5 degree seq :: [ 8^4, 32 ] E12.99 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 16, 16}) Quotient :: dipole Aut^+ = C16 (small group id <16, 1>) Aut = D32 (small group id <32, 18>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (R * Y1)^2, (R * Y3)^2, Y1^4, (Y2^-1, Y1^-1), Y2^-4 * Y1, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^4, (Y3 * Y2^-1)^16 ] Map:: R = (1, 17, 2, 18, 6, 22, 4, 20)(3, 19, 7, 23, 13, 29, 10, 26)(5, 21, 8, 24, 14, 30, 11, 27)(9, 25, 15, 31, 16, 32, 12, 28)(33, 49, 35, 51, 41, 57, 40, 56, 34, 50, 39, 55, 47, 63, 46, 62, 38, 54, 45, 61, 48, 64, 43, 59, 36, 52, 42, 58, 44, 60, 37, 53) L = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) 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 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 5 e = 32 f = 5 degree seq :: [ 8^4, 32 ] E12.100 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 16, 16}) Quotient :: dipole Aut^+ = C16 (small group id <16, 1>) Aut = D32 (small group id <32, 18>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y3 * Y1^-2, (R * Y3)^2, (Y2, Y1^-1), (Y2^-1 * R)^2, (R * Y1)^2, Y2^-1 * Y3 * Y2 * Y3, Y2^4 * Y1, Y2^4 * Y1 ] Map:: non-degenerate R = (1, 17, 2, 18, 4, 20, 5, 21)(3, 19, 7, 23, 10, 26, 11, 27)(6, 22, 8, 24, 12, 28, 13, 29)(9, 25, 14, 30, 15, 31, 16, 32)(33, 49, 35, 51, 41, 57, 45, 61, 37, 53, 43, 59, 48, 64, 44, 60, 36, 52, 42, 58, 47, 63, 40, 56, 34, 50, 39, 55, 46, 62, 38, 54) L = (1, 36)(2, 37)(3, 42)(4, 33)(5, 34)(6, 44)(7, 43)(8, 45)(9, 47)(10, 35)(11, 39)(12, 38)(13, 40)(14, 48)(15, 41)(16, 46)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) 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 ) } Outer automorphisms :: reflexible Dual of E12.101 Graph:: bipartite v = 5 e = 32 f = 5 degree seq :: [ 8^4, 32 ] E12.101 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 16, 16}) Quotient :: dipole Aut^+ = C16 (small group id <16, 1>) Aut = D32 (small group id <32, 18>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y3 * Y1^2, (Y1^-1, Y2^-1), (R * Y1)^2, (R * Y3)^2, (Y2^-1 * R)^2, Y3 * Y2 * Y3 * Y2^-1, Y2^-4 * Y1, Y2^-2 * Y1 * Y2^-2 ] Map:: non-degenerate R = (1, 17, 2, 18, 4, 20, 5, 21)(3, 19, 7, 23, 10, 26, 11, 27)(6, 22, 8, 24, 12, 28, 13, 29)(9, 25, 15, 31, 16, 32, 14, 30)(33, 49, 35, 51, 41, 57, 40, 56, 34, 50, 39, 55, 47, 63, 44, 60, 36, 52, 42, 58, 48, 64, 45, 61, 37, 53, 43, 59, 46, 62, 38, 54) L = (1, 36)(2, 37)(3, 42)(4, 33)(5, 34)(6, 44)(7, 43)(8, 45)(9, 48)(10, 35)(11, 39)(12, 38)(13, 40)(14, 47)(15, 46)(16, 41)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) 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 ) } Outer automorphisms :: reflexible Dual of E12.100 Graph:: bipartite v = 5 e = 32 f = 5 degree seq :: [ 8^4, 32 ] E12.102 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 9, 9, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2 * Y3, (R * Y1)^2, (R * Y3)^2, Y3 * Y1 * Y3^-1 * Y1, Y2 * Y1 * Y2^-1 * Y1, Y2^9, Y3^18, (Y3 * Y2^-1)^9 ] Map:: non-degenerate R = (1, 19, 2, 20)(3, 21, 5, 23)(4, 22, 6, 24)(7, 25, 9, 27)(8, 26, 10, 28)(11, 29, 13, 31)(12, 30, 14, 32)(15, 33, 17, 35)(16, 34, 18, 36)(37, 55, 39, 57, 43, 61, 47, 65, 51, 69, 52, 70, 48, 66, 44, 62, 40, 58)(38, 56, 41, 59, 45, 63, 49, 67, 53, 71, 54, 72, 50, 68, 46, 64, 42, 60) L = (1, 40)(2, 42)(3, 37)(4, 44)(5, 38)(6, 46)(7, 39)(8, 48)(9, 41)(10, 50)(11, 43)(12, 52)(13, 45)(14, 54)(15, 47)(16, 51)(17, 49)(18, 53)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 18, 36, 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 E12.108 Graph:: bipartite v = 11 e = 36 f = 3 degree seq :: [ 4^9, 18^2 ] E12.103 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 9, 9, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^2 * Y3^-1, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y1 * Y2 * Y1, Y3 * Y1 * Y3^-1 * Y1, Y3^2 * Y2 * Y3^2 ] Map:: non-degenerate R = (1, 19, 2, 20)(3, 21, 7, 25)(4, 22, 8, 26)(5, 23, 9, 27)(6, 24, 10, 28)(11, 29, 15, 33)(12, 30, 16, 34)(13, 31, 17, 35)(14, 32, 18, 36)(37, 55, 39, 57, 40, 58, 47, 65, 48, 66, 50, 68, 49, 67, 42, 60, 41, 59)(38, 56, 43, 61, 44, 62, 51, 69, 52, 70, 54, 72, 53, 71, 46, 64, 45, 63) L = (1, 40)(2, 44)(3, 47)(4, 48)(5, 39)(6, 37)(7, 51)(8, 52)(9, 43)(10, 38)(11, 50)(12, 49)(13, 41)(14, 42)(15, 54)(16, 53)(17, 45)(18, 46)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 18, 36, 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 E12.109 Graph:: bipartite v = 11 e = 36 f = 3 degree seq :: [ 4^9, 18^2 ] E12.104 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 9, 9, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^-1 * Y3^2, (R * Y1)^2, (R * Y2)^2, Y3 * Y1 * Y3^-1 * Y1, (R * Y3)^2, Y2^-1 * Y1 * Y2 * Y1, Y2^2 * Y3 * Y2^2 ] Map:: non-degenerate R = (1, 19, 2, 20)(3, 21, 7, 25)(4, 22, 8, 26)(5, 23, 9, 27)(6, 24, 10, 28)(11, 29, 15, 33)(12, 30, 16, 34)(13, 31, 17, 35)(14, 32, 18, 36)(37, 55, 39, 57, 47, 65, 50, 68, 42, 60, 40, 58, 48, 66, 49, 67, 41, 59)(38, 56, 43, 61, 51, 69, 54, 72, 46, 64, 44, 62, 52, 70, 53, 71, 45, 63) L = (1, 40)(2, 44)(3, 48)(4, 39)(5, 42)(6, 37)(7, 52)(8, 43)(9, 46)(10, 38)(11, 49)(12, 47)(13, 50)(14, 41)(15, 53)(16, 51)(17, 54)(18, 45)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 18, 36, 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 E12.107 Graph:: bipartite v = 11 e = 36 f = 3 degree seq :: [ 4^9, 18^2 ] E12.105 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 9, 9, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1^-2, Y3 * Y2^-1 * Y3, (R * Y3)^2, (R * Y2)^2, (Y1^-1, Y3^-1), (R * Y1)^2, Y2^4 * Y1^-1 ] Map:: non-degenerate R = (1, 19, 2, 20, 6, 24, 9, 27, 15, 33, 11, 29, 13, 31, 3, 21, 5, 23)(4, 22, 8, 26, 7, 25, 10, 28, 16, 34, 17, 35, 18, 36, 12, 30, 14, 32)(37, 55, 39, 57, 47, 65, 45, 63, 38, 56, 41, 59, 49, 67, 51, 69, 42, 60)(40, 58, 48, 66, 53, 71, 46, 64, 44, 62, 50, 68, 54, 72, 52, 70, 43, 61) L = (1, 40)(2, 44)(3, 48)(4, 39)(5, 50)(6, 43)(7, 37)(8, 41)(9, 46)(10, 38)(11, 53)(12, 47)(13, 54)(14, 49)(15, 52)(16, 42)(17, 45)(18, 51)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36 ) } Outer automorphisms :: reflexible Dual of E12.106 Graph:: bipartite v = 4 e = 36 f = 10 degree seq :: [ 18^4 ] E12.106 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 9, 9, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ Y2^2, R^2, Y3 * Y1^-1, (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y2 * Y1 * Y2, (R * Y2 * Y3^-1)^2, Y1^-9 * Y2, (Y3 * Y2)^9, (Y3^-1 * Y1^-1)^9 ] Map:: non-degenerate R = (1, 19, 2, 20, 5, 23, 9, 27, 13, 31, 17, 35, 15, 33, 11, 29, 7, 25, 3, 21, 6, 24, 10, 28, 14, 32, 18, 36, 16, 34, 12, 30, 8, 26, 4, 22)(37, 55, 39, 57)(38, 56, 42, 60)(40, 58, 43, 61)(41, 59, 46, 64)(44, 62, 47, 65)(45, 63, 50, 68)(48, 66, 51, 69)(49, 67, 54, 72)(52, 70, 53, 71) L = (1, 38)(2, 41)(3, 42)(4, 37)(5, 45)(6, 46)(7, 39)(8, 40)(9, 49)(10, 50)(11, 43)(12, 44)(13, 53)(14, 54)(15, 47)(16, 48)(17, 51)(18, 52)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 18^4 ), ( 18^36 ) } Outer automorphisms :: reflexible Dual of E12.105 Graph:: bipartite v = 10 e = 36 f = 4 degree seq :: [ 4^9, 36 ] E12.107 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 9, 9, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1, (Y2, Y1^-1), (R * Y3)^2, (R * Y1)^2, Y1^2 * Y2^-2, (Y3 * Y2^-1)^2, (R * Y2 * Y3^-1)^2, Y2^8 * Y1, (Y3^-1 * Y1^-1)^9 ] Map:: non-degenerate R = (1, 19, 2, 20, 6, 24, 11, 29, 15, 33, 17, 35, 13, 31, 9, 27, 4, 22)(3, 21, 7, 25, 12, 30, 16, 34, 18, 36, 14, 32, 10, 28, 5, 23, 8, 26)(37, 55, 39, 57, 42, 60, 48, 66, 51, 69, 54, 72, 49, 67, 46, 64, 40, 58, 44, 62, 38, 56, 43, 61, 47, 65, 52, 70, 53, 71, 50, 68, 45, 63, 41, 59) L = (1, 38)(2, 42)(3, 43)(4, 37)(5, 44)(6, 47)(7, 48)(8, 39)(9, 40)(10, 41)(11, 51)(12, 52)(13, 45)(14, 46)(15, 53)(16, 54)(17, 49)(18, 50)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) 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 ) } Outer automorphisms :: reflexible Dual of E12.104 Graph:: bipartite v = 3 e = 36 f = 11 degree seq :: [ 18^2, 36 ] E12.108 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 9, 9, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-2, Y1 * Y2^2, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, Y1^-4 * Y3, Y2 * Y1^-1 * Y3 * Y2 * Y1^-2 ] Map:: non-degenerate R = (1, 19, 2, 20, 8, 26, 14, 32, 4, 22, 7, 25, 10, 28, 15, 33, 5, 23)(3, 21, 6, 24, 9, 27, 17, 35, 11, 29, 13, 31, 16, 34, 18, 36, 12, 30)(37, 55, 39, 57, 41, 59, 48, 66, 51, 69, 54, 72, 46, 64, 52, 70, 43, 61, 49, 67, 40, 58, 47, 65, 50, 68, 53, 71, 44, 62, 45, 63, 38, 56, 42, 60) L = (1, 40)(2, 43)(3, 47)(4, 41)(5, 50)(6, 49)(7, 37)(8, 46)(9, 52)(10, 38)(11, 48)(12, 53)(13, 39)(14, 51)(15, 44)(16, 42)(17, 54)(18, 45)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) 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 ) } Outer automorphisms :: reflexible Dual of E12.102 Graph:: bipartite v = 3 e = 36 f = 11 degree seq :: [ 18^2, 36 ] E12.109 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 9, 9, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y1^2 * Y3, Y2^2 * Y3^-2, (Y3, Y2^-1), (Y2 * Y3^-1)^2, (R * Y1)^2, (R * Y3)^2, (Y1^-1, Y2^-1), (R * Y2)^2, Y1 * Y2^-1 * Y3^-2 * Y2^-1 ] Map:: non-degenerate R = (1, 19, 2, 20, 7, 25, 10, 28, 17, 35, 11, 29, 15, 33, 4, 22, 5, 23)(3, 21, 8, 26, 14, 32, 16, 34, 6, 24, 9, 27, 18, 36, 12, 30, 13, 31)(37, 55, 39, 57, 47, 65, 45, 63, 38, 56, 44, 62, 51, 69, 54, 72, 43, 61, 50, 68, 40, 58, 48, 66, 46, 64, 52, 70, 41, 59, 49, 67, 53, 71, 42, 60) L = (1, 40)(2, 41)(3, 48)(4, 47)(5, 51)(6, 50)(7, 37)(8, 49)(9, 52)(10, 38)(11, 46)(12, 45)(13, 54)(14, 39)(15, 53)(16, 44)(17, 43)(18, 42)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) 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 ) } Outer automorphisms :: reflexible Dual of E12.103 Graph:: bipartite v = 3 e = 36 f = 11 degree seq :: [ 18^2, 36 ] E12.110 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y1^3, (R * Y3)^2, (R * Y1)^2, (Y1, Y2^-1), (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^3, Y1 * Y2^6, (Y3 * Y2^-1)^18 ] Map:: R = (1, 19, 2, 20, 4, 22)(3, 21, 6, 24, 9, 27)(5, 23, 7, 25, 10, 28)(8, 26, 12, 30, 15, 33)(11, 29, 13, 31, 16, 34)(14, 32, 17, 35, 18, 36)(37, 55, 39, 57, 44, 62, 50, 68, 52, 70, 46, 64, 40, 58, 45, 63, 51, 69, 54, 72, 49, 67, 43, 61, 38, 56, 42, 60, 48, 66, 53, 71, 47, 65, 41, 59) L = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 6, 36, 6, 36, 6, 36 ), ( 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 7 e = 36 f = 7 degree seq :: [ 6^6, 36 ] E12.111 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y1^3, (R * Y3)^2, (R * Y1)^2, (Y2, Y1^-1), (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^3, Y2^-6 * Y1, (Y3 * Y2^-1)^18 ] Map:: R = (1, 19, 2, 20, 4, 22)(3, 21, 6, 24, 9, 27)(5, 23, 7, 25, 10, 28)(8, 26, 12, 30, 15, 33)(11, 29, 13, 31, 16, 34)(14, 32, 18, 36, 17, 35)(37, 55, 39, 57, 44, 62, 50, 68, 49, 67, 43, 61, 38, 56, 42, 60, 48, 66, 54, 72, 52, 70, 46, 64, 40, 58, 45, 63, 51, 69, 53, 71, 47, 65, 41, 59) L = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 6, 36, 6, 36, 6, 36 ), ( 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 7 e = 36 f = 7 degree seq :: [ 6^6, 36 ] E12.112 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-1, Y3^-1 * Y1^-2, Y1^3, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y2^-1), (Y2^-1 * R)^2, (Y2^-1, Y1^-1), (Y3^-1 * Y1^-1)^3, Y2^6 * 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 ] Map:: non-degenerate R = (1, 19, 2, 20, 4, 22)(3, 21, 6, 24, 9, 27)(5, 23, 7, 25, 10, 28)(8, 26, 12, 30, 15, 33)(11, 29, 13, 31, 16, 34)(14, 32, 17, 35, 18, 36)(37, 55, 39, 57, 44, 62, 50, 68, 52, 70, 46, 64, 40, 58, 45, 63, 51, 69, 54, 72, 49, 67, 43, 61, 38, 56, 42, 60, 48, 66, 53, 71, 47, 65, 41, 59) L = (1, 38)(2, 40)(3, 42)(4, 37)(5, 43)(6, 45)(7, 46)(8, 48)(9, 39)(10, 41)(11, 49)(12, 51)(13, 52)(14, 53)(15, 44)(16, 47)(17, 54)(18, 50)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 6, 36, 6, 36, 6, 36 ), ( 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36 ) } Outer automorphisms :: reflexible Dual of E12.113 Graph:: bipartite v = 7 e = 36 f = 7 degree seq :: [ 6^6, 36 ] E12.113 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-1, Y1^3, (R * Y1)^2, (Y2^-1 * R)^2, (R * Y3)^2, (Y3^-1, Y2^-1), (Y2^-1, Y1^-1), (Y3^-1 * Y1^-1)^3, Y2^6 * 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 ] Map:: non-degenerate R = (1, 19, 2, 20, 4, 22)(3, 21, 6, 24, 9, 27)(5, 23, 7, 25, 10, 28)(8, 26, 12, 30, 15, 33)(11, 29, 13, 31, 16, 34)(14, 32, 18, 36, 17, 35)(37, 55, 39, 57, 44, 62, 50, 68, 49, 67, 43, 61, 38, 56, 42, 60, 48, 66, 54, 72, 52, 70, 46, 64, 40, 58, 45, 63, 51, 69, 53, 71, 47, 65, 41, 59) L = (1, 38)(2, 40)(3, 42)(4, 37)(5, 43)(6, 45)(7, 46)(8, 48)(9, 39)(10, 41)(11, 49)(12, 51)(13, 52)(14, 54)(15, 44)(16, 47)(17, 50)(18, 53)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 6, 36, 6, 36, 6, 36 ), ( 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36, 6, 36 ) } Outer automorphisms :: reflexible Dual of E12.112 Graph:: bipartite v = 7 e = 36 f = 7 degree seq :: [ 6^6, 36 ] E12.114 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^-3 * Y1, (R * Y3)^2, (R * Y1)^2, (Y3, Y2), (R * Y2)^2, Y3 * Y1 * Y3^-1 * Y1, Y3 * Y2^2 * Y3^2 ] Map:: non-degenerate R = (1, 19, 2, 20)(3, 21, 7, 25)(4, 22, 8, 26)(5, 23, 9, 27)(6, 24, 10, 28)(11, 29, 17, 35)(12, 30, 13, 31)(14, 32, 16, 34)(15, 33, 18, 36)(37, 55, 39, 57, 45, 63, 38, 56, 43, 61, 41, 59)(40, 58, 47, 65, 52, 70, 44, 62, 53, 71, 50, 68)(42, 60, 48, 66, 54, 72, 46, 64, 49, 67, 51, 69) L = (1, 40)(2, 44)(3, 47)(4, 49)(5, 50)(6, 37)(7, 53)(8, 48)(9, 52)(10, 38)(11, 51)(12, 39)(13, 43)(14, 46)(15, 41)(16, 42)(17, 54)(18, 45)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 36^4 ), ( 36^12 ) } Outer automorphisms :: reflexible Dual of E12.119 Graph:: bipartite v = 12 e = 36 f = 2 degree seq :: [ 4^9, 12^3 ] E12.115 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y3^3, Y1^2 * Y3^-1, Y2 * Y1 * Y2^2, (R * Y2)^2, (R * Y3)^2, (Y2, Y1^-1), (Y3^-1 * Y1^-1)^2, (R * Y1)^2, (Y3^-1, Y2^-1), Y2^-1 * Y1 * Y2^-1 * Y3^-1 * Y2^-1, Y3^-1 * Y2^2 * Y3^-1 * Y2 * Y1^-1, Y2^-1 * Y3^-1 * Y1^-1 * 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 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 19, 2, 20, 4, 22, 9, 27, 7, 25, 5, 23)(3, 21, 8, 26, 12, 30, 17, 35, 14, 32, 13, 31)(6, 24, 10, 28, 15, 33, 18, 36, 16, 34, 11, 29)(37, 55, 39, 57, 47, 65, 41, 59, 49, 67, 52, 70, 43, 61, 50, 68, 54, 72, 45, 63, 53, 71, 51, 69, 40, 58, 48, 66, 46, 64, 38, 56, 44, 62, 42, 60) L = (1, 40)(2, 45)(3, 48)(4, 43)(5, 38)(6, 51)(7, 37)(8, 53)(9, 41)(10, 54)(11, 46)(12, 50)(13, 44)(14, 39)(15, 52)(16, 42)(17, 49)(18, 47)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36 ), ( 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36 ) } Outer automorphisms :: reflexible Dual of E12.117 Graph:: bipartite v = 4 e = 36 f = 10 degree seq :: [ 12^3, 36 ] E12.116 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y3^3, Y1^2 * Y3^-1, Y2^3 * Y1^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y2, Y3), (Y3^-1 * Y1^-1)^2, Y1 * Y3 * Y2 * Y1 * Y3 * Y2 * Y1 * Y3 * Y2 * Y1 * Y3 * Y2 * Y1 * Y3 * Y2 * Y1 * Y3 * Y2 * Y1 * Y3 * Y2 * Y1 * Y2^-1 ] Map:: non-degenerate R = (1, 19, 2, 20, 4, 22, 9, 27, 7, 25, 5, 23)(3, 21, 8, 26, 11, 29, 17, 35, 13, 31, 12, 30)(6, 24, 10, 28, 14, 32, 18, 36, 16, 34, 15, 33)(37, 55, 39, 57, 46, 64, 38, 56, 44, 62, 50, 68, 40, 58, 47, 65, 54, 72, 45, 63, 53, 71, 52, 70, 43, 61, 49, 67, 51, 69, 41, 59, 48, 66, 42, 60) L = (1, 40)(2, 45)(3, 47)(4, 43)(5, 38)(6, 50)(7, 37)(8, 53)(9, 41)(10, 54)(11, 49)(12, 44)(13, 39)(14, 52)(15, 46)(16, 42)(17, 48)(18, 51)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36 ), ( 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36 ) } Outer automorphisms :: reflexible Dual of E12.118 Graph:: bipartite v = 4 e = 36 f = 10 degree seq :: [ 12^3, 36 ] E12.117 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ Y2^2, R^2, Y3^3, (R * Y1)^2, (R * Y2)^2, (Y3^-1, Y1^-1), (R * Y3)^2, Y2 * Y1 * Y2 * Y1^-1, Y3 * Y2 * Y3^-1 * Y2, Y1^-1 * Y2 * Y3 * Y1^-2 ] Map:: non-degenerate R = (1, 19, 2, 20, 7, 25, 11, 29, 18, 36, 16, 34, 6, 24, 10, 28, 12, 30, 3, 21, 8, 26, 14, 32, 4, 22, 9, 27, 17, 35, 13, 31, 15, 33, 5, 23)(37, 55, 39, 57)(38, 56, 44, 62)(40, 58, 47, 65)(41, 59, 48, 66)(42, 60, 49, 67)(43, 61, 50, 68)(45, 63, 54, 72)(46, 64, 51, 69)(52, 70, 53, 71) L = (1, 40)(2, 45)(3, 47)(4, 42)(5, 50)(6, 37)(7, 53)(8, 54)(9, 46)(10, 38)(11, 49)(12, 43)(13, 39)(14, 52)(15, 44)(16, 41)(17, 48)(18, 51)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) 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, 12, 36 ) } Outer automorphisms :: reflexible Dual of E12.115 Graph:: bipartite v = 10 e = 36 f = 4 degree seq :: [ 4^9, 36 ] E12.118 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ Y2^2, R^2, Y3^3, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y3^-1, Y1^-1), Y3 * Y2 * Y3^-1 * Y2, Y2 * Y1 * Y2 * Y1^-1, Y1^-1 * Y2 * Y3^-1 * Y1^-2 ] Map:: non-degenerate R = (1, 19, 2, 20, 7, 25, 13, 31, 18, 36, 14, 32, 4, 22, 9, 27, 12, 30, 3, 21, 8, 26, 16, 34, 6, 24, 10, 28, 17, 35, 11, 29, 15, 33, 5, 23)(37, 55, 39, 57)(38, 56, 44, 62)(40, 58, 47, 65)(41, 59, 48, 66)(42, 60, 49, 67)(43, 61, 52, 70)(45, 63, 51, 69)(46, 64, 54, 72)(50, 68, 53, 71) L = (1, 40)(2, 45)(3, 47)(4, 42)(5, 50)(6, 37)(7, 48)(8, 51)(9, 46)(10, 38)(11, 49)(12, 53)(13, 39)(14, 52)(15, 54)(16, 41)(17, 43)(18, 44)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) 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, 12, 36 ) } Outer automorphisms :: reflexible Dual of E12.116 Graph:: bipartite v = 10 e = 36 f = 4 degree seq :: [ 4^9, 36 ] E12.119 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 18, 18}) Quotient :: dipole Aut^+ = C18 (small group id <18, 2>) Aut = D36 (small group id <36, 4>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^2, (Y3 * Y2^-1)^2, (Y1, Y2), (R * Y3)^2, (R * Y1)^2, Y2^-2 * Y3^2, (R * Y2)^2, Y1 * Y3 * Y2^-1 * Y1 * Y2^-1, Y2^2 * Y1 * Y3 * Y2 ] Map:: non-degenerate R = (1, 19, 2, 20, 4, 22, 9, 27, 11, 29, 18, 36, 15, 33, 6, 24, 10, 28, 14, 32, 13, 31, 3, 21, 8, 26, 12, 30, 17, 35, 16, 34, 7, 25, 5, 23)(37, 55, 39, 57, 47, 65, 52, 70, 46, 64, 38, 56, 44, 62, 54, 72, 43, 61, 50, 68, 40, 58, 48, 66, 51, 69, 41, 59, 49, 67, 45, 63, 53, 71, 42, 60) L = (1, 40)(2, 45)(3, 48)(4, 47)(5, 38)(6, 50)(7, 37)(8, 53)(9, 54)(10, 49)(11, 51)(12, 52)(13, 44)(14, 39)(15, 46)(16, 41)(17, 43)(18, 42)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) 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 E12.114 Graph:: bipartite v = 2 e = 36 f = 12 degree seq :: [ 36^2 ] E12.120 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 5, 5}) Quotient :: edge^2 Aut^+ = C5 : C4 (small group id <20, 1>) Aut = C4 x D10 (small group id <40, 5>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1^-1, Y3 * Y1 * Y3 * Y1^-1, (R * Y3)^2, R * Y1 * R * Y2, Y2^4, Y1^4, Y3 * Y2 * Y3 * Y2^-1, Y3^5 ] Map:: non-degenerate R = (1, 21, 4, 24, 11, 31, 12, 32, 5, 25)(2, 22, 7, 27, 15, 35, 16, 36, 8, 28)(3, 23, 9, 29, 17, 37, 18, 38, 10, 30)(6, 26, 13, 33, 19, 39, 20, 40, 14, 34)(41, 42, 46, 43)(44, 48, 53, 50)(45, 47, 54, 49)(51, 56, 59, 58)(52, 55, 60, 57)(61, 63, 66, 62)(64, 70, 73, 68)(65, 69, 74, 67)(71, 78, 79, 76)(72, 77, 80, 75) L = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 20^4 ), ( 20^10 ) } Outer automorphisms :: reflexible Dual of E12.123 Graph:: simple bipartite v = 14 e = 40 f = 4 degree seq :: [ 4^10, 10^4 ] E12.121 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 5, 5}) Quotient :: edge^2 Aut^+ = C5 : C4 (small group id <20, 1>) Aut = C4 x D10 (small group id <40, 5>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3 * Y2, Y1 * Y2 * Y3^-1, Y2^4, Y1^2 * Y2^-2, (R * Y3)^2, R * Y2 * R * Y1, Y3^5, Y3^2 * Y1^-1 * Y3^-2 * Y2^-1 ] Map:: non-degenerate R = (1, 21, 4, 24, 13, 33, 16, 36, 7, 27)(2, 22, 6, 26, 15, 35, 18, 38, 10, 30)(3, 23, 11, 31, 19, 39, 14, 34, 5, 25)(8, 28, 9, 29, 17, 37, 20, 40, 12, 32)(41, 42, 48, 45)(43, 47, 46, 52)(44, 50, 49, 54)(51, 56, 55, 60)(53, 58, 57, 59)(61, 63, 68, 66)(62, 64, 65, 69)(67, 71, 72, 75)(70, 73, 74, 77)(76, 79, 80, 78) L = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 20^4 ), ( 20^10 ) } Outer automorphisms :: reflexible Dual of E12.124 Graph:: simple bipartite v = 14 e = 40 f = 4 degree seq :: [ 4^10, 10^4 ] E12.122 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 5, 5}) Quotient :: edge^2 Aut^+ = C5 : C4 (small group id <20, 1>) Aut = (C10 x C2) : C2 (small group id <40, 8>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y2^-1, R * Y2 * R * Y1, (R * Y3)^2, Y3^4, Y3 * Y1 * Y3^-1 * Y2^-1, Y3 * Y2 * Y3^-1 * Y1^-1, Y2^5, Y1^5 ] Map:: non-degenerate R = (1, 21, 4, 24, 12, 32, 5, 25)(2, 22, 7, 27, 15, 35, 8, 28)(3, 23, 10, 30, 18, 38, 11, 31)(6, 26, 13, 33, 19, 39, 14, 34)(9, 29, 16, 36, 20, 40, 17, 37)(41, 42, 46, 49, 43)(44, 50, 56, 53, 47)(45, 51, 57, 54, 48)(52, 55, 59, 60, 58)(61, 63, 69, 66, 62)(64, 67, 73, 76, 70)(65, 68, 74, 77, 71)(72, 78, 80, 79, 75) L = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 16^5 ), ( 16^8 ) } Outer automorphisms :: reflexible Dual of E12.125 Graph:: simple bipartite v = 13 e = 40 f = 5 degree seq :: [ 5^8, 8^5 ] E12.123 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 5, 5}) Quotient :: loop^2 Aut^+ = C5 : C4 (small group id <20, 1>) Aut = C4 x D10 (small group id <40, 5>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1^-1, Y3 * Y1 * Y3 * Y1^-1, (R * Y3)^2, R * Y1 * R * Y2, Y2^4, Y1^4, Y3 * Y2 * Y3 * Y2^-1, Y3^5 ] Map:: non-degenerate R = (1, 21, 41, 61, 4, 24, 44, 64, 11, 31, 51, 71, 12, 32, 52, 72, 5, 25, 45, 65)(2, 22, 42, 62, 7, 27, 47, 67, 15, 35, 55, 75, 16, 36, 56, 76, 8, 28, 48, 68)(3, 23, 43, 63, 9, 29, 49, 69, 17, 37, 57, 77, 18, 38, 58, 78, 10, 30, 50, 70)(6, 26, 46, 66, 13, 33, 53, 73, 19, 39, 59, 79, 20, 40, 60, 80, 14, 34, 54, 74) L = (1, 22)(2, 26)(3, 21)(4, 28)(5, 27)(6, 23)(7, 34)(8, 33)(9, 25)(10, 24)(11, 36)(12, 35)(13, 30)(14, 29)(15, 40)(16, 39)(17, 32)(18, 31)(19, 38)(20, 37)(41, 63)(42, 61)(43, 66)(44, 70)(45, 69)(46, 62)(47, 65)(48, 64)(49, 74)(50, 73)(51, 78)(52, 77)(53, 68)(54, 67)(55, 72)(56, 71)(57, 80)(58, 79)(59, 76)(60, 75) local type(s) :: { ( 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 E12.120 Transitivity :: VT+ Graph:: bipartite v = 4 e = 40 f = 14 degree seq :: [ 20^4 ] E12.124 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 5, 5}) Quotient :: loop^2 Aut^+ = C5 : C4 (small group id <20, 1>) Aut = C4 x D10 (small group id <40, 5>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3 * Y2, Y1 * Y2 * Y3^-1, Y2^4, Y1^2 * Y2^-2, (R * Y3)^2, R * Y2 * R * Y1, Y3^5, Y3^2 * Y1^-1 * Y3^-2 * Y2^-1 ] Map:: non-degenerate R = (1, 21, 41, 61, 4, 24, 44, 64, 13, 33, 53, 73, 16, 36, 56, 76, 7, 27, 47, 67)(2, 22, 42, 62, 6, 26, 46, 66, 15, 35, 55, 75, 18, 38, 58, 78, 10, 30, 50, 70)(3, 23, 43, 63, 11, 31, 51, 71, 19, 39, 59, 79, 14, 34, 54, 74, 5, 25, 45, 65)(8, 28, 48, 68, 9, 29, 49, 69, 17, 37, 57, 77, 20, 40, 60, 80, 12, 32, 52, 72) L = (1, 22)(2, 28)(3, 27)(4, 30)(5, 21)(6, 32)(7, 26)(8, 25)(9, 34)(10, 29)(11, 36)(12, 23)(13, 38)(14, 24)(15, 40)(16, 35)(17, 39)(18, 37)(19, 33)(20, 31)(41, 63)(42, 64)(43, 68)(44, 65)(45, 69)(46, 61)(47, 71)(48, 66)(49, 62)(50, 73)(51, 72)(52, 75)(53, 74)(54, 77)(55, 67)(56, 79)(57, 70)(58, 76)(59, 80)(60, 78) local type(s) :: { ( 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 E12.121 Transitivity :: VT+ Graph:: bipartite v = 4 e = 40 f = 14 degree seq :: [ 20^4 ] E12.125 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 5, 5}) Quotient :: loop^2 Aut^+ = C5 : C4 (small group id <20, 1>) Aut = (C10 x C2) : C2 (small group id <40, 8>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y2^-1, R * Y2 * R * Y1, (R * Y3)^2, Y3^4, Y3 * Y1 * Y3^-1 * Y2^-1, Y3 * Y2 * Y3^-1 * Y1^-1, Y2^5, Y1^5 ] Map:: non-degenerate R = (1, 21, 41, 61, 4, 24, 44, 64, 12, 32, 52, 72, 5, 25, 45, 65)(2, 22, 42, 62, 7, 27, 47, 67, 15, 35, 55, 75, 8, 28, 48, 68)(3, 23, 43, 63, 10, 30, 50, 70, 18, 38, 58, 78, 11, 31, 51, 71)(6, 26, 46, 66, 13, 33, 53, 73, 19, 39, 59, 79, 14, 34, 54, 74)(9, 29, 49, 69, 16, 36, 56, 76, 20, 40, 60, 80, 17, 37, 57, 77) L = (1, 22)(2, 26)(3, 21)(4, 30)(5, 31)(6, 29)(7, 24)(8, 25)(9, 23)(10, 36)(11, 37)(12, 35)(13, 27)(14, 28)(15, 39)(16, 33)(17, 34)(18, 32)(19, 40)(20, 38)(41, 63)(42, 61)(43, 69)(44, 67)(45, 68)(46, 62)(47, 73)(48, 74)(49, 66)(50, 64)(51, 65)(52, 78)(53, 76)(54, 77)(55, 72)(56, 70)(57, 71)(58, 80)(59, 75)(60, 79) local type(s) :: { ( 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8 ) } Outer automorphisms :: reflexible Dual of E12.122 Transitivity :: VT+ Graph:: v = 5 e = 40 f = 13 degree seq :: [ 16^5 ] E12.126 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 5, 5}) Quotient :: dipole Aut^+ = C5 : C4 (small group id <20, 1>) Aut = (C10 x C2) : C2 (small group id <40, 8>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y2^-1 * Y1 * Y2^-1, Y1^4, Y2^5, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^4, (Y3 * Y2^-1)^5 ] Map:: R = (1, 21, 2, 22, 6, 26, 4, 24)(3, 23, 8, 28, 13, 33, 10, 30)(5, 25, 7, 27, 14, 34, 11, 31)(9, 29, 16, 36, 19, 39, 17, 37)(12, 32, 15, 35, 20, 40, 18, 38)(41, 61, 43, 63, 49, 69, 52, 72, 45, 65)(42, 62, 47, 67, 55, 75, 56, 76, 48, 68)(44, 64, 51, 71, 58, 78, 57, 77, 50, 70)(46, 66, 53, 73, 59, 79, 60, 80, 54, 74) L = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 8, 10, 8, 10, 8, 10, 8, 10 ), ( 8, 10, 8, 10, 8, 10, 8, 10, 8, 10 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 9 e = 40 f = 9 degree seq :: [ 8^5, 10^4 ] E12.127 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 5, 5}) Quotient :: dipole Aut^+ = C5 : C4 (small group id <20, 1>) Aut = (C10 x C2) : C2 (small group id <40, 8>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3, (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y3 * Y1 * Y2^-1, Y1^4, Y2 * Y1 * Y3^-1 * Y1^-1, Y2^5, (Y1^-1 * Y2^-1)^4, (Y3 * Y2^-1)^5 ] Map:: non-degenerate R = (1, 21, 2, 22, 6, 26, 5, 25)(3, 23, 8, 28, 13, 33, 10, 30)(4, 24, 7, 27, 14, 34, 12, 32)(9, 29, 16, 36, 19, 39, 17, 37)(11, 31, 15, 35, 20, 40, 18, 38)(41, 61, 43, 63, 49, 69, 51, 71, 44, 64)(42, 62, 47, 67, 55, 75, 56, 76, 48, 68)(45, 65, 52, 72, 58, 78, 57, 77, 50, 70)(46, 66, 53, 73, 59, 79, 60, 80, 54, 74) L = (1, 44)(2, 48)(3, 41)(4, 51)(5, 50)(6, 54)(7, 42)(8, 56)(9, 43)(10, 57)(11, 49)(12, 45)(13, 46)(14, 60)(15, 47)(16, 55)(17, 58)(18, 52)(19, 53)(20, 59)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 8, 10, 8, 10, 8, 10, 8, 10 ), ( 8, 10, 8, 10, 8, 10, 8, 10, 8, 10 ) } Outer automorphisms :: reflexible Dual of E12.129 Graph:: bipartite v = 9 e = 40 f = 9 degree seq :: [ 8^5, 10^4 ] E12.128 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 5, 5}) Quotient :: dipole Aut^+ = C5 : C4 (small group id <20, 1>) Aut = (C10 x C2) : C2 (small group id <40, 8>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2 * Y3, Y2^2 * Y3^-1, (R * Y3)^2, (R * Y1)^2, Y3 * Y1^-1 * Y3 * Y1, Y2 * Y1^-1 * Y2 * Y1, (R * Y2)^2, Y1^4 ] Map:: non-degenerate R = (1, 21, 2, 22, 8, 28, 5, 25)(3, 23, 11, 31, 17, 37, 13, 33)(4, 24, 12, 32, 18, 38, 14, 34)(6, 26, 9, 29, 19, 39, 15, 35)(7, 27, 10, 30, 20, 40, 16, 36)(41, 61, 43, 63, 44, 64, 47, 67, 46, 66)(42, 62, 49, 69, 50, 70, 52, 72, 51, 71)(45, 65, 55, 75, 56, 76, 54, 74, 53, 73)(48, 68, 57, 77, 58, 78, 60, 80, 59, 79) L = (1, 44)(2, 50)(3, 47)(4, 46)(5, 56)(6, 43)(7, 41)(8, 58)(9, 52)(10, 51)(11, 49)(12, 42)(13, 55)(14, 45)(15, 54)(16, 53)(17, 60)(18, 59)(19, 57)(20, 48)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 8, 10, 8, 10, 8, 10, 8, 10 ), ( 8, 10, 8, 10, 8, 10, 8, 10, 8, 10 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 9 e = 40 f = 9 degree seq :: [ 8^5, 10^4 ] E12.129 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 5, 5}) Quotient :: dipole Aut^+ = C5 : C4 (small group id <20, 1>) Aut = (C10 x C2) : C2 (small group id <40, 8>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^2, Y2 * Y3^-2, (R * Y3)^2, (R * Y1)^2, Y3 * Y1^-1 * Y3 * Y1, Y2 * Y1^-1 * Y2 * Y1, (R * Y2)^2, Y1^4 ] Map:: non-degenerate R = (1, 21, 2, 22, 8, 28, 5, 25)(3, 23, 11, 31, 17, 37, 13, 33)(4, 24, 12, 32, 18, 38, 14, 34)(6, 26, 9, 29, 19, 39, 15, 35)(7, 27, 10, 30, 20, 40, 16, 36)(41, 61, 43, 63, 47, 67, 44, 64, 46, 66)(42, 62, 49, 69, 52, 72, 50, 70, 51, 71)(45, 65, 55, 75, 54, 74, 56, 76, 53, 73)(48, 68, 57, 77, 60, 80, 58, 78, 59, 79) L = (1, 44)(2, 50)(3, 46)(4, 43)(5, 56)(6, 47)(7, 41)(8, 58)(9, 51)(10, 49)(11, 52)(12, 42)(13, 54)(14, 45)(15, 53)(16, 55)(17, 59)(18, 57)(19, 60)(20, 48)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 8, 10, 8, 10, 8, 10, 8, 10 ), ( 8, 10, 8, 10, 8, 10, 8, 10, 8, 10 ) } Outer automorphisms :: reflexible Dual of E12.127 Graph:: bipartite v = 9 e = 40 f = 9 degree seq :: [ 8^5, 10^4 ] E12.130 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 5, 5}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (R * Y3)^2, (R * Y1)^2, Y1^4, (Y2^-1, Y1^-1), Y2^5, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^4, (Y3 * Y2^-1)^5 ] Map:: R = (1, 21, 2, 22, 6, 26, 4, 24)(3, 23, 7, 27, 13, 33, 10, 30)(5, 25, 8, 28, 14, 34, 11, 31)(9, 29, 15, 35, 19, 39, 17, 37)(12, 32, 16, 36, 20, 40, 18, 38)(41, 61, 43, 63, 49, 69, 52, 72, 45, 65)(42, 62, 47, 67, 55, 75, 56, 76, 48, 68)(44, 64, 50, 70, 57, 77, 58, 78, 51, 71)(46, 66, 53, 73, 59, 79, 60, 80, 54, 74) L = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 8, 10, 8, 10, 8, 10, 8, 10 ), ( 8, 10, 8, 10, 8, 10, 8, 10, 8, 10 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 9 e = 40 f = 9 degree seq :: [ 8^5, 10^4 ] E12.131 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 5, 5}) Quotient :: edge^2 Aut^+ = C5 : C4 (small group id <20, 3>) Aut = C2 x (C5 : C4) (small group id <40, 12>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2, (R * Y3)^2, Y2^4, R * Y1 * R * Y2, Y1^4, Y1 * Y3 * Y2 * Y3^2, Y3^5, Y1 * Y3^-1 * Y2 * Y3^-2, Y1 * Y3^2 * Y1^-1 * Y3^-1, Y2 * Y3^-1 * Y2 * Y1^-1 * Y3^-1 * Y1^-1, Y2 * Y3 * Y2 * Y1^-1 * Y3 * Y1^-1 ] Map:: non-degenerate R = (1, 21, 4, 24, 13, 33, 16, 36, 5, 25)(2, 22, 7, 27, 11, 31, 14, 34, 8, 28)(3, 23, 9, 29, 15, 35, 12, 32, 10, 30)(6, 26, 17, 37, 19, 39, 20, 40, 18, 38)(41, 42, 46, 43)(44, 51, 58, 52)(45, 54, 57, 55)(47, 59, 50, 56)(48, 60, 49, 53)(61, 63, 66, 62)(64, 72, 78, 71)(65, 75, 77, 74)(67, 76, 70, 79)(68, 73, 69, 80) L = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 20^4 ), ( 20^10 ) } Outer automorphisms :: reflexible Dual of E12.138 Graph:: simple bipartite v = 14 e = 40 f = 4 degree seq :: [ 4^10, 10^4 ] E12.132 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 5, 5}) Quotient :: edge^2 Aut^+ = C5 : C4 (small group id <20, 3>) Aut = C2 x (C5 : C4) (small group id <40, 12>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y2^-1 * Y3, Y1^-1 * Y3^-2 * Y2^-1, Y2^-1 * Y3^-1 * Y1^-1 * Y3, (Y2^-1 * Y1)^2, (Y2^-1 * Y1)^2, Y1 * Y3 * Y2 * Y3^-1, R * Y2 * R * Y1, (R * Y3)^2, (Y2 * Y1^-1)^2, Y1 * Y2 * Y3^2, Y2^4, Y1^4 ] Map:: non-degenerate R = (1, 21, 4, 24, 17, 37, 9, 29, 7, 27)(2, 22, 10, 30, 15, 35, 19, 39, 6, 26)(3, 23, 13, 33, 5, 25, 16, 36, 14, 34)(8, 28, 20, 40, 12, 32, 18, 38, 11, 31)(41, 42, 48, 45)(43, 44, 55, 51)(46, 58, 56, 57)(47, 59, 60, 54)(49, 50, 52, 53)(61, 63, 72, 66)(62, 69, 74, 71)(64, 76, 80, 70)(65, 78, 75, 67)(68, 79, 77, 73) L = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 20^4 ), ( 20^10 ) } Outer automorphisms :: reflexible Dual of E12.137 Graph:: simple bipartite v = 14 e = 40 f = 4 degree seq :: [ 4^10, 10^4 ] E12.133 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 5, 5}) Quotient :: edge^2 Aut^+ = C5 : C4 (small group id <20, 3>) Aut = C2 x (C5 : C4) (small group id <40, 12>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2 * Y3^-1, Y3^-2 * Y2 * Y1, Y2 * Y3 * Y1 * Y3, Y1^-1 * Y3^-1 * Y2^-1 * Y3^-1, Y3^-1 * Y2 * Y1 * Y3^-1, R * Y2 * R * Y1, (R * Y3)^2, Y3^2 * Y1^-1 * Y2^-1, Y1^4, (Y1 * Y2^-1)^2, Y1^-1 * Y3^-1 * Y2^-1 * Y3^-1, Y2^4 ] Map:: non-degenerate R = (1, 21, 4, 24, 12, 32, 19, 39, 7, 27)(2, 22, 9, 29, 15, 35, 6, 26, 11, 31)(3, 23, 14, 34, 17, 37, 16, 36, 5, 25)(8, 28, 18, 38, 20, 40, 10, 30, 13, 33)(41, 42, 48, 45)(43, 52, 51, 50)(44, 55, 53, 57)(46, 58, 54, 47)(49, 60, 56, 59)(61, 63, 73, 66)(62, 64, 76, 70)(65, 78, 71, 79)(67, 77, 68, 69)(72, 74, 80, 75) L = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 20^4 ), ( 20^10 ) } Outer automorphisms :: reflexible Dual of E12.136 Graph:: simple bipartite v = 14 e = 40 f = 4 degree seq :: [ 4^10, 10^4 ] E12.134 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 5, 5}) Quotient :: edge^2 Aut^+ = C5 : C4 (small group id <20, 3>) Aut = C2 x (C5 : C4) (small group id <40, 12>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1 * Y3, (Y1^-1 * Y2)^2, Y1 * Y3^-1 * Y2 * Y3, (Y2^-1 * Y1)^2, Y3 * Y1^-1 * Y3^-1 * Y2^-1, Y1^-1 * Y3^2 * Y2^-1, Y3^-1 * Y1 * Y2 * Y3^-1, R * Y2 * R * Y1, (R * Y3)^2, Y2^4, Y1^4, Y3 * Y1^-1 * Y3^-1 * Y2^-1, (Y2 * Y1^-1)^2, Y1^-1 * Y3^2 * Y2^-1 ] Map:: non-degenerate R = (1, 21, 4, 24, 9, 29, 19, 39, 7, 27)(2, 22, 6, 26, 15, 35, 16, 36, 11, 31)(3, 23, 13, 33, 18, 38, 5, 25, 14, 34)(8, 28, 10, 30, 17, 37, 12, 32, 20, 40)(41, 42, 48, 45)(43, 47, 56, 50)(44, 55, 60, 53)(46, 57, 58, 59)(49, 51, 52, 54)(61, 63, 72, 66)(62, 69, 73, 70)(64, 65, 77, 76)(67, 78, 80, 71)(68, 75, 79, 74) L = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 20^4 ), ( 20^10 ) } Outer automorphisms :: reflexible Dual of E12.135 Graph:: simple bipartite v = 14 e = 40 f = 4 degree seq :: [ 4^10, 10^4 ] E12.135 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 5, 5}) Quotient :: loop^2 Aut^+ = C5 : C4 (small group id <20, 3>) Aut = C2 x (C5 : C4) (small group id <40, 12>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2, (R * Y3)^2, Y2^4, R * Y1 * R * Y2, Y1^4, Y1 * Y3 * Y2 * Y3^2, Y3^5, Y1 * Y3^-1 * Y2 * Y3^-2, Y1 * Y3^2 * Y1^-1 * Y3^-1, Y2 * Y3^-1 * Y2 * Y1^-1 * Y3^-1 * Y1^-1, Y2 * Y3 * Y2 * Y1^-1 * Y3 * Y1^-1 ] Map:: non-degenerate R = (1, 21, 41, 61, 4, 24, 44, 64, 13, 33, 53, 73, 16, 36, 56, 76, 5, 25, 45, 65)(2, 22, 42, 62, 7, 27, 47, 67, 11, 31, 51, 71, 14, 34, 54, 74, 8, 28, 48, 68)(3, 23, 43, 63, 9, 29, 49, 69, 15, 35, 55, 75, 12, 32, 52, 72, 10, 30, 50, 70)(6, 26, 46, 66, 17, 37, 57, 77, 19, 39, 59, 79, 20, 40, 60, 80, 18, 38, 58, 78) L = (1, 22)(2, 26)(3, 21)(4, 31)(5, 34)(6, 23)(7, 39)(8, 40)(9, 33)(10, 36)(11, 38)(12, 24)(13, 28)(14, 37)(15, 25)(16, 27)(17, 35)(18, 32)(19, 30)(20, 29)(41, 63)(42, 61)(43, 66)(44, 72)(45, 75)(46, 62)(47, 76)(48, 73)(49, 80)(50, 79)(51, 64)(52, 78)(53, 69)(54, 65)(55, 77)(56, 70)(57, 74)(58, 71)(59, 67)(60, 68) local type(s) :: { ( 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 E12.134 Transitivity :: VT+ Graph:: bipartite v = 4 e = 40 f = 14 degree seq :: [ 20^4 ] E12.136 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 5, 5}) Quotient :: loop^2 Aut^+ = C5 : C4 (small group id <20, 3>) Aut = C2 x (C5 : C4) (small group id <40, 12>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y2^-1 * Y3, Y1^-1 * Y3^-2 * Y2^-1, Y2^-1 * Y3^-1 * Y1^-1 * Y3, (Y2^-1 * Y1)^2, (Y2^-1 * Y1)^2, Y1 * Y3 * Y2 * Y3^-1, R * Y2 * R * Y1, (R * Y3)^2, (Y2 * Y1^-1)^2, Y1 * Y2 * Y3^2, Y2^4, Y1^4 ] Map:: non-degenerate R = (1, 21, 41, 61, 4, 24, 44, 64, 17, 37, 57, 77, 9, 29, 49, 69, 7, 27, 47, 67)(2, 22, 42, 62, 10, 30, 50, 70, 15, 35, 55, 75, 19, 39, 59, 79, 6, 26, 46, 66)(3, 23, 43, 63, 13, 33, 53, 73, 5, 25, 45, 65, 16, 36, 56, 76, 14, 34, 54, 74)(8, 28, 48, 68, 20, 40, 60, 80, 12, 32, 52, 72, 18, 38, 58, 78, 11, 31, 51, 71) L = (1, 22)(2, 28)(3, 24)(4, 35)(5, 21)(6, 38)(7, 39)(8, 25)(9, 30)(10, 32)(11, 23)(12, 33)(13, 29)(14, 27)(15, 31)(16, 37)(17, 26)(18, 36)(19, 40)(20, 34)(41, 63)(42, 69)(43, 72)(44, 76)(45, 78)(46, 61)(47, 65)(48, 79)(49, 74)(50, 64)(51, 62)(52, 66)(53, 68)(54, 71)(55, 67)(56, 80)(57, 73)(58, 75)(59, 77)(60, 70) local type(s) :: { ( 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 E12.133 Transitivity :: VT+ Graph:: bipartite v = 4 e = 40 f = 14 degree seq :: [ 20^4 ] E12.137 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 5, 5}) Quotient :: loop^2 Aut^+ = C5 : C4 (small group id <20, 3>) Aut = C2 x (C5 : C4) (small group id <40, 12>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2 * Y3^-1, Y3^-2 * Y2 * Y1, Y2 * Y3 * Y1 * Y3, Y1^-1 * Y3^-1 * Y2^-1 * Y3^-1, Y3^-1 * Y2 * Y1 * Y3^-1, R * Y2 * R * Y1, (R * Y3)^2, Y3^2 * Y1^-1 * Y2^-1, Y1^4, (Y1 * Y2^-1)^2, Y1^-1 * Y3^-1 * Y2^-1 * Y3^-1, Y2^4 ] Map:: non-degenerate R = (1, 21, 41, 61, 4, 24, 44, 64, 12, 32, 52, 72, 19, 39, 59, 79, 7, 27, 47, 67)(2, 22, 42, 62, 9, 29, 49, 69, 15, 35, 55, 75, 6, 26, 46, 66, 11, 31, 51, 71)(3, 23, 43, 63, 14, 34, 54, 74, 17, 37, 57, 77, 16, 36, 56, 76, 5, 25, 45, 65)(8, 28, 48, 68, 18, 38, 58, 78, 20, 40, 60, 80, 10, 30, 50, 70, 13, 33, 53, 73) L = (1, 22)(2, 28)(3, 32)(4, 35)(5, 21)(6, 38)(7, 26)(8, 25)(9, 40)(10, 23)(11, 30)(12, 31)(13, 37)(14, 27)(15, 33)(16, 39)(17, 24)(18, 34)(19, 29)(20, 36)(41, 63)(42, 64)(43, 73)(44, 76)(45, 78)(46, 61)(47, 77)(48, 69)(49, 67)(50, 62)(51, 79)(52, 74)(53, 66)(54, 80)(55, 72)(56, 70)(57, 68)(58, 71)(59, 65)(60, 75) local type(s) :: { ( 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 E12.132 Transitivity :: VT+ Graph:: bipartite v = 4 e = 40 f = 14 degree seq :: [ 20^4 ] E12.138 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 5, 5}) Quotient :: loop^2 Aut^+ = C5 : C4 (small group id <20, 3>) Aut = C2 x (C5 : C4) (small group id <40, 12>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1 * Y3, (Y1^-1 * Y2)^2, Y1 * Y3^-1 * Y2 * Y3, (Y2^-1 * Y1)^2, Y3 * Y1^-1 * Y3^-1 * Y2^-1, Y1^-1 * Y3^2 * Y2^-1, Y3^-1 * Y1 * Y2 * Y3^-1, R * Y2 * R * Y1, (R * Y3)^2, Y2^4, Y1^4, Y3 * Y1^-1 * Y3^-1 * Y2^-1, (Y2 * Y1^-1)^2, Y1^-1 * Y3^2 * Y2^-1 ] Map:: non-degenerate R = (1, 21, 41, 61, 4, 24, 44, 64, 9, 29, 49, 69, 19, 39, 59, 79, 7, 27, 47, 67)(2, 22, 42, 62, 6, 26, 46, 66, 15, 35, 55, 75, 16, 36, 56, 76, 11, 31, 51, 71)(3, 23, 43, 63, 13, 33, 53, 73, 18, 38, 58, 78, 5, 25, 45, 65, 14, 34, 54, 74)(8, 28, 48, 68, 10, 30, 50, 70, 17, 37, 57, 77, 12, 32, 52, 72, 20, 40, 60, 80) L = (1, 22)(2, 28)(3, 27)(4, 35)(5, 21)(6, 37)(7, 36)(8, 25)(9, 31)(10, 23)(11, 32)(12, 34)(13, 24)(14, 29)(15, 40)(16, 30)(17, 38)(18, 39)(19, 26)(20, 33)(41, 63)(42, 69)(43, 72)(44, 65)(45, 77)(46, 61)(47, 78)(48, 75)(49, 73)(50, 62)(51, 67)(52, 66)(53, 70)(54, 68)(55, 79)(56, 64)(57, 76)(58, 80)(59, 74)(60, 71) local type(s) :: { ( 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 E12.131 Transitivity :: VT+ Graph:: bipartite v = 4 e = 40 f = 14 degree seq :: [ 20^4 ] E12.139 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 5, 10, 10}) Quotient :: dipole Aut^+ = C10 x C2 (small group id <20, 5>) Aut = C2 x C2 x D10 (small group id <40, 13>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y3 * Y2)^2, Y3^-2 * Y2^-2, (R * Y3)^2, (R * Y1)^2, (Y2^-1 * R)^2, Y2^-1 * Y1 * Y2 * Y1, Y3 * Y1 * Y3^-1 * Y1, Y3^-2 * Y2^3 ] Map:: non-degenerate R = (1, 21, 2, 22)(3, 23, 7, 27)(4, 24, 8, 28)(5, 25, 9, 29)(6, 26, 10, 30)(11, 31, 16, 36)(12, 32, 17, 37)(13, 33, 18, 38)(14, 34, 19, 39)(15, 35, 20, 40)(41, 61, 43, 63, 51, 71, 54, 74, 45, 65)(42, 62, 47, 67, 56, 76, 59, 79, 49, 69)(44, 64, 52, 72, 46, 66, 53, 73, 55, 75)(48, 68, 57, 77, 50, 70, 58, 78, 60, 80) L = (1, 44)(2, 48)(3, 52)(4, 54)(5, 55)(6, 41)(7, 57)(8, 59)(9, 60)(10, 42)(11, 46)(12, 45)(13, 43)(14, 53)(15, 51)(16, 50)(17, 49)(18, 47)(19, 58)(20, 56)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 20^4 ), ( 20^10 ) } Outer automorphisms :: reflexible Dual of E12.146 Graph:: simple bipartite v = 14 e = 40 f = 4 degree seq :: [ 4^10, 10^4 ] E12.140 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 5, 10, 10}) Quotient :: dipole Aut^+ = C10 x C2 (small group id <20, 5>) Aut = C2 x C2 x D10 (small group id <40, 13>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y3^-2 * Y2^-1, (Y1^-1 * Y3^-1)^2, (Y2^-1 * Y1)^2, (Y2^-1 * R)^2, (Y3, Y2^-1), (R * Y1)^2, (R * Y3)^2, (Y1, Y3^-1), Y2^2 * Y1^-2, Y1 * Y3^-1 * Y2^2 * Y3^-1, Y2^2 * Y1^3 ] Map:: non-degenerate R = (1, 21, 2, 22, 8, 28, 15, 35, 5, 25)(3, 23, 9, 29, 18, 38, 6, 26, 11, 31)(4, 24, 10, 30, 7, 27, 12, 32, 16, 36)(13, 33, 19, 39, 14, 34, 17, 37, 20, 40)(41, 61, 43, 63, 48, 68, 58, 78, 45, 65, 51, 71, 42, 62, 49, 69, 55, 75, 46, 66)(44, 64, 53, 73, 47, 67, 54, 74, 56, 76, 60, 80, 50, 70, 59, 79, 52, 72, 57, 77) L = (1, 44)(2, 50)(3, 53)(4, 55)(5, 56)(6, 57)(7, 41)(8, 47)(9, 59)(10, 45)(11, 60)(12, 42)(13, 46)(14, 43)(15, 52)(16, 48)(17, 49)(18, 54)(19, 51)(20, 58)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) 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 ) } Outer automorphisms :: reflexible Dual of E12.144 Graph:: bipartite v = 6 e = 40 f = 12 degree seq :: [ 10^4, 20^2 ] E12.141 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 5, 10, 10}) Quotient :: dipole Aut^+ = C10 x C2 (small group id <20, 5>) Aut = C2 x C2 x D10 (small group id <40, 13>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2^-2, (Y3, Y2), Y3^-2 * Y1^-2, (Y3^-1, Y1), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y1^-1 * Y3^4, Y1^5, (Y2^-1 * Y3)^10 ] Map:: non-degenerate R = (1, 21, 2, 22, 8, 28, 14, 34, 5, 25)(3, 23, 9, 29, 19, 39, 17, 37, 6, 26)(4, 24, 10, 30, 7, 27, 11, 31, 15, 35)(12, 32, 18, 38, 13, 33, 20, 40, 16, 36)(41, 61, 43, 63, 42, 62, 49, 69, 48, 68, 59, 79, 54, 74, 57, 77, 45, 65, 46, 66)(44, 64, 52, 72, 50, 70, 58, 78, 47, 67, 53, 73, 51, 71, 60, 80, 55, 75, 56, 76) L = (1, 44)(2, 50)(3, 52)(4, 54)(5, 55)(6, 56)(7, 41)(8, 47)(9, 58)(10, 45)(11, 42)(12, 57)(13, 43)(14, 51)(15, 48)(16, 59)(17, 60)(18, 46)(19, 53)(20, 49)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) 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 ) } Outer automorphisms :: reflexible Dual of E12.143 Graph:: bipartite v = 6 e = 40 f = 12 degree seq :: [ 10^4, 20^2 ] E12.142 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 5, 10, 10}) Quotient :: dipole Aut^+ = C10 x C2 (small group id <20, 5>) Aut = C2 x C2 x D10 (small group id <40, 13>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2^2, Y1^2 * Y3^2, (R * Y3)^2, (Y1^-1, Y3^-1), (R * Y2)^2, (Y3, Y2^-1), (R * Y1)^2, Y1 * Y3^-4, Y1^5, Y1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 21, 2, 22, 8, 28, 15, 35, 5, 25)(3, 23, 6, 26, 10, 30, 19, 39, 13, 33)(4, 24, 9, 29, 7, 27, 11, 31, 16, 36)(12, 32, 17, 37, 14, 34, 18, 38, 20, 40)(41, 61, 43, 63, 45, 65, 53, 73, 55, 75, 59, 79, 48, 68, 50, 70, 42, 62, 46, 66)(44, 64, 52, 72, 56, 76, 60, 80, 51, 71, 58, 78, 47, 67, 54, 74, 49, 69, 57, 77) L = (1, 44)(2, 49)(3, 52)(4, 55)(5, 56)(6, 57)(7, 41)(8, 47)(9, 45)(10, 54)(11, 42)(12, 59)(13, 60)(14, 43)(15, 51)(16, 48)(17, 53)(18, 46)(19, 58)(20, 50)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) 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 ) } Outer automorphisms :: reflexible Dual of E12.145 Graph:: bipartite v = 6 e = 40 f = 12 degree seq :: [ 10^4, 20^2 ] E12.143 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 5, 10, 10}) Quotient :: dipole Aut^+ = C10 x C2 (small group id <20, 5>) Aut = C2 x C2 x D10 (small group id <40, 13>) |r| :: 2 Presentation :: [ Y2^2, R^2, (Y3, Y1^-1), Y1^-2 * Y3^2, (R * Y1)^2, (R * Y3)^2, Y2 * Y1 * Y2 * Y1^-1, Y3 * Y2 * Y3^-1 * Y2, (R * Y2)^2, Y3^-2 * Y2 * Y3^-1 * Y1^-2, Y1^2 * Y3^3 * 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 * Y2 ] Map:: non-degenerate R = (1, 21, 2, 22, 7, 27, 16, 36, 13, 33, 20, 40, 11, 31, 19, 39, 14, 34, 5, 25)(3, 23, 8, 28, 17, 37, 15, 35, 6, 26, 10, 30, 4, 24, 9, 29, 18, 38, 12, 32)(41, 61, 43, 63)(42, 62, 48, 68)(44, 64, 51, 71)(45, 65, 52, 72)(46, 66, 53, 73)(47, 67, 57, 77)(49, 69, 59, 79)(50, 70, 60, 80)(54, 74, 58, 78)(55, 75, 56, 76) L = (1, 44)(2, 49)(3, 51)(4, 47)(5, 50)(6, 41)(7, 58)(8, 59)(9, 56)(10, 42)(11, 57)(12, 60)(13, 43)(14, 46)(15, 45)(16, 52)(17, 54)(18, 53)(19, 55)(20, 48)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 10, 20, 10, 20 ), ( 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20 ) } Outer automorphisms :: reflexible Dual of E12.141 Graph:: bipartite v = 12 e = 40 f = 6 degree seq :: [ 4^10, 20^2 ] E12.144 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 5, 10, 10}) Quotient :: dipole Aut^+ = C10 x C2 (small group id <20, 5>) Aut = C2 x C2 x D10 (small group id <40, 13>) |r| :: 2 Presentation :: [ Y2^2, R^2, Y3 * Y1^-1 * Y2 * Y1^-1, (Y3^-1, Y1^-1), Y1^-2 * Y3 * Y2, Y1^-1 * Y2 * Y3 * Y1^-1, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y3^4 * Y1^2, (Y1^-1 * Y3^-1)^10 ] Map:: non-degenerate R = (1, 21, 2, 22, 7, 27, 15, 35, 12, 32, 17, 37, 14, 34, 18, 38, 11, 31, 5, 25)(3, 23, 8, 28, 4, 24, 9, 29, 16, 36, 20, 40, 19, 39, 13, 33, 6, 26, 10, 30)(41, 61, 43, 63)(42, 62, 48, 68)(44, 64, 47, 67)(45, 65, 50, 70)(46, 66, 51, 71)(49, 69, 55, 75)(52, 72, 56, 76)(53, 73, 58, 78)(54, 74, 59, 79)(57, 77, 60, 80) L = (1, 44)(2, 49)(3, 47)(4, 52)(5, 48)(6, 41)(7, 56)(8, 55)(9, 57)(10, 42)(11, 43)(12, 59)(13, 45)(14, 46)(15, 60)(16, 54)(17, 53)(18, 50)(19, 51)(20, 58)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 10, 20, 10, 20 ), ( 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20 ) } Outer automorphisms :: reflexible Dual of E12.140 Graph:: bipartite v = 12 e = 40 f = 6 degree seq :: [ 4^10, 20^2 ] E12.145 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 5, 10, 10}) Quotient :: dipole Aut^+ = C10 x C2 (small group id <20, 5>) Aut = C2 x C2 x D10 (small group id <40, 13>) |r| :: 2 Presentation :: [ Y2^2, R^2, Y3 * Y2 * Y3^-1 * Y2, Y1^-2 * Y3^-1 * Y2, Y2 * Y1^-1 * Y3^-1 * Y1^-1, (R * Y2)^2, Y1^-2 * Y2 * Y3^-1, (R * Y3)^2, (R * Y1)^2, Y3^2 * Y1 * Y3^-2 * Y1^-1, (Y3^2 * Y1^-1)^2, Y3^-1 * Y1^6 * Y3^-1 ] Map:: non-degenerate R = (1, 21, 2, 22, 7, 27, 15, 35, 14, 34, 18, 38, 12, 32, 17, 37, 11, 31, 5, 25)(3, 23, 8, 28, 6, 26, 10, 30, 16, 36, 20, 40, 19, 39, 13, 33, 4, 24, 9, 29)(41, 61, 43, 63)(42, 62, 48, 68)(44, 64, 51, 71)(45, 65, 49, 69)(46, 66, 47, 67)(50, 70, 55, 75)(52, 72, 59, 79)(53, 73, 57, 77)(54, 74, 56, 76)(58, 78, 60, 80) L = (1, 44)(2, 49)(3, 51)(4, 52)(5, 53)(6, 41)(7, 43)(8, 45)(9, 57)(10, 42)(11, 59)(12, 56)(13, 58)(14, 46)(15, 48)(16, 47)(17, 60)(18, 50)(19, 54)(20, 55)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 10, 20, 10, 20 ), ( 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20 ) } Outer automorphisms :: reflexible Dual of E12.142 Graph:: bipartite v = 12 e = 40 f = 6 degree seq :: [ 4^10, 20^2 ] E12.146 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 5, 10, 10}) Quotient :: dipole Aut^+ = C10 x C2 (small group id <20, 5>) Aut = C2 x C2 x D10 (small group id <40, 13>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1^-1 * Y2 * Y3, Y3 * Y2^2 * Y1^-1, Y3^3 * Y1^-1, (Y3, Y2^-1), Y1^-2 * Y3^-1 * Y1^-1, (R * Y1)^2, Y3^-1 * Y2^2 * Y3^-1, (Y2^-1, Y1^-1), (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^-1 * Y3 * Y1^-1 * Y2^-1 * Y1^-2 ] Map:: non-degenerate R = (1, 21, 2, 22, 8, 28, 7, 27, 12, 32, 19, 39, 15, 35, 4, 24, 10, 30, 5, 25)(3, 23, 9, 29, 17, 37, 14, 34, 20, 40, 16, 36, 6, 26, 11, 31, 18, 38, 13, 33)(41, 61, 43, 63, 52, 72, 60, 80, 50, 70, 58, 78, 48, 68, 57, 77, 55, 75, 46, 66)(42, 62, 49, 69, 59, 79, 56, 76, 45, 65, 53, 73, 47, 67, 54, 74, 44, 64, 51, 71) L = (1, 44)(2, 50)(3, 51)(4, 52)(5, 55)(6, 54)(7, 41)(8, 45)(9, 58)(10, 59)(11, 60)(12, 42)(13, 46)(14, 43)(15, 47)(16, 57)(17, 53)(18, 56)(19, 48)(20, 49)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 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 E12.139 Graph:: bipartite v = 4 e = 40 f = 14 degree seq :: [ 20^4 ] E12.147 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y1 * Y2^-2, (Y2^-1, Y3), (R * Y1)^2, Y3^-1 * Y1 * Y3 * Y1, (Y3, Y2^-1), (R * Y3)^2, (R * Y2)^2, Y3^-5 * Y2^-1, (Y2^-1 * Y3)^10 ] Map:: non-degenerate R = (1, 21, 2, 22)(3, 23, 5, 25)(4, 24, 7, 27)(6, 26, 8, 28)(9, 29, 12, 32)(10, 30, 13, 33)(11, 31, 15, 35)(14, 34, 16, 36)(17, 37, 20, 40)(18, 38, 19, 39)(41, 61, 43, 63, 42, 62, 45, 65)(44, 64, 49, 69, 47, 67, 52, 72)(46, 66, 50, 70, 48, 68, 53, 73)(51, 71, 57, 77, 55, 75, 60, 80)(54, 74, 58, 78, 56, 76, 59, 79) L = (1, 44)(2, 47)(3, 49)(4, 51)(5, 52)(6, 41)(7, 55)(8, 42)(9, 57)(10, 43)(11, 59)(12, 60)(13, 45)(14, 46)(15, 58)(16, 48)(17, 54)(18, 50)(19, 53)(20, 56)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 20, 40, 20, 40 ), ( 20, 40, 20, 40, 20, 40, 20, 40 ) } Outer automorphisms :: reflexible Dual of E12.150 Graph:: bipartite v = 15 e = 40 f = 3 degree seq :: [ 4^10, 8^5 ] E12.148 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-1, (R * Y3)^2, (Y3^-1, Y2^-1), (Y2^-1 * R)^2, (R * Y1)^2, (Y1, Y2^-1), Y1^4, (Y3^-1 * Y1^-1)^2, Y1^-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 ] Map:: non-degenerate R = (1, 21, 2, 22, 6, 26, 4, 24)(3, 23, 7, 27, 13, 33, 10, 30)(5, 25, 8, 28, 14, 34, 11, 31)(9, 29, 15, 35, 20, 40, 18, 38)(12, 32, 16, 36, 17, 37, 19, 39)(41, 61, 43, 63, 49, 69, 57, 77, 54, 74, 46, 66, 53, 73, 60, 80, 52, 72, 45, 65)(42, 62, 47, 67, 55, 75, 59, 79, 51, 71, 44, 64, 50, 70, 58, 78, 56, 76, 48, 68) L = (1, 42)(2, 46)(3, 47)(4, 41)(5, 48)(6, 44)(7, 53)(8, 54)(9, 55)(10, 43)(11, 45)(12, 56)(13, 50)(14, 51)(15, 60)(16, 57)(17, 59)(18, 49)(19, 52)(20, 58)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) 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 ) } Outer automorphisms :: reflexible Dual of E12.149 Graph:: bipartite v = 7 e = 40 f = 11 degree seq :: [ 8^5, 20^2 ] E12.149 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ Y2^2, R^2, Y2 * Y3^-2, Y1 * Y2 * Y1^-1 * Y2, (R * Y3)^2, (Y3^-1, Y1), (R * Y1)^2, (R * Y2)^2, Y1^2 * Y3^-1 * Y1^3, 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 ] Map:: non-degenerate R = (1, 21, 2, 22, 7, 27, 15, 35, 12, 32, 4, 24, 9, 29, 17, 37, 19, 39, 11, 31, 3, 23, 8, 28, 16, 36, 20, 40, 14, 34, 6, 26, 10, 30, 18, 38, 13, 33, 5, 25)(41, 61, 43, 63)(42, 62, 48, 68)(44, 64, 46, 66)(45, 65, 51, 71)(47, 67, 56, 76)(49, 69, 50, 70)(52, 72, 54, 74)(53, 73, 59, 79)(55, 75, 60, 80)(57, 77, 58, 78) L = (1, 44)(2, 49)(3, 46)(4, 43)(5, 52)(6, 41)(7, 57)(8, 50)(9, 48)(10, 42)(11, 54)(12, 51)(13, 55)(14, 45)(15, 59)(16, 58)(17, 56)(18, 47)(19, 60)(20, 53)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) 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, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20 ) } Outer automorphisms :: reflexible Dual of E12.148 Graph:: bipartite v = 11 e = 40 f = 7 degree seq :: [ 4^10, 40 ] E12.150 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2 * Y1^2, (Y3^-1 * Y2)^2, (Y2^-1, Y1^-1), Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1, Y2^-1 * Y1^-1 * Y3^-1 * Y1^-1, (R * Y3)^2, Y2^-1 * Y3^2 * Y2^-1, (R * Y1)^2, (R * Y2)^2, Y1^3 * Y2^-2, Y3^-1 * Y2^-1 * Y3^-1 * Y1 * Y3^-1 ] Map:: non-degenerate R = (1, 21, 2, 22, 8, 28, 13, 33, 19, 39, 16, 36, 20, 40, 18, 38, 14, 34, 5, 25)(3, 23, 9, 29, 7, 27, 12, 32, 17, 37, 4, 24, 10, 30, 6, 26, 11, 31, 15, 35)(41, 61, 43, 63, 53, 73, 52, 72, 60, 80, 50, 70, 45, 65, 55, 75, 48, 68, 47, 67, 56, 76, 44, 64, 54, 74, 51, 71, 42, 62, 49, 69, 59, 79, 57, 77, 58, 78, 46, 66) L = (1, 44)(2, 50)(3, 54)(4, 53)(5, 57)(6, 56)(7, 41)(8, 46)(9, 45)(10, 59)(11, 60)(12, 42)(13, 51)(14, 52)(15, 58)(16, 43)(17, 48)(18, 47)(19, 55)(20, 49)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) 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 ) } Outer automorphisms :: reflexible Dual of E12.147 Graph:: bipartite v = 3 e = 40 f = 15 degree seq :: [ 20^2, 40 ] E12.151 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y3, Y2), Y3 * Y1 * Y3^-1 * Y1, Y2^-1 * Y1 * Y2 * Y1, Y3^2 * Y2^3, Y1 * Y2^2 * Y3^-2, Y2 * Y1 * Y3^-1 * Y2 * Y3^-1 ] Map:: non-degenerate R = (1, 21, 2, 22)(3, 23, 7, 27)(4, 24, 8, 28)(5, 25, 9, 29)(6, 26, 10, 30)(11, 31, 14, 34)(12, 32, 19, 39)(13, 33, 15, 35)(16, 36, 18, 38)(17, 37, 20, 40)(41, 61, 43, 63, 51, 71, 58, 78, 49, 69, 42, 62, 47, 67, 54, 74, 56, 76, 45, 65)(44, 64, 52, 72, 57, 77, 46, 66, 53, 73, 48, 68, 59, 79, 60, 80, 50, 70, 55, 75) L = (1, 44)(2, 48)(3, 52)(4, 54)(5, 55)(6, 41)(7, 59)(8, 51)(9, 53)(10, 42)(11, 57)(12, 56)(13, 43)(14, 60)(15, 47)(16, 50)(17, 45)(18, 46)(19, 58)(20, 49)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) 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 ) } Outer automorphisms :: reflexible Dual of E12.152 Graph:: bipartite v = 12 e = 40 f = 6 degree seq :: [ 4^10, 20^2 ] E12.152 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10, 20}) Quotient :: dipole Aut^+ = C20 (small group id <20, 2>) Aut = D40 (small group id <40, 6>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-1, (R * Y3)^2, (Y3^-1, Y2^-1), (Y2^-1 * R)^2, (R * Y1)^2, (Y1, Y2^-1), Y1^4, (Y3^-1 * Y1^-1)^2, Y1^-1 * 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 ] Map:: non-degenerate R = (1, 21, 2, 22, 6, 26, 4, 24)(3, 23, 7, 27, 13, 33, 10, 30)(5, 25, 8, 28, 14, 34, 11, 31)(9, 29, 15, 35, 19, 39, 18, 38)(12, 32, 16, 36, 20, 40, 17, 37)(41, 61, 43, 63, 49, 69, 57, 77, 51, 71, 44, 64, 50, 70, 58, 78, 60, 80, 54, 74, 46, 66, 53, 73, 59, 79, 56, 76, 48, 68, 42, 62, 47, 67, 55, 75, 52, 72, 45, 65) L = (1, 42)(2, 46)(3, 47)(4, 41)(5, 48)(6, 44)(7, 53)(8, 54)(9, 55)(10, 43)(11, 45)(12, 56)(13, 50)(14, 51)(15, 59)(16, 60)(17, 52)(18, 49)(19, 58)(20, 57)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) 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 ) } Outer automorphisms :: reflexible Dual of E12.151 Graph:: bipartite v = 6 e = 40 f = 12 degree seq :: [ 8^5, 40 ] E12.153 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {3, 3, 7, 7}) Quotient :: edge^2 Aut^+ = C7 : C3 (small group id <21, 1>) Aut = (C7 : C3) : C2 (small group id <42, 1>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1, Y2^3, Y2 * Y1^-2, (R * Y3)^2, R * Y2 * R * Y1, Y3 * Y1 * Y3^-2 * Y1^-1, Y3 * Y2^-1 * Y3^-2 * Y1^-1, Y2 * Y3 * Y2^-1 * Y3^-2, Y1 * Y3^-2 * Y1^-1 * Y3, Y2^-1 * Y3^-1 * Y1^-1 * Y3^-3, Y3^3 * Y2^-1 * Y3 * Y1^-1 ] Map:: non-degenerate R = (1, 22, 4, 25, 12, 33, 19, 40, 17, 38, 15, 36, 5, 26)(2, 23, 6, 27, 10, 31, 21, 42, 20, 41, 13, 34, 7, 28)(3, 24, 8, 29, 16, 37, 14, 35, 11, 32, 18, 39, 9, 30)(43, 44, 45)(46, 52, 53)(47, 55, 56)(48, 58, 59)(49, 60, 61)(50, 54, 62)(51, 57, 63)(64, 66, 65)(67, 74, 73)(68, 77, 76)(69, 80, 79)(70, 82, 81)(71, 83, 75)(72, 84, 78) L = (1, 43)(2, 44)(3, 45)(4, 46)(5, 47)(6, 48)(7, 49)(8, 50)(9, 51)(10, 52)(11, 53)(12, 54)(13, 55)(14, 56)(15, 57)(16, 58)(17, 59)(18, 60)(19, 61)(20, 62)(21, 63)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84) local type(s) :: { ( 28^3 ), ( 28^14 ) } Outer automorphisms :: reflexible Dual of E12.163 Graph:: simple bipartite v = 17 e = 42 f = 3 degree seq :: [ 3^14, 14^3 ] E12.154 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {3, 3, 7, 7}) Quotient :: edge^2 Aut^+ = C7 : C3 (small group id <21, 1>) Aut = (C7 : C3) : C2 (small group id <42, 1>) |r| :: 2 Presentation :: [ R^2, Y2^3, Y1^3, Y2 * Y3^-1 * Y1, R * Y2 * R * Y1, (R * Y3)^2, Y2 * Y1 * Y3^-2, (Y2 * Y1^-1)^3, Y2 * Y1 * Y3^5 ] Map:: non-degenerate R = (1, 22, 4, 25, 11, 32, 21, 42, 20, 41, 16, 37, 7, 28)(2, 23, 8, 29, 14, 35, 19, 40, 13, 34, 6, 27, 10, 31)(3, 24, 12, 33, 18, 39, 15, 36, 9, 30, 17, 38, 5, 26)(43, 44, 47)(45, 53, 55)(46, 56, 57)(48, 60, 49)(50, 54, 62)(51, 63, 52)(58, 61, 59)(64, 66, 69)(65, 67, 72)(68, 71, 79)(70, 78, 82)(73, 83, 81)(74, 75, 77)(76, 84, 80) L = (1, 43)(2, 44)(3, 45)(4, 46)(5, 47)(6, 48)(7, 49)(8, 50)(9, 51)(10, 52)(11, 53)(12, 54)(13, 55)(14, 56)(15, 57)(16, 58)(17, 59)(18, 60)(19, 61)(20, 62)(21, 63)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84) local type(s) :: { ( 28^3 ), ( 28^14 ) } Outer automorphisms :: reflexible Dual of E12.160 Graph:: simple bipartite v = 17 e = 42 f = 3 degree seq :: [ 3^14, 14^3 ] E12.155 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {3, 3, 7, 7}) Quotient :: edge^2 Aut^+ = C7 : C3 (small group id <21, 1>) Aut = (C7 : C3) : C2 (small group id <42, 1>) |r| :: 2 Presentation :: [ R^2, Y2^3, Y1^3, Y3^-2 * Y2^-1 * Y1^-1, Y1 * Y3^-1 * Y2 * Y3^-1, Y2 * Y3^-1 * Y2 * Y1^-1, R * Y2 * R * Y1, Y3 * Y1^-1 * Y2 * Y1^-1, (R * Y3)^2, Y3^-2 * Y1 * Y3 * Y2 ] Map:: non-degenerate R = (1, 22, 4, 25, 16, 37, 12, 33, 19, 40, 8, 29, 7, 28)(2, 23, 9, 30, 14, 35, 20, 41, 6, 27, 17, 38, 11, 32)(3, 24, 13, 34, 5, 26, 18, 39, 15, 36, 21, 42, 10, 31)(43, 44, 47)(45, 54, 53)(46, 56, 52)(48, 60, 58)(49, 59, 63)(50, 62, 55)(51, 57, 61)(64, 66, 69)(65, 71, 73)(67, 78, 74)(68, 80, 82)(70, 81, 77)(72, 79, 76)(75, 84, 83) L = (1, 43)(2, 44)(3, 45)(4, 46)(5, 47)(6, 48)(7, 49)(8, 50)(9, 51)(10, 52)(11, 53)(12, 54)(13, 55)(14, 56)(15, 57)(16, 58)(17, 59)(18, 60)(19, 61)(20, 62)(21, 63)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84) local type(s) :: { ( 28^3 ), ( 28^14 ) } Outer automorphisms :: reflexible Dual of E12.162 Graph:: simple bipartite v = 17 e = 42 f = 3 degree seq :: [ 3^14, 14^3 ] E12.156 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {3, 3, 7, 7}) Quotient :: edge^2 Aut^+ = C7 : C3 (small group id <21, 1>) Aut = (C7 : C3) : C2 (small group id <42, 1>) |r| :: 2 Presentation :: [ R^2, Y2^3, Y1^3, Y3 * Y2 * Y1^-1 * Y2, Y3^-1 * Y2^-1 * Y1 * Y2^-1, Y2 * Y3 * Y1 * Y3, (R * Y3)^2, Y3^2 * Y2^-1 * Y1^-1, Y3^-1 * Y1^-1 * Y2 * Y1^-1, R * Y2 * R * Y1, Y2 * Y1 * Y2 * Y1 * Y3^-1, Y2 * Y1^-1 * Y3 * Y1^-1 * Y3^-1, Y3^2 * Y1^-1 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 22, 4, 25, 8, 29, 18, 39, 12, 33, 20, 41, 7, 28)(2, 23, 9, 30, 14, 35, 6, 27, 19, 40, 17, 38, 11, 32)(3, 24, 10, 31, 16, 37, 21, 42, 15, 36, 5, 26, 13, 34)(43, 44, 47)(45, 54, 51)(46, 56, 58)(48, 57, 62)(49, 59, 52)(50, 61, 55)(53, 63, 60)(64, 66, 69)(65, 71, 73)(67, 78, 80)(68, 77, 81)(70, 84, 72)(74, 83, 76)(75, 79, 82) L = (1, 43)(2, 44)(3, 45)(4, 46)(5, 47)(6, 48)(7, 49)(8, 50)(9, 51)(10, 52)(11, 53)(12, 54)(13, 55)(14, 56)(15, 57)(16, 58)(17, 59)(18, 60)(19, 61)(20, 62)(21, 63)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84) local type(s) :: { ( 28^3 ), ( 28^14 ) } Outer automorphisms :: reflexible Dual of E12.161 Graph:: simple bipartite v = 17 e = 42 f = 3 degree seq :: [ 3^14, 14^3 ] E12.157 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {3, 3, 7, 7}) Quotient :: edge^2 Aut^+ = C7 : C3 (small group id <21, 1>) Aut = (C7 : C3) : C2 (small group id <42, 1>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1 * Y3, Y2^3, Y1^3, (R * Y3)^2, R * Y1 * R * Y2, Y3^-1 * Y2^-1 * Y3 * Y1^-1, Y3 * Y1^-1 * Y3 * Y1 * Y2^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 22, 4, 25, 15, 36, 8, 29, 18, 39, 19, 40, 7, 28)(2, 23, 6, 27, 14, 35, 16, 37, 21, 42, 12, 33, 10, 31)(3, 24, 11, 32, 20, 41, 17, 38, 5, 26, 9, 30, 13, 34)(43, 44, 47)(45, 49, 54)(46, 56, 53)(48, 55, 60)(50, 52, 62)(51, 57, 63)(58, 59, 61)(64, 66, 69)(65, 71, 72)(67, 68, 79)(70, 80, 73)(74, 75, 78)(76, 84, 82)(77, 81, 83) L = (1, 43)(2, 44)(3, 45)(4, 46)(5, 47)(6, 48)(7, 49)(8, 50)(9, 51)(10, 52)(11, 53)(12, 54)(13, 55)(14, 56)(15, 57)(16, 58)(17, 59)(18, 60)(19, 61)(20, 62)(21, 63)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84) local type(s) :: { ( 28^3 ), ( 28^14 ) } Outer automorphisms :: reflexible Dual of E12.159 Graph:: simple bipartite v = 17 e = 42 f = 3 degree seq :: [ 3^14, 14^3 ] E12.158 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {3, 3, 7, 7}) Quotient :: edge^2 Aut^+ = C7 : C3 (small group id <21, 1>) Aut = (C7 : C3) : C2 (small group id <42, 1>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y2^-1 * Y3, Y2^3, Y1^3, R * Y1 * R * Y2, (R * Y3)^2, Y2 * Y3^-1 * Y1 * Y3, Y3^-1 * Y1^-1 * Y3^-1 * Y1 * Y2^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 22, 4, 25, 15, 36, 17, 38, 8, 29, 19, 40, 7, 28)(2, 23, 9, 30, 12, 33, 21, 42, 16, 37, 18, 39, 6, 27)(3, 24, 11, 32, 10, 31, 5, 26, 14, 35, 20, 41, 13, 34)(43, 44, 47)(45, 46, 54)(48, 53, 59)(49, 60, 55)(50, 51, 62)(52, 61, 63)(56, 57, 58)(64, 66, 69)(65, 71, 73)(67, 77, 72)(68, 79, 70)(74, 84, 78)(75, 82, 76)(80, 83, 81) L = (1, 43)(2, 44)(3, 45)(4, 46)(5, 47)(6, 48)(7, 49)(8, 50)(9, 51)(10, 52)(11, 53)(12, 54)(13, 55)(14, 56)(15, 57)(16, 58)(17, 59)(18, 60)(19, 61)(20, 62)(21, 63)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84) local type(s) :: { ( 28^3 ), ( 28^14 ) } Outer automorphisms :: reflexible Dual of E12.164 Graph:: simple bipartite v = 17 e = 42 f = 3 degree seq :: [ 3^14, 14^3 ] E12.159 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {3, 3, 7, 7}) Quotient :: loop^2 Aut^+ = C7 : C3 (small group id <21, 1>) Aut = (C7 : C3) : C2 (small group id <42, 1>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1, Y2^3, Y2 * Y1^-2, (R * Y3)^2, R * Y2 * R * Y1, Y3 * Y1 * Y3^-2 * Y1^-1, Y3 * Y2^-1 * Y3^-2 * Y1^-1, Y2 * Y3 * Y2^-1 * Y3^-2, Y1 * Y3^-2 * Y1^-1 * Y3, Y2^-1 * Y3^-1 * Y1^-1 * Y3^-3, Y3^3 * Y2^-1 * Y3 * Y1^-1 ] Map:: non-degenerate R = (1, 22, 43, 64, 4, 25, 46, 67, 12, 33, 54, 75, 19, 40, 61, 82, 17, 38, 59, 80, 15, 36, 57, 78, 5, 26, 47, 68)(2, 23, 44, 65, 6, 27, 48, 69, 10, 31, 52, 73, 21, 42, 63, 84, 20, 41, 62, 83, 13, 34, 55, 76, 7, 28, 49, 70)(3, 24, 45, 66, 8, 29, 50, 71, 16, 37, 58, 79, 14, 35, 56, 77, 11, 32, 53, 74, 18, 39, 60, 81, 9, 30, 51, 72) L = (1, 23)(2, 24)(3, 22)(4, 31)(5, 34)(6, 37)(7, 39)(8, 33)(9, 36)(10, 32)(11, 25)(12, 41)(13, 35)(14, 26)(15, 42)(16, 38)(17, 27)(18, 40)(19, 28)(20, 29)(21, 30)(43, 66)(44, 64)(45, 65)(46, 74)(47, 77)(48, 80)(49, 82)(50, 83)(51, 84)(52, 67)(53, 73)(54, 71)(55, 68)(56, 76)(57, 72)(58, 69)(59, 79)(60, 70)(61, 81)(62, 75)(63, 78) local type(s) :: { ( 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14 ) } Outer automorphisms :: reflexible Dual of E12.157 Transitivity :: VT+ Graph:: v = 3 e = 42 f = 17 degree seq :: [ 28^3 ] E12.160 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {3, 3, 7, 7}) Quotient :: loop^2 Aut^+ = C7 : C3 (small group id <21, 1>) Aut = (C7 : C3) : C2 (small group id <42, 1>) |r| :: 2 Presentation :: [ R^2, Y2^3, Y1^3, Y2 * Y3^-1 * Y1, R * Y2 * R * Y1, (R * Y3)^2, Y2 * Y1 * Y3^-2, (Y2 * Y1^-1)^3, Y2 * Y1 * Y3^5 ] Map:: non-degenerate R = (1, 22, 43, 64, 4, 25, 46, 67, 11, 32, 53, 74, 21, 42, 63, 84, 20, 41, 62, 83, 16, 37, 58, 79, 7, 28, 49, 70)(2, 23, 44, 65, 8, 29, 50, 71, 14, 35, 56, 77, 19, 40, 61, 82, 13, 34, 55, 76, 6, 27, 48, 69, 10, 31, 52, 73)(3, 24, 45, 66, 12, 33, 54, 75, 18, 39, 60, 81, 15, 36, 57, 78, 9, 30, 51, 72, 17, 38, 59, 80, 5, 26, 47, 68) L = (1, 23)(2, 26)(3, 32)(4, 35)(5, 22)(6, 39)(7, 27)(8, 33)(9, 42)(10, 30)(11, 34)(12, 41)(13, 24)(14, 36)(15, 25)(16, 40)(17, 37)(18, 28)(19, 38)(20, 29)(21, 31)(43, 66)(44, 67)(45, 69)(46, 72)(47, 71)(48, 64)(49, 78)(50, 79)(51, 65)(52, 83)(53, 75)(54, 77)(55, 84)(56, 74)(57, 82)(58, 68)(59, 76)(60, 73)(61, 70)(62, 81)(63, 80) local type(s) :: { ( 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14 ) } Outer automorphisms :: reflexible Dual of E12.154 Transitivity :: VT+ Graph:: v = 3 e = 42 f = 17 degree seq :: [ 28^3 ] E12.161 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {3, 3, 7, 7}) Quotient :: loop^2 Aut^+ = C7 : C3 (small group id <21, 1>) Aut = (C7 : C3) : C2 (small group id <42, 1>) |r| :: 2 Presentation :: [ R^2, Y2^3, Y1^3, Y3^-2 * Y2^-1 * Y1^-1, Y1 * Y3^-1 * Y2 * Y3^-1, Y2 * Y3^-1 * Y2 * Y1^-1, R * Y2 * R * Y1, Y3 * Y1^-1 * Y2 * Y1^-1, (R * Y3)^2, Y3^-2 * Y1 * Y3 * Y2 ] Map:: non-degenerate R = (1, 22, 43, 64, 4, 25, 46, 67, 16, 37, 58, 79, 12, 33, 54, 75, 19, 40, 61, 82, 8, 29, 50, 71, 7, 28, 49, 70)(2, 23, 44, 65, 9, 30, 51, 72, 14, 35, 56, 77, 20, 41, 62, 83, 6, 27, 48, 69, 17, 38, 59, 80, 11, 32, 53, 74)(3, 24, 45, 66, 13, 34, 55, 76, 5, 26, 47, 68, 18, 39, 60, 81, 15, 36, 57, 78, 21, 42, 63, 84, 10, 31, 52, 73) L = (1, 23)(2, 26)(3, 33)(4, 35)(5, 22)(6, 39)(7, 38)(8, 41)(9, 36)(10, 25)(11, 24)(12, 32)(13, 29)(14, 31)(15, 40)(16, 27)(17, 42)(18, 37)(19, 30)(20, 34)(21, 28)(43, 66)(44, 71)(45, 69)(46, 78)(47, 80)(48, 64)(49, 81)(50, 73)(51, 79)(52, 65)(53, 67)(54, 84)(55, 72)(56, 70)(57, 74)(58, 76)(59, 82)(60, 77)(61, 68)(62, 75)(63, 83) local type(s) :: { ( 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14 ) } Outer automorphisms :: reflexible Dual of E12.156 Transitivity :: VT+ Graph:: v = 3 e = 42 f = 17 degree seq :: [ 28^3 ] E12.162 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {3, 3, 7, 7}) Quotient :: loop^2 Aut^+ = C7 : C3 (small group id <21, 1>) Aut = (C7 : C3) : C2 (small group id <42, 1>) |r| :: 2 Presentation :: [ R^2, Y2^3, Y1^3, Y3 * Y2 * Y1^-1 * Y2, Y3^-1 * Y2^-1 * Y1 * Y2^-1, Y2 * Y3 * Y1 * Y3, (R * Y3)^2, Y3^2 * Y2^-1 * Y1^-1, Y3^-1 * Y1^-1 * Y2 * Y1^-1, R * Y2 * R * Y1, Y2 * Y1 * Y2 * Y1 * Y3^-1, Y2 * Y1^-1 * Y3 * Y1^-1 * Y3^-1, Y3^2 * Y1^-1 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 22, 43, 64, 4, 25, 46, 67, 8, 29, 50, 71, 18, 39, 60, 81, 12, 33, 54, 75, 20, 41, 62, 83, 7, 28, 49, 70)(2, 23, 44, 65, 9, 30, 51, 72, 14, 35, 56, 77, 6, 27, 48, 69, 19, 40, 61, 82, 17, 38, 59, 80, 11, 32, 53, 74)(3, 24, 45, 66, 10, 31, 52, 73, 16, 37, 58, 79, 21, 42, 63, 84, 15, 36, 57, 78, 5, 26, 47, 68, 13, 34, 55, 76) L = (1, 23)(2, 26)(3, 33)(4, 35)(5, 22)(6, 36)(7, 38)(8, 40)(9, 24)(10, 28)(11, 42)(12, 30)(13, 29)(14, 37)(15, 41)(16, 25)(17, 31)(18, 32)(19, 34)(20, 27)(21, 39)(43, 66)(44, 71)(45, 69)(46, 78)(47, 77)(48, 64)(49, 84)(50, 73)(51, 70)(52, 65)(53, 83)(54, 79)(55, 74)(56, 81)(57, 80)(58, 82)(59, 67)(60, 68)(61, 75)(62, 76)(63, 72) local type(s) :: { ( 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14 ) } Outer automorphisms :: reflexible Dual of E12.155 Transitivity :: VT+ Graph:: v = 3 e = 42 f = 17 degree seq :: [ 28^3 ] E12.163 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {3, 3, 7, 7}) Quotient :: loop^2 Aut^+ = C7 : C3 (small group id <21, 1>) Aut = (C7 : C3) : C2 (small group id <42, 1>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1 * Y3, Y2^3, Y1^3, (R * Y3)^2, R * Y1 * R * Y2, Y3^-1 * Y2^-1 * Y3 * Y1^-1, Y3 * Y1^-1 * Y3 * Y1 * Y2^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 22, 43, 64, 4, 25, 46, 67, 15, 36, 57, 78, 8, 29, 50, 71, 18, 39, 60, 81, 19, 40, 61, 82, 7, 28, 49, 70)(2, 23, 44, 65, 6, 27, 48, 69, 14, 35, 56, 77, 16, 37, 58, 79, 21, 42, 63, 84, 12, 33, 54, 75, 10, 31, 52, 73)(3, 24, 45, 66, 11, 32, 53, 74, 20, 41, 62, 83, 17, 38, 59, 80, 5, 26, 47, 68, 9, 30, 51, 72, 13, 34, 55, 76) L = (1, 23)(2, 26)(3, 28)(4, 35)(5, 22)(6, 34)(7, 33)(8, 31)(9, 36)(10, 41)(11, 25)(12, 24)(13, 39)(14, 32)(15, 42)(16, 38)(17, 40)(18, 27)(19, 37)(20, 29)(21, 30)(43, 66)(44, 71)(45, 69)(46, 68)(47, 79)(48, 64)(49, 80)(50, 72)(51, 65)(52, 70)(53, 75)(54, 78)(55, 84)(56, 81)(57, 74)(58, 67)(59, 73)(60, 83)(61, 76)(62, 77)(63, 82) local type(s) :: { ( 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14 ) } Outer automorphisms :: reflexible Dual of E12.153 Transitivity :: VT+ Graph:: v = 3 e = 42 f = 17 degree seq :: [ 28^3 ] E12.164 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {3, 3, 7, 7}) Quotient :: loop^2 Aut^+ = C7 : C3 (small group id <21, 1>) Aut = (C7 : C3) : C2 (small group id <42, 1>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y2^-1 * Y3, Y2^3, Y1^3, R * Y1 * R * Y2, (R * Y3)^2, Y2 * Y3^-1 * Y1 * Y3, Y3^-1 * Y1^-1 * Y3^-1 * Y1 * Y2^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 22, 43, 64, 4, 25, 46, 67, 15, 36, 57, 78, 17, 38, 59, 80, 8, 29, 50, 71, 19, 40, 61, 82, 7, 28, 49, 70)(2, 23, 44, 65, 9, 30, 51, 72, 12, 33, 54, 75, 21, 42, 63, 84, 16, 37, 58, 79, 18, 39, 60, 81, 6, 27, 48, 69)(3, 24, 45, 66, 11, 32, 53, 74, 10, 31, 52, 73, 5, 26, 47, 68, 14, 35, 56, 77, 20, 41, 62, 83, 13, 34, 55, 76) L = (1, 23)(2, 26)(3, 25)(4, 33)(5, 22)(6, 32)(7, 39)(8, 30)(9, 41)(10, 40)(11, 38)(12, 24)(13, 28)(14, 36)(15, 37)(16, 35)(17, 27)(18, 34)(19, 42)(20, 29)(21, 31)(43, 66)(44, 71)(45, 69)(46, 77)(47, 79)(48, 64)(49, 68)(50, 73)(51, 67)(52, 65)(53, 84)(54, 82)(55, 75)(56, 72)(57, 74)(58, 70)(59, 83)(60, 80)(61, 76)(62, 81)(63, 78) local type(s) :: { ( 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14 ) } Outer automorphisms :: reflexible Dual of E12.158 Transitivity :: VT+ Graph:: v = 3 e = 42 f = 17 degree seq :: [ 28^3 ] E12.165 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 7, 7}) Quotient :: dipole Aut^+ = C21 (small group id <21, 2>) Aut = D42 (small group id <42, 5>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y1^3, (R * Y3)^2, (R * Y1)^2, (Y2, Y1^-1), (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^3, Y2^7, (Y3 * Y2^-1)^7 ] Map:: R = (1, 22, 2, 23, 4, 25)(3, 24, 6, 27, 9, 30)(5, 26, 7, 28, 10, 31)(8, 29, 12, 33, 15, 36)(11, 32, 13, 34, 16, 37)(14, 35, 18, 39, 20, 41)(17, 38, 19, 40, 21, 42)(43, 64, 45, 66, 50, 71, 56, 77, 59, 80, 53, 74, 47, 68)(44, 65, 48, 69, 54, 75, 60, 81, 61, 82, 55, 76, 49, 70)(46, 67, 51, 72, 57, 78, 62, 83, 63, 84, 58, 79, 52, 73) L = (1, 43)(2, 44)(3, 45)(4, 46)(5, 47)(6, 48)(7, 49)(8, 50)(9, 51)(10, 52)(11, 53)(12, 54)(13, 55)(14, 56)(15, 57)(16, 58)(17, 59)(18, 60)(19, 61)(20, 62)(21, 63)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84) local type(s) :: { ( 6, 14, 6, 14, 6, 14 ), ( 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14, 6, 14 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 10 e = 42 f = 10 degree seq :: [ 6^7, 14^3 ] E12.166 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 4, 4}) Quotient :: dipole Aut^+ = C3 : Q8 (small group id <24, 4>) Aut = (C12 x C2) : C2 (small group id <48, 37>) |r| :: 2 Presentation :: [ R^2, Y1^3, Y2^-1 * Y3^2 * Y2^-1, Y3^2 * Y2^2, (R * Y1)^2, Y3^-1 * Y2^-1 * Y3 * Y2^-1, Y3^-1 * Y2 * Y3^-1 * Y2^-1, (R * Y3)^2, R * Y2 * R * Y2^-1, Y3^4, Y3 * Y1^-1 * Y3^-1 * Y1^-1, Y2 * Y1^-1 * Y2^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 25, 2, 26, 5, 29)(3, 27, 12, 36, 8, 32)(4, 28, 16, 40, 9, 33)(6, 30, 17, 41, 10, 34)(7, 31, 18, 42, 11, 35)(13, 37, 19, 43, 22, 46)(14, 38, 20, 44, 23, 47)(15, 39, 21, 45, 24, 48)(49, 73, 51, 75, 61, 85, 54, 78)(50, 74, 56, 80, 67, 91, 58, 82)(52, 76, 63, 87, 55, 79, 62, 86)(53, 77, 60, 84, 70, 94, 65, 89)(57, 81, 69, 93, 59, 83, 68, 92)(64, 88, 72, 96, 66, 90, 71, 95) L = (1, 52)(2, 57)(3, 62)(4, 61)(5, 64)(6, 63)(7, 49)(8, 68)(9, 67)(10, 69)(11, 50)(12, 71)(13, 55)(14, 54)(15, 51)(16, 70)(17, 72)(18, 53)(19, 59)(20, 58)(21, 56)(22, 66)(23, 65)(24, 60)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8^6 ), ( 8^8 ) } Outer automorphisms :: reflexible Dual of E12.167 Graph:: simple bipartite v = 14 e = 48 f = 12 degree seq :: [ 6^8, 8^6 ] E12.167 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 4, 4}) Quotient :: dipole Aut^+ = C3 : Q8 (small group id <24, 4>) Aut = (C12 x C2) : C2 (small group id <48, 37>) |r| :: 2 Presentation :: [ R^2, Y2^-2 * Y1^-2, Y3^-2 * Y2^-2, Y3 * Y2 * Y3 * Y2^-1, Y1^-1 * Y2^2 * Y1^-1, R * Y2 * R * Y2^-1, Y3 * Y2^-1 * Y3^-1 * Y2^-1, (R * Y1)^2, Y1^4, (R * Y3)^2, Y2^4, Y2 * Y1^-1 * Y2^-1 * Y1^-1, (Y3^-1 * Y1^-1)^3 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 5, 29)(3, 27, 11, 35, 6, 30, 9, 33)(4, 28, 15, 39, 7, 31, 16, 40)(10, 34, 19, 43, 12, 36, 20, 44)(13, 37, 21, 45, 14, 38, 22, 46)(17, 41, 23, 47, 18, 42, 24, 48)(49, 73, 51, 75, 56, 80, 54, 78)(50, 74, 57, 81, 53, 77, 59, 83)(52, 76, 62, 86, 55, 79, 61, 85)(58, 82, 66, 90, 60, 84, 65, 89)(63, 87, 69, 93, 64, 88, 70, 94)(67, 91, 71, 95, 68, 92, 72, 96) L = (1, 52)(2, 58)(3, 61)(4, 56)(5, 60)(6, 62)(7, 49)(8, 55)(9, 65)(10, 53)(11, 66)(12, 50)(13, 54)(14, 51)(15, 68)(16, 67)(17, 59)(18, 57)(19, 63)(20, 64)(21, 71)(22, 72)(23, 70)(24, 69)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E12.166 Graph:: bipartite v = 12 e = 48 f = 14 degree seq :: [ 8^12 ] E12.168 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {3, 3, 4, 6}) Quotient :: edge^2 Aut^+ = SL(2,3) (small group id <24, 3>) Aut = GL(2,3) (small group id <48, 29>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1, Y1^3, Y2^3, R * Y2 * R * Y1, Y3^4, (R * Y3)^2, Y3^-1 * Y1 * Y3^-2 * Y1^-1 * Y3^-1, Y3 * Y1^-1 * Y3^-1 * Y1^-1 * Y3 * Y1^-1, (Y1^-1 * Y3^-1 * Y2^-1)^6 ] Map:: non-degenerate R = (1, 25, 3, 27, 9, 33, 5, 29)(2, 26, 6, 30, 16, 40, 7, 31)(4, 28, 11, 35, 22, 46, 12, 36)(8, 32, 20, 44, 13, 37, 21, 45)(10, 34, 15, 39, 14, 38, 18, 42)(17, 41, 23, 47, 19, 43, 24, 48)(49, 50, 52)(51, 56, 58)(53, 61, 62)(54, 63, 65)(55, 66, 67)(57, 64, 70)(59, 71, 69)(60, 72, 68)(73, 74, 76)(75, 80, 82)(77, 85, 86)(78, 87, 89)(79, 90, 91)(81, 88, 94)(83, 95, 93)(84, 96, 92) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 24^3 ), ( 24^8 ) } Outer automorphisms :: reflexible Dual of E12.171 Graph:: simple bipartite v = 22 e = 48 f = 4 degree seq :: [ 3^16, 8^6 ] E12.169 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {3, 3, 4, 6}) Quotient :: edge^2 Aut^+ = SL(2,3) (small group id <24, 3>) Aut = GL(2,3) (small group id <48, 29>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2^-1, Y1^3, Y2^3, R * Y1 * R * Y2, (R * Y3)^2, Y3^-1 * Y2 * Y3^2 * Y1, Y3^2 * Y2 * Y3^-1 * Y1, Y3^6, (Y1^-1 * Y3^-1)^3, (Y1^-1 * Y3^-1 * Y2^-1)^4 ] Map:: non-degenerate R = (1, 25, 3, 27, 9, 33, 21, 45, 15, 39, 5, 29)(2, 26, 6, 30, 10, 34, 23, 47, 19, 43, 7, 31)(4, 28, 11, 35, 17, 41, 24, 48, 13, 37, 12, 36)(8, 32, 20, 44, 22, 46, 18, 42, 16, 40, 14, 38)(49, 50, 52)(51, 56, 58)(53, 61, 62)(54, 64, 65)(55, 63, 66)(57, 59, 70)(60, 67, 68)(69, 71, 72)(73, 74, 76)(75, 80, 82)(77, 85, 86)(78, 88, 89)(79, 87, 90)(81, 83, 94)(84, 91, 92)(93, 95, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 16^3 ), ( 16^12 ) } Outer automorphisms :: reflexible Dual of E12.170 Graph:: simple bipartite v = 20 e = 48 f = 6 degree seq :: [ 3^16, 12^4 ] E12.170 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {3, 3, 4, 6}) Quotient :: loop^2 Aut^+ = SL(2,3) (small group id <24, 3>) Aut = GL(2,3) (small group id <48, 29>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1, Y1^3, Y2^3, R * Y2 * R * Y1, Y3^4, (R * Y3)^2, Y3^-1 * Y1 * Y3^-2 * Y1^-1 * Y3^-1, Y3 * Y1^-1 * Y3^-1 * Y1^-1 * Y3 * Y1^-1, (Y1^-1 * Y3^-1 * Y2^-1)^6 ] Map:: non-degenerate R = (1, 25, 49, 73, 3, 27, 51, 75, 9, 33, 57, 81, 5, 29, 53, 77)(2, 26, 50, 74, 6, 30, 54, 78, 16, 40, 64, 88, 7, 31, 55, 79)(4, 28, 52, 76, 11, 35, 59, 83, 22, 46, 70, 94, 12, 36, 60, 84)(8, 32, 56, 80, 20, 44, 68, 92, 13, 37, 61, 85, 21, 45, 69, 93)(10, 34, 58, 82, 15, 39, 63, 87, 14, 38, 62, 86, 18, 42, 66, 90)(17, 41, 65, 89, 23, 47, 71, 95, 19, 43, 67, 91, 24, 48, 72, 96) L = (1, 26)(2, 28)(3, 32)(4, 25)(5, 37)(6, 39)(7, 42)(8, 34)(9, 40)(10, 27)(11, 47)(12, 48)(13, 38)(14, 29)(15, 41)(16, 46)(17, 30)(18, 43)(19, 31)(20, 36)(21, 35)(22, 33)(23, 45)(24, 44)(49, 74)(50, 76)(51, 80)(52, 73)(53, 85)(54, 87)(55, 90)(56, 82)(57, 88)(58, 75)(59, 95)(60, 96)(61, 86)(62, 77)(63, 89)(64, 94)(65, 78)(66, 91)(67, 79)(68, 84)(69, 83)(70, 81)(71, 93)(72, 92) local type(s) :: { ( 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12 ) } Outer automorphisms :: reflexible Dual of E12.169 Transitivity :: VT+ Graph:: v = 6 e = 48 f = 20 degree seq :: [ 16^6 ] E12.171 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {3, 3, 4, 6}) Quotient :: loop^2 Aut^+ = SL(2,3) (small group id <24, 3>) Aut = GL(2,3) (small group id <48, 29>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2^-1, Y1^3, Y2^3, R * Y1 * R * Y2, (R * Y3)^2, Y3^-1 * Y2 * Y3^2 * Y1, Y3^2 * Y2 * Y3^-1 * Y1, Y3^6, (Y1^-1 * Y3^-1)^3, (Y1^-1 * Y3^-1 * Y2^-1)^4 ] Map:: non-degenerate R = (1, 25, 49, 73, 3, 27, 51, 75, 9, 33, 57, 81, 21, 45, 69, 93, 15, 39, 63, 87, 5, 29, 53, 77)(2, 26, 50, 74, 6, 30, 54, 78, 10, 34, 58, 82, 23, 47, 71, 95, 19, 43, 67, 91, 7, 31, 55, 79)(4, 28, 52, 76, 11, 35, 59, 83, 17, 41, 65, 89, 24, 48, 72, 96, 13, 37, 61, 85, 12, 36, 60, 84)(8, 32, 56, 80, 20, 44, 68, 92, 22, 46, 70, 94, 18, 42, 66, 90, 16, 40, 64, 88, 14, 38, 62, 86) L = (1, 26)(2, 28)(3, 32)(4, 25)(5, 37)(6, 40)(7, 39)(8, 34)(9, 35)(10, 27)(11, 46)(12, 43)(13, 38)(14, 29)(15, 42)(16, 41)(17, 30)(18, 31)(19, 44)(20, 36)(21, 47)(22, 33)(23, 48)(24, 45)(49, 74)(50, 76)(51, 80)(52, 73)(53, 85)(54, 88)(55, 87)(56, 82)(57, 83)(58, 75)(59, 94)(60, 91)(61, 86)(62, 77)(63, 90)(64, 89)(65, 78)(66, 79)(67, 92)(68, 84)(69, 95)(70, 81)(71, 96)(72, 93) local type(s) :: { ( 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8, 3, 8 ) } Outer automorphisms :: reflexible Dual of E12.168 Transitivity :: VT+ Graph:: v = 4 e = 48 f = 22 degree seq :: [ 24^4 ] E12.172 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 4, 6}) Quotient :: dipole Aut^+ = SL(2,3) (small group id <24, 3>) Aut = GL(2,3) (small group id <48, 29>) |r| :: 2 Presentation :: [ R^2, Y1^3, Y2^3, Y3^3, Y1 * Y3^-1 * Y2^-1 * Y3, Y1 * Y2^-1 * Y1^-1 * Y3, Y3 * Y1 * Y3^-1 * Y2^-1, Y1^-1 * Y3 * Y1 * Y2^-1, (R * Y1)^2, (R * Y3)^2, Y1^-1 * Y2 * Y3 * Y2^-1, (R * Y2 * Y3^-1)^2, (Y2^-1 * Y1)^4 ] Map:: non-degenerate R = (1, 25, 2, 26, 5, 29)(3, 27, 12, 36, 13, 37)(4, 28, 8, 32, 16, 40)(6, 30, 17, 41, 19, 43)(7, 31, 10, 34, 21, 45)(9, 33, 14, 38, 23, 47)(11, 35, 18, 42, 24, 48)(15, 39, 22, 46, 20, 44)(49, 73, 51, 75, 54, 78)(50, 74, 56, 80, 58, 82)(52, 76, 63, 87, 65, 89)(53, 77, 62, 86, 66, 90)(55, 79, 59, 83, 67, 91)(57, 81, 70, 94, 69, 93)(60, 84, 64, 88, 71, 95)(61, 85, 68, 92, 72, 96) L = (1, 52)(2, 57)(3, 56)(4, 55)(5, 61)(6, 64)(7, 49)(8, 62)(9, 59)(10, 71)(11, 50)(12, 70)(13, 67)(14, 51)(15, 58)(16, 68)(17, 69)(18, 60)(19, 53)(20, 54)(21, 72)(22, 66)(23, 63)(24, 65)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E12.177 Graph:: simple bipartite v = 16 e = 48 f = 10 degree seq :: [ 6^16 ] E12.173 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 4, 6}) Quotient :: dipole Aut^+ = SL(2,3) (small group id <24, 3>) Aut = GL(2,3) (small group id <48, 29>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-1, Y1^3, (R * Y1)^2, (R * Y3)^2, Y2^4, (R * Y2 * Y3^-1)^2, Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2, (Y1^-1 * Y2^-1)^3, (Y3^-1 * Y1^-1)^3, (Y3 * Y2^-1)^6 ] Map:: non-degenerate R = (1, 25, 2, 26, 4, 28)(3, 27, 8, 32, 10, 34)(5, 29, 13, 37, 14, 38)(6, 30, 15, 39, 17, 41)(7, 31, 18, 42, 19, 43)(9, 33, 16, 40, 22, 46)(11, 35, 23, 47, 21, 45)(12, 36, 24, 48, 20, 44)(49, 73, 51, 75, 57, 81, 53, 77)(50, 74, 54, 78, 64, 88, 55, 79)(52, 76, 59, 83, 70, 94, 60, 84)(56, 80, 68, 92, 61, 85, 69, 93)(58, 82, 63, 87, 62, 86, 66, 90)(65, 89, 71, 95, 67, 91, 72, 96) L = (1, 50)(2, 52)(3, 56)(4, 49)(5, 61)(6, 63)(7, 66)(8, 58)(9, 64)(10, 51)(11, 71)(12, 72)(13, 62)(14, 53)(15, 65)(16, 70)(17, 54)(18, 67)(19, 55)(20, 60)(21, 59)(22, 57)(23, 69)(24, 68)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 6, 12, 6, 12, 6, 12 ), ( 6, 12, 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E12.175 Graph:: bipartite v = 14 e = 48 f = 12 degree seq :: [ 6^8, 8^6 ] E12.174 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 4, 6}) Quotient :: dipole Aut^+ = SL(2,3) (small group id <24, 3>) Aut = GL(2,3) (small group id <48, 29>) |r| :: 2 Presentation :: [ R^2, Y1^3, Y2 * Y1^-1 * Y3, (R * Y3^-1)^2, Y3^-2 * Y2^-1 * Y1^-1, Y2^4, (R * Y1)^2, Y2 * Y1 * Y2 * Y3^-1 * Y2, Y3^-1 * Y2 * Y3 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 25, 2, 26, 5, 29)(3, 27, 11, 35, 7, 31)(4, 28, 15, 39, 17, 41)(6, 30, 20, 44, 16, 40)(8, 32, 22, 46, 10, 34)(9, 33, 23, 47, 21, 45)(12, 36, 18, 42, 14, 38)(13, 37, 19, 43, 24, 48)(49, 73, 51, 75, 60, 84, 54, 78)(50, 74, 56, 80, 66, 90, 52, 76)(53, 77, 67, 91, 62, 86, 57, 81)(55, 79, 70, 94, 64, 88, 63, 87)(58, 82, 72, 96, 65, 89, 71, 95)(59, 83, 69, 93, 68, 92, 61, 85) L = (1, 52)(2, 57)(3, 61)(4, 64)(5, 54)(6, 69)(7, 49)(8, 55)(9, 65)(10, 50)(11, 63)(12, 56)(13, 53)(14, 51)(15, 72)(16, 60)(17, 66)(18, 67)(19, 58)(20, 70)(21, 62)(22, 71)(23, 59)(24, 68)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 6, 12, 6, 12, 6, 12 ), ( 6, 12, 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E12.176 Graph:: bipartite v = 14 e = 48 f = 12 degree seq :: [ 6^8, 8^6 ] E12.175 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 4, 6}) Quotient :: dipole Aut^+ = SL(2,3) (small group id <24, 3>) Aut = GL(2,3) (small group id <48, 29>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y2^-1, Y2^3, Y3^2 * Y2^-1, (R * Y1)^2, R * Y2 * R * Y3^-1, Y2^-1 * Y1 * Y2^-1 * Y1^-2, Y3 * Y1^-1 * Y3 * Y1^-1 * Y2^-1 * Y1^-1, Y1^6, (Y3^-1 * Y1^-1)^4 ] Map:: non-degenerate R = (1, 25, 2, 26, 6, 30, 16, 40, 15, 39, 5, 29)(3, 27, 9, 33, 8, 32, 19, 43, 23, 47, 10, 34)(4, 28, 11, 35, 21, 45, 24, 48, 13, 37, 12, 36)(7, 31, 18, 42, 17, 41, 22, 46, 20, 44, 14, 38)(49, 73, 51, 75, 52, 76)(50, 74, 55, 79, 56, 80)(53, 77, 61, 85, 62, 86)(54, 78, 59, 83, 65, 89)(57, 81, 68, 92, 69, 93)(58, 82, 63, 87, 70, 94)(60, 84, 71, 95, 66, 90)(64, 88, 67, 91, 72, 96) L = (1, 52)(2, 56)(3, 49)(4, 51)(5, 62)(6, 65)(7, 50)(8, 55)(9, 69)(10, 70)(11, 54)(12, 66)(13, 53)(14, 61)(15, 58)(16, 72)(17, 59)(18, 71)(19, 64)(20, 57)(21, 68)(22, 63)(23, 60)(24, 67)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 6, 8, 6, 8, 6, 8 ), ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E12.173 Graph:: bipartite v = 12 e = 48 f = 14 degree seq :: [ 6^8, 12^4 ] E12.176 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 4, 6}) Quotient :: dipole Aut^+ = SL(2,3) (small group id <24, 3>) Aut = GL(2,3) (small group id <48, 29>) |r| :: 2 Presentation :: [ R^2, Y2^3, Y3^-1 * Y2 * Y1^-1 * Y2^-1, (R * Y1)^2, Y3 * Y2 * Y1 * Y2^-1, Y1^2 * Y3 * Y2^-1, (R * Y3)^2, Y1^-1 * Y3^-2 * Y2^-1, Y2^-1 * Y3 * Y2^-1 * Y3^-1 * Y1^-1, Y2 * Y3^-1 * Y2^-1 * Y1 * Y3^-1, Y1^-1 * Y2 * Y1 * Y3^-2, Y1^-1 * Y3^-1 * Y1^2 * Y3^-1, Y3^-2 * Y1 * Y3^-1 * Y2^-1, (Y1 * Y2)^3, (R * Y2 * Y3^-1)^2 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 24, 48, 19, 43, 5, 29)(3, 27, 13, 37, 11, 35, 20, 44, 12, 36, 15, 39)(4, 28, 16, 40, 21, 45, 9, 33, 14, 38, 18, 42)(6, 30, 22, 46, 7, 31, 23, 47, 10, 34, 17, 41)(49, 73, 51, 75, 54, 78)(50, 74, 57, 81, 59, 83)(52, 76, 63, 87, 67, 91)(53, 77, 58, 82, 69, 93)(55, 79, 61, 85, 64, 88)(56, 80, 70, 94, 66, 90)(60, 84, 62, 86, 65, 89)(68, 92, 71, 95, 72, 96) L = (1, 52)(2, 58)(3, 62)(4, 65)(5, 68)(6, 69)(7, 49)(8, 51)(9, 55)(10, 61)(11, 54)(12, 50)(13, 67)(14, 53)(15, 71)(16, 56)(17, 72)(18, 59)(19, 70)(20, 64)(21, 63)(22, 60)(23, 66)(24, 57)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 6, 8, 6, 8, 6, 8 ), ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E12.174 Graph:: bipartite v = 12 e = 48 f = 14 degree seq :: [ 6^8, 12^4 ] E12.177 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 4, 6}) Quotient :: dipole Aut^+ = SL(2,3) (small group id <24, 3>) Aut = GL(2,3) (small group id <48, 29>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2^-1 * Y3^-1, Y3^3, (R * Y3^-1)^2, Y1^-1 * Y2^2 * Y3^-1, Y2^-1 * Y1 * Y3 * Y2^-1, (R * Y3)^2, (R * Y1)^2, Y1^4, Y3^-1 * Y1^-1 * Y2^2, Y2 * Y1 * Y2 * Y1 * Y3^-1, Y1^-1 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1, Y2^6 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 5, 29)(3, 27, 12, 36, 21, 45, 7, 31)(4, 28, 15, 39, 18, 42, 16, 40)(6, 30, 14, 38, 10, 34, 20, 44)(9, 33, 19, 43, 17, 41, 11, 35)(13, 37, 24, 48, 22, 46, 23, 47)(49, 73, 51, 75, 58, 82, 56, 80, 69, 93, 54, 78)(50, 74, 57, 81, 66, 90, 53, 77, 65, 89, 52, 76)(55, 79, 63, 87, 61, 85, 60, 84, 64, 88, 70, 94)(59, 83, 68, 92, 71, 95, 67, 91, 62, 86, 72, 96) L = (1, 52)(2, 58)(3, 61)(4, 55)(5, 54)(6, 67)(7, 49)(8, 66)(9, 71)(10, 59)(11, 50)(12, 56)(13, 62)(14, 51)(15, 57)(16, 65)(17, 72)(18, 60)(19, 53)(20, 69)(21, 70)(22, 68)(23, 63)(24, 64)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 6^8 ), ( 6^12 ) } Outer automorphisms :: reflexible Dual of E12.172 Graph:: bipartite v = 10 e = 48 f = 16 degree seq :: [ 8^6, 12^4 ] E12.178 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = SL(2,3) (small group id <24, 3>) Aut = GL(2,3) (small group id <48, 29>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-1, (R * Y1)^2, Y1^4, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, Y1^-2 * Y2^3, (R * Y2 * Y3^-1)^2, (Y1 * Y2)^3, Y2^-1 * Y1^-1 * R * Y2^2 * R * Y1^-1, (Y3 * Y2^-1)^6 ] Map:: non-degenerate R = (1, 25, 2, 26, 6, 30, 4, 28)(3, 27, 9, 33, 16, 40, 11, 35)(5, 29, 14, 38, 10, 34, 15, 39)(7, 31, 17, 41, 12, 36, 18, 42)(8, 32, 19, 43, 13, 37, 20, 44)(21, 45, 24, 48, 22, 46, 23, 47)(49, 73, 51, 75, 58, 82, 54, 78, 64, 88, 53, 77)(50, 74, 55, 79, 61, 85, 52, 76, 60, 84, 56, 80)(57, 81, 67, 91, 70, 94, 59, 83, 68, 92, 69, 93)(62, 86, 71, 95, 65, 89, 63, 87, 72, 96, 66, 90) L = (1, 50)(2, 54)(3, 57)(4, 49)(5, 62)(6, 52)(7, 65)(8, 67)(9, 64)(10, 63)(11, 51)(12, 66)(13, 68)(14, 58)(15, 53)(16, 59)(17, 60)(18, 55)(19, 61)(20, 56)(21, 72)(22, 71)(23, 69)(24, 70)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 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 E12.179 Graph:: bipartite v = 10 e = 48 f = 16 degree seq :: [ 8^6, 12^4 ] E12.179 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = SL(2,3) (small group id <24, 3>) Aut = GL(2,3) (small group id <48, 29>) |r| :: 2 Presentation :: [ Y2^2, R^2, Y3 * Y2 * Y3, Y1^-1 * Y2 * Y1 * Y2, Y1^3 * Y2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y1^-1)^3 ] Map:: non-degenerate R = (1, 25, 2, 26, 7, 31, 3, 27, 8, 32, 5, 29)(4, 28, 11, 35, 16, 40, 6, 30, 15, 39, 12, 36)(9, 33, 17, 41, 20, 44, 10, 34, 19, 43, 18, 42)(13, 37, 23, 47, 22, 46, 14, 38, 24, 48, 21, 45)(49, 73, 51, 75)(50, 74, 56, 80)(52, 76, 54, 78)(53, 77, 55, 79)(57, 81, 58, 82)(59, 83, 63, 87)(60, 84, 64, 88)(61, 85, 62, 86)(65, 89, 67, 91)(66, 90, 68, 92)(69, 93, 70, 94)(71, 95, 72, 96) L = (1, 52)(2, 57)(3, 54)(4, 51)(5, 61)(6, 49)(7, 62)(8, 58)(9, 56)(10, 50)(11, 69)(12, 67)(13, 55)(14, 53)(15, 70)(16, 65)(17, 60)(18, 71)(19, 64)(20, 72)(21, 63)(22, 59)(23, 68)(24, 66)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E12.178 Graph:: bipartite v = 16 e = 48 f = 10 degree seq :: [ 4^12, 12^4 ] E12.180 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C3 x D8 (small group id <24, 10>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^-1 * Y3 * Y2^-1 * Y3^-1, (R * Y3)^2, (R * Y1)^2, R * Y2 * R * Y2^-1, (Y2^-1 * Y1)^2, Y2^4, Y3 * Y1 * Y3^-1 * Y1, Y2^-2 * Y3^-3 * Y1, Y1 * Y2^-2 * Y3^3, Y3 * Y2 * Y1 * Y3^-1 * Y2^-1 * Y1 ] Map:: non-degenerate R = (1, 25, 2, 26)(3, 27, 9, 33)(4, 28, 8, 32)(5, 29, 7, 31)(6, 30, 10, 34)(11, 35, 18, 42)(12, 36, 21, 45)(13, 37, 23, 47)(14, 38, 19, 43)(15, 39, 22, 46)(16, 40, 20, 44)(17, 41, 24, 48)(49, 73, 51, 75, 59, 83, 53, 77)(50, 74, 55, 79, 66, 90, 57, 81)(52, 76, 62, 86, 72, 96, 60, 84)(54, 78, 64, 88, 70, 94, 61, 85)(56, 80, 69, 93, 65, 89, 67, 91)(58, 82, 71, 95, 63, 87, 68, 92) L = (1, 52)(2, 56)(3, 60)(4, 63)(5, 62)(6, 49)(7, 67)(8, 70)(9, 69)(10, 50)(11, 72)(12, 68)(13, 51)(14, 71)(15, 66)(16, 53)(17, 54)(18, 65)(19, 61)(20, 55)(21, 64)(22, 59)(23, 57)(24, 58)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 12^4 ), ( 12^8 ) } Outer automorphisms :: reflexible Dual of E12.195 Graph:: simple bipartite v = 18 e = 48 f = 8 degree seq :: [ 4^12, 8^6 ] E12.181 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C3 x D8 (small group id <24, 10>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, Y3^2, (R * Y3)^2, (Y1^-1 * Y3)^2, (R * Y1)^2, Y3 * Y2 * Y3 * Y2^-1, (Y2^-1 * R)^2, (Y1, Y2^-1), Y1^4, Y1^2 * Y2^-3 ] Map:: non-degenerate R = (1, 25, 2, 26, 7, 31, 5, 29)(3, 27, 8, 32, 17, 41, 13, 37)(4, 28, 14, 38, 18, 42, 9, 33)(6, 30, 10, 34, 11, 35, 16, 40)(12, 36, 22, 46, 24, 48, 19, 43)(15, 39, 23, 47, 21, 45, 20, 44)(49, 73, 51, 75, 59, 83, 55, 79, 65, 89, 54, 78)(50, 74, 56, 80, 64, 88, 53, 77, 61, 85, 58, 82)(52, 76, 60, 84, 69, 93, 66, 90, 72, 96, 63, 87)(57, 81, 67, 91, 71, 95, 62, 86, 70, 94, 68, 92) L = (1, 52)(2, 57)(3, 60)(4, 49)(5, 62)(6, 63)(7, 66)(8, 67)(9, 50)(10, 68)(11, 69)(12, 51)(13, 70)(14, 53)(15, 54)(16, 71)(17, 72)(18, 55)(19, 56)(20, 58)(21, 59)(22, 61)(23, 64)(24, 65)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 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 E12.190 Graph:: bipartite v = 10 e = 48 f = 16 degree seq :: [ 8^6, 12^4 ] E12.182 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = (C6 x C2) : C2 (small group id <24, 8>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, Y3^2, (R * Y3)^2, (Y1^-1 * Y3)^2, (R * Y1)^2, Y3 * Y2 * Y3 * Y2^-1, (Y2^-1 * R)^2, Y1^4, Y2 * Y1 * Y2 * Y1^-1, Y1^-2 * Y2^3 ] Map:: non-degenerate R = (1, 25, 2, 26, 7, 31, 5, 29)(3, 27, 10, 34, 17, 41, 13, 37)(4, 28, 14, 38, 18, 42, 9, 33)(6, 30, 8, 32, 11, 35, 16, 40)(12, 36, 22, 46, 24, 48, 20, 44)(15, 39, 23, 47, 21, 45, 19, 43)(49, 73, 51, 75, 59, 83, 55, 79, 65, 89, 54, 78)(50, 74, 56, 80, 61, 85, 53, 77, 64, 88, 58, 82)(52, 76, 60, 84, 69, 93, 66, 90, 72, 96, 63, 87)(57, 81, 67, 91, 70, 94, 62, 86, 71, 95, 68, 92) L = (1, 52)(2, 57)(3, 60)(4, 49)(5, 62)(6, 63)(7, 66)(8, 67)(9, 50)(10, 68)(11, 69)(12, 51)(13, 70)(14, 53)(15, 54)(16, 71)(17, 72)(18, 55)(19, 56)(20, 58)(21, 59)(22, 61)(23, 64)(24, 65)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 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 E12.192 Graph:: bipartite v = 10 e = 48 f = 16 degree seq :: [ 8^6, 12^4 ] E12.183 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = (C6 x C2) : C2 (small group id <24, 8>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, Y3^-2 * Y2^-2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y1 * Y2 * Y1^-1 * Y2, (Y2^-1 * R)^2, (Y3 * Y1^-1)^2, (Y3^-1 * Y1^-1)^2, Y1^4, Y1^-2 * Y3^2 * Y2^-1, Y2 * Y1^2 * Y3^-2, Y3^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y3^-1, Y2^-1 * Y1^2 * Y2^-2, Y1^-2 * Y3^-1 * Y2 * Y3^-1 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 5, 29)(3, 27, 11, 35, 18, 42, 15, 39)(4, 28, 17, 41, 16, 40, 12, 36)(6, 30, 9, 33, 13, 37, 20, 44)(7, 31, 21, 45, 19, 43, 10, 34)(14, 38, 24, 48, 23, 47, 22, 46)(49, 73, 51, 75, 61, 85, 56, 80, 66, 90, 54, 78)(50, 74, 57, 81, 63, 87, 53, 77, 68, 92, 59, 83)(52, 76, 62, 86, 55, 79, 64, 88, 71, 95, 67, 91)(58, 82, 70, 94, 60, 84, 69, 93, 72, 96, 65, 89) L = (1, 52)(2, 58)(3, 62)(4, 66)(5, 69)(6, 67)(7, 49)(8, 64)(9, 70)(10, 68)(11, 65)(12, 50)(13, 55)(14, 54)(15, 60)(16, 51)(17, 53)(18, 71)(19, 56)(20, 72)(21, 57)(22, 59)(23, 61)(24, 63)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 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 E12.194 Graph:: bipartite v = 10 e = 48 f = 16 degree seq :: [ 8^6, 12^4 ] E12.184 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C3 x D8 (small group id <24, 10>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, Y3^2, (Y1^-1 * Y3)^2, Y2 * Y1^-1 * Y2^-1 * Y1^-1, (R * Y1)^2, (R * Y3)^2, Y1^4, Y3 * Y2 * Y3 * Y2^-1, (Y2^-1 * R)^2, Y3 * Y2^-3 * Y1^-2, Y1^-1 * Y2 * Y3 * Y2^2 * Y1^-1, Y1^-1 * Y2^-3 * Y3 * Y1^-1, Y2^6 ] Map:: non-degenerate R = (1, 25, 2, 26, 7, 31, 5, 29)(3, 27, 11, 35, 18, 42, 8, 32)(4, 28, 14, 38, 19, 43, 9, 33)(6, 30, 16, 40, 20, 44, 10, 34)(12, 36, 21, 45, 15, 39, 23, 47)(13, 37, 22, 46, 17, 41, 24, 48)(49, 73, 51, 75, 60, 84, 67, 91, 65, 89, 54, 78)(50, 74, 56, 80, 69, 93, 62, 86, 72, 96, 58, 82)(52, 76, 61, 85, 68, 92, 55, 79, 66, 90, 63, 87)(53, 77, 59, 83, 71, 95, 57, 81, 70, 94, 64, 88) L = (1, 52)(2, 57)(3, 61)(4, 49)(5, 62)(6, 63)(7, 67)(8, 70)(9, 50)(10, 71)(11, 72)(12, 68)(13, 51)(14, 53)(15, 54)(16, 69)(17, 66)(18, 65)(19, 55)(20, 60)(21, 64)(22, 56)(23, 58)(24, 59)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 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 E12.189 Graph:: bipartite v = 10 e = 48 f = 16 degree seq :: [ 8^6, 12^4 ] E12.185 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = (C6 x C2) : C2 (small group id <24, 8>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, Y3^2, (Y2 * Y1^-1)^2, Y2^-1 * Y3 * Y2 * Y3, (R * Y1)^2, (R * Y3)^2, Y1^4, (Y1^-1 * Y2^-1)^2, (Y1^-1 * Y3)^2, (Y2^-1 * R)^2, Y3 * Y2^-3 * Y1^-2, Y1^-1 * Y2^-1 * Y1^2 * Y2 * Y1^-1, Y2^6 ] Map:: non-degenerate R = (1, 25, 2, 26, 7, 31, 5, 29)(3, 27, 11, 35, 18, 42, 10, 34)(4, 28, 14, 38, 19, 43, 9, 33)(6, 30, 16, 40, 20, 44, 8, 32)(12, 36, 24, 48, 15, 39, 22, 46)(13, 37, 23, 47, 17, 41, 21, 45)(49, 73, 51, 75, 60, 84, 67, 91, 65, 89, 54, 78)(50, 74, 56, 80, 69, 93, 62, 86, 72, 96, 58, 82)(52, 76, 61, 85, 68, 92, 55, 79, 66, 90, 63, 87)(53, 77, 64, 88, 71, 95, 57, 81, 70, 94, 59, 83) L = (1, 52)(2, 57)(3, 61)(4, 49)(5, 62)(6, 63)(7, 67)(8, 70)(9, 50)(10, 71)(11, 69)(12, 68)(13, 51)(14, 53)(15, 54)(16, 72)(17, 66)(18, 65)(19, 55)(20, 60)(21, 59)(22, 56)(23, 58)(24, 64)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 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 E12.191 Graph:: bipartite v = 10 e = 48 f = 16 degree seq :: [ 8^6, 12^4 ] E12.186 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C3 x D8 (small group id <24, 10>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, Y1^4, (R * Y1)^2, Y1^-1 * Y2 * Y1^-1 * Y2^-1, (R * Y2 * Y3^-1)^2, Y2^6, (Y3 * Y2^-1)^6 ] Map:: non-degenerate R = (1, 25, 2, 26, 6, 30, 4, 28)(3, 27, 9, 33, 13, 37, 7, 31)(5, 29, 11, 35, 14, 38, 8, 32)(10, 34, 15, 39, 20, 44, 17, 41)(12, 36, 16, 40, 21, 45, 19, 43)(18, 42, 23, 47, 24, 48, 22, 46)(49, 73, 51, 75, 58, 82, 66, 90, 60, 84, 53, 77)(50, 74, 55, 79, 63, 87, 70, 94, 64, 88, 56, 80)(52, 76, 57, 81, 65, 89, 71, 95, 67, 91, 59, 83)(54, 78, 61, 85, 68, 92, 72, 96, 69, 93, 62, 86) L = (1, 50)(2, 54)(3, 57)(4, 49)(5, 59)(6, 52)(7, 51)(8, 53)(9, 61)(10, 63)(11, 62)(12, 64)(13, 55)(14, 56)(15, 68)(16, 69)(17, 58)(18, 71)(19, 60)(20, 65)(21, 67)(22, 66)(23, 72)(24, 70)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 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 E12.188 Graph:: bipartite v = 10 e = 48 f = 16 degree seq :: [ 8^6, 12^4 ] E12.187 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = (C6 x C2) : C2 (small group id <24, 8>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, Y3^2 * Y2^2, Y3 * Y1^2 * Y2, Y2 * Y1 * Y3^-1 * Y1^-1, Y2 * Y3 * Y1^-2, (R * Y2)^2, Y1^4, (Y1^-1 * Y2^-1)^2, Y2^-1 * Y3^-1 * Y1^-2, (R * Y3)^2, (Y3 * Y1^-1)^2, (Y3^-1 * Y1^-1)^2, (Y2, Y3^-1), (R * Y1)^2, Y2^6 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 5, 29)(3, 27, 10, 34, 7, 31, 11, 35)(4, 28, 9, 33, 6, 30, 12, 36)(13, 37, 19, 43, 14, 38, 20, 44)(15, 39, 17, 41, 16, 40, 18, 42)(21, 45, 24, 48, 22, 46, 23, 47)(49, 73, 51, 75, 61, 85, 69, 93, 63, 87, 54, 78)(50, 74, 57, 81, 65, 89, 71, 95, 67, 91, 59, 83)(52, 76, 56, 80, 55, 79, 62, 86, 70, 94, 64, 88)(53, 77, 60, 84, 66, 90, 72, 96, 68, 92, 58, 82) L = (1, 52)(2, 58)(3, 56)(4, 63)(5, 59)(6, 64)(7, 49)(8, 54)(9, 53)(10, 67)(11, 68)(12, 50)(13, 55)(14, 51)(15, 70)(16, 69)(17, 60)(18, 57)(19, 72)(20, 71)(21, 62)(22, 61)(23, 66)(24, 65)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 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 E12.193 Graph:: bipartite v = 10 e = 48 f = 16 degree seq :: [ 8^6, 12^4 ] E12.188 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C3 x D8 (small group id <24, 10>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ Y2^2, R^2, Y2 * Y3^-2, (R * Y2)^2, Y2 * Y1^-1 * Y2 * Y1, (R * Y1)^2, (R * Y3)^2, Y3 * Y1 * Y3 * Y1^-1, Y1^6 ] Map:: non-degenerate R = (1, 25, 2, 26, 7, 31, 15, 39, 14, 38, 5, 29)(3, 27, 8, 32, 16, 40, 22, 46, 19, 43, 11, 35)(4, 28, 10, 34, 17, 41, 24, 48, 20, 44, 12, 36)(6, 30, 9, 33, 18, 42, 23, 47, 21, 45, 13, 37)(49, 73, 51, 75)(50, 74, 56, 80)(52, 76, 54, 78)(53, 77, 59, 83)(55, 79, 64, 88)(57, 81, 58, 82)(60, 84, 61, 85)(62, 86, 67, 91)(63, 87, 70, 94)(65, 89, 66, 90)(68, 92, 69, 93)(71, 95, 72, 96) L = (1, 52)(2, 57)(3, 54)(4, 51)(5, 61)(6, 49)(7, 65)(8, 58)(9, 56)(10, 50)(11, 60)(12, 53)(13, 59)(14, 68)(15, 71)(16, 66)(17, 64)(18, 55)(19, 69)(20, 67)(21, 62)(22, 72)(23, 70)(24, 63)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E12.186 Graph:: simple bipartite v = 16 e = 48 f = 10 degree seq :: [ 4^12, 12^4 ] E12.189 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C3 x D8 (small group id <24, 10>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (R * Y1)^2, (R * Y3)^2, Y1^-1 * Y3 * Y1 * Y3, Y2 * Y1 * Y2 * Y1^-1, (R * Y2 * Y3)^2, Y1^6, Y1 * Y2 * Y1^2 * Y3 * Y2 * Y3 ] Map:: non-degenerate R = (1, 25, 2, 26, 6, 30, 14, 38, 13, 37, 5, 29)(3, 27, 7, 31, 15, 39, 22, 46, 21, 45, 10, 34)(4, 28, 8, 32, 16, 40, 19, 43, 24, 48, 12, 36)(9, 33, 17, 41, 23, 47, 11, 35, 18, 42, 20, 44)(49, 73, 51, 75)(50, 74, 55, 79)(52, 76, 59, 83)(53, 77, 58, 82)(54, 78, 63, 87)(56, 80, 66, 90)(57, 81, 67, 91)(60, 84, 71, 95)(61, 85, 69, 93)(62, 86, 70, 94)(64, 88, 68, 92)(65, 89, 72, 96) L = (1, 52)(2, 56)(3, 57)(4, 49)(5, 60)(6, 64)(7, 65)(8, 50)(9, 51)(10, 68)(11, 70)(12, 53)(13, 72)(14, 67)(15, 71)(16, 54)(17, 55)(18, 69)(19, 62)(20, 58)(21, 66)(22, 59)(23, 63)(24, 61)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E12.184 Graph:: simple bipartite v = 16 e = 48 f = 10 degree seq :: [ 4^12, 12^4 ] E12.190 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C3 x D8 (small group id <24, 10>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y1^-1 * Y3 * Y1 * Y3, (R * Y1)^2, (R * Y3)^2, Y2 * Y3 * Y1^-2 * Y2 * Y1^-1, Y3 * Y2 * Y3 * Y1 * Y2 * Y1^-1, Y1^-1 * Y2 * Y3 * Y2 * Y1^-2, (R * Y2 * Y3)^2, Y1^6, (Y1 * Y2 * Y1^-1 * Y2)^2 ] Map:: non-degenerate R = (1, 25, 2, 26, 6, 30, 16, 40, 15, 39, 5, 29)(3, 27, 9, 33, 17, 41, 12, 36, 20, 44, 11, 35)(4, 28, 8, 32, 18, 42, 24, 48, 23, 47, 13, 37)(7, 31, 19, 43, 10, 34, 22, 46, 14, 38, 21, 45)(49, 73, 51, 75)(50, 74, 55, 79)(52, 76, 60, 84)(53, 77, 62, 86)(54, 78, 65, 89)(56, 80, 70, 94)(57, 81, 71, 95)(58, 82, 64, 88)(59, 83, 66, 90)(61, 85, 67, 91)(63, 87, 68, 92)(69, 93, 72, 96) L = (1, 52)(2, 56)(3, 58)(4, 49)(5, 61)(6, 66)(7, 68)(8, 50)(9, 70)(10, 51)(11, 67)(12, 69)(13, 53)(14, 65)(15, 71)(16, 72)(17, 62)(18, 54)(19, 59)(20, 55)(21, 60)(22, 57)(23, 63)(24, 64)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E12.181 Graph:: simple bipartite v = 16 e = 48 f = 10 degree seq :: [ 4^12, 12^4 ] E12.191 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = (C6 x C2) : C2 (small group id <24, 8>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (R * Y1)^2, (R * Y3)^2, Y1^-1 * Y3 * Y1 * Y3, (Y2 * Y1)^2, (R * Y2 * Y3)^2, Y1^6, Y1 * Y2 * Y1^-2 * Y3 * Y2 * Y3 ] Map:: non-degenerate R = (1, 25, 2, 26, 6, 30, 14, 38, 13, 37, 5, 29)(3, 27, 9, 33, 19, 43, 23, 47, 15, 39, 7, 31)(4, 28, 8, 32, 16, 40, 21, 45, 24, 48, 12, 36)(10, 34, 20, 44, 18, 42, 11, 35, 22, 46, 17, 41)(49, 73, 51, 75)(50, 74, 55, 79)(52, 76, 59, 83)(53, 77, 57, 81)(54, 78, 63, 87)(56, 80, 66, 90)(58, 82, 69, 93)(60, 84, 70, 94)(61, 85, 67, 91)(62, 86, 71, 95)(64, 88, 68, 92)(65, 89, 72, 96) L = (1, 52)(2, 56)(3, 58)(4, 49)(5, 60)(6, 64)(7, 65)(8, 50)(9, 68)(10, 51)(11, 71)(12, 53)(13, 72)(14, 69)(15, 70)(16, 54)(17, 55)(18, 67)(19, 66)(20, 57)(21, 62)(22, 63)(23, 59)(24, 61)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E12.185 Graph:: simple bipartite v = 16 e = 48 f = 10 degree seq :: [ 4^12, 12^4 ] E12.192 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = (C6 x C2) : C2 (small group id <24, 8>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y3 * Y1 * Y3 * Y1^-1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3)^2, Y2 * Y1 * Y2 * Y3 * Y1^-2, (Y2 * Y1^-2)^2, (Y2 * Y1^-1 * Y3)^2, Y2 * Y1 * R * Y2 * R * Y1, Y1^6, (Y3 * Y2)^4 ] Map:: non-degenerate R = (1, 25, 2, 26, 6, 30, 16, 40, 15, 39, 5, 29)(3, 27, 9, 33, 20, 44, 12, 36, 17, 41, 11, 35)(4, 28, 8, 32, 18, 42, 24, 48, 23, 47, 13, 37)(7, 31, 19, 43, 14, 38, 22, 46, 10, 34, 21, 45)(49, 73, 51, 75)(50, 74, 55, 79)(52, 76, 60, 84)(53, 77, 62, 86)(54, 78, 65, 89)(56, 80, 70, 94)(57, 81, 66, 90)(58, 82, 64, 88)(59, 83, 71, 95)(61, 85, 69, 93)(63, 87, 68, 92)(67, 91, 72, 96) L = (1, 52)(2, 56)(3, 58)(4, 49)(5, 61)(6, 66)(7, 68)(8, 50)(9, 69)(10, 51)(11, 70)(12, 67)(13, 53)(14, 65)(15, 71)(16, 72)(17, 62)(18, 54)(19, 60)(20, 55)(21, 57)(22, 59)(23, 63)(24, 64)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E12.182 Graph:: simple bipartite v = 16 e = 48 f = 10 degree seq :: [ 4^12, 12^4 ] E12.193 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = (C6 x C2) : C2 (small group id <24, 8>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ Y2^2, R^2, (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y3)^2, Y3^2 * Y1^-2, (Y2 * Y1)^2, R * Y2 * Y1 * R * Y2, Y2 * Y3 * Y2 * Y3^-1 * Y1^-1, Y3^2 * Y1^4, (Y3^-1 * Y1^-1)^6 ] Map:: non-degenerate R = (1, 25, 2, 26, 7, 31, 18, 42, 15, 39, 5, 29)(3, 27, 11, 35, 23, 47, 24, 48, 19, 43, 8, 32)(4, 28, 9, 33, 20, 44, 16, 40, 6, 30, 10, 34)(12, 36, 14, 38, 22, 46, 17, 41, 13, 37, 21, 45)(49, 73, 51, 75)(50, 74, 56, 80)(52, 76, 62, 86)(53, 77, 59, 83)(54, 78, 65, 89)(55, 79, 67, 91)(57, 81, 60, 84)(58, 82, 70, 94)(61, 85, 64, 88)(63, 87, 71, 95)(66, 90, 72, 96)(68, 92, 69, 93) L = (1, 52)(2, 57)(3, 60)(4, 55)(5, 58)(6, 49)(7, 68)(8, 69)(9, 66)(10, 50)(11, 62)(12, 71)(13, 51)(14, 72)(15, 54)(16, 53)(17, 56)(18, 64)(19, 61)(20, 63)(21, 59)(22, 67)(23, 70)(24, 65)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E12.187 Graph:: simple bipartite v = 16 e = 48 f = 10 degree seq :: [ 4^12, 12^4 ] E12.194 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = (C6 x C2) : C2 (small group id <24, 8>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ Y2^2, R^2, (Y3^-1 * Y1)^2, Y1^-1 * Y3^2 * Y1^-1, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1^-1), Y2 * Y3^-1 * Y2 * Y1^-1, (R * Y2 * Y3^-1)^2, Y3^2 * Y1^4, (Y1^-1 * Y3^-1)^6 ] Map:: non-degenerate R = (1, 25, 2, 26, 7, 31, 16, 40, 14, 38, 5, 29)(3, 27, 11, 35, 21, 45, 24, 48, 17, 41, 13, 37)(4, 28, 9, 33, 18, 42, 15, 39, 6, 30, 10, 34)(8, 32, 19, 43, 12, 36, 22, 46, 23, 47, 20, 44)(49, 73, 51, 75)(50, 74, 56, 80)(52, 76, 61, 85)(53, 77, 60, 84)(54, 78, 59, 83)(55, 79, 65, 89)(57, 81, 68, 92)(58, 82, 67, 91)(62, 86, 69, 93)(63, 87, 70, 94)(64, 88, 71, 95)(66, 90, 72, 96) L = (1, 52)(2, 57)(3, 60)(4, 55)(5, 58)(6, 49)(7, 66)(8, 51)(9, 64)(10, 50)(11, 70)(12, 69)(13, 67)(14, 54)(15, 53)(16, 63)(17, 56)(18, 62)(19, 59)(20, 61)(21, 71)(22, 72)(23, 65)(24, 68)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E12.183 Graph:: simple bipartite v = 16 e = 48 f = 10 degree seq :: [ 4^12, 12^4 ] E12.195 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C3 x D8 (small group id <24, 10>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, Y3^2 * Y2^-2, Y1^-2 * Y3^-2, (R * Y1)^2, (Y1^-1 * Y2^-1)^2, Y1^-2 * Y2^-2, (Y3^-1, Y2^-1), (Y1^-1, Y2), (R * Y3)^2, (R * Y2)^2, Y1 * Y3 * Y1 * Y3^-1 * Y2^-1, Y2 * Y1 * Y3^-1 * Y1 * Y3^-1, Y3^6, Y3^2 * Y2^4 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 22, 46, 13, 37, 5, 29)(3, 27, 9, 33, 6, 30, 11, 35, 23, 47, 15, 39)(4, 28, 17, 41, 7, 31, 21, 45, 24, 48, 18, 42)(10, 34, 14, 38, 12, 36, 16, 40, 19, 43, 20, 44)(49, 73, 51, 75, 61, 85, 71, 95, 56, 80, 54, 78)(50, 74, 57, 81, 53, 77, 63, 87, 70, 94, 59, 83)(52, 76, 62, 86, 72, 96, 68, 92, 55, 79, 64, 88)(58, 82, 69, 93, 67, 91, 65, 89, 60, 84, 66, 90) L = (1, 52)(2, 58)(3, 62)(4, 61)(5, 67)(6, 64)(7, 49)(8, 55)(9, 69)(10, 53)(11, 66)(12, 50)(13, 72)(14, 71)(15, 65)(16, 51)(17, 59)(18, 57)(19, 70)(20, 54)(21, 63)(22, 60)(23, 68)(24, 56)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E12.180 Graph:: bipartite v = 8 e = 48 f = 18 degree seq :: [ 12^8 ] E12.196 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 8, 8}) Quotient :: dipole Aut^+ = C3 : C8 (small group id <24, 1>) Aut = (C3 x D8) : C2 (small group id <48, 15>) |r| :: 2 Presentation :: [ R^2, Y1^3, Y1 * Y3^-2, (Y3^-1 * Y1^-1)^2, (R * Y3)^2, Y2^-1 * Y3 * Y2 * Y3, Y1 * Y2 * Y1 * Y2^-1, (R * Y1)^2, Y2 * Y3 * Y2^3 * Y1^-1, Y3^-1 * Y2^-1 * Y1 * Y3 * Y2 * Y1^-1, (R * Y2 * Y3^-1)^2 ] Map:: non-degenerate R = (1, 25, 2, 26, 5, 29)(3, 27, 11, 35, 8, 32)(4, 28, 9, 33, 7, 31)(6, 30, 16, 40, 10, 34)(12, 36, 19, 43, 23, 47)(13, 37, 20, 44, 14, 38)(15, 39, 17, 41, 21, 45)(18, 42, 22, 46, 24, 48)(49, 73, 51, 75, 60, 84, 69, 93, 57, 81, 68, 92, 66, 90, 54, 78)(50, 74, 56, 80, 67, 91, 65, 89, 55, 79, 61, 85, 70, 94, 58, 82)(52, 76, 62, 86, 72, 96, 64, 88, 53, 77, 59, 83, 71, 95, 63, 87) L = (1, 52)(2, 57)(3, 61)(4, 50)(5, 55)(6, 65)(7, 49)(8, 62)(9, 53)(10, 63)(11, 68)(12, 72)(13, 59)(14, 51)(15, 54)(16, 69)(17, 64)(18, 71)(19, 66)(20, 56)(21, 58)(22, 60)(23, 70)(24, 67)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) 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 ) } Outer automorphisms :: reflexible Dual of E12.197 Graph:: bipartite v = 11 e = 48 f = 15 degree seq :: [ 6^8, 16^3 ] E12.197 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 8, 8}) Quotient :: dipole Aut^+ = C3 : C8 (small group id <24, 1>) Aut = (C3 x D8) : C2 (small group id <48, 15>) |r| :: 2 Presentation :: [ Y2^2, R^2, Y3^-3 * Y2, (R * Y1)^2, (R * Y3)^2, Y1^-1 * Y3^-1 * Y1 * Y3^-1, (R * Y2)^2, Y2 * Y1 * Y2 * Y1^-1, Y2 * Y1^4 ] Map:: non-degenerate R = (1, 25, 2, 26, 7, 31, 12, 36, 3, 27, 8, 32, 16, 40, 5, 29)(4, 28, 10, 34, 17, 41, 21, 45, 11, 35, 20, 44, 23, 47, 14, 38)(6, 30, 9, 33, 18, 42, 22, 46, 13, 37, 19, 43, 24, 48, 15, 39)(49, 73, 51, 75)(50, 74, 56, 80)(52, 76, 59, 83)(53, 77, 60, 84)(54, 78, 61, 85)(55, 79, 64, 88)(57, 81, 67, 91)(58, 82, 68, 92)(62, 86, 69, 93)(63, 87, 70, 94)(65, 89, 71, 95)(66, 90, 72, 96) L = (1, 52)(2, 57)(3, 59)(4, 61)(5, 63)(6, 49)(7, 65)(8, 67)(9, 68)(10, 50)(11, 54)(12, 70)(13, 51)(14, 53)(15, 69)(16, 71)(17, 72)(18, 55)(19, 58)(20, 56)(21, 60)(22, 62)(23, 66)(24, 64)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 6, 16, 6, 16 ), ( 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16 ) } Outer automorphisms :: reflexible Dual of E12.196 Graph:: bipartite v = 15 e = 48 f = 11 degree seq :: [ 4^12, 16^3 ] E12.198 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = C3 : Q8 (small group id <24, 4>) Aut = (C12 x C2) : C2 (small group id <48, 37>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2 * Y1 * Y2, (R * Y1)^2, Y3 * Y1 * Y3^-1 * Y1, (R * Y3)^2, Y2 * Y3^-1 * Y2^-1 * Y3^-1, Y3^2 * Y2 * Y3^2 * Y2^-1, (R * Y2 * Y3^-1)^2, Y3^-6 * Y1 ] Map:: non-degenerate R = (1, 25, 2, 26)(3, 27, 5, 29)(4, 28, 7, 31)(6, 30, 8, 32)(9, 33, 13, 37)(10, 34, 12, 36)(11, 35, 15, 39)(14, 38, 16, 40)(17, 41, 21, 45)(18, 42, 20, 44)(19, 43, 22, 46)(23, 47, 24, 48)(49, 73, 51, 75, 50, 74, 53, 77)(52, 76, 58, 82, 55, 79, 60, 84)(54, 78, 57, 81, 56, 80, 61, 85)(59, 83, 66, 90, 63, 87, 68, 92)(62, 86, 65, 89, 64, 88, 69, 93)(67, 91, 72, 96, 70, 94, 71, 95) L = (1, 52)(2, 55)(3, 57)(4, 59)(5, 61)(6, 49)(7, 63)(8, 50)(9, 65)(10, 51)(11, 67)(12, 53)(13, 69)(14, 54)(15, 70)(16, 56)(17, 71)(18, 58)(19, 64)(20, 60)(21, 72)(22, 62)(23, 68)(24, 66)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24 ) } Outer automorphisms :: reflexible Dual of E12.199 Graph:: bipartite v = 18 e = 48 f = 8 degree seq :: [ 4^12, 8^6 ] E12.199 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = C3 : Q8 (small group id <24, 4>) Aut = (C12 x C2) : C2 (small group id <48, 37>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y2 * Y3^-1 * Y1^-1, Y2^-1 * Y3 * Y1^2, Y1^-2 * Y3 * Y2^-1, Y3 * Y1^-1 * Y2 * Y1^-1, (R * Y1)^2, Y3 * Y1 * Y3 * Y1^-1, Y1^-1 * Y2^-1 * Y3 * Y1^-1, (R * Y3)^2, (R * Y2)^2, Y2^-3 * Y3^-1 * Y2^-2, Y2^-3 * Y1^-1 * Y3^-1 * Y2^-2 * Y1^-1 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 5, 29)(3, 27, 11, 35, 4, 28, 12, 36)(6, 30, 9, 33, 7, 31, 10, 34)(13, 37, 19, 43, 14, 38, 20, 44)(15, 39, 17, 41, 16, 40, 18, 42)(21, 45, 24, 48, 22, 46, 23, 47)(49, 73, 51, 75, 61, 85, 69, 93, 64, 88, 55, 79, 56, 80, 52, 76, 62, 86, 70, 94, 63, 87, 54, 78)(50, 74, 57, 81, 65, 89, 71, 95, 68, 92, 60, 84, 53, 77, 58, 82, 66, 90, 72, 96, 67, 91, 59, 83) L = (1, 52)(2, 58)(3, 62)(4, 61)(5, 57)(6, 56)(7, 49)(8, 51)(9, 66)(10, 65)(11, 53)(12, 50)(13, 70)(14, 69)(15, 55)(16, 54)(17, 72)(18, 71)(19, 60)(20, 59)(21, 63)(22, 64)(23, 67)(24, 68)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) 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 ) } Outer automorphisms :: reflexible Dual of E12.198 Graph:: bipartite v = 8 e = 48 f = 18 degree seq :: [ 8^6, 24^2 ] E12.200 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 12}) Quotient :: dipole Aut^+ = C3 x D8 (small group id <24, 10>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^3, Y2 * Y3^-2, (Y2 * Y3)^2, Y1 * Y2^-1 * Y1 * Y2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1, Y1 * Y3^-1 * Y2^-1 * Y1 * Y3^-1 * Y2^-1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y2 ] Map:: non-degenerate R = (1, 25, 2, 26)(3, 27, 7, 31)(4, 28, 12, 36)(5, 29, 9, 33)(6, 30, 13, 37)(8, 32, 15, 39)(10, 34, 16, 40)(11, 35, 17, 41)(14, 38, 21, 45)(18, 42, 22, 46)(19, 43, 23, 47)(20, 44, 24, 48)(49, 73, 51, 75, 53, 77)(50, 74, 55, 79, 57, 81)(52, 76, 59, 83, 54, 78)(56, 80, 62, 86, 58, 82)(60, 84, 65, 89, 61, 85)(63, 87, 69, 93, 64, 88)(66, 90, 68, 92, 67, 91)(70, 94, 72, 96, 71, 95) L = (1, 52)(2, 56)(3, 59)(4, 51)(5, 54)(6, 49)(7, 62)(8, 55)(9, 58)(10, 50)(11, 53)(12, 66)(13, 67)(14, 57)(15, 70)(16, 71)(17, 68)(18, 65)(19, 60)(20, 61)(21, 72)(22, 69)(23, 63)(24, 64)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 12, 24, 12, 24 ), ( 12, 24, 12, 24, 12, 24 ) } Outer automorphisms :: reflexible Dual of E12.203 Graph:: simple bipartite v = 20 e = 48 f = 6 degree seq :: [ 4^12, 6^8 ] E12.201 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 12}) Quotient :: dipole Aut^+ = C3 x D8 (small group id <24, 10>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, Y1^3, Y1 * Y3^-2, Y2 * Y1 * Y2, (R * Y3)^2, (R * Y1)^2, (Y1 * Y2^-1)^2, (Y3^-1 * Y1^-1)^2, Y2^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1, (R * Y2 * Y3^-1)^2, (Y2^-1, Y3^-1, Y2^-1), (Y3 * Y2^-1)^12 ] Map:: non-degenerate R = (1, 25, 2, 26, 5, 29)(3, 27, 6, 30, 9, 33)(4, 28, 8, 32, 7, 31)(10, 34, 14, 38, 11, 35)(12, 36, 13, 37, 15, 39)(16, 40, 17, 41, 18, 42)(19, 43, 21, 45, 20, 44)(22, 46, 24, 48, 23, 47)(49, 73, 51, 75, 53, 77, 57, 81, 50, 74, 54, 78)(52, 76, 60, 84, 55, 79, 63, 87, 56, 80, 61, 85)(58, 82, 64, 88, 59, 83, 66, 90, 62, 86, 65, 89)(67, 91, 70, 94, 68, 92, 71, 95, 69, 93, 72, 96) L = (1, 52)(2, 56)(3, 58)(4, 50)(5, 55)(6, 62)(7, 49)(8, 53)(9, 59)(10, 54)(11, 51)(12, 67)(13, 69)(14, 57)(15, 68)(16, 70)(17, 72)(18, 71)(19, 61)(20, 60)(21, 63)(22, 65)(23, 64)(24, 66)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 4, 24, 4, 24, 4, 24 ), ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E12.202 Graph:: bipartite v = 12 e = 48 f = 14 degree seq :: [ 6^8, 12^4 ] E12.202 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 12}) Quotient :: dipole Aut^+ = C3 x D8 (small group id <24, 10>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ Y2^2, R^2, Y3^-3 * Y2, Y3^-1 * Y2 * Y3 * Y2, (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y3 * Y1 * Y2 * Y1, Y3 * Y2 * Y1^-4 ] Map:: non-degenerate R = (1, 25, 2, 26, 7, 31, 17, 41, 12, 36, 21, 45, 24, 48, 23, 47, 13, 37, 22, 46, 16, 40, 5, 29)(3, 27, 11, 35, 18, 42, 10, 34, 4, 28, 14, 38, 19, 43, 8, 32, 6, 30, 15, 39, 20, 44, 9, 33)(49, 73, 51, 75)(50, 74, 56, 80)(52, 76, 60, 84)(53, 77, 62, 86)(54, 78, 61, 85)(55, 79, 66, 90)(57, 81, 69, 93)(58, 82, 70, 94)(59, 83, 71, 95)(63, 87, 65, 89)(64, 88, 68, 92)(67, 91, 72, 96) L = (1, 52)(2, 57)(3, 60)(4, 61)(5, 63)(6, 49)(7, 67)(8, 69)(9, 70)(10, 50)(11, 53)(12, 54)(13, 51)(14, 65)(15, 71)(16, 66)(17, 59)(18, 72)(19, 64)(20, 55)(21, 58)(22, 56)(23, 62)(24, 68)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) 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 ) } Outer automorphisms :: reflexible Dual of E12.201 Graph:: bipartite v = 14 e = 48 f = 12 degree seq :: [ 4^12, 24^2 ] E12.203 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 12}) Quotient :: dipole Aut^+ = C3 x D8 (small group id <24, 10>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1, (Y2^-1 * Y1)^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, (R * Y2 * Y3^-1)^2, Y2 * Y1^2 * Y2^-1 * Y1^-2, Y2^-3 * Y1^-2 * Y2^-1, Y2^-1 * Y1^-3 * Y2^-1 * Y1^-1, (Y2^-2 * R)^2, (Y3^-1 * Y1^-1)^3 ] Map:: non-degenerate R = (1, 25, 2, 26, 6, 30, 16, 40, 12, 36, 4, 28)(3, 27, 9, 33, 17, 41, 13, 37, 21, 45, 8, 32)(5, 29, 11, 35, 18, 42, 7, 31, 19, 43, 14, 38)(10, 34, 20, 44, 15, 39, 22, 46, 24, 48, 23, 47)(49, 73, 51, 75, 58, 82, 67, 91, 60, 84, 69, 93, 72, 96, 66, 90, 54, 78, 65, 89, 63, 87, 53, 77)(50, 74, 55, 79, 68, 92, 61, 85, 52, 76, 59, 83, 71, 95, 57, 81, 64, 88, 62, 86, 70, 94, 56, 80) L = (1, 50)(2, 54)(3, 57)(4, 49)(5, 59)(6, 64)(7, 67)(8, 51)(9, 65)(10, 68)(11, 66)(12, 52)(13, 69)(14, 53)(15, 70)(16, 60)(17, 61)(18, 55)(19, 62)(20, 63)(21, 56)(22, 72)(23, 58)(24, 71)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) 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 ) } Outer automorphisms :: reflexible Dual of E12.200 Graph:: bipartite v = 6 e = 48 f = 20 degree seq :: [ 12^4, 24^2 ] E12.204 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 12}) Quotient :: dipole Aut^+ = C3 x D8 (small group id <24, 10>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2 * Y3, (R * Y3)^2, (R * Y1)^2, Y2 * Y3^-1 * Y1 * Y3 * Y2^-1 * Y1, Y3 * Y1 * Y3^-2 * Y1 * Y2^-1, (Y3 * Y2^-1)^3, Y2^6, Y3 * Y1 * Y2 * Y1 * Y2 * Y1 * Y3 * Y1, Y2 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y2^-1 * Y1, (Y1 * Y3^-1 * Y2 * Y3^-1)^4 ] Map:: non-degenerate R = (1, 25, 2, 26)(3, 27, 7, 31)(4, 28, 9, 33)(5, 29, 11, 35)(6, 30, 13, 37)(8, 32, 12, 36)(10, 34, 14, 38)(15, 39, 19, 43)(16, 40, 20, 44)(17, 41, 23, 47)(18, 42, 22, 46)(21, 45, 24, 48)(49, 73, 51, 75, 56, 80, 65, 89, 58, 82, 52, 76)(50, 74, 53, 77, 60, 84, 69, 93, 62, 86, 54, 78)(55, 79, 63, 87, 71, 95, 66, 90, 57, 81, 64, 88)(59, 83, 67, 91, 72, 96, 70, 94, 61, 85, 68, 92) L = (1, 52)(2, 54)(3, 49)(4, 58)(5, 50)(6, 62)(7, 64)(8, 51)(9, 66)(10, 65)(11, 68)(12, 53)(13, 70)(14, 69)(15, 55)(16, 57)(17, 56)(18, 71)(19, 59)(20, 61)(21, 60)(22, 72)(23, 63)(24, 67)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 6, 24, 6, 24 ), ( 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24 ) } Outer automorphisms :: reflexible Dual of E12.205 Graph:: bipartite v = 16 e = 48 f = 10 degree seq :: [ 4^12, 12^4 ] E12.205 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 12}) Quotient :: dipole Aut^+ = C3 x D8 (small group id <24, 10>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ R^2, Y1^3, Y1 * Y3^-2, (Y1^-1, Y2), (R * Y1)^2, (R * Y3)^2, (Y2 * Y3)^2, (Y3^-1 * Y1^-1)^2, Y1 * Y2^-4, R * Y2 * Y1 * R * Y2^-1, Y3^-1 * Y1^-1 * Y2 * Y3^-1 * Y2 ] Map:: non-degenerate R = (1, 25, 2, 26, 5, 29)(3, 27, 8, 32, 13, 37)(4, 28, 9, 33, 7, 31)(6, 30, 10, 34, 17, 41)(11, 35, 21, 45, 19, 43)(12, 36, 16, 40, 14, 38)(15, 39, 18, 42, 20, 44)(22, 46, 24, 48, 23, 47)(49, 73, 51, 75, 59, 83, 58, 82, 50, 74, 56, 80, 69, 93, 65, 89, 53, 77, 61, 85, 67, 91, 54, 78)(52, 76, 63, 87, 70, 94, 62, 86, 57, 81, 66, 90, 72, 96, 60, 84, 55, 79, 68, 92, 71, 95, 64, 88) L = (1, 52)(2, 57)(3, 60)(4, 50)(5, 55)(6, 66)(7, 49)(8, 64)(9, 53)(10, 68)(11, 70)(12, 56)(13, 62)(14, 51)(15, 54)(16, 61)(17, 63)(18, 58)(19, 71)(20, 65)(21, 72)(22, 69)(23, 59)(24, 67)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) 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 ) } Outer automorphisms :: reflexible Dual of E12.204 Graph:: bipartite v = 10 e = 48 f = 16 degree seq :: [ 6^8, 24^2 ] E12.206 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 24, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ 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, Y2^12 * Y1, (Y3 * Y2^-1)^24 ] Map:: R = (1, 25, 2, 26)(3, 27, 5, 29)(4, 28, 6, 30)(7, 31, 9, 33)(8, 32, 10, 34)(11, 35, 13, 37)(12, 36, 14, 38)(15, 39, 17, 41)(16, 40, 18, 42)(19, 43, 21, 45)(20, 44, 22, 46)(23, 47, 24, 48)(49, 73, 51, 75, 55, 79, 59, 83, 63, 87, 67, 91, 71, 95, 70, 94, 66, 90, 62, 86, 58, 82, 54, 78, 50, 74, 53, 77, 57, 81, 61, 85, 65, 89, 69, 93, 72, 96, 68, 92, 64, 88, 60, 84, 56, 80, 52, 76) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) 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 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 13 e = 48 f = 13 degree seq :: [ 4^12, 48 ] E12.207 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {25, 25, 25}) Quotient :: edge Aut^+ = C25 (small group id <25, 1>) Aut = D50 (small group id <50, 1>) |r| :: 2 Presentation :: [ F^2, T2 * T1^-2, (F * T2)^2, (F * T1)^2, T1 * T2^12, (T2^-1 * T1^-1)^25 ] Map:: non-degenerate R = (1, 3, 7, 11, 15, 19, 23, 24, 20, 16, 12, 8, 4, 2, 6, 10, 14, 18, 22, 25, 21, 17, 13, 9, 5)(26, 27, 28, 31, 32, 35, 36, 39, 40, 43, 44, 47, 48, 50, 49, 46, 45, 42, 41, 38, 37, 34, 33, 30, 29) L = (1, 26)(2, 27)(3, 28)(4, 29)(5, 30)(6, 31)(7, 32)(8, 33)(9, 34)(10, 35)(11, 36)(12, 37)(13, 38)(14, 39)(15, 40)(16, 41)(17, 42)(18, 43)(19, 44)(20, 45)(21, 46)(22, 47)(23, 48)(24, 49)(25, 50) local type(s) :: { ( 50^25 ) } Outer automorphisms :: reflexible Dual of E12.217 Transitivity :: ET+ Graph:: bipartite v = 2 e = 25 f = 1 degree seq :: [ 25^2 ] E12.208 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {25, 25, 25}) Quotient :: edge Aut^+ = C25 (small group id <25, 1>) Aut = D50 (small group id <50, 1>) |r| :: 2 Presentation :: [ F^2, T2 * T1^2, (F * T1)^2, (F * T2)^2, T1 * T2^-12 ] Map:: non-degenerate R = (1, 3, 7, 11, 15, 19, 23, 22, 18, 14, 10, 6, 2, 4, 8, 12, 16, 20, 24, 25, 21, 17, 13, 9, 5)(26, 27, 30, 31, 34, 35, 38, 39, 42, 43, 46, 47, 50, 48, 49, 44, 45, 40, 41, 36, 37, 32, 33, 28, 29) L = (1, 26)(2, 27)(3, 28)(4, 29)(5, 30)(6, 31)(7, 32)(8, 33)(9, 34)(10, 35)(11, 36)(12, 37)(13, 38)(14, 39)(15, 40)(16, 41)(17, 42)(18, 43)(19, 44)(20, 45)(21, 46)(22, 47)(23, 48)(24, 49)(25, 50) local type(s) :: { ( 50^25 ) } Outer automorphisms :: reflexible Dual of E12.214 Transitivity :: ET+ Graph:: bipartite v = 2 e = 25 f = 1 degree seq :: [ 25^2 ] E12.209 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {25, 25, 25}) Quotient :: edge Aut^+ = C25 (small group id <25, 1>) Aut = D50 (small group id <50, 1>) |r| :: 2 Presentation :: [ F^2, T2 * T1^-3, (F * T1)^2, (F * T2)^2, T1 * T2^8, (T2^-1 * T1^-1)^25 ] Map:: non-degenerate R = (1, 3, 9, 15, 21, 22, 16, 10, 4, 6, 12, 18, 24, 25, 20, 14, 8, 2, 7, 13, 19, 23, 17, 11, 5)(26, 27, 31, 28, 32, 37, 34, 38, 43, 40, 44, 49, 46, 48, 50, 47, 42, 45, 41, 36, 39, 35, 30, 33, 29) L = (1, 26)(2, 27)(3, 28)(4, 29)(5, 30)(6, 31)(7, 32)(8, 33)(9, 34)(10, 35)(11, 36)(12, 37)(13, 38)(14, 39)(15, 40)(16, 41)(17, 42)(18, 43)(19, 44)(20, 45)(21, 46)(22, 47)(23, 48)(24, 49)(25, 50) local type(s) :: { ( 50^25 ) } Outer automorphisms :: reflexible Dual of E12.218 Transitivity :: ET+ Graph:: bipartite v = 2 e = 25 f = 1 degree seq :: [ 25^2 ] E12.210 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {25, 25, 25}) Quotient :: edge Aut^+ = C25 (small group id <25, 1>) Aut = D50 (small group id <50, 1>) |r| :: 2 Presentation :: [ F^2, T1^-2 * T2^-1 * T1^-1, (F * T1)^2, (F * T2)^2, T1 * T2^-8 ] Map:: non-degenerate R = (1, 3, 9, 15, 21, 20, 14, 8, 2, 7, 13, 19, 25, 24, 18, 12, 6, 4, 10, 16, 22, 23, 17, 11, 5)(26, 27, 31, 30, 33, 37, 36, 39, 43, 42, 45, 49, 48, 46, 50, 47, 40, 44, 41, 34, 38, 35, 28, 32, 29) L = (1, 26)(2, 27)(3, 28)(4, 29)(5, 30)(6, 31)(7, 32)(8, 33)(9, 34)(10, 35)(11, 36)(12, 37)(13, 38)(14, 39)(15, 40)(16, 41)(17, 42)(18, 43)(19, 44)(20, 45)(21, 46)(22, 47)(23, 48)(24, 49)(25, 50) local type(s) :: { ( 50^25 ) } Outer automorphisms :: reflexible Dual of E12.215 Transitivity :: ET+ Graph:: bipartite v = 2 e = 25 f = 1 degree seq :: [ 25^2 ] E12.211 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {25, 25, 25}) Quotient :: edge Aut^+ = C25 (small group id <25, 1>) Aut = D50 (small group id <50, 1>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^4 * T2, T2^2 * T1^-1 * T2^4, T2 * T1^-2 * T2^2 * T1 * T2^3 ] Map:: non-degenerate R = (1, 3, 9, 17, 16, 8, 2, 7, 15, 23, 22, 14, 6, 11, 19, 24, 25, 20, 12, 4, 10, 18, 21, 13, 5)(26, 27, 31, 37, 30, 33, 39, 45, 38, 41, 47, 50, 46, 42, 48, 49, 43, 34, 40, 44, 35, 28, 32, 36, 29) L = (1, 26)(2, 27)(3, 28)(4, 29)(5, 30)(6, 31)(7, 32)(8, 33)(9, 34)(10, 35)(11, 36)(12, 37)(13, 38)(14, 39)(15, 40)(16, 41)(17, 42)(18, 43)(19, 44)(20, 45)(21, 46)(22, 47)(23, 48)(24, 49)(25, 50) local type(s) :: { ( 50^25 ) } Outer automorphisms :: reflexible Dual of E12.216 Transitivity :: ET+ Graph:: bipartite v = 2 e = 25 f = 1 degree seq :: [ 25^2 ] E12.212 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {25, 25, 25}) Quotient :: edge Aut^+ = C25 (small group id <25, 1>) Aut = D50 (small group id <50, 1>) |r| :: 2 Presentation :: [ F^2, (T2, T1), (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^3 * T2 * T1 * T2^2, T1 * T2^-1 * T1 * T2^-3 * T1 ] Map:: non-degenerate R = (1, 3, 9, 19, 14, 24, 12, 4, 10, 20, 16, 6, 15, 23, 11, 21, 18, 8, 2, 7, 17, 22, 25, 13, 5)(26, 27, 31, 39, 50, 46, 35, 28, 32, 40, 49, 38, 43, 45, 34, 42, 48, 37, 30, 33, 41, 44, 47, 36, 29) L = (1, 26)(2, 27)(3, 28)(4, 29)(5, 30)(6, 31)(7, 32)(8, 33)(9, 34)(10, 35)(11, 36)(12, 37)(13, 38)(14, 39)(15, 40)(16, 41)(17, 42)(18, 43)(19, 44)(20, 45)(21, 46)(22, 47)(23, 48)(24, 49)(25, 50) local type(s) :: { ( 50^25 ) } Outer automorphisms :: reflexible Dual of E12.219 Transitivity :: ET+ Graph:: bipartite v = 2 e = 25 f = 1 degree seq :: [ 25^2 ] E12.213 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {25, 25, 25}) Quotient :: edge Aut^+ = C25 (small group id <25, 1>) Aut = D50 (small group id <50, 1>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^-1 * T2^-1 * T1^-1 * T2^-2, T1^5 * T2^-1 * T1 * T2^-1 * T1, T1^-1 * T2^11 ] Map:: non-degenerate R = (1, 3, 9, 11, 18, 23, 25, 21, 14, 16, 8, 2, 7, 12, 4, 10, 17, 19, 24, 20, 22, 15, 6, 13, 5)(26, 27, 31, 39, 45, 48, 42, 34, 37, 30, 33, 40, 46, 49, 43, 35, 28, 32, 38, 41, 47, 50, 44, 36, 29) L = (1, 26)(2, 27)(3, 28)(4, 29)(5, 30)(6, 31)(7, 32)(8, 33)(9, 34)(10, 35)(11, 36)(12, 37)(13, 38)(14, 39)(15, 40)(16, 41)(17, 42)(18, 43)(19, 44)(20, 45)(21, 46)(22, 47)(23, 48)(24, 49)(25, 50) local type(s) :: { ( 50^25 ) } Outer automorphisms :: reflexible Dual of E12.220 Transitivity :: ET+ Graph:: bipartite v = 2 e = 25 f = 1 degree seq :: [ 25^2 ] E12.214 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {25, 25, 25}) Quotient :: loop Aut^+ = C25 (small group id <25, 1>) Aut = D50 (small group id <50, 1>) |r| :: 2 Presentation :: [ F^2, T2 * T1^-1, (F * T1)^2, (F * T2)^2, T2^25, T1^25, (T2^-1 * T1^-1)^25 ] Map:: non-degenerate R = (1, 26, 2, 27, 4, 29, 6, 31, 8, 33, 10, 35, 12, 37, 14, 39, 16, 41, 18, 43, 20, 45, 22, 47, 24, 49, 25, 50, 23, 48, 21, 46, 19, 44, 17, 42, 15, 40, 13, 38, 11, 36, 9, 34, 7, 32, 5, 30, 3, 28) L = (1, 27)(2, 29)(3, 26)(4, 31)(5, 28)(6, 33)(7, 30)(8, 35)(9, 32)(10, 37)(11, 34)(12, 39)(13, 36)(14, 41)(15, 38)(16, 43)(17, 40)(18, 45)(19, 42)(20, 47)(21, 44)(22, 49)(23, 46)(24, 50)(25, 48) local type(s) :: { ( 25^50 ) } Outer automorphisms :: reflexible Dual of E12.208 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 25 f = 2 degree seq :: [ 50 ] E12.215 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {25, 25, 25}) Quotient :: loop Aut^+ = C25 (small group id <25, 1>) Aut = D50 (small group id <50, 1>) |r| :: 2 Presentation :: [ F^2, T2 * T1^-2, (F * T2)^2, (F * T1)^2, T1 * T2^12, (T2^-1 * T1^-1)^25 ] Map:: non-degenerate R = (1, 26, 3, 28, 7, 32, 11, 36, 15, 40, 19, 44, 23, 48, 24, 49, 20, 45, 16, 41, 12, 37, 8, 33, 4, 29, 2, 27, 6, 31, 10, 35, 14, 39, 18, 43, 22, 47, 25, 50, 21, 46, 17, 42, 13, 38, 9, 34, 5, 30) L = (1, 27)(2, 28)(3, 31)(4, 26)(5, 29)(6, 32)(7, 35)(8, 30)(9, 33)(10, 36)(11, 39)(12, 34)(13, 37)(14, 40)(15, 43)(16, 38)(17, 41)(18, 44)(19, 47)(20, 42)(21, 45)(22, 48)(23, 50)(24, 46)(25, 49) local type(s) :: { ( 25^50 ) } Outer automorphisms :: reflexible Dual of E12.210 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 25 f = 2 degree seq :: [ 50 ] E12.216 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {25, 25, 25}) Quotient :: loop Aut^+ = C25 (small group id <25, 1>) Aut = D50 (small group id <50, 1>) |r| :: 2 Presentation :: [ F^2, T2 * T1^-3, (F * T1)^2, (F * T2)^2, T1 * T2^8, (T2^-1 * T1^-1)^25 ] Map:: non-degenerate R = (1, 26, 3, 28, 9, 34, 15, 40, 21, 46, 22, 47, 16, 41, 10, 35, 4, 29, 6, 31, 12, 37, 18, 43, 24, 49, 25, 50, 20, 45, 14, 39, 8, 33, 2, 27, 7, 32, 13, 38, 19, 44, 23, 48, 17, 42, 11, 36, 5, 30) L = (1, 27)(2, 31)(3, 32)(4, 26)(5, 33)(6, 28)(7, 37)(8, 29)(9, 38)(10, 30)(11, 39)(12, 34)(13, 43)(14, 35)(15, 44)(16, 36)(17, 45)(18, 40)(19, 49)(20, 41)(21, 48)(22, 42)(23, 50)(24, 46)(25, 47) local type(s) :: { ( 25^50 ) } Outer automorphisms :: reflexible Dual of E12.211 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 25 f = 2 degree seq :: [ 50 ] E12.217 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {25, 25, 25}) Quotient :: loop Aut^+ = C25 (small group id <25, 1>) Aut = D50 (small group id <50, 1>) |r| :: 2 Presentation :: [ F^2, T1^-2 * T2^-1 * T1^-1, (F * T1)^2, (F * T2)^2, T1 * T2^-8 ] Map:: non-degenerate R = (1, 26, 3, 28, 9, 34, 15, 40, 21, 46, 20, 45, 14, 39, 8, 33, 2, 27, 7, 32, 13, 38, 19, 44, 25, 50, 24, 49, 18, 43, 12, 37, 6, 31, 4, 29, 10, 35, 16, 41, 22, 47, 23, 48, 17, 42, 11, 36, 5, 30) L = (1, 27)(2, 31)(3, 32)(4, 26)(5, 33)(6, 30)(7, 29)(8, 37)(9, 38)(10, 28)(11, 39)(12, 36)(13, 35)(14, 43)(15, 44)(16, 34)(17, 45)(18, 42)(19, 41)(20, 49)(21, 50)(22, 40)(23, 46)(24, 48)(25, 47) local type(s) :: { ( 25^50 ) } Outer automorphisms :: reflexible Dual of E12.207 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 25 f = 2 degree seq :: [ 50 ] E12.218 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {25, 25, 25}) Quotient :: loop Aut^+ = C25 (small group id <25, 1>) Aut = D50 (small group id <50, 1>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^4 * T2, T2^2 * T1^-1 * T2^4, T2 * T1^-2 * T2^2 * T1 * T2^3 ] Map:: non-degenerate R = (1, 26, 3, 28, 9, 34, 17, 42, 16, 41, 8, 33, 2, 27, 7, 32, 15, 40, 23, 48, 22, 47, 14, 39, 6, 31, 11, 36, 19, 44, 24, 49, 25, 50, 20, 45, 12, 37, 4, 29, 10, 35, 18, 43, 21, 46, 13, 38, 5, 30) L = (1, 27)(2, 31)(3, 32)(4, 26)(5, 33)(6, 37)(7, 36)(8, 39)(9, 40)(10, 28)(11, 29)(12, 30)(13, 41)(14, 45)(15, 44)(16, 47)(17, 48)(18, 34)(19, 35)(20, 38)(21, 42)(22, 50)(23, 49)(24, 43)(25, 46) local type(s) :: { ( 25^50 ) } Outer automorphisms :: reflexible Dual of E12.209 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 25 f = 2 degree seq :: [ 50 ] E12.219 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {25, 25, 25}) Quotient :: loop Aut^+ = C25 (small group id <25, 1>) Aut = D50 (small group id <50, 1>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2 * T1 * T2^3, T1^-1 * T2 * T1^-5, T1^2 * T2 * T1^2 * T2 * T1^3 * T2 ] Map:: non-degenerate R = (1, 26, 3, 28, 9, 34, 12, 37, 4, 29, 10, 35, 18, 43, 21, 46, 11, 36, 19, 44, 24, 49, 25, 50, 20, 45, 14, 39, 22, 47, 23, 48, 16, 41, 6, 31, 15, 40, 17, 42, 8, 33, 2, 27, 7, 32, 13, 38, 5, 30) L = (1, 27)(2, 31)(3, 32)(4, 26)(5, 33)(6, 39)(7, 40)(8, 41)(9, 38)(10, 28)(11, 29)(12, 30)(13, 42)(14, 44)(15, 47)(16, 45)(17, 48)(18, 34)(19, 35)(20, 36)(21, 37)(22, 49)(23, 50)(24, 43)(25, 46) local type(s) :: { ( 25^50 ) } Outer automorphisms :: reflexible Dual of E12.212 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 25 f = 2 degree seq :: [ 50 ] E12.220 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {25, 25, 25}) Quotient :: loop Aut^+ = C25 (small group id <25, 1>) Aut = D50 (small group id <50, 1>) |r| :: 2 Presentation :: [ F^2, T2^3 * T1, (T2^-1, T1), (F * T1)^2, (F * T2)^2, T1^-8 * T2 ] Map:: non-degenerate R = (1, 26, 3, 28, 9, 34, 4, 29, 10, 35, 15, 40, 11, 36, 16, 41, 21, 46, 17, 42, 22, 47, 25, 50, 23, 48, 18, 43, 24, 49, 20, 45, 12, 37, 19, 44, 14, 39, 6, 31, 13, 38, 8, 33, 2, 27, 7, 32, 5, 30) L = (1, 27)(2, 31)(3, 32)(4, 26)(5, 33)(6, 37)(7, 38)(8, 39)(9, 30)(10, 28)(11, 29)(12, 43)(13, 44)(14, 45)(15, 34)(16, 35)(17, 36)(18, 47)(19, 49)(20, 48)(21, 40)(22, 41)(23, 42)(24, 50)(25, 46) local type(s) :: { ( 25^50 ) } Outer automorphisms :: reflexible Dual of E12.213 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 25 f = 2 degree seq :: [ 50 ] E12.221 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {25, 25, 25}) Quotient :: dipole Aut^+ = C25 (small group id <25, 1>) Aut = D50 (small group id <50, 1>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y2^2 * Y3^-1, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y3^12 * Y2, Y2 * Y1^-12 ] Map:: R = (1, 26, 2, 27, 6, 31, 10, 35, 14, 39, 18, 43, 22, 47, 24, 49, 20, 45, 16, 41, 12, 37, 8, 33, 3, 28, 5, 30, 7, 32, 11, 36, 15, 40, 19, 44, 23, 48, 25, 50, 21, 46, 17, 42, 13, 38, 9, 34, 4, 29)(51, 76, 53, 78, 54, 79, 58, 83, 59, 84, 62, 87, 63, 88, 66, 91, 67, 92, 70, 95, 71, 96, 74, 99, 75, 100, 72, 97, 73, 98, 68, 93, 69, 94, 64, 89, 65, 90, 60, 85, 61, 86, 56, 81, 57, 82, 52, 77, 55, 80) L = (1, 54)(2, 51)(3, 58)(4, 59)(5, 53)(6, 52)(7, 55)(8, 62)(9, 63)(10, 56)(11, 57)(12, 66)(13, 67)(14, 60)(15, 61)(16, 70)(17, 71)(18, 64)(19, 65)(20, 74)(21, 75)(22, 68)(23, 69)(24, 72)(25, 73)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100) local type(s) :: { ( 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50 ) } Outer automorphisms :: reflexible Dual of E12.228 Graph:: bipartite v = 2 e = 50 f = 26 degree seq :: [ 50^2 ] E12.222 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {25, 25, 25}) Quotient :: dipole Aut^+ = C25 (small group id <25, 1>) Aut = D50 (small group id <50, 1>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y1 * Y2^-2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y2, Y3^-1), Y3^5 * Y2^-1 * Y1^-5 * Y3 * Y1^-1, Y3^-1 * Y1^7 * 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 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * 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:: R = (1, 26, 2, 27, 6, 31, 10, 35, 14, 39, 18, 43, 22, 47, 25, 50, 21, 46, 17, 42, 13, 38, 9, 34, 5, 30, 3, 28, 7, 32, 11, 36, 15, 40, 19, 44, 23, 48, 24, 49, 20, 45, 16, 41, 12, 37, 8, 33, 4, 29)(51, 76, 53, 78, 52, 77, 57, 82, 56, 81, 61, 86, 60, 85, 65, 90, 64, 89, 69, 94, 68, 93, 73, 98, 72, 97, 74, 99, 75, 100, 70, 95, 71, 96, 66, 91, 67, 92, 62, 87, 63, 88, 58, 83, 59, 84, 54, 79, 55, 80) L = (1, 54)(2, 51)(3, 55)(4, 58)(5, 59)(6, 52)(7, 53)(8, 62)(9, 63)(10, 56)(11, 57)(12, 66)(13, 67)(14, 60)(15, 61)(16, 70)(17, 71)(18, 64)(19, 65)(20, 74)(21, 75)(22, 68)(23, 69)(24, 73)(25, 72)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100) local type(s) :: { ( 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50 ) } Outer automorphisms :: reflexible Dual of E12.233 Graph:: bipartite v = 2 e = 50 f = 26 degree seq :: [ 50^2 ] E12.223 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {25, 25, 25}) Quotient :: dipole Aut^+ = C25 (small group id <25, 1>) Aut = D50 (small group id <50, 1>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y2^-1 * Y1^-1 * Y2^-2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y1^-1, Y2), (Y3^-1, Y2^-1), Y1^-1 * Y2 * Y3^6 * Y1^-1, Y2 * Y3^2 * Y2 * Y1^-1 * Y3^-3 * Y2 * Y3^3 * 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 ] Map:: R = (1, 26, 2, 27, 6, 31, 12, 37, 18, 43, 22, 47, 16, 41, 10, 35, 3, 28, 7, 32, 13, 38, 19, 44, 24, 49, 25, 50, 21, 46, 15, 40, 9, 34, 5, 30, 8, 33, 14, 39, 20, 45, 23, 48, 17, 42, 11, 36, 4, 29)(51, 76, 53, 78, 59, 84, 54, 79, 60, 85, 65, 90, 61, 86, 66, 91, 71, 96, 67, 92, 72, 97, 75, 100, 73, 98, 68, 93, 74, 99, 70, 95, 62, 87, 69, 94, 64, 89, 56, 81, 63, 88, 58, 83, 52, 77, 57, 82, 55, 80) L = (1, 54)(2, 51)(3, 60)(4, 61)(5, 59)(6, 52)(7, 53)(8, 55)(9, 65)(10, 66)(11, 67)(12, 56)(13, 57)(14, 58)(15, 71)(16, 72)(17, 73)(18, 62)(19, 63)(20, 64)(21, 75)(22, 68)(23, 70)(24, 69)(25, 74)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100) local type(s) :: { ( 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50 ) } Outer automorphisms :: reflexible Dual of E12.234 Graph:: bipartite v = 2 e = 50 f = 26 degree seq :: [ 50^2 ] E12.224 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {25, 25, 25}) Quotient :: dipole Aut^+ = C25 (small group id <25, 1>) Aut = D50 (small group id <50, 1>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, Y1 * Y2^-3, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y3^-1, Y2^-1), Y2 * Y1^8, 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 ] Map:: R = (1, 26, 2, 27, 6, 31, 12, 37, 18, 43, 23, 48, 17, 42, 11, 36, 5, 30, 8, 33, 14, 39, 20, 45, 24, 49, 25, 50, 21, 46, 15, 40, 9, 34, 3, 28, 7, 32, 13, 38, 19, 44, 22, 47, 16, 41, 10, 35, 4, 29)(51, 76, 53, 78, 58, 83, 52, 77, 57, 82, 64, 89, 56, 81, 63, 88, 70, 95, 62, 87, 69, 94, 74, 99, 68, 93, 72, 97, 75, 100, 73, 98, 66, 91, 71, 96, 67, 92, 60, 85, 65, 90, 61, 86, 54, 79, 59, 84, 55, 80) L = (1, 54)(2, 51)(3, 59)(4, 60)(5, 61)(6, 52)(7, 53)(8, 55)(9, 65)(10, 66)(11, 67)(12, 56)(13, 57)(14, 58)(15, 71)(16, 72)(17, 73)(18, 62)(19, 63)(20, 64)(21, 75)(22, 69)(23, 68)(24, 70)(25, 74)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100) local type(s) :: { ( 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50 ) } Outer automorphisms :: reflexible Dual of E12.231 Graph:: bipartite v = 2 e = 50 f = 26 degree seq :: [ 50^2 ] E12.225 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {25, 25, 25}) Quotient :: dipole Aut^+ = C25 (small group id <25, 1>) Aut = D50 (small group id <50, 1>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y1)^2, (R * Y3)^2, (Y2, Y1^-1), (R * Y2)^2, (Y3^-1, Y2^-1), Y2^2 * Y3^-1 * Y2^2, Y1^4 * Y2^-1 * Y3^-2, Y3 * Y2 * Y3^5, Y3^-2 * Y2 * Y3^-2 * Y2 * Y3^-3 * Y2 ] Map:: R = (1, 26, 2, 27, 6, 31, 14, 39, 19, 44, 10, 35, 3, 28, 7, 32, 15, 40, 22, 47, 24, 49, 18, 43, 9, 34, 13, 38, 17, 42, 23, 48, 25, 50, 21, 46, 12, 37, 5, 30, 8, 33, 16, 41, 20, 45, 11, 36, 4, 29)(51, 76, 53, 78, 59, 84, 62, 87, 54, 79, 60, 85, 68, 93, 71, 96, 61, 86, 69, 94, 74, 99, 75, 100, 70, 95, 64, 89, 72, 97, 73, 98, 66, 91, 56, 81, 65, 90, 67, 92, 58, 83, 52, 77, 57, 82, 63, 88, 55, 80) L = (1, 54)(2, 51)(3, 60)(4, 61)(5, 62)(6, 52)(7, 53)(8, 55)(9, 68)(10, 69)(11, 70)(12, 71)(13, 59)(14, 56)(15, 57)(16, 58)(17, 63)(18, 74)(19, 64)(20, 66)(21, 75)(22, 65)(23, 67)(24, 72)(25, 73)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100) local type(s) :: { ( 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50 ) } Outer automorphisms :: reflexible Dual of E12.232 Graph:: bipartite v = 2 e = 50 f = 26 degree seq :: [ 50^2 ] E12.226 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {25, 25, 25}) Quotient :: dipole Aut^+ = C25 (small group id <25, 1>) Aut = D50 (small group id <50, 1>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y3^-1 * Y2^-1 * Y1^-1 * Y2, Y3^-1 * Y2^-1 * Y1^-1 * Y2, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), (R * Y2)^2, (Y3^-1, Y2^-1), Y1^2 * Y2^-1 * Y3^2 * Y2, Y2 * Y1 * Y2 * Y1 * Y2 * Y3^-2, Y3^-1 * Y2^-1 * Y1 * Y2^-2 * Y3^-1 * Y2^-1, Y1 * Y2 * Y1^2 * Y2^2 * Y3^-1, Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * 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 * Y1 ] Map:: R = (1, 26, 2, 27, 6, 31, 14, 39, 25, 50, 21, 46, 10, 35, 3, 28, 7, 32, 15, 40, 24, 49, 13, 38, 18, 43, 20, 45, 9, 34, 17, 42, 23, 48, 12, 37, 5, 30, 8, 33, 16, 41, 19, 44, 22, 47, 11, 36, 4, 29)(51, 76, 53, 78, 59, 84, 69, 94, 64, 89, 74, 99, 62, 87, 54, 79, 60, 85, 70, 95, 66, 91, 56, 81, 65, 90, 73, 98, 61, 86, 71, 96, 68, 93, 58, 83, 52, 77, 57, 82, 67, 92, 72, 97, 75, 100, 63, 88, 55, 80) L = (1, 54)(2, 51)(3, 60)(4, 61)(5, 62)(6, 52)(7, 53)(8, 55)(9, 70)(10, 71)(11, 72)(12, 73)(13, 74)(14, 56)(15, 57)(16, 58)(17, 59)(18, 63)(19, 66)(20, 68)(21, 75)(22, 69)(23, 67)(24, 65)(25, 64)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100) local type(s) :: { ( 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50 ) } Outer automorphisms :: reflexible Dual of E12.230 Graph:: bipartite v = 2 e = 50 f = 26 degree seq :: [ 50^2 ] E12.227 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {25, 25, 25}) Quotient :: dipole Aut^+ = C25 (small group id <25, 1>) Aut = D50 (small group id <50, 1>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, (R * Y1)^2, (Y2^-1, Y1^-1), (R * Y3)^2, (R * Y2)^2, (Y3^-1, Y2^-1), Y1 * Y2 * Y1 * Y2 * Y3^-1, Y2^-7 * Y1^2, Y1^25, 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, Y2^82 * Y1^-1 * Y3 ] Map:: R = (1, 26, 2, 27, 6, 31, 13, 38, 15, 40, 20, 45, 25, 50, 23, 48, 16, 41, 18, 43, 10, 35, 3, 28, 7, 32, 12, 37, 5, 30, 8, 33, 14, 39, 19, 44, 21, 46, 22, 47, 24, 49, 17, 42, 9, 34, 11, 36, 4, 29)(51, 76, 53, 78, 59, 84, 66, 91, 72, 97, 70, 95, 64, 89, 56, 81, 62, 87, 54, 79, 60, 85, 67, 92, 73, 98, 71, 96, 65, 90, 58, 83, 52, 77, 57, 82, 61, 86, 68, 93, 74, 99, 75, 100, 69, 94, 63, 88, 55, 80) L = (1, 54)(2, 51)(3, 60)(4, 61)(5, 62)(6, 52)(7, 53)(8, 55)(9, 67)(10, 68)(11, 59)(12, 57)(13, 56)(14, 58)(15, 63)(16, 73)(17, 74)(18, 66)(19, 64)(20, 65)(21, 69)(22, 71)(23, 75)(24, 72)(25, 70)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100) local type(s) :: { ( 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50 ) } Outer automorphisms :: reflexible Dual of E12.229 Graph:: bipartite v = 2 e = 50 f = 26 degree seq :: [ 50^2 ] E12.228 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {25, 25, 25}) Quotient :: dipole Aut^+ = C25 (small group id <25, 1>) Aut = D50 (small group id <50, 1>) |r| :: 2 Presentation :: [ Y1, R^2, Y3 * Y2, (R * Y1)^2, R * Y2 * R * Y3^-1, Y2^25, (Y3^-1 * Y1^-1)^25, (Y3 * Y2^-1)^25 ] Map:: R = (1, 26)(2, 27)(3, 28)(4, 29)(5, 30)(6, 31)(7, 32)(8, 33)(9, 34)(10, 35)(11, 36)(12, 37)(13, 38)(14, 39)(15, 40)(16, 41)(17, 42)(18, 43)(19, 44)(20, 45)(21, 46)(22, 47)(23, 48)(24, 49)(25, 50)(51, 76, 52, 77, 54, 79, 56, 81, 58, 83, 60, 85, 62, 87, 64, 89, 66, 91, 68, 93, 70, 95, 72, 97, 74, 99, 75, 100, 73, 98, 71, 96, 69, 94, 67, 92, 65, 90, 63, 88, 61, 86, 59, 84, 57, 82, 55, 80, 53, 78) L = (1, 53)(2, 51)(3, 55)(4, 52)(5, 57)(6, 54)(7, 59)(8, 56)(9, 61)(10, 58)(11, 63)(12, 60)(13, 65)(14, 62)(15, 67)(16, 64)(17, 69)(18, 66)(19, 71)(20, 68)(21, 73)(22, 70)(23, 75)(24, 72)(25, 74)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100) local type(s) :: { ( 50, 50 ), ( 50^50 ) } Outer automorphisms :: reflexible Dual of E12.221 Graph:: bipartite v = 26 e = 50 f = 2 degree seq :: [ 2^25, 50 ] E12.229 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {25, 25, 25}) Quotient :: dipole Aut^+ = C25 (small group id <25, 1>) Aut = D50 (small group id <50, 1>) |r| :: 2 Presentation :: [ Y1, R^2, Y2 * Y3 * Y2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2 * Y3^-12, (Y3 * Y2^-1)^25, (Y3^-1 * Y1^-1)^25 ] Map:: R = (1, 26)(2, 27)(3, 28)(4, 29)(5, 30)(6, 31)(7, 32)(8, 33)(9, 34)(10, 35)(11, 36)(12, 37)(13, 38)(14, 39)(15, 40)(16, 41)(17, 42)(18, 43)(19, 44)(20, 45)(21, 46)(22, 47)(23, 48)(24, 49)(25, 50)(51, 76, 52, 77, 55, 80, 56, 81, 59, 84, 60, 85, 63, 88, 64, 89, 67, 92, 68, 93, 71, 96, 72, 97, 75, 100, 73, 98, 74, 99, 69, 94, 70, 95, 65, 90, 66, 91, 61, 86, 62, 87, 57, 82, 58, 83, 53, 78, 54, 79) L = (1, 53)(2, 54)(3, 57)(4, 58)(5, 51)(6, 52)(7, 61)(8, 62)(9, 55)(10, 56)(11, 65)(12, 66)(13, 59)(14, 60)(15, 69)(16, 70)(17, 63)(18, 64)(19, 73)(20, 74)(21, 67)(22, 68)(23, 72)(24, 75)(25, 71)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100) local type(s) :: { ( 50, 50 ), ( 50^50 ) } Outer automorphisms :: reflexible Dual of E12.227 Graph:: bipartite v = 26 e = 50 f = 2 degree seq :: [ 2^25, 50 ] E12.230 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {25, 25, 25}) Quotient :: dipole Aut^+ = C25 (small group id <25, 1>) Aut = D50 (small group id <50, 1>) |r| :: 2 Presentation :: [ Y1, R^2, Y2^-1 * Y3^-1 * Y2^-2, (Y2^-1 * R)^2, (R * Y3)^2, (R * Y1)^2, (Y2, Y3^-1), 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^-1 * Y1^-1)^25 ] Map:: R = (1, 26)(2, 27)(3, 28)(4, 29)(5, 30)(6, 31)(7, 32)(8, 33)(9, 34)(10, 35)(11, 36)(12, 37)(13, 38)(14, 39)(15, 40)(16, 41)(17, 42)(18, 43)(19, 44)(20, 45)(21, 46)(22, 47)(23, 48)(24, 49)(25, 50)(51, 76, 52, 77, 56, 81, 55, 80, 58, 83, 62, 87, 61, 86, 64, 89, 68, 93, 67, 92, 70, 95, 74, 99, 73, 98, 71, 96, 75, 100, 72, 97, 65, 90, 69, 94, 66, 91, 59, 84, 63, 88, 60, 85, 53, 78, 57, 82, 54, 79) L = (1, 53)(2, 57)(3, 59)(4, 60)(5, 51)(6, 54)(7, 63)(8, 52)(9, 65)(10, 66)(11, 55)(12, 56)(13, 69)(14, 58)(15, 71)(16, 72)(17, 61)(18, 62)(19, 75)(20, 64)(21, 70)(22, 73)(23, 67)(24, 68)(25, 74)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100) local type(s) :: { ( 50, 50 ), ( 50^50 ) } Outer automorphisms :: reflexible Dual of E12.226 Graph:: bipartite v = 26 e = 50 f = 2 degree seq :: [ 2^25, 50 ] E12.231 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {25, 25, 25}) Quotient :: dipole Aut^+ = C25 (small group id <25, 1>) Aut = D50 (small group id <50, 1>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y2, Y3^-1), Y3^-4 * Y2, Y2^3 * Y3 * Y2^3, Y2 * Y3^2 * Y2^2 * Y3^-1 * Y2^3, (Y3^-1 * Y1^-1)^25 ] Map:: R = (1, 26)(2, 27)(3, 28)(4, 29)(5, 30)(6, 31)(7, 32)(8, 33)(9, 34)(10, 35)(11, 36)(12, 37)(13, 38)(14, 39)(15, 40)(16, 41)(17, 42)(18, 43)(19, 44)(20, 45)(21, 46)(22, 47)(23, 48)(24, 49)(25, 50)(51, 76, 52, 77, 56, 81, 64, 89, 70, 95, 62, 87, 55, 80, 58, 83, 66, 91, 72, 97, 75, 100, 71, 96, 63, 88, 59, 84, 67, 92, 73, 98, 74, 99, 68, 93, 60, 85, 53, 78, 57, 82, 65, 90, 69, 94, 61, 86, 54, 79) L = (1, 53)(2, 57)(3, 59)(4, 60)(5, 51)(6, 65)(7, 67)(8, 52)(9, 58)(10, 63)(11, 68)(12, 54)(13, 55)(14, 69)(15, 73)(16, 56)(17, 66)(18, 71)(19, 74)(20, 61)(21, 62)(22, 64)(23, 72)(24, 75)(25, 70)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100) local type(s) :: { ( 50, 50 ), ( 50^50 ) } Outer automorphisms :: reflexible Dual of E12.224 Graph:: bipartite v = 26 e = 50 f = 2 degree seq :: [ 2^25, 50 ] E12.232 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {25, 25, 25}) Quotient :: dipole Aut^+ = C25 (small group id <25, 1>) Aut = D50 (small group id <50, 1>) |r| :: 2 Presentation :: [ Y1, R^2, (Y3^-1, Y2), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2^4 * Y3^-3, Y2 * Y3 * Y2 * Y3^3 * Y2, (Y3^-1 * Y1^-1)^25 ] Map:: R = (1, 26)(2, 27)(3, 28)(4, 29)(5, 30)(6, 31)(7, 32)(8, 33)(9, 34)(10, 35)(11, 36)(12, 37)(13, 38)(14, 39)(15, 40)(16, 41)(17, 42)(18, 43)(19, 44)(20, 45)(21, 46)(22, 47)(23, 48)(24, 49)(25, 50)(51, 76, 52, 77, 56, 81, 64, 89, 69, 94, 73, 98, 62, 87, 55, 80, 58, 83, 66, 91, 70, 95, 59, 84, 67, 92, 74, 99, 63, 88, 68, 93, 71, 96, 60, 85, 53, 78, 57, 82, 65, 90, 75, 100, 72, 97, 61, 86, 54, 79) L = (1, 53)(2, 57)(3, 59)(4, 60)(5, 51)(6, 65)(7, 67)(8, 52)(9, 69)(10, 70)(11, 71)(12, 54)(13, 55)(14, 75)(15, 74)(16, 56)(17, 73)(18, 58)(19, 72)(20, 64)(21, 66)(22, 68)(23, 61)(24, 62)(25, 63)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100) local type(s) :: { ( 50, 50 ), ( 50^50 ) } Outer automorphisms :: reflexible Dual of E12.225 Graph:: bipartite v = 26 e = 50 f = 2 degree seq :: [ 2^25, 50 ] E12.233 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {25, 25, 25}) Quotient :: dipole Aut^+ = C25 (small group id <25, 1>) Aut = D50 (small group id <50, 1>) |r| :: 2 Presentation :: [ Y1, R^2, Y3^-3 * Y2, (Y3, Y2), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2^3 * Y3 * Y2^5, (Y3^-1 * Y1^-1)^25 ] Map:: R = (1, 26)(2, 27)(3, 28)(4, 29)(5, 30)(6, 31)(7, 32)(8, 33)(9, 34)(10, 35)(11, 36)(12, 37)(13, 38)(14, 39)(15, 40)(16, 41)(17, 42)(18, 43)(19, 44)(20, 45)(21, 46)(22, 47)(23, 48)(24, 49)(25, 50)(51, 76, 52, 77, 56, 81, 62, 87, 68, 93, 73, 98, 67, 92, 61, 86, 55, 80, 58, 83, 64, 89, 70, 95, 74, 99, 75, 100, 71, 96, 65, 90, 59, 84, 53, 78, 57, 82, 63, 88, 69, 94, 72, 97, 66, 91, 60, 85, 54, 79) L = (1, 53)(2, 57)(3, 58)(4, 59)(5, 51)(6, 63)(7, 64)(8, 52)(9, 55)(10, 65)(11, 54)(12, 69)(13, 70)(14, 56)(15, 61)(16, 71)(17, 60)(18, 72)(19, 74)(20, 62)(21, 67)(22, 75)(23, 66)(24, 68)(25, 73)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100) local type(s) :: { ( 50, 50 ), ( 50^50 ) } Outer automorphisms :: reflexible Dual of E12.222 Graph:: bipartite v = 26 e = 50 f = 2 degree seq :: [ 2^25, 50 ] E12.234 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {25, 25, 25}) Quotient :: dipole Aut^+ = C25 (small group id <25, 1>) Aut = D50 (small group id <50, 1>) |r| :: 2 Presentation :: [ Y1, R^2, (Y2^-1, Y3^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y2, Y3^-1), Y2 * Y3^-1 * Y2 * Y3^-1 * Y2, Y3^5 * Y2 * Y3 * Y2 * Y3, (Y3^-1 * Y1^-1)^25 ] Map:: R = (1, 26)(2, 27)(3, 28)(4, 29)(5, 30)(6, 31)(7, 32)(8, 33)(9, 34)(10, 35)(11, 36)(12, 37)(13, 38)(14, 39)(15, 40)(16, 41)(17, 42)(18, 43)(19, 44)(20, 45)(21, 46)(22, 47)(23, 48)(24, 49)(25, 50)(51, 76, 52, 77, 56, 81, 59, 84, 65, 90, 70, 95, 72, 97, 74, 99, 69, 94, 67, 92, 62, 87, 55, 80, 58, 83, 60, 85, 53, 78, 57, 82, 64, 89, 66, 91, 71, 96, 75, 100, 73, 98, 68, 93, 63, 88, 61, 86, 54, 79) L = (1, 53)(2, 57)(3, 59)(4, 60)(5, 51)(6, 64)(7, 65)(8, 52)(9, 66)(10, 56)(11, 58)(12, 54)(13, 55)(14, 70)(15, 71)(16, 72)(17, 61)(18, 62)(19, 63)(20, 75)(21, 74)(22, 73)(23, 67)(24, 68)(25, 69)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100) local type(s) :: { ( 50, 50 ), ( 50^50 ) } Outer automorphisms :: reflexible Dual of E12.223 Graph:: bipartite v = 26 e = 50 f = 2 degree seq :: [ 2^25, 50 ] E12.235 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 13, 13}) Quotient :: halfedge^2 Aut^+ = D26 (small group id <26, 1>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y2 * Y3, (R * Y1)^2, R * Y3 * R * Y2, Y1^-1 * Y3 * Y1^-1 * Y2, Y1^13 ] Map:: R = (1, 28, 2, 31, 5, 35, 9, 39, 13, 43, 17, 47, 21, 50, 24, 46, 20, 42, 16, 38, 12, 34, 8, 30, 4, 27)(3, 33, 7, 37, 11, 41, 15, 45, 19, 49, 23, 52, 26, 51, 25, 48, 22, 44, 18, 40, 14, 36, 10, 32, 6, 29) L = (1, 3)(2, 6)(4, 7)(5, 10)(8, 11)(9, 14)(12, 15)(13, 18)(16, 19)(17, 22)(20, 23)(21, 25)(24, 26)(27, 29)(28, 32)(30, 33)(31, 36)(34, 37)(35, 40)(38, 41)(39, 44)(42, 45)(43, 48)(46, 49)(47, 51)(50, 52) local type(s) :: { ( 26^26 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 26 f = 2 degree seq :: [ 26^2 ] E12.236 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 13, 13}) Quotient :: halfedge^2 Aut^+ = D26 (small group id <26, 1>) Aut = D52 (small group id <52, 4>) |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 * Y2 * Y1^-2 * Y3 * Y1, Y1^-1 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3, Y1 * Y2 * Y3 * Y2 * Y1^-1 * Y3 * Y2 * Y1^-1 * Y3 * Y2 * Y1^-1 * Y3 * Y2 * Y1^-1 * Y3 * Y1^2 ] Map:: non-degenerate R = (1, 28, 2, 32, 6, 40, 14, 38, 12, 44, 18, 50, 24, 52, 26, 46, 20, 36, 10, 43, 17, 39, 13, 31, 5, 27)(3, 35, 9, 45, 19, 51, 25, 47, 21, 48, 22, 49, 23, 42, 16, 34, 8, 30, 4, 37, 11, 41, 15, 33, 7, 29) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 15)(8, 18)(10, 21)(11, 14)(13, 19)(16, 24)(17, 25)(20, 22)(23, 26)(27, 30)(28, 34)(29, 36)(31, 37)(32, 42)(33, 43)(35, 46)(38, 48)(39, 41)(40, 49)(44, 47)(45, 52)(50, 51) local type(s) :: { ( 26^26 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 26 f = 2 degree seq :: [ 26^2 ] E12.237 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 13, 13}) Quotient :: halfedge^2 Aut^+ = D26 (small group id <26, 1>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (Y3 * Y1^-1)^2, R * Y3 * R * Y2, (R * Y1)^2, (Y2 * Y1^-1)^2, Y1 * Y3 * Y1^-2 * Y2 * Y1, Y2 * Y3 * Y2 * Y3 * Y1 * Y2 * Y3, Y2 * Y1^-2 * Y3 * Y2 * Y1^-2 * Y3 * Y2 * Y1^-2 * Y3 * Y2 * Y1^-2 * Y3 * Y2 * Y1^-2 * Y3 * Y2 * Y3 * Y2 * Y1^-1 * Y3 ] Map:: non-degenerate R = (1, 28, 2, 32, 6, 40, 14, 36, 10, 43, 17, 50, 24, 52, 26, 47, 21, 38, 12, 44, 18, 39, 13, 31, 5, 27)(3, 35, 9, 42, 16, 34, 8, 30, 4, 37, 11, 46, 20, 51, 25, 48, 22, 45, 19, 49, 23, 41, 15, 33, 7, 29) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 15)(8, 18)(10, 19)(11, 21)(13, 16)(14, 23)(17, 22)(20, 26)(24, 25)(27, 30)(28, 34)(29, 36)(31, 37)(32, 42)(33, 43)(35, 40)(38, 48)(39, 46)(41, 50)(44, 51)(45, 47)(49, 52) local type(s) :: { ( 26^26 ) } Outer automorphisms :: reflexible Dual of E12.238 Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 26 f = 2 degree seq :: [ 26^2 ] E12.238 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 13, 13}) Quotient :: halfedge^2 Aut^+ = D26 (small group id <26, 1>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (Y3 * Y1^-1)^2, R * Y3 * R * Y2, (R * Y1)^2, (Y2 * Y1^-1)^2, Y2 * Y3 * Y2 * Y3 * Y1^3, Y1^3 * Y3 * Y1^-2 * Y2, Y1 * Y2 * Y1^-1 * Y3 * Y2 * Y1^-1 * Y3 ] Map:: non-degenerate R = (1, 28, 2, 32, 6, 40, 14, 46, 20, 36, 10, 43, 17, 49, 23, 38, 12, 44, 18, 51, 25, 39, 13, 31, 5, 27)(3, 35, 9, 45, 19, 42, 16, 34, 8, 30, 4, 37, 11, 48, 22, 47, 21, 52, 26, 50, 24, 41, 15, 33, 7, 29) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 15)(8, 18)(10, 21)(11, 23)(13, 19)(14, 24)(16, 25)(17, 22)(20, 26)(27, 30)(28, 34)(29, 36)(31, 37)(32, 42)(33, 43)(35, 46)(38, 50)(39, 48)(40, 45)(41, 49)(44, 52)(47, 51) local type(s) :: { ( 26^26 ) } Outer automorphisms :: reflexible Dual of E12.237 Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 26 f = 2 degree seq :: [ 26^2 ] E12.239 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 13, 13}) Quotient :: halfedge^2 Aut^+ = D26 (small group id <26, 1>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (Y1 * Y2)^2, R * Y3 * R * Y2, (Y3 * Y1^-1)^2, (R * Y1)^2, Y1^2 * Y2 * Y1^-3 * Y3, Y1^2 * Y3 * Y1^-1 * Y2 * Y3 * Y2 ] Map:: non-degenerate R = (1, 28, 2, 32, 6, 40, 14, 49, 23, 38, 12, 44, 18, 46, 20, 36, 10, 43, 17, 51, 25, 39, 13, 31, 5, 27)(3, 35, 9, 45, 19, 50, 24, 52, 26, 47, 21, 42, 16, 34, 8, 30, 4, 37, 11, 48, 22, 41, 15, 33, 7, 29) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 15)(8, 18)(10, 21)(11, 23)(13, 19)(14, 22)(16, 20)(17, 26)(24, 25)(27, 30)(28, 34)(29, 36)(31, 37)(32, 42)(33, 43)(35, 46)(38, 50)(39, 48)(40, 47)(41, 51)(44, 45)(49, 52) local type(s) :: { ( 26^26 ) } Outer automorphisms :: reflexible Dual of E12.240 Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 26 f = 2 degree seq :: [ 26^2 ] E12.240 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 13, 13}) Quotient :: halfedge^2 Aut^+ = D26 (small group id <26, 1>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y1 * Y2 * Y3, Y2 * Y1^-1 * Y3, R * Y2 * R * Y3, (R * Y1)^2, Y1^13 ] Map:: non-degenerate R = (1, 28, 2, 32, 6, 36, 10, 40, 14, 44, 18, 48, 22, 51, 25, 47, 21, 43, 17, 39, 13, 35, 9, 31, 5, 27)(3, 34, 8, 38, 12, 42, 16, 46, 20, 50, 24, 52, 26, 49, 23, 45, 19, 41, 15, 37, 11, 33, 7, 30, 4, 29) L = (1, 3)(2, 4)(5, 8)(6, 7)(9, 12)(10, 11)(13, 16)(14, 15)(17, 20)(18, 19)(21, 24)(22, 23)(25, 26)(27, 30)(28, 33)(29, 31)(32, 37)(34, 35)(36, 41)(38, 39)(40, 45)(42, 43)(44, 49)(46, 47)(48, 52)(50, 51) local type(s) :: { ( 26^26 ) } Outer automorphisms :: reflexible Dual of E12.239 Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 26 f = 2 degree seq :: [ 26^2 ] E12.241 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 13, 13}) Quotient :: edge^2 Aut^+ = D26 (small group id <26, 1>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y1 * Y2, (R * Y3)^2, R * Y1 * R * Y2, (Y3 * Y2)^2, (Y3^-1 * Y1)^2, Y3^13 ] Map:: R = (1, 27, 3, 29, 7, 33, 11, 37, 15, 41, 19, 45, 23, 49, 24, 50, 20, 46, 16, 42, 12, 38, 8, 34, 4, 30)(2, 28, 5, 31, 9, 35, 13, 39, 17, 43, 21, 47, 25, 51, 26, 52, 22, 48, 18, 44, 14, 40, 10, 36, 6, 32)(53, 54)(55, 58)(56, 57)(59, 62)(60, 61)(63, 66)(64, 65)(67, 70)(68, 69)(71, 74)(72, 73)(75, 78)(76, 77)(79, 80)(81, 84)(82, 83)(85, 88)(86, 87)(89, 92)(90, 91)(93, 96)(94, 95)(97, 100)(98, 99)(101, 104)(102, 103) L = (1, 53)(2, 54)(3, 55)(4, 56)(5, 57)(6, 58)(7, 59)(8, 60)(9, 61)(10, 62)(11, 63)(12, 64)(13, 65)(14, 66)(15, 67)(16, 68)(17, 69)(18, 70)(19, 71)(20, 72)(21, 73)(22, 74)(23, 75)(24, 76)(25, 77)(26, 78)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104) local type(s) :: { ( 52, 52 ), ( 52^26 ) } Outer automorphisms :: reflexible Dual of E12.248 Graph:: simple bipartite v = 28 e = 52 f = 2 degree seq :: [ 2^26, 26^2 ] E12.242 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 13, 13}) Quotient :: edge^2 Aut^+ = D26 (small group id <26, 1>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y3^-1 * Y2)^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y1)^2, Y3^-1 * Y2 * Y3^3 * Y1, Y1 * Y2 * Y1 * Y3 * Y2 * 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^-3 ] Map:: R = (1, 27, 4, 30, 12, 38, 21, 47, 9, 35, 20, 46, 26, 52, 24, 50, 16, 42, 6, 32, 15, 41, 13, 39, 5, 31)(2, 28, 7, 33, 17, 43, 23, 49, 14, 40, 19, 45, 25, 51, 22, 48, 11, 37, 3, 29, 10, 36, 18, 44, 8, 34)(53, 54)(55, 61)(56, 60)(57, 59)(58, 66)(62, 73)(63, 72)(64, 70)(65, 69)(67, 75)(68, 71)(74, 78)(76, 77)(79, 81)(80, 84)(82, 89)(83, 88)(85, 94)(86, 93)(87, 97)(90, 100)(91, 96)(92, 98)(95, 102)(99, 103)(101, 104) L = (1, 53)(2, 54)(3, 55)(4, 56)(5, 57)(6, 58)(7, 59)(8, 60)(9, 61)(10, 62)(11, 63)(12, 64)(13, 65)(14, 66)(15, 67)(16, 68)(17, 69)(18, 70)(19, 71)(20, 72)(21, 73)(22, 74)(23, 75)(24, 76)(25, 77)(26, 78)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104) local type(s) :: { ( 52, 52 ), ( 52^26 ) } Outer automorphisms :: reflexible Dual of E12.252 Graph:: simple bipartite v = 28 e = 52 f = 2 degree seq :: [ 2^26, 26^2 ] E12.243 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 13, 13}) Quotient :: edge^2 Aut^+ = D26 (small group id <26, 1>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y3^-1 * Y1)^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y2)^2, Y3^-3 * Y1 * Y3 * Y2, Y1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y2 ] Map:: R = (1, 27, 4, 30, 12, 38, 16, 42, 6, 32, 15, 41, 24, 50, 26, 52, 21, 47, 9, 35, 20, 46, 13, 39, 5, 31)(2, 28, 7, 33, 17, 43, 11, 37, 3, 29, 10, 36, 22, 48, 25, 51, 19, 45, 14, 40, 23, 49, 18, 44, 8, 34)(53, 54)(55, 61)(56, 60)(57, 59)(58, 66)(62, 73)(63, 72)(64, 70)(65, 69)(67, 71)(68, 75)(74, 78)(76, 77)(79, 81)(80, 84)(82, 89)(83, 88)(85, 94)(86, 93)(87, 97)(90, 95)(91, 100)(92, 99)(96, 102)(98, 103)(101, 104) L = (1, 53)(2, 54)(3, 55)(4, 56)(5, 57)(6, 58)(7, 59)(8, 60)(9, 61)(10, 62)(11, 63)(12, 64)(13, 65)(14, 66)(15, 67)(16, 68)(17, 69)(18, 70)(19, 71)(20, 72)(21, 73)(22, 74)(23, 75)(24, 76)(25, 77)(26, 78)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104) local type(s) :: { ( 52, 52 ), ( 52^26 ) } Outer automorphisms :: reflexible Dual of E12.250 Graph:: simple bipartite v = 28 e = 52 f = 2 degree seq :: [ 2^26, 26^2 ] E12.244 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 13, 13}) Quotient :: edge^2 Aut^+ = D26 (small group id <26, 1>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y1)^2, (Y3 * Y2)^2, Y3^-2 * Y1 * Y3 * Y2 * Y3^-2, Y1 * Y3^-1 * Y2 * Y1 * Y3^-2 * Y2, Y2 * Y3^-1 * Y1 * Y2 * Y3^-1 * Y1 * Y2 * Y1 ] Map:: R = (1, 27, 4, 30, 12, 38, 24, 50, 16, 42, 6, 32, 15, 41, 21, 47, 9, 35, 20, 46, 25, 51, 13, 39, 5, 31)(2, 28, 7, 33, 17, 43, 23, 49, 11, 37, 3, 29, 10, 36, 22, 48, 14, 40, 26, 52, 19, 45, 18, 44, 8, 34)(53, 54)(55, 61)(56, 60)(57, 59)(58, 66)(62, 73)(63, 72)(64, 70)(65, 69)(67, 74)(68, 78)(71, 76)(75, 77)(79, 81)(80, 84)(82, 89)(83, 88)(85, 94)(86, 93)(87, 97)(90, 101)(91, 100)(92, 103)(95, 102)(96, 99)(98, 104) L = (1, 53)(2, 54)(3, 55)(4, 56)(5, 57)(6, 58)(7, 59)(8, 60)(9, 61)(10, 62)(11, 63)(12, 64)(13, 65)(14, 66)(15, 67)(16, 68)(17, 69)(18, 70)(19, 71)(20, 72)(21, 73)(22, 74)(23, 75)(24, 76)(25, 77)(26, 78)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104) local type(s) :: { ( 52, 52 ), ( 52^26 ) } Outer automorphisms :: reflexible Dual of E12.253 Graph:: simple bipartite v = 28 e = 52 f = 2 degree seq :: [ 2^26, 26^2 ] E12.245 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 13, 13}) Quotient :: edge^2 Aut^+ = D26 (small group id <26, 1>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y1 * Y3^-1)^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y2)^2, Y1 * Y2 * Y1 * Y3 * Y2 * Y3^-2, Y1 * Y3^-5 * Y2 ] Map:: R = (1, 27, 4, 30, 12, 38, 24, 50, 21, 47, 9, 35, 20, 46, 16, 42, 6, 32, 15, 41, 25, 51, 13, 39, 5, 31)(2, 28, 7, 33, 17, 43, 19, 45, 26, 52, 14, 40, 23, 49, 11, 37, 3, 29, 10, 36, 22, 48, 18, 44, 8, 34)(53, 54)(55, 61)(56, 60)(57, 59)(58, 66)(62, 73)(63, 72)(64, 70)(65, 69)(67, 78)(68, 75)(71, 77)(74, 76)(79, 81)(80, 84)(82, 89)(83, 88)(85, 94)(86, 93)(87, 97)(90, 101)(91, 100)(92, 102)(95, 98)(96, 103)(99, 104) L = (1, 53)(2, 54)(3, 55)(4, 56)(5, 57)(6, 58)(7, 59)(8, 60)(9, 61)(10, 62)(11, 63)(12, 64)(13, 65)(14, 66)(15, 67)(16, 68)(17, 69)(18, 70)(19, 71)(20, 72)(21, 73)(22, 74)(23, 75)(24, 76)(25, 77)(26, 78)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104) local type(s) :: { ( 52, 52 ), ( 52^26 ) } Outer automorphisms :: reflexible Dual of E12.249 Graph:: simple bipartite v = 28 e = 52 f = 2 degree seq :: [ 2^26, 26^2 ] E12.246 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 13, 13}) Quotient :: edge^2 Aut^+ = D26 (small group id <26, 1>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y1 * Y3, Y1 * Y2 * Y3^-1, (R * Y3)^2, R * Y2 * R * Y1, Y3^13 ] Map:: R = (1, 27, 4, 30, 8, 34, 12, 38, 16, 42, 20, 46, 24, 50, 25, 51, 21, 47, 17, 43, 13, 39, 9, 35, 5, 31)(2, 28, 3, 29, 7, 33, 11, 37, 15, 41, 19, 45, 23, 49, 26, 52, 22, 48, 18, 44, 14, 40, 10, 36, 6, 32)(53, 54)(55, 57)(56, 58)(59, 61)(60, 62)(63, 65)(64, 66)(67, 69)(68, 70)(71, 73)(72, 74)(75, 77)(76, 78)(79, 81)(80, 82)(83, 85)(84, 86)(87, 89)(88, 90)(91, 93)(92, 94)(95, 97)(96, 98)(99, 101)(100, 102)(103, 104) L = (1, 53)(2, 54)(3, 55)(4, 56)(5, 57)(6, 58)(7, 59)(8, 60)(9, 61)(10, 62)(11, 63)(12, 64)(13, 65)(14, 66)(15, 67)(16, 68)(17, 69)(18, 70)(19, 71)(20, 72)(21, 73)(22, 74)(23, 75)(24, 76)(25, 77)(26, 78)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104) local type(s) :: { ( 52, 52 ), ( 52^26 ) } Outer automorphisms :: reflexible Dual of E12.251 Graph:: simple bipartite v = 28 e = 52 f = 2 degree seq :: [ 2^26, 26^2 ] E12.247 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 13, 13}) Quotient :: edge^2 Aut^+ = D26 (small group id <26, 1>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, (R * Y3)^2, R * Y1 * R * Y2, Y3 * Y2 * Y3 * Y1^-1, Y2^13, Y1^13 ] Map:: non-degenerate R = (1, 27, 4, 30)(2, 28, 6, 32)(3, 29, 8, 34)(5, 31, 10, 36)(7, 33, 12, 38)(9, 35, 14, 40)(11, 37, 16, 42)(13, 39, 18, 44)(15, 41, 20, 46)(17, 43, 22, 48)(19, 45, 24, 50)(21, 47, 25, 51)(23, 49, 26, 52)(53, 54, 57, 61, 65, 69, 73, 75, 71, 67, 63, 59, 55)(56, 60, 64, 68, 72, 76, 78, 77, 74, 70, 66, 62, 58)(79, 81, 85, 89, 93, 97, 101, 99, 95, 91, 87, 83, 80)(82, 84, 88, 92, 96, 100, 103, 104, 102, 98, 94, 90, 86) L = (1, 53)(2, 54)(3, 55)(4, 56)(5, 57)(6, 58)(7, 59)(8, 60)(9, 61)(10, 62)(11, 63)(12, 64)(13, 65)(14, 66)(15, 67)(16, 68)(17, 69)(18, 70)(19, 71)(20, 72)(21, 73)(22, 74)(23, 75)(24, 76)(25, 77)(26, 78)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104) local type(s) :: { ( 8^4 ), ( 8^13 ) } Outer automorphisms :: reflexible Dual of E12.254 Graph:: simple bipartite v = 17 e = 52 f = 13 degree seq :: [ 4^13, 13^4 ] E12.248 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 13, 13}) Quotient :: loop^2 Aut^+ = D26 (small group id <26, 1>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y1 * Y2, (R * Y3)^2, R * Y1 * R * Y2, (Y3 * Y2)^2, (Y3^-1 * Y1)^2, Y3^13 ] Map:: R = (1, 27, 53, 79, 3, 29, 55, 81, 7, 33, 59, 85, 11, 37, 63, 89, 15, 41, 67, 93, 19, 45, 71, 97, 23, 49, 75, 101, 24, 50, 76, 102, 20, 46, 72, 98, 16, 42, 68, 94, 12, 38, 64, 90, 8, 34, 60, 86, 4, 30, 56, 82)(2, 28, 54, 80, 5, 31, 57, 83, 9, 35, 61, 87, 13, 39, 65, 91, 17, 43, 69, 95, 21, 47, 73, 99, 25, 51, 77, 103, 26, 52, 78, 104, 22, 48, 74, 100, 18, 44, 70, 96, 14, 40, 66, 92, 10, 36, 62, 88, 6, 32, 58, 84) L = (1, 28)(2, 27)(3, 32)(4, 31)(5, 30)(6, 29)(7, 36)(8, 35)(9, 34)(10, 33)(11, 40)(12, 39)(13, 38)(14, 37)(15, 44)(16, 43)(17, 42)(18, 41)(19, 48)(20, 47)(21, 46)(22, 45)(23, 52)(24, 51)(25, 50)(26, 49)(53, 80)(54, 79)(55, 84)(56, 83)(57, 82)(58, 81)(59, 88)(60, 87)(61, 86)(62, 85)(63, 92)(64, 91)(65, 90)(66, 89)(67, 96)(68, 95)(69, 94)(70, 93)(71, 100)(72, 99)(73, 98)(74, 97)(75, 104)(76, 103)(77, 102)(78, 101) local type(s) :: { ( 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26 ) } Outer automorphisms :: reflexible Dual of E12.241 Transitivity :: VT+ Graph:: bipartite v = 2 e = 52 f = 28 degree seq :: [ 52^2 ] E12.249 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 13, 13}) Quotient :: loop^2 Aut^+ = D26 (small group id <26, 1>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y3^-1 * Y2)^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y1)^2, Y3^-1 * Y2 * Y3^3 * Y1, Y1 * Y2 * Y1 * Y3 * Y2 * 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^-3 ] Map:: R = (1, 27, 53, 79, 4, 30, 56, 82, 12, 38, 64, 90, 21, 47, 73, 99, 9, 35, 61, 87, 20, 46, 72, 98, 26, 52, 78, 104, 24, 50, 76, 102, 16, 42, 68, 94, 6, 32, 58, 84, 15, 41, 67, 93, 13, 39, 65, 91, 5, 31, 57, 83)(2, 28, 54, 80, 7, 33, 59, 85, 17, 43, 69, 95, 23, 49, 75, 101, 14, 40, 66, 92, 19, 45, 71, 97, 25, 51, 77, 103, 22, 48, 74, 100, 11, 37, 63, 89, 3, 29, 55, 81, 10, 36, 62, 88, 18, 44, 70, 96, 8, 34, 60, 86) L = (1, 28)(2, 27)(3, 35)(4, 34)(5, 33)(6, 40)(7, 31)(8, 30)(9, 29)(10, 47)(11, 46)(12, 44)(13, 43)(14, 32)(15, 49)(16, 45)(17, 39)(18, 38)(19, 42)(20, 37)(21, 36)(22, 52)(23, 41)(24, 51)(25, 50)(26, 48)(53, 81)(54, 84)(55, 79)(56, 89)(57, 88)(58, 80)(59, 94)(60, 93)(61, 97)(62, 83)(63, 82)(64, 100)(65, 96)(66, 98)(67, 86)(68, 85)(69, 102)(70, 91)(71, 87)(72, 92)(73, 103)(74, 90)(75, 104)(76, 95)(77, 99)(78, 101) local type(s) :: { ( 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26 ) } Outer automorphisms :: reflexible Dual of E12.245 Transitivity :: VT+ Graph:: bipartite v = 2 e = 52 f = 28 degree seq :: [ 52^2 ] E12.250 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 13, 13}) Quotient :: loop^2 Aut^+ = D26 (small group id <26, 1>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y3^-1 * Y1)^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y2)^2, Y3^-3 * Y1 * Y3 * Y2, Y1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y2 ] Map:: R = (1, 27, 53, 79, 4, 30, 56, 82, 12, 38, 64, 90, 16, 42, 68, 94, 6, 32, 58, 84, 15, 41, 67, 93, 24, 50, 76, 102, 26, 52, 78, 104, 21, 47, 73, 99, 9, 35, 61, 87, 20, 46, 72, 98, 13, 39, 65, 91, 5, 31, 57, 83)(2, 28, 54, 80, 7, 33, 59, 85, 17, 43, 69, 95, 11, 37, 63, 89, 3, 29, 55, 81, 10, 36, 62, 88, 22, 48, 74, 100, 25, 51, 77, 103, 19, 45, 71, 97, 14, 40, 66, 92, 23, 49, 75, 101, 18, 44, 70, 96, 8, 34, 60, 86) L = (1, 28)(2, 27)(3, 35)(4, 34)(5, 33)(6, 40)(7, 31)(8, 30)(9, 29)(10, 47)(11, 46)(12, 44)(13, 43)(14, 32)(15, 45)(16, 49)(17, 39)(18, 38)(19, 41)(20, 37)(21, 36)(22, 52)(23, 42)(24, 51)(25, 50)(26, 48)(53, 81)(54, 84)(55, 79)(56, 89)(57, 88)(58, 80)(59, 94)(60, 93)(61, 97)(62, 83)(63, 82)(64, 95)(65, 100)(66, 99)(67, 86)(68, 85)(69, 90)(70, 102)(71, 87)(72, 103)(73, 92)(74, 91)(75, 104)(76, 96)(77, 98)(78, 101) local type(s) :: { ( 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26 ) } Outer automorphisms :: reflexible Dual of E12.243 Transitivity :: VT+ Graph:: bipartite v = 2 e = 52 f = 28 degree seq :: [ 52^2 ] E12.251 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 13, 13}) Quotient :: loop^2 Aut^+ = D26 (small group id <26, 1>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y1)^2, (Y3 * Y2)^2, Y3^-2 * Y1 * Y3 * Y2 * Y3^-2, Y1 * Y3^-1 * Y2 * Y1 * Y3^-2 * Y2, Y2 * Y3^-1 * Y1 * Y2 * Y3^-1 * Y1 * Y2 * Y1 ] Map:: R = (1, 27, 53, 79, 4, 30, 56, 82, 12, 38, 64, 90, 24, 50, 76, 102, 16, 42, 68, 94, 6, 32, 58, 84, 15, 41, 67, 93, 21, 47, 73, 99, 9, 35, 61, 87, 20, 46, 72, 98, 25, 51, 77, 103, 13, 39, 65, 91, 5, 31, 57, 83)(2, 28, 54, 80, 7, 33, 59, 85, 17, 43, 69, 95, 23, 49, 75, 101, 11, 37, 63, 89, 3, 29, 55, 81, 10, 36, 62, 88, 22, 48, 74, 100, 14, 40, 66, 92, 26, 52, 78, 104, 19, 45, 71, 97, 18, 44, 70, 96, 8, 34, 60, 86) L = (1, 28)(2, 27)(3, 35)(4, 34)(5, 33)(6, 40)(7, 31)(8, 30)(9, 29)(10, 47)(11, 46)(12, 44)(13, 43)(14, 32)(15, 48)(16, 52)(17, 39)(18, 38)(19, 50)(20, 37)(21, 36)(22, 41)(23, 51)(24, 45)(25, 49)(26, 42)(53, 81)(54, 84)(55, 79)(56, 89)(57, 88)(58, 80)(59, 94)(60, 93)(61, 97)(62, 83)(63, 82)(64, 101)(65, 100)(66, 103)(67, 86)(68, 85)(69, 102)(70, 99)(71, 87)(72, 104)(73, 96)(74, 91)(75, 90)(76, 95)(77, 92)(78, 98) local type(s) :: { ( 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26 ) } Outer automorphisms :: reflexible Dual of E12.246 Transitivity :: VT+ Graph:: bipartite v = 2 e = 52 f = 28 degree seq :: [ 52^2 ] E12.252 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 13, 13}) Quotient :: loop^2 Aut^+ = D26 (small group id <26, 1>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y1 * Y3^-1)^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y2)^2, Y1 * Y2 * Y1 * Y3 * Y2 * Y3^-2, Y1 * Y3^-5 * Y2 ] Map:: R = (1, 27, 53, 79, 4, 30, 56, 82, 12, 38, 64, 90, 24, 50, 76, 102, 21, 47, 73, 99, 9, 35, 61, 87, 20, 46, 72, 98, 16, 42, 68, 94, 6, 32, 58, 84, 15, 41, 67, 93, 25, 51, 77, 103, 13, 39, 65, 91, 5, 31, 57, 83)(2, 28, 54, 80, 7, 33, 59, 85, 17, 43, 69, 95, 19, 45, 71, 97, 26, 52, 78, 104, 14, 40, 66, 92, 23, 49, 75, 101, 11, 37, 63, 89, 3, 29, 55, 81, 10, 36, 62, 88, 22, 48, 74, 100, 18, 44, 70, 96, 8, 34, 60, 86) L = (1, 28)(2, 27)(3, 35)(4, 34)(5, 33)(6, 40)(7, 31)(8, 30)(9, 29)(10, 47)(11, 46)(12, 44)(13, 43)(14, 32)(15, 52)(16, 49)(17, 39)(18, 38)(19, 51)(20, 37)(21, 36)(22, 50)(23, 42)(24, 48)(25, 45)(26, 41)(53, 81)(54, 84)(55, 79)(56, 89)(57, 88)(58, 80)(59, 94)(60, 93)(61, 97)(62, 83)(63, 82)(64, 101)(65, 100)(66, 102)(67, 86)(68, 85)(69, 98)(70, 103)(71, 87)(72, 95)(73, 104)(74, 91)(75, 90)(76, 92)(77, 96)(78, 99) local type(s) :: { ( 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26 ) } Outer automorphisms :: reflexible Dual of E12.242 Transitivity :: VT+ Graph:: bipartite v = 2 e = 52 f = 28 degree seq :: [ 52^2 ] E12.253 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 13, 13}) Quotient :: loop^2 Aut^+ = D26 (small group id <26, 1>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y1 * Y3, Y1 * Y2 * Y3^-1, (R * Y3)^2, R * Y2 * R * Y1, Y3^13 ] Map:: R = (1, 27, 53, 79, 4, 30, 56, 82, 8, 34, 60, 86, 12, 38, 64, 90, 16, 42, 68, 94, 20, 46, 72, 98, 24, 50, 76, 102, 25, 51, 77, 103, 21, 47, 73, 99, 17, 43, 69, 95, 13, 39, 65, 91, 9, 35, 61, 87, 5, 31, 57, 83)(2, 28, 54, 80, 3, 29, 55, 81, 7, 33, 59, 85, 11, 37, 63, 89, 15, 41, 67, 93, 19, 45, 71, 97, 23, 49, 75, 101, 26, 52, 78, 104, 22, 48, 74, 100, 18, 44, 70, 96, 14, 40, 66, 92, 10, 36, 62, 88, 6, 32, 58, 84) L = (1, 28)(2, 27)(3, 31)(4, 32)(5, 29)(6, 30)(7, 35)(8, 36)(9, 33)(10, 34)(11, 39)(12, 40)(13, 37)(14, 38)(15, 43)(16, 44)(17, 41)(18, 42)(19, 47)(20, 48)(21, 45)(22, 46)(23, 51)(24, 52)(25, 49)(26, 50)(53, 81)(54, 82)(55, 79)(56, 80)(57, 85)(58, 86)(59, 83)(60, 84)(61, 89)(62, 90)(63, 87)(64, 88)(65, 93)(66, 94)(67, 91)(68, 92)(69, 97)(70, 98)(71, 95)(72, 96)(73, 101)(74, 102)(75, 99)(76, 100)(77, 104)(78, 103) local type(s) :: { ( 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26 ) } Outer automorphisms :: reflexible Dual of E12.244 Transitivity :: VT+ Graph:: bipartite v = 2 e = 52 f = 28 degree seq :: [ 52^2 ] E12.254 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 13, 13}) Quotient :: loop^2 Aut^+ = D26 (small group id <26, 1>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, (R * Y3)^2, R * Y1 * R * Y2, Y3 * Y2 * Y3 * Y1^-1, Y2^13, Y1^13 ] Map:: non-degenerate R = (1, 27, 53, 79, 4, 30, 56, 82)(2, 28, 54, 80, 6, 32, 58, 84)(3, 29, 55, 81, 8, 34, 60, 86)(5, 31, 57, 83, 10, 36, 62, 88)(7, 33, 59, 85, 12, 38, 64, 90)(9, 35, 61, 87, 14, 40, 66, 92)(11, 37, 63, 89, 16, 42, 68, 94)(13, 39, 65, 91, 18, 44, 70, 96)(15, 41, 67, 93, 20, 46, 72, 98)(17, 43, 69, 95, 22, 48, 74, 100)(19, 45, 71, 97, 24, 50, 76, 102)(21, 47, 73, 99, 25, 51, 77, 103)(23, 49, 75, 101, 26, 52, 78, 104) L = (1, 28)(2, 31)(3, 27)(4, 34)(5, 35)(6, 30)(7, 29)(8, 38)(9, 39)(10, 32)(11, 33)(12, 42)(13, 43)(14, 36)(15, 37)(16, 46)(17, 47)(18, 40)(19, 41)(20, 50)(21, 49)(22, 44)(23, 45)(24, 52)(25, 48)(26, 51)(53, 81)(54, 79)(55, 85)(56, 84)(57, 80)(58, 88)(59, 89)(60, 82)(61, 83)(62, 92)(63, 93)(64, 86)(65, 87)(66, 96)(67, 97)(68, 90)(69, 91)(70, 100)(71, 101)(72, 94)(73, 95)(74, 103)(75, 99)(76, 98)(77, 104)(78, 102) local type(s) :: { ( 4, 13, 4, 13, 4, 13, 4, 13 ) } Outer automorphisms :: reflexible Dual of E12.247 Transitivity :: VT+ Graph:: v = 13 e = 52 f = 17 degree seq :: [ 8^13 ] E12.255 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 13, 13}) Quotient :: dipole Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ 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, Y2^13, (Y3 * Y2^-1)^13 ] Map:: R = (1, 27, 2, 28)(3, 29, 5, 31)(4, 30, 6, 32)(7, 33, 9, 35)(8, 34, 10, 36)(11, 37, 13, 39)(12, 38, 14, 40)(15, 41, 17, 43)(16, 42, 18, 44)(19, 45, 21, 47)(20, 46, 22, 48)(23, 49, 25, 51)(24, 50, 26, 52)(53, 79, 55, 81, 59, 85, 63, 89, 67, 93, 71, 97, 75, 101, 76, 102, 72, 98, 68, 94, 64, 90, 60, 86, 56, 82)(54, 80, 57, 83, 61, 87, 65, 91, 69, 95, 73, 99, 77, 103, 78, 104, 74, 100, 70, 96, 66, 92, 62, 88, 58, 84) L = (1, 53)(2, 54)(3, 55)(4, 56)(5, 57)(6, 58)(7, 59)(8, 60)(9, 61)(10, 62)(11, 63)(12, 64)(13, 65)(14, 66)(15, 67)(16, 68)(17, 69)(18, 70)(19, 71)(20, 72)(21, 73)(22, 74)(23, 75)(24, 76)(25, 77)(26, 78)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104) local type(s) :: { ( 4, 26, 4, 26 ), ( 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 15 e = 52 f = 15 degree seq :: [ 4^13, 26^2 ] E12.256 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 13, 13}) Quotient :: dipole Aut^+ = D26 (small group id <26, 1>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ 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^-1 * Y1)^2, (R * Y2 * Y3^-1)^2, Y2^13, (Y3 * Y2^-1)^13 ] Map:: R = (1, 27, 2, 28)(3, 29, 6, 32)(4, 30, 5, 31)(7, 33, 10, 36)(8, 34, 9, 35)(11, 37, 14, 40)(12, 38, 13, 39)(15, 41, 18, 44)(16, 42, 17, 43)(19, 45, 22, 48)(20, 46, 21, 47)(23, 49, 26, 52)(24, 50, 25, 51)(53, 79, 55, 81, 59, 85, 63, 89, 67, 93, 71, 97, 75, 101, 76, 102, 72, 98, 68, 94, 64, 90, 60, 86, 56, 82)(54, 80, 57, 83, 61, 87, 65, 91, 69, 95, 73, 99, 77, 103, 78, 104, 74, 100, 70, 96, 66, 92, 62, 88, 58, 84) L = (1, 53)(2, 54)(3, 55)(4, 56)(5, 57)(6, 58)(7, 59)(8, 60)(9, 61)(10, 62)(11, 63)(12, 64)(13, 65)(14, 66)(15, 67)(16, 68)(17, 69)(18, 70)(19, 71)(20, 72)(21, 73)(22, 74)(23, 75)(24, 76)(25, 77)(26, 78)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104) local type(s) :: { ( 4, 26, 4, 26 ), ( 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 15 e = 52 f = 15 degree seq :: [ 4^13, 26^2 ] E12.257 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 13, 13}) Quotient :: dipole Aut^+ = D26 (small group id <26, 1>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3 * Y2, (Y3^-1 * Y1)^2, R * Y2 * R * Y3^-1, (R * Y1)^2, Y2^13, (Y3 * Y2^-1)^13 ] Map:: non-degenerate R = (1, 27, 2, 28)(3, 29, 6, 32)(4, 30, 5, 31)(7, 33, 10, 36)(8, 34, 9, 35)(11, 37, 14, 40)(12, 38, 13, 39)(15, 41, 18, 44)(16, 42, 17, 43)(19, 45, 22, 48)(20, 46, 21, 47)(23, 49, 26, 52)(24, 50, 25, 51)(53, 79, 55, 81, 59, 85, 63, 89, 67, 93, 71, 97, 75, 101, 76, 102, 72, 98, 68, 94, 64, 90, 60, 86, 56, 82)(54, 80, 57, 83, 61, 87, 65, 91, 69, 95, 73, 99, 77, 103, 78, 104, 74, 100, 70, 96, 66, 92, 62, 88, 58, 84) L = (1, 56)(2, 58)(3, 53)(4, 60)(5, 54)(6, 62)(7, 55)(8, 64)(9, 57)(10, 66)(11, 59)(12, 68)(13, 61)(14, 70)(15, 63)(16, 72)(17, 65)(18, 74)(19, 67)(20, 76)(21, 69)(22, 78)(23, 71)(24, 75)(25, 73)(26, 77)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104) local type(s) :: { ( 4, 26, 4, 26 ), ( 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26 ) } Outer automorphisms :: reflexible Dual of E12.267 Graph:: bipartite v = 15 e = 52 f = 15 degree seq :: [ 4^13, 26^2 ] E12.258 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 13, 13}) Quotient :: dipole Aut^+ = D26 (small group id <26, 1>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^2 * Y3^-1, (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2 * Y1)^2, Y3^3 * Y2 * Y3^3 ] Map:: non-degenerate R = (1, 27, 2, 28)(3, 29, 9, 35)(4, 30, 10, 36)(5, 31, 7, 33)(6, 32, 8, 34)(11, 37, 17, 43)(12, 38, 18, 44)(13, 39, 15, 41)(14, 40, 16, 42)(19, 45, 25, 51)(20, 46, 26, 52)(21, 47, 23, 49)(22, 48, 24, 50)(53, 79, 55, 81, 56, 82, 63, 89, 64, 90, 71, 97, 72, 98, 74, 100, 73, 99, 66, 92, 65, 91, 58, 84, 57, 83)(54, 80, 59, 85, 60, 86, 67, 93, 68, 94, 75, 101, 76, 102, 78, 104, 77, 103, 70, 96, 69, 95, 62, 88, 61, 87) L = (1, 56)(2, 60)(3, 63)(4, 64)(5, 55)(6, 53)(7, 67)(8, 68)(9, 59)(10, 54)(11, 71)(12, 72)(13, 57)(14, 58)(15, 75)(16, 76)(17, 61)(18, 62)(19, 74)(20, 73)(21, 65)(22, 66)(23, 78)(24, 77)(25, 69)(26, 70)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104) local type(s) :: { ( 4, 26, 4, 26 ), ( 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 15 e = 52 f = 15 degree seq :: [ 4^13, 26^2 ] E12.259 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 13, 13}) Quotient :: dipole Aut^+ = D26 (small group id <26, 1>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^2 * Y3, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1)^2, (R * Y2)^2, (Y2^-1 * Y1)^2, Y2 * Y3^-6, (Y3 * Y2^-1)^13 ] Map:: non-degenerate R = (1, 27, 2, 28)(3, 29, 9, 35)(4, 30, 10, 36)(5, 31, 7, 33)(6, 32, 8, 34)(11, 37, 17, 43)(12, 38, 18, 44)(13, 39, 15, 41)(14, 40, 16, 42)(19, 45, 25, 51)(20, 46, 26, 52)(21, 47, 23, 49)(22, 48, 24, 50)(53, 79, 55, 81, 58, 84, 63, 89, 66, 92, 71, 97, 74, 100, 72, 98, 73, 99, 64, 90, 65, 91, 56, 82, 57, 83)(54, 80, 59, 85, 62, 88, 67, 93, 70, 96, 75, 101, 78, 104, 76, 102, 77, 103, 68, 94, 69, 95, 60, 86, 61, 87) L = (1, 56)(2, 60)(3, 57)(4, 64)(5, 65)(6, 53)(7, 61)(8, 68)(9, 69)(10, 54)(11, 55)(12, 72)(13, 73)(14, 58)(15, 59)(16, 76)(17, 77)(18, 62)(19, 63)(20, 71)(21, 74)(22, 66)(23, 67)(24, 75)(25, 78)(26, 70)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104) local type(s) :: { ( 4, 26, 4, 26 ), ( 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26 ) } Outer automorphisms :: reflexible Dual of E12.264 Graph:: bipartite v = 15 e = 52 f = 15 degree seq :: [ 4^13, 26^2 ] E12.260 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 13, 13}) Quotient :: dipole Aut^+ = D26 (small group id <26, 1>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3 * Y2^-3, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y3^-1 * Y1)^2, (Y2 * Y1)^2, Y3^2 * Y2 * Y3^2 ] Map:: non-degenerate R = (1, 27, 2, 28)(3, 29, 9, 35)(4, 30, 10, 36)(5, 31, 7, 33)(6, 32, 8, 34)(11, 37, 19, 45)(12, 38, 21, 47)(13, 39, 17, 43)(14, 40, 22, 48)(15, 41, 18, 44)(16, 42, 20, 46)(23, 49, 26, 52)(24, 50, 25, 51)(53, 79, 55, 81, 63, 89, 56, 82, 64, 90, 75, 101, 66, 92, 68, 94, 76, 102, 67, 93, 58, 84, 65, 91, 57, 83)(54, 80, 59, 85, 69, 95, 60, 86, 70, 96, 77, 103, 72, 98, 74, 100, 78, 104, 73, 99, 62, 88, 71, 97, 61, 87) L = (1, 56)(2, 60)(3, 64)(4, 66)(5, 63)(6, 53)(7, 70)(8, 72)(9, 69)(10, 54)(11, 75)(12, 68)(13, 55)(14, 67)(15, 57)(16, 58)(17, 77)(18, 74)(19, 59)(20, 73)(21, 61)(22, 62)(23, 76)(24, 65)(25, 78)(26, 71)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104) local type(s) :: { ( 4, 26, 4, 26 ), ( 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26 ) } Outer automorphisms :: reflexible Dual of E12.265 Graph:: bipartite v = 15 e = 52 f = 15 degree seq :: [ 4^13, 26^2 ] E12.261 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 13, 13}) Quotient :: dipole Aut^+ = D26 (small group id <26, 1>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^-1 * Y3^-1 * Y2^-2, (Y3^-1, Y2^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y3^-1 * Y1)^2, (Y2 * Y1)^2, Y3 * Y2^-1 * Y3^3 ] Map:: non-degenerate R = (1, 27, 2, 28)(3, 29, 9, 35)(4, 30, 10, 36)(5, 31, 7, 33)(6, 32, 8, 34)(11, 37, 18, 44)(12, 38, 17, 43)(13, 39, 21, 47)(14, 40, 22, 48)(15, 41, 19, 45)(16, 42, 20, 46)(23, 49, 26, 52)(24, 50, 25, 51)(53, 79, 55, 81, 63, 89, 58, 84, 65, 91, 75, 101, 68, 94, 66, 92, 76, 102, 67, 93, 56, 82, 64, 90, 57, 83)(54, 80, 59, 85, 69, 95, 62, 88, 71, 97, 77, 103, 74, 100, 72, 98, 78, 104, 73, 99, 60, 86, 70, 96, 61, 87) L = (1, 56)(2, 60)(3, 64)(4, 66)(5, 67)(6, 53)(7, 70)(8, 72)(9, 73)(10, 54)(11, 57)(12, 76)(13, 55)(14, 65)(15, 68)(16, 58)(17, 61)(18, 78)(19, 59)(20, 71)(21, 74)(22, 62)(23, 63)(24, 75)(25, 69)(26, 77)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104) local type(s) :: { ( 4, 26, 4, 26 ), ( 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26 ) } Outer automorphisms :: reflexible Dual of E12.262 Graph:: bipartite v = 15 e = 52 f = 15 degree seq :: [ 4^13, 26^2 ] E12.262 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 13, 13}) Quotient :: dipole Aut^+ = D26 (small group id <26, 1>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^-1 * Y3^-3, (Y3, Y2^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y3^-1 * Y1)^2, (Y2^-1 * Y1)^2, Y3^-1 * Y2^4 ] Map:: non-degenerate R = (1, 27, 2, 28)(3, 29, 9, 35)(4, 30, 10, 36)(5, 31, 7, 33)(6, 32, 8, 34)(11, 37, 22, 48)(12, 38, 20, 46)(13, 39, 21, 47)(14, 40, 18, 44)(15, 41, 19, 45)(16, 42, 17, 43)(23, 49, 26, 52)(24, 50, 25, 51)(53, 79, 55, 81, 63, 89, 67, 93, 56, 82, 64, 90, 75, 101, 76, 102, 66, 92, 58, 84, 65, 91, 68, 94, 57, 83)(54, 80, 59, 85, 69, 95, 73, 99, 60, 86, 70, 96, 77, 103, 78, 104, 72, 98, 62, 88, 71, 97, 74, 100, 61, 87) L = (1, 56)(2, 60)(3, 64)(4, 66)(5, 67)(6, 53)(7, 70)(8, 72)(9, 73)(10, 54)(11, 75)(12, 58)(13, 55)(14, 57)(15, 76)(16, 63)(17, 77)(18, 62)(19, 59)(20, 61)(21, 78)(22, 69)(23, 65)(24, 68)(25, 71)(26, 74)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104) local type(s) :: { ( 4, 26, 4, 26 ), ( 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26 ) } Outer automorphisms :: reflexible Dual of E12.261 Graph:: bipartite v = 15 e = 52 f = 15 degree seq :: [ 4^13, 26^2 ] E12.263 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 13, 13}) Quotient :: dipole Aut^+ = D26 (small group id <26, 1>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^2 * Y2^-1 * Y3, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y2, Y3^-1), (Y3^-1 * Y1)^2, (Y2 * Y1)^2, Y3 * Y2^4 ] Map:: non-degenerate R = (1, 27, 2, 28)(3, 29, 9, 35)(4, 30, 10, 36)(5, 31, 7, 33)(6, 32, 8, 34)(11, 37, 21, 47)(12, 38, 22, 48)(13, 39, 20, 46)(14, 40, 19, 45)(15, 41, 17, 43)(16, 42, 18, 44)(23, 49, 26, 52)(24, 50, 25, 51)(53, 79, 55, 81, 63, 89, 68, 94, 58, 84, 65, 91, 75, 101, 76, 102, 66, 92, 56, 82, 64, 90, 67, 93, 57, 83)(54, 80, 59, 85, 69, 95, 74, 100, 62, 88, 71, 97, 77, 103, 78, 104, 72, 98, 60, 86, 70, 96, 73, 99, 61, 87) L = (1, 56)(2, 60)(3, 64)(4, 65)(5, 66)(6, 53)(7, 70)(8, 71)(9, 72)(10, 54)(11, 67)(12, 75)(13, 55)(14, 58)(15, 76)(16, 57)(17, 73)(18, 77)(19, 59)(20, 62)(21, 78)(22, 61)(23, 63)(24, 68)(25, 69)(26, 74)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104) local type(s) :: { ( 4, 26, 4, 26 ), ( 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26 ) } Outer automorphisms :: reflexible Dual of E12.266 Graph:: bipartite v = 15 e = 52 f = 15 degree seq :: [ 4^13, 26^2 ] E12.264 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 13, 13}) Quotient :: dipole Aut^+ = D26 (small group id <26, 1>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y2), (Y3^-1 * Y1)^2, (R * Y2)^2, (Y2 * Y1)^2, Y2 * Y3 * Y2^2 * Y3, Y3^-1 * Y2 * Y3^-2 * Y2 ] Map:: non-degenerate R = (1, 27, 2, 28)(3, 29, 9, 35)(4, 30, 10, 36)(5, 31, 7, 33)(6, 32, 8, 34)(11, 37, 24, 50)(12, 38, 25, 51)(13, 39, 23, 49)(14, 40, 26, 52)(15, 41, 21, 47)(16, 42, 19, 45)(17, 43, 20, 46)(18, 44, 22, 48)(53, 79, 55, 81, 63, 89, 70, 96, 67, 93, 56, 82, 64, 90, 69, 95, 58, 84, 65, 91, 66, 92, 68, 94, 57, 83)(54, 80, 59, 85, 71, 97, 78, 104, 75, 101, 60, 86, 72, 98, 77, 103, 62, 88, 73, 99, 74, 100, 76, 102, 61, 87) L = (1, 56)(2, 60)(3, 64)(4, 66)(5, 67)(6, 53)(7, 72)(8, 74)(9, 75)(10, 54)(11, 69)(12, 68)(13, 55)(14, 63)(15, 65)(16, 70)(17, 57)(18, 58)(19, 77)(20, 76)(21, 59)(22, 71)(23, 73)(24, 78)(25, 61)(26, 62)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104) local type(s) :: { ( 4, 26, 4, 26 ), ( 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26 ) } Outer automorphisms :: reflexible Dual of E12.259 Graph:: bipartite v = 15 e = 52 f = 15 degree seq :: [ 4^13, 26^2 ] E12.265 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 13, 13}) Quotient :: dipole Aut^+ = D26 (small group id <26, 1>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y2), (Y3^-1 * Y1)^2, (R * Y2)^2, (Y2 * Y1)^2, Y3^3 * Y2^2, Y3^-1 * Y2^2 * Y3^-1 * Y2, Y2^13 ] Map:: non-degenerate R = (1, 27, 2, 28)(3, 29, 9, 35)(4, 30, 10, 36)(5, 31, 7, 33)(6, 32, 8, 34)(11, 37, 24, 50)(12, 38, 25, 51)(13, 39, 23, 49)(14, 40, 26, 52)(15, 41, 21, 47)(16, 42, 19, 45)(17, 43, 20, 46)(18, 44, 22, 48)(53, 79, 55, 81, 63, 89, 66, 92, 69, 95, 58, 84, 65, 91, 67, 93, 56, 82, 64, 90, 70, 96, 68, 94, 57, 83)(54, 80, 59, 85, 71, 97, 74, 100, 77, 103, 62, 88, 73, 99, 75, 101, 60, 86, 72, 98, 78, 104, 76, 102, 61, 87) L = (1, 56)(2, 60)(3, 64)(4, 66)(5, 67)(6, 53)(7, 72)(8, 74)(9, 75)(10, 54)(11, 70)(12, 69)(13, 55)(14, 68)(15, 63)(16, 65)(17, 57)(18, 58)(19, 78)(20, 77)(21, 59)(22, 76)(23, 71)(24, 73)(25, 61)(26, 62)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104) local type(s) :: { ( 4, 26, 4, 26 ), ( 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26 ) } Outer automorphisms :: reflexible Dual of E12.260 Graph:: bipartite v = 15 e = 52 f = 15 degree seq :: [ 4^13, 26^2 ] E12.266 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 13, 13}) Quotient :: dipole Aut^+ = D26 (small group id <26, 1>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2 * Y3^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1)^2, (R * Y2)^2, (Y2 * Y1)^2, Y2^6 * Y3^-1, (Y3 * Y2^-1)^13 ] Map:: non-degenerate R = (1, 27, 2, 28)(3, 29, 9, 35)(4, 30, 10, 36)(5, 31, 7, 33)(6, 32, 8, 34)(11, 37, 18, 44)(12, 38, 17, 43)(13, 39, 16, 42)(14, 40, 15, 41)(19, 45, 26, 52)(20, 46, 25, 51)(21, 47, 24, 50)(22, 48, 23, 49)(53, 79, 55, 81, 63, 89, 71, 97, 73, 99, 65, 91, 56, 82, 58, 84, 64, 90, 72, 98, 74, 100, 66, 92, 57, 83)(54, 80, 59, 85, 67, 93, 75, 101, 77, 103, 69, 95, 60, 86, 62, 88, 68, 94, 76, 102, 78, 104, 70, 96, 61, 87) L = (1, 56)(2, 60)(3, 58)(4, 57)(5, 65)(6, 53)(7, 62)(8, 61)(9, 69)(10, 54)(11, 64)(12, 55)(13, 66)(14, 73)(15, 68)(16, 59)(17, 70)(18, 77)(19, 72)(20, 63)(21, 74)(22, 71)(23, 76)(24, 67)(25, 78)(26, 75)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104) local type(s) :: { ( 4, 26, 4, 26 ), ( 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26 ) } Outer automorphisms :: reflexible Dual of E12.263 Graph:: bipartite v = 15 e = 52 f = 15 degree seq :: [ 4^13, 26^2 ] E12.267 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 13, 13}) Quotient :: dipole Aut^+ = D26 (small group id <26, 1>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2 * Y3^-2, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1)^2, (Y2^-1 * Y1)^2, Y2^-6 * Y3^-1 ] Map:: non-degenerate R = (1, 27, 2, 28)(3, 29, 9, 35)(4, 30, 10, 36)(5, 31, 7, 33)(6, 32, 8, 34)(11, 37, 17, 43)(12, 38, 18, 44)(13, 39, 15, 41)(14, 40, 16, 42)(19, 45, 25, 51)(20, 46, 26, 52)(21, 47, 23, 49)(22, 48, 24, 50)(53, 79, 55, 81, 63, 89, 71, 97, 74, 100, 66, 92, 58, 84, 56, 82, 64, 90, 72, 98, 73, 99, 65, 91, 57, 83)(54, 80, 59, 85, 67, 93, 75, 101, 78, 104, 70, 96, 62, 88, 60, 86, 68, 94, 76, 102, 77, 103, 69, 95, 61, 87) L = (1, 56)(2, 60)(3, 64)(4, 55)(5, 58)(6, 53)(7, 68)(8, 59)(9, 62)(10, 54)(11, 72)(12, 63)(13, 66)(14, 57)(15, 76)(16, 67)(17, 70)(18, 61)(19, 73)(20, 71)(21, 74)(22, 65)(23, 77)(24, 75)(25, 78)(26, 69)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104) local type(s) :: { ( 4, 26, 4, 26 ), ( 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26, 4, 26 ) } Outer automorphisms :: reflexible Dual of E12.257 Graph:: bipartite v = 15 e = 52 f = 15 degree seq :: [ 4^13, 26^2 ] E12.268 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {13, 26, 26}) Quotient :: edge Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ F^2, (T2, T1^-1), (F * T1)^2, (F * T2)^2, T1^2 * T2^-2, T2^12 * 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 ] Map:: non-degenerate R = (1, 3, 6, 12, 15, 20, 23, 26, 21, 18, 13, 10, 4, 8, 2, 7, 11, 16, 19, 24, 25, 22, 17, 14, 9, 5)(27, 28, 32, 37, 41, 45, 49, 51, 47, 43, 39, 35, 30)(29, 33, 38, 42, 46, 50, 52, 48, 44, 40, 36, 31, 34) L = (1, 27)(2, 28)(3, 29)(4, 30)(5, 31)(6, 32)(7, 33)(8, 34)(9, 35)(10, 36)(11, 37)(12, 38)(13, 39)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52) local type(s) :: { ( 52^13 ), ( 52^26 ) } Outer automorphisms :: reflexible Dual of E12.293 Transitivity :: ET+ Graph:: bipartite v = 3 e = 26 f = 1 degree seq :: [ 13^2, 26 ] E12.269 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {13, 26, 26}) Quotient :: edge Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2 * T1 * T2^3, T2 * T1^-1 * T2 * T1^-5 ] Map:: non-degenerate R = (1, 3, 9, 12, 4, 10, 18, 21, 11, 19, 22, 26, 20, 24, 14, 23, 25, 16, 6, 15, 17, 8, 2, 7, 13, 5)(27, 28, 32, 40, 48, 44, 35, 39, 43, 51, 46, 37, 30)(29, 33, 41, 49, 52, 47, 38, 31, 34, 42, 50, 45, 36) L = (1, 27)(2, 28)(3, 29)(4, 30)(5, 31)(6, 32)(7, 33)(8, 34)(9, 35)(10, 36)(11, 37)(12, 38)(13, 39)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52) local type(s) :: { ( 52^13 ), ( 52^26 ) } Outer automorphisms :: reflexible Dual of E12.291 Transitivity :: ET+ Graph:: bipartite v = 3 e = 26 f = 1 degree seq :: [ 13^2, 26 ] E12.270 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {13, 26, 26}) Quotient :: edge Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2, T1), T2^-4 * T1, T1 * T2 * T1^5 * T2, T2^-1 * T1^3 * T2^-1 * T1^4 ] Map:: non-degenerate R = (1, 3, 9, 8, 2, 7, 17, 16, 6, 15, 25, 24, 14, 23, 19, 26, 22, 20, 11, 18, 21, 12, 4, 10, 13, 5)(27, 28, 32, 40, 48, 47, 39, 35, 43, 51, 45, 37, 30)(29, 33, 41, 49, 46, 38, 31, 34, 42, 50, 52, 44, 36) L = (1, 27)(2, 28)(3, 29)(4, 30)(5, 31)(6, 32)(7, 33)(8, 34)(9, 35)(10, 36)(11, 37)(12, 38)(13, 39)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52) local type(s) :: { ( 52^13 ), ( 52^26 ) } Outer automorphisms :: reflexible Dual of E12.294 Transitivity :: ET+ Graph:: bipartite v = 3 e = 26 f = 1 degree seq :: [ 13^2, 26 ] E12.271 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {13, 26, 26}) Quotient :: edge Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^2 * T1^3, T1 * T2^-8 ] Map:: non-degenerate R = (1, 3, 9, 16, 22, 21, 15, 8, 2, 7, 11, 18, 24, 26, 20, 14, 6, 12, 4, 10, 17, 23, 25, 19, 13, 5)(27, 28, 32, 39, 41, 46, 51, 48, 50, 43, 35, 37, 30)(29, 33, 38, 31, 34, 40, 45, 47, 52, 49, 42, 44, 36) L = (1, 27)(2, 28)(3, 29)(4, 30)(5, 31)(6, 32)(7, 33)(8, 34)(9, 35)(10, 36)(11, 37)(12, 38)(13, 39)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52) local type(s) :: { ( 52^13 ), ( 52^26 ) } Outer automorphisms :: reflexible Dual of E12.289 Transitivity :: ET+ Graph:: bipartite v = 3 e = 26 f = 1 degree seq :: [ 13^2, 26 ] E12.272 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {13, 26, 26}) Quotient :: edge Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2 * T1^-1 * T2 * T1^-2, T2 * T1 * T2^7, (T1^-1 * T2^-1)^26 ] Map:: non-degenerate R = (1, 3, 9, 16, 22, 24, 18, 12, 4, 10, 6, 14, 20, 26, 23, 17, 11, 8, 2, 7, 15, 21, 25, 19, 13, 5)(27, 28, 32, 35, 41, 46, 48, 51, 49, 44, 39, 37, 30)(29, 33, 40, 42, 47, 52, 50, 45, 43, 38, 31, 34, 36) L = (1, 27)(2, 28)(3, 29)(4, 30)(5, 31)(6, 32)(7, 33)(8, 34)(9, 35)(10, 36)(11, 37)(12, 38)(13, 39)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52) local type(s) :: { ( 52^13 ), ( 52^26 ) } Outer automorphisms :: reflexible Dual of E12.292 Transitivity :: ET+ Graph:: bipartite v = 3 e = 26 f = 1 degree seq :: [ 13^2, 26 ] E12.273 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {13, 26, 26}) Quotient :: edge Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ F^2, T2 * T1^-1 * T2, (F * T1)^2, (F * T2)^2, T1^13, (T2^-1 * T1^-1)^26 ] Map:: non-degenerate R = (1, 3, 2, 7, 6, 11, 10, 15, 14, 19, 18, 23, 22, 26, 24, 25, 20, 21, 16, 17, 12, 13, 8, 9, 4, 5)(27, 28, 32, 36, 40, 44, 48, 50, 46, 42, 38, 34, 30)(29, 33, 37, 41, 45, 49, 52, 51, 47, 43, 39, 35, 31) L = (1, 27)(2, 28)(3, 29)(4, 30)(5, 31)(6, 32)(7, 33)(8, 34)(9, 35)(10, 36)(11, 37)(12, 38)(13, 39)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52) local type(s) :: { ( 52^13 ), ( 52^26 ) } Outer automorphisms :: reflexible Dual of E12.287 Transitivity :: ET+ Graph:: bipartite v = 3 e = 26 f = 1 degree seq :: [ 13^2, 26 ] E12.274 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {13, 26, 26}) Quotient :: edge Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ F^2, T2^2 * T1, (F * T1)^2, (F * T2)^2, T1^13 ] Map:: non-degenerate R = (1, 3, 4, 8, 9, 12, 13, 16, 17, 20, 21, 24, 25, 26, 22, 23, 18, 19, 14, 15, 10, 11, 6, 7, 2, 5)(27, 28, 32, 36, 40, 44, 48, 51, 47, 43, 39, 35, 30)(29, 31, 33, 37, 41, 45, 49, 52, 50, 46, 42, 38, 34) L = (1, 27)(2, 28)(3, 29)(4, 30)(5, 31)(6, 32)(7, 33)(8, 34)(9, 35)(10, 36)(11, 37)(12, 38)(13, 39)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52) local type(s) :: { ( 52^13 ), ( 52^26 ) } Outer automorphisms :: reflexible Dual of E12.290 Transitivity :: ET+ Graph:: bipartite v = 3 e = 26 f = 1 degree seq :: [ 13^2, 26 ] E12.275 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {13, 26, 26}) Quotient :: edge Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1), T2 * T1^-2 * T2^-1 * T1^2, T1^-5 * T2^2, T2 * T1^2 * T2^3 * T1, T1 * T2^-2 * T1^2 * T2^-2 * T1^2 * T2^-2 * T1^2 * T2^-2 * T1^2 * T2^-2 * T1^3 ] Map:: non-degenerate R = (1, 3, 9, 19, 22, 16, 6, 15, 24, 12, 4, 10, 20, 26, 18, 8, 2, 7, 17, 23, 11, 21, 14, 25, 13, 5)(27, 28, 32, 40, 46, 35, 43, 50, 39, 44, 48, 37, 30)(29, 33, 41, 51, 52, 45, 49, 38, 31, 34, 42, 47, 36) L = (1, 27)(2, 28)(3, 29)(4, 30)(5, 31)(6, 32)(7, 33)(8, 34)(9, 35)(10, 36)(11, 37)(12, 38)(13, 39)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52) local type(s) :: { ( 52^13 ), ( 52^26 ) } Outer automorphisms :: reflexible Dual of E12.285 Transitivity :: ET+ Graph:: bipartite v = 3 e = 26 f = 1 degree seq :: [ 13^2, 26 ] E12.276 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {13, 26, 26}) Quotient :: edge Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1 * T2^-1 * T1 * T2^-3 * T1, T1^3 * T2 * T1 * T2 * T1, 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^-3 * T1 * T2^-1 ] Map:: non-degenerate R = (1, 3, 9, 19, 14, 23, 11, 21, 18, 8, 2, 7, 17, 26, 24, 12, 4, 10, 20, 16, 6, 15, 22, 25, 13, 5)(27, 28, 32, 40, 50, 39, 44, 46, 35, 43, 48, 37, 30)(29, 33, 41, 49, 38, 31, 34, 42, 45, 52, 51, 47, 36) L = (1, 27)(2, 28)(3, 29)(4, 30)(5, 31)(6, 32)(7, 33)(8, 34)(9, 35)(10, 36)(11, 37)(12, 38)(13, 39)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52) local type(s) :: { ( 52^13 ), ( 52^26 ) } Outer automorphisms :: reflexible Dual of E12.288 Transitivity :: ET+ Graph:: bipartite v = 3 e = 26 f = 1 degree seq :: [ 13^2, 26 ] E12.277 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {13, 26, 26}) Quotient :: edge Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2, T1), T2^-2 * T1^-4, T2^6 * T1^-1, T1 * T2^-1 * T1 * T2^-1 * T1^2 * T2^-2 * T1 ] Map:: non-degenerate R = (1, 3, 9, 19, 18, 8, 2, 7, 17, 25, 24, 16, 6, 15, 11, 21, 26, 23, 14, 12, 4, 10, 20, 22, 13, 5)(27, 28, 32, 40, 39, 44, 50, 52, 46, 35, 43, 37, 30)(29, 33, 41, 38, 31, 34, 42, 49, 48, 45, 51, 47, 36) L = (1, 27)(2, 28)(3, 29)(4, 30)(5, 31)(6, 32)(7, 33)(8, 34)(9, 35)(10, 36)(11, 37)(12, 38)(13, 39)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52) local type(s) :: { ( 52^13 ), ( 52^26 ) } Outer automorphisms :: reflexible Dual of E12.284 Transitivity :: ET+ Graph:: bipartite v = 3 e = 26 f = 1 degree seq :: [ 13^2, 26 ] E12.278 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {13, 26, 26}) Quotient :: edge Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ F^2, (T1, T2^-1), (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1^-3 * T2, T2^5 * T1 * T2, T1^-1 * T2^3 * 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 ] Map:: non-degenerate R = (1, 3, 9, 19, 21, 12, 4, 10, 14, 23, 26, 20, 11, 16, 6, 15, 24, 25, 18, 8, 2, 7, 17, 22, 13, 5)(27, 28, 32, 40, 35, 43, 50, 52, 47, 39, 44, 37, 30)(29, 33, 41, 49, 45, 48, 51, 46, 38, 31, 34, 42, 36) L = (1, 27)(2, 28)(3, 29)(4, 30)(5, 31)(6, 32)(7, 33)(8, 34)(9, 35)(10, 36)(11, 37)(12, 38)(13, 39)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52) local type(s) :: { ( 52^13 ), ( 52^26 ) } Outer automorphisms :: reflexible Dual of E12.286 Transitivity :: ET+ Graph:: bipartite v = 3 e = 26 f = 1 degree seq :: [ 13^2, 26 ] E12.279 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {13, 26, 26}) Quotient :: edge Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ F^2, T2 * T1^-3, (F * T1)^2, (F * T2)^2, T2 * T1^-1 * T2^8, (T2^-1 * T1^-1)^13 ] Map:: non-degenerate R = (1, 3, 9, 15, 21, 26, 20, 14, 8, 2, 7, 13, 19, 25, 22, 16, 10, 4, 6, 12, 18, 24, 23, 17, 11, 5)(27, 28, 32, 29, 33, 38, 35, 39, 44, 41, 45, 50, 47, 51, 49, 52, 48, 43, 46, 42, 37, 40, 36, 31, 34, 30) L = (1, 27)(2, 28)(3, 29)(4, 30)(5, 31)(6, 32)(7, 33)(8, 34)(9, 35)(10, 36)(11, 37)(12, 38)(13, 39)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52) local type(s) :: { ( 26^26 ) } Outer automorphisms :: reflexible Dual of E12.297 Transitivity :: ET+ Graph:: bipartite v = 2 e = 26 f = 2 degree seq :: [ 26^2 ] E12.280 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {13, 26, 26}) Quotient :: edge Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ F^2, T1^-2 * T2^-1 * T1^-1, (F * T1)^2, (F * T2)^2, T2^-8 * T1^2, T2^-4 * T1 * T2^4 * T1^-1 ] Map:: non-degenerate R = (1, 3, 9, 15, 21, 24, 18, 12, 6, 4, 10, 16, 22, 26, 20, 14, 8, 2, 7, 13, 19, 25, 23, 17, 11, 5)(27, 28, 32, 31, 34, 38, 37, 40, 44, 43, 46, 50, 49, 52, 47, 51, 48, 41, 45, 42, 35, 39, 36, 29, 33, 30) L = (1, 27)(2, 28)(3, 29)(4, 30)(5, 31)(6, 32)(7, 33)(8, 34)(9, 35)(10, 36)(11, 37)(12, 38)(13, 39)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52) local type(s) :: { ( 26^26 ) } Outer automorphisms :: reflexible Dual of E12.296 Transitivity :: ET+ Graph:: bipartite v = 2 e = 26 f = 2 degree seq :: [ 26^2 ] E12.281 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {13, 26, 26}) Quotient :: edge Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^-1 * T2 * T1^-4, T1^-1 * T2^-5, T1^-1 * T2^3 * T1^-1 * T2^3 * T1^-1 * T2^3 * T1^-1 * T2^3 * T1^-1 * T2^3 * T1^-1 * T2^2 * T1^-1 ] Map:: non-degenerate R = (1, 3, 9, 19, 12, 4, 10, 20, 25, 21, 11, 14, 22, 26, 24, 16, 6, 15, 23, 18, 8, 2, 7, 17, 13, 5)(27, 28, 32, 40, 36, 29, 33, 41, 48, 46, 35, 43, 49, 52, 51, 45, 39, 44, 50, 47, 38, 31, 34, 42, 37, 30) L = (1, 27)(2, 28)(3, 29)(4, 30)(5, 31)(6, 32)(7, 33)(8, 34)(9, 35)(10, 36)(11, 37)(12, 38)(13, 39)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52) local type(s) :: { ( 26^26 ) } Outer automorphisms :: reflexible Dual of E12.299 Transitivity :: ET+ Graph:: bipartite v = 2 e = 26 f = 2 degree seq :: [ 26^2 ] E12.282 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {13, 26, 26}) Quotient :: edge Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ F^2, (T2^-1, T1), (F * T1)^2, (F * T2)^2, T2^-2 * T1 * T2^-1 * T1 * T2^-1, T2^-1 * T1^-5 * T2^-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 * T1^3 ] Map:: non-degenerate R = (1, 3, 9, 16, 6, 15, 26, 20, 23, 22, 12, 4, 10, 18, 8, 2, 7, 17, 25, 14, 24, 21, 11, 19, 13, 5)(27, 28, 32, 40, 49, 45, 36, 29, 33, 41, 50, 48, 39, 44, 35, 43, 52, 47, 38, 31, 34, 42, 51, 46, 37, 30) L = (1, 27)(2, 28)(3, 29)(4, 30)(5, 31)(6, 32)(7, 33)(8, 34)(9, 35)(10, 36)(11, 37)(12, 38)(13, 39)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52) local type(s) :: { ( 26^26 ) } Outer automorphisms :: reflexible Dual of E12.298 Transitivity :: ET+ Graph:: bipartite v = 2 e = 26 f = 2 degree seq :: [ 26^2 ] E12.283 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {13, 26, 26}) Quotient :: edge Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ F^2, (T1, T2), (F * T1)^2, (F * T2)^2, T2^3 * T1 * T2 * T1, T2 * T1^-1 * T2 * T1^-4 * T2 ] Map:: non-degenerate R = (1, 3, 9, 19, 11, 21, 25, 14, 24, 18, 8, 2, 7, 17, 12, 4, 10, 20, 23, 22, 26, 16, 6, 15, 13, 5)(27, 28, 32, 40, 49, 45, 38, 31, 34, 42, 51, 46, 35, 43, 39, 44, 52, 47, 36, 29, 33, 41, 50, 48, 37, 30) L = (1, 27)(2, 28)(3, 29)(4, 30)(5, 31)(6, 32)(7, 33)(8, 34)(9, 35)(10, 36)(11, 37)(12, 38)(13, 39)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52) local type(s) :: { ( 26^26 ) } Outer automorphisms :: reflexible Dual of E12.295 Transitivity :: ET+ Graph:: bipartite v = 2 e = 26 f = 2 degree seq :: [ 26^2 ] E12.284 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {13, 26, 26}) Quotient :: loop Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ F^2, (T2, T1^-1), (F * T1)^2, (F * T2)^2, T1^2 * T2^-2, T2^12 * 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 ] Map:: non-degenerate R = (1, 27, 3, 29, 6, 32, 12, 38, 15, 41, 20, 46, 23, 49, 26, 52, 21, 47, 18, 44, 13, 39, 10, 36, 4, 30, 8, 34, 2, 28, 7, 33, 11, 37, 16, 42, 19, 45, 24, 50, 25, 51, 22, 48, 17, 43, 14, 40, 9, 35, 5, 31) L = (1, 28)(2, 32)(3, 33)(4, 27)(5, 34)(6, 37)(7, 38)(8, 29)(9, 30)(10, 31)(11, 41)(12, 42)(13, 35)(14, 36)(15, 45)(16, 46)(17, 39)(18, 40)(19, 49)(20, 50)(21, 43)(22, 44)(23, 51)(24, 52)(25, 47)(26, 48) local type(s) :: { ( 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26 ) } Outer automorphisms :: reflexible Dual of E12.277 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 26 f = 3 degree seq :: [ 52 ] E12.285 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {13, 26, 26}) Quotient :: loop Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2 * T1 * T2^3, T2 * T1^-1 * T2 * T1^-5 ] Map:: non-degenerate R = (1, 27, 3, 29, 9, 35, 12, 38, 4, 30, 10, 36, 18, 44, 21, 47, 11, 37, 19, 45, 22, 48, 26, 52, 20, 46, 24, 50, 14, 40, 23, 49, 25, 51, 16, 42, 6, 32, 15, 41, 17, 43, 8, 34, 2, 28, 7, 33, 13, 39, 5, 31) L = (1, 28)(2, 32)(3, 33)(4, 27)(5, 34)(6, 40)(7, 41)(8, 42)(9, 39)(10, 29)(11, 30)(12, 31)(13, 43)(14, 48)(15, 49)(16, 50)(17, 51)(18, 35)(19, 36)(20, 37)(21, 38)(22, 44)(23, 52)(24, 45)(25, 46)(26, 47) local type(s) :: { ( 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26 ) } Outer automorphisms :: reflexible Dual of E12.275 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 26 f = 3 degree seq :: [ 52 ] E12.286 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {13, 26, 26}) Quotient :: loop Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2, T1), T2^-4 * T1, T1 * T2 * T1^5 * T2, T2^-1 * T1^3 * T2^-1 * T1^4 ] Map:: non-degenerate R = (1, 27, 3, 29, 9, 35, 8, 34, 2, 28, 7, 33, 17, 43, 16, 42, 6, 32, 15, 41, 25, 51, 24, 50, 14, 40, 23, 49, 19, 45, 26, 52, 22, 48, 20, 46, 11, 37, 18, 44, 21, 47, 12, 38, 4, 30, 10, 36, 13, 39, 5, 31) L = (1, 28)(2, 32)(3, 33)(4, 27)(5, 34)(6, 40)(7, 41)(8, 42)(9, 43)(10, 29)(11, 30)(12, 31)(13, 35)(14, 48)(15, 49)(16, 50)(17, 51)(18, 36)(19, 37)(20, 38)(21, 39)(22, 47)(23, 46)(24, 52)(25, 45)(26, 44) local type(s) :: { ( 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26 ) } Outer automorphisms :: reflexible Dual of E12.278 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 26 f = 3 degree seq :: [ 52 ] E12.287 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {13, 26, 26}) Quotient :: loop Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^2 * T1^3, T1 * T2^-8 ] Map:: non-degenerate R = (1, 27, 3, 29, 9, 35, 16, 42, 22, 48, 21, 47, 15, 41, 8, 34, 2, 28, 7, 33, 11, 37, 18, 44, 24, 50, 26, 52, 20, 46, 14, 40, 6, 32, 12, 38, 4, 30, 10, 36, 17, 43, 23, 49, 25, 51, 19, 45, 13, 39, 5, 31) L = (1, 28)(2, 32)(3, 33)(4, 27)(5, 34)(6, 39)(7, 38)(8, 40)(9, 37)(10, 29)(11, 30)(12, 31)(13, 41)(14, 45)(15, 46)(16, 44)(17, 35)(18, 36)(19, 47)(20, 51)(21, 52)(22, 50)(23, 42)(24, 43)(25, 48)(26, 49) local type(s) :: { ( 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26 ) } Outer automorphisms :: reflexible Dual of E12.273 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 26 f = 3 degree seq :: [ 52 ] E12.288 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {13, 26, 26}) Quotient :: loop Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2 * T1^-1 * T2 * T1^-2, T2 * T1 * T2^7, (T1^-1 * T2^-1)^26 ] Map:: non-degenerate R = (1, 27, 3, 29, 9, 35, 16, 42, 22, 48, 24, 50, 18, 44, 12, 38, 4, 30, 10, 36, 6, 32, 14, 40, 20, 46, 26, 52, 23, 49, 17, 43, 11, 37, 8, 34, 2, 28, 7, 33, 15, 41, 21, 47, 25, 51, 19, 45, 13, 39, 5, 31) L = (1, 28)(2, 32)(3, 33)(4, 27)(5, 34)(6, 35)(7, 40)(8, 36)(9, 41)(10, 29)(11, 30)(12, 31)(13, 37)(14, 42)(15, 46)(16, 47)(17, 38)(18, 39)(19, 43)(20, 48)(21, 52)(22, 51)(23, 44)(24, 45)(25, 49)(26, 50) local type(s) :: { ( 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26 ) } Outer automorphisms :: reflexible Dual of E12.276 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 26 f = 3 degree seq :: [ 52 ] E12.289 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {13, 26, 26}) Quotient :: loop Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ F^2, T2 * T1^-1 * T2, (F * T1)^2, (F * T2)^2, T1^13, (T2^-1 * T1^-1)^26 ] Map:: non-degenerate R = (1, 27, 3, 29, 2, 28, 7, 33, 6, 32, 11, 37, 10, 36, 15, 41, 14, 40, 19, 45, 18, 44, 23, 49, 22, 48, 26, 52, 24, 50, 25, 51, 20, 46, 21, 47, 16, 42, 17, 43, 12, 38, 13, 39, 8, 34, 9, 35, 4, 30, 5, 31) L = (1, 28)(2, 32)(3, 33)(4, 27)(5, 29)(6, 36)(7, 37)(8, 30)(9, 31)(10, 40)(11, 41)(12, 34)(13, 35)(14, 44)(15, 45)(16, 38)(17, 39)(18, 48)(19, 49)(20, 42)(21, 43)(22, 50)(23, 52)(24, 46)(25, 47)(26, 51) local type(s) :: { ( 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26 ) } Outer automorphisms :: reflexible Dual of E12.271 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 26 f = 3 degree seq :: [ 52 ] E12.290 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {13, 26, 26}) Quotient :: loop Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ F^2, T2^2 * T1, (F * T1)^2, (F * T2)^2, T1^13 ] Map:: non-degenerate R = (1, 27, 3, 29, 4, 30, 8, 34, 9, 35, 12, 38, 13, 39, 16, 42, 17, 43, 20, 46, 21, 47, 24, 50, 25, 51, 26, 52, 22, 48, 23, 49, 18, 44, 19, 45, 14, 40, 15, 41, 10, 36, 11, 37, 6, 32, 7, 33, 2, 28, 5, 31) L = (1, 28)(2, 32)(3, 31)(4, 27)(5, 33)(6, 36)(7, 37)(8, 29)(9, 30)(10, 40)(11, 41)(12, 34)(13, 35)(14, 44)(15, 45)(16, 38)(17, 39)(18, 48)(19, 49)(20, 42)(21, 43)(22, 51)(23, 52)(24, 46)(25, 47)(26, 50) local type(s) :: { ( 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26 ) } Outer automorphisms :: reflexible Dual of E12.274 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 26 f = 3 degree seq :: [ 52 ] E12.291 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {13, 26, 26}) Quotient :: loop Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1), T2 * T1^-2 * T2^-1 * T1^2, T1^-5 * T2^2, T2 * T1^2 * T2^3 * T1, T1 * T2^-2 * T1^2 * T2^-2 * T1^2 * T2^-2 * T1^2 * T2^-2 * T1^2 * T2^-2 * T1^3 ] Map:: non-degenerate R = (1, 27, 3, 29, 9, 35, 19, 45, 22, 48, 16, 42, 6, 32, 15, 41, 24, 50, 12, 38, 4, 30, 10, 36, 20, 46, 26, 52, 18, 44, 8, 34, 2, 28, 7, 33, 17, 43, 23, 49, 11, 37, 21, 47, 14, 40, 25, 51, 13, 39, 5, 31) L = (1, 28)(2, 32)(3, 33)(4, 27)(5, 34)(6, 40)(7, 41)(8, 42)(9, 43)(10, 29)(11, 30)(12, 31)(13, 44)(14, 46)(15, 51)(16, 47)(17, 50)(18, 48)(19, 49)(20, 35)(21, 36)(22, 37)(23, 38)(24, 39)(25, 52)(26, 45) local type(s) :: { ( 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26 ) } Outer automorphisms :: reflexible Dual of E12.269 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 26 f = 3 degree seq :: [ 52 ] E12.292 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {13, 26, 26}) Quotient :: loop Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1 * T2^-1 * T1 * T2^-3 * T1, T1^3 * T2 * T1 * T2 * T1, 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^-3 * T1 * T2^-1 ] Map:: non-degenerate R = (1, 27, 3, 29, 9, 35, 19, 45, 14, 40, 23, 49, 11, 37, 21, 47, 18, 44, 8, 34, 2, 28, 7, 33, 17, 43, 26, 52, 24, 50, 12, 38, 4, 30, 10, 36, 20, 46, 16, 42, 6, 32, 15, 41, 22, 48, 25, 51, 13, 39, 5, 31) L = (1, 28)(2, 32)(3, 33)(4, 27)(5, 34)(6, 40)(7, 41)(8, 42)(9, 43)(10, 29)(11, 30)(12, 31)(13, 44)(14, 50)(15, 49)(16, 45)(17, 48)(18, 46)(19, 52)(20, 35)(21, 36)(22, 37)(23, 38)(24, 39)(25, 47)(26, 51) local type(s) :: { ( 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26 ) } Outer automorphisms :: reflexible Dual of E12.272 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 26 f = 3 degree seq :: [ 52 ] E12.293 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {13, 26, 26}) Quotient :: loop Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2, T1), T2^-2 * T1^-4, T2^6 * T1^-1, T1 * T2^-1 * T1 * T2^-1 * T1^2 * T2^-2 * T1 ] Map:: non-degenerate R = (1, 27, 3, 29, 9, 35, 19, 45, 18, 44, 8, 34, 2, 28, 7, 33, 17, 43, 25, 51, 24, 50, 16, 42, 6, 32, 15, 41, 11, 37, 21, 47, 26, 52, 23, 49, 14, 40, 12, 38, 4, 30, 10, 36, 20, 46, 22, 48, 13, 39, 5, 31) L = (1, 28)(2, 32)(3, 33)(4, 27)(5, 34)(6, 40)(7, 41)(8, 42)(9, 43)(10, 29)(11, 30)(12, 31)(13, 44)(14, 39)(15, 38)(16, 49)(17, 37)(18, 50)(19, 51)(20, 35)(21, 36)(22, 45)(23, 48)(24, 52)(25, 47)(26, 46) local type(s) :: { ( 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26 ) } Outer automorphisms :: reflexible Dual of E12.268 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 26 f = 3 degree seq :: [ 52 ] E12.294 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {13, 26, 26}) Quotient :: loop Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ F^2, (T1, T2^-1), (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1^-3 * T2, T2^5 * T1 * T2, T1^-1 * T2^3 * 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 ] Map:: non-degenerate R = (1, 27, 3, 29, 9, 35, 19, 45, 21, 47, 12, 38, 4, 30, 10, 36, 14, 40, 23, 49, 26, 52, 20, 46, 11, 37, 16, 42, 6, 32, 15, 41, 24, 50, 25, 51, 18, 44, 8, 34, 2, 28, 7, 33, 17, 43, 22, 48, 13, 39, 5, 31) L = (1, 28)(2, 32)(3, 33)(4, 27)(5, 34)(6, 40)(7, 41)(8, 42)(9, 43)(10, 29)(11, 30)(12, 31)(13, 44)(14, 35)(15, 49)(16, 36)(17, 50)(18, 37)(19, 48)(20, 38)(21, 39)(22, 51)(23, 45)(24, 52)(25, 46)(26, 47) local type(s) :: { ( 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26, 13, 26 ) } Outer automorphisms :: reflexible Dual of E12.270 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 26 f = 3 degree seq :: [ 52 ] E12.295 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {13, 26, 26}) Quotient :: loop Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ F^2, (T2 * T1^-1)^2, (T2, T1^-1), (F * T1)^2, (F * T2)^2, T2^-1 * T1^2 * T2^-1, T2^5 * T1 * T2^-5 * T1^-1, T1^2 * T2^11, 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 ] Map:: non-degenerate R = (1, 27, 3, 29, 6, 32, 12, 38, 15, 41, 20, 46, 23, 49, 25, 51, 22, 48, 17, 43, 14, 40, 9, 35, 5, 31)(2, 28, 7, 33, 11, 37, 16, 42, 19, 45, 24, 50, 26, 52, 21, 47, 18, 44, 13, 39, 10, 36, 4, 30, 8, 34) L = (1, 28)(2, 32)(3, 33)(4, 27)(5, 34)(6, 37)(7, 38)(8, 29)(9, 30)(10, 31)(11, 41)(12, 42)(13, 35)(14, 36)(15, 45)(16, 46)(17, 39)(18, 40)(19, 49)(20, 50)(21, 43)(22, 44)(23, 52)(24, 51)(25, 47)(26, 48) local type(s) :: { ( 26^26 ) } Outer automorphisms :: reflexible Dual of E12.283 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 26 f = 2 degree seq :: [ 26^2 ] E12.296 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {13, 26, 26}) Quotient :: loop Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ F^2, T1^-2 * T2, (F * T2)^2, (F * T1)^2, T2^13, (T2^-1 * T1^-1)^26 ] Map:: non-degenerate R = (1, 27, 3, 29, 7, 33, 11, 37, 15, 41, 19, 45, 23, 49, 25, 51, 21, 47, 17, 43, 13, 39, 9, 35, 5, 31)(2, 28, 6, 32, 10, 36, 14, 40, 18, 44, 22, 48, 26, 52, 24, 50, 20, 46, 16, 42, 12, 38, 8, 34, 4, 30) L = (1, 28)(2, 29)(3, 32)(4, 27)(5, 30)(6, 33)(7, 36)(8, 31)(9, 34)(10, 37)(11, 40)(12, 35)(13, 38)(14, 41)(15, 44)(16, 39)(17, 42)(18, 45)(19, 48)(20, 43)(21, 46)(22, 49)(23, 52)(24, 47)(25, 50)(26, 51) local type(s) :: { ( 26^26 ) } Outer automorphisms :: reflexible Dual of E12.280 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 26 f = 2 degree seq :: [ 26^2 ] E12.297 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {13, 26, 26}) Quotient :: loop Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ F^2, (T2^-1, T1), (F * T1)^2, (F * T2)^2, T2^-5 * T1^2, T2^3 * T1^4 ] Map:: non-degenerate R = (1, 27, 3, 29, 9, 35, 19, 45, 16, 42, 6, 32, 15, 41, 23, 49, 11, 37, 21, 47, 25, 51, 13, 39, 5, 31)(2, 28, 7, 33, 17, 43, 22, 48, 26, 52, 14, 40, 24, 50, 12, 38, 4, 30, 10, 36, 20, 46, 18, 44, 8, 34) L = (1, 28)(2, 32)(3, 33)(4, 27)(5, 34)(6, 40)(7, 41)(8, 42)(9, 43)(10, 29)(11, 30)(12, 31)(13, 44)(14, 51)(15, 50)(16, 52)(17, 49)(18, 45)(19, 48)(20, 35)(21, 36)(22, 37)(23, 38)(24, 39)(25, 46)(26, 47) local type(s) :: { ( 26^26 ) } Outer automorphisms :: reflexible Dual of E12.279 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 26 f = 2 degree seq :: [ 26^2 ] E12.298 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {13, 26, 26}) Quotient :: loop Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T1^-1, T2^-1), T2 * T1 * T2^4 * T1, T1^3 * T2^-1 * T1 * T2^-2 ] Map:: non-degenerate R = (1, 27, 3, 29, 9, 35, 19, 45, 23, 49, 11, 37, 21, 47, 16, 42, 6, 32, 15, 41, 25, 51, 13, 39, 5, 31)(2, 28, 7, 33, 17, 43, 24, 50, 12, 38, 4, 30, 10, 36, 20, 46, 14, 40, 26, 52, 22, 48, 18, 44, 8, 34) L = (1, 28)(2, 32)(3, 33)(4, 27)(5, 34)(6, 40)(7, 41)(8, 42)(9, 43)(10, 29)(11, 30)(12, 31)(13, 44)(14, 45)(15, 52)(16, 46)(17, 51)(18, 47)(19, 50)(20, 35)(21, 36)(22, 37)(23, 38)(24, 39)(25, 48)(26, 49) local type(s) :: { ( 26^26 ) } Outer automorphisms :: reflexible Dual of E12.282 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 26 f = 2 degree seq :: [ 26^2 ] E12.299 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {13, 26, 26}) Quotient :: loop Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ F^2, (T1, T2), (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1^-3, T1 * T2 * T1 * T2^5, T1^-1 * T2^3 * T1^-1 * T2^4 ] Map:: non-degenerate R = (1, 27, 3, 29, 9, 35, 17, 43, 25, 51, 19, 45, 11, 37, 6, 32, 14, 40, 22, 48, 21, 47, 13, 39, 5, 31)(2, 28, 7, 33, 15, 41, 23, 49, 20, 46, 12, 38, 4, 30, 10, 36, 18, 44, 26, 52, 24, 50, 16, 42, 8, 34) L = (1, 28)(2, 32)(3, 33)(4, 27)(5, 34)(6, 36)(7, 40)(8, 37)(9, 41)(10, 29)(11, 30)(12, 31)(13, 42)(14, 44)(15, 48)(16, 45)(17, 49)(18, 35)(19, 38)(20, 39)(21, 50)(22, 52)(23, 47)(24, 51)(25, 46)(26, 43) local type(s) :: { ( 26^26 ) } Outer automorphisms :: reflexible Dual of E12.281 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 26 f = 2 degree seq :: [ 26^2 ] E12.300 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {13, 26, 26}) Quotient :: dipole Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, (Y2^-1, Y1^-1), (R * Y1)^2, Y2 * Y3 * Y1^-1 * Y2, Y2 * Y3 * Y2 * Y1^-1, (R * Y3)^2, (R * Y2)^2, Y1^5 * Y2 * Y1 * Y2 * Y3^-5, Y1^13, (Y1 * Y3^-1)^13, (Y3 * Y2^-1)^26 ] Map:: R = (1, 27, 2, 28, 6, 32, 11, 37, 15, 41, 19, 45, 23, 49, 25, 51, 21, 47, 17, 43, 13, 39, 9, 35, 4, 30)(3, 29, 7, 33, 12, 38, 16, 42, 20, 46, 24, 50, 26, 52, 22, 48, 18, 44, 14, 40, 10, 36, 5, 31, 8, 34)(53, 79, 55, 81, 58, 84, 64, 90, 67, 93, 72, 98, 75, 101, 78, 104, 73, 99, 70, 96, 65, 91, 62, 88, 56, 82, 60, 86, 54, 80, 59, 85, 63, 89, 68, 94, 71, 97, 76, 102, 77, 103, 74, 100, 69, 95, 66, 92, 61, 87, 57, 83) L = (1, 56)(2, 53)(3, 60)(4, 61)(5, 62)(6, 54)(7, 55)(8, 57)(9, 65)(10, 66)(11, 58)(12, 59)(13, 69)(14, 70)(15, 63)(16, 64)(17, 73)(18, 74)(19, 67)(20, 68)(21, 77)(22, 78)(23, 71)(24, 72)(25, 75)(26, 76)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104) local type(s) :: { ( 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52 ), ( 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52 ) } Outer automorphisms :: reflexible Dual of E12.330 Graph:: bipartite v = 3 e = 52 f = 27 degree seq :: [ 26^2, 52 ] E12.301 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {13, 26, 26}) Quotient :: dipole Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y2^2 * Y3^-1, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y3^13, Y1^13 ] Map:: R = (1, 27, 2, 28, 6, 32, 10, 36, 14, 40, 18, 44, 22, 48, 25, 51, 21, 47, 17, 43, 13, 39, 9, 35, 4, 30)(3, 29, 5, 31, 7, 33, 11, 37, 15, 41, 19, 45, 23, 49, 26, 52, 24, 50, 20, 46, 16, 42, 12, 38, 8, 34)(53, 79, 55, 81, 56, 82, 60, 86, 61, 87, 64, 90, 65, 91, 68, 94, 69, 95, 72, 98, 73, 99, 76, 102, 77, 103, 78, 104, 74, 100, 75, 101, 70, 96, 71, 97, 66, 92, 67, 93, 62, 88, 63, 89, 58, 84, 59, 85, 54, 80, 57, 83) L = (1, 56)(2, 53)(3, 60)(4, 61)(5, 55)(6, 54)(7, 57)(8, 64)(9, 65)(10, 58)(11, 59)(12, 68)(13, 69)(14, 62)(15, 63)(16, 72)(17, 73)(18, 66)(19, 67)(20, 76)(21, 77)(22, 70)(23, 71)(24, 78)(25, 74)(26, 75)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104) local type(s) :: { ( 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52 ), ( 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52 ) } Outer automorphisms :: reflexible Dual of E12.327 Graph:: bipartite v = 3 e = 52 f = 27 degree seq :: [ 26^2, 52 ] E12.302 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {13, 26, 26}) Quotient :: dipole Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y1 * Y2^-2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2, Y3^-1), Y1^13, 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 * Y1^-1 ] Map:: R = (1, 27, 2, 28, 6, 32, 10, 36, 14, 40, 18, 44, 22, 48, 24, 50, 20, 46, 16, 42, 12, 38, 8, 34, 4, 30)(3, 29, 7, 33, 11, 37, 15, 41, 19, 45, 23, 49, 26, 52, 25, 51, 21, 47, 17, 43, 13, 39, 9, 35, 5, 31)(53, 79, 55, 81, 54, 80, 59, 85, 58, 84, 63, 89, 62, 88, 67, 93, 66, 92, 71, 97, 70, 96, 75, 101, 74, 100, 78, 104, 76, 102, 77, 103, 72, 98, 73, 99, 68, 94, 69, 95, 64, 90, 65, 91, 60, 86, 61, 87, 56, 82, 57, 83) L = (1, 56)(2, 53)(3, 57)(4, 60)(5, 61)(6, 54)(7, 55)(8, 64)(9, 65)(10, 58)(11, 59)(12, 68)(13, 69)(14, 62)(15, 63)(16, 72)(17, 73)(18, 66)(19, 67)(20, 76)(21, 77)(22, 70)(23, 71)(24, 74)(25, 78)(26, 75)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104) local type(s) :: { ( 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52 ), ( 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52 ) } Outer automorphisms :: reflexible Dual of E12.324 Graph:: bipartite v = 3 e = 52 f = 27 degree seq :: [ 26^2, 52 ] E12.303 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {13, 26, 26}) Quotient :: dipole Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, Y3^-1 * Y2^-1 * Y1^-1 * Y2, (Y3^-1, Y2^-1), (R * Y2)^2, (R * Y1)^2, (Y2^-1, Y1^-1), (R * Y3)^2, Y3^-1 * Y2^-1 * Y1 * Y3^2 * Y2, Y1^3 * Y2 * Y1 * Y2 * Y3^-1, Y2 * Y1 * Y2 * Y1 * Y3^-3, Y1 * Y2 * Y1^2 * Y2 * Y3^-2, Y2^2 * Y3 * Y2^2 * 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 ] Map:: R = (1, 27, 2, 28, 6, 32, 14, 40, 24, 50, 13, 39, 18, 44, 20, 46, 9, 35, 17, 43, 22, 48, 11, 37, 4, 30)(3, 29, 7, 33, 15, 41, 23, 49, 12, 38, 5, 31, 8, 34, 16, 42, 19, 45, 26, 52, 25, 51, 21, 47, 10, 36)(53, 79, 55, 81, 61, 87, 71, 97, 66, 92, 75, 101, 63, 89, 73, 99, 70, 96, 60, 86, 54, 80, 59, 85, 69, 95, 78, 104, 76, 102, 64, 90, 56, 82, 62, 88, 72, 98, 68, 94, 58, 84, 67, 93, 74, 100, 77, 103, 65, 91, 57, 83) L = (1, 56)(2, 53)(3, 62)(4, 63)(5, 64)(6, 54)(7, 55)(8, 57)(9, 72)(10, 73)(11, 74)(12, 75)(13, 76)(14, 58)(15, 59)(16, 60)(17, 61)(18, 65)(19, 68)(20, 70)(21, 77)(22, 69)(23, 67)(24, 66)(25, 78)(26, 71)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104) local type(s) :: { ( 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52 ), ( 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52 ) } Outer automorphisms :: reflexible Dual of E12.325 Graph:: bipartite v = 3 e = 52 f = 27 degree seq :: [ 26^2, 52 ] E12.304 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {13, 26, 26}) Quotient :: dipole Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, Y3 * Y1, Y3 * Y1, (Y2^-1, Y1^-1), Y2 * Y3^-1 * Y2^-1 * Y1^-1, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y2^4 * Y1^2 * Y3^-1, Y3^-1 * Y2 * Y3^-1 * Y1 * Y2^3, Y2^-1 * Y1^3 * Y3^-2 * Y2^-1, Y1^4 * Y2^-2 * Y3^-1, Y2^-1 * Y1 * Y2^-1 * Y1 * Y3^-3, Y2^-1 * Y3 * Y2^-1 * Y1^-2 * Y3^-1 * Y2 * 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 * Y2^2 * Y1 * Y2 * Y1^-1 ] Map:: R = (1, 27, 2, 28, 6, 32, 14, 40, 20, 46, 9, 35, 17, 43, 24, 50, 13, 39, 18, 44, 22, 48, 11, 37, 4, 30)(3, 29, 7, 33, 15, 41, 25, 51, 26, 52, 19, 45, 23, 49, 12, 38, 5, 31, 8, 34, 16, 42, 21, 47, 10, 36)(53, 79, 55, 81, 61, 87, 71, 97, 74, 100, 68, 94, 58, 84, 67, 93, 76, 102, 64, 90, 56, 82, 62, 88, 72, 98, 78, 104, 70, 96, 60, 86, 54, 80, 59, 85, 69, 95, 75, 101, 63, 89, 73, 99, 66, 92, 77, 103, 65, 91, 57, 83) L = (1, 56)(2, 53)(3, 62)(4, 63)(5, 64)(6, 54)(7, 55)(8, 57)(9, 72)(10, 73)(11, 74)(12, 75)(13, 76)(14, 58)(15, 59)(16, 60)(17, 61)(18, 65)(19, 78)(20, 66)(21, 68)(22, 70)(23, 71)(24, 69)(25, 67)(26, 77)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104) local type(s) :: { ( 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52 ), ( 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52 ) } Outer automorphisms :: reflexible Dual of E12.322 Graph:: bipartite v = 3 e = 52 f = 27 degree seq :: [ 26^2, 52 ] E12.305 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {13, 26, 26}) Quotient :: dipole Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, (R * Y1)^2, Y2 * Y3^-1 * Y2^-1 * Y1^-1, (R * Y3)^2, (R * Y2)^2, Y2^3 * Y1 * Y2, Y3^-2 * Y2 * Y3^2 * Y2^-1, Y2 * Y1^-1 * Y2 * Y1^-3 * Y3^2, Y2 * Y1^-1 * Y2 * Y3^4 * Y1^-1, Y3^-1 * Y2 * Y1^-1 * Y2 * Y1^7, Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^4 ] Map:: R = (1, 27, 2, 28, 6, 32, 14, 40, 22, 48, 18, 44, 9, 35, 13, 39, 17, 43, 25, 51, 20, 46, 11, 37, 4, 30)(3, 29, 7, 33, 15, 41, 23, 49, 26, 52, 21, 47, 12, 38, 5, 31, 8, 34, 16, 42, 24, 50, 19, 45, 10, 36)(53, 79, 55, 81, 61, 87, 64, 90, 56, 82, 62, 88, 70, 96, 73, 99, 63, 89, 71, 97, 74, 100, 78, 104, 72, 98, 76, 102, 66, 92, 75, 101, 77, 103, 68, 94, 58, 84, 67, 93, 69, 95, 60, 86, 54, 80, 59, 85, 65, 91, 57, 83) L = (1, 56)(2, 53)(3, 62)(4, 63)(5, 64)(6, 54)(7, 55)(8, 57)(9, 70)(10, 71)(11, 72)(12, 73)(13, 61)(14, 58)(15, 59)(16, 60)(17, 65)(18, 74)(19, 76)(20, 77)(21, 78)(22, 66)(23, 67)(24, 68)(25, 69)(26, 75)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104) local type(s) :: { ( 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52 ), ( 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52 ) } Outer automorphisms :: reflexible Dual of E12.328 Graph:: bipartite v = 3 e = 52 f = 27 degree seq :: [ 26^2, 52 ] E12.306 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {13, 26, 26}) Quotient :: dipole Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, (Y2, Y3^-1), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2^-1, Y1^-1), Y2 * Y3 * Y2^3, Y3^-1 * Y2 * Y1^3 * Y3^-2 * Y2, Y1^7 * Y2^-2, Y1^2 * Y2^-1 * Y1^5 * Y2^-1, Y2^-1 * Y1 * 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 ] Map:: R = (1, 27, 2, 28, 6, 32, 14, 40, 22, 48, 21, 47, 13, 39, 9, 35, 17, 43, 25, 51, 19, 45, 11, 37, 4, 30)(3, 29, 7, 33, 15, 41, 23, 49, 20, 46, 12, 38, 5, 31, 8, 34, 16, 42, 24, 50, 26, 52, 18, 44, 10, 36)(53, 79, 55, 81, 61, 87, 60, 86, 54, 80, 59, 85, 69, 95, 68, 94, 58, 84, 67, 93, 77, 103, 76, 102, 66, 92, 75, 101, 71, 97, 78, 104, 74, 100, 72, 98, 63, 89, 70, 96, 73, 99, 64, 90, 56, 82, 62, 88, 65, 91, 57, 83) L = (1, 56)(2, 53)(3, 62)(4, 63)(5, 64)(6, 54)(7, 55)(8, 57)(9, 65)(10, 70)(11, 71)(12, 72)(13, 73)(14, 58)(15, 59)(16, 60)(17, 61)(18, 78)(19, 77)(20, 75)(21, 74)(22, 66)(23, 67)(24, 68)(25, 69)(26, 76)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104) local type(s) :: { ( 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52 ), ( 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52 ) } Outer automorphisms :: reflexible Dual of E12.331 Graph:: bipartite v = 3 e = 52 f = 27 degree seq :: [ 26^2, 52 ] E12.307 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {13, 26, 26}) Quotient :: dipole Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), (Y3^-1, Y2^-1), (R * Y2)^2, Y1 * Y2 * Y1^2 * Y2, Y2^-8 * 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 ] Map:: R = (1, 27, 2, 28, 6, 32, 13, 39, 15, 41, 20, 46, 25, 51, 22, 48, 24, 50, 17, 43, 9, 35, 11, 37, 4, 30)(3, 29, 7, 33, 12, 38, 5, 31, 8, 34, 14, 40, 19, 45, 21, 47, 26, 52, 23, 49, 16, 42, 18, 44, 10, 36)(53, 79, 55, 81, 61, 87, 68, 94, 74, 100, 73, 99, 67, 93, 60, 86, 54, 80, 59, 85, 63, 89, 70, 96, 76, 102, 78, 104, 72, 98, 66, 92, 58, 84, 64, 90, 56, 82, 62, 88, 69, 95, 75, 101, 77, 103, 71, 97, 65, 91, 57, 83) L = (1, 56)(2, 53)(3, 62)(4, 63)(5, 64)(6, 54)(7, 55)(8, 57)(9, 69)(10, 70)(11, 61)(12, 59)(13, 58)(14, 60)(15, 65)(16, 75)(17, 76)(18, 68)(19, 66)(20, 67)(21, 71)(22, 77)(23, 78)(24, 74)(25, 72)(26, 73)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104) local type(s) :: { ( 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52 ), ( 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52 ) } Outer automorphisms :: reflexible Dual of E12.326 Graph:: bipartite v = 3 e = 52 f = 27 degree seq :: [ 26^2, 52 ] E12.308 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {13, 26, 26}) Quotient :: dipole Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y2^-1, Y1^-1), (Y3^-1, Y2^-1), Y2 * Y1^-1 * Y2 * Y1^-2, Y2 * Y1 * Y2^7, 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 ] Map:: R = (1, 27, 2, 28, 6, 32, 9, 35, 15, 41, 20, 46, 22, 48, 25, 51, 23, 49, 18, 44, 13, 39, 11, 37, 4, 30)(3, 29, 7, 33, 14, 40, 16, 42, 21, 47, 26, 52, 24, 50, 19, 45, 17, 43, 12, 38, 5, 31, 8, 34, 10, 36)(53, 79, 55, 81, 61, 87, 68, 94, 74, 100, 76, 102, 70, 96, 64, 90, 56, 82, 62, 88, 58, 84, 66, 92, 72, 98, 78, 104, 75, 101, 69, 95, 63, 89, 60, 86, 54, 80, 59, 85, 67, 93, 73, 99, 77, 103, 71, 97, 65, 91, 57, 83) L = (1, 56)(2, 53)(3, 62)(4, 63)(5, 64)(6, 54)(7, 55)(8, 57)(9, 58)(10, 60)(11, 65)(12, 69)(13, 70)(14, 59)(15, 61)(16, 66)(17, 71)(18, 75)(19, 76)(20, 67)(21, 68)(22, 72)(23, 77)(24, 78)(25, 74)(26, 73)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104) local type(s) :: { ( 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52 ), ( 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52 ) } Outer automorphisms :: reflexible Dual of E12.329 Graph:: bipartite v = 3 e = 52 f = 27 degree seq :: [ 26^2, 52 ] E12.309 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {13, 26, 26}) Quotient :: dipole Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, (R * Y2)^2, Y2 * Y3^-1 * Y2^-1 * Y1^-1, (R * Y1)^2, (R * Y3)^2, Y1^-1 * Y2 * Y3 * Y2 * Y1^-2, Y3^3 * Y2^2 * Y1^-1, Y2 * Y3^-1 * Y2^5, Y2 * Y1^9 * 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 * Y3^-2 ] Map:: R = (1, 27, 2, 28, 6, 32, 14, 40, 9, 35, 17, 43, 24, 50, 26, 52, 21, 47, 13, 39, 18, 44, 11, 37, 4, 30)(3, 29, 7, 33, 15, 41, 23, 49, 19, 45, 22, 48, 25, 51, 20, 46, 12, 38, 5, 31, 8, 34, 16, 42, 10, 36)(53, 79, 55, 81, 61, 87, 71, 97, 73, 99, 64, 90, 56, 82, 62, 88, 66, 92, 75, 101, 78, 104, 72, 98, 63, 89, 68, 94, 58, 84, 67, 93, 76, 102, 77, 103, 70, 96, 60, 86, 54, 80, 59, 85, 69, 95, 74, 100, 65, 91, 57, 83) L = (1, 56)(2, 53)(3, 62)(4, 63)(5, 64)(6, 54)(7, 55)(8, 57)(9, 66)(10, 68)(11, 70)(12, 72)(13, 73)(14, 58)(15, 59)(16, 60)(17, 61)(18, 65)(19, 75)(20, 77)(21, 78)(22, 71)(23, 67)(24, 69)(25, 74)(26, 76)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104) local type(s) :: { ( 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52 ), ( 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52 ) } Outer automorphisms :: reflexible Dual of E12.323 Graph:: bipartite v = 3 e = 52 f = 27 degree seq :: [ 26^2, 52 ] E12.310 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {13, 26, 26}) Quotient :: dipole Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, (Y2, Y1^-1), (R * Y2)^2, (R * Y3)^2, (Y3^-1, Y2^-1), (R * Y1)^2, (Y2^-1, Y1^-1), Y3 * Y2^-2 * Y1^-3, Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y1^-1, Y2 * Y3 * Y2^5, Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y3^-2 * Y2^-2, Y2^-2 * Y1^9 ] Map:: R = (1, 27, 2, 28, 6, 32, 14, 40, 13, 39, 18, 44, 24, 50, 26, 52, 20, 46, 9, 35, 17, 43, 11, 37, 4, 30)(3, 29, 7, 33, 15, 41, 12, 38, 5, 31, 8, 34, 16, 42, 23, 49, 22, 48, 19, 45, 25, 51, 21, 47, 10, 36)(53, 79, 55, 81, 61, 87, 71, 97, 70, 96, 60, 86, 54, 80, 59, 85, 69, 95, 77, 103, 76, 102, 68, 94, 58, 84, 67, 93, 63, 89, 73, 99, 78, 104, 75, 101, 66, 92, 64, 90, 56, 82, 62, 88, 72, 98, 74, 100, 65, 91, 57, 83) L = (1, 56)(2, 53)(3, 62)(4, 63)(5, 64)(6, 54)(7, 55)(8, 57)(9, 72)(10, 73)(11, 69)(12, 67)(13, 66)(14, 58)(15, 59)(16, 60)(17, 61)(18, 65)(19, 74)(20, 78)(21, 77)(22, 75)(23, 68)(24, 70)(25, 71)(26, 76)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104) local type(s) :: { ( 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52 ), ( 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52 ) } Outer automorphisms :: reflexible Dual of E12.321 Graph:: bipartite v = 3 e = 52 f = 27 degree seq :: [ 26^2, 52 ] E12.311 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {13, 26, 26}) Quotient :: dipole Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-1, Y2^3 * Y1^-1, (R * Y1)^2, R * Y2 * R * Y3, Y1 * Y2^-1 * Y1^8, (Y3^-1 * Y1^-1)^13 ] Map:: R = (1, 27, 2, 28, 6, 32, 12, 38, 18, 44, 24, 50, 21, 47, 15, 41, 9, 35, 3, 29, 7, 33, 13, 39, 19, 45, 25, 51, 23, 49, 17, 43, 11, 37, 5, 31, 8, 34, 14, 40, 20, 46, 26, 52, 22, 48, 16, 42, 10, 36, 4, 30)(53, 79, 55, 81, 60, 86, 54, 80, 59, 85, 66, 92, 58, 84, 65, 91, 72, 98, 64, 90, 71, 97, 78, 104, 70, 96, 77, 103, 74, 100, 76, 102, 75, 101, 68, 94, 73, 99, 69, 95, 62, 88, 67, 93, 63, 89, 56, 82, 61, 87, 57, 83) L = (1, 55)(2, 59)(3, 60)(4, 61)(5, 53)(6, 65)(7, 66)(8, 54)(9, 57)(10, 67)(11, 56)(12, 71)(13, 72)(14, 58)(15, 63)(16, 73)(17, 62)(18, 77)(19, 78)(20, 64)(21, 69)(22, 76)(23, 68)(24, 75)(25, 74)(26, 70)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104) local type(s) :: { ( 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26 ) } Outer automorphisms :: reflexible Dual of E12.318 Graph:: bipartite v = 2 e = 52 f = 28 degree seq :: [ 52^2 ] E12.312 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {13, 26, 26}) Quotient :: dipole Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-1, Y2^-1 * Y1^-1 * Y2^-2, (R * Y1)^2, R * Y2 * R * Y3, (Y2^-1, Y1^-1), Y2^-1 * Y1^-9, (Y3^-1 * Y1^-1)^13 ] Map:: R = (1, 27, 2, 28, 6, 32, 12, 38, 18, 44, 24, 50, 21, 47, 15, 41, 9, 35, 5, 31, 8, 34, 14, 40, 20, 46, 26, 52, 22, 48, 16, 42, 10, 36, 3, 29, 7, 33, 13, 39, 19, 45, 25, 51, 23, 49, 17, 43, 11, 37, 4, 30)(53, 79, 55, 81, 61, 87, 56, 82, 62, 88, 67, 93, 63, 89, 68, 94, 73, 99, 69, 95, 74, 100, 76, 102, 75, 101, 78, 104, 70, 96, 77, 103, 72, 98, 64, 90, 71, 97, 66, 92, 58, 84, 65, 91, 60, 86, 54, 80, 59, 85, 57, 83) L = (1, 55)(2, 59)(3, 61)(4, 62)(5, 53)(6, 65)(7, 57)(8, 54)(9, 56)(10, 67)(11, 68)(12, 71)(13, 60)(14, 58)(15, 63)(16, 73)(17, 74)(18, 77)(19, 66)(20, 64)(21, 69)(22, 76)(23, 78)(24, 75)(25, 72)(26, 70)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104) local type(s) :: { ( 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26 ) } Outer automorphisms :: reflexible Dual of E12.320 Graph:: bipartite v = 2 e = 52 f = 28 degree seq :: [ 52^2 ] E12.313 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {13, 26, 26}) Quotient :: dipole Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-1, (R * Y1)^2, R * Y2 * R * Y3, (Y1, Y2^-1), Y2^-1 * Y1^-5, Y2^4 * Y1^-1 * Y2, (Y3^-1 * Y1^-1)^13 ] Map:: R = (1, 27, 2, 28, 6, 32, 14, 40, 12, 38, 5, 31, 8, 34, 16, 42, 22, 48, 21, 47, 13, 39, 18, 44, 24, 50, 26, 52, 25, 51, 19, 45, 9, 35, 17, 43, 23, 49, 20, 46, 10, 36, 3, 29, 7, 33, 15, 41, 11, 37, 4, 30)(53, 79, 55, 81, 61, 87, 70, 96, 60, 86, 54, 80, 59, 85, 69, 95, 76, 102, 68, 94, 58, 84, 67, 93, 75, 101, 78, 104, 74, 100, 66, 92, 63, 89, 72, 98, 77, 103, 73, 99, 64, 90, 56, 82, 62, 88, 71, 97, 65, 91, 57, 83) L = (1, 55)(2, 59)(3, 61)(4, 62)(5, 53)(6, 67)(7, 69)(8, 54)(9, 70)(10, 71)(11, 72)(12, 56)(13, 57)(14, 63)(15, 75)(16, 58)(17, 76)(18, 60)(19, 65)(20, 77)(21, 64)(22, 66)(23, 78)(24, 68)(25, 73)(26, 74)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104) local type(s) :: { ( 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26 ) } Outer automorphisms :: reflexible Dual of E12.317 Graph:: bipartite v = 2 e = 52 f = 28 degree seq :: [ 52^2 ] E12.314 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {13, 26, 26}) Quotient :: dipole Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-1, (R * Y1)^2, R * Y2 * R * Y3, (Y2^-1, Y1^-1), Y2 * Y1^-1 * Y2 * Y1^-3, Y2^-1 * Y1^-1 * Y2^-4 * Y1^-2, (Y3^-1 * Y1^-1)^13 ] Map:: R = (1, 27, 2, 28, 6, 32, 14, 40, 9, 35, 17, 43, 24, 50, 22, 48, 26, 52, 20, 46, 12, 38, 5, 31, 8, 34, 16, 42, 10, 36, 3, 29, 7, 33, 15, 41, 23, 49, 19, 45, 25, 51, 21, 47, 13, 39, 18, 44, 11, 37, 4, 30)(53, 79, 55, 81, 61, 87, 71, 97, 78, 104, 70, 96, 60, 86, 54, 80, 59, 85, 69, 95, 77, 103, 72, 98, 63, 89, 68, 94, 58, 84, 67, 93, 76, 102, 73, 99, 64, 90, 56, 82, 62, 88, 66, 92, 75, 101, 74, 100, 65, 91, 57, 83) L = (1, 55)(2, 59)(3, 61)(4, 62)(5, 53)(6, 67)(7, 69)(8, 54)(9, 71)(10, 66)(11, 68)(12, 56)(13, 57)(14, 75)(15, 76)(16, 58)(17, 77)(18, 60)(19, 78)(20, 63)(21, 64)(22, 65)(23, 74)(24, 73)(25, 72)(26, 70)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104) local type(s) :: { ( 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26 ) } Outer automorphisms :: reflexible Dual of E12.319 Graph:: bipartite v = 2 e = 52 f = 28 degree seq :: [ 52^2 ] E12.315 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {13, 26, 26}) Quotient :: dipole Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-1, (R * Y1)^2, (Y2, Y1), R * Y2 * R * Y3, Y1^-3 * Y2^-1 * Y1^-1 * Y2^-1, Y2^-4 * Y1^3 * Y2^-1, Y2^2 * Y1^2 * Y2^-2 * Y1^-2, (Y3^-1 * Y1^-1)^13 ] Map:: R = (1, 27, 2, 28, 6, 32, 14, 40, 13, 39, 18, 44, 24, 50, 19, 45, 25, 51, 21, 47, 10, 36, 3, 29, 7, 33, 15, 41, 12, 38, 5, 31, 8, 34, 16, 42, 23, 49, 22, 48, 26, 52, 20, 46, 9, 35, 17, 43, 11, 37, 4, 30)(53, 79, 55, 81, 61, 87, 71, 97, 75, 101, 66, 92, 64, 90, 56, 82, 62, 88, 72, 98, 76, 102, 68, 94, 58, 84, 67, 93, 63, 89, 73, 99, 78, 104, 70, 96, 60, 86, 54, 80, 59, 85, 69, 95, 77, 103, 74, 100, 65, 91, 57, 83) L = (1, 55)(2, 59)(3, 61)(4, 62)(5, 53)(6, 67)(7, 69)(8, 54)(9, 71)(10, 72)(11, 73)(12, 56)(13, 57)(14, 64)(15, 63)(16, 58)(17, 77)(18, 60)(19, 75)(20, 76)(21, 78)(22, 65)(23, 66)(24, 68)(25, 74)(26, 70)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104) local type(s) :: { ( 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26 ) } Outer automorphisms :: reflexible Dual of E12.316 Graph:: bipartite v = 2 e = 52 f = 28 degree seq :: [ 52^2 ] E12.316 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {13, 26, 26}) Quotient :: dipole Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ Y1, R^2, Y2^-2 * Y3^-2, (Y2^-1 * R)^2, (R * Y3)^2, (R * Y1)^2, (Y2, Y3^-1), Y2^-1 * Y3^12, Y2^4 * Y3^-1 * Y2^2 * Y3^-5 * Y2, Y2^13, 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^-1 * Y1^-1)^26 ] Map:: R = (1, 27)(2, 28)(3, 29)(4, 30)(5, 31)(6, 32)(7, 33)(8, 34)(9, 35)(10, 36)(11, 37)(12, 38)(13, 39)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52)(53, 79, 54, 80, 58, 84, 63, 89, 67, 93, 71, 97, 75, 101, 77, 103, 74, 100, 69, 95, 66, 92, 61, 87, 56, 82)(55, 81, 59, 85, 57, 83, 60, 86, 64, 90, 68, 94, 72, 98, 76, 102, 78, 104, 73, 99, 70, 96, 65, 91, 62, 88) L = (1, 55)(2, 59)(3, 61)(4, 62)(5, 53)(6, 57)(7, 56)(8, 54)(9, 65)(10, 66)(11, 60)(12, 58)(13, 69)(14, 70)(15, 64)(16, 63)(17, 73)(18, 74)(19, 68)(20, 67)(21, 77)(22, 78)(23, 72)(24, 71)(25, 76)(26, 75)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104) local type(s) :: { ( 52, 52 ), ( 52^26 ) } Outer automorphisms :: reflexible Dual of E12.315 Graph:: simple bipartite v = 28 e = 52 f = 2 degree seq :: [ 2^26, 26^2 ] E12.317 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {13, 26, 26}) Quotient :: dipole Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y3^-1, Y2^-1), Y3 * Y2 * Y3^3, Y2 * Y3^-1 * Y2 * Y3^-1 * Y2^4, 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^-1 * Y1^-1)^26 ] Map:: R = (1, 27)(2, 28)(3, 29)(4, 30)(5, 31)(6, 32)(7, 33)(8, 34)(9, 35)(10, 36)(11, 37)(12, 38)(13, 39)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52)(53, 79, 54, 80, 58, 84, 66, 92, 74, 100, 70, 96, 61, 87, 65, 91, 69, 95, 77, 103, 72, 98, 63, 89, 56, 82)(55, 81, 59, 85, 67, 93, 75, 101, 78, 104, 73, 99, 64, 90, 57, 83, 60, 86, 68, 94, 76, 102, 71, 97, 62, 88) L = (1, 55)(2, 59)(3, 61)(4, 62)(5, 53)(6, 67)(7, 65)(8, 54)(9, 64)(10, 70)(11, 71)(12, 56)(13, 57)(14, 75)(15, 69)(16, 58)(17, 60)(18, 73)(19, 74)(20, 76)(21, 63)(22, 78)(23, 77)(24, 66)(25, 68)(26, 72)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104) local type(s) :: { ( 52, 52 ), ( 52^26 ) } Outer automorphisms :: reflexible Dual of E12.313 Graph:: simple bipartite v = 28 e = 52 f = 2 degree seq :: [ 2^26, 26^2 ] E12.318 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {13, 26, 26}) Quotient :: dipole Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ Y1, R^2, (Y3, Y2), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3^-4 * Y2, (Y2^-1 * Y3^-1 * Y2^-2)^2, Y2^2 * Y3^-1 * Y2^4 * Y3^-1 * Y2, (Y3^-1 * Y1^-1)^26 ] Map:: R = (1, 27)(2, 28)(3, 29)(4, 30)(5, 31)(6, 32)(7, 33)(8, 34)(9, 35)(10, 36)(11, 37)(12, 38)(13, 39)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52)(53, 79, 54, 80, 58, 84, 66, 92, 74, 100, 73, 99, 65, 91, 61, 87, 69, 95, 77, 103, 71, 97, 63, 89, 56, 82)(55, 81, 59, 85, 67, 93, 75, 101, 72, 98, 64, 90, 57, 83, 60, 86, 68, 94, 76, 102, 78, 104, 70, 96, 62, 88) L = (1, 55)(2, 59)(3, 61)(4, 62)(5, 53)(6, 67)(7, 69)(8, 54)(9, 60)(10, 65)(11, 70)(12, 56)(13, 57)(14, 75)(15, 77)(16, 58)(17, 68)(18, 73)(19, 78)(20, 63)(21, 64)(22, 72)(23, 71)(24, 66)(25, 76)(26, 74)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104) local type(s) :: { ( 52, 52 ), ( 52^26 ) } Outer automorphisms :: reflexible Dual of E12.311 Graph:: simple bipartite v = 28 e = 52 f = 2 degree seq :: [ 2^26, 26^2 ] E12.319 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {13, 26, 26}) Quotient :: dipole Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y2, Y3^-1), Y2 * Y3 * Y2 * Y3 * 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^-1 * Y1^-1)^26 ] Map:: R = (1, 27)(2, 28)(3, 29)(4, 30)(5, 31)(6, 32)(7, 33)(8, 34)(9, 35)(10, 36)(11, 37)(12, 38)(13, 39)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52)(53, 79, 54, 80, 58, 84, 65, 91, 67, 93, 72, 98, 77, 103, 74, 100, 76, 102, 69, 95, 61, 87, 63, 89, 56, 82)(55, 81, 59, 85, 64, 90, 57, 83, 60, 86, 66, 92, 71, 97, 73, 99, 78, 104, 75, 101, 68, 94, 70, 96, 62, 88) L = (1, 55)(2, 59)(3, 61)(4, 62)(5, 53)(6, 64)(7, 63)(8, 54)(9, 68)(10, 69)(11, 70)(12, 56)(13, 57)(14, 58)(15, 60)(16, 74)(17, 75)(18, 76)(19, 65)(20, 66)(21, 67)(22, 73)(23, 77)(24, 78)(25, 71)(26, 72)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104) local type(s) :: { ( 52, 52 ), ( 52^26 ) } Outer automorphisms :: reflexible Dual of E12.314 Graph:: simple bipartite v = 28 e = 52 f = 2 degree seq :: [ 2^26, 26^2 ] E12.320 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {13, 26, 26}) Quotient :: dipole Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y2, Y3^-1), Y2^3 * Y3^-2, Y2 * Y3^8, (Y3^-1 * Y1^-1)^26 ] Map:: R = (1, 27)(2, 28)(3, 29)(4, 30)(5, 31)(6, 32)(7, 33)(8, 34)(9, 35)(10, 36)(11, 37)(12, 38)(13, 39)(14, 40)(15, 41)(16, 42)(17, 43)(18, 44)(19, 45)(20, 46)(21, 47)(22, 48)(23, 49)(24, 50)(25, 51)(26, 52)(53, 79, 54, 80, 58, 84, 61, 87, 67, 93, 72, 98, 74, 100, 77, 103, 75, 101, 70, 96, 65, 91, 63, 89, 56, 82)(55, 81, 59, 85, 66, 92, 68, 94, 73, 99, 78, 104, 76, 102, 71, 97, 69, 95, 64, 90, 57, 83, 60, 86, 62, 88) L = (1, 55)(2, 59)(3, 61)(4, 62)(5, 53)(6, 66)(7, 67)(8, 54)(9, 68)(10, 58)(11, 60)(12, 56)(13, 57)(14, 72)(15, 73)(16, 74)(17, 63)(18, 64)(19, 65)(20, 78)(21, 77)(22, 76)(23, 69)(24, 70)(25, 71)(26, 75)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104) local type(s) :: { ( 52, 52 ), ( 52^26 ) } Outer automorphisms :: reflexible Dual of E12.312 Graph:: simple bipartite v = 28 e = 52 f = 2 degree seq :: [ 2^26, 26^2 ] E12.321 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {13, 26, 26}) Quotient :: dipole Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ Y2, R^2, (Y3 * Y1^-1)^2, (Y3, Y1^-1), (R * Y1)^2, (R * Y3)^2, Y3^-1 * Y1^2 * Y3^-1, (R * Y2 * Y3^-1)^2, Y3^6 * Y1 * Y3^5 * Y1, (Y3 * Y2^-1)^13, 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 ] Map:: R = (1, 27, 2, 28, 6, 32, 11, 37, 15, 41, 19, 45, 23, 49, 26, 52, 22, 48, 18, 44, 14, 40, 10, 36, 5, 31, 8, 34, 3, 29, 7, 33, 12, 38, 16, 42, 20, 46, 24, 50, 25, 51, 21, 47, 17, 43, 13, 39, 9, 35, 4, 30)(53, 79)(54, 80)(55, 81)(56, 82)(57, 83)(58, 84)(59, 85)(60, 86)(61, 87)(62, 88)(63, 89)(64, 90)(65, 91)(66, 92)(67, 93)(68, 94)(69, 95)(70, 96)(71, 97)(72, 98)(73, 99)(74, 100)(75, 101)(76, 102)(77, 103)(78, 104) L = (1, 55)(2, 59)(3, 58)(4, 60)(5, 53)(6, 64)(7, 63)(8, 54)(9, 57)(10, 56)(11, 68)(12, 67)(13, 62)(14, 61)(15, 72)(16, 71)(17, 66)(18, 65)(19, 76)(20, 75)(21, 70)(22, 69)(23, 77)(24, 78)(25, 74)(26, 73)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104) local type(s) :: { ( 26, 52 ), ( 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52 ) } Outer automorphisms :: reflexible Dual of E12.310 Graph:: bipartite v = 27 e = 52 f = 3 degree seq :: [ 2^26, 52 ] E12.322 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {13, 26, 26}) Quotient :: dipole Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ Y2, R^2, (Y3^-1, Y1), (R * Y1)^2, (R * Y3)^2, Y1 * Y3 * Y1^3, (R * Y2 * Y3^-1)^2, Y3^4 * Y1^-1 * Y3 * Y1^-1 * Y3, (Y3 * Y2^-1)^13 ] Map:: R = (1, 27, 2, 28, 6, 32, 12, 38, 5, 31, 8, 34, 14, 40, 20, 46, 13, 39, 16, 42, 22, 48, 26, 52, 21, 47, 24, 50, 17, 43, 23, 49, 25, 51, 18, 44, 9, 35, 15, 41, 19, 45, 10, 36, 3, 29, 7, 33, 11, 37, 4, 30)(53, 79)(54, 80)(55, 81)(56, 82)(57, 83)(58, 84)(59, 85)(60, 86)(61, 87)(62, 88)(63, 89)(64, 90)(65, 91)(66, 92)(67, 93)(68, 94)(69, 95)(70, 96)(71, 97)(72, 98)(73, 99)(74, 100)(75, 101)(76, 102)(77, 103)(78, 104) L = (1, 55)(2, 59)(3, 61)(4, 62)(5, 53)(6, 63)(7, 67)(8, 54)(9, 69)(10, 70)(11, 71)(12, 56)(13, 57)(14, 58)(15, 75)(16, 60)(17, 74)(18, 76)(19, 77)(20, 64)(21, 65)(22, 66)(23, 78)(24, 68)(25, 73)(26, 72)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104) local type(s) :: { ( 26, 52 ), ( 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52 ) } Outer automorphisms :: reflexible Dual of E12.304 Graph:: bipartite v = 27 e = 52 f = 3 degree seq :: [ 2^26, 52 ] E12.323 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {13, 26, 26}) Quotient :: dipole Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ Y2, R^2, (Y1, Y3), (R * Y1)^2, (R * Y3)^2, Y1^2 * Y3^-1 * Y1^2, (R * Y2 * Y3^-1)^2, Y1 * Y3 * Y1 * Y3^5, Y1^-1 * Y3^3 * Y1^-1 * Y3^4, (Y3 * Y2^-1)^13 ] Map:: R = (1, 27, 2, 28, 6, 32, 10, 36, 3, 29, 7, 33, 14, 40, 18, 44, 9, 35, 15, 41, 22, 48, 26, 52, 17, 43, 23, 49, 21, 47, 24, 50, 25, 51, 20, 46, 13, 39, 16, 42, 19, 45, 12, 38, 5, 31, 8, 34, 11, 37, 4, 30)(53, 79)(54, 80)(55, 81)(56, 82)(57, 83)(58, 84)(59, 85)(60, 86)(61, 87)(62, 88)(63, 89)(64, 90)(65, 91)(66, 92)(67, 93)(68, 94)(69, 95)(70, 96)(71, 97)(72, 98)(73, 99)(74, 100)(75, 101)(76, 102)(77, 103)(78, 104) L = (1, 55)(2, 59)(3, 61)(4, 62)(5, 53)(6, 66)(7, 67)(8, 54)(9, 69)(10, 70)(11, 58)(12, 56)(13, 57)(14, 74)(15, 75)(16, 60)(17, 77)(18, 78)(19, 63)(20, 64)(21, 65)(22, 73)(23, 72)(24, 68)(25, 71)(26, 76)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104) local type(s) :: { ( 26, 52 ), ( 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52 ) } Outer automorphisms :: reflexible Dual of E12.309 Graph:: bipartite v = 27 e = 52 f = 3 degree seq :: [ 2^26, 52 ] E12.324 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {13, 26, 26}) Quotient :: dipole Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1^-1), Y3^3 * Y1^2, (R * Y2 * Y3^-1)^2, Y3 * Y1^-8, (Y3 * Y2^-1)^13 ] Map:: R = (1, 27, 2, 28, 6, 32, 14, 40, 20, 46, 24, 50, 18, 44, 10, 36, 3, 29, 7, 33, 13, 39, 16, 42, 22, 48, 26, 52, 23, 49, 17, 43, 9, 35, 12, 38, 5, 31, 8, 34, 15, 41, 21, 47, 25, 51, 19, 45, 11, 37, 4, 30)(53, 79)(54, 80)(55, 81)(56, 82)(57, 83)(58, 84)(59, 85)(60, 86)(61, 87)(62, 88)(63, 89)(64, 90)(65, 91)(66, 92)(67, 93)(68, 94)(69, 95)(70, 96)(71, 97)(72, 98)(73, 99)(74, 100)(75, 101)(76, 102)(77, 103)(78, 104) L = (1, 55)(2, 59)(3, 61)(4, 62)(5, 53)(6, 65)(7, 64)(8, 54)(9, 63)(10, 69)(11, 70)(12, 56)(13, 57)(14, 68)(15, 58)(16, 60)(17, 71)(18, 75)(19, 76)(20, 74)(21, 66)(22, 67)(23, 77)(24, 78)(25, 72)(26, 73)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104) local type(s) :: { ( 26, 52 ), ( 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52 ) } Outer automorphisms :: reflexible Dual of E12.302 Graph:: bipartite v = 27 e = 52 f = 3 degree seq :: [ 2^26, 52 ] E12.325 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {13, 26, 26}) Quotient :: dipole Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1^-1), Y3^-1 * Y1 * Y3^-2 * Y1, (R * Y2 * Y3^-1)^2, Y1^3 * Y3 * Y1^5, (Y3 * Y2^-1)^13, (Y1^-1 * Y3^-1)^26 ] Map:: R = (1, 27, 2, 28, 6, 32, 14, 40, 20, 46, 24, 50, 18, 44, 12, 38, 5, 31, 8, 34, 9, 35, 16, 42, 22, 48, 26, 52, 25, 51, 19, 45, 13, 39, 10, 36, 3, 29, 7, 33, 15, 41, 21, 47, 23, 49, 17, 43, 11, 37, 4, 30)(53, 79)(54, 80)(55, 81)(56, 82)(57, 83)(58, 84)(59, 85)(60, 86)(61, 87)(62, 88)(63, 89)(64, 90)(65, 91)(66, 92)(67, 93)(68, 94)(69, 95)(70, 96)(71, 97)(72, 98)(73, 99)(74, 100)(75, 101)(76, 102)(77, 103)(78, 104) L = (1, 55)(2, 59)(3, 61)(4, 62)(5, 53)(6, 67)(7, 68)(8, 54)(9, 58)(10, 60)(11, 65)(12, 56)(13, 57)(14, 73)(15, 74)(16, 66)(17, 71)(18, 63)(19, 64)(20, 75)(21, 78)(22, 72)(23, 77)(24, 69)(25, 70)(26, 76)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104) local type(s) :: { ( 26, 52 ), ( 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52 ) } Outer automorphisms :: reflexible Dual of E12.303 Graph:: bipartite v = 27 e = 52 f = 3 degree seq :: [ 2^26, 52 ] E12.326 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {13, 26, 26}) Quotient :: dipole Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ Y2, R^2, Y1^2 * Y3^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^13, (Y3 * Y2^-1)^13, (Y3^-1 * Y1^-1)^26 ] Map:: R = (1, 27, 2, 28, 3, 29, 6, 32, 7, 33, 10, 36, 11, 37, 14, 40, 15, 41, 18, 44, 19, 45, 22, 48, 23, 49, 26, 52, 25, 51, 24, 50, 21, 47, 20, 46, 17, 43, 16, 42, 13, 39, 12, 38, 9, 35, 8, 34, 5, 31, 4, 30)(53, 79)(54, 80)(55, 81)(56, 82)(57, 83)(58, 84)(59, 85)(60, 86)(61, 87)(62, 88)(63, 89)(64, 90)(65, 91)(66, 92)(67, 93)(68, 94)(69, 95)(70, 96)(71, 97)(72, 98)(73, 99)(74, 100)(75, 101)(76, 102)(77, 103)(78, 104) L = (1, 55)(2, 58)(3, 59)(4, 54)(5, 53)(6, 62)(7, 63)(8, 56)(9, 57)(10, 66)(11, 67)(12, 60)(13, 61)(14, 70)(15, 71)(16, 64)(17, 65)(18, 74)(19, 75)(20, 68)(21, 69)(22, 78)(23, 77)(24, 72)(25, 73)(26, 76)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104) local type(s) :: { ( 26, 52 ), ( 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52 ) } Outer automorphisms :: reflexible Dual of E12.307 Graph:: bipartite v = 27 e = 52 f = 3 degree seq :: [ 2^26, 52 ] E12.327 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {13, 26, 26}) Quotient :: dipole Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ Y2, R^2, Y1^2 * Y3, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^13, (Y3^6 * Y1^-1)^2, (Y3 * Y2^-1)^13 ] Map:: R = (1, 27, 2, 28, 5, 31, 6, 32, 9, 35, 10, 36, 13, 39, 14, 40, 17, 43, 18, 44, 21, 47, 22, 48, 25, 51, 26, 52, 23, 49, 24, 50, 19, 45, 20, 46, 15, 41, 16, 42, 11, 37, 12, 38, 7, 33, 8, 34, 3, 29, 4, 30)(53, 79)(54, 80)(55, 81)(56, 82)(57, 83)(58, 84)(59, 85)(60, 86)(61, 87)(62, 88)(63, 89)(64, 90)(65, 91)(66, 92)(67, 93)(68, 94)(69, 95)(70, 96)(71, 97)(72, 98)(73, 99)(74, 100)(75, 101)(76, 102)(77, 103)(78, 104) L = (1, 55)(2, 56)(3, 59)(4, 60)(5, 53)(6, 54)(7, 63)(8, 64)(9, 57)(10, 58)(11, 67)(12, 68)(13, 61)(14, 62)(15, 71)(16, 72)(17, 65)(18, 66)(19, 75)(20, 76)(21, 69)(22, 70)(23, 77)(24, 78)(25, 73)(26, 74)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104) local type(s) :: { ( 26, 52 ), ( 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52 ) } Outer automorphisms :: reflexible Dual of E12.301 Graph:: bipartite v = 27 e = 52 f = 3 degree seq :: [ 2^26, 52 ] E12.328 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {13, 26, 26}) Quotient :: dipole Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1), (R * Y2 * Y3^-1)^2, Y3^-5 * Y1^2, Y3^3 * Y1^4, Y1^2 * Y3^-18, (Y3 * Y2^-1)^13 ] Map:: R = (1, 27, 2, 28, 6, 32, 14, 40, 25, 51, 20, 46, 9, 35, 17, 43, 23, 49, 12, 38, 5, 31, 8, 34, 16, 42, 26, 52, 21, 47, 10, 36, 3, 29, 7, 33, 15, 41, 24, 50, 13, 39, 18, 44, 19, 45, 22, 48, 11, 37, 4, 30)(53, 79)(54, 80)(55, 81)(56, 82)(57, 83)(58, 84)(59, 85)(60, 86)(61, 87)(62, 88)(63, 89)(64, 90)(65, 91)(66, 92)(67, 93)(68, 94)(69, 95)(70, 96)(71, 97)(72, 98)(73, 99)(74, 100)(75, 101)(76, 102)(77, 103)(78, 104) L = (1, 55)(2, 59)(3, 61)(4, 62)(5, 53)(6, 67)(7, 69)(8, 54)(9, 71)(10, 72)(11, 73)(12, 56)(13, 57)(14, 76)(15, 75)(16, 58)(17, 74)(18, 60)(19, 68)(20, 70)(21, 77)(22, 78)(23, 63)(24, 64)(25, 65)(26, 66)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104) local type(s) :: { ( 26, 52 ), ( 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52 ) } Outer automorphisms :: reflexible Dual of E12.305 Graph:: bipartite v = 27 e = 52 f = 3 degree seq :: [ 2^26, 52 ] E12.329 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {13, 26, 26}) Quotient :: dipole Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y1^-1, Y3^-1), (R * Y2 * Y3^-1)^2, Y1^3 * Y3^-1 * Y1 * Y3^-2, Y3 * Y1 * Y3^4 * Y1, (Y3 * Y2^-1)^13 ] Map:: R = (1, 27, 2, 28, 6, 32, 14, 40, 19, 45, 24, 50, 13, 39, 18, 44, 21, 47, 10, 36, 3, 29, 7, 33, 15, 41, 26, 52, 23, 49, 12, 38, 5, 31, 8, 34, 16, 42, 20, 46, 9, 35, 17, 43, 25, 51, 22, 48, 11, 37, 4, 30)(53, 79)(54, 80)(55, 81)(56, 82)(57, 83)(58, 84)(59, 85)(60, 86)(61, 87)(62, 88)(63, 89)(64, 90)(65, 91)(66, 92)(67, 93)(68, 94)(69, 95)(70, 96)(71, 97)(72, 98)(73, 99)(74, 100)(75, 101)(76, 102)(77, 103)(78, 104) L = (1, 55)(2, 59)(3, 61)(4, 62)(5, 53)(6, 67)(7, 69)(8, 54)(9, 71)(10, 72)(11, 73)(12, 56)(13, 57)(14, 78)(15, 77)(16, 58)(17, 76)(18, 60)(19, 75)(20, 66)(21, 68)(22, 70)(23, 63)(24, 64)(25, 65)(26, 74)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104) local type(s) :: { ( 26, 52 ), ( 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52 ) } Outer automorphisms :: reflexible Dual of E12.308 Graph:: bipartite v = 27 e = 52 f = 3 degree seq :: [ 2^26, 52 ] E12.330 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {13, 26, 26}) Quotient :: dipole Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3, Y1), (R * Y2 * Y3^-1)^2, Y3^-1 * Y1^-2 * Y3^-3, Y1^4 * Y3^-1 * Y1^2, Y1^-2 * Y3^18 * Y1^-2, (Y3 * Y2^-1)^13 ] Map:: R = (1, 27, 2, 28, 6, 32, 14, 40, 21, 47, 10, 36, 3, 29, 7, 33, 15, 41, 23, 49, 26, 52, 20, 46, 9, 35, 17, 43, 13, 39, 18, 44, 24, 50, 25, 51, 19, 45, 12, 38, 5, 31, 8, 34, 16, 42, 22, 48, 11, 37, 4, 30)(53, 79)(54, 80)(55, 81)(56, 82)(57, 83)(58, 84)(59, 85)(60, 86)(61, 87)(62, 88)(63, 89)(64, 90)(65, 91)(66, 92)(67, 93)(68, 94)(69, 95)(70, 96)(71, 97)(72, 98)(73, 99)(74, 100)(75, 101)(76, 102)(77, 103)(78, 104) L = (1, 55)(2, 59)(3, 61)(4, 62)(5, 53)(6, 67)(7, 69)(8, 54)(9, 71)(10, 72)(11, 73)(12, 56)(13, 57)(14, 75)(15, 65)(16, 58)(17, 64)(18, 60)(19, 63)(20, 77)(21, 78)(22, 66)(23, 70)(24, 68)(25, 74)(26, 76)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104) local type(s) :: { ( 26, 52 ), ( 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52 ) } Outer automorphisms :: reflexible Dual of E12.300 Graph:: bipartite v = 27 e = 52 f = 3 degree seq :: [ 2^26, 52 ] E12.331 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {13, 26, 26}) Quotient :: dipole Aut^+ = C26 (small group id <26, 2>) Aut = D52 (small group id <52, 4>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1), Y1^-1 * Y3^3 * Y1^-1 * Y3, (R * Y2 * Y3^-1)^2, Y1^2 * Y3 * Y1^4, (Y3 * Y2^-1)^13, 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 * Y1^3 ] Map:: R = (1, 27, 2, 28, 6, 32, 14, 40, 21, 47, 12, 38, 5, 31, 8, 34, 16, 42, 23, 49, 26, 52, 22, 48, 13, 39, 18, 44, 9, 35, 17, 43, 24, 50, 25, 51, 19, 45, 10, 36, 3, 29, 7, 33, 15, 41, 20, 46, 11, 37, 4, 30)(53, 79)(54, 80)(55, 81)(56, 82)(57, 83)(58, 84)(59, 85)(60, 86)(61, 87)(62, 88)(63, 89)(64, 90)(65, 91)(66, 92)(67, 93)(68, 94)(69, 95)(70, 96)(71, 97)(72, 98)(73, 99)(74, 100)(75, 101)(76, 102)(77, 103)(78, 104) L = (1, 55)(2, 59)(3, 61)(4, 62)(5, 53)(6, 67)(7, 69)(8, 54)(9, 68)(10, 70)(11, 71)(12, 56)(13, 57)(14, 72)(15, 76)(16, 58)(17, 75)(18, 60)(19, 65)(20, 77)(21, 63)(22, 64)(23, 66)(24, 78)(25, 74)(26, 73)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104) local type(s) :: { ( 26, 52 ), ( 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52, 26, 52 ) } Outer automorphisms :: reflexible Dual of E12.306 Graph:: bipartite v = 27 e = 52 f = 3 degree seq :: [ 2^26, 52 ] E12.332 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {9, 27, 27}) Quotient :: edge Aut^+ = C27 (small group id <27, 1>) Aut = D54 (small group id <54, 1>) |r| :: 2 Presentation :: [ F^2, T2^3 * T1^-1, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^9, (T1^-1 * T2^-1)^27 ] Map:: non-degenerate R = (1, 3, 8, 2, 7, 14, 6, 13, 20, 12, 19, 25, 18, 24, 27, 22, 26, 23, 16, 21, 17, 10, 15, 11, 4, 9, 5)(28, 29, 33, 39, 45, 49, 43, 37, 31)(30, 34, 40, 46, 51, 53, 48, 42, 36)(32, 35, 41, 47, 52, 54, 50, 44, 38) L = (1, 28)(2, 29)(3, 30)(4, 31)(5, 32)(6, 33)(7, 34)(8, 35)(9, 36)(10, 37)(11, 38)(12, 39)(13, 40)(14, 41)(15, 42)(16, 43)(17, 44)(18, 45)(19, 46)(20, 47)(21, 48)(22, 49)(23, 50)(24, 51)(25, 52)(26, 53)(27, 54) local type(s) :: { ( 54^9 ), ( 54^27 ) } Outer automorphisms :: reflexible Dual of E12.346 Transitivity :: ET+ Graph:: bipartite v = 4 e = 27 f = 1 degree seq :: [ 9^3, 27 ] E12.333 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {9, 27, 27}) Quotient :: edge Aut^+ = C27 (small group id <27, 1>) Aut = D54 (small group id <54, 1>) |r| :: 2 Presentation :: [ F^2, T2^-3 * T1^-1, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^9 ] Map:: non-degenerate R = (1, 3, 9, 4, 10, 15, 11, 16, 21, 17, 22, 26, 23, 27, 25, 18, 24, 20, 12, 19, 14, 6, 13, 8, 2, 7, 5)(28, 29, 33, 39, 45, 50, 44, 38, 31)(30, 34, 40, 46, 51, 54, 49, 43, 37)(32, 35, 41, 47, 52, 53, 48, 42, 36) L = (1, 28)(2, 29)(3, 30)(4, 31)(5, 32)(6, 33)(7, 34)(8, 35)(9, 36)(10, 37)(11, 38)(12, 39)(13, 40)(14, 41)(15, 42)(16, 43)(17, 44)(18, 45)(19, 46)(20, 47)(21, 48)(22, 49)(23, 50)(24, 51)(25, 52)(26, 53)(27, 54) local type(s) :: { ( 54^9 ), ( 54^27 ) } Outer automorphisms :: reflexible Dual of E12.344 Transitivity :: ET+ Graph:: bipartite v = 4 e = 27 f = 1 degree seq :: [ 9^3, 27 ] E12.334 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {9, 27, 27}) Quotient :: edge Aut^+ = C27 (small group id <27, 1>) Aut = D54 (small group id <54, 1>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-3 * T1^2, T1^9, T1^9, (T1^-1 * T2^-1)^27 ] Map:: non-degenerate R = (1, 3, 9, 6, 15, 22, 20, 26, 24, 17, 19, 12, 4, 10, 8, 2, 7, 16, 14, 21, 27, 23, 25, 18, 11, 13, 5)(28, 29, 33, 41, 47, 50, 44, 38, 31)(30, 34, 42, 48, 53, 52, 46, 40, 37)(32, 35, 36, 43, 49, 54, 51, 45, 39) L = (1, 28)(2, 29)(3, 30)(4, 31)(5, 32)(6, 33)(7, 34)(8, 35)(9, 36)(10, 37)(11, 38)(12, 39)(13, 40)(14, 41)(15, 42)(16, 43)(17, 44)(18, 45)(19, 46)(20, 47)(21, 48)(22, 49)(23, 50)(24, 51)(25, 52)(26, 53)(27, 54) local type(s) :: { ( 54^9 ), ( 54^27 ) } Outer automorphisms :: reflexible Dual of E12.345 Transitivity :: ET+ Graph:: bipartite v = 4 e = 27 f = 1 degree seq :: [ 9^3, 27 ] E12.335 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {9, 27, 27}) Quotient :: edge Aut^+ = C27 (small group id <27, 1>) Aut = D54 (small group id <54, 1>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^3 * T1^2, T1^9, T1^-9, T1^9 ] Map:: non-degenerate R = (1, 3, 9, 11, 18, 23, 25, 27, 21, 14, 16, 8, 2, 7, 12, 4, 10, 17, 19, 24, 26, 20, 22, 15, 6, 13, 5)(28, 29, 33, 41, 47, 52, 46, 38, 31)(30, 34, 40, 43, 49, 54, 51, 45, 37)(32, 35, 42, 48, 53, 50, 44, 36, 39) L = (1, 28)(2, 29)(3, 30)(4, 31)(5, 32)(6, 33)(7, 34)(8, 35)(9, 36)(10, 37)(11, 38)(12, 39)(13, 40)(14, 41)(15, 42)(16, 43)(17, 44)(18, 45)(19, 46)(20, 47)(21, 48)(22, 49)(23, 50)(24, 51)(25, 52)(26, 53)(27, 54) local type(s) :: { ( 54^9 ), ( 54^27 ) } Outer automorphisms :: reflexible Dual of E12.342 Transitivity :: ET+ Graph:: bipartite v = 4 e = 27 f = 1 degree seq :: [ 9^3, 27 ] E12.336 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {9, 27, 27}) Quotient :: edge Aut^+ = C27 (small group id <27, 1>) Aut = D54 (small group id <54, 1>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T1^-1, T2^-1), T2^6 * T1, T1^3 * T2^-1 * T1 * T2^-2, 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^-1 * T1^-1 * T2^-1 * T1^-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^-1 * T1 ] Map:: non-degenerate R = (1, 3, 9, 19, 24, 12, 4, 10, 20, 14, 26, 23, 11, 21, 16, 6, 15, 27, 22, 18, 8, 2, 7, 17, 25, 13, 5)(28, 29, 33, 41, 46, 52, 49, 38, 31)(30, 34, 42, 53, 51, 40, 45, 48, 37)(32, 35, 43, 47, 36, 44, 54, 50, 39) L = (1, 28)(2, 29)(3, 30)(4, 31)(5, 32)(6, 33)(7, 34)(8, 35)(9, 36)(10, 37)(11, 38)(12, 39)(13, 40)(14, 41)(15, 42)(16, 43)(17, 44)(18, 45)(19, 46)(20, 47)(21, 48)(22, 49)(23, 50)(24, 51)(25, 52)(26, 53)(27, 54) local type(s) :: { ( 54^9 ), ( 54^27 ) } Outer automorphisms :: reflexible Dual of E12.343 Transitivity :: ET+ Graph:: bipartite v = 4 e = 27 f = 1 degree seq :: [ 9^3, 27 ] E12.337 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {9, 27, 27}) Quotient :: edge Aut^+ = C27 (small group id <27, 1>) Aut = D54 (small group id <54, 1>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T1^-1, T2^-1), T1 * T2^-6, T2 * T1^2 * T2^2 * T1^2, T1^-2 * T2^2 * T1^-3 * T2, T1^9 ] Map:: non-degenerate R = (1, 3, 9, 19, 18, 8, 2, 7, 17, 22, 27, 16, 6, 15, 23, 11, 21, 26, 14, 24, 12, 4, 10, 20, 25, 13, 5)(28, 29, 33, 41, 52, 46, 49, 38, 31)(30, 34, 42, 51, 40, 45, 54, 48, 37)(32, 35, 43, 53, 47, 36, 44, 50, 39) L = (1, 28)(2, 29)(3, 30)(4, 31)(5, 32)(6, 33)(7, 34)(8, 35)(9, 36)(10, 37)(11, 38)(12, 39)(13, 40)(14, 41)(15, 42)(16, 43)(17, 44)(18, 45)(19, 46)(20, 47)(21, 48)(22, 49)(23, 50)(24, 51)(25, 52)(26, 53)(27, 54) local type(s) :: { ( 54^9 ), ( 54^27 ) } Outer automorphisms :: reflexible Dual of E12.341 Transitivity :: ET+ Graph:: bipartite v = 4 e = 27 f = 1 degree seq :: [ 9^3, 27 ] E12.338 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {9, 27, 27}) Quotient :: edge Aut^+ = C27 (small group id <27, 1>) Aut = D54 (small group id <54, 1>) |r| :: 2 Presentation :: [ F^2, T2 * T1^-2, (F * T2)^2, (F * T1)^2, T1 * T2^13, (T2^-1 * T1^-1)^9 ] Map:: non-degenerate R = (1, 3, 7, 11, 15, 19, 23, 27, 24, 20, 16, 12, 8, 4, 2, 6, 10, 14, 18, 22, 26, 25, 21, 17, 13, 9, 5)(28, 29, 30, 33, 34, 37, 38, 41, 42, 45, 46, 49, 50, 53, 54, 52, 51, 48, 47, 44, 43, 40, 39, 36, 35, 32, 31) L = (1, 28)(2, 29)(3, 30)(4, 31)(5, 32)(6, 33)(7, 34)(8, 35)(9, 36)(10, 37)(11, 38)(12, 39)(13, 40)(14, 41)(15, 42)(16, 43)(17, 44)(18, 45)(19, 46)(20, 47)(21, 48)(22, 49)(23, 50)(24, 51)(25, 52)(26, 53)(27, 54) local type(s) :: { ( 18^27 ) } Outer automorphisms :: reflexible Dual of E12.348 Transitivity :: ET+ Graph:: bipartite v = 2 e = 27 f = 3 degree seq :: [ 27^2 ] E12.339 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {9, 27, 27}) Quotient :: edge Aut^+ = C27 (small group id <27, 1>) Aut = D54 (small group id <54, 1>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^-3 * T2^-1 * T1^-1, T2^-1 * T1^-1 * T2^-6, (T2^-2 * T1)^3 ] Map:: non-degenerate R = (1, 3, 9, 17, 25, 20, 12, 4, 10, 18, 26, 22, 14, 6, 11, 19, 27, 24, 16, 8, 2, 7, 15, 23, 21, 13, 5)(28, 29, 33, 39, 32, 35, 41, 47, 40, 43, 49, 52, 48, 51, 53, 44, 50, 54, 45, 36, 42, 46, 37, 30, 34, 38, 31) L = (1, 28)(2, 29)(3, 30)(4, 31)(5, 32)(6, 33)(7, 34)(8, 35)(9, 36)(10, 37)(11, 38)(12, 39)(13, 40)(14, 41)(15, 42)(16, 43)(17, 44)(18, 45)(19, 46)(20, 47)(21, 48)(22, 49)(23, 50)(24, 51)(25, 52)(26, 53)(27, 54) local type(s) :: { ( 18^27 ) } Outer automorphisms :: reflexible Dual of E12.347 Transitivity :: ET+ Graph:: bipartite v = 2 e = 27 f = 3 degree seq :: [ 27^2 ] E12.340 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {9, 27, 27}) Quotient :: edge Aut^+ = C27 (small group id <27, 1>) Aut = D54 (small group id <54, 1>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^-1 * T2 * T1^-4, T1 * T2 * T1 * T2^4, T1^-2 * T2^-1 * T1^-3 * T2^2 ] Map:: non-degenerate R = (1, 3, 9, 19, 21, 11, 14, 24, 26, 18, 8, 2, 7, 17, 22, 12, 4, 10, 20, 27, 25, 16, 6, 15, 23, 13, 5)(28, 29, 33, 41, 37, 30, 34, 42, 51, 47, 36, 44, 50, 53, 54, 46, 49, 40, 45, 52, 48, 39, 32, 35, 43, 38, 31) L = (1, 28)(2, 29)(3, 30)(4, 31)(5, 32)(6, 33)(7, 34)(8, 35)(9, 36)(10, 37)(11, 38)(12, 39)(13, 40)(14, 41)(15, 42)(16, 43)(17, 44)(18, 45)(19, 46)(20, 47)(21, 48)(22, 49)(23, 50)(24, 51)(25, 52)(26, 53)(27, 54) local type(s) :: { ( 18^27 ) } Outer automorphisms :: reflexible Dual of E12.349 Transitivity :: ET+ Graph:: bipartite v = 2 e = 27 f = 3 degree seq :: [ 27^2 ] E12.341 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {9, 27, 27}) Quotient :: loop Aut^+ = C27 (small group id <27, 1>) Aut = D54 (small group id <54, 1>) |r| :: 2 Presentation :: [ F^2, T2^3 * T1^-1, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^9, (T1^-1 * T2^-1)^27 ] Map:: non-degenerate R = (1, 28, 3, 30, 8, 35, 2, 29, 7, 34, 14, 41, 6, 33, 13, 40, 20, 47, 12, 39, 19, 46, 25, 52, 18, 45, 24, 51, 27, 54, 22, 49, 26, 53, 23, 50, 16, 43, 21, 48, 17, 44, 10, 37, 15, 42, 11, 38, 4, 31, 9, 36, 5, 32) L = (1, 29)(2, 33)(3, 34)(4, 28)(5, 35)(6, 39)(7, 40)(8, 41)(9, 30)(10, 31)(11, 32)(12, 45)(13, 46)(14, 47)(15, 36)(16, 37)(17, 38)(18, 49)(19, 51)(20, 52)(21, 42)(22, 43)(23, 44)(24, 53)(25, 54)(26, 48)(27, 50) local type(s) :: { ( 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27 ) } Outer automorphisms :: reflexible Dual of E12.337 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 27 f = 4 degree seq :: [ 54 ] E12.342 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {9, 27, 27}) Quotient :: loop Aut^+ = C27 (small group id <27, 1>) Aut = D54 (small group id <54, 1>) |r| :: 2 Presentation :: [ F^2, T2^-3 * T1^-1, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^9 ] Map:: non-degenerate R = (1, 28, 3, 30, 9, 36, 4, 31, 10, 37, 15, 42, 11, 38, 16, 43, 21, 48, 17, 44, 22, 49, 26, 53, 23, 50, 27, 54, 25, 52, 18, 45, 24, 51, 20, 47, 12, 39, 19, 46, 14, 41, 6, 33, 13, 40, 8, 35, 2, 29, 7, 34, 5, 32) L = (1, 29)(2, 33)(3, 34)(4, 28)(5, 35)(6, 39)(7, 40)(8, 41)(9, 32)(10, 30)(11, 31)(12, 45)(13, 46)(14, 47)(15, 36)(16, 37)(17, 38)(18, 50)(19, 51)(20, 52)(21, 42)(22, 43)(23, 44)(24, 54)(25, 53)(26, 48)(27, 49) local type(s) :: { ( 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27 ) } Outer automorphisms :: reflexible Dual of E12.335 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 27 f = 4 degree seq :: [ 54 ] E12.343 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {9, 27, 27}) Quotient :: loop Aut^+ = C27 (small group id <27, 1>) Aut = D54 (small group id <54, 1>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-3 * T1^2, T1^9, T1^9, (T1^-1 * T2^-1)^27 ] Map:: non-degenerate R = (1, 28, 3, 30, 9, 36, 6, 33, 15, 42, 22, 49, 20, 47, 26, 53, 24, 51, 17, 44, 19, 46, 12, 39, 4, 31, 10, 37, 8, 35, 2, 29, 7, 34, 16, 43, 14, 41, 21, 48, 27, 54, 23, 50, 25, 52, 18, 45, 11, 38, 13, 40, 5, 32) L = (1, 29)(2, 33)(3, 34)(4, 28)(5, 35)(6, 41)(7, 42)(8, 36)(9, 43)(10, 30)(11, 31)(12, 32)(13, 37)(14, 47)(15, 48)(16, 49)(17, 38)(18, 39)(19, 40)(20, 50)(21, 53)(22, 54)(23, 44)(24, 45)(25, 46)(26, 52)(27, 51) local type(s) :: { ( 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27 ) } Outer automorphisms :: reflexible Dual of E12.336 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 27 f = 4 degree seq :: [ 54 ] E12.344 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {9, 27, 27}) Quotient :: loop Aut^+ = C27 (small group id <27, 1>) Aut = D54 (small group id <54, 1>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^3 * T1^2, T1^9, T1^-9, T1^9 ] Map:: non-degenerate R = (1, 28, 3, 30, 9, 36, 11, 38, 18, 45, 23, 50, 25, 52, 27, 54, 21, 48, 14, 41, 16, 43, 8, 35, 2, 29, 7, 34, 12, 39, 4, 31, 10, 37, 17, 44, 19, 46, 24, 51, 26, 53, 20, 47, 22, 49, 15, 42, 6, 33, 13, 40, 5, 32) L = (1, 29)(2, 33)(3, 34)(4, 28)(5, 35)(6, 41)(7, 40)(8, 42)(9, 39)(10, 30)(11, 31)(12, 32)(13, 43)(14, 47)(15, 48)(16, 49)(17, 36)(18, 37)(19, 38)(20, 52)(21, 53)(22, 54)(23, 44)(24, 45)(25, 46)(26, 50)(27, 51) local type(s) :: { ( 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27 ) } Outer automorphisms :: reflexible Dual of E12.333 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 27 f = 4 degree seq :: [ 54 ] E12.345 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {9, 27, 27}) Quotient :: loop Aut^+ = C27 (small group id <27, 1>) Aut = D54 (small group id <54, 1>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T1^-1, T2^-1), T2^6 * T1, T1^3 * T2^-1 * T1 * T2^-2, 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^-1 * T1^-1 * T2^-1 * T1^-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^-1 * T1 ] Map:: non-degenerate R = (1, 28, 3, 30, 9, 36, 19, 46, 24, 51, 12, 39, 4, 31, 10, 37, 20, 47, 14, 41, 26, 53, 23, 50, 11, 38, 21, 48, 16, 43, 6, 33, 15, 42, 27, 54, 22, 49, 18, 45, 8, 35, 2, 29, 7, 34, 17, 44, 25, 52, 13, 40, 5, 32) L = (1, 29)(2, 33)(3, 34)(4, 28)(5, 35)(6, 41)(7, 42)(8, 43)(9, 44)(10, 30)(11, 31)(12, 32)(13, 45)(14, 46)(15, 53)(16, 47)(17, 54)(18, 48)(19, 52)(20, 36)(21, 37)(22, 38)(23, 39)(24, 40)(25, 49)(26, 51)(27, 50) local type(s) :: { ( 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27 ) } Outer automorphisms :: reflexible Dual of E12.334 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 27 f = 4 degree seq :: [ 54 ] E12.346 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {9, 27, 27}) Quotient :: loop Aut^+ = C27 (small group id <27, 1>) Aut = D54 (small group id <54, 1>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T1^-1, T2^-1), T1 * T2^-6, T2 * T1^2 * T2^2 * T1^2, T1^-2 * T2^2 * T1^-3 * T2, T1^9 ] Map:: non-degenerate R = (1, 28, 3, 30, 9, 36, 19, 46, 18, 45, 8, 35, 2, 29, 7, 34, 17, 44, 22, 49, 27, 54, 16, 43, 6, 33, 15, 42, 23, 50, 11, 38, 21, 48, 26, 53, 14, 41, 24, 51, 12, 39, 4, 31, 10, 37, 20, 47, 25, 52, 13, 40, 5, 32) L = (1, 29)(2, 33)(3, 34)(4, 28)(5, 35)(6, 41)(7, 42)(8, 43)(9, 44)(10, 30)(11, 31)(12, 32)(13, 45)(14, 52)(15, 51)(16, 53)(17, 50)(18, 54)(19, 49)(20, 36)(21, 37)(22, 38)(23, 39)(24, 40)(25, 46)(26, 47)(27, 48) local type(s) :: { ( 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27, 9, 27 ) } Outer automorphisms :: reflexible Dual of E12.332 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 27 f = 4 degree seq :: [ 54 ] E12.347 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {9, 27, 27}) Quotient :: loop Aut^+ = C27 (small group id <27, 1>) Aut = D54 (small group id <54, 1>) |r| :: 2 Presentation :: [ F^2, T2 * T1^-3, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^9, (T1^-1 * T2^-1)^27 ] Map:: non-degenerate R = (1, 28, 3, 30, 9, 36, 15, 42, 21, 48, 23, 50, 17, 44, 11, 38, 5, 32)(2, 29, 7, 34, 13, 40, 19, 46, 25, 52, 26, 53, 20, 47, 14, 41, 8, 35)(4, 31, 6, 33, 12, 39, 18, 45, 24, 51, 27, 54, 22, 49, 16, 43, 10, 37) L = (1, 29)(2, 33)(3, 34)(4, 28)(5, 35)(6, 30)(7, 39)(8, 31)(9, 40)(10, 32)(11, 41)(12, 36)(13, 45)(14, 37)(15, 46)(16, 38)(17, 47)(18, 42)(19, 51)(20, 43)(21, 52)(22, 44)(23, 53)(24, 48)(25, 54)(26, 49)(27, 50) local type(s) :: { ( 27^18 ) } Outer automorphisms :: reflexible Dual of E12.339 Transitivity :: ET+ VT+ AT Graph:: v = 3 e = 27 f = 2 degree seq :: [ 18^3 ] E12.348 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {9, 27, 27}) Quotient :: loop Aut^+ = C27 (small group id <27, 1>) Aut = D54 (small group id <54, 1>) |r| :: 2 Presentation :: [ F^2, T2^-1 * T1^-3, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^9 ] Map:: non-degenerate R = (1, 28, 3, 30, 9, 36, 15, 42, 21, 48, 23, 50, 17, 44, 11, 38, 5, 32)(2, 29, 7, 34, 13, 40, 19, 46, 25, 52, 26, 53, 20, 47, 14, 41, 8, 35)(4, 31, 10, 37, 16, 43, 22, 49, 27, 54, 24, 51, 18, 45, 12, 39, 6, 33) L = (1, 29)(2, 33)(3, 34)(4, 28)(5, 35)(6, 32)(7, 31)(8, 39)(9, 40)(10, 30)(11, 41)(12, 38)(13, 37)(14, 45)(15, 46)(16, 36)(17, 47)(18, 44)(19, 43)(20, 51)(21, 52)(22, 42)(23, 53)(24, 50)(25, 49)(26, 54)(27, 48) local type(s) :: { ( 27^18 ) } Outer automorphisms :: reflexible Dual of E12.338 Transitivity :: ET+ VT+ AT Graph:: v = 3 e = 27 f = 2 degree seq :: [ 18^3 ] E12.349 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {9, 27, 27}) Quotient :: loop Aut^+ = C27 (small group id <27, 1>) Aut = D54 (small group id <54, 1>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1), T2^-4 * T1^3, T2^-1 * T1^-6, T2^-2 * T1^-1 * T2^-3 * 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^-3 ] Map:: non-degenerate R = (1, 28, 3, 30, 9, 36, 19, 46, 14, 41, 22, 49, 25, 52, 13, 40, 5, 32)(2, 29, 7, 34, 17, 44, 27, 54, 23, 50, 11, 38, 21, 48, 18, 45, 8, 35)(4, 31, 10, 37, 20, 47, 16, 43, 6, 33, 15, 42, 26, 53, 24, 51, 12, 39) L = (1, 29)(2, 33)(3, 34)(4, 28)(5, 35)(6, 41)(7, 42)(8, 43)(9, 44)(10, 30)(11, 31)(12, 32)(13, 45)(14, 50)(15, 49)(16, 46)(17, 53)(18, 47)(19, 54)(20, 36)(21, 37)(22, 38)(23, 39)(24, 40)(25, 48)(26, 52)(27, 51) local type(s) :: { ( 27^18 ) } Outer automorphisms :: reflexible Dual of E12.340 Transitivity :: ET+ VT+ AT Graph:: v = 3 e = 27 f = 2 degree seq :: [ 18^3 ] E12.350 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 27, 27}) Quotient :: dipole Aut^+ = C27 (small group id <27, 1>) Aut = D54 (small group id <54, 1>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, Y2^-3 * Y1^-1, (Y3^-1, Y2^-1), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2^-1, Y1^-1), 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 ] Map:: R = (1, 28, 2, 29, 6, 33, 12, 39, 18, 45, 23, 50, 17, 44, 11, 38, 4, 31)(3, 30, 7, 34, 13, 40, 19, 46, 24, 51, 27, 54, 22, 49, 16, 43, 10, 37)(5, 32, 8, 35, 14, 41, 20, 47, 25, 52, 26, 53, 21, 48, 15, 42, 9, 36)(55, 82, 57, 84, 63, 90, 58, 85, 64, 91, 69, 96, 65, 92, 70, 97, 75, 102, 71, 98, 76, 103, 80, 107, 77, 104, 81, 108, 79, 106, 72, 99, 78, 105, 74, 101, 66, 93, 73, 100, 68, 95, 60, 87, 67, 94, 62, 89, 56, 83, 61, 88, 59, 86) L = (1, 58)(2, 55)(3, 64)(4, 65)(5, 63)(6, 56)(7, 57)(8, 59)(9, 69)(10, 70)(11, 71)(12, 60)(13, 61)(14, 62)(15, 75)(16, 76)(17, 77)(18, 66)(19, 67)(20, 68)(21, 80)(22, 81)(23, 72)(24, 73)(25, 74)(26, 79)(27, 78)(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) :: { ( 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54 ), ( 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54 ) } Outer automorphisms :: reflexible Dual of E12.365 Graph:: bipartite v = 4 e = 54 f = 28 degree seq :: [ 18^3, 54 ] E12.351 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 27, 27}) Quotient :: dipole Aut^+ = C27 (small group id <27, 1>) Aut = D54 (small group id <54, 1>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y2^3 * Y1^-1, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y3^-1, Y2^-1), 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 ] Map:: R = (1, 28, 2, 29, 6, 33, 12, 39, 18, 45, 22, 49, 16, 43, 10, 37, 4, 31)(3, 30, 7, 34, 13, 40, 19, 46, 24, 51, 26, 53, 21, 48, 15, 42, 9, 36)(5, 32, 8, 35, 14, 41, 20, 47, 25, 52, 27, 54, 23, 50, 17, 44, 11, 38)(55, 82, 57, 84, 62, 89, 56, 83, 61, 88, 68, 95, 60, 87, 67, 94, 74, 101, 66, 93, 73, 100, 79, 106, 72, 99, 78, 105, 81, 108, 76, 103, 80, 107, 77, 104, 70, 97, 75, 102, 71, 98, 64, 91, 69, 96, 65, 92, 58, 85, 63, 90, 59, 86) L = (1, 58)(2, 55)(3, 63)(4, 64)(5, 65)(6, 56)(7, 57)(8, 59)(9, 69)(10, 70)(11, 71)(12, 60)(13, 61)(14, 62)(15, 75)(16, 76)(17, 77)(18, 66)(19, 67)(20, 68)(21, 80)(22, 72)(23, 81)(24, 73)(25, 74)(26, 78)(27, 79)(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) :: { ( 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54 ), ( 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54 ) } Outer automorphisms :: reflexible Dual of E12.367 Graph:: bipartite v = 4 e = 54 f = 28 degree seq :: [ 18^3, 54 ] E12.352 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 27, 27}) Quotient :: dipole Aut^+ = C27 (small group id <27, 1>) Aut = D54 (small group id <54, 1>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, Y1 * Y3, Y3 * Y1, (R * Y2)^2, (R * Y1)^2, Y1 * Y2 * Y3 * Y2^-1, (R * Y3)^2, Y2^-6 * Y1, Y2 * Y1 * Y2^2 * Y3^-3, Y3 * Y2 * Y3 * Y2^2 * Y1^-3, 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 ] Map:: R = (1, 28, 2, 29, 6, 33, 14, 41, 25, 52, 19, 46, 22, 49, 11, 38, 4, 31)(3, 30, 7, 34, 15, 42, 24, 51, 13, 40, 18, 45, 27, 54, 21, 48, 10, 37)(5, 32, 8, 35, 16, 43, 26, 53, 20, 47, 9, 36, 17, 44, 23, 50, 12, 39)(55, 82, 57, 84, 63, 90, 73, 100, 72, 99, 62, 89, 56, 83, 61, 88, 71, 98, 76, 103, 81, 108, 70, 97, 60, 87, 69, 96, 77, 104, 65, 92, 75, 102, 80, 107, 68, 95, 78, 105, 66, 93, 58, 85, 64, 91, 74, 101, 79, 106, 67, 94, 59, 86) L = (1, 58)(2, 55)(3, 64)(4, 65)(5, 66)(6, 56)(7, 57)(8, 59)(9, 74)(10, 75)(11, 76)(12, 77)(13, 78)(14, 60)(15, 61)(16, 62)(17, 63)(18, 67)(19, 79)(20, 80)(21, 81)(22, 73)(23, 71)(24, 69)(25, 68)(26, 70)(27, 72)(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) :: { ( 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54 ), ( 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54 ) } Outer automorphisms :: reflexible Dual of E12.362 Graph:: bipartite v = 4 e = 54 f = 28 degree seq :: [ 18^3, 54 ] E12.353 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 27, 27}) Quotient :: dipole Aut^+ = C27 (small group id <27, 1>) Aut = D54 (small group id <54, 1>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y3^-1 * Y2^-1 * Y1^-1 * Y2, (Y3^-1, Y2^-1), (Y2^-1, Y1^-1), (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y1 * Y2^-1 * Y1 * Y2 * Y3^2, Y2 * Y1 * Y2^5, Y2^-1 * Y3^-1 * Y2^-1 * Y3^-3 * 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 ] Map:: R = (1, 28, 2, 29, 6, 33, 14, 41, 19, 46, 25, 52, 22, 49, 11, 38, 4, 31)(3, 30, 7, 34, 15, 42, 26, 53, 24, 51, 13, 40, 18, 45, 21, 48, 10, 37)(5, 32, 8, 35, 16, 43, 20, 47, 9, 36, 17, 44, 27, 54, 23, 50, 12, 39)(55, 82, 57, 84, 63, 90, 73, 100, 78, 105, 66, 93, 58, 85, 64, 91, 74, 101, 68, 95, 80, 107, 77, 104, 65, 92, 75, 102, 70, 97, 60, 87, 69, 96, 81, 108, 76, 103, 72, 99, 62, 89, 56, 83, 61, 88, 71, 98, 79, 106, 67, 94, 59, 86) L = (1, 58)(2, 55)(3, 64)(4, 65)(5, 66)(6, 56)(7, 57)(8, 59)(9, 74)(10, 75)(11, 76)(12, 77)(13, 78)(14, 60)(15, 61)(16, 62)(17, 63)(18, 67)(19, 68)(20, 70)(21, 72)(22, 79)(23, 81)(24, 80)(25, 73)(26, 69)(27, 71)(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) :: { ( 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54 ), ( 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54 ) } Outer automorphisms :: reflexible Dual of E12.364 Graph:: bipartite v = 4 e = 54 f = 28 degree seq :: [ 18^3, 54 ] E12.354 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 27, 27}) Quotient :: dipole Aut^+ = C27 (small group id <27, 1>) Aut = D54 (small group id <54, 1>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, Y1^2 * Y3^2, (R * Y3)^2, (Y3^-1, Y2^-1), (R * Y1)^2, (R * Y2)^2, (Y2^-1, Y1^-1), Y3^-2 * Y2^3, Y2 * Y3^2 * Y2^2 * Y1^4, Y3 * Y1^-8, Y3^18 ] Map:: R = (1, 28, 2, 29, 6, 33, 14, 41, 20, 47, 25, 52, 19, 46, 11, 38, 4, 31)(3, 30, 7, 34, 13, 40, 16, 43, 22, 49, 27, 54, 24, 51, 18, 45, 10, 37)(5, 32, 8, 35, 15, 42, 21, 48, 26, 53, 23, 50, 17, 44, 9, 36, 12, 39)(55, 82, 57, 84, 63, 90, 65, 92, 72, 99, 77, 104, 79, 106, 81, 108, 75, 102, 68, 95, 70, 97, 62, 89, 56, 83, 61, 88, 66, 93, 58, 85, 64, 91, 71, 98, 73, 100, 78, 105, 80, 107, 74, 101, 76, 103, 69, 96, 60, 87, 67, 94, 59, 86) L = (1, 58)(2, 55)(3, 64)(4, 65)(5, 66)(6, 56)(7, 57)(8, 59)(9, 71)(10, 72)(11, 73)(12, 63)(13, 61)(14, 60)(15, 62)(16, 67)(17, 77)(18, 78)(19, 79)(20, 68)(21, 69)(22, 70)(23, 80)(24, 81)(25, 74)(26, 75)(27, 76)(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) :: { ( 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54 ), ( 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54 ) } Outer automorphisms :: reflexible Dual of E12.363 Graph:: bipartite v = 4 e = 54 f = 28 degree seq :: [ 18^3, 54 ] E12.355 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 27, 27}) Quotient :: dipole Aut^+ = C27 (small group id <27, 1>) Aut = D54 (small group id <54, 1>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), (Y3^-1, Y2^-1), Y2^-1 * Y1 * Y2^-2 * Y1, Y3^9, Y3^4 * Y1^-5, Y2^-27 ] Map:: R = (1, 28, 2, 29, 6, 33, 14, 41, 20, 47, 23, 50, 17, 44, 11, 38, 4, 31)(3, 30, 7, 34, 15, 42, 21, 48, 26, 53, 25, 52, 19, 46, 13, 40, 10, 37)(5, 32, 8, 35, 9, 36, 16, 43, 22, 49, 27, 54, 24, 51, 18, 45, 12, 39)(55, 82, 57, 84, 63, 90, 60, 87, 69, 96, 76, 103, 74, 101, 80, 107, 78, 105, 71, 98, 73, 100, 66, 93, 58, 85, 64, 91, 62, 89, 56, 83, 61, 88, 70, 97, 68, 95, 75, 102, 81, 108, 77, 104, 79, 106, 72, 99, 65, 92, 67, 94, 59, 86) L = (1, 58)(2, 55)(3, 64)(4, 65)(5, 66)(6, 56)(7, 57)(8, 59)(9, 62)(10, 67)(11, 71)(12, 72)(13, 73)(14, 60)(15, 61)(16, 63)(17, 77)(18, 78)(19, 79)(20, 68)(21, 69)(22, 70)(23, 74)(24, 81)(25, 80)(26, 75)(27, 76)(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) :: { ( 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54 ), ( 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54, 2, 54 ) } Outer automorphisms :: reflexible Dual of E12.366 Graph:: bipartite v = 4 e = 54 f = 28 degree seq :: [ 18^3, 54 ] E12.356 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 27, 27}) Quotient :: dipole Aut^+ = C27 (small group id <27, 1>) Aut = D54 (small group id <54, 1>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-1, Y1 * Y2^-2, (R * Y1)^2, R * Y2 * R * Y3, Y2 * Y1^13, (Y3^-1 * Y1^-1)^9 ] Map:: R = (1, 28, 2, 29, 6, 33, 10, 37, 14, 41, 18, 45, 22, 49, 26, 53, 25, 52, 21, 48, 17, 44, 13, 40, 9, 36, 5, 32, 3, 30, 7, 34, 11, 38, 15, 42, 19, 46, 23, 50, 27, 54, 24, 51, 20, 47, 16, 43, 12, 39, 8, 35, 4, 31)(55, 82, 57, 84, 56, 83, 61, 88, 60, 87, 65, 92, 64, 91, 69, 96, 68, 95, 73, 100, 72, 99, 77, 104, 76, 103, 81, 108, 80, 107, 78, 105, 79, 106, 74, 101, 75, 102, 70, 97, 71, 98, 66, 93, 67, 94, 62, 89, 63, 90, 58, 85, 59, 86) L = (1, 57)(2, 61)(3, 56)(4, 59)(5, 55)(6, 65)(7, 60)(8, 63)(9, 58)(10, 69)(11, 64)(12, 67)(13, 62)(14, 73)(15, 68)(16, 71)(17, 66)(18, 77)(19, 72)(20, 75)(21, 70)(22, 81)(23, 76)(24, 79)(25, 74)(26, 78)(27, 80)(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) :: { ( 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 E12.359 Graph:: bipartite v = 2 e = 54 f = 30 degree seq :: [ 54^2 ] E12.357 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 27, 27}) Quotient :: dipole Aut^+ = C27 (small group id <27, 1>) Aut = D54 (small group id <54, 1>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-1, (R * Y1)^2, R * Y2 * R * Y3, (Y1, Y2^-1), Y2^2 * Y1 * Y2^2, Y1^-6 * Y2^-1 * Y1^-1, Y1^2 * Y2^-1 * Y1^3 * Y2^-2 * Y1, (Y3^-1 * Y1^-1)^9 ] Map:: R = (1, 28, 2, 29, 6, 33, 14, 41, 22, 49, 21, 48, 12, 39, 5, 32, 8, 35, 16, 43, 24, 51, 26, 53, 18, 45, 9, 36, 13, 40, 17, 44, 25, 52, 27, 54, 19, 46, 10, 37, 3, 30, 7, 34, 15, 42, 23, 50, 20, 47, 11, 38, 4, 31)(55, 82, 57, 84, 63, 90, 66, 93, 58, 85, 64, 91, 72, 99, 75, 102, 65, 92, 73, 100, 80, 107, 76, 103, 74, 101, 81, 108, 78, 105, 68, 95, 77, 104, 79, 106, 70, 97, 60, 87, 69, 96, 71, 98, 62, 89, 56, 83, 61, 88, 67, 94, 59, 86) 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, 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) :: { ( 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 E12.360 Graph:: bipartite v = 2 e = 54 f = 30 degree seq :: [ 54^2 ] E12.358 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 27, 27}) Quotient :: dipole Aut^+ = C27 (small group id <27, 1>) Aut = D54 (small group id <54, 1>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-1, (Y2^-1, Y1^-1), (R * Y1)^2, (Y2^-1, Y1^-1), R * Y2 * R * Y3, Y2^4 * Y1^-1 * Y2, Y1^2 * Y2 * Y1 * Y2 * Y1^2, (Y3^-1 * Y1^-1)^9 ] Map:: R = (1, 28, 2, 29, 6, 33, 14, 41, 23, 50, 13, 40, 18, 45, 25, 52, 27, 54, 20, 47, 10, 37, 3, 30, 7, 34, 15, 42, 22, 49, 12, 39, 5, 32, 8, 35, 16, 43, 24, 51, 26, 53, 19, 46, 9, 36, 17, 44, 21, 48, 11, 38, 4, 31)(55, 82, 57, 84, 63, 90, 72, 99, 62, 89, 56, 83, 61, 88, 71, 98, 79, 106, 70, 97, 60, 87, 69, 96, 75, 102, 81, 108, 78, 105, 68, 95, 76, 103, 65, 92, 74, 101, 80, 107, 77, 104, 66, 93, 58, 85, 64, 91, 73, 100, 67, 94, 59, 86) L = (1, 57)(2, 61)(3, 63)(4, 64)(5, 55)(6, 69)(7, 71)(8, 56)(9, 72)(10, 73)(11, 74)(12, 58)(13, 59)(14, 76)(15, 75)(16, 60)(17, 79)(18, 62)(19, 67)(20, 80)(21, 81)(22, 65)(23, 66)(24, 68)(25, 70)(26, 77)(27, 78)(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) :: { ( 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 E12.361 Graph:: bipartite v = 2 e = 54 f = 30 degree seq :: [ 54^2 ] E12.359 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 27, 27}) Quotient :: dipole Aut^+ = C27 (small group id <27, 1>) Aut = D54 (small group id <54, 1>) |r| :: 2 Presentation :: [ Y1, R^2, Y3^-2 * Y2 * Y3^-1, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y2^9, (Y3^-1 * Y1^-1)^27 ] Map:: R = (1, 28)(2, 29)(3, 30)(4, 31)(5, 32)(6, 33)(7, 34)(8, 35)(9, 36)(10, 37)(11, 38)(12, 39)(13, 40)(14, 41)(15, 42)(16, 43)(17, 44)(18, 45)(19, 46)(20, 47)(21, 48)(22, 49)(23, 50)(24, 51)(25, 52)(26, 53)(27, 54)(55, 82, 56, 83, 60, 87, 66, 93, 72, 99, 76, 103, 70, 97, 64, 91, 58, 85)(57, 84, 61, 88, 67, 94, 73, 100, 78, 105, 80, 107, 75, 102, 69, 96, 63, 90)(59, 86, 62, 89, 68, 95, 74, 101, 79, 106, 81, 108, 77, 104, 71, 98, 65, 92) L = (1, 57)(2, 61)(3, 62)(4, 63)(5, 55)(6, 67)(7, 68)(8, 56)(9, 59)(10, 69)(11, 58)(12, 73)(13, 74)(14, 60)(15, 65)(16, 75)(17, 64)(18, 78)(19, 79)(20, 66)(21, 71)(22, 80)(23, 70)(24, 81)(25, 72)(26, 77)(27, 76)(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) :: { ( 54, 54 ), ( 54^18 ) } Outer automorphisms :: reflexible Dual of E12.356 Graph:: simple bipartite v = 30 e = 54 f = 2 degree seq :: [ 2^27, 18^3 ] E12.360 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 27, 27}) Quotient :: dipole Aut^+ = C27 (small group id <27, 1>) Aut = D54 (small group id <54, 1>) |r| :: 2 Presentation :: [ Y1, R^2, Y2^-1 * Y3^-3, (Y2^-1 * R)^2, (R * Y3)^2, (R * Y1)^2, Y2^9, (Y3^-1 * Y1^-1)^27, (Y3 * Y2^-1)^27 ] Map:: R = (1, 28)(2, 29)(3, 30)(4, 31)(5, 32)(6, 33)(7, 34)(8, 35)(9, 36)(10, 37)(11, 38)(12, 39)(13, 40)(14, 41)(15, 42)(16, 43)(17, 44)(18, 45)(19, 46)(20, 47)(21, 48)(22, 49)(23, 50)(24, 51)(25, 52)(26, 53)(27, 54)(55, 82, 56, 83, 60, 87, 66, 93, 72, 99, 77, 104, 71, 98, 65, 92, 58, 85)(57, 84, 61, 88, 67, 94, 73, 100, 78, 105, 81, 108, 76, 103, 70, 97, 64, 91)(59, 86, 62, 89, 68, 95, 74, 101, 79, 106, 80, 107, 75, 102, 69, 96, 63, 90) L = (1, 57)(2, 61)(3, 63)(4, 64)(5, 55)(6, 67)(7, 59)(8, 56)(9, 58)(10, 69)(11, 70)(12, 73)(13, 62)(14, 60)(15, 65)(16, 75)(17, 76)(18, 78)(19, 68)(20, 66)(21, 71)(22, 80)(23, 81)(24, 74)(25, 72)(26, 77)(27, 79)(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) :: { ( 54, 54 ), ( 54^18 ) } Outer automorphisms :: reflexible Dual of E12.357 Graph:: simple bipartite v = 30 e = 54 f = 2 degree seq :: [ 2^27, 18^3 ] E12.361 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 27, 27}) Quotient :: dipole Aut^+ = C27 (small group id <27, 1>) Aut = D54 (small group id <54, 1>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y2, Y3^-1), Y2^2 * Y3^3, Y2^9, Y2^9, 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^-1 * Y1^-1)^27 ] Map:: R = (1, 28)(2, 29)(3, 30)(4, 31)(5, 32)(6, 33)(7, 34)(8, 35)(9, 36)(10, 37)(11, 38)(12, 39)(13, 40)(14, 41)(15, 42)(16, 43)(17, 44)(18, 45)(19, 46)(20, 47)(21, 48)(22, 49)(23, 50)(24, 51)(25, 52)(26, 53)(27, 54)(55, 82, 56, 83, 60, 87, 68, 95, 74, 101, 79, 106, 73, 100, 65, 92, 58, 85)(57, 84, 61, 88, 67, 94, 70, 97, 76, 103, 81, 108, 78, 105, 72, 99, 64, 91)(59, 86, 62, 89, 69, 96, 75, 102, 80, 107, 77, 104, 71, 98, 63, 90, 66, 93) L = (1, 57)(2, 61)(3, 63)(4, 64)(5, 55)(6, 67)(7, 66)(8, 56)(9, 65)(10, 71)(11, 72)(12, 58)(13, 59)(14, 70)(15, 60)(16, 62)(17, 73)(18, 77)(19, 78)(20, 76)(21, 68)(22, 69)(23, 79)(24, 80)(25, 81)(26, 74)(27, 75)(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) :: { ( 54, 54 ), ( 54^18 ) } Outer automorphisms :: reflexible Dual of E12.358 Graph:: simple bipartite v = 30 e = 54 f = 2 degree seq :: [ 2^27, 18^3 ] E12.362 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 27, 27}) Quotient :: dipole Aut^+ = C27 (small group id <27, 1>) Aut = D54 (small group id <54, 1>) |r| :: 2 Presentation :: [ Y2, R^2, Y3 * Y1^-3, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1^-1), (R * Y2 * Y3^-1)^2, Y3^9, (Y3 * Y2^-1)^9, (Y1^-1 * Y3^-1)^27 ] Map:: R = (1, 28, 2, 29, 6, 33, 3, 30, 7, 34, 12, 39, 9, 36, 13, 40, 18, 45, 15, 42, 19, 46, 24, 51, 21, 48, 25, 52, 27, 54, 23, 50, 26, 53, 22, 49, 17, 44, 20, 47, 16, 43, 11, 38, 14, 41, 10, 37, 5, 32, 8, 35, 4, 31)(55, 82)(56, 83)(57, 84)(58, 85)(59, 86)(60, 87)(61, 88)(62, 89)(63, 90)(64, 91)(65, 92)(66, 93)(67, 94)(68, 95)(69, 96)(70, 97)(71, 98)(72, 99)(73, 100)(74, 101)(75, 102)(76, 103)(77, 104)(78, 105)(79, 106)(80, 107)(81, 108) 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, 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) :: { ( 18, 54 ), ( 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54 ) } Outer automorphisms :: reflexible Dual of E12.352 Graph:: bipartite v = 28 e = 54 f = 4 degree seq :: [ 2^27, 54 ] E12.363 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 27, 27}) Quotient :: dipole Aut^+ = C27 (small group id <27, 1>) Aut = D54 (small group id <54, 1>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^-1 * Y1^-3, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1^-1), (R * Y2 * Y3^-1)^2, Y3^9, (Y3 * Y2^-1)^9 ] Map:: R = (1, 28, 2, 29, 6, 33, 5, 32, 8, 35, 12, 39, 11, 38, 14, 41, 18, 45, 17, 44, 20, 47, 24, 51, 23, 50, 26, 53, 27, 54, 21, 48, 25, 52, 22, 49, 15, 42, 19, 46, 16, 43, 9, 36, 13, 40, 10, 37, 3, 30, 7, 34, 4, 31)(55, 82)(56, 83)(57, 84)(58, 85)(59, 86)(60, 87)(61, 88)(62, 89)(63, 90)(64, 91)(65, 92)(66, 93)(67, 94)(68, 95)(69, 96)(70, 97)(71, 98)(72, 99)(73, 100)(74, 101)(75, 102)(76, 103)(77, 104)(78, 105)(79, 106)(80, 107)(81, 108) 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, 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) :: { ( 18, 54 ), ( 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54 ) } Outer automorphisms :: reflexible Dual of E12.354 Graph:: bipartite v = 28 e = 54 f = 4 degree seq :: [ 2^27, 54 ] E12.364 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 27, 27}) Quotient :: dipole Aut^+ = C27 (small group id <27, 1>) Aut = D54 (small group id <54, 1>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1^-1), Y3^-2 * Y1^3, (R * Y2 * Y3^-1)^2, Y3^-9, Y3^9, Y3^18, (Y3 * Y2^-1)^9 ] Map:: R = (1, 28, 2, 29, 6, 33, 9, 36, 15, 42, 20, 47, 22, 49, 27, 54, 24, 51, 19, 46, 17, 44, 12, 39, 5, 32, 8, 35, 10, 37, 3, 30, 7, 34, 14, 41, 16, 43, 21, 48, 26, 53, 25, 52, 23, 50, 18, 45, 13, 40, 11, 38, 4, 31)(55, 82)(56, 83)(57, 84)(58, 85)(59, 86)(60, 87)(61, 88)(62, 89)(63, 90)(64, 91)(65, 92)(66, 93)(67, 94)(68, 95)(69, 96)(70, 97)(71, 98)(72, 99)(73, 100)(74, 101)(75, 102)(76, 103)(77, 104)(78, 105)(79, 106)(80, 107)(81, 108) 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, 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) :: { ( 18, 54 ), ( 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54 ) } Outer automorphisms :: reflexible Dual of E12.353 Graph:: bipartite v = 28 e = 54 f = 4 degree seq :: [ 2^27, 54 ] E12.365 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 27, 27}) Quotient :: dipole Aut^+ = C27 (small group id <27, 1>) Aut = D54 (small group id <54, 1>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1^-1), Y3^2 * Y1^3, (R * Y2 * Y3^-1)^2, Y3^9, Y3^-9, Y3^-9, Y3^18, (Y3 * Y2^-1)^9 ] Map:: R = (1, 28, 2, 29, 6, 33, 13, 40, 15, 42, 20, 47, 25, 52, 27, 54, 23, 50, 16, 43, 18, 45, 10, 37, 3, 30, 7, 34, 12, 39, 5, 32, 8, 35, 14, 41, 19, 46, 21, 48, 26, 53, 22, 49, 24, 51, 17, 44, 9, 36, 11, 38, 4, 31)(55, 82)(56, 83)(57, 84)(58, 85)(59, 86)(60, 87)(61, 88)(62, 89)(63, 90)(64, 91)(65, 92)(66, 93)(67, 94)(68, 95)(69, 96)(70, 97)(71, 98)(72, 99)(73, 100)(74, 101)(75, 102)(76, 103)(77, 104)(78, 105)(79, 106)(80, 107)(81, 108) 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, 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) :: { ( 18, 54 ), ( 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54 ) } Outer automorphisms :: reflexible Dual of E12.350 Graph:: bipartite v = 28 e = 54 f = 4 degree seq :: [ 2^27, 54 ] E12.366 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 27, 27}) Quotient :: dipole Aut^+ = C27 (small group id <27, 1>) Aut = D54 (small group id <54, 1>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1), (R * Y2 * Y3^-1)^2, Y1 * Y3^-1 * Y1^2 * Y3^-3, Y1^2 * Y3 * Y1^4, Y3^-2 * Y1^-1 * Y3^-3 * Y1^-2, (Y3 * Y2^-1)^9, Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-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:: R = (1, 28, 2, 29, 6, 33, 14, 41, 23, 50, 12, 39, 5, 32, 8, 35, 16, 43, 19, 46, 27, 54, 24, 51, 13, 40, 18, 45, 20, 47, 9, 36, 17, 44, 26, 53, 25, 52, 21, 48, 10, 37, 3, 30, 7, 34, 15, 42, 22, 49, 11, 38, 4, 31)(55, 82)(56, 83)(57, 84)(58, 85)(59, 86)(60, 87)(61, 88)(62, 89)(63, 90)(64, 91)(65, 92)(66, 93)(67, 94)(68, 95)(69, 96)(70, 97)(71, 98)(72, 99)(73, 100)(74, 101)(75, 102)(76, 103)(77, 104)(78, 105)(79, 106)(80, 107)(81, 108) 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, 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) :: { ( 18, 54 ), ( 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54 ) } Outer automorphisms :: reflexible Dual of E12.355 Graph:: bipartite v = 28 e = 54 f = 4 degree seq :: [ 2^27, 54 ] E12.367 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {9, 27, 27}) Quotient :: dipole Aut^+ = C27 (small group id <27, 1>) Aut = D54 (small group id <54, 1>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1^-1), (R * Y2 * Y3^-1)^2, Y1^-2 * Y3 * Y1^-4, Y1 * Y3 * Y1^2 * Y3^3, Y3^2 * Y1^-1 * Y3^3 * Y1^-2, (Y3 * Y2^-1)^9 ] Map:: R = (1, 28, 2, 29, 6, 33, 14, 41, 21, 48, 10, 37, 3, 30, 7, 34, 15, 42, 25, 52, 27, 54, 20, 47, 9, 36, 17, 44, 24, 51, 13, 40, 18, 45, 26, 53, 19, 46, 23, 50, 12, 39, 5, 32, 8, 35, 16, 43, 22, 49, 11, 38, 4, 31)(55, 82)(56, 83)(57, 84)(58, 85)(59, 86)(60, 87)(61, 88)(62, 89)(63, 90)(64, 91)(65, 92)(66, 93)(67, 94)(68, 95)(69, 96)(70, 97)(71, 98)(72, 99)(73, 100)(74, 101)(75, 102)(76, 103)(77, 104)(78, 105)(79, 106)(80, 107)(81, 108) 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, 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) :: { ( 18, 54 ), ( 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54, 18, 54 ) } Outer automorphisms :: reflexible Dual of E12.351 Graph:: bipartite v = 28 e = 54 f = 4 degree seq :: [ 2^27, 54 ] E12.368 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 7, 14}) Quotient :: halfedge^2 Aut^+ = D28 (small group id <28, 3>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (Y2 * Y3)^2, R * Y3 * R * Y2, (Y3 * Y1)^2, (Y1^-1 * Y2)^2, (R * Y1)^2, Y1^3 * Y2 * Y1^-4 * Y3, Y1^-5 * Y2 * Y1^2 * Y3 ] Map:: non-degenerate R = (1, 30, 2, 34, 6, 41, 13, 49, 21, 54, 26, 46, 18, 38, 10, 44, 16, 52, 24, 56, 28, 48, 20, 40, 12, 33, 5, 29)(3, 37, 9, 45, 17, 53, 25, 51, 23, 43, 15, 36, 8, 32, 4, 39, 11, 47, 19, 55, 27, 50, 22, 42, 14, 35, 7, 31) L = (1, 3)(2, 7)(4, 10)(5, 9)(6, 14)(8, 16)(11, 18)(12, 17)(13, 22)(15, 24)(19, 26)(20, 25)(21, 27)(23, 28)(29, 32)(30, 36)(31, 38)(33, 39)(34, 43)(35, 44)(37, 46)(40, 47)(41, 51)(42, 52)(45, 54)(48, 55)(49, 53)(50, 56) local type(s) :: { ( 14^28 ) } Outer automorphisms :: reflexible Dual of E12.371 Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 28 f = 4 degree seq :: [ 28^2 ] E12.369 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 7, 14}) Quotient :: halfedge^2 Aut^+ = D28 (small group id <28, 3>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (Y2 * Y1^-1)^2, (R * Y1)^2, (Y3 * Y1^-1)^2, Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y2 * Y3, Y1^3 * Y3 * Y1^-2 * Y2, Y3 * Y1 * Y2 * Y3 * Y1 * Y2 * Y1^-2 ] Map:: non-degenerate R = (1, 30, 2, 34, 6, 42, 14, 48, 20, 38, 10, 45, 17, 55, 27, 51, 23, 40, 12, 46, 18, 53, 25, 41, 13, 33, 5, 29)(3, 37, 9, 47, 19, 44, 16, 36, 8, 32, 4, 39, 11, 50, 22, 56, 28, 49, 21, 52, 24, 54, 26, 43, 15, 35, 7, 31) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 15)(8, 18)(10, 21)(11, 23)(13, 19)(14, 26)(16, 25)(17, 28)(20, 24)(22, 27)(29, 32)(30, 36)(31, 38)(33, 39)(34, 44)(35, 45)(37, 48)(40, 52)(41, 50)(42, 47)(43, 55)(46, 49)(51, 54)(53, 56) local type(s) :: { ( 14^28 ) } Outer automorphisms :: reflexible Dual of E12.372 Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 28 f = 4 degree seq :: [ 28^2 ] E12.370 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 7, 14}) Quotient :: halfedge^2 Aut^+ = D28 (small group id <28, 3>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (Y2 * Y1^-1)^2, (R * Y1)^2, (Y1^-1 * Y3)^2, Y1^2 * Y3 * Y1^-1 * Y2, Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y1^-1 * Y3 * Y1 ] Map:: non-degenerate R = (1, 30, 2, 34, 6, 38, 10, 43, 15, 48, 20, 50, 22, 55, 27, 53, 25, 51, 23, 46, 18, 40, 12, 41, 13, 33, 5, 29)(3, 37, 9, 36, 8, 32, 4, 39, 11, 45, 17, 47, 19, 52, 24, 56, 28, 54, 26, 49, 21, 44, 16, 42, 14, 35, 7, 31) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 14)(8, 13)(10, 16)(11, 18)(15, 21)(17, 23)(19, 25)(20, 26)(22, 28)(24, 27)(29, 32)(30, 36)(31, 38)(33, 39)(34, 37)(35, 43)(40, 47)(41, 45)(42, 48)(44, 50)(46, 52)(49, 55)(51, 56)(53, 54) local type(s) :: { ( 14^28 ) } Outer automorphisms :: reflexible Dual of E12.373 Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 28 f = 4 degree seq :: [ 28^2 ] E12.371 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 7, 14}) Quotient :: halfedge^2 Aut^+ = D28 (small group id <28, 3>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (Y3 * Y1)^2, (R * Y1)^2, (Y3 * Y2)^2, (Y1^-1 * Y2)^2, Y1^7 ] Map:: non-degenerate R = (1, 30, 2, 34, 6, 41, 13, 48, 20, 40, 12, 33, 5, 29)(3, 37, 9, 45, 17, 52, 24, 49, 21, 42, 14, 35, 7, 31)(4, 39, 11, 47, 19, 54, 26, 50, 22, 43, 15, 36, 8, 32)(10, 44, 16, 51, 23, 55, 27, 56, 28, 53, 25, 46, 18, 38) L = (1, 3)(2, 7)(4, 10)(5, 9)(6, 14)(8, 16)(11, 18)(12, 17)(13, 21)(15, 23)(19, 25)(20, 24)(22, 27)(26, 28)(29, 32)(30, 36)(31, 38)(33, 39)(34, 43)(35, 44)(37, 46)(40, 47)(41, 50)(42, 51)(45, 53)(48, 54)(49, 55)(52, 56) local type(s) :: { ( 28^14 ) } Outer automorphisms :: reflexible Dual of E12.368 Transitivity :: VT+ AT Graph:: bipartite v = 4 e = 28 f = 2 degree seq :: [ 14^4 ] E12.372 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 7, 14}) Quotient :: halfedge^2 Aut^+ = D28 (small group id <28, 3>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (Y1^-1 * Y3)^2, (R * Y1)^2, (Y1^-1 * Y2)^2, Y2 * Y1^-1 * Y3 * Y2 * Y3, Y1^7, (Y2 * Y1 * Y3)^14 ] Map:: non-degenerate R = (1, 30, 2, 34, 6, 42, 14, 49, 21, 41, 13, 33, 5, 29)(3, 37, 9, 46, 18, 53, 25, 50, 22, 43, 15, 35, 7, 31)(4, 39, 11, 48, 20, 55, 27, 51, 23, 44, 16, 36, 8, 32)(10, 40, 12, 45, 17, 52, 24, 56, 28, 54, 26, 47, 19, 38) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 15)(8, 17)(10, 11)(13, 18)(14, 22)(16, 24)(19, 20)(21, 25)(23, 28)(26, 27)(29, 32)(30, 36)(31, 38)(33, 39)(34, 44)(35, 40)(37, 47)(41, 48)(42, 51)(43, 45)(46, 54)(49, 55)(50, 52)(53, 56) local type(s) :: { ( 28^14 ) } Outer automorphisms :: reflexible Dual of E12.369 Transitivity :: VT+ AT Graph:: bipartite v = 4 e = 28 f = 2 degree seq :: [ 14^4 ] E12.373 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 7, 14}) Quotient :: halfedge^2 Aut^+ = D28 (small group id <28, 3>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (Y1^-1 * Y3)^2, (R * Y1)^2, (Y2 * Y1^-1)^2, Y1^-1 * Y2 * Y3 * Y2 * Y3, Y1^7 ] Map:: non-degenerate R = (1, 30, 2, 34, 6, 42, 14, 49, 21, 41, 13, 33, 5, 29)(3, 37, 9, 46, 18, 53, 25, 50, 22, 43, 15, 35, 7, 31)(4, 39, 11, 47, 19, 54, 26, 51, 23, 44, 16, 36, 8, 32)(10, 45, 17, 52, 24, 56, 28, 55, 27, 48, 20, 40, 12, 38) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 15)(8, 10)(11, 20)(13, 18)(14, 22)(16, 17)(19, 27)(21, 25)(23, 24)(26, 28)(29, 32)(30, 36)(31, 38)(33, 39)(34, 44)(35, 45)(37, 40)(41, 47)(42, 51)(43, 52)(46, 48)(49, 54)(50, 56)(53, 55) local type(s) :: { ( 28^14 ) } Outer automorphisms :: reflexible Dual of E12.370 Transitivity :: VT+ AT Graph:: bipartite v = 4 e = 28 f = 2 degree seq :: [ 14^4 ] E12.374 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 7, 14}) Quotient :: edge^2 Aut^+ = D28 (small group id <28, 3>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y2 * Y1)^2, (Y3^-1 * Y2)^2, (Y3^-1 * Y1)^2, Y3^7, (Y3 * Y1 * Y2)^14 ] Map:: R = (1, 29, 4, 32, 11, 39, 19, 47, 20, 48, 12, 40, 5, 33)(2, 30, 7, 35, 15, 43, 23, 51, 24, 52, 16, 44, 8, 36)(3, 31, 9, 37, 17, 45, 25, 53, 26, 54, 18, 46, 10, 38)(6, 34, 13, 41, 21, 49, 27, 55, 28, 56, 22, 50, 14, 42)(57, 58)(59, 62)(60, 64)(61, 63)(65, 70)(66, 69)(67, 72)(68, 71)(73, 78)(74, 77)(75, 80)(76, 79)(81, 84)(82, 83)(85, 87)(86, 90)(88, 94)(89, 93)(91, 98)(92, 97)(95, 102)(96, 101)(99, 106)(100, 105)(103, 110)(104, 109)(107, 112)(108, 111) 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 ), ( 56^14 ) } Outer automorphisms :: reflexible Dual of E12.383 Graph:: simple bipartite v = 32 e = 56 f = 2 degree seq :: [ 2^28, 14^4 ] E12.375 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 7, 14}) Quotient :: edge^2 Aut^+ = D28 (small group id <28, 3>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3^-1 * Y1)^2, (Y3 * Y2)^2, Y3 * Y1 * Y2 * Y1 * Y2, Y3^7 ] Map:: R = (1, 29, 4, 32, 12, 40, 20, 48, 21, 49, 13, 41, 5, 33)(2, 30, 7, 35, 15, 43, 23, 51, 24, 52, 16, 44, 8, 36)(3, 31, 10, 38, 18, 46, 26, 54, 27, 55, 19, 47, 11, 39)(6, 34, 9, 37, 17, 45, 25, 53, 28, 56, 22, 50, 14, 42)(57, 58)(59, 65)(60, 64)(61, 63)(62, 66)(67, 73)(68, 72)(69, 71)(70, 74)(75, 81)(76, 80)(77, 79)(78, 82)(83, 84)(85, 87)(86, 90)(88, 95)(89, 94)(91, 98)(92, 93)(96, 103)(97, 102)(99, 106)(100, 101)(104, 111)(105, 110)(107, 112)(108, 109) 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 ), ( 56^14 ) } Outer automorphisms :: reflexible Dual of E12.385 Graph:: simple bipartite v = 32 e = 56 f = 2 degree seq :: [ 2^28, 14^4 ] E12.376 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 7, 14}) Quotient :: edge^2 Aut^+ = D28 (small group id <28, 3>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y1)^2, (Y3^-1 * Y2)^2, Y3^-1 * Y1 * Y2 * Y1 * Y2, Y3^7, Y3^3 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * 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, 29, 4, 32, 12, 40, 20, 48, 21, 49, 13, 41, 5, 33)(2, 30, 7, 35, 15, 43, 23, 51, 24, 52, 16, 44, 8, 36)(3, 31, 10, 38, 18, 46, 26, 54, 27, 55, 19, 47, 11, 39)(6, 34, 14, 42, 22, 50, 28, 56, 25, 53, 17, 45, 9, 37)(57, 58)(59, 65)(60, 64)(61, 63)(62, 67)(66, 73)(68, 72)(69, 71)(70, 75)(74, 81)(76, 80)(77, 79)(78, 83)(82, 84)(85, 87)(86, 90)(88, 95)(89, 94)(91, 93)(92, 98)(96, 103)(97, 102)(99, 101)(100, 106)(104, 111)(105, 110)(107, 109)(108, 112) 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 ), ( 56^14 ) } Outer automorphisms :: reflexible Dual of E12.384 Graph:: simple bipartite v = 32 e = 56 f = 2 degree seq :: [ 2^28, 14^4 ] E12.377 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 7, 14}) Quotient :: edge^2 Aut^+ = D28 (small group id <28, 3>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y2 * Y1)^2, (Y3^-1 * Y2)^2, (Y3 * Y1)^2, Y3^-3 * Y1 * Y2 * Y3^-4, Y3^2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 ] Map:: R = (1, 29, 4, 32, 11, 39, 19, 47, 27, 55, 22, 50, 14, 42, 6, 34, 13, 41, 21, 49, 28, 56, 20, 48, 12, 40, 5, 33)(2, 30, 7, 35, 15, 43, 23, 51, 26, 54, 18, 46, 10, 38, 3, 31, 9, 37, 17, 45, 25, 53, 24, 52, 16, 44, 8, 36)(57, 58)(59, 62)(60, 64)(61, 63)(65, 70)(66, 69)(67, 72)(68, 71)(73, 78)(74, 77)(75, 80)(76, 79)(81, 83)(82, 84)(85, 87)(86, 90)(88, 94)(89, 93)(91, 98)(92, 97)(95, 102)(96, 101)(99, 106)(100, 105)(103, 110)(104, 109)(107, 111)(108, 112) 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) :: { ( 28, 28 ), ( 28^28 ) } Outer automorphisms :: reflexible Dual of E12.380 Graph:: simple bipartite v = 30 e = 56 f = 4 degree seq :: [ 2^28, 28^2 ] E12.378 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 7, 14}) Quotient :: edge^2 Aut^+ = D28 (small group id <28, 3>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y1)^2, (Y3 * Y2)^2, Y1 * Y3^-5 * Y2, Y1 * Y3^-1 * Y2 * Y1 * Y2 * Y1 * Y2, Y3 * Y2 * Y3^-1 * Y1 * Y3^2 * Y2 * Y1 ] Map:: R = (1, 29, 4, 32, 12, 40, 24, 52, 21, 49, 9, 37, 20, 48, 27, 55, 16, 44, 6, 34, 15, 43, 25, 53, 13, 41, 5, 33)(2, 30, 7, 35, 17, 45, 28, 56, 19, 47, 14, 42, 26, 54, 23, 51, 11, 39, 3, 31, 10, 38, 22, 50, 18, 46, 8, 36)(57, 58)(59, 65)(60, 64)(61, 63)(62, 70)(66, 77)(67, 76)(68, 74)(69, 73)(71, 75)(72, 82)(78, 80)(79, 83)(81, 84)(85, 87)(86, 90)(88, 95)(89, 94)(91, 100)(92, 99)(93, 103)(96, 107)(97, 106)(98, 105)(101, 111)(102, 109)(104, 112)(108, 110) 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) :: { ( 28, 28 ), ( 28^28 ) } Outer automorphisms :: reflexible Dual of E12.382 Graph:: simple bipartite v = 30 e = 56 f = 4 degree seq :: [ 2^28, 28^2 ] E12.379 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 7, 14}) Quotient :: edge^2 Aut^+ = D28 (small group id <28, 3>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3^-1 * Y1)^2, (Y3 * Y2)^2, Y2 * Y3^3 * Y1, Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y3^-1 * Y1 * Y3 * Y2 ] Map:: R = (1, 29, 4, 32, 12, 40, 9, 37, 18, 46, 25, 53, 23, 51, 27, 55, 20, 48, 22, 50, 15, 43, 6, 34, 13, 41, 5, 33)(2, 30, 7, 35, 16, 44, 14, 42, 21, 49, 28, 56, 26, 54, 24, 52, 17, 45, 19, 47, 11, 39, 3, 31, 10, 38, 8, 36)(57, 58)(59, 65)(60, 64)(61, 63)(62, 70)(66, 68)(67, 74)(69, 72)(71, 77)(73, 79)(75, 81)(76, 82)(78, 84)(80, 83)(85, 87)(86, 90)(88, 95)(89, 94)(91, 99)(92, 97)(93, 101)(96, 103)(98, 104)(100, 106)(102, 108)(105, 111)(107, 112)(109, 110) 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) :: { ( 28, 28 ), ( 28^28 ) } Outer automorphisms :: reflexible Dual of E12.381 Graph:: simple bipartite v = 30 e = 56 f = 4 degree seq :: [ 2^28, 28^2 ] E12.380 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 7, 14}) Quotient :: loop^2 Aut^+ = D28 (small group id <28, 3>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y2 * Y1)^2, (Y3^-1 * Y2)^2, (Y3^-1 * Y1)^2, Y3^7, (Y3 * Y1 * Y2)^14 ] Map:: R = (1, 29, 57, 85, 4, 32, 60, 88, 11, 39, 67, 95, 19, 47, 75, 103, 20, 48, 76, 104, 12, 40, 68, 96, 5, 33, 61, 89)(2, 30, 58, 86, 7, 35, 63, 91, 15, 43, 71, 99, 23, 51, 79, 107, 24, 52, 80, 108, 16, 44, 72, 100, 8, 36, 64, 92)(3, 31, 59, 87, 9, 37, 65, 93, 17, 45, 73, 101, 25, 53, 81, 109, 26, 54, 82, 110, 18, 46, 74, 102, 10, 38, 66, 94)(6, 34, 62, 90, 13, 41, 69, 97, 21, 49, 77, 105, 27, 55, 83, 111, 28, 56, 84, 112, 22, 50, 78, 106, 14, 42, 70, 98) L = (1, 30)(2, 29)(3, 34)(4, 36)(5, 35)(6, 31)(7, 33)(8, 32)(9, 42)(10, 41)(11, 44)(12, 43)(13, 38)(14, 37)(15, 40)(16, 39)(17, 50)(18, 49)(19, 52)(20, 51)(21, 46)(22, 45)(23, 48)(24, 47)(25, 56)(26, 55)(27, 54)(28, 53)(57, 87)(58, 90)(59, 85)(60, 94)(61, 93)(62, 86)(63, 98)(64, 97)(65, 89)(66, 88)(67, 102)(68, 101)(69, 92)(70, 91)(71, 106)(72, 105)(73, 96)(74, 95)(75, 110)(76, 109)(77, 100)(78, 99)(79, 112)(80, 111)(81, 104)(82, 103)(83, 108)(84, 107) 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 ) } Outer automorphisms :: reflexible Dual of E12.377 Transitivity :: VT+ Graph:: bipartite v = 4 e = 56 f = 30 degree seq :: [ 28^4 ] E12.381 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 7, 14}) Quotient :: loop^2 Aut^+ = D28 (small group id <28, 3>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3^-1 * Y1)^2, (Y3 * Y2)^2, Y3 * Y1 * Y2 * Y1 * Y2, Y3^7 ] Map:: R = (1, 29, 57, 85, 4, 32, 60, 88, 12, 40, 68, 96, 20, 48, 76, 104, 21, 49, 77, 105, 13, 41, 69, 97, 5, 33, 61, 89)(2, 30, 58, 86, 7, 35, 63, 91, 15, 43, 71, 99, 23, 51, 79, 107, 24, 52, 80, 108, 16, 44, 72, 100, 8, 36, 64, 92)(3, 31, 59, 87, 10, 38, 66, 94, 18, 46, 74, 102, 26, 54, 82, 110, 27, 55, 83, 111, 19, 47, 75, 103, 11, 39, 67, 95)(6, 34, 62, 90, 9, 37, 65, 93, 17, 45, 73, 101, 25, 53, 81, 109, 28, 56, 84, 112, 22, 50, 78, 106, 14, 42, 70, 98) L = (1, 30)(2, 29)(3, 37)(4, 36)(5, 35)(6, 38)(7, 33)(8, 32)(9, 31)(10, 34)(11, 45)(12, 44)(13, 43)(14, 46)(15, 41)(16, 40)(17, 39)(18, 42)(19, 53)(20, 52)(21, 51)(22, 54)(23, 49)(24, 48)(25, 47)(26, 50)(27, 56)(28, 55)(57, 87)(58, 90)(59, 85)(60, 95)(61, 94)(62, 86)(63, 98)(64, 93)(65, 92)(66, 89)(67, 88)(68, 103)(69, 102)(70, 91)(71, 106)(72, 101)(73, 100)(74, 97)(75, 96)(76, 111)(77, 110)(78, 99)(79, 112)(80, 109)(81, 108)(82, 105)(83, 104)(84, 107) 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 ) } Outer automorphisms :: reflexible Dual of E12.379 Transitivity :: VT+ Graph:: bipartite v = 4 e = 56 f = 30 degree seq :: [ 28^4 ] E12.382 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 7, 14}) Quotient :: loop^2 Aut^+ = D28 (small group id <28, 3>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y1)^2, (Y3^-1 * Y2)^2, Y3^-1 * Y1 * Y2 * Y1 * Y2, Y3^7, Y3^3 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * 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, 29, 57, 85, 4, 32, 60, 88, 12, 40, 68, 96, 20, 48, 76, 104, 21, 49, 77, 105, 13, 41, 69, 97, 5, 33, 61, 89)(2, 30, 58, 86, 7, 35, 63, 91, 15, 43, 71, 99, 23, 51, 79, 107, 24, 52, 80, 108, 16, 44, 72, 100, 8, 36, 64, 92)(3, 31, 59, 87, 10, 38, 66, 94, 18, 46, 74, 102, 26, 54, 82, 110, 27, 55, 83, 111, 19, 47, 75, 103, 11, 39, 67, 95)(6, 34, 62, 90, 14, 42, 70, 98, 22, 50, 78, 106, 28, 56, 84, 112, 25, 53, 81, 109, 17, 45, 73, 101, 9, 37, 65, 93) L = (1, 30)(2, 29)(3, 37)(4, 36)(5, 35)(6, 39)(7, 33)(8, 32)(9, 31)(10, 45)(11, 34)(12, 44)(13, 43)(14, 47)(15, 41)(16, 40)(17, 38)(18, 53)(19, 42)(20, 52)(21, 51)(22, 55)(23, 49)(24, 48)(25, 46)(26, 56)(27, 50)(28, 54)(57, 87)(58, 90)(59, 85)(60, 95)(61, 94)(62, 86)(63, 93)(64, 98)(65, 91)(66, 89)(67, 88)(68, 103)(69, 102)(70, 92)(71, 101)(72, 106)(73, 99)(74, 97)(75, 96)(76, 111)(77, 110)(78, 100)(79, 109)(80, 112)(81, 107)(82, 105)(83, 104)(84, 108) 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 ) } Outer automorphisms :: reflexible Dual of E12.378 Transitivity :: VT+ Graph:: bipartite v = 4 e = 56 f = 30 degree seq :: [ 28^4 ] E12.383 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 7, 14}) Quotient :: loop^2 Aut^+ = D28 (small group id <28, 3>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y2 * Y1)^2, (Y3^-1 * Y2)^2, (Y3 * Y1)^2, Y3^-3 * Y1 * Y2 * Y3^-4, Y3^2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 ] Map:: R = (1, 29, 57, 85, 4, 32, 60, 88, 11, 39, 67, 95, 19, 47, 75, 103, 27, 55, 83, 111, 22, 50, 78, 106, 14, 42, 70, 98, 6, 34, 62, 90, 13, 41, 69, 97, 21, 49, 77, 105, 28, 56, 84, 112, 20, 48, 76, 104, 12, 40, 68, 96, 5, 33, 61, 89)(2, 30, 58, 86, 7, 35, 63, 91, 15, 43, 71, 99, 23, 51, 79, 107, 26, 54, 82, 110, 18, 46, 74, 102, 10, 38, 66, 94, 3, 31, 59, 87, 9, 37, 65, 93, 17, 45, 73, 101, 25, 53, 81, 109, 24, 52, 80, 108, 16, 44, 72, 100, 8, 36, 64, 92) L = (1, 30)(2, 29)(3, 34)(4, 36)(5, 35)(6, 31)(7, 33)(8, 32)(9, 42)(10, 41)(11, 44)(12, 43)(13, 38)(14, 37)(15, 40)(16, 39)(17, 50)(18, 49)(19, 52)(20, 51)(21, 46)(22, 45)(23, 48)(24, 47)(25, 55)(26, 56)(27, 53)(28, 54)(57, 87)(58, 90)(59, 85)(60, 94)(61, 93)(62, 86)(63, 98)(64, 97)(65, 89)(66, 88)(67, 102)(68, 101)(69, 92)(70, 91)(71, 106)(72, 105)(73, 96)(74, 95)(75, 110)(76, 109)(77, 100)(78, 99)(79, 111)(80, 112)(81, 104)(82, 103)(83, 107)(84, 108) 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 ) } Outer automorphisms :: reflexible Dual of E12.374 Transitivity :: VT+ Graph:: bipartite v = 2 e = 56 f = 32 degree seq :: [ 56^2 ] E12.384 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 7, 14}) Quotient :: loop^2 Aut^+ = D28 (small group id <28, 3>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y1)^2, (Y3 * Y2)^2, Y1 * Y3^-5 * Y2, Y1 * Y3^-1 * Y2 * Y1 * Y2 * Y1 * Y2, Y3 * Y2 * Y3^-1 * Y1 * Y3^2 * Y2 * Y1 ] Map:: R = (1, 29, 57, 85, 4, 32, 60, 88, 12, 40, 68, 96, 24, 52, 80, 108, 21, 49, 77, 105, 9, 37, 65, 93, 20, 48, 76, 104, 27, 55, 83, 111, 16, 44, 72, 100, 6, 34, 62, 90, 15, 43, 71, 99, 25, 53, 81, 109, 13, 41, 69, 97, 5, 33, 61, 89)(2, 30, 58, 86, 7, 35, 63, 91, 17, 45, 73, 101, 28, 56, 84, 112, 19, 47, 75, 103, 14, 42, 70, 98, 26, 54, 82, 110, 23, 51, 79, 107, 11, 39, 67, 95, 3, 31, 59, 87, 10, 38, 66, 94, 22, 50, 78, 106, 18, 46, 74, 102, 8, 36, 64, 92) L = (1, 30)(2, 29)(3, 37)(4, 36)(5, 35)(6, 42)(7, 33)(8, 32)(9, 31)(10, 49)(11, 48)(12, 46)(13, 45)(14, 34)(15, 47)(16, 54)(17, 41)(18, 40)(19, 43)(20, 39)(21, 38)(22, 52)(23, 55)(24, 50)(25, 56)(26, 44)(27, 51)(28, 53)(57, 87)(58, 90)(59, 85)(60, 95)(61, 94)(62, 86)(63, 100)(64, 99)(65, 103)(66, 89)(67, 88)(68, 107)(69, 106)(70, 105)(71, 92)(72, 91)(73, 111)(74, 109)(75, 93)(76, 112)(77, 98)(78, 97)(79, 96)(80, 110)(81, 102)(82, 108)(83, 101)(84, 104) 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 ) } Outer automorphisms :: reflexible Dual of E12.376 Transitivity :: VT+ Graph:: bipartite v = 2 e = 56 f = 32 degree seq :: [ 56^2 ] E12.385 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 7, 14}) Quotient :: loop^2 Aut^+ = D28 (small group id <28, 3>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3^-1 * Y1)^2, (Y3 * Y2)^2, Y2 * Y3^3 * Y1, Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y3^-1 * Y1 * Y3 * Y2 ] Map:: R = (1, 29, 57, 85, 4, 32, 60, 88, 12, 40, 68, 96, 9, 37, 65, 93, 18, 46, 74, 102, 25, 53, 81, 109, 23, 51, 79, 107, 27, 55, 83, 111, 20, 48, 76, 104, 22, 50, 78, 106, 15, 43, 71, 99, 6, 34, 62, 90, 13, 41, 69, 97, 5, 33, 61, 89)(2, 30, 58, 86, 7, 35, 63, 91, 16, 44, 72, 100, 14, 42, 70, 98, 21, 49, 77, 105, 28, 56, 84, 112, 26, 54, 82, 110, 24, 52, 80, 108, 17, 45, 73, 101, 19, 47, 75, 103, 11, 39, 67, 95, 3, 31, 59, 87, 10, 38, 66, 94, 8, 36, 64, 92) L = (1, 30)(2, 29)(3, 37)(4, 36)(5, 35)(6, 42)(7, 33)(8, 32)(9, 31)(10, 40)(11, 46)(12, 38)(13, 44)(14, 34)(15, 49)(16, 41)(17, 51)(18, 39)(19, 53)(20, 54)(21, 43)(22, 56)(23, 45)(24, 55)(25, 47)(26, 48)(27, 52)(28, 50)(57, 87)(58, 90)(59, 85)(60, 95)(61, 94)(62, 86)(63, 99)(64, 97)(65, 101)(66, 89)(67, 88)(68, 103)(69, 92)(70, 104)(71, 91)(72, 106)(73, 93)(74, 108)(75, 96)(76, 98)(77, 111)(78, 100)(79, 112)(80, 102)(81, 110)(82, 109)(83, 105)(84, 107) 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 ) } Outer automorphisms :: reflexible Dual of E12.375 Transitivity :: VT+ Graph:: bipartite v = 2 e = 56 f = 32 degree seq :: [ 56^2 ] E12.386 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 7, 14}) Quotient :: dipole Aut^+ = C14 x C2 (small group id <28, 4>) Aut = C2 x C2 x D14 (small group id <56, 12>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, (Y2^-1 * R)^2, (R * Y3)^2, Y3 * Y2 * Y3 * Y2^-1, (R * Y1)^2, (Y3 * Y1)^2, Y2 * Y1 * Y2^-1 * Y1, Y2^7 ] Map:: non-degenerate R = (1, 29, 2, 30)(3, 31, 6, 34)(4, 32, 7, 35)(5, 33, 8, 36)(9, 37, 13, 41)(10, 38, 14, 42)(11, 39, 15, 43)(12, 40, 16, 44)(17, 45, 21, 49)(18, 46, 22, 50)(19, 47, 23, 51)(20, 48, 24, 52)(25, 53, 27, 55)(26, 54, 28, 56)(57, 85, 59, 87, 65, 93, 73, 101, 76, 104, 68, 96, 61, 89)(58, 86, 62, 90, 69, 97, 77, 105, 80, 108, 72, 100, 64, 92)(60, 88, 66, 94, 74, 102, 81, 109, 82, 110, 75, 103, 67, 95)(63, 91, 70, 98, 78, 106, 83, 111, 84, 112, 79, 107, 71, 99) L = (1, 60)(2, 63)(3, 66)(4, 57)(5, 67)(6, 70)(7, 58)(8, 71)(9, 74)(10, 59)(11, 61)(12, 75)(13, 78)(14, 62)(15, 64)(16, 79)(17, 81)(18, 65)(19, 68)(20, 82)(21, 83)(22, 69)(23, 72)(24, 84)(25, 73)(26, 76)(27, 77)(28, 80)(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) :: { ( 4, 28, 4, 28 ), ( 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28 ) } Outer automorphisms :: reflexible Dual of E12.393 Graph:: simple bipartite v = 18 e = 56 f = 16 degree seq :: [ 4^14, 14^4 ] E12.387 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 7, 14}) Quotient :: dipole Aut^+ = D28 (small group id <28, 3>) Aut = C2 x C2 x D14 (small group id <56, 12>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, (Y2^-1 * R)^2, (R * Y3)^2, Y3 * Y2 * Y3 * Y2^-1, (R * Y1)^2, (Y3 * Y1)^2, (Y2^-1 * Y1)^2, Y2^7 ] Map:: non-degenerate R = (1, 29, 2, 30)(3, 31, 8, 36)(4, 32, 7, 35)(5, 33, 6, 34)(9, 37, 16, 44)(10, 38, 15, 43)(11, 39, 14, 42)(12, 40, 13, 41)(17, 45, 24, 52)(18, 46, 23, 51)(19, 47, 22, 50)(20, 48, 21, 49)(25, 53, 28, 56)(26, 54, 27, 55)(57, 85, 59, 87, 65, 93, 73, 101, 76, 104, 68, 96, 61, 89)(58, 86, 62, 90, 69, 97, 77, 105, 80, 108, 72, 100, 64, 92)(60, 88, 66, 94, 74, 102, 81, 109, 82, 110, 75, 103, 67, 95)(63, 91, 70, 98, 78, 106, 83, 111, 84, 112, 79, 107, 71, 99) L = (1, 60)(2, 63)(3, 66)(4, 57)(5, 67)(6, 70)(7, 58)(8, 71)(9, 74)(10, 59)(11, 61)(12, 75)(13, 78)(14, 62)(15, 64)(16, 79)(17, 81)(18, 65)(19, 68)(20, 82)(21, 83)(22, 69)(23, 72)(24, 84)(25, 73)(26, 76)(27, 77)(28, 80)(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) :: { ( 4, 28, 4, 28 ), ( 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28 ) } Outer automorphisms :: reflexible Dual of E12.394 Graph:: simple bipartite v = 18 e = 56 f = 16 degree seq :: [ 4^14, 14^4 ] E12.388 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 7, 14}) Quotient :: dipole Aut^+ = D28 (small group id <28, 3>) Aut = C2 x C2 x D14 (small group id <56, 12>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^2 * Y3^2, Y3^-2 * Y2^-2, (Y3, Y2^-1), (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y2^-1)^2, (R * Y2)^2, (Y3^-1 * Y1)^2, (Y2^-1 * Y1)^2, Y2^-1 * Y3^6, Y2^7 ] Map:: non-degenerate R = (1, 29, 2, 30)(3, 31, 9, 37)(4, 32, 10, 38)(5, 33, 7, 35)(6, 34, 8, 36)(11, 39, 19, 47)(12, 40, 17, 45)(13, 41, 20, 48)(14, 42, 16, 44)(15, 43, 18, 46)(21, 49, 28, 56)(22, 50, 27, 55)(23, 51, 26, 54)(24, 52, 25, 53)(57, 85, 59, 87, 67, 95, 77, 105, 80, 108, 70, 98, 61, 89)(58, 86, 63, 91, 72, 100, 81, 109, 84, 112, 75, 103, 65, 93)(60, 88, 68, 96, 62, 90, 69, 97, 78, 106, 79, 107, 71, 99)(64, 92, 73, 101, 66, 94, 74, 102, 82, 110, 83, 111, 76, 104) L = (1, 60)(2, 64)(3, 68)(4, 70)(5, 71)(6, 57)(7, 73)(8, 75)(9, 76)(10, 58)(11, 62)(12, 61)(13, 59)(14, 79)(15, 80)(16, 66)(17, 65)(18, 63)(19, 83)(20, 84)(21, 69)(22, 67)(23, 77)(24, 78)(25, 74)(26, 72)(27, 81)(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) :: { ( 4, 28, 4, 28 ), ( 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28 ) } Outer automorphisms :: reflexible Dual of E12.398 Graph:: simple bipartite v = 18 e = 56 f = 16 degree seq :: [ 4^14, 14^4 ] E12.389 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 7, 14}) Quotient :: dipole Aut^+ = D28 (small group id <28, 3>) Aut = C2 x C2 x D14 (small group id <56, 12>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2 * Y3^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1)^2, (R * Y2)^2, (Y2^-1 * Y1)^2, Y2^7, (Y3 * Y2^-1)^14 ] Map:: non-degenerate R = (1, 29, 2, 30)(3, 31, 9, 37)(4, 32, 10, 38)(5, 33, 7, 35)(6, 34, 8, 36)(11, 39, 18, 46)(12, 40, 17, 45)(13, 41, 16, 44)(14, 42, 15, 43)(19, 47, 26, 54)(20, 48, 25, 53)(21, 49, 24, 52)(22, 50, 23, 51)(27, 55, 28, 56)(57, 85, 59, 87, 67, 95, 75, 103, 78, 106, 70, 98, 61, 89)(58, 86, 63, 91, 71, 99, 79, 107, 82, 110, 74, 102, 65, 93)(60, 88, 62, 90, 68, 96, 76, 104, 83, 111, 77, 105, 69, 97)(64, 92, 66, 94, 72, 100, 80, 108, 84, 112, 81, 109, 73, 101) L = (1, 60)(2, 64)(3, 62)(4, 61)(5, 69)(6, 57)(7, 66)(8, 65)(9, 73)(10, 58)(11, 68)(12, 59)(13, 70)(14, 77)(15, 72)(16, 63)(17, 74)(18, 81)(19, 76)(20, 67)(21, 78)(22, 83)(23, 80)(24, 71)(25, 82)(26, 84)(27, 75)(28, 79)(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) :: { ( 4, 28, 4, 28 ), ( 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28 ) } Outer automorphisms :: reflexible Dual of E12.397 Graph:: simple bipartite v = 18 e = 56 f = 16 degree seq :: [ 4^14, 14^4 ] E12.390 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 7, 14}) Quotient :: dipole Aut^+ = D28 (small group id <28, 3>) Aut = C2 x C2 x D14 (small group id <56, 12>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2 * Y3^-2, (R * Y3)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y2)^2, (Y2 * Y1)^2, Y2^7 ] Map:: non-degenerate R = (1, 29, 2, 30)(3, 31, 9, 37)(4, 32, 10, 38)(5, 33, 7, 35)(6, 34, 8, 36)(11, 39, 17, 45)(12, 40, 18, 46)(13, 41, 15, 43)(14, 42, 16, 44)(19, 47, 25, 53)(20, 48, 26, 54)(21, 49, 23, 51)(22, 50, 24, 52)(27, 55, 28, 56)(57, 85, 59, 87, 67, 95, 75, 103, 77, 105, 69, 97, 61, 89)(58, 86, 63, 91, 71, 99, 79, 107, 81, 109, 73, 101, 65, 93)(60, 88, 68, 96, 76, 104, 83, 111, 78, 106, 70, 98, 62, 90)(64, 92, 72, 100, 80, 108, 84, 112, 82, 110, 74, 102, 66, 94) L = (1, 60)(2, 64)(3, 68)(4, 59)(5, 62)(6, 57)(7, 72)(8, 63)(9, 66)(10, 58)(11, 76)(12, 67)(13, 70)(14, 61)(15, 80)(16, 71)(17, 74)(18, 65)(19, 83)(20, 75)(21, 78)(22, 69)(23, 84)(24, 79)(25, 82)(26, 73)(27, 77)(28, 81)(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) :: { ( 4, 28, 4, 28 ), ( 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28 ) } Outer automorphisms :: reflexible Dual of E12.395 Graph:: simple bipartite v = 18 e = 56 f = 16 degree seq :: [ 4^14, 14^4 ] E12.391 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 7, 14}) Quotient :: dipole Aut^+ = D28 (small group id <28, 3>) Aut = C2 x C2 x D14 (small group id <56, 12>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y3^-1, Y2^-1), (R * Y3)^2, (R * Y1)^2, (Y2 * Y1)^2, (Y3^-1 * Y1)^2, (R * Y2)^2, Y3^-2 * Y2^3, Y2 * Y3^4 ] Map:: non-degenerate R = (1, 29, 2, 30)(3, 31, 9, 37)(4, 32, 10, 38)(5, 33, 7, 35)(6, 34, 8, 36)(11, 39, 24, 52)(12, 40, 25, 53)(13, 41, 23, 51)(14, 42, 26, 54)(15, 43, 21, 49)(16, 44, 19, 47)(17, 45, 20, 48)(18, 46, 22, 50)(27, 55, 28, 56)(57, 85, 59, 87, 67, 95, 70, 98, 74, 102, 72, 100, 61, 89)(58, 86, 63, 91, 75, 103, 78, 106, 82, 110, 80, 108, 65, 93)(60, 88, 68, 96, 83, 111, 73, 101, 62, 90, 69, 97, 71, 99)(64, 92, 76, 104, 84, 112, 81, 109, 66, 94, 77, 105, 79, 107) L = (1, 60)(2, 64)(3, 68)(4, 70)(5, 71)(6, 57)(7, 76)(8, 78)(9, 79)(10, 58)(11, 83)(12, 74)(13, 59)(14, 73)(15, 67)(16, 69)(17, 61)(18, 62)(19, 84)(20, 82)(21, 63)(22, 81)(23, 75)(24, 77)(25, 65)(26, 66)(27, 72)(28, 80)(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) :: { ( 4, 28, 4, 28 ), ( 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28 ) } Outer automorphisms :: reflexible Dual of E12.399 Graph:: simple bipartite v = 18 e = 56 f = 16 degree seq :: [ 4^14, 14^4 ] E12.392 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 7, 14}) Quotient :: dipole Aut^+ = D28 (small group id <28, 3>) Aut = C2 x C2 x D14 (small group id <56, 12>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y3, Y2^-1), (R * Y3)^2, (R * Y1)^2, (Y2 * Y1)^2, (Y3^-1 * Y1)^2, (R * Y2)^2, Y2^-1 * Y3^4, Y3 * Y2 * Y3 * Y2^2 ] Map:: non-degenerate R = (1, 29, 2, 30)(3, 31, 9, 37)(4, 32, 10, 38)(5, 33, 7, 35)(6, 34, 8, 36)(11, 39, 24, 52)(12, 40, 25, 53)(13, 41, 23, 51)(14, 42, 26, 54)(15, 43, 21, 49)(16, 44, 19, 47)(17, 45, 20, 48)(18, 46, 22, 50)(27, 55, 28, 56)(57, 85, 59, 87, 67, 95, 74, 102, 70, 98, 72, 100, 61, 89)(58, 86, 63, 91, 75, 103, 82, 110, 78, 106, 80, 108, 65, 93)(60, 88, 68, 96, 73, 101, 62, 90, 69, 97, 83, 111, 71, 99)(64, 92, 76, 104, 81, 109, 66, 94, 77, 105, 84, 112, 79, 107) L = (1, 60)(2, 64)(3, 68)(4, 70)(5, 71)(6, 57)(7, 76)(8, 78)(9, 79)(10, 58)(11, 73)(12, 72)(13, 59)(14, 69)(15, 74)(16, 83)(17, 61)(18, 62)(19, 81)(20, 80)(21, 63)(22, 77)(23, 82)(24, 84)(25, 65)(26, 66)(27, 67)(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) :: { ( 4, 28, 4, 28 ), ( 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28 ) } Outer automorphisms :: reflexible Dual of E12.396 Graph:: simple bipartite v = 18 e = 56 f = 16 degree seq :: [ 4^14, 14^4 ] E12.393 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 7, 14}) Quotient :: dipole Aut^+ = C14 x C2 (small group id <28, 4>) Aut = C2 x C2 x D14 (small group id <56, 12>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y1^-1 * Y3 * Y1 * Y3, Y1^-1 * Y2 * Y1 * Y2, (Y3 * Y2)^2, Y1^-7 * Y3, Y3 * Y2 * Y1^-3 * Y2 * Y3 * Y1^3 ] Map:: non-degenerate R = (1, 29, 2, 30, 6, 34, 13, 41, 21, 49, 19, 47, 11, 39, 4, 32, 8, 36, 15, 43, 23, 51, 20, 48, 12, 40, 5, 33)(3, 31, 7, 35, 14, 42, 22, 50, 27, 55, 25, 53, 17, 45, 9, 37, 16, 44, 24, 52, 28, 56, 26, 54, 18, 46, 10, 38)(57, 85, 59, 87)(58, 86, 63, 91)(60, 88, 65, 93)(61, 89, 66, 94)(62, 90, 70, 98)(64, 92, 72, 100)(67, 95, 73, 101)(68, 96, 74, 102)(69, 97, 78, 106)(71, 99, 80, 108)(75, 103, 81, 109)(76, 104, 82, 110)(77, 105, 83, 111)(79, 107, 84, 112) L = (1, 60)(2, 64)(3, 65)(4, 57)(5, 67)(6, 71)(7, 72)(8, 58)(9, 59)(10, 73)(11, 61)(12, 75)(13, 79)(14, 80)(15, 62)(16, 63)(17, 66)(18, 81)(19, 68)(20, 77)(21, 76)(22, 84)(23, 69)(24, 70)(25, 74)(26, 83)(27, 82)(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) :: { ( 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 E12.386 Graph:: bipartite v = 16 e = 56 f = 18 degree seq :: [ 4^14, 28^2 ] E12.394 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 7, 14}) Quotient :: dipole Aut^+ = D28 (small group id <28, 3>) Aut = C2 x C2 x D14 (small group id <56, 12>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (R * Y2)^2, (R * Y3)^2, (Y3 * Y2)^2, (Y1^-1 * Y2)^2, (R * Y1)^2, Y1^-1 * Y3 * Y1 * Y3, Y1^-7 * Y3 ] Map:: non-degenerate R = (1, 29, 2, 30, 6, 34, 13, 41, 21, 49, 19, 47, 11, 39, 4, 32, 8, 36, 15, 43, 23, 51, 20, 48, 12, 40, 5, 33)(3, 31, 9, 37, 17, 45, 25, 53, 28, 56, 24, 52, 16, 44, 10, 38, 18, 46, 26, 54, 27, 55, 22, 50, 14, 42, 7, 35)(57, 85, 59, 87)(58, 86, 63, 91)(60, 88, 66, 94)(61, 89, 65, 93)(62, 90, 70, 98)(64, 92, 72, 100)(67, 95, 74, 102)(68, 96, 73, 101)(69, 97, 78, 106)(71, 99, 80, 108)(75, 103, 82, 110)(76, 104, 81, 109)(77, 105, 83, 111)(79, 107, 84, 112) L = (1, 60)(2, 64)(3, 66)(4, 57)(5, 67)(6, 71)(7, 72)(8, 58)(9, 74)(10, 59)(11, 61)(12, 75)(13, 79)(14, 80)(15, 62)(16, 63)(17, 82)(18, 65)(19, 68)(20, 77)(21, 76)(22, 84)(23, 69)(24, 70)(25, 83)(26, 73)(27, 81)(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) :: { ( 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 E12.387 Graph:: bipartite v = 16 e = 56 f = 18 degree seq :: [ 4^14, 28^2 ] E12.395 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 7, 14}) Quotient :: dipole Aut^+ = D28 (small group id <28, 3>) Aut = C2 x C2 x D14 (small group id <56, 12>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (Y2 * Y1)^2, (Y3 * Y2)^2, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^7, Y1^14 ] Map:: non-degenerate R = (1, 29, 2, 30, 5, 33, 9, 37, 13, 41, 17, 45, 21, 49, 25, 53, 24, 52, 20, 48, 16, 44, 12, 40, 8, 36, 4, 32)(3, 31, 7, 35, 11, 39, 15, 43, 19, 47, 23, 51, 27, 55, 28, 56, 26, 54, 22, 50, 18, 46, 14, 42, 10, 38, 6, 34)(57, 85, 59, 87)(58, 86, 62, 90)(60, 88, 63, 91)(61, 89, 66, 94)(64, 92, 67, 95)(65, 93, 70, 98)(68, 96, 71, 99)(69, 97, 74, 102)(72, 100, 75, 103)(73, 101, 78, 106)(76, 104, 79, 107)(77, 105, 82, 110)(80, 108, 83, 111)(81, 109, 84, 112) L = (1, 58)(2, 61)(3, 63)(4, 57)(5, 65)(6, 59)(7, 67)(8, 60)(9, 69)(10, 62)(11, 71)(12, 64)(13, 73)(14, 66)(15, 75)(16, 68)(17, 77)(18, 70)(19, 79)(20, 72)(21, 81)(22, 74)(23, 83)(24, 76)(25, 80)(26, 78)(27, 84)(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) :: { ( 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 E12.390 Graph:: bipartite v = 16 e = 56 f = 18 degree seq :: [ 4^14, 28^2 ] E12.396 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 7, 14}) Quotient :: dipole Aut^+ = D28 (small group id <28, 3>) Aut = C2 x C2 x D14 (small group id <56, 12>) |r| :: 2 Presentation :: [ Y2^2, R^2, Y3^3 * Y1^-1, (R * Y1)^2, (Y3 * Y2)^2, (Y2 * Y1)^2, (R * Y3)^2, (Y1 * Y2 * Y3)^2, Y3^-2 * Y1^-4, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^7 ] Map:: non-degenerate R = (1, 29, 2, 30, 7, 35, 17, 45, 14, 42, 4, 32, 9, 37, 19, 47, 16, 44, 6, 34, 10, 38, 20, 48, 15, 43, 5, 33)(3, 31, 11, 39, 23, 51, 27, 55, 21, 49, 12, 40, 24, 52, 28, 56, 22, 50, 13, 41, 25, 53, 26, 54, 18, 46, 8, 36)(57, 85, 59, 87)(58, 86, 64, 92)(60, 88, 69, 97)(61, 89, 67, 95)(62, 90, 68, 96)(63, 91, 74, 102)(65, 93, 78, 106)(66, 94, 77, 105)(70, 98, 81, 109)(71, 99, 79, 107)(72, 100, 80, 108)(73, 101, 82, 110)(75, 103, 84, 112)(76, 104, 83, 111) L = (1, 60)(2, 65)(3, 68)(4, 66)(5, 70)(6, 57)(7, 75)(8, 77)(9, 76)(10, 58)(11, 80)(12, 81)(13, 59)(14, 62)(15, 73)(16, 61)(17, 72)(18, 83)(19, 71)(20, 63)(21, 69)(22, 64)(23, 84)(24, 82)(25, 67)(26, 79)(27, 78)(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) :: { ( 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 E12.392 Graph:: bipartite v = 16 e = 56 f = 18 degree seq :: [ 4^14, 28^2 ] E12.397 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 7, 14}) Quotient :: dipole Aut^+ = D28 (small group id <28, 3>) Aut = C2 x C2 x D14 (small group id <56, 12>) |r| :: 2 Presentation :: [ Y2^2, R^2, Y3^-1 * Y1^-1 * Y3^-2, (Y3^-1, Y1^-1), (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y2 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, (Y1^-1 * Y3 * Y1^-1)^2, Y1^-1 * Y2 * Y1^2 * Y3 * Y2 * Y1^-2 ] Map:: non-degenerate R = (1, 29, 2, 30, 7, 35, 17, 45, 14, 42, 6, 34, 10, 38, 20, 48, 15, 43, 4, 32, 9, 37, 19, 47, 16, 44, 5, 33)(3, 31, 11, 39, 23, 51, 28, 56, 22, 50, 13, 41, 25, 53, 27, 55, 21, 49, 12, 40, 24, 52, 26, 54, 18, 46, 8, 36)(57, 85, 59, 87)(58, 86, 64, 92)(60, 88, 69, 97)(61, 89, 67, 95)(62, 90, 68, 96)(63, 91, 74, 102)(65, 93, 78, 106)(66, 94, 77, 105)(70, 98, 80, 108)(71, 99, 81, 109)(72, 100, 79, 107)(73, 101, 82, 110)(75, 103, 84, 112)(76, 104, 83, 111) L = (1, 60)(2, 65)(3, 68)(4, 70)(5, 71)(6, 57)(7, 75)(8, 77)(9, 62)(10, 58)(11, 80)(12, 78)(13, 59)(14, 61)(15, 73)(16, 76)(17, 72)(18, 83)(19, 66)(20, 63)(21, 84)(22, 64)(23, 82)(24, 69)(25, 67)(26, 81)(27, 79)(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) :: { ( 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 E12.389 Graph:: bipartite v = 16 e = 56 f = 18 degree seq :: [ 4^14, 28^2 ] E12.398 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 7, 14}) Quotient :: dipole Aut^+ = D28 (small group id <28, 3>) Aut = C2 x C2 x D14 (small group id <56, 12>) |r| :: 2 Presentation :: [ Y2^2, R^2, Y3 * Y1^-3, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2)^2, (Y2 * Y1)^2, (R * Y2 * Y3^-1)^2, Y3 * Y1^-1 * Y3^4, (Y3^-1 * Y1^-1)^7 ] Map:: non-degenerate R = (1, 29, 2, 30, 7, 35, 4, 32, 9, 37, 18, 46, 14, 42, 21, 49, 16, 44, 22, 50, 15, 43, 6, 34, 10, 38, 5, 33)(3, 31, 11, 39, 19, 47, 12, 40, 23, 51, 27, 55, 24, 52, 28, 56, 25, 53, 26, 54, 20, 48, 13, 41, 17, 45, 8, 36)(57, 85, 59, 87)(58, 86, 64, 92)(60, 88, 69, 97)(61, 89, 67, 95)(62, 90, 68, 96)(63, 91, 73, 101)(65, 93, 76, 104)(66, 94, 75, 103)(70, 98, 81, 109)(71, 99, 79, 107)(72, 100, 80, 108)(74, 102, 82, 110)(77, 105, 84, 112)(78, 106, 83, 111) L = (1, 60)(2, 65)(3, 68)(4, 70)(5, 63)(6, 57)(7, 74)(8, 75)(9, 77)(10, 58)(11, 79)(12, 80)(13, 59)(14, 78)(15, 61)(16, 62)(17, 67)(18, 72)(19, 83)(20, 64)(21, 71)(22, 66)(23, 84)(24, 82)(25, 69)(26, 73)(27, 81)(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) :: { ( 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 E12.388 Graph:: bipartite v = 16 e = 56 f = 18 degree seq :: [ 4^14, 28^2 ] E12.399 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 7, 14}) Quotient :: dipole Aut^+ = D28 (small group id <28, 3>) Aut = C2 x C2 x D14 (small group id <56, 12>) |r| :: 2 Presentation :: [ Y2^2, R^2, Y3^-1 * Y1^-3, (Y3 * Y2)^2, (R * Y1)^2, (Y2 * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y3^-4 * Y1^2, Y3^-2 * Y1 * Y3^2 * Y1^-1 ] Map:: non-degenerate R = (1, 29, 2, 30, 7, 35, 6, 34, 10, 38, 18, 46, 16, 44, 22, 50, 14, 42, 21, 49, 15, 43, 4, 32, 9, 37, 5, 33)(3, 31, 11, 39, 20, 48, 13, 41, 23, 51, 28, 56, 25, 53, 27, 55, 24, 52, 26, 54, 19, 47, 12, 40, 17, 45, 8, 36)(57, 85, 59, 87)(58, 86, 64, 92)(60, 88, 69, 97)(61, 89, 67, 95)(62, 90, 68, 96)(63, 91, 73, 101)(65, 93, 76, 104)(66, 94, 75, 103)(70, 98, 81, 109)(71, 99, 79, 107)(72, 100, 80, 108)(74, 102, 82, 110)(77, 105, 84, 112)(78, 106, 83, 111) L = (1, 60)(2, 65)(3, 68)(4, 70)(5, 71)(6, 57)(7, 61)(8, 75)(9, 77)(10, 58)(11, 73)(12, 80)(13, 59)(14, 74)(15, 78)(16, 62)(17, 82)(18, 63)(19, 83)(20, 64)(21, 72)(22, 66)(23, 67)(24, 84)(25, 69)(26, 81)(27, 79)(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) :: { ( 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 E12.391 Graph:: bipartite v = 16 e = 56 f = 18 degree seq :: [ 4^14, 28^2 ] E12.400 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {14, 14, 14}) Quotient :: edge Aut^+ = C14 x C2 (small group id <28, 4>) Aut = C2 x C2 x D14 (small group id <56, 12>) |r| :: 2 Presentation :: [ F^2, (T1, T2), (F * T1)^2, (F * T2)^2, T2 * T1 * T2^3 * T1, T1^-5 * T2 * T1^-1 * T2 ] Map:: non-degenerate R = (1, 3, 9, 19, 11, 21, 23, 28, 26, 16, 6, 15, 13, 5)(2, 7, 17, 12, 4, 10, 20, 27, 22, 25, 14, 24, 18, 8)(29, 30, 34, 42, 51, 48, 37, 45, 41, 46, 54, 50, 39, 32)(31, 35, 43, 52, 56, 55, 47, 40, 33, 36, 44, 53, 49, 38) L = (1, 29)(2, 30)(3, 31)(4, 32)(5, 33)(6, 34)(7, 35)(8, 36)(9, 37)(10, 38)(11, 39)(12, 40)(13, 41)(14, 42)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56) local type(s) :: { ( 28^14 ) } Outer automorphisms :: reflexible Dual of E12.402 Transitivity :: ET+ Graph:: bipartite v = 4 e = 28 f = 2 degree seq :: [ 14^4 ] E12.401 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {14, 14, 14}) Quotient :: edge Aut^+ = C14 x C2 (small group id <28, 4>) Aut = C2 x C2 x D14 (small group id <56, 12>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1), T1 * T2^-1 * T1 * T2^-3, T2 * T1 * T2 * T1^5, 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^-2 ] Map:: non-degenerate R = (1, 3, 9, 16, 6, 15, 26, 28, 23, 21, 11, 19, 13, 5)(2, 7, 17, 25, 14, 24, 20, 27, 22, 12, 4, 10, 18, 8)(29, 30, 34, 42, 51, 50, 41, 46, 37, 45, 54, 48, 39, 32)(31, 35, 43, 52, 49, 40, 33, 36, 44, 53, 56, 55, 47, 38) L = (1, 29)(2, 30)(3, 31)(4, 32)(5, 33)(6, 34)(7, 35)(8, 36)(9, 37)(10, 38)(11, 39)(12, 40)(13, 41)(14, 42)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56) local type(s) :: { ( 28^14 ) } Outer automorphisms :: reflexible Dual of E12.403 Transitivity :: ET+ Graph:: bipartite v = 4 e = 28 f = 2 degree seq :: [ 14^4 ] E12.402 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {14, 14, 14}) Quotient :: loop Aut^+ = C14 x C2 (small group id <28, 4>) Aut = C2 x C2 x D14 (small group id <56, 12>) |r| :: 2 Presentation :: [ F^2, T1^-1 * T2^2 * T1^-1, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^2 * T1^12, (T1^-1 * T2^-1)^14 ] Map:: non-degenerate R = (1, 29, 3, 31, 6, 34, 12, 40, 15, 43, 20, 48, 23, 51, 28, 56, 25, 53, 22, 50, 17, 45, 14, 42, 9, 37, 5, 33)(2, 30, 7, 35, 11, 39, 16, 44, 19, 47, 24, 52, 27, 55, 26, 54, 21, 49, 18, 46, 13, 41, 10, 38, 4, 32, 8, 36) L = (1, 30)(2, 34)(3, 35)(4, 29)(5, 36)(6, 39)(7, 40)(8, 31)(9, 32)(10, 33)(11, 43)(12, 44)(13, 37)(14, 38)(15, 47)(16, 48)(17, 41)(18, 42)(19, 51)(20, 52)(21, 45)(22, 46)(23, 55)(24, 56)(25, 49)(26, 50)(27, 53)(28, 54) local type(s) :: { ( 14^28 ) } Outer automorphisms :: reflexible Dual of E12.400 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 28 f = 4 degree seq :: [ 28^2 ] E12.403 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {14, 14, 14}) Quotient :: loop Aut^+ = C14 x C2 (small group id <28, 4>) Aut = C2 x C2 x D14 (small group id <56, 12>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1), T1 * T2^-1 * T1 * T2^-3, T2 * T1 * T2 * T1^5, 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^-2 ] Map:: non-degenerate R = (1, 29, 3, 31, 9, 37, 16, 44, 6, 34, 15, 43, 26, 54, 28, 56, 23, 51, 21, 49, 11, 39, 19, 47, 13, 41, 5, 33)(2, 30, 7, 35, 17, 45, 25, 53, 14, 42, 24, 52, 20, 48, 27, 55, 22, 50, 12, 40, 4, 32, 10, 38, 18, 46, 8, 36) L = (1, 30)(2, 34)(3, 35)(4, 29)(5, 36)(6, 42)(7, 43)(8, 44)(9, 45)(10, 31)(11, 32)(12, 33)(13, 46)(14, 51)(15, 52)(16, 53)(17, 54)(18, 37)(19, 38)(20, 39)(21, 40)(22, 41)(23, 50)(24, 49)(25, 56)(26, 48)(27, 47)(28, 55) local type(s) :: { ( 14^28 ) } Outer automorphisms :: reflexible Dual of E12.401 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 28 f = 4 degree seq :: [ 28^2 ] E12.404 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {14, 14, 14}) Quotient :: dipole Aut^+ = C14 x C2 (small group id <28, 4>) Aut = C2 x C2 x D14 (small group id <56, 12>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, Y2^-1 * Y3^-1 * Y2 * Y1^-1, (R * Y2)^2, Y2 * Y3^-1 * Y2^-1 * Y1^-1, (R * Y3)^2, (R * Y1)^2, Y2 * Y1^-1 * Y2 * Y1^-3, Y3 * Y2^-1 * Y1^-1 * Y2^-5, Y2 * Y1^-1 * Y2 * Y1^11, 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 ] Map:: R = (1, 29, 2, 30, 6, 34, 14, 42, 9, 37, 17, 45, 24, 52, 28, 56, 27, 55, 21, 49, 13, 41, 18, 46, 11, 39, 4, 32)(3, 31, 7, 35, 15, 43, 23, 51, 19, 47, 25, 53, 22, 50, 26, 54, 20, 48, 12, 40, 5, 33, 8, 36, 16, 44, 10, 38)(57, 85, 59, 87, 65, 93, 75, 103, 83, 111, 76, 104, 67, 95, 72, 100, 62, 90, 71, 99, 80, 108, 78, 106, 69, 97, 61, 89)(58, 86, 63, 91, 73, 101, 81, 109, 77, 105, 68, 96, 60, 88, 66, 94, 70, 98, 79, 107, 84, 112, 82, 110, 74, 102, 64, 92) L = (1, 60)(2, 57)(3, 66)(4, 67)(5, 68)(6, 58)(7, 59)(8, 61)(9, 70)(10, 72)(11, 74)(12, 76)(13, 77)(14, 62)(15, 63)(16, 64)(17, 65)(18, 69)(19, 79)(20, 82)(21, 83)(22, 81)(23, 71)(24, 73)(25, 75)(26, 78)(27, 84)(28, 80)(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) :: { ( 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 E12.407 Graph:: bipartite v = 4 e = 56 f = 30 degree seq :: [ 28^4 ] E12.405 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {14, 14, 14}) Quotient :: dipole Aut^+ = C14 x C2 (small group id <28, 4>) Aut = C2 x C2 x D14 (small group id <56, 12>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, (Y2^-1, Y1^-1), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y2^-1 * Y3^2 * Y2^-1 * Y1^-2, Y2^2 * Y3 * Y2^4 * Y1^-1 ] Map:: R = (1, 29, 2, 30, 6, 34, 14, 42, 13, 41, 18, 46, 24, 52, 28, 56, 27, 55, 20, 48, 9, 37, 17, 45, 11, 39, 4, 32)(3, 31, 7, 35, 15, 43, 12, 40, 5, 33, 8, 36, 16, 44, 23, 51, 22, 50, 26, 54, 19, 47, 25, 53, 21, 49, 10, 38)(57, 85, 59, 87, 65, 93, 75, 103, 80, 108, 72, 100, 62, 90, 71, 99, 67, 95, 77, 105, 83, 111, 78, 106, 69, 97, 61, 89)(58, 86, 63, 91, 73, 101, 81, 109, 84, 112, 79, 107, 70, 98, 68, 96, 60, 88, 66, 94, 76, 104, 82, 110, 74, 102, 64, 92) L = (1, 60)(2, 57)(3, 66)(4, 67)(5, 68)(6, 58)(7, 59)(8, 61)(9, 76)(10, 77)(11, 73)(12, 71)(13, 70)(14, 62)(15, 63)(16, 64)(17, 65)(18, 69)(19, 82)(20, 83)(21, 81)(22, 79)(23, 72)(24, 74)(25, 75)(26, 78)(27, 84)(28, 80)(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) :: { ( 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 E12.406 Graph:: bipartite v = 4 e = 56 f = 30 degree seq :: [ 28^4 ] E12.406 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {14, 14, 14}) Quotient :: dipole Aut^+ = C14 x C2 (small group id <28, 4>) Aut = C2 x C2 x D14 (small group id <56, 12>) |r| :: 2 Presentation :: [ Y1, R^2, Y2^-2 * Y3^-2, (Y2^-1 * R)^2, (R * Y3)^2, (R * Y1)^2, (Y2, Y3^-1), Y3^14, Y2^14, (Y3^-1 * Y1^-1)^14 ] Map:: R = (1, 29)(2, 30)(3, 31)(4, 32)(5, 33)(6, 34)(7, 35)(8, 36)(9, 37)(10, 38)(11, 39)(12, 40)(13, 41)(14, 42)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56)(57, 85, 58, 86, 62, 90, 67, 95, 71, 99, 75, 103, 79, 107, 83, 111, 81, 109, 78, 106, 73, 101, 70, 98, 65, 93, 60, 88)(59, 87, 63, 91, 61, 89, 64, 92, 68, 96, 72, 100, 76, 104, 80, 108, 84, 112, 82, 110, 77, 105, 74, 102, 69, 97, 66, 94) 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, 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) :: { ( 28, 28 ), ( 28^28 ) } Outer automorphisms :: reflexible Dual of E12.405 Graph:: simple bipartite v = 30 e = 56 f = 4 degree seq :: [ 2^28, 28^2 ] E12.407 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {14, 14, 14}) Quotient :: dipole Aut^+ = C14 x C2 (small group id <28, 4>) Aut = C2 x C2 x D14 (small group id <56, 12>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, (Y2, Y3), (R * Y2)^2, Y3^-1 * Y2^-1 * Y3^-3 * Y2^-1, Y2^-1 * Y3 * Y2^-5 * Y3, Y2^4 * Y3^2 * Y2^3 * Y3 * Y2^-1 * Y3^2 * Y2^-1 * Y3^2 * Y2^-1 * Y3, (Y3^-1 * Y1^-1)^14 ] Map:: R = (1, 29)(2, 30)(3, 31)(4, 32)(5, 33)(6, 34)(7, 35)(8, 36)(9, 37)(10, 38)(11, 39)(12, 40)(13, 41)(14, 42)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56)(57, 85, 58, 86, 62, 90, 70, 98, 79, 107, 76, 104, 65, 93, 73, 101, 69, 97, 74, 102, 82, 110, 78, 106, 67, 95, 60, 88)(59, 87, 63, 91, 71, 99, 80, 108, 84, 112, 83, 111, 75, 103, 68, 96, 61, 89, 64, 92, 72, 100, 81, 109, 77, 105, 66, 94) 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, 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) :: { ( 28, 28 ), ( 28^28 ) } Outer automorphisms :: reflexible Dual of E12.404 Graph:: simple bipartite v = 30 e = 56 f = 4 degree seq :: [ 2^28, 28^2 ] E12.408 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {7, 28, 28}) Quotient :: edge Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^4 * T1^3, T1^7, T1^-1 * T2 * T1^-2 * T2^3 * T1^-1 ] Map:: non-degenerate R = (1, 3, 9, 19, 22, 28, 18, 8, 2, 7, 17, 23, 11, 21, 27, 16, 6, 15, 24, 12, 4, 10, 20, 26, 14, 25, 13, 5)(29, 30, 34, 42, 50, 39, 32)(31, 35, 43, 53, 56, 49, 38)(33, 36, 44, 54, 47, 51, 40)(37, 45, 52, 41, 46, 55, 48) L = (1, 29)(2, 30)(3, 31)(4, 32)(5, 33)(6, 34)(7, 35)(8, 36)(9, 37)(10, 38)(11, 39)(12, 40)(13, 41)(14, 42)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56) local type(s) :: { ( 56^7 ), ( 56^28 ) } Outer automorphisms :: reflexible Dual of E12.418 Transitivity :: ET+ Graph:: bipartite v = 5 e = 28 f = 1 degree seq :: [ 7^4, 28 ] E12.409 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {7, 28, 28}) Quotient :: edge Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ F^2, (T1, T2), (F * T1)^2, (F * T2)^2, T1^-2 * T2^-4, T1^7, T1^2 * T2^-1 * T1 * T2^-1 * T1^2 * T2^-2 ] Map:: non-degenerate R = (1, 3, 9, 19, 11, 21, 27, 24, 14, 23, 18, 8, 2, 7, 17, 12, 4, 10, 20, 26, 22, 28, 25, 16, 6, 15, 13, 5)(29, 30, 34, 42, 50, 39, 32)(31, 35, 43, 51, 56, 49, 38)(33, 36, 44, 52, 54, 47, 40)(37, 45, 41, 46, 53, 55, 48) L = (1, 29)(2, 30)(3, 31)(4, 32)(5, 33)(6, 34)(7, 35)(8, 36)(9, 37)(10, 38)(11, 39)(12, 40)(13, 41)(14, 42)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56) local type(s) :: { ( 56^7 ), ( 56^28 ) } Outer automorphisms :: reflexible Dual of E12.416 Transitivity :: ET+ Graph:: bipartite v = 5 e = 28 f = 1 degree seq :: [ 7^4, 28 ] E12.410 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {7, 28, 28}) Quotient :: edge Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ F^2, (T2^-1, T1^-1), (F * T1)^2, (F * T2)^2, T2^-4 * T1^2, T1^7, (T1^-1 * T2^-1)^28 ] Map:: non-degenerate R = (1, 3, 9, 16, 6, 15, 25, 27, 20, 26, 22, 12, 4, 10, 18, 8, 2, 7, 17, 24, 14, 23, 28, 21, 11, 19, 13, 5)(29, 30, 34, 42, 48, 39, 32)(31, 35, 43, 51, 54, 47, 38)(33, 36, 44, 52, 55, 49, 40)(37, 45, 53, 56, 50, 41, 46) L = (1, 29)(2, 30)(3, 31)(4, 32)(5, 33)(6, 34)(7, 35)(8, 36)(9, 37)(10, 38)(11, 39)(12, 40)(13, 41)(14, 42)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56) local type(s) :: { ( 56^7 ), ( 56^28 ) } Outer automorphisms :: reflexible Dual of E12.419 Transitivity :: ET+ Graph:: bipartite v = 5 e = 28 f = 1 degree seq :: [ 7^4, 28 ] E12.411 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {7, 28, 28}) Quotient :: edge Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^4 * T1, T1^7, T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2^2 * T1^-1 * T2^2 * T1^-1 ] Map:: non-degenerate R = (1, 3, 9, 12, 4, 10, 18, 21, 11, 19, 25, 27, 20, 26, 28, 23, 14, 22, 24, 16, 6, 15, 17, 8, 2, 7, 13, 5)(29, 30, 34, 42, 48, 39, 32)(31, 35, 43, 50, 54, 47, 38)(33, 36, 44, 51, 55, 49, 40)(37, 41, 45, 52, 56, 53, 46) L = (1, 29)(2, 30)(3, 31)(4, 32)(5, 33)(6, 34)(7, 35)(8, 36)(9, 37)(10, 38)(11, 39)(12, 40)(13, 41)(14, 42)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56) local type(s) :: { ( 56^7 ), ( 56^28 ) } Outer automorphisms :: reflexible Dual of E12.415 Transitivity :: ET+ Graph:: bipartite v = 5 e = 28 f = 1 degree seq :: [ 7^4, 28 ] E12.412 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {7, 28, 28}) Quotient :: edge Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^4 * T1^-1, T1^7, (T1^-1 * T2^-1)^28 ] Map:: non-degenerate R = (1, 3, 9, 8, 2, 7, 17, 16, 6, 15, 24, 23, 14, 22, 28, 26, 19, 25, 27, 20, 11, 18, 21, 12, 4, 10, 13, 5)(29, 30, 34, 42, 47, 39, 32)(31, 35, 43, 50, 53, 46, 38)(33, 36, 44, 51, 54, 48, 40)(37, 45, 52, 56, 55, 49, 41) L = (1, 29)(2, 30)(3, 31)(4, 32)(5, 33)(6, 34)(7, 35)(8, 36)(9, 37)(10, 38)(11, 39)(12, 40)(13, 41)(14, 42)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56) local type(s) :: { ( 56^7 ), ( 56^28 ) } Outer automorphisms :: reflexible Dual of E12.417 Transitivity :: ET+ Graph:: bipartite v = 5 e = 28 f = 1 degree seq :: [ 7^4, 28 ] E12.413 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {7, 28, 28}) Quotient :: edge Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ F^2, T2 * T1^-3, (F * T1)^2, (F * T2)^2, T1 * T2^9, (T2^-1 * T1^-1)^7 ] Map:: non-degenerate R = (1, 3, 9, 15, 21, 27, 22, 16, 10, 4, 6, 12, 18, 24, 28, 26, 20, 14, 8, 2, 7, 13, 19, 25, 23, 17, 11, 5)(29, 30, 34, 31, 35, 40, 37, 41, 46, 43, 47, 52, 49, 53, 56, 55, 51, 54, 50, 45, 48, 44, 39, 42, 38, 33, 36, 32) L = (1, 29)(2, 30)(3, 31)(4, 32)(5, 33)(6, 34)(7, 35)(8, 36)(9, 37)(10, 38)(11, 39)(12, 40)(13, 41)(14, 42)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56) local type(s) :: { ( 14^28 ) } Outer automorphisms :: reflexible Dual of E12.420 Transitivity :: ET+ Graph:: bipartite v = 2 e = 28 f = 4 degree seq :: [ 28^2 ] E12.414 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {7, 28, 28}) Quotient :: edge Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ F^2, (T2^-1, T1^-1), (F * T1)^2, (F * T2)^2, T2^-1 * T1^-5, T2 * T1^-1 * T2^3 * T1^-1 * T2 * T1^-1 ] Map:: non-degenerate R = (1, 3, 9, 19, 24, 14, 11, 21, 28, 18, 8, 2, 7, 17, 27, 22, 12, 4, 10, 20, 26, 16, 6, 15, 25, 23, 13, 5)(29, 30, 34, 42, 40, 33, 36, 44, 52, 50, 41, 46, 54, 47, 55, 51, 56, 48, 37, 45, 53, 49, 38, 31, 35, 43, 39, 32) L = (1, 29)(2, 30)(3, 31)(4, 32)(5, 33)(6, 34)(7, 35)(8, 36)(9, 37)(10, 38)(11, 39)(12, 40)(13, 41)(14, 42)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56) local type(s) :: { ( 14^28 ) } Outer automorphisms :: reflexible Dual of E12.421 Transitivity :: ET+ Graph:: bipartite v = 2 e = 28 f = 4 degree seq :: [ 28^2 ] E12.415 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {7, 28, 28}) Quotient :: loop Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^4 * T1^3, T1^7, T1^-1 * T2 * T1^-2 * T2^3 * T1^-1 ] Map:: non-degenerate R = (1, 29, 3, 31, 9, 37, 19, 47, 22, 50, 28, 56, 18, 46, 8, 36, 2, 30, 7, 35, 17, 45, 23, 51, 11, 39, 21, 49, 27, 55, 16, 44, 6, 34, 15, 43, 24, 52, 12, 40, 4, 32, 10, 38, 20, 48, 26, 54, 14, 42, 25, 53, 13, 41, 5, 33) L = (1, 30)(2, 34)(3, 35)(4, 29)(5, 36)(6, 42)(7, 43)(8, 44)(9, 45)(10, 31)(11, 32)(12, 33)(13, 46)(14, 50)(15, 53)(16, 54)(17, 52)(18, 55)(19, 51)(20, 37)(21, 38)(22, 39)(23, 40)(24, 41)(25, 56)(26, 47)(27, 48)(28, 49) local type(s) :: { ( 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28 ) } Outer automorphisms :: reflexible Dual of E12.411 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 28 f = 5 degree seq :: [ 56 ] E12.416 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {7, 28, 28}) Quotient :: loop Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ F^2, (T1, T2), (F * T1)^2, (F * T2)^2, T1^-2 * T2^-4, T1^7, T1^2 * T2^-1 * T1 * T2^-1 * T1^2 * T2^-2 ] Map:: non-degenerate R = (1, 29, 3, 31, 9, 37, 19, 47, 11, 39, 21, 49, 27, 55, 24, 52, 14, 42, 23, 51, 18, 46, 8, 36, 2, 30, 7, 35, 17, 45, 12, 40, 4, 32, 10, 38, 20, 48, 26, 54, 22, 50, 28, 56, 25, 53, 16, 44, 6, 34, 15, 43, 13, 41, 5, 33) L = (1, 30)(2, 34)(3, 35)(4, 29)(5, 36)(6, 42)(7, 43)(8, 44)(9, 45)(10, 31)(11, 32)(12, 33)(13, 46)(14, 50)(15, 51)(16, 52)(17, 41)(18, 53)(19, 40)(20, 37)(21, 38)(22, 39)(23, 56)(24, 54)(25, 55)(26, 47)(27, 48)(28, 49) local type(s) :: { ( 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28 ) } Outer automorphisms :: reflexible Dual of E12.409 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 28 f = 5 degree seq :: [ 56 ] E12.417 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {7, 28, 28}) Quotient :: loop Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ F^2, (T2^-1, T1^-1), (F * T1)^2, (F * T2)^2, T2^-4 * T1^2, T1^7, (T1^-1 * T2^-1)^28 ] Map:: non-degenerate R = (1, 29, 3, 31, 9, 37, 16, 44, 6, 34, 15, 43, 25, 53, 27, 55, 20, 48, 26, 54, 22, 50, 12, 40, 4, 32, 10, 38, 18, 46, 8, 36, 2, 30, 7, 35, 17, 45, 24, 52, 14, 42, 23, 51, 28, 56, 21, 49, 11, 39, 19, 47, 13, 41, 5, 33) L = (1, 30)(2, 34)(3, 35)(4, 29)(5, 36)(6, 42)(7, 43)(8, 44)(9, 45)(10, 31)(11, 32)(12, 33)(13, 46)(14, 48)(15, 51)(16, 52)(17, 53)(18, 37)(19, 38)(20, 39)(21, 40)(22, 41)(23, 54)(24, 55)(25, 56)(26, 47)(27, 49)(28, 50) local type(s) :: { ( 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28 ) } Outer automorphisms :: reflexible Dual of E12.412 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 28 f = 5 degree seq :: [ 56 ] E12.418 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {7, 28, 28}) Quotient :: loop Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^4 * T1, T1^7, T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2 * T1^-2 * T2^2 * T1^-1 * T2^2 * T1^-1 ] Map:: non-degenerate R = (1, 29, 3, 31, 9, 37, 12, 40, 4, 32, 10, 38, 18, 46, 21, 49, 11, 39, 19, 47, 25, 53, 27, 55, 20, 48, 26, 54, 28, 56, 23, 51, 14, 42, 22, 50, 24, 52, 16, 44, 6, 34, 15, 43, 17, 45, 8, 36, 2, 30, 7, 35, 13, 41, 5, 33) L = (1, 30)(2, 34)(3, 35)(4, 29)(5, 36)(6, 42)(7, 43)(8, 44)(9, 41)(10, 31)(11, 32)(12, 33)(13, 45)(14, 48)(15, 50)(16, 51)(17, 52)(18, 37)(19, 38)(20, 39)(21, 40)(22, 54)(23, 55)(24, 56)(25, 46)(26, 47)(27, 49)(28, 53) local type(s) :: { ( 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28 ) } Outer automorphisms :: reflexible Dual of E12.408 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 28 f = 5 degree seq :: [ 56 ] E12.419 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {7, 28, 28}) Quotient :: loop Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^4 * T1^-1, T1^7, (T1^-1 * T2^-1)^28 ] Map:: non-degenerate R = (1, 29, 3, 31, 9, 37, 8, 36, 2, 30, 7, 35, 17, 45, 16, 44, 6, 34, 15, 43, 24, 52, 23, 51, 14, 42, 22, 50, 28, 56, 26, 54, 19, 47, 25, 53, 27, 55, 20, 48, 11, 39, 18, 46, 21, 49, 12, 40, 4, 32, 10, 38, 13, 41, 5, 33) L = (1, 30)(2, 34)(3, 35)(4, 29)(5, 36)(6, 42)(7, 43)(8, 44)(9, 45)(10, 31)(11, 32)(12, 33)(13, 37)(14, 47)(15, 50)(16, 51)(17, 52)(18, 38)(19, 39)(20, 40)(21, 41)(22, 53)(23, 54)(24, 56)(25, 46)(26, 48)(27, 49)(28, 55) local type(s) :: { ( 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28, 7, 28 ) } Outer automorphisms :: reflexible Dual of E12.410 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 28 f = 5 degree seq :: [ 56 ] E12.420 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {7, 28, 28}) Quotient :: loop Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ F^2, (T1, T2^-1), (F * T1)^2, (F * T2)^2, T1^4 * T2^3, T2^7, T1^-1 * T2 * T1^-1 * T2^2 * T1^-2 * T2 ] Map:: non-degenerate R = (1, 29, 3, 31, 9, 37, 19, 47, 25, 53, 13, 41, 5, 33)(2, 30, 7, 35, 17, 45, 22, 50, 28, 56, 18, 46, 8, 36)(4, 32, 10, 38, 20, 48, 26, 54, 14, 42, 24, 52, 12, 40)(6, 34, 15, 43, 23, 51, 11, 39, 21, 49, 27, 55, 16, 44) L = (1, 30)(2, 34)(3, 35)(4, 29)(5, 36)(6, 42)(7, 43)(8, 44)(9, 45)(10, 31)(11, 32)(12, 33)(13, 46)(14, 53)(15, 52)(16, 54)(17, 51)(18, 55)(19, 50)(20, 37)(21, 38)(22, 39)(23, 40)(24, 41)(25, 56)(26, 47)(27, 48)(28, 49) local type(s) :: { ( 28^14 ) } Outer automorphisms :: reflexible Dual of E12.413 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 4 e = 28 f = 2 degree seq :: [ 14^4 ] E12.421 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {7, 28, 28}) Quotient :: loop Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ F^2, (T1, T2^-1), (F * T1)^2, (F * T2)^2, T1^-4 * T2^2, T2^7, T2 * T1 * T2 * T1 * T2^3 * T1^2, T2^2 * T1 * T2^2 * T1 * T2^2 * T1 * T2^2 * T1 * T2^2 * T1 * T2^2 * T1^-1 ] Map:: non-degenerate R = (1, 29, 3, 31, 9, 37, 19, 47, 22, 50, 13, 41, 5, 33)(2, 30, 7, 35, 17, 45, 25, 53, 26, 54, 18, 46, 8, 36)(4, 32, 10, 38, 14, 42, 23, 51, 28, 56, 21, 49, 12, 40)(6, 34, 15, 43, 24, 52, 27, 55, 20, 48, 11, 39, 16, 44) L = (1, 30)(2, 34)(3, 35)(4, 29)(5, 36)(6, 42)(7, 43)(8, 44)(9, 45)(10, 31)(11, 32)(12, 33)(13, 46)(14, 37)(15, 51)(16, 38)(17, 52)(18, 39)(19, 53)(20, 40)(21, 41)(22, 54)(23, 47)(24, 56)(25, 55)(26, 48)(27, 49)(28, 50) local type(s) :: { ( 28^14 ) } Outer automorphisms :: reflexible Dual of E12.414 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 4 e = 28 f = 2 degree seq :: [ 14^4 ] E12.422 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 28, 28}) Quotient :: dipole Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y1^-1 * Y3^-1, Y2 * Y1^-1 * Y2^-1 * Y3^-1, (R * Y3)^2, (R * Y1)^2, Y2 * Y3^-1 * Y2^-1 * Y1^-1, (R * Y2)^2, Y1^7, Y1 * Y2 * Y3^-1 * Y1 * Y2^3, Y1^-1 * Y2 * Y3 * Y2^3 * Y1^-2, Y3^21, Y2^-1 * Y1^-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 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * 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, 29, 2, 30, 6, 34, 14, 42, 22, 50, 11, 39, 4, 32)(3, 31, 7, 35, 15, 43, 25, 53, 28, 56, 21, 49, 10, 38)(5, 33, 8, 36, 16, 44, 26, 54, 19, 47, 23, 51, 12, 40)(9, 37, 17, 45, 24, 52, 13, 41, 18, 46, 27, 55, 20, 48)(57, 85, 59, 87, 65, 93, 75, 103, 78, 106, 84, 112, 74, 102, 64, 92, 58, 86, 63, 91, 73, 101, 79, 107, 67, 95, 77, 105, 83, 111, 72, 100, 62, 90, 71, 99, 80, 108, 68, 96, 60, 88, 66, 94, 76, 104, 82, 110, 70, 98, 81, 109, 69, 97, 61, 89) L = (1, 60)(2, 57)(3, 66)(4, 67)(5, 68)(6, 58)(7, 59)(8, 61)(9, 76)(10, 77)(11, 78)(12, 79)(13, 80)(14, 62)(15, 63)(16, 64)(17, 65)(18, 69)(19, 82)(20, 83)(21, 84)(22, 70)(23, 75)(24, 73)(25, 71)(26, 72)(27, 74)(28, 81)(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) :: { ( 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56 ), ( 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 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 E12.434 Graph:: bipartite v = 5 e = 56 f = 29 degree seq :: [ 14^4, 56 ] E12.423 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 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 * Y3^-1, (R * Y2)^2, (R * Y1)^2, (Y3^-1, Y2), (R * Y3)^2, (Y2^-1, Y1^-1), Y3^2 * Y2^-4, Y1^7, Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y3^-2 * Y2^-2, Y3^14 ] Map:: R = (1, 29, 2, 30, 6, 34, 14, 42, 22, 50, 11, 39, 4, 32)(3, 31, 7, 35, 15, 43, 23, 51, 28, 56, 21, 49, 10, 38)(5, 33, 8, 36, 16, 44, 24, 52, 26, 54, 19, 47, 12, 40)(9, 37, 17, 45, 13, 41, 18, 46, 25, 53, 27, 55, 20, 48)(57, 85, 59, 87, 65, 93, 75, 103, 67, 95, 77, 105, 83, 111, 80, 108, 70, 98, 79, 107, 74, 102, 64, 92, 58, 86, 63, 91, 73, 101, 68, 96, 60, 88, 66, 94, 76, 104, 82, 110, 78, 106, 84, 112, 81, 109, 72, 100, 62, 90, 71, 99, 69, 97, 61, 89) L = (1, 60)(2, 57)(3, 66)(4, 67)(5, 68)(6, 58)(7, 59)(8, 61)(9, 76)(10, 77)(11, 78)(12, 75)(13, 73)(14, 62)(15, 63)(16, 64)(17, 65)(18, 69)(19, 82)(20, 83)(21, 84)(22, 70)(23, 71)(24, 72)(25, 74)(26, 80)(27, 81)(28, 79)(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) :: { ( 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56 ), ( 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 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 E12.432 Graph:: bipartite v = 5 e = 56 f = 29 degree seq :: [ 14^4, 56 ] E12.424 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 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, (R * Y1)^2, (R * Y3)^2, Y2 * Y3^-1 * Y2^-1 * Y1^-1, (R * Y2)^2, Y2^-4 * Y1^2, Y1^3 * Y3^-4, Y1^7, 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 ] Map:: R = (1, 29, 2, 30, 6, 34, 14, 42, 20, 48, 11, 39, 4, 32)(3, 31, 7, 35, 15, 43, 23, 51, 26, 54, 19, 47, 10, 38)(5, 33, 8, 36, 16, 44, 24, 52, 27, 55, 21, 49, 12, 40)(9, 37, 17, 45, 25, 53, 28, 56, 22, 50, 13, 41, 18, 46)(57, 85, 59, 87, 65, 93, 72, 100, 62, 90, 71, 99, 81, 109, 83, 111, 76, 104, 82, 110, 78, 106, 68, 96, 60, 88, 66, 94, 74, 102, 64, 92, 58, 86, 63, 91, 73, 101, 80, 108, 70, 98, 79, 107, 84, 112, 77, 105, 67, 95, 75, 103, 69, 97, 61, 89) L = (1, 60)(2, 57)(3, 66)(4, 67)(5, 68)(6, 58)(7, 59)(8, 61)(9, 74)(10, 75)(11, 76)(12, 77)(13, 78)(14, 62)(15, 63)(16, 64)(17, 65)(18, 69)(19, 82)(20, 70)(21, 83)(22, 84)(23, 71)(24, 72)(25, 73)(26, 79)(27, 80)(28, 81)(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) :: { ( 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56 ), ( 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 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 E12.435 Graph:: bipartite v = 5 e = 56 f = 29 degree seq :: [ 14^4, 56 ] E12.425 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 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, (R * Y3)^2, (R * Y2)^2, (Y3^-1, Y2^-1), (R * Y1)^2, (Y2^-1, Y1^-1), Y3 * Y2^4, Y3^7, Y1^7, 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 ] Map:: R = (1, 29, 2, 30, 6, 34, 14, 42, 19, 47, 11, 39, 4, 32)(3, 31, 7, 35, 15, 43, 22, 50, 25, 53, 18, 46, 10, 38)(5, 33, 8, 36, 16, 44, 23, 51, 26, 54, 20, 48, 12, 40)(9, 37, 17, 45, 24, 52, 28, 56, 27, 55, 21, 49, 13, 41)(57, 85, 59, 87, 65, 93, 64, 92, 58, 86, 63, 91, 73, 101, 72, 100, 62, 90, 71, 99, 80, 108, 79, 107, 70, 98, 78, 106, 84, 112, 82, 110, 75, 103, 81, 109, 83, 111, 76, 104, 67, 95, 74, 102, 77, 105, 68, 96, 60, 88, 66, 94, 69, 97, 61, 89) L = (1, 60)(2, 57)(3, 66)(4, 67)(5, 68)(6, 58)(7, 59)(8, 61)(9, 69)(10, 74)(11, 75)(12, 76)(13, 77)(14, 62)(15, 63)(16, 64)(17, 65)(18, 81)(19, 70)(20, 82)(21, 83)(22, 71)(23, 72)(24, 73)(25, 78)(26, 79)(27, 84)(28, 80)(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) :: { ( 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56 ), ( 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 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 E12.433 Graph:: bipartite v = 5 e = 56 f = 29 degree seq :: [ 14^4, 56 ] E12.426 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 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 * Y3^-1, (Y3^-1, Y2^-1), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2^-1, Y1^-1), Y2^4 * Y1, Y1^7, 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 ] Map:: R = (1, 29, 2, 30, 6, 34, 14, 42, 20, 48, 11, 39, 4, 32)(3, 31, 7, 35, 15, 43, 22, 50, 26, 54, 19, 47, 10, 38)(5, 33, 8, 36, 16, 44, 23, 51, 27, 55, 21, 49, 12, 40)(9, 37, 13, 41, 17, 45, 24, 52, 28, 56, 25, 53, 18, 46)(57, 85, 59, 87, 65, 93, 68, 96, 60, 88, 66, 94, 74, 102, 77, 105, 67, 95, 75, 103, 81, 109, 83, 111, 76, 104, 82, 110, 84, 112, 79, 107, 70, 98, 78, 106, 80, 108, 72, 100, 62, 90, 71, 99, 73, 101, 64, 92, 58, 86, 63, 91, 69, 97, 61, 89) L = (1, 60)(2, 57)(3, 66)(4, 67)(5, 68)(6, 58)(7, 59)(8, 61)(9, 74)(10, 75)(11, 76)(12, 77)(13, 65)(14, 62)(15, 63)(16, 64)(17, 69)(18, 81)(19, 82)(20, 70)(21, 83)(22, 71)(23, 72)(24, 73)(25, 84)(26, 78)(27, 79)(28, 80)(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) :: { ( 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56 ), ( 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 2, 56, 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 E12.431 Graph:: bipartite v = 5 e = 56 f = 29 degree seq :: [ 14^4, 56 ] E12.427 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 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^-1, Y2^3 * Y1^-1, (R * Y1)^2, R * Y2 * R * Y3, Y2 * Y1^9, (Y3^-1 * Y1^-1)^7 ] 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, 59)(2, 63)(3, 64)(4, 65)(5, 57)(6, 69)(7, 70)(8, 58)(9, 61)(10, 71)(11, 60)(12, 75)(13, 76)(14, 62)(15, 67)(16, 77)(17, 66)(18, 81)(19, 82)(20, 68)(21, 73)(22, 83)(23, 72)(24, 78)(25, 84)(26, 74)(27, 79)(28, 80)(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) :: { ( 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 E12.429 Graph:: bipartite v = 2 e = 56 f = 32 degree seq :: [ 56^2 ] E12.428 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 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^-1, (R * Y1)^2, R * Y2 * R * Y3, (Y1, Y2^-1), Y1^-1 * Y2^-5, Y2^2 * Y1^-1 * Y2 * Y1^-4, (Y3^-1 * Y1^-1)^7 ] 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, 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, 81)(15, 83)(16, 62)(17, 69)(18, 64)(19, 68)(20, 80)(21, 82)(22, 84)(23, 67)(24, 79)(25, 78)(26, 70)(27, 74)(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) :: { ( 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 E12.430 Graph:: bipartite v = 2 e = 56 f = 32 degree seq :: [ 56^2 ] E12.429 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 28, 28}) Quotient :: dipole Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ Y1, R^2, (Y2, Y3), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2^3 * Y3^-4, Y2^7, (Y3^-1 * Y1^-1)^28 ] Map:: R = (1, 29)(2, 30)(3, 31)(4, 32)(5, 33)(6, 34)(7, 35)(8, 36)(9, 37)(10, 38)(11, 39)(12, 40)(13, 41)(14, 42)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56)(57, 85, 58, 86, 62, 90, 70, 98, 78, 106, 67, 95, 60, 88)(59, 87, 63, 91, 71, 99, 82, 110, 81, 109, 77, 105, 66, 94)(61, 89, 64, 92, 72, 100, 75, 103, 84, 112, 79, 107, 68, 96)(65, 93, 73, 101, 83, 111, 80, 108, 69, 97, 74, 102, 76, 104) 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, 82)(15, 83)(16, 62)(17, 84)(18, 64)(19, 70)(20, 72)(21, 74)(22, 81)(23, 67)(24, 68)(25, 69)(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 ), ( 56^14 ) } Outer automorphisms :: reflexible Dual of E12.427 Graph:: simple bipartite v = 32 e = 56 f = 2 degree seq :: [ 2^28, 14^4 ] E12.430 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 28, 28}) Quotient :: dipole Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, (Y2, Y3), (R * Y2)^2, Y2^-2 * Y3^-4, Y2^7, Y2^2 * Y3^-1 * Y2 * Y3^-1 * Y2^2 * Y3^-2, Y3^-1 * Y2^2 * Y3^-1 * Y2^2 * Y3^-1 * Y2^2 * Y3^-1 * Y2^2 * Y3^-1 * Y2^2 * Y3^-1 * Y2 * Y3^-2 * Y2^-1, (Y3^-1 * Y1^-1)^28 ] Map:: R = (1, 29)(2, 30)(3, 31)(4, 32)(5, 33)(6, 34)(7, 35)(8, 36)(9, 37)(10, 38)(11, 39)(12, 40)(13, 41)(14, 42)(15, 43)(16, 44)(17, 45)(18, 46)(19, 47)(20, 48)(21, 49)(22, 50)(23, 51)(24, 52)(25, 53)(26, 54)(27, 55)(28, 56)(57, 85, 58, 86, 62, 90, 70, 98, 78, 106, 67, 95, 60, 88)(59, 87, 63, 91, 71, 99, 79, 107, 84, 112, 77, 105, 66, 94)(61, 89, 64, 92, 72, 100, 80, 108, 82, 110, 75, 103, 68, 96)(65, 93, 73, 101, 69, 97, 74, 102, 81, 109, 83, 111, 76, 104) 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, 79)(15, 69)(16, 62)(17, 68)(18, 64)(19, 67)(20, 82)(21, 83)(22, 84)(23, 74)(24, 70)(25, 72)(26, 78)(27, 80)(28, 81)(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 ), ( 56^14 ) } Outer automorphisms :: reflexible Dual of E12.428 Graph:: simple bipartite v = 32 e = 56 f = 2 degree seq :: [ 2^28, 14^4 ] E12.431 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 28, 28}) Quotient :: dipole Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1), (R * Y2 * Y3^-1)^2, Y3^3 * Y1^4, Y3^7, Y1^-3 * Y3^3 * Y1^-1 * Y3, (Y3 * Y2^-1)^7 ] Map:: R = (1, 29, 2, 30, 6, 34, 14, 42, 25, 53, 28, 56, 21, 49, 10, 38, 3, 31, 7, 35, 15, 43, 24, 52, 13, 41, 18, 46, 27, 55, 20, 48, 9, 37, 17, 45, 23, 51, 12, 40, 5, 33, 8, 36, 16, 44, 26, 54, 19, 47, 22, 50, 11, 39, 4, 32)(57, 85)(58, 86)(59, 87)(60, 88)(61, 89)(62, 90)(63, 91)(64, 92)(65, 93)(66, 94)(67, 95)(68, 96)(69, 97)(70, 98)(71, 99)(72, 100)(73, 101)(74, 102)(75, 103)(76, 104)(77, 105)(78, 106)(79, 107)(80, 108)(81, 109)(82, 110)(83, 111)(84, 112) 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, 79)(16, 62)(17, 78)(18, 64)(19, 81)(20, 82)(21, 83)(22, 84)(23, 67)(24, 68)(25, 69)(26, 70)(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) :: { ( 14, 56 ), ( 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56 ) } Outer automorphisms :: reflexible Dual of E12.426 Graph:: bipartite v = 29 e = 56 f = 5 degree seq :: [ 2^28, 56 ] E12.432 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 28, 28}) Quotient :: dipole Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3, Y1), Y3^-2 * Y1^-4, (R * Y2 * Y3^-1)^2, Y3^-7, (Y3 * Y2^-1)^7 ] Map:: R = (1, 29, 2, 30, 6, 34, 14, 42, 13, 41, 18, 46, 24, 52, 27, 55, 19, 47, 25, 53, 21, 49, 10, 38, 3, 31, 7, 35, 15, 43, 12, 40, 5, 33, 8, 36, 16, 44, 23, 51, 22, 50, 26, 54, 28, 56, 20, 48, 9, 37, 17, 45, 11, 39, 4, 32)(57, 85)(58, 86)(59, 87)(60, 88)(61, 89)(62, 90)(63, 91)(64, 92)(65, 93)(66, 94)(67, 95)(68, 96)(69, 97)(70, 98)(71, 99)(72, 100)(73, 101)(74, 102)(75, 103)(76, 104)(77, 105)(78, 106)(79, 107)(80, 108)(81, 109)(82, 110)(83, 111)(84, 112) 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, 68)(15, 67)(16, 62)(17, 81)(18, 64)(19, 78)(20, 83)(21, 84)(22, 69)(23, 70)(24, 72)(25, 82)(26, 74)(27, 79)(28, 80)(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) :: { ( 14, 56 ), ( 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56 ) } Outer automorphisms :: reflexible Dual of E12.423 Graph:: bipartite v = 29 e = 56 f = 5 degree seq :: [ 2^28, 56 ] E12.433 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 28, 28}) Quotient :: dipole Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ Y2, R^2, (Y1, Y3^-1), (R * Y1)^2, (R * Y3)^2, Y1^-4 * Y3^2, (R * Y2 * Y3^-1)^2, Y3^7, Y3^7, (Y3 * Y2^-1)^7, Y3^14, Y3^2 * Y1 * Y3^2 * Y1 * Y3^2 * Y1 * Y3^2 * Y1 * Y3^2 * Y1 * Y3^2 * Y1^-1 ] Map:: R = (1, 29, 2, 30, 6, 34, 14, 42, 9, 37, 17, 45, 24, 52, 28, 56, 22, 50, 26, 54, 20, 48, 12, 40, 5, 33, 8, 36, 16, 44, 10, 38, 3, 31, 7, 35, 15, 43, 23, 51, 19, 47, 25, 53, 27, 55, 21, 49, 13, 41, 18, 46, 11, 39, 4, 32)(57, 85)(58, 86)(59, 87)(60, 88)(61, 89)(62, 90)(63, 91)(64, 92)(65, 93)(66, 94)(67, 95)(68, 96)(69, 97)(70, 98)(71, 99)(72, 100)(73, 101)(74, 102)(75, 103)(76, 104)(77, 105)(78, 106)(79, 107)(80, 108)(81, 109)(82, 110)(83, 111)(84, 112) L = (1, 59)(2, 63)(3, 65)(4, 66)(5, 57)(6, 71)(7, 73)(8, 58)(9, 75)(10, 70)(11, 72)(12, 60)(13, 61)(14, 79)(15, 80)(16, 62)(17, 81)(18, 64)(19, 78)(20, 67)(21, 68)(22, 69)(23, 84)(24, 83)(25, 82)(26, 74)(27, 76)(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) :: { ( 14, 56 ), ( 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56 ) } Outer automorphisms :: reflexible Dual of E12.425 Graph:: bipartite v = 29 e = 56 f = 5 degree seq :: [ 2^28, 56 ] E12.434 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 28, 28}) Quotient :: dipole Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1^-1), Y3 * Y1^4, (R * Y2 * Y3^-1)^2, Y3^7, Y1 * Y3^-3 * Y1 * Y3^-2 * Y1^2 * Y3^-1, (Y3 * Y2^-1)^7 ] Map:: R = (1, 29, 2, 30, 6, 34, 12, 40, 5, 33, 8, 36, 14, 42, 20, 48, 13, 41, 16, 44, 22, 50, 27, 55, 21, 49, 24, 52, 28, 56, 25, 53, 17, 45, 23, 51, 26, 54, 18, 46, 9, 37, 15, 43, 19, 47, 10, 38, 3, 31, 7, 35, 11, 39, 4, 32)(57, 85)(58, 86)(59, 87)(60, 88)(61, 89)(62, 90)(63, 91)(64, 92)(65, 93)(66, 94)(67, 95)(68, 96)(69, 97)(70, 98)(71, 99)(72, 100)(73, 101)(74, 102)(75, 103)(76, 104)(77, 105)(78, 106)(79, 107)(80, 108)(81, 109)(82, 110)(83, 111)(84, 112) L = (1, 59)(2, 63)(3, 65)(4, 66)(5, 57)(6, 67)(7, 71)(8, 58)(9, 73)(10, 74)(11, 75)(12, 60)(13, 61)(14, 62)(15, 79)(16, 64)(17, 77)(18, 81)(19, 82)(20, 68)(21, 69)(22, 70)(23, 80)(24, 72)(25, 83)(26, 84)(27, 76)(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) :: { ( 14, 56 ), ( 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56 ) } Outer automorphisms :: reflexible Dual of E12.422 Graph:: bipartite v = 29 e = 56 f = 5 degree seq :: [ 2^28, 56 ] E12.435 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {7, 28, 28}) Quotient :: dipole Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1^-1), Y3^-1 * Y1^4, (R * Y2 * Y3^-1)^2, Y3^7, (Y3 * Y2^-1)^7, (Y1^-1 * Y3^-1)^28 ] Map:: R = (1, 29, 2, 30, 6, 34, 10, 38, 3, 31, 7, 35, 14, 42, 18, 46, 9, 37, 15, 43, 22, 50, 25, 53, 17, 45, 23, 51, 28, 56, 27, 55, 21, 49, 24, 52, 26, 54, 20, 48, 13, 41, 16, 44, 19, 47, 12, 40, 5, 33, 8, 36, 11, 39, 4, 32)(57, 85)(58, 86)(59, 87)(60, 88)(61, 89)(62, 90)(63, 91)(64, 92)(65, 93)(66, 94)(67, 95)(68, 96)(69, 97)(70, 98)(71, 99)(72, 100)(73, 101)(74, 102)(75, 103)(76, 104)(77, 105)(78, 106)(79, 107)(80, 108)(81, 109)(82, 110)(83, 111)(84, 112) L = (1, 59)(2, 63)(3, 65)(4, 66)(5, 57)(6, 70)(7, 71)(8, 58)(9, 73)(10, 74)(11, 62)(12, 60)(13, 61)(14, 78)(15, 79)(16, 64)(17, 77)(18, 81)(19, 67)(20, 68)(21, 69)(22, 84)(23, 80)(24, 72)(25, 83)(26, 75)(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) :: { ( 14, 56 ), ( 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56 ) } Outer automorphisms :: reflexible Dual of E12.424 Graph:: bipartite v = 29 e = 56 f = 5 degree seq :: [ 2^28, 56 ] E12.436 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 5, 15}) Quotient :: dipole Aut^+ = C5 x S3 (small group id <30, 1>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^3, (R * Y3)^2, (Y2, Y3^-1), (R * Y1)^2, (Y3^-1 * Y1)^2, (R * Y2)^2, Y2 * Y1 * Y2^-1 * Y1, Y2^5 ] Map:: non-degenerate R = (1, 31, 2, 32)(3, 33, 7, 37)(4, 34, 10, 40)(5, 35, 9, 39)(6, 36, 8, 38)(11, 41, 17, 47)(12, 42, 19, 49)(13, 43, 18, 48)(14, 44, 22, 52)(15, 45, 21, 51)(16, 46, 20, 50)(23, 53, 28, 58)(24, 54, 27, 57)(25, 55, 30, 60)(26, 56, 29, 59)(61, 91, 63, 93, 71, 101, 75, 105, 65, 95)(62, 92, 67, 97, 77, 107, 81, 111, 69, 99)(64, 94, 72, 102, 83, 113, 85, 115, 74, 104)(66, 96, 73, 103, 84, 114, 86, 116, 76, 106)(68, 98, 78, 108, 87, 117, 89, 119, 80, 110)(70, 100, 79, 109, 88, 118, 90, 120, 82, 112) L = (1, 64)(2, 68)(3, 72)(4, 66)(5, 74)(6, 61)(7, 78)(8, 70)(9, 80)(10, 62)(11, 83)(12, 73)(13, 63)(14, 76)(15, 85)(16, 65)(17, 87)(18, 79)(19, 67)(20, 82)(21, 89)(22, 69)(23, 84)(24, 71)(25, 86)(26, 75)(27, 88)(28, 77)(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) :: { ( 4, 30, 4, 30 ), ( 4, 30, 4, 30, 4, 30, 4, 30, 4, 30 ) } Outer automorphisms :: reflexible Dual of E12.437 Graph:: simple bipartite v = 21 e = 60 f = 17 degree seq :: [ 4^15, 10^6 ] E12.437 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 5, 15}) Quotient :: dipole Aut^+ = C5 x S3 (small group id <30, 1>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ Y2^2, R^2, Y3^3, (Y1^-1, Y3), (R * Y1)^2, (R * Y3)^2, (Y3 * Y2)^2, Y1 * Y3^-1 * Y2 * Y1^-1 * Y2, Y1^5 * Y3^-1, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2 * Y1 * Y3 * Y2 * Y1^-1, (Y1^-1 * Y3^-1)^5 ] Map:: non-degenerate R = (1, 31, 2, 32, 7, 37, 19, 49, 15, 45, 4, 34, 9, 39, 21, 51, 30, 60, 18, 48, 6, 36, 10, 40, 22, 52, 17, 47, 5, 35)(3, 33, 11, 41, 25, 55, 28, 58, 16, 46, 12, 42, 24, 54, 20, 50, 29, 59, 27, 57, 14, 44, 8, 38, 23, 53, 26, 56, 13, 43)(61, 91, 63, 93)(62, 92, 68, 98)(64, 94, 74, 104)(65, 95, 76, 106)(66, 96, 72, 102)(67, 97, 80, 110)(69, 99, 84, 114)(70, 100, 71, 101)(73, 103, 75, 105)(77, 107, 89, 119)(78, 108, 87, 117)(79, 109, 88, 118)(81, 111, 85, 115)(82, 112, 83, 113)(86, 116, 90, 120) L = (1, 64)(2, 69)(3, 72)(4, 66)(5, 75)(6, 61)(7, 81)(8, 71)(9, 70)(10, 62)(11, 84)(12, 74)(13, 76)(14, 63)(15, 78)(16, 87)(17, 79)(18, 65)(19, 90)(20, 83)(21, 82)(22, 67)(23, 85)(24, 68)(25, 80)(26, 88)(27, 73)(28, 89)(29, 86)(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) :: { ( 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, 4, 10, 4, 10, 4, 10, 4, 10 ) } Outer automorphisms :: reflexible Dual of E12.436 Graph:: bipartite v = 17 e = 60 f = 21 degree seq :: [ 4^15, 30^2 ] E12.438 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 5, 15}) Quotient :: halfedge^2 Aut^+ = D30 (small group id <30, 3>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (Y1^-1 * Y3)^2, (R * Y1)^2, (Y2 * Y1)^2, (Y3 * Y2)^3, Y3 * Y1 * Y2 * Y1^-4, Y1^2 * Y3 * Y1^-2 * Y2 * Y3 * Y1^-1 * Y2 ] Map:: non-degenerate R = (1, 32, 2, 36, 6, 44, 14, 53, 23, 42, 12, 48, 18, 56, 26, 59, 29, 50, 20, 40, 10, 47, 17, 54, 24, 43, 13, 35, 5, 31)(3, 39, 9, 49, 19, 58, 28, 57, 27, 51, 21, 60, 30, 55, 25, 46, 16, 38, 8, 34, 4, 41, 11, 52, 22, 45, 15, 37, 7, 33) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 15)(8, 18)(10, 21)(11, 23)(13, 19)(14, 22)(16, 26)(17, 27)(20, 30)(24, 28)(25, 29)(31, 34)(32, 38)(33, 40)(35, 41)(36, 46)(37, 47)(39, 50)(42, 51)(43, 52)(44, 55)(45, 54)(48, 57)(49, 59)(53, 60)(56, 58) local type(s) :: { ( 10^30 ) } Outer automorphisms :: reflexible Dual of E12.440 Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 30 f = 6 degree seq :: [ 30^2 ] E12.439 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 5, 15}) Quotient :: halfedge^2 Aut^+ = D30 (small group id <30, 3>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (Y3 * Y1^-1)^2, R * Y3 * R * Y2, (R * Y1)^2, (Y2 * Y1^-1)^2, Y1 * Y3 * Y1^-2 * Y2 * Y1, Y2 * Y1^-2 * Y3 * Y2 * Y3 * Y2 * Y1^-1 * Y3, Y1^2 * Y2 * Y1^-1 * Y3 * Y2 * Y3 * Y2 * Y3 ] Map:: non-degenerate R = (1, 32, 2, 36, 6, 44, 14, 40, 10, 47, 17, 54, 24, 60, 30, 57, 27, 58, 28, 51, 21, 42, 12, 48, 18, 43, 13, 35, 5, 31)(3, 39, 9, 46, 16, 38, 8, 34, 4, 41, 11, 50, 20, 56, 26, 52, 22, 59, 29, 55, 25, 49, 19, 53, 23, 45, 15, 37, 7, 33) 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, 29)(26, 27)(31, 34)(32, 38)(33, 40)(35, 41)(36, 46)(37, 47)(39, 44)(42, 52)(43, 50)(45, 54)(48, 56)(49, 57)(51, 59)(53, 60)(55, 58) local type(s) :: { ( 10^30 ) } Outer automorphisms :: reflexible Dual of E12.441 Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 30 f = 6 degree seq :: [ 30^2 ] E12.440 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 5, 15}) Quotient :: halfedge^2 Aut^+ = D30 (small group id <30, 3>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (Y2 * Y1)^2, (R * Y1)^2, (Y3 * Y1^-1)^2, Y1^5, (Y3 * Y2)^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 ] Map:: non-degenerate R = (1, 32, 2, 36, 6, 43, 13, 35, 5, 31)(3, 39, 9, 48, 18, 44, 14, 37, 7, 33)(4, 41, 11, 51, 21, 45, 15, 38, 8, 34)(10, 46, 16, 53, 23, 56, 26, 49, 19, 40)(12, 47, 17, 54, 24, 58, 28, 52, 22, 42)(20, 57, 27, 60, 30, 59, 29, 55, 25, 50) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 14)(8, 17)(10, 20)(11, 22)(13, 18)(15, 24)(16, 25)(19, 27)(21, 28)(23, 29)(26, 30)(31, 34)(32, 38)(33, 40)(35, 41)(36, 45)(37, 46)(39, 49)(42, 50)(43, 51)(44, 53)(47, 55)(48, 56)(52, 57)(54, 59)(58, 60) local type(s) :: { ( 30^10 ) } Outer automorphisms :: reflexible Dual of E12.438 Transitivity :: VT+ AT Graph:: bipartite v = 6 e = 30 f = 2 degree seq :: [ 10^6 ] E12.441 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 5, 15}) Quotient :: halfedge^2 Aut^+ = D30 (small group id <30, 3>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (Y2 * Y1)^2, (R * Y1)^2, (Y3 * Y1)^2, Y1^5, Y1^-1 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y1^-1, 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 * Y3 * Y2 ] Map:: non-degenerate R = (1, 32, 2, 36, 6, 43, 13, 35, 5, 31)(3, 39, 9, 48, 18, 44, 14, 37, 7, 33)(4, 41, 11, 51, 21, 45, 15, 38, 8, 34)(10, 46, 16, 54, 24, 58, 28, 49, 19, 40)(12, 47, 17, 55, 25, 59, 29, 52, 22, 42)(20, 57, 27, 53, 23, 60, 30, 56, 26, 50) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 14)(8, 17)(10, 20)(11, 22)(13, 18)(15, 25)(16, 26)(19, 27)(21, 29)(23, 28)(24, 30)(31, 34)(32, 38)(33, 40)(35, 41)(36, 45)(37, 46)(39, 49)(42, 53)(43, 51)(44, 54)(47, 57)(48, 58)(50, 55)(52, 60)(56, 59) local type(s) :: { ( 30^10 ) } Outer automorphisms :: reflexible Dual of E12.439 Transitivity :: VT+ AT Graph:: bipartite v = 6 e = 30 f = 2 degree seq :: [ 10^6 ] E12.442 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 5, 15}) Quotient :: edge^2 Aut^+ = D30 (small group id <30, 3>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3^-1 * Y1)^2, (Y3 * Y2)^2, Y3^5, (Y2 * Y1)^3, (Y3 * Y1 * Y2)^15 ] Map:: R = (1, 31, 4, 34, 12, 42, 13, 43, 5, 35)(2, 32, 7, 37, 17, 47, 18, 48, 8, 38)(3, 33, 10, 40, 21, 51, 22, 52, 11, 41)(6, 36, 15, 45, 25, 55, 26, 56, 16, 46)(9, 39, 19, 49, 27, 57, 28, 58, 20, 50)(14, 44, 23, 53, 29, 59, 30, 60, 24, 54)(61, 62)(63, 69)(64, 68)(65, 67)(66, 74)(70, 80)(71, 79)(72, 78)(73, 77)(75, 84)(76, 83)(81, 88)(82, 87)(85, 90)(86, 89)(91, 93)(92, 96)(94, 101)(95, 100)(97, 106)(98, 105)(99, 104)(102, 112)(103, 111)(107, 116)(108, 115)(109, 114)(110, 113)(117, 120)(118, 119) 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, 60 ), ( 60^10 ) } Outer automorphisms :: reflexible Dual of E12.448 Graph:: simple bipartite v = 36 e = 60 f = 2 degree seq :: [ 2^30, 10^6 ] E12.443 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 5, 15}) Quotient :: edge^2 Aut^+ = D30 (small group id <30, 3>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y1)^2, (Y3 * Y2)^2, Y3^5, Y2 * Y3 * Y1 * Y2 * Y3 * Y1 * Y2 * Y1, Y1 * Y3 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 ] Map:: R = (1, 31, 4, 34, 12, 42, 13, 43, 5, 35)(2, 32, 7, 37, 17, 47, 18, 48, 8, 38)(3, 33, 10, 40, 22, 52, 23, 53, 11, 41)(6, 36, 15, 45, 27, 57, 28, 58, 16, 46)(9, 39, 20, 50, 30, 60, 24, 54, 21, 51)(14, 44, 25, 55, 29, 59, 19, 49, 26, 56)(61, 62)(63, 69)(64, 68)(65, 67)(66, 74)(70, 81)(71, 80)(72, 78)(73, 77)(75, 86)(76, 85)(79, 87)(82, 84)(83, 90)(88, 89)(91, 93)(92, 96)(94, 101)(95, 100)(97, 106)(98, 105)(99, 109)(102, 113)(103, 112)(104, 114)(107, 118)(108, 117)(110, 119)(111, 116)(115, 120) 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, 60 ), ( 60^10 ) } Outer automorphisms :: reflexible Dual of E12.449 Graph:: simple bipartite v = 36 e = 60 f = 2 degree seq :: [ 2^30, 10^6 ] E12.444 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 5, 15}) Quotient :: edge^2 Aut^+ = D30 (small group id <30, 3>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y1 * Y3^-1)^2, (Y3 * Y2)^2, (Y2 * Y1)^3, Y2 * Y3^-1 * Y1 * Y3^4, (Y3 * Y1 * Y2)^5 ] Map:: R = (1, 31, 4, 34, 12, 42, 23, 53, 16, 46, 6, 36, 15, 45, 27, 57, 29, 59, 20, 50, 9, 39, 19, 49, 24, 54, 13, 43, 5, 35)(2, 32, 7, 37, 17, 47, 22, 52, 11, 41, 3, 33, 10, 40, 21, 51, 30, 60, 26, 56, 14, 44, 25, 55, 28, 58, 18, 48, 8, 38)(61, 62)(63, 69)(64, 68)(65, 67)(66, 74)(70, 80)(71, 79)(72, 78)(73, 77)(75, 86)(76, 85)(81, 89)(82, 84)(83, 88)(87, 90)(91, 93)(92, 96)(94, 101)(95, 100)(97, 106)(98, 105)(99, 104)(102, 112)(103, 111)(107, 113)(108, 117)(109, 116)(110, 115)(114, 120)(118, 119) 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, 20 ), ( 20^30 ) } Outer automorphisms :: reflexible Dual of E12.446 Graph:: simple bipartite v = 32 e = 60 f = 6 degree seq :: [ 2^30, 30^2 ] E12.445 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 5, 15}) Quotient :: edge^2 Aut^+ = D30 (small group id <30, 3>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y3 * Y1)^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y2)^2, Y3^2 * Y1 * Y3^-2 * Y2, Y3^-1 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y1 * Y2 ] Map:: R = (1, 31, 4, 34, 12, 42, 21, 51, 9, 39, 20, 50, 30, 60, 23, 53, 27, 57, 26, 56, 16, 46, 6, 36, 15, 45, 13, 43, 5, 35)(2, 32, 7, 37, 17, 47, 25, 55, 14, 44, 24, 54, 29, 59, 19, 49, 28, 58, 22, 52, 11, 41, 3, 33, 10, 40, 18, 48, 8, 38)(61, 62)(63, 69)(64, 68)(65, 67)(66, 74)(70, 81)(71, 80)(72, 78)(73, 77)(75, 85)(76, 84)(79, 87)(82, 90)(83, 88)(86, 89)(91, 93)(92, 96)(94, 101)(95, 100)(97, 106)(98, 105)(99, 109)(102, 112)(103, 108)(104, 113)(107, 116)(110, 119)(111, 118)(114, 120)(115, 117) 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, 20 ), ( 20^30 ) } Outer automorphisms :: reflexible Dual of E12.447 Graph:: simple bipartite v = 32 e = 60 f = 6 degree seq :: [ 2^30, 30^2 ] E12.446 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 5, 15}) Quotient :: loop^2 Aut^+ = D30 (small group id <30, 3>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3^-1 * Y1)^2, (Y3 * Y2)^2, Y3^5, (Y2 * Y1)^3, (Y3 * Y1 * Y2)^15 ] Map:: R = (1, 31, 61, 91, 4, 34, 64, 94, 12, 42, 72, 102, 13, 43, 73, 103, 5, 35, 65, 95)(2, 32, 62, 92, 7, 37, 67, 97, 17, 47, 77, 107, 18, 48, 78, 108, 8, 38, 68, 98)(3, 33, 63, 93, 10, 40, 70, 100, 21, 51, 81, 111, 22, 52, 82, 112, 11, 41, 71, 101)(6, 36, 66, 96, 15, 45, 75, 105, 25, 55, 85, 115, 26, 56, 86, 116, 16, 46, 76, 106)(9, 39, 69, 99, 19, 49, 79, 109, 27, 57, 87, 117, 28, 58, 88, 118, 20, 50, 80, 110)(14, 44, 74, 104, 23, 53, 83, 113, 29, 59, 89, 119, 30, 60, 90, 120, 24, 54, 84, 114) L = (1, 32)(2, 31)(3, 39)(4, 38)(5, 37)(6, 44)(7, 35)(8, 34)(9, 33)(10, 50)(11, 49)(12, 48)(13, 47)(14, 36)(15, 54)(16, 53)(17, 43)(18, 42)(19, 41)(20, 40)(21, 58)(22, 57)(23, 46)(24, 45)(25, 60)(26, 59)(27, 52)(28, 51)(29, 56)(30, 55)(61, 93)(62, 96)(63, 91)(64, 101)(65, 100)(66, 92)(67, 106)(68, 105)(69, 104)(70, 95)(71, 94)(72, 112)(73, 111)(74, 99)(75, 98)(76, 97)(77, 116)(78, 115)(79, 114)(80, 113)(81, 103)(82, 102)(83, 110)(84, 109)(85, 108)(86, 107)(87, 120)(88, 119)(89, 118)(90, 117) local type(s) :: { ( 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 E12.444 Transitivity :: VT+ Graph:: bipartite v = 6 e = 60 f = 32 degree seq :: [ 20^6 ] E12.447 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 5, 15}) Quotient :: loop^2 Aut^+ = D30 (small group id <30, 3>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y1)^2, (Y3 * Y2)^2, Y3^5, Y2 * Y3 * Y1 * Y2 * Y3 * Y1 * Y2 * Y1, Y1 * Y3 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 ] Map:: R = (1, 31, 61, 91, 4, 34, 64, 94, 12, 42, 72, 102, 13, 43, 73, 103, 5, 35, 65, 95)(2, 32, 62, 92, 7, 37, 67, 97, 17, 47, 77, 107, 18, 48, 78, 108, 8, 38, 68, 98)(3, 33, 63, 93, 10, 40, 70, 100, 22, 52, 82, 112, 23, 53, 83, 113, 11, 41, 71, 101)(6, 36, 66, 96, 15, 45, 75, 105, 27, 57, 87, 117, 28, 58, 88, 118, 16, 46, 76, 106)(9, 39, 69, 99, 20, 50, 80, 110, 30, 60, 90, 120, 24, 54, 84, 114, 21, 51, 81, 111)(14, 44, 74, 104, 25, 55, 85, 115, 29, 59, 89, 119, 19, 49, 79, 109, 26, 56, 86, 116) L = (1, 32)(2, 31)(3, 39)(4, 38)(5, 37)(6, 44)(7, 35)(8, 34)(9, 33)(10, 51)(11, 50)(12, 48)(13, 47)(14, 36)(15, 56)(16, 55)(17, 43)(18, 42)(19, 57)(20, 41)(21, 40)(22, 54)(23, 60)(24, 52)(25, 46)(26, 45)(27, 49)(28, 59)(29, 58)(30, 53)(61, 93)(62, 96)(63, 91)(64, 101)(65, 100)(66, 92)(67, 106)(68, 105)(69, 109)(70, 95)(71, 94)(72, 113)(73, 112)(74, 114)(75, 98)(76, 97)(77, 118)(78, 117)(79, 99)(80, 119)(81, 116)(82, 103)(83, 102)(84, 104)(85, 120)(86, 111)(87, 108)(88, 107)(89, 110)(90, 115) local type(s) :: { ( 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 E12.445 Transitivity :: VT+ Graph:: bipartite v = 6 e = 60 f = 32 degree seq :: [ 20^6 ] E12.448 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 5, 15}) Quotient :: loop^2 Aut^+ = D30 (small group id <30, 3>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y1 * Y3^-1)^2, (Y3 * Y2)^2, (Y2 * Y1)^3, Y2 * Y3^-1 * Y1 * Y3^4, (Y3 * Y1 * Y2)^5 ] Map:: R = (1, 31, 61, 91, 4, 34, 64, 94, 12, 42, 72, 102, 23, 53, 83, 113, 16, 46, 76, 106, 6, 36, 66, 96, 15, 45, 75, 105, 27, 57, 87, 117, 29, 59, 89, 119, 20, 50, 80, 110, 9, 39, 69, 99, 19, 49, 79, 109, 24, 54, 84, 114, 13, 43, 73, 103, 5, 35, 65, 95)(2, 32, 62, 92, 7, 37, 67, 97, 17, 47, 77, 107, 22, 52, 82, 112, 11, 41, 71, 101, 3, 33, 63, 93, 10, 40, 70, 100, 21, 51, 81, 111, 30, 60, 90, 120, 26, 56, 86, 116, 14, 44, 74, 104, 25, 55, 85, 115, 28, 58, 88, 118, 18, 48, 78, 108, 8, 38, 68, 98) L = (1, 32)(2, 31)(3, 39)(4, 38)(5, 37)(6, 44)(7, 35)(8, 34)(9, 33)(10, 50)(11, 49)(12, 48)(13, 47)(14, 36)(15, 56)(16, 55)(17, 43)(18, 42)(19, 41)(20, 40)(21, 59)(22, 54)(23, 58)(24, 52)(25, 46)(26, 45)(27, 60)(28, 53)(29, 51)(30, 57)(61, 93)(62, 96)(63, 91)(64, 101)(65, 100)(66, 92)(67, 106)(68, 105)(69, 104)(70, 95)(71, 94)(72, 112)(73, 111)(74, 99)(75, 98)(76, 97)(77, 113)(78, 117)(79, 116)(80, 115)(81, 103)(82, 102)(83, 107)(84, 120)(85, 110)(86, 109)(87, 108)(88, 119)(89, 118)(90, 114) 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, 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, 2, 10, 2, 10 ) } Outer automorphisms :: reflexible Dual of E12.442 Transitivity :: VT+ Graph:: bipartite v = 2 e = 60 f = 36 degree seq :: [ 60^2 ] E12.449 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 5, 15}) Quotient :: loop^2 Aut^+ = D30 (small group id <30, 3>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y3 * Y1)^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y2)^2, Y3^2 * Y1 * Y3^-2 * Y2, Y3^-1 * Y1 * Y2 * Y3^-2 * Y1 * Y2 * Y1 * Y2 ] Map:: R = (1, 31, 61, 91, 4, 34, 64, 94, 12, 42, 72, 102, 21, 51, 81, 111, 9, 39, 69, 99, 20, 50, 80, 110, 30, 60, 90, 120, 23, 53, 83, 113, 27, 57, 87, 117, 26, 56, 86, 116, 16, 46, 76, 106, 6, 36, 66, 96, 15, 45, 75, 105, 13, 43, 73, 103, 5, 35, 65, 95)(2, 32, 62, 92, 7, 37, 67, 97, 17, 47, 77, 107, 25, 55, 85, 115, 14, 44, 74, 104, 24, 54, 84, 114, 29, 59, 89, 119, 19, 49, 79, 109, 28, 58, 88, 118, 22, 52, 82, 112, 11, 41, 71, 101, 3, 33, 63, 93, 10, 40, 70, 100, 18, 48, 78, 108, 8, 38, 68, 98) L = (1, 32)(2, 31)(3, 39)(4, 38)(5, 37)(6, 44)(7, 35)(8, 34)(9, 33)(10, 51)(11, 50)(12, 48)(13, 47)(14, 36)(15, 55)(16, 54)(17, 43)(18, 42)(19, 57)(20, 41)(21, 40)(22, 60)(23, 58)(24, 46)(25, 45)(26, 59)(27, 49)(28, 53)(29, 56)(30, 52)(61, 93)(62, 96)(63, 91)(64, 101)(65, 100)(66, 92)(67, 106)(68, 105)(69, 109)(70, 95)(71, 94)(72, 112)(73, 108)(74, 113)(75, 98)(76, 97)(77, 116)(78, 103)(79, 99)(80, 119)(81, 118)(82, 102)(83, 104)(84, 120)(85, 117)(86, 107)(87, 115)(88, 111)(89, 110)(90, 114) 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, 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, 2, 10, 2, 10 ) } Outer automorphisms :: reflexible Dual of E12.443 Transitivity :: VT+ Graph:: bipartite v = 2 e = 60 f = 36 degree seq :: [ 60^2 ] E12.450 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 5, 15}) Quotient :: dipole Aut^+ = D30 (small group id <30, 3>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^3, (R * Y3)^2, (Y2, Y3^-1), (R * Y1)^2, (Y3^-1 * Y1)^2, (Y2^-1 * Y1)^2, (R * Y2)^2, Y2^5 ] Map:: non-degenerate R = (1, 31, 2, 32)(3, 33, 9, 39)(4, 34, 10, 40)(5, 35, 7, 37)(6, 36, 8, 38)(11, 41, 21, 51)(12, 42, 22, 52)(13, 43, 20, 50)(14, 44, 19, 49)(15, 45, 17, 47)(16, 46, 18, 48)(23, 53, 30, 60)(24, 54, 29, 59)(25, 55, 28, 58)(26, 56, 27, 57)(61, 91, 63, 93, 71, 101, 75, 105, 65, 95)(62, 92, 67, 97, 77, 107, 81, 111, 69, 99)(64, 94, 72, 102, 83, 113, 85, 115, 74, 104)(66, 96, 73, 103, 84, 114, 86, 116, 76, 106)(68, 98, 78, 108, 87, 117, 89, 119, 80, 110)(70, 100, 79, 109, 88, 118, 90, 120, 82, 112) L = (1, 64)(2, 68)(3, 72)(4, 66)(5, 74)(6, 61)(7, 78)(8, 70)(9, 80)(10, 62)(11, 83)(12, 73)(13, 63)(14, 76)(15, 85)(16, 65)(17, 87)(18, 79)(19, 67)(20, 82)(21, 89)(22, 69)(23, 84)(24, 71)(25, 86)(26, 75)(27, 88)(28, 77)(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) :: { ( 4, 30, 4, 30 ), ( 4, 30, 4, 30, 4, 30, 4, 30, 4, 30 ) } Outer automorphisms :: reflexible Dual of E12.454 Graph:: simple bipartite v = 21 e = 60 f = 17 degree seq :: [ 4^15, 10^6 ] E12.451 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 5, 15}) Quotient :: dipole Aut^+ = D30 (small group id <30, 3>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y2), (Y3^-1 * Y1)^2, (Y2^-1 * Y1)^2, Y3^-3 * Y2^2, Y2^5 ] Map:: non-degenerate R = (1, 31, 2, 32)(3, 33, 9, 39)(4, 34, 10, 40)(5, 35, 7, 37)(6, 36, 8, 38)(11, 41, 24, 54)(12, 42, 25, 55)(13, 43, 23, 53)(14, 44, 26, 56)(15, 45, 21, 51)(16, 46, 19, 49)(17, 47, 20, 50)(18, 48, 22, 52)(27, 57, 30, 60)(28, 58, 29, 59)(61, 91, 63, 93, 71, 101, 76, 106, 65, 95)(62, 92, 67, 97, 79, 109, 84, 114, 69, 99)(64, 94, 72, 102, 87, 117, 78, 108, 75, 105)(66, 96, 73, 103, 74, 104, 88, 118, 77, 107)(68, 98, 80, 110, 89, 119, 86, 116, 83, 113)(70, 100, 81, 111, 82, 112, 90, 120, 85, 115) L = (1, 64)(2, 68)(3, 72)(4, 74)(5, 75)(6, 61)(7, 80)(8, 82)(9, 83)(10, 62)(11, 87)(12, 88)(13, 63)(14, 71)(15, 73)(16, 78)(17, 65)(18, 66)(19, 89)(20, 90)(21, 67)(22, 79)(23, 81)(24, 86)(25, 69)(26, 70)(27, 77)(28, 76)(29, 85)(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) :: { ( 4, 30, 4, 30 ), ( 4, 30, 4, 30, 4, 30, 4, 30, 4, 30 ) } Outer automorphisms :: reflexible Dual of E12.457 Graph:: simple bipartite v = 21 e = 60 f = 17 degree seq :: [ 4^15, 10^6 ] E12.452 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 5, 15}) Quotient :: dipole Aut^+ = D30 (small group id <30, 3>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^3 * Y2^-1, (Y3^-1, Y2^-1), (R * Y3)^2, (R * Y1)^2, (Y2 * Y1)^2, (Y3^-1 * Y1)^2, (R * Y2)^2, Y2^5 ] Map:: non-degenerate R = (1, 31, 2, 32)(3, 33, 9, 39)(4, 34, 10, 40)(5, 35, 7, 37)(6, 36, 8, 38)(11, 41, 21, 51)(12, 42, 22, 52)(13, 43, 20, 50)(14, 44, 19, 49)(15, 45, 17, 47)(16, 46, 18, 48)(23, 53, 30, 60)(24, 54, 29, 59)(25, 55, 28, 58)(26, 56, 27, 57)(61, 91, 63, 93, 71, 101, 75, 105, 65, 95)(62, 92, 67, 97, 77, 107, 81, 111, 69, 99)(64, 94, 72, 102, 83, 113, 85, 115, 74, 104)(66, 96, 73, 103, 84, 114, 86, 116, 76, 106)(68, 98, 78, 108, 87, 117, 89, 119, 80, 110)(70, 100, 79, 109, 88, 118, 90, 120, 82, 112) L = (1, 64)(2, 68)(3, 72)(4, 73)(5, 74)(6, 61)(7, 78)(8, 79)(9, 80)(10, 62)(11, 83)(12, 84)(13, 63)(14, 66)(15, 85)(16, 65)(17, 87)(18, 88)(19, 67)(20, 70)(21, 89)(22, 69)(23, 86)(24, 71)(25, 76)(26, 75)(27, 90)(28, 77)(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) :: { ( 4, 30, 4, 30 ), ( 4, 30, 4, 30, 4, 30, 4, 30, 4, 30 ) } Outer automorphisms :: reflexible Dual of E12.455 Graph:: simple bipartite v = 21 e = 60 f = 17 degree seq :: [ 4^15, 10^6 ] E12.453 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 5, 15}) Quotient :: dipole Aut^+ = D30 (small group id <30, 3>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^-1 * Y3^-3, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y2, Y3^-1), (Y3^-1 * Y1)^2, (Y2 * Y1)^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 ] Map:: non-degenerate R = (1, 31, 2, 32)(3, 33, 9, 39)(4, 34, 10, 40)(5, 35, 7, 37)(6, 36, 8, 38)(11, 41, 22, 52)(12, 42, 20, 50)(13, 43, 21, 51)(14, 44, 18, 48)(15, 45, 19, 49)(16, 46, 17, 47)(23, 53, 29, 59)(24, 54, 30, 60)(25, 55, 27, 57)(26, 56, 28, 58)(61, 91, 63, 93, 71, 101, 76, 106, 65, 95)(62, 92, 67, 97, 77, 107, 82, 112, 69, 99)(64, 94, 72, 102, 83, 113, 86, 116, 75, 105)(66, 96, 73, 103, 84, 114, 85, 115, 74, 104)(68, 98, 78, 108, 87, 117, 90, 120, 81, 111)(70, 100, 79, 109, 88, 118, 89, 119, 80, 110) L = (1, 64)(2, 68)(3, 72)(4, 74)(5, 75)(6, 61)(7, 78)(8, 80)(9, 81)(10, 62)(11, 83)(12, 66)(13, 63)(14, 65)(15, 85)(16, 86)(17, 87)(18, 70)(19, 67)(20, 69)(21, 89)(22, 90)(23, 73)(24, 71)(25, 76)(26, 84)(27, 79)(28, 77)(29, 82)(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) :: { ( 4, 30, 4, 30 ), ( 4, 30, 4, 30, 4, 30, 4, 30, 4, 30 ) } Outer automorphisms :: reflexible Dual of E12.456 Graph:: simple bipartite v = 21 e = 60 f = 17 degree seq :: [ 4^15, 10^6 ] E12.454 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 5, 15}) Quotient :: dipole Aut^+ = D30 (small group id <30, 3>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ Y2^2, R^2, Y3^3, (Y2 * Y1^-1)^2, (R * Y1)^2, (Y3^-1, Y1), (Y3 * Y2)^2, (R * Y3)^2, Y3 * Y1^-5, (R * Y2 * Y3^-1)^2, Y1^-3 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 31, 2, 32, 7, 37, 17, 47, 14, 44, 4, 34, 9, 39, 19, 49, 26, 56, 16, 46, 6, 36, 10, 40, 20, 50, 15, 45, 5, 35)(3, 33, 11, 41, 23, 53, 28, 58, 21, 51, 12, 42, 24, 54, 30, 60, 29, 59, 22, 52, 13, 43, 25, 55, 27, 57, 18, 48, 8, 38)(61, 91, 63, 93)(62, 92, 68, 98)(64, 94, 73, 103)(65, 95, 71, 101)(66, 96, 72, 102)(67, 97, 78, 108)(69, 99, 82, 112)(70, 100, 81, 111)(74, 104, 85, 115)(75, 105, 83, 113)(76, 106, 84, 114)(77, 107, 87, 117)(79, 109, 89, 119)(80, 110, 88, 118)(86, 116, 90, 120) L = (1, 64)(2, 69)(3, 72)(4, 66)(5, 74)(6, 61)(7, 79)(8, 81)(9, 70)(10, 62)(11, 84)(12, 73)(13, 63)(14, 76)(15, 77)(16, 65)(17, 86)(18, 88)(19, 80)(20, 67)(21, 82)(22, 68)(23, 90)(24, 85)(25, 71)(26, 75)(27, 83)(28, 89)(29, 78)(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) :: { ( 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, 4, 10, 4, 10, 4, 10, 4, 10 ) } Outer automorphisms :: reflexible Dual of E12.450 Graph:: bipartite v = 17 e = 60 f = 21 degree seq :: [ 4^15, 30^2 ] E12.455 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 5, 15}) Quotient :: dipole Aut^+ = D30 (small group id <30, 3>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ Y2^2, R^2, Y1 * Y3^-2, (Y3 * Y2)^2, (Y2 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^5, Y1^15 ] Map:: non-degenerate R = (1, 31, 2, 32, 7, 37, 15, 45, 23, 53, 22, 52, 14, 44, 6, 36, 4, 34, 9, 39, 17, 47, 25, 55, 21, 51, 13, 43, 5, 35)(3, 33, 10, 40, 19, 49, 27, 57, 30, 60, 26, 56, 18, 48, 12, 42, 11, 41, 20, 50, 28, 58, 29, 59, 24, 54, 16, 46, 8, 38)(61, 91, 63, 93)(62, 92, 68, 98)(64, 94, 72, 102)(65, 95, 70, 100)(66, 96, 71, 101)(67, 97, 76, 106)(69, 99, 78, 108)(73, 103, 79, 109)(74, 104, 80, 110)(75, 105, 84, 114)(77, 107, 86, 116)(81, 111, 87, 117)(82, 112, 88, 118)(83, 113, 89, 119)(85, 115, 90, 120) L = (1, 64)(2, 69)(3, 71)(4, 62)(5, 66)(6, 61)(7, 77)(8, 72)(9, 67)(10, 80)(11, 70)(12, 63)(13, 74)(14, 65)(15, 85)(16, 78)(17, 75)(18, 68)(19, 88)(20, 79)(21, 82)(22, 73)(23, 81)(24, 86)(25, 83)(26, 76)(27, 89)(28, 87)(29, 90)(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) :: { ( 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, 4, 10, 4, 10, 4, 10, 4, 10 ) } Outer automorphisms :: reflexible Dual of E12.452 Graph:: bipartite v = 17 e = 60 f = 21 degree seq :: [ 4^15, 30^2 ] E12.456 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 5, 15}) Quotient :: dipole Aut^+ = D30 (small group id <30, 3>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ Y2^2, R^2, (R * Y1)^2, (Y3 * Y2)^2, (Y3^-1, Y1^-1), (R * Y3)^2, (Y2 * Y1)^2, Y3 * Y1 * Y3^3, Y3 * Y1^4, (R * Y2 * Y3^-1)^2, Y3 * Y1^-1 * Y3^2 * Y1^-2 ] Map:: non-degenerate R = (1, 31, 2, 32, 7, 37, 17, 47, 6, 36, 10, 40, 20, 50, 14, 44, 18, 48, 23, 53, 15, 45, 4, 34, 9, 39, 16, 46, 5, 35)(3, 33, 11, 41, 24, 54, 22, 52, 13, 43, 26, 56, 30, 60, 27, 57, 28, 58, 29, 59, 21, 51, 12, 42, 25, 55, 19, 49, 8, 38)(61, 91, 63, 93)(62, 92, 68, 98)(64, 94, 73, 103)(65, 95, 71, 101)(66, 96, 72, 102)(67, 97, 79, 109)(69, 99, 82, 112)(70, 100, 81, 111)(74, 104, 88, 118)(75, 105, 86, 116)(76, 106, 84, 114)(77, 107, 85, 115)(78, 108, 87, 117)(80, 110, 89, 119)(83, 113, 90, 120) L = (1, 64)(2, 69)(3, 72)(4, 74)(5, 75)(6, 61)(7, 76)(8, 81)(9, 78)(10, 62)(11, 85)(12, 87)(13, 63)(14, 77)(15, 80)(16, 83)(17, 65)(18, 66)(19, 89)(20, 67)(21, 90)(22, 68)(23, 70)(24, 79)(25, 88)(26, 71)(27, 82)(28, 73)(29, 86)(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) :: { ( 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, 4, 10, 4, 10, 4, 10, 4, 10 ) } Outer automorphisms :: reflexible Dual of E12.453 Graph:: bipartite v = 17 e = 60 f = 21 degree seq :: [ 4^15, 30^2 ] E12.457 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 5, 15}) Quotient :: dipole Aut^+ = D30 (small group id <30, 3>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ Y2^2, R^2, Y1^2 * Y3^-1, (R * Y3)^2, (Y3 * Y2)^2, (R * Y1)^2, (Y2 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y1 * Y3^7, (Y3^-1 * Y1^-1)^5 ] Map:: non-degenerate R = (1, 31, 2, 32, 4, 34, 8, 38, 12, 42, 16, 46, 20, 50, 24, 54, 28, 58, 22, 52, 21, 51, 14, 44, 13, 43, 6, 36, 5, 35)(3, 33, 9, 39, 10, 40, 17, 47, 18, 48, 25, 55, 26, 56, 30, 60, 29, 59, 27, 57, 23, 53, 19, 49, 15, 45, 11, 41, 7, 37)(61, 91, 63, 93)(62, 92, 67, 97)(64, 94, 71, 101)(65, 95, 69, 99)(66, 96, 70, 100)(68, 98, 75, 105)(72, 102, 79, 109)(73, 103, 77, 107)(74, 104, 78, 108)(76, 106, 83, 113)(80, 110, 87, 117)(81, 111, 85, 115)(82, 112, 86, 116)(84, 114, 89, 119)(88, 118, 90, 120) L = (1, 64)(2, 68)(3, 70)(4, 72)(5, 62)(6, 61)(7, 69)(8, 76)(9, 77)(10, 78)(11, 63)(12, 80)(13, 65)(14, 66)(15, 67)(16, 84)(17, 85)(18, 86)(19, 71)(20, 88)(21, 73)(22, 74)(23, 75)(24, 82)(25, 90)(26, 89)(27, 79)(28, 81)(29, 83)(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) :: { ( 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, 4, 10, 4, 10, 4, 10, 4, 10 ) } Outer automorphisms :: reflexible Dual of E12.451 Graph:: bipartite v = 17 e = 60 f = 21 degree seq :: [ 4^15, 30^2 ] E12.458 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {10, 10, 15}) Quotient :: edge Aut^+ = C5 x S3 (small group id <30, 1>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^2 * T1^-1)^2, T1^-1 * T2^4 * T1^-1, T2 * T1 * T2 * T1^-1 * T2 * T1, T2^-1 * T1^-1 * T2 * T1^-1 * T2 * T1^-1, (T1^-1 * T2^-1 * T1^-1)^2, T2 * T1^2 * T2^-1 * T1^-2, T2^2 * T1 * T2^-2 * T1^-1 ] Map:: non-degenerate R = (1, 3, 10, 20, 6, 19, 13, 28, 17, 5)(2, 7, 22, 29, 18, 14, 4, 12, 26, 8)(9, 25, 30, 23, 16, 24, 11, 21, 15, 27)(31, 32, 36, 48, 47, 56, 40, 52, 43, 34)(33, 39, 49, 46, 35, 45, 50, 60, 58, 41)(37, 51, 44, 55, 38, 54, 59, 57, 42, 53) L = (1, 31)(2, 32)(3, 33)(4, 34)(5, 35)(6, 36)(7, 37)(8, 38)(9, 39)(10, 40)(11, 41)(12, 42)(13, 43)(14, 44)(15, 45)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60) local type(s) :: { ( 30^10 ) } Outer automorphisms :: reflexible Dual of E12.465 Transitivity :: ET+ Graph:: bipartite v = 6 e = 30 f = 2 degree seq :: [ 10^6 ] E12.459 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {10, 10, 15}) Quotient :: edge Aut^+ = C5 x S3 (small group id <30, 1>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-1)^2, T1^2 * T2^3, T1^10, (T2^-1 * T1^-1)^10 ] Map:: non-degenerate R = (1, 3, 10, 12, 19, 28, 30, 24, 18, 26, 27, 17, 6, 15, 5)(2, 7, 13, 4, 11, 22, 23, 14, 25, 29, 21, 9, 16, 20, 8)(31, 32, 36, 46, 56, 59, 60, 53, 42, 34)(33, 39, 45, 55, 57, 52, 54, 43, 49, 38)(35, 41, 47, 37, 48, 50, 58, 51, 40, 44) L = (1, 31)(2, 32)(3, 33)(4, 34)(5, 35)(6, 36)(7, 37)(8, 38)(9, 39)(10, 40)(11, 41)(12, 42)(13, 43)(14, 44)(15, 45)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60) local type(s) :: { ( 20^10 ), ( 20^15 ) } Outer automorphisms :: reflexible Dual of E12.463 Transitivity :: ET+ Graph:: bipartite v = 5 e = 30 f = 3 degree seq :: [ 10^3, 15^2 ] E12.460 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {10, 10, 15}) Quotient :: edge Aut^+ = C5 x S3 (small group id <30, 1>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1 * T2 * T1 * T2^-2, (T2 * T1 * T2)^2, T2 * T1^-1 * T2 * T1^-3, T2^15 ] Map:: non-degenerate R = (1, 3, 10, 27, 24, 20, 6, 19, 29, 13, 23, 22, 30, 17, 5)(2, 7, 21, 28, 15, 11, 18, 26, 14, 4, 12, 9, 25, 16, 8)(31, 32, 36, 48, 60, 55, 57, 58, 43, 34)(33, 39, 49, 51, 47, 44, 54, 38, 53, 41)(35, 45, 50, 42, 52, 37, 40, 56, 59, 46) L = (1, 31)(2, 32)(3, 33)(4, 34)(5, 35)(6, 36)(7, 37)(8, 38)(9, 39)(10, 40)(11, 41)(12, 42)(13, 43)(14, 44)(15, 45)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60) local type(s) :: { ( 20^10 ), ( 20^15 ) } Outer automorphisms :: reflexible Dual of E12.464 Transitivity :: ET+ Graph:: bipartite v = 5 e = 30 f = 3 degree seq :: [ 10^3, 15^2 ] E12.461 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {10, 10, 15}) Quotient :: edge Aut^+ = C5 x S3 (small group id <30, 1>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^-1 * T1 * T2^2 * T1, (T2^-1 * T1 * T2^-1)^2, T1^-3 * T2^-1 * T1^-1 * T2^-1, (T2 * T1^-1 * T2)^2, T2 * T1^2 * T2^-1 * T1^-2, T2^15 ] Map:: non-degenerate R = (1, 3, 10, 26, 23, 21, 13, 28, 20, 6, 19, 22, 30, 17, 5)(2, 7, 11, 27, 15, 14, 4, 12, 29, 18, 16, 9, 25, 24, 8)(31, 32, 36, 48, 56, 57, 60, 55, 43, 34)(33, 39, 49, 44, 53, 38, 47, 59, 58, 41)(35, 45, 50, 54, 40, 42, 52, 37, 51, 46) L = (1, 31)(2, 32)(3, 33)(4, 34)(5, 35)(6, 36)(7, 37)(8, 38)(9, 39)(10, 40)(11, 41)(12, 42)(13, 43)(14, 44)(15, 45)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60) local type(s) :: { ( 20^10 ), ( 20^15 ) } Outer automorphisms :: reflexible Dual of E12.462 Transitivity :: ET+ Graph:: bipartite v = 5 e = 30 f = 3 degree seq :: [ 10^3, 15^2 ] E12.462 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {10, 10, 15}) Quotient :: loop Aut^+ = C5 x S3 (small group id <30, 1>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ F^2, T2^2 * T1^-2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2^-1 * T1 * T2^-1 * T1^-1, T1^10, (T2^-1 * T1^-1)^15 ] Map:: non-degenerate R = (1, 31, 3, 33, 6, 36, 15, 45, 22, 52, 29, 59, 25, 55, 20, 50, 11, 41, 5, 35)(2, 32, 7, 37, 14, 44, 23, 53, 28, 58, 26, 56, 19, 49, 12, 42, 4, 34, 8, 38)(9, 39, 16, 46, 24, 54, 30, 60, 27, 57, 21, 51, 13, 43, 18, 48, 10, 40, 17, 47) L = (1, 32)(2, 36)(3, 39)(4, 31)(5, 40)(6, 44)(7, 46)(8, 47)(9, 45)(10, 33)(11, 34)(12, 48)(13, 35)(14, 52)(15, 54)(16, 53)(17, 37)(18, 38)(19, 41)(20, 43)(21, 42)(22, 58)(23, 60)(24, 59)(25, 49)(26, 51)(27, 50)(28, 55)(29, 57)(30, 56) local type(s) :: { ( 10, 15, 10, 15, 10, 15, 10, 15, 10, 15, 10, 15, 10, 15, 10, 15, 10, 15, 10, 15 ) } Outer automorphisms :: reflexible Dual of E12.461 Transitivity :: ET+ VT+ AT Graph:: v = 3 e = 30 f = 5 degree seq :: [ 20^3 ] E12.463 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {10, 10, 15}) Quotient :: loop Aut^+ = C5 x S3 (small group id <30, 1>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^2 * T1^-1)^2, T1^-1 * T2^4 * T1^-1, T2 * T1 * T2 * T1^-1 * T2 * T1, T2^-1 * T1^-1 * T2 * T1^-1 * T2 * T1^-1, (T1^-1 * T2^-1 * T1^-1)^2, T2 * T1^2 * T2^-1 * T1^-2, T2^2 * T1 * T2^-2 * T1^-1 ] Map:: non-degenerate R = (1, 31, 3, 33, 10, 40, 20, 50, 6, 36, 19, 49, 13, 43, 28, 58, 17, 47, 5, 35)(2, 32, 7, 37, 22, 52, 29, 59, 18, 48, 14, 44, 4, 34, 12, 42, 26, 56, 8, 38)(9, 39, 25, 55, 30, 60, 23, 53, 16, 46, 24, 54, 11, 41, 21, 51, 15, 45, 27, 57) L = (1, 32)(2, 36)(3, 39)(4, 31)(5, 45)(6, 48)(7, 51)(8, 54)(9, 49)(10, 52)(11, 33)(12, 53)(13, 34)(14, 55)(15, 50)(16, 35)(17, 56)(18, 47)(19, 46)(20, 60)(21, 44)(22, 43)(23, 37)(24, 59)(25, 38)(26, 40)(27, 42)(28, 41)(29, 57)(30, 58) local type(s) :: { ( 10, 15, 10, 15, 10, 15, 10, 15, 10, 15, 10, 15, 10, 15, 10, 15, 10, 15, 10, 15 ) } Outer automorphisms :: reflexible Dual of E12.459 Transitivity :: ET+ VT+ AT Graph:: v = 3 e = 30 f = 5 degree seq :: [ 20^3 ] E12.464 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {10, 10, 15}) Quotient :: loop Aut^+ = C5 x S3 (small group id <30, 1>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^-1 * T2^2 * T1^-3, T2 * T1 * T2 * T1^-1 * T2 * T1^-1, T2^-1 * T1^-1 * T2 * T1^-1 * T2^-1 * T1^-1, T2^-1 * T1^-2 * T2^-3, T2 * T1^2 * T2^-1 * T1^-2, T2^2 * T1 * T2^-2 * T1^-1 ] Map:: non-degenerate R = (1, 31, 3, 33, 10, 40, 28, 58, 13, 43, 20, 50, 6, 36, 19, 49, 17, 47, 5, 35)(2, 32, 7, 37, 22, 52, 14, 44, 4, 34, 12, 42, 18, 48, 29, 59, 26, 56, 8, 38)(9, 39, 24, 54, 16, 46, 21, 51, 11, 41, 25, 55, 30, 60, 23, 53, 15, 45, 27, 57) L = (1, 32)(2, 36)(3, 39)(4, 31)(5, 45)(6, 48)(7, 51)(8, 54)(9, 49)(10, 52)(11, 33)(12, 53)(13, 34)(14, 55)(15, 50)(16, 35)(17, 56)(18, 40)(19, 60)(20, 41)(21, 59)(22, 47)(23, 37)(24, 42)(25, 38)(26, 43)(27, 44)(28, 46)(29, 57)(30, 58) local type(s) :: { ( 10, 15, 10, 15, 10, 15, 10, 15, 10, 15, 10, 15, 10, 15, 10, 15, 10, 15, 10, 15 ) } Outer automorphisms :: reflexible Dual of E12.460 Transitivity :: ET+ VT+ AT Graph:: v = 3 e = 30 f = 5 degree seq :: [ 20^3 ] E12.465 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {10, 10, 15}) Quotient :: loop Aut^+ = C5 x S3 (small group id <30, 1>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-1)^2, T1^2 * T2^3, T1^10, (T2^-1 * T1^-1)^10 ] Map:: non-degenerate R = (1, 31, 3, 33, 10, 40, 12, 42, 19, 49, 28, 58, 30, 60, 24, 54, 18, 48, 26, 56, 27, 57, 17, 47, 6, 36, 15, 45, 5, 35)(2, 32, 7, 37, 13, 43, 4, 34, 11, 41, 22, 52, 23, 53, 14, 44, 25, 55, 29, 59, 21, 51, 9, 39, 16, 46, 20, 50, 8, 38) L = (1, 32)(2, 36)(3, 39)(4, 31)(5, 41)(6, 46)(7, 48)(8, 33)(9, 45)(10, 44)(11, 47)(12, 34)(13, 49)(14, 35)(15, 55)(16, 56)(17, 37)(18, 50)(19, 38)(20, 58)(21, 40)(22, 54)(23, 42)(24, 43)(25, 57)(26, 59)(27, 52)(28, 51)(29, 60)(30, 53) local type(s) :: { ( 10^30 ) } Outer automorphisms :: reflexible Dual of E12.458 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 30 f = 6 degree seq :: [ 30^2 ] E12.466 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {10, 10, 15}) Quotient :: dipole Aut^+ = C5 x S3 (small group id <30, 1>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, (R * Y2 * Y3^-1)^2, Y2^-1 * Y1 * Y2 * Y3^-1 * Y2^-1 * Y3^-1, Y3^2 * Y1^-1 * Y2^-2 * Y1^-1, Y3^2 * Y1^-2 * Y2^-2, Y2^-1 * Y3 * Y2 * Y1^-1 * Y2 * Y1^-1, Y3 * Y2^-1 * Y1 * Y3^-1 * Y2 * Y1^-1, Y2^2 * Y3^-1 * Y2^-2 * Y1^-1, Y2 * Y1^2 * Y2^-1 * Y1^-2, Y1^2 * Y2 * Y3^-2 * Y2, (Y3 * Y2^-1 * Y1^-1)^2, Y2^2 * Y3 * Y2^2 * Y1^-1, Y1^10, (Y3 * Y2^-1)^15 ] Map:: R = (1, 31, 2, 32, 6, 36, 18, 48, 17, 47, 26, 56, 10, 40, 22, 52, 13, 43, 4, 34)(3, 33, 9, 39, 19, 49, 16, 46, 5, 35, 15, 45, 20, 50, 30, 60, 28, 58, 11, 41)(7, 37, 21, 51, 14, 44, 25, 55, 8, 38, 24, 54, 29, 59, 27, 57, 12, 42, 23, 53)(61, 91, 63, 93, 70, 100, 80, 110, 66, 96, 79, 109, 73, 103, 88, 118, 77, 107, 65, 95)(62, 92, 67, 97, 82, 112, 89, 119, 78, 108, 74, 104, 64, 94, 72, 102, 86, 116, 68, 98)(69, 99, 85, 115, 90, 120, 83, 113, 76, 106, 84, 114, 71, 101, 81, 111, 75, 105, 87, 117) L = (1, 64)(2, 61)(3, 71)(4, 73)(5, 76)(6, 62)(7, 83)(8, 85)(9, 63)(10, 86)(11, 88)(12, 87)(13, 82)(14, 81)(15, 65)(16, 79)(17, 78)(18, 66)(19, 69)(20, 75)(21, 67)(22, 70)(23, 72)(24, 68)(25, 74)(26, 77)(27, 89)(28, 90)(29, 84)(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) :: { ( 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 E12.473 Graph:: bipartite v = 6 e = 60 f = 32 degree seq :: [ 20^6 ] E12.467 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {10, 10, 15}) Quotient :: dipole Aut^+ = C5 x S3 (small group id <30, 1>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-1, (R * Y1)^2, R * Y2 * R * Y3, (Y2^-1 * Y1)^2, Y2 * Y1^2 * Y2^2, Y1^10, (Y3^-1 * Y1^-1)^10 ] Map:: R = (1, 31, 2, 32, 6, 36, 16, 46, 26, 56, 29, 59, 30, 60, 23, 53, 12, 42, 4, 34)(3, 33, 9, 39, 15, 45, 25, 55, 27, 57, 22, 52, 24, 54, 13, 43, 19, 49, 8, 38)(5, 35, 11, 41, 17, 47, 7, 37, 18, 48, 20, 50, 28, 58, 21, 51, 10, 40, 14, 44)(61, 91, 63, 93, 70, 100, 72, 102, 79, 109, 88, 118, 90, 120, 84, 114, 78, 108, 86, 116, 87, 117, 77, 107, 66, 96, 75, 105, 65, 95)(62, 92, 67, 97, 73, 103, 64, 94, 71, 101, 82, 112, 83, 113, 74, 104, 85, 115, 89, 119, 81, 111, 69, 99, 76, 106, 80, 110, 68, 98) L = (1, 63)(2, 67)(3, 70)(4, 71)(5, 61)(6, 75)(7, 73)(8, 62)(9, 76)(10, 72)(11, 82)(12, 79)(13, 64)(14, 85)(15, 65)(16, 80)(17, 66)(18, 86)(19, 88)(20, 68)(21, 69)(22, 83)(23, 74)(24, 78)(25, 89)(26, 87)(27, 77)(28, 90)(29, 81)(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) :: { ( 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20 ), ( 2, 20, 2, 20, 2, 20, 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 E12.472 Graph:: bipartite v = 5 e = 60 f = 33 degree seq :: [ 20^3, 30^2 ] E12.468 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {10, 10, 15}) Quotient :: dipole Aut^+ = C5 x S3 (small group id <30, 1>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y1 * Y2^-2 * Y1 * Y2, Y1^-1 * Y2 * Y1^2 * Y2^-1 * Y1^-1, Y2 * Y1^-1 * Y2 * Y1^-3, (Y2^-1 * Y1^-1 * Y2^-1)^2, Y2^15, (Y3^-1 * Y1^-1)^10 ] Map:: R = (1, 31, 2, 32, 6, 36, 18, 48, 30, 60, 25, 55, 27, 57, 28, 58, 13, 43, 4, 34)(3, 33, 9, 39, 19, 49, 21, 51, 17, 47, 14, 44, 24, 54, 8, 38, 23, 53, 11, 41)(5, 35, 15, 45, 20, 50, 12, 42, 22, 52, 7, 37, 10, 40, 26, 56, 29, 59, 16, 46)(61, 91, 63, 93, 70, 100, 87, 117, 84, 114, 80, 110, 66, 96, 79, 109, 89, 119, 73, 103, 83, 113, 82, 112, 90, 120, 77, 107, 65, 95)(62, 92, 67, 97, 81, 111, 88, 118, 75, 105, 71, 101, 78, 108, 86, 116, 74, 104, 64, 94, 72, 102, 69, 99, 85, 115, 76, 106, 68, 98) L = (1, 63)(2, 67)(3, 70)(4, 72)(5, 61)(6, 79)(7, 81)(8, 62)(9, 85)(10, 87)(11, 78)(12, 69)(13, 83)(14, 64)(15, 71)(16, 68)(17, 65)(18, 86)(19, 89)(20, 66)(21, 88)(22, 90)(23, 82)(24, 80)(25, 76)(26, 74)(27, 84)(28, 75)(29, 73)(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) :: { ( 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20 ), ( 2, 20, 2, 20, 2, 20, 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 E12.470 Graph:: bipartite v = 5 e = 60 f = 33 degree seq :: [ 20^3, 30^2 ] E12.469 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {10, 10, 15}) Quotient :: dipole Aut^+ = C5 x S3 (small group id <30, 1>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y1 * Y2^-1 * Y1 * Y2^2, (Y2^-2 * Y1)^2, Y2^-1 * Y1^-3 * Y2^-1 * Y1^-1, (Y2 * Y1^-1 * Y2)^2, Y2 * Y1^2 * Y2^-1 * Y1^-2, Y2^15, (Y3^-1 * Y1^-1)^10 ] Map:: R = (1, 31, 2, 32, 6, 36, 18, 48, 26, 56, 27, 57, 30, 60, 25, 55, 13, 43, 4, 34)(3, 33, 9, 39, 19, 49, 14, 44, 23, 53, 8, 38, 17, 47, 29, 59, 28, 58, 11, 41)(5, 35, 15, 45, 20, 50, 24, 54, 10, 40, 12, 42, 22, 52, 7, 37, 21, 51, 16, 46)(61, 91, 63, 93, 70, 100, 86, 116, 83, 113, 81, 111, 73, 103, 88, 118, 80, 110, 66, 96, 79, 109, 82, 112, 90, 120, 77, 107, 65, 95)(62, 92, 67, 97, 71, 101, 87, 117, 75, 105, 74, 104, 64, 94, 72, 102, 89, 119, 78, 108, 76, 106, 69, 99, 85, 115, 84, 114, 68, 98) L = (1, 63)(2, 67)(3, 70)(4, 72)(5, 61)(6, 79)(7, 71)(8, 62)(9, 85)(10, 86)(11, 87)(12, 89)(13, 88)(14, 64)(15, 74)(16, 69)(17, 65)(18, 76)(19, 82)(20, 66)(21, 73)(22, 90)(23, 81)(24, 68)(25, 84)(26, 83)(27, 75)(28, 80)(29, 78)(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) :: { ( 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20 ), ( 2, 20, 2, 20, 2, 20, 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 E12.471 Graph:: bipartite v = 5 e = 60 f = 33 degree seq :: [ 20^3, 30^2 ] E12.470 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {10, 10, 15}) Quotient :: dipole Aut^+ = C5 x S3 (small group id <30, 1>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ Y1, R^2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y2^2 * Y3^-3, Y2 * R * Y2^-1 * Y3^-2 * R, Y2^10, (Y3 * Y2^-1)^10, (Y3^-1 * Y1^-1)^15 ] Map:: R = (1, 31)(2, 32)(3, 33)(4, 34)(5, 35)(6, 36)(7, 37)(8, 38)(9, 39)(10, 40)(11, 41)(12, 42)(13, 43)(14, 44)(15, 45)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60)(61, 91, 62, 92, 66, 96, 76, 106, 86, 116, 89, 119, 90, 120, 83, 113, 73, 103, 64, 94)(63, 93, 69, 99, 77, 107, 68, 98, 80, 110, 78, 108, 88, 118, 85, 115, 75, 105, 71, 101)(65, 95, 74, 104, 70, 100, 82, 112, 87, 117, 81, 111, 84, 114, 72, 102, 79, 109, 67, 97) L = (1, 63)(2, 67)(3, 70)(4, 72)(5, 61)(6, 77)(7, 78)(8, 62)(9, 64)(10, 66)(11, 83)(12, 68)(13, 75)(14, 85)(15, 65)(16, 74)(17, 87)(18, 76)(19, 73)(20, 84)(21, 69)(22, 71)(23, 81)(24, 90)(25, 89)(26, 80)(27, 86)(28, 79)(29, 82)(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 ) } Outer automorphisms :: reflexible Dual of E12.468 Graph:: simple bipartite v = 33 e = 60 f = 5 degree seq :: [ 2^30, 20^3 ] E12.471 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {10, 10, 15}) Quotient :: dipole Aut^+ = C5 x S3 (small group id <30, 1>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, Y3^-1 * Y2 * R * Y2^-1 * R, Y3 * Y2 * Y3^-2 * Y2, (Y3 * Y2 * Y3)^2, Y3 * Y2^-1 * Y3 * Y2^-3, (Y3^-1 * Y2^-1 * Y3^-1)^2, (Y3^-1 * Y1^-1)^15 ] Map:: R = (1, 31)(2, 32)(3, 33)(4, 34)(5, 35)(6, 36)(7, 37)(8, 38)(9, 39)(10, 40)(11, 41)(12, 42)(13, 43)(14, 44)(15, 45)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60)(61, 91, 62, 92, 66, 96, 78, 108, 90, 120, 85, 115, 87, 117, 88, 118, 73, 103, 64, 94)(63, 93, 69, 99, 79, 109, 81, 111, 77, 107, 74, 104, 84, 114, 68, 98, 83, 113, 71, 101)(65, 95, 75, 105, 80, 110, 72, 102, 82, 112, 67, 97, 70, 100, 86, 116, 89, 119, 76, 106) L = (1, 63)(2, 67)(3, 70)(4, 72)(5, 61)(6, 79)(7, 81)(8, 62)(9, 85)(10, 87)(11, 78)(12, 69)(13, 83)(14, 64)(15, 71)(16, 68)(17, 65)(18, 86)(19, 89)(20, 66)(21, 88)(22, 90)(23, 82)(24, 80)(25, 76)(26, 74)(27, 84)(28, 75)(29, 73)(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) :: { ( 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 E12.469 Graph:: simple bipartite v = 33 e = 60 f = 5 degree seq :: [ 2^30, 20^3 ] E12.472 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {10, 10, 15}) Quotient :: dipole Aut^+ = C5 x S3 (small group id <30, 1>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, R * Y2 * Y3 * R * Y2^-1, Y2 * Y3^-1 * Y2 * Y3^2, (Y3^-1 * Y2 * Y3^-1)^2, Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-2, (Y3 * Y2^-1 * Y3)^2, (Y2^-2 * R)^2, Y3^15, (Y3^-1 * Y1^-1)^15 ] Map:: R = (1, 31)(2, 32)(3, 33)(4, 34)(5, 35)(6, 36)(7, 37)(8, 38)(9, 39)(10, 40)(11, 41)(12, 42)(13, 43)(14, 44)(15, 45)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60)(61, 91, 62, 92, 66, 96, 78, 108, 86, 116, 87, 117, 90, 120, 85, 115, 73, 103, 64, 94)(63, 93, 69, 99, 79, 109, 74, 104, 83, 113, 68, 98, 77, 107, 89, 119, 88, 118, 71, 101)(65, 95, 75, 105, 80, 110, 84, 114, 70, 100, 72, 102, 82, 112, 67, 97, 81, 111, 76, 106) L = (1, 63)(2, 67)(3, 70)(4, 72)(5, 61)(6, 79)(7, 71)(8, 62)(9, 85)(10, 86)(11, 87)(12, 89)(13, 88)(14, 64)(15, 74)(16, 69)(17, 65)(18, 76)(19, 82)(20, 66)(21, 73)(22, 90)(23, 81)(24, 68)(25, 84)(26, 83)(27, 75)(28, 80)(29, 78)(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) :: { ( 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 E12.467 Graph:: simple bipartite v = 33 e = 60 f = 5 degree seq :: [ 2^30, 20^3 ] E12.473 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {10, 10, 15}) Quotient :: dipole Aut^+ = C5 x S3 (small group id <30, 1>) Aut = S3 x D10 (small group id <60, 8>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y1^-1)^2, Y1^3 * Y3^2, (R * Y2 * Y3^-1)^2, Y3^10, (Y3^-1 * Y1^-1)^10, (Y3 * Y2^-1)^10 ] Map:: R = (1, 31, 2, 32, 6, 36, 15, 45, 19, 49, 27, 57, 30, 60, 25, 55, 20, 50, 28, 58, 29, 59, 21, 51, 10, 40, 12, 42, 4, 34)(3, 33, 9, 39, 14, 44, 5, 35, 11, 41, 22, 52, 24, 54, 13, 43, 23, 53, 26, 56, 16, 46, 7, 37, 17, 47, 18, 48, 8, 38)(61, 91)(62, 92)(63, 93)(64, 94)(65, 95)(66, 96)(67, 97)(68, 98)(69, 99)(70, 100)(71, 101)(72, 102)(73, 103)(74, 104)(75, 105)(76, 106)(77, 107)(78, 108)(79, 109)(80, 110)(81, 111)(82, 112)(83, 113)(84, 114)(85, 115)(86, 116)(87, 117)(88, 118)(89, 119)(90, 120) L = (1, 63)(2, 67)(3, 70)(4, 71)(5, 61)(6, 73)(7, 72)(8, 62)(9, 80)(10, 77)(11, 81)(12, 83)(13, 64)(14, 79)(15, 65)(16, 66)(17, 88)(18, 87)(19, 68)(20, 78)(21, 69)(22, 85)(23, 89)(24, 75)(25, 74)(26, 90)(27, 76)(28, 86)(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, 20 ), ( 20^30 ) } Outer automorphisms :: reflexible Dual of E12.466 Graph:: simple bipartite v = 32 e = 60 f = 6 degree seq :: [ 2^30, 30^2 ] E12.474 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {6, 15, 30}) Quotient :: edge Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^6, T2^-5 * T1^2 ] Map:: non-degenerate R = (1, 3, 9, 19, 16, 6, 15, 27, 29, 22, 11, 21, 24, 13, 5)(2, 7, 17, 28, 26, 14, 25, 30, 23, 12, 4, 10, 20, 18, 8)(31, 32, 36, 44, 41, 34)(33, 37, 45, 55, 51, 40)(35, 38, 46, 56, 52, 42)(39, 47, 57, 60, 54, 50)(43, 48, 49, 58, 59, 53) L = (1, 31)(2, 32)(3, 33)(4, 34)(5, 35)(6, 36)(7, 37)(8, 38)(9, 39)(10, 40)(11, 41)(12, 42)(13, 43)(14, 44)(15, 45)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60) local type(s) :: { ( 60^6 ), ( 60^15 ) } Outer automorphisms :: reflexible Dual of E12.478 Transitivity :: ET+ Graph:: bipartite v = 7 e = 30 f = 1 degree seq :: [ 6^5, 15^2 ] E12.475 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {6, 15, 30}) Quotient :: edge Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2 * T1^-1 * T2^3, T1 * T2 * T1^6 * T2, (T2^-1 * T1^4)^2 ] Map:: non-degenerate R = (1, 3, 9, 8, 2, 7, 17, 16, 6, 15, 25, 24, 14, 23, 27, 30, 22, 28, 19, 26, 29, 20, 11, 18, 21, 12, 4, 10, 13, 5)(31, 32, 36, 44, 52, 59, 51, 43, 39, 47, 55, 57, 49, 41, 34)(33, 37, 45, 53, 58, 50, 42, 35, 38, 46, 54, 60, 56, 48, 40) L = (1, 31)(2, 32)(3, 33)(4, 34)(5, 35)(6, 36)(7, 37)(8, 38)(9, 39)(10, 40)(11, 41)(12, 42)(13, 43)(14, 44)(15, 45)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60) local type(s) :: { ( 12^15 ), ( 12^30 ) } Outer automorphisms :: reflexible Dual of E12.479 Transitivity :: ET+ Graph:: bipartite v = 3 e = 30 f = 5 degree seq :: [ 15^2, 30 ] E12.476 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {6, 15, 30}) Quotient :: edge Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-1 * T1^-5, T2^6, T2^2 * T1^-1 * T2 * T1^-1 * T2^3 * T1^2, T1^3 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^2 * T2^-2 ] Map:: non-degenerate R = (1, 3, 9, 19, 13, 5)(2, 7, 17, 26, 18, 8)(4, 10, 20, 27, 22, 12)(6, 15, 24, 30, 25, 16)(11, 21, 28, 29, 23, 14)(31, 32, 36, 44, 42, 35, 38, 46, 53, 52, 43, 48, 55, 59, 57, 49, 56, 60, 58, 50, 39, 47, 54, 51, 40, 33, 37, 45, 41, 34) L = (1, 31)(2, 32)(3, 33)(4, 34)(5, 35)(6, 36)(7, 37)(8, 38)(9, 39)(10, 40)(11, 41)(12, 42)(13, 43)(14, 44)(15, 45)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60) local type(s) :: { ( 30^6 ), ( 30^30 ) } Outer automorphisms :: reflexible Dual of E12.477 Transitivity :: ET+ Graph:: bipartite v = 6 e = 30 f = 2 degree seq :: [ 6^5, 30 ] E12.477 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {6, 15, 30}) Quotient :: loop Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^6, T2^-5 * T1^2 ] Map:: non-degenerate R = (1, 31, 3, 33, 9, 39, 19, 49, 16, 46, 6, 36, 15, 45, 27, 57, 29, 59, 22, 52, 11, 41, 21, 51, 24, 54, 13, 43, 5, 35)(2, 32, 7, 37, 17, 47, 28, 58, 26, 56, 14, 44, 25, 55, 30, 60, 23, 53, 12, 42, 4, 34, 10, 40, 20, 50, 18, 48, 8, 38) L = (1, 32)(2, 36)(3, 37)(4, 31)(5, 38)(6, 44)(7, 45)(8, 46)(9, 47)(10, 33)(11, 34)(12, 35)(13, 48)(14, 41)(15, 55)(16, 56)(17, 57)(18, 49)(19, 58)(20, 39)(21, 40)(22, 42)(23, 43)(24, 50)(25, 51)(26, 52)(27, 60)(28, 59)(29, 53)(30, 54) local type(s) :: { ( 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30, 6, 30 ) } Outer automorphisms :: reflexible Dual of E12.476 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 30 f = 6 degree seq :: [ 30^2 ] E12.478 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {6, 15, 30}) Quotient :: loop Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2 * T1^-1 * T2^3, T1 * T2 * T1^6 * T2, (T2^-1 * T1^4)^2 ] Map:: non-degenerate R = (1, 31, 3, 33, 9, 39, 8, 38, 2, 32, 7, 37, 17, 47, 16, 46, 6, 36, 15, 45, 25, 55, 24, 54, 14, 44, 23, 53, 27, 57, 30, 60, 22, 52, 28, 58, 19, 49, 26, 56, 29, 59, 20, 50, 11, 41, 18, 48, 21, 51, 12, 42, 4, 34, 10, 40, 13, 43, 5, 35) L = (1, 32)(2, 36)(3, 37)(4, 31)(5, 38)(6, 44)(7, 45)(8, 46)(9, 47)(10, 33)(11, 34)(12, 35)(13, 39)(14, 52)(15, 53)(16, 54)(17, 55)(18, 40)(19, 41)(20, 42)(21, 43)(22, 59)(23, 58)(24, 60)(25, 57)(26, 48)(27, 49)(28, 50)(29, 51)(30, 56) local type(s) :: { ( 6, 15, 6, 15, 6, 15, 6, 15, 6, 15, 6, 15, 6, 15, 6, 15, 6, 15, 6, 15, 6, 15, 6, 15, 6, 15, 6, 15, 6, 15, 6, 15, 6, 15, 6, 15, 6, 15, 6, 15, 6, 15, 6, 15, 6, 15, 6, 15, 6, 15, 6, 15, 6, 15, 6, 15, 6, 15, 6, 15 ) } Outer automorphisms :: reflexible Dual of E12.474 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 30 f = 7 degree seq :: [ 60 ] E12.479 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {6, 15, 30}) Quotient :: loop Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-1 * T1^-5, T2^6, T2^2 * T1^-1 * T2 * T1^-1 * T2^3 * T1^2, T1^3 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^2 * T2^-2 ] Map:: non-degenerate R = (1, 31, 3, 33, 9, 39, 19, 49, 13, 43, 5, 35)(2, 32, 7, 37, 17, 47, 26, 56, 18, 48, 8, 38)(4, 34, 10, 40, 20, 50, 27, 57, 22, 52, 12, 42)(6, 36, 15, 45, 24, 54, 30, 60, 25, 55, 16, 46)(11, 41, 21, 51, 28, 58, 29, 59, 23, 53, 14, 44) L = (1, 32)(2, 36)(3, 37)(4, 31)(5, 38)(6, 44)(7, 45)(8, 46)(9, 47)(10, 33)(11, 34)(12, 35)(13, 48)(14, 42)(15, 41)(16, 53)(17, 54)(18, 55)(19, 56)(20, 39)(21, 40)(22, 43)(23, 52)(24, 51)(25, 59)(26, 60)(27, 49)(28, 50)(29, 57)(30, 58) local type(s) :: { ( 15, 30, 15, 30, 15, 30, 15, 30, 15, 30, 15, 30 ) } Outer automorphisms :: reflexible Dual of E12.475 Transitivity :: ET+ VT+ AT Graph:: v = 5 e = 30 f = 3 degree seq :: [ 12^5 ] E12.480 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 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, (R * Y2)^2, (R * Y3)^2, (Y2^-1, Y1^-1), (R * Y1)^2, (Y3^-1, Y2^-1), Y1^6, Y2^-5 * 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^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * 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, 31, 2, 32, 6, 36, 14, 44, 11, 41, 4, 34)(3, 33, 7, 37, 15, 45, 25, 55, 21, 51, 10, 40)(5, 35, 8, 38, 16, 46, 26, 56, 22, 52, 12, 42)(9, 39, 17, 47, 27, 57, 30, 60, 24, 54, 20, 50)(13, 43, 18, 48, 19, 49, 28, 58, 29, 59, 23, 53)(61, 91, 63, 93, 69, 99, 79, 109, 76, 106, 66, 96, 75, 105, 87, 117, 89, 119, 82, 112, 71, 101, 81, 111, 84, 114, 73, 103, 65, 95)(62, 92, 67, 97, 77, 107, 88, 118, 86, 116, 74, 104, 85, 115, 90, 120, 83, 113, 72, 102, 64, 94, 70, 100, 80, 110, 78, 108, 68, 98) L = (1, 64)(2, 61)(3, 70)(4, 71)(5, 72)(6, 62)(7, 63)(8, 65)(9, 80)(10, 81)(11, 74)(12, 82)(13, 83)(14, 66)(15, 67)(16, 68)(17, 69)(18, 73)(19, 78)(20, 84)(21, 85)(22, 86)(23, 89)(24, 90)(25, 75)(26, 76)(27, 77)(28, 79)(29, 88)(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) :: { ( 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 E12.483 Graph:: bipartite v = 7 e = 60 f = 31 degree seq :: [ 12^5, 30^2 ] E12.481 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 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^-1, (R * Y1)^2, R * Y2 * R * Y3, (Y1, Y2^-1), Y2 * Y1^-1 * Y2^3, Y1 * Y2 * Y1^6 * Y2, (Y3^-1 * Y1^-1)^6 ] Map:: 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, 63)(2, 67)(3, 69)(4, 70)(5, 61)(6, 75)(7, 77)(8, 62)(9, 68)(10, 73)(11, 78)(12, 64)(13, 65)(14, 83)(15, 85)(16, 66)(17, 76)(18, 81)(19, 86)(20, 71)(21, 72)(22, 88)(23, 87)(24, 74)(25, 84)(26, 89)(27, 90)(28, 79)(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) :: { ( 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 E12.482 Graph:: bipartite v = 3 e = 60 f = 35 degree seq :: [ 30^2, 60 ] E12.482 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 15, 30}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y2, Y3^-1), Y2^-1 * Y3^5, Y2^6, Y3^-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^-2, (Y3^-1 * Y1^-1)^30 ] Map:: R = (1, 31)(2, 32)(3, 33)(4, 34)(5, 35)(6, 36)(7, 37)(8, 38)(9, 39)(10, 40)(11, 41)(12, 42)(13, 43)(14, 44)(15, 45)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60)(61, 91, 62, 92, 66, 96, 74, 104, 71, 101, 64, 94)(63, 93, 67, 97, 75, 105, 83, 113, 80, 110, 70, 100)(65, 95, 68, 98, 76, 106, 84, 114, 81, 111, 72, 102)(69, 99, 77, 107, 85, 115, 89, 119, 87, 117, 79, 109)(73, 103, 78, 108, 86, 116, 90, 120, 88, 118, 82, 112) L = (1, 63)(2, 67)(3, 69)(4, 70)(5, 61)(6, 75)(7, 77)(8, 62)(9, 78)(10, 79)(11, 80)(12, 64)(13, 65)(14, 83)(15, 85)(16, 66)(17, 86)(18, 68)(19, 73)(20, 87)(21, 71)(22, 72)(23, 89)(24, 74)(25, 90)(26, 76)(27, 82)(28, 81)(29, 88)(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 ) } Outer automorphisms :: reflexible Dual of E12.481 Graph:: simple bipartite v = 35 e = 60 f = 3 degree seq :: [ 2^30, 12^5 ] E12.483 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 15, 30}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1^-1), Y3 * Y1^2 * Y3^-1 * Y1^-2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y1^-5, Y3^6, Y3^2 * Y1^-1 * Y3 * Y1^-1 * Y3^3 * Y1^2, (Y3 * Y2^-1)^6 ] Map:: R = (1, 31, 2, 32, 6, 36, 14, 44, 12, 42, 5, 35, 8, 38, 16, 46, 23, 53, 22, 52, 13, 43, 18, 48, 25, 55, 29, 59, 27, 57, 19, 49, 26, 56, 30, 60, 28, 58, 20, 50, 9, 39, 17, 47, 24, 54, 21, 51, 10, 40, 3, 33, 7, 37, 15, 45, 11, 41, 4, 34)(61, 91)(62, 92)(63, 93)(64, 94)(65, 95)(66, 96)(67, 97)(68, 98)(69, 99)(70, 100)(71, 101)(72, 102)(73, 103)(74, 104)(75, 105)(76, 106)(77, 107)(78, 108)(79, 109)(80, 110)(81, 111)(82, 112)(83, 113)(84, 114)(85, 115)(86, 116)(87, 117)(88, 118)(89, 119)(90, 120) L = (1, 63)(2, 67)(3, 69)(4, 70)(5, 61)(6, 75)(7, 77)(8, 62)(9, 79)(10, 80)(11, 81)(12, 64)(13, 65)(14, 71)(15, 84)(16, 66)(17, 86)(18, 68)(19, 73)(20, 87)(21, 88)(22, 72)(23, 74)(24, 90)(25, 76)(26, 78)(27, 82)(28, 89)(29, 83)(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) :: { ( 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 E12.480 Graph:: bipartite v = 31 e = 60 f = 7 degree seq :: [ 2^30, 60 ] E12.484 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 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, (Y3^-1, Y2), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2^-1, Y1^-1), Y2^-5 * Y1^-1, Y1^6, Y2^-1 * Y3 * Y1^-1 * Y2^-2 * Y3 * Y1^-1 * Y2^-2 * Y3 * Y1^-1 * Y2^-2 * Y3 * Y1^-1 * Y2^-2 * Y3 * Y1^-1 * Y2^-2 * Y3 * Y1^-1 * Y2^-2 * Y3 * Y1^-1 * Y2^-2 * Y3 ] Map:: R = (1, 31, 2, 32, 6, 36, 14, 44, 11, 41, 4, 34)(3, 33, 7, 37, 15, 45, 23, 53, 21, 51, 10, 40)(5, 35, 8, 38, 16, 46, 24, 54, 22, 52, 12, 42)(9, 39, 17, 47, 25, 55, 29, 59, 28, 58, 20, 50)(13, 43, 18, 48, 26, 56, 30, 60, 27, 57, 19, 49)(61, 91, 63, 93, 69, 99, 79, 109, 72, 102, 64, 94, 70, 100, 80, 110, 87, 117, 82, 112, 71, 101, 81, 111, 88, 118, 90, 120, 84, 114, 74, 104, 83, 113, 89, 119, 86, 116, 76, 106, 66, 96, 75, 105, 85, 115, 78, 108, 68, 98, 62, 92, 67, 97, 77, 107, 73, 103, 65, 95) L = (1, 64)(2, 61)(3, 70)(4, 71)(5, 72)(6, 62)(7, 63)(8, 65)(9, 80)(10, 81)(11, 74)(12, 82)(13, 79)(14, 66)(15, 67)(16, 68)(17, 69)(18, 73)(19, 87)(20, 88)(21, 83)(22, 84)(23, 75)(24, 76)(25, 77)(26, 78)(27, 90)(28, 89)(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) :: { ( 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 E12.485 Graph:: bipartite v = 6 e = 60 f = 32 degree seq :: [ 12^5, 60 ] E12.485 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 15, 30}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1^-1), Y3 * Y1^-1 * Y3^3, (R * Y2 * Y3^-1)^2, Y1^4 * Y3 * Y1 * Y3 * Y1^2, (Y3^-1 * Y1^4)^2, (Y3 * Y2^-1)^30 ] Map:: 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)(62, 92)(63, 93)(64, 94)(65, 95)(66, 96)(67, 97)(68, 98)(69, 99)(70, 100)(71, 101)(72, 102)(73, 103)(74, 104)(75, 105)(76, 106)(77, 107)(78, 108)(79, 109)(80, 110)(81, 111)(82, 112)(83, 113)(84, 114)(85, 115)(86, 116)(87, 117)(88, 118)(89, 119)(90, 120) L = (1, 63)(2, 67)(3, 69)(4, 70)(5, 61)(6, 75)(7, 77)(8, 62)(9, 68)(10, 73)(11, 78)(12, 64)(13, 65)(14, 83)(15, 85)(16, 66)(17, 76)(18, 81)(19, 86)(20, 71)(21, 72)(22, 88)(23, 87)(24, 74)(25, 84)(26, 89)(27, 90)(28, 79)(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) :: { ( 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 E12.484 Graph:: simple bipartite v = 32 e = 60 f = 6 degree seq :: [ 2^30, 30^2 ] E12.486 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {5, 30, 30}) Quotient :: edge Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^5, T2^6 * T1^-1, (T1^-1 * T2^-1)^30 ] Map:: non-degenerate R = (1, 3, 9, 18, 17, 8, 2, 7, 16, 26, 25, 15, 6, 14, 24, 30, 28, 21, 11, 20, 27, 29, 22, 12, 4, 10, 19, 23, 13, 5)(31, 32, 36, 41, 34)(33, 37, 44, 50, 40)(35, 38, 45, 51, 42)(39, 46, 54, 57, 49)(43, 47, 55, 58, 52)(48, 56, 60, 59, 53) L = (1, 31)(2, 32)(3, 33)(4, 34)(5, 35)(6, 36)(7, 37)(8, 38)(9, 39)(10, 40)(11, 41)(12, 42)(13, 43)(14, 44)(15, 45)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60) local type(s) :: { ( 60^5 ), ( 60^30 ) } Outer automorphisms :: reflexible Dual of E12.492 Transitivity :: ET+ Graph:: bipartite v = 7 e = 30 f = 1 degree seq :: [ 5^6, 30 ] E12.487 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {5, 30, 30}) Quotient :: edge Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ F^2, (T1, T2^-1), (F * T1)^2, (F * T2)^2, T1^-5, T1^5, T1^-2 * T2^6, 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 ] Map:: non-degenerate R = (1, 3, 9, 18, 25, 15, 6, 14, 24, 30, 22, 12, 4, 10, 19, 27, 17, 8, 2, 7, 16, 26, 29, 21, 11, 20, 28, 23, 13, 5)(31, 32, 36, 41, 34)(33, 37, 44, 50, 40)(35, 38, 45, 51, 42)(39, 46, 54, 58, 49)(43, 47, 55, 59, 52)(48, 56, 60, 53, 57) L = (1, 31)(2, 32)(3, 33)(4, 34)(5, 35)(6, 36)(7, 37)(8, 38)(9, 39)(10, 40)(11, 41)(12, 42)(13, 43)(14, 44)(15, 45)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60) local type(s) :: { ( 60^5 ), ( 60^30 ) } Outer automorphisms :: reflexible Dual of E12.491 Transitivity :: ET+ Graph:: bipartite v = 7 e = 30 f = 1 degree seq :: [ 5^6, 30 ] E12.488 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {5, 30, 30}) Quotient :: edge Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ F^2, (T1, T2), (F * T1)^2, (F * T2)^2, T1^-5, T1^-2 * T2^-6, T2^-1 * T1 * T2^-2 * T1 * T2^-3 * T1 ] Map:: non-degenerate R = (1, 3, 9, 18, 28, 21, 11, 20, 30, 27, 17, 8, 2, 7, 16, 26, 22, 12, 4, 10, 19, 29, 25, 15, 6, 14, 24, 23, 13, 5)(31, 32, 36, 41, 34)(33, 37, 44, 50, 40)(35, 38, 45, 51, 42)(39, 46, 54, 60, 49)(43, 47, 55, 58, 52)(48, 56, 53, 57, 59) L = (1, 31)(2, 32)(3, 33)(4, 34)(5, 35)(6, 36)(7, 37)(8, 38)(9, 39)(10, 40)(11, 41)(12, 42)(13, 43)(14, 44)(15, 45)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60) local type(s) :: { ( 60^5 ), ( 60^30 ) } Outer automorphisms :: reflexible Dual of E12.490 Transitivity :: ET+ Graph:: bipartite v = 7 e = 30 f = 1 degree seq :: [ 5^6, 30 ] E12.489 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {5, 30, 30}) Quotient :: edge Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1), T2^-1 * T1 * T2^-1 * T1 * T2^-2, T1 * T2^-2 * T1^-1 * T2^-2 * T1^2, T2^-1 * T1^-7, T2^2 * T1^2 * T2^3 * T1^3 ] Map:: non-degenerate R = (1, 3, 9, 16, 6, 15, 26, 29, 23, 20, 27, 22, 12, 4, 10, 18, 8, 2, 7, 17, 25, 14, 24, 30, 28, 21, 11, 19, 13, 5)(31, 32, 36, 44, 53, 51, 42, 35, 38, 46, 55, 59, 58, 52, 43, 48, 39, 47, 56, 60, 57, 49, 40, 33, 37, 45, 54, 50, 41, 34) L = (1, 31)(2, 32)(3, 33)(4, 34)(5, 35)(6, 36)(7, 37)(8, 38)(9, 39)(10, 40)(11, 41)(12, 42)(13, 43)(14, 44)(15, 45)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60) local type(s) :: { ( 10^30 ) } Outer automorphisms :: reflexible Dual of E12.493 Transitivity :: ET+ Graph:: bipartite v = 2 e = 30 f = 6 degree seq :: [ 30^2 ] E12.490 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {5, 30, 30}) Quotient :: loop Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^5, T2^6 * T1^-1, (T1^-1 * T2^-1)^30 ] Map:: non-degenerate R = (1, 31, 3, 33, 9, 39, 18, 48, 17, 47, 8, 38, 2, 32, 7, 37, 16, 46, 26, 56, 25, 55, 15, 45, 6, 36, 14, 44, 24, 54, 30, 60, 28, 58, 21, 51, 11, 41, 20, 50, 27, 57, 29, 59, 22, 52, 12, 42, 4, 34, 10, 40, 19, 49, 23, 53, 13, 43, 5, 35) L = (1, 32)(2, 36)(3, 37)(4, 31)(5, 38)(6, 41)(7, 44)(8, 45)(9, 46)(10, 33)(11, 34)(12, 35)(13, 47)(14, 50)(15, 51)(16, 54)(17, 55)(18, 56)(19, 39)(20, 40)(21, 42)(22, 43)(23, 48)(24, 57)(25, 58)(26, 60)(27, 49)(28, 52)(29, 53)(30, 59) local type(s) :: { ( 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30 ) } Outer automorphisms :: reflexible Dual of E12.488 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 30 f = 7 degree seq :: [ 60 ] E12.491 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {5, 30, 30}) Quotient :: loop Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ F^2, (T1, T2^-1), (F * T1)^2, (F * T2)^2, T1^-5, T1^5, T1^-2 * T2^6, 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 ] Map:: non-degenerate R = (1, 31, 3, 33, 9, 39, 18, 48, 25, 55, 15, 45, 6, 36, 14, 44, 24, 54, 30, 60, 22, 52, 12, 42, 4, 34, 10, 40, 19, 49, 27, 57, 17, 47, 8, 38, 2, 32, 7, 37, 16, 46, 26, 56, 29, 59, 21, 51, 11, 41, 20, 50, 28, 58, 23, 53, 13, 43, 5, 35) L = (1, 32)(2, 36)(3, 37)(4, 31)(5, 38)(6, 41)(7, 44)(8, 45)(9, 46)(10, 33)(11, 34)(12, 35)(13, 47)(14, 50)(15, 51)(16, 54)(17, 55)(18, 56)(19, 39)(20, 40)(21, 42)(22, 43)(23, 57)(24, 58)(25, 59)(26, 60)(27, 48)(28, 49)(29, 52)(30, 53) local type(s) :: { ( 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30 ) } Outer automorphisms :: reflexible Dual of E12.487 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 30 f = 7 degree seq :: [ 60 ] E12.492 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {5, 30, 30}) Quotient :: loop Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ F^2, (T1, T2), (F * T1)^2, (F * T2)^2, T1^-5, T1^-2 * T2^-6, T2^-1 * T1 * T2^-2 * T1 * T2^-3 * T1 ] Map:: non-degenerate R = (1, 31, 3, 33, 9, 39, 18, 48, 28, 58, 21, 51, 11, 41, 20, 50, 30, 60, 27, 57, 17, 47, 8, 38, 2, 32, 7, 37, 16, 46, 26, 56, 22, 52, 12, 42, 4, 34, 10, 40, 19, 49, 29, 59, 25, 55, 15, 45, 6, 36, 14, 44, 24, 54, 23, 53, 13, 43, 5, 35) L = (1, 32)(2, 36)(3, 37)(4, 31)(5, 38)(6, 41)(7, 44)(8, 45)(9, 46)(10, 33)(11, 34)(12, 35)(13, 47)(14, 50)(15, 51)(16, 54)(17, 55)(18, 56)(19, 39)(20, 40)(21, 42)(22, 43)(23, 57)(24, 60)(25, 58)(26, 53)(27, 59)(28, 52)(29, 48)(30, 49) local type(s) :: { ( 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30, 5, 30 ) } Outer automorphisms :: reflexible Dual of E12.486 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 30 f = 7 degree seq :: [ 60 ] E12.493 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {5, 30, 30}) Quotient :: loop Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^5, T2^-1 * T1^6, (T1^-1 * T2^-1)^30 ] Map:: non-degenerate R = (1, 31, 3, 33, 9, 39, 13, 43, 5, 35)(2, 32, 7, 37, 17, 47, 18, 48, 8, 38)(4, 34, 10, 40, 19, 49, 23, 53, 12, 42)(6, 36, 15, 45, 25, 55, 26, 56, 16, 46)(11, 41, 20, 50, 27, 57, 29, 59, 22, 52)(14, 44, 24, 54, 30, 60, 28, 58, 21, 51) L = (1, 32)(2, 36)(3, 37)(4, 31)(5, 38)(6, 44)(7, 45)(8, 46)(9, 47)(10, 33)(11, 34)(12, 35)(13, 48)(14, 50)(15, 54)(16, 51)(17, 55)(18, 56)(19, 39)(20, 40)(21, 41)(22, 42)(23, 43)(24, 57)(25, 60)(26, 58)(27, 49)(28, 52)(29, 53)(30, 59) local type(s) :: { ( 30^10 ) } Outer automorphisms :: reflexible Dual of E12.489 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 6 e = 30 f = 2 degree seq :: [ 10^6 ] E12.494 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 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, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, (Y3^-1, Y2^-1), (Y2^-1, Y1^-1), Y3^5, Y1^5, Y3 * Y2^6, 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 ] Map:: R = (1, 31, 2, 32, 6, 36, 11, 41, 4, 34)(3, 33, 7, 37, 14, 44, 20, 50, 10, 40)(5, 35, 8, 38, 15, 45, 21, 51, 12, 42)(9, 39, 16, 46, 24, 54, 27, 57, 19, 49)(13, 43, 17, 47, 25, 55, 28, 58, 22, 52)(18, 48, 26, 56, 30, 60, 29, 59, 23, 53)(61, 91, 63, 93, 69, 99, 78, 108, 77, 107, 68, 98, 62, 92, 67, 97, 76, 106, 86, 116, 85, 115, 75, 105, 66, 96, 74, 104, 84, 114, 90, 120, 88, 118, 81, 111, 71, 101, 80, 110, 87, 117, 89, 119, 82, 112, 72, 102, 64, 94, 70, 100, 79, 109, 83, 113, 73, 103, 65, 95) L = (1, 64)(2, 61)(3, 70)(4, 71)(5, 72)(6, 62)(7, 63)(8, 65)(9, 79)(10, 80)(11, 66)(12, 81)(13, 82)(14, 67)(15, 68)(16, 69)(17, 73)(18, 83)(19, 87)(20, 74)(21, 75)(22, 88)(23, 89)(24, 76)(25, 77)(26, 78)(27, 84)(28, 85)(29, 90)(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) :: { ( 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 E12.501 Graph:: bipartite v = 7 e = 60 f = 31 degree seq :: [ 10^6, 60 ] E12.495 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 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^-1, (R * Y1)^2, (Y2^-1, Y1^-1), (R * Y3)^2, (R * Y2)^2, (Y3^-1, Y2^-1), Y1^5, Y1 * Y2 * Y1 * Y3^-1 * Y2^-1 * Y1 * Y3^-1, Y2 * Y3 * Y2^5 * Y1^-1, (Y1^-2 * Y3)^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 ] Map:: R = (1, 31, 2, 32, 6, 36, 11, 41, 4, 34)(3, 33, 7, 37, 14, 44, 20, 50, 10, 40)(5, 35, 8, 38, 15, 45, 21, 51, 12, 42)(9, 39, 16, 46, 24, 54, 28, 58, 19, 49)(13, 43, 17, 47, 25, 55, 29, 59, 22, 52)(18, 48, 26, 56, 30, 60, 23, 53, 27, 57)(61, 91, 63, 93, 69, 99, 78, 108, 85, 115, 75, 105, 66, 96, 74, 104, 84, 114, 90, 120, 82, 112, 72, 102, 64, 94, 70, 100, 79, 109, 87, 117, 77, 107, 68, 98, 62, 92, 67, 97, 76, 106, 86, 116, 89, 119, 81, 111, 71, 101, 80, 110, 88, 118, 83, 113, 73, 103, 65, 95) L = (1, 64)(2, 61)(3, 70)(4, 71)(5, 72)(6, 62)(7, 63)(8, 65)(9, 79)(10, 80)(11, 66)(12, 81)(13, 82)(14, 67)(15, 68)(16, 69)(17, 73)(18, 87)(19, 88)(20, 74)(21, 75)(22, 89)(23, 90)(24, 76)(25, 77)(26, 78)(27, 83)(28, 84)(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) :: { ( 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 E12.500 Graph:: bipartite v = 7 e = 60 f = 31 degree seq :: [ 10^6, 60 ] E12.496 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 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, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), (Y3^-1, Y2^-1), Y1^5, Y2^-1 * Y1 * Y3^-2 * Y2 * Y1^2, Y2^-1 * Y3 * Y2^-5 * Y1^-1, Y3^10, Y3^-3 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y2^-4 ] Map:: R = (1, 31, 2, 32, 6, 36, 11, 41, 4, 34)(3, 33, 7, 37, 14, 44, 20, 50, 10, 40)(5, 35, 8, 38, 15, 45, 21, 51, 12, 42)(9, 39, 16, 46, 24, 54, 30, 60, 19, 49)(13, 43, 17, 47, 25, 55, 28, 58, 22, 52)(18, 48, 26, 56, 23, 53, 27, 57, 29, 59)(61, 91, 63, 93, 69, 99, 78, 108, 88, 118, 81, 111, 71, 101, 80, 110, 90, 120, 87, 117, 77, 107, 68, 98, 62, 92, 67, 97, 76, 106, 86, 116, 82, 112, 72, 102, 64, 94, 70, 100, 79, 109, 89, 119, 85, 115, 75, 105, 66, 96, 74, 104, 84, 114, 83, 113, 73, 103, 65, 95) L = (1, 64)(2, 61)(3, 70)(4, 71)(5, 72)(6, 62)(7, 63)(8, 65)(9, 79)(10, 80)(11, 66)(12, 81)(13, 82)(14, 67)(15, 68)(16, 69)(17, 73)(18, 89)(19, 90)(20, 74)(21, 75)(22, 88)(23, 86)(24, 76)(25, 77)(26, 78)(27, 83)(28, 85)(29, 87)(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) :: { ( 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 E12.499 Graph:: bipartite v = 7 e = 60 f = 31 degree seq :: [ 10^6, 60 ] E12.497 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 30, 30}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-1, (R * Y1)^2, R * Y2 * R * Y3, (Y2^-1, Y1^-1), Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-2, Y2^-1 * Y1^-1 * Y2^-6, (Y3^-1 * Y1^-1)^5 ] Map:: R = (1, 31, 2, 32, 6, 36, 14, 44, 9, 39, 17, 47, 24, 54, 29, 59, 27, 57, 22, 52, 26, 56, 20, 50, 12, 42, 5, 35, 8, 38, 16, 46, 10, 40, 3, 33, 7, 37, 15, 45, 23, 53, 19, 49, 25, 55, 30, 60, 28, 58, 21, 51, 13, 43, 18, 48, 11, 41, 4, 34)(61, 91, 63, 93, 69, 99, 79, 109, 87, 117, 81, 111, 72, 102, 64, 94, 70, 100, 74, 104, 83, 113, 89, 119, 88, 118, 80, 110, 71, 101, 76, 106, 66, 96, 75, 105, 84, 114, 90, 120, 86, 116, 78, 108, 68, 98, 62, 92, 67, 97, 77, 107, 85, 115, 82, 112, 73, 103, 65, 95) L = (1, 63)(2, 67)(3, 69)(4, 70)(5, 61)(6, 75)(7, 77)(8, 62)(9, 79)(10, 74)(11, 76)(12, 64)(13, 65)(14, 83)(15, 84)(16, 66)(17, 85)(18, 68)(19, 87)(20, 71)(21, 72)(22, 73)(23, 89)(24, 90)(25, 82)(26, 78)(27, 81)(28, 80)(29, 88)(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) :: { ( 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, 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, 2, 10, 2, 10 ) } Outer automorphisms :: reflexible Dual of E12.498 Graph:: bipartite v = 2 e = 60 f = 36 degree seq :: [ 60^2 ] E12.498 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 30, 30}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y2, Y3^-1), Y2^5, Y2 * Y3^6, 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^-1 * Y1^-1)^30 ] Map:: R = (1, 31)(2, 32)(3, 33)(4, 34)(5, 35)(6, 36)(7, 37)(8, 38)(9, 39)(10, 40)(11, 41)(12, 42)(13, 43)(14, 44)(15, 45)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60)(61, 91, 62, 92, 66, 96, 71, 101, 64, 94)(63, 93, 67, 97, 74, 104, 80, 110, 70, 100)(65, 95, 68, 98, 75, 105, 81, 111, 72, 102)(69, 99, 76, 106, 84, 114, 88, 118, 79, 109)(73, 103, 77, 107, 85, 115, 89, 119, 82, 112)(78, 108, 83, 113, 86, 116, 90, 120, 87, 117) L = (1, 63)(2, 67)(3, 69)(4, 70)(5, 61)(6, 74)(7, 76)(8, 62)(9, 78)(10, 79)(11, 80)(12, 64)(13, 65)(14, 84)(15, 66)(16, 83)(17, 68)(18, 82)(19, 87)(20, 88)(21, 71)(22, 72)(23, 73)(24, 86)(25, 75)(26, 77)(27, 89)(28, 90)(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) :: { ( 60, 60 ), ( 60^10 ) } Outer automorphisms :: reflexible Dual of E12.497 Graph:: simple bipartite v = 36 e = 60 f = 2 degree seq :: [ 2^30, 10^6 ] E12.499 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 30, 30}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1^-1), Y3^5, (R * Y2 * Y3^-1)^2, Y3^-1 * Y1^6, (Y3 * Y2^-1)^5, (Y1^-1 * Y3^-1)^30 ] Map:: R = (1, 31, 2, 32, 6, 36, 14, 44, 20, 50, 10, 40, 3, 33, 7, 37, 15, 45, 24, 54, 27, 57, 19, 49, 9, 39, 17, 47, 25, 55, 30, 60, 29, 59, 23, 53, 13, 43, 18, 48, 26, 56, 28, 58, 22, 52, 12, 42, 5, 35, 8, 38, 16, 46, 21, 51, 11, 41, 4, 34)(61, 91)(62, 92)(63, 93)(64, 94)(65, 95)(66, 96)(67, 97)(68, 98)(69, 99)(70, 100)(71, 101)(72, 102)(73, 103)(74, 104)(75, 105)(76, 106)(77, 107)(78, 108)(79, 109)(80, 110)(81, 111)(82, 112)(83, 113)(84, 114)(85, 115)(86, 116)(87, 117)(88, 118)(89, 119)(90, 120) L = (1, 63)(2, 67)(3, 69)(4, 70)(5, 61)(6, 75)(7, 77)(8, 62)(9, 73)(10, 79)(11, 80)(12, 64)(13, 65)(14, 84)(15, 85)(16, 66)(17, 78)(18, 68)(19, 83)(20, 87)(21, 74)(22, 71)(23, 72)(24, 90)(25, 86)(26, 76)(27, 89)(28, 81)(29, 82)(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) :: { ( 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 E12.496 Graph:: bipartite v = 31 e = 60 f = 7 degree seq :: [ 2^30, 60 ] E12.500 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 30, 30}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1^-1), Y3^5, Y3^5, (R * Y2 * Y3^-1)^2, Y3^2 * Y1^-6, (Y3 * Y2^-1)^5, (Y1^-1 * Y3^-1)^30 ] Map:: R = (1, 31, 2, 32, 6, 36, 14, 44, 24, 54, 19, 49, 9, 39, 17, 47, 27, 57, 29, 59, 22, 52, 12, 42, 5, 35, 8, 38, 16, 46, 26, 56, 20, 50, 10, 40, 3, 33, 7, 37, 15, 45, 25, 55, 30, 60, 23, 53, 13, 43, 18, 48, 28, 58, 21, 51, 11, 41, 4, 34)(61, 91)(62, 92)(63, 93)(64, 94)(65, 95)(66, 96)(67, 97)(68, 98)(69, 99)(70, 100)(71, 101)(72, 102)(73, 103)(74, 104)(75, 105)(76, 106)(77, 107)(78, 108)(79, 109)(80, 110)(81, 111)(82, 112)(83, 113)(84, 114)(85, 115)(86, 116)(87, 117)(88, 118)(89, 119)(90, 120) L = (1, 63)(2, 67)(3, 69)(4, 70)(5, 61)(6, 75)(7, 77)(8, 62)(9, 73)(10, 79)(11, 80)(12, 64)(13, 65)(14, 85)(15, 87)(16, 66)(17, 78)(18, 68)(19, 83)(20, 84)(21, 86)(22, 71)(23, 72)(24, 90)(25, 89)(26, 74)(27, 88)(28, 76)(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) :: { ( 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 E12.495 Graph:: bipartite v = 31 e = 60 f = 7 degree seq :: [ 2^30, 60 ] E12.501 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 30, 30}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3, Y1), Y3^5, (R * Y2 * Y3^-1)^2, Y3^-2 * Y1^-6, (Y3 * Y2^-1)^5 ] Map:: R = (1, 31, 2, 32, 6, 36, 14, 44, 24, 54, 23, 53, 13, 43, 18, 48, 28, 58, 30, 60, 20, 50, 10, 40, 3, 33, 7, 37, 15, 45, 25, 55, 22, 52, 12, 42, 5, 35, 8, 38, 16, 46, 26, 56, 29, 59, 19, 49, 9, 39, 17, 47, 27, 57, 21, 51, 11, 41, 4, 34)(61, 91)(62, 92)(63, 93)(64, 94)(65, 95)(66, 96)(67, 97)(68, 98)(69, 99)(70, 100)(71, 101)(72, 102)(73, 103)(74, 104)(75, 105)(76, 106)(77, 107)(78, 108)(79, 109)(80, 110)(81, 111)(82, 112)(83, 113)(84, 114)(85, 115)(86, 116)(87, 117)(88, 118)(89, 119)(90, 120) L = (1, 63)(2, 67)(3, 69)(4, 70)(5, 61)(6, 75)(7, 77)(8, 62)(9, 73)(10, 79)(11, 80)(12, 64)(13, 65)(14, 85)(15, 87)(16, 66)(17, 78)(18, 68)(19, 83)(20, 89)(21, 90)(22, 71)(23, 72)(24, 82)(25, 81)(26, 74)(27, 88)(28, 76)(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) :: { ( 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 E12.494 Graph:: bipartite v = 31 e = 60 f = 7 degree seq :: [ 2^30, 60 ] E12.502 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 4, 16}) Quotient :: halfedge^2 Aut^+ = D32 (small group id <32, 18>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (R * Y1)^2, (Y3 * Y1^-1)^2, (Y2 * Y1^-1)^2, Y1^2 * Y2 * Y1^-1 * Y3, Y3 * Y1^-1 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2, (Y2 * Y1 * Y3)^4 ] Map:: non-degenerate R = (1, 34, 2, 38, 6, 44, 12, 47, 15, 52, 20, 57, 25, 59, 27, 64, 32, 61, 29, 56, 24, 54, 22, 49, 17, 42, 10, 45, 13, 37, 5, 33)(3, 41, 9, 48, 16, 50, 18, 55, 23, 60, 28, 62, 30, 63, 31, 58, 26, 53, 21, 51, 19, 46, 14, 40, 8, 36, 4, 43, 11, 39, 7, 35) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 11)(8, 15)(10, 18)(13, 16)(14, 20)(17, 23)(19, 25)(21, 27)(22, 28)(24, 30)(26, 32)(29, 31)(33, 36)(34, 40)(35, 42)(37, 43)(38, 46)(39, 45)(41, 49)(44, 51)(47, 53)(48, 54)(50, 56)(52, 58)(55, 61)(57, 63)(59, 62)(60, 64) local type(s) :: { ( 8^32 ) } Outer automorphisms :: reflexible Dual of E12.503 Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 32 f = 8 degree seq :: [ 32^2 ] E12.503 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 4, 16}) Quotient :: halfedge^2 Aut^+ = D32 (small group id <32, 18>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (Y2 * Y1)^2, (R * Y1)^2, (Y3 * Y1^-1)^2, Y1^4, Y1^-1 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3, (Y1^-1 * Y3 * Y2 * Y3 * Y2)^8 ] Map:: non-degenerate R = (1, 34, 2, 38, 6, 37, 5, 33)(3, 41, 9, 45, 13, 39, 7, 35)(4, 43, 11, 46, 14, 40, 8, 36)(10, 47, 15, 53, 21, 49, 17, 42)(12, 48, 16, 54, 22, 51, 19, 44)(18, 57, 25, 61, 29, 55, 23, 50)(20, 59, 27, 62, 30, 56, 24, 52)(26, 63, 31, 64, 32, 60, 28, 58) 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, 26)(27, 32)(30, 31)(33, 36)(34, 40)(35, 42)(37, 43)(38, 46)(39, 47)(41, 49)(44, 52)(45, 53)(48, 56)(50, 58)(51, 59)(54, 62)(55, 63)(57, 60)(61, 64) local type(s) :: { ( 32^8 ) } Outer automorphisms :: reflexible Dual of E12.502 Transitivity :: VT+ AT Graph:: bipartite v = 8 e = 32 f = 2 degree seq :: [ 8^8 ] E12.504 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 4, 16}) Quotient :: edge^2 Aut^+ = D32 (small group id <32, 18>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y3^-1 * Y1)^2, (R * Y3)^2, R * Y1 * R * Y2, (Y3 * Y2)^2, Y3^4, Y1 * Y2 * Y1 * Y3 * Y2 * Y1 * Y2 * Y1 * Y2, (Y3 * Y1 * Y2)^16 ] Map:: R = (1, 33, 4, 36, 12, 44, 5, 37)(2, 34, 7, 39, 16, 48, 8, 40)(3, 35, 10, 42, 20, 52, 11, 43)(6, 38, 14, 46, 24, 56, 15, 47)(9, 41, 18, 50, 28, 60, 19, 51)(13, 45, 22, 54, 30, 62, 23, 55)(17, 49, 26, 58, 32, 64, 27, 59)(21, 53, 29, 61, 31, 63, 25, 57)(65, 66)(67, 73)(68, 72)(69, 71)(70, 77)(74, 83)(75, 82)(76, 80)(78, 87)(79, 86)(81, 89)(84, 92)(85, 91)(88, 94)(90, 95)(93, 96)(97, 99)(98, 102)(100, 107)(101, 106)(103, 111)(104, 110)(105, 113)(108, 116)(109, 117)(112, 120)(114, 123)(115, 122)(118, 121)(119, 125)(124, 128)(126, 127) 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, 64 ), ( 64^8 ) } Outer automorphisms :: reflexible Dual of E12.507 Graph:: simple bipartite v = 40 e = 64 f = 2 degree seq :: [ 2^32, 8^8 ] E12.505 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 4, 16}) Quotient :: edge^2 Aut^+ = D32 (small group id <32, 18>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3^-1 * Y2)^2, (Y3 * Y1)^2, Y2 * Y3^-3 * Y1, Y3 * Y2 * Y1 * Y2 * Y1 * Y2 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2, Y1 * Y3^-1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 ] Map:: R = (1, 33, 4, 36, 12, 44, 6, 38, 15, 47, 22, 54, 20, 52, 27, 59, 32, 64, 30, 62, 23, 55, 25, 57, 18, 50, 9, 41, 13, 45, 5, 37)(2, 34, 7, 39, 11, 43, 3, 35, 10, 42, 19, 51, 17, 49, 24, 56, 31, 63, 29, 61, 26, 58, 28, 60, 21, 53, 14, 46, 16, 48, 8, 40)(65, 66)(67, 73)(68, 72)(69, 71)(70, 78)(74, 82)(75, 77)(76, 80)(79, 85)(81, 87)(83, 89)(84, 90)(86, 92)(88, 94)(91, 93)(95, 96)(97, 99)(98, 102)(100, 107)(101, 106)(103, 108)(104, 111)(105, 113)(109, 115)(110, 116)(112, 118)(114, 120)(117, 123)(119, 125)(121, 127)(122, 126)(124, 128) 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, 16 ), ( 16^32 ) } Outer automorphisms :: reflexible Dual of E12.506 Graph:: simple bipartite v = 34 e = 64 f = 8 degree seq :: [ 2^32, 32^2 ] E12.506 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 4, 16}) Quotient :: loop^2 Aut^+ = D32 (small group id <32, 18>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y3^-1 * Y1)^2, (R * Y3)^2, R * Y1 * R * Y2, (Y3 * Y2)^2, Y3^4, Y1 * Y2 * Y1 * Y3 * Y2 * Y1 * Y2 * Y1 * Y2, (Y3 * Y1 * Y2)^16 ] Map:: R = (1, 33, 65, 97, 4, 36, 68, 100, 12, 44, 76, 108, 5, 37, 69, 101)(2, 34, 66, 98, 7, 39, 71, 103, 16, 48, 80, 112, 8, 40, 72, 104)(3, 35, 67, 99, 10, 42, 74, 106, 20, 52, 84, 116, 11, 43, 75, 107)(6, 38, 70, 102, 14, 46, 78, 110, 24, 56, 88, 120, 15, 47, 79, 111)(9, 41, 73, 105, 18, 50, 82, 114, 28, 60, 92, 124, 19, 51, 83, 115)(13, 45, 77, 109, 22, 54, 86, 118, 30, 62, 94, 126, 23, 55, 87, 119)(17, 49, 81, 113, 26, 58, 90, 122, 32, 64, 96, 128, 27, 59, 91, 123)(21, 53, 85, 117, 29, 61, 93, 125, 31, 63, 95, 127, 25, 57, 89, 121) L = (1, 34)(2, 33)(3, 41)(4, 40)(5, 39)(6, 45)(7, 37)(8, 36)(9, 35)(10, 51)(11, 50)(12, 48)(13, 38)(14, 55)(15, 54)(16, 44)(17, 57)(18, 43)(19, 42)(20, 60)(21, 59)(22, 47)(23, 46)(24, 62)(25, 49)(26, 63)(27, 53)(28, 52)(29, 64)(30, 56)(31, 58)(32, 61)(65, 99)(66, 102)(67, 97)(68, 107)(69, 106)(70, 98)(71, 111)(72, 110)(73, 113)(74, 101)(75, 100)(76, 116)(77, 117)(78, 104)(79, 103)(80, 120)(81, 105)(82, 123)(83, 122)(84, 108)(85, 109)(86, 121)(87, 125)(88, 112)(89, 118)(90, 115)(91, 114)(92, 128)(93, 119)(94, 127)(95, 126)(96, 124) local type(s) :: { ( 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32 ) } Outer automorphisms :: reflexible Dual of E12.505 Transitivity :: VT+ Graph:: bipartite v = 8 e = 64 f = 34 degree seq :: [ 16^8 ] E12.507 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 4, 16}) Quotient :: loop^2 Aut^+ = D32 (small group id <32, 18>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3^-1 * Y2)^2, (Y3 * Y1)^2, Y2 * Y3^-3 * Y1, Y3 * Y2 * Y1 * Y2 * Y1 * Y2 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2, Y1 * Y3^-1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 ] Map:: R = (1, 33, 65, 97, 4, 36, 68, 100, 12, 44, 76, 108, 6, 38, 70, 102, 15, 47, 79, 111, 22, 54, 86, 118, 20, 52, 84, 116, 27, 59, 91, 123, 32, 64, 96, 128, 30, 62, 94, 126, 23, 55, 87, 119, 25, 57, 89, 121, 18, 50, 82, 114, 9, 41, 73, 105, 13, 45, 77, 109, 5, 37, 69, 101)(2, 34, 66, 98, 7, 39, 71, 103, 11, 43, 75, 107, 3, 35, 67, 99, 10, 42, 74, 106, 19, 51, 83, 115, 17, 49, 81, 113, 24, 56, 88, 120, 31, 63, 95, 127, 29, 61, 93, 125, 26, 58, 90, 122, 28, 60, 92, 124, 21, 53, 85, 117, 14, 46, 78, 110, 16, 48, 80, 112, 8, 40, 72, 104) L = (1, 34)(2, 33)(3, 41)(4, 40)(5, 39)(6, 46)(7, 37)(8, 36)(9, 35)(10, 50)(11, 45)(12, 48)(13, 43)(14, 38)(15, 53)(16, 44)(17, 55)(18, 42)(19, 57)(20, 58)(21, 47)(22, 60)(23, 49)(24, 62)(25, 51)(26, 52)(27, 61)(28, 54)(29, 59)(30, 56)(31, 64)(32, 63)(65, 99)(66, 102)(67, 97)(68, 107)(69, 106)(70, 98)(71, 108)(72, 111)(73, 113)(74, 101)(75, 100)(76, 103)(77, 115)(78, 116)(79, 104)(80, 118)(81, 105)(82, 120)(83, 109)(84, 110)(85, 123)(86, 112)(87, 125)(88, 114)(89, 127)(90, 126)(91, 117)(92, 128)(93, 119)(94, 122)(95, 121)(96, 124) 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 E12.504 Transitivity :: VT+ Graph:: bipartite v = 2 e = 64 f = 40 degree seq :: [ 64^2 ] E12.508 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = QD32 (small group id <32, 19>) Aut = (C2 x D16) : C2 (small group id <64, 190>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y3^-2, (Y1 * Y2)^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 6, 38)(4, 36, 9, 41)(5, 37, 10, 42)(7, 39, 11, 43)(8, 40, 12, 44)(13, 45, 17, 49)(14, 46, 18, 50)(15, 47, 19, 51)(16, 48, 20, 52)(21, 53, 25, 57)(22, 54, 26, 58)(23, 55, 27, 59)(24, 56, 28, 60)(29, 61, 32, 64)(30, 62, 31, 63)(65, 97, 67, 99)(66, 98, 70, 102)(68, 100, 69, 101)(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)(91, 123, 92, 124)(93, 125, 94, 126)(95, 127, 96, 128) L = (1, 68)(2, 71)(3, 69)(4, 67)(5, 65)(6, 72)(7, 70)(8, 66)(9, 77)(10, 78)(11, 79)(12, 80)(13, 74)(14, 73)(15, 76)(16, 75)(17, 85)(18, 86)(19, 87)(20, 88)(21, 82)(22, 81)(23, 84)(24, 83)(25, 93)(26, 94)(27, 95)(28, 96)(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 ) } Outer automorphisms :: reflexible Dual of E12.517 Graph:: simple bipartite v = 32 e = 64 f = 10 degree seq :: [ 4^32 ] E12.509 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = D32 (small group id <32, 18>) Aut = C2 x D32 (small group id <64, 186>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y3, Y2), (R * Y3)^2, (R * Y1)^2, Y2^4, (Y2 * Y1)^2, (Y3^-1 * Y1)^2, (R * Y2)^2, Y2 * Y3^4, 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 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 9, 41)(4, 36, 10, 42)(5, 37, 7, 39)(6, 38, 8, 40)(11, 43, 18, 50)(12, 44, 23, 55)(13, 45, 22, 54)(14, 46, 24, 56)(15, 47, 20, 52)(16, 48, 19, 51)(17, 49, 21, 53)(25, 57, 30, 62)(26, 58, 29, 61)(27, 59, 32, 64)(28, 60, 31, 63)(65, 97, 67, 99, 75, 107, 69, 101)(66, 98, 71, 103, 82, 114, 73, 105)(68, 100, 76, 108, 89, 121, 79, 111)(70, 102, 77, 109, 90, 122, 80, 112)(72, 104, 83, 115, 93, 125, 86, 118)(74, 106, 84, 116, 94, 126, 87, 119)(78, 110, 81, 113, 91, 123, 92, 124)(85, 117, 88, 120, 95, 127, 96, 128) L = (1, 68)(2, 72)(3, 76)(4, 78)(5, 79)(6, 65)(7, 83)(8, 85)(9, 86)(10, 66)(11, 89)(12, 81)(13, 67)(14, 80)(15, 92)(16, 69)(17, 70)(18, 93)(19, 88)(20, 71)(21, 87)(22, 96)(23, 73)(24, 74)(25, 91)(26, 75)(27, 77)(28, 90)(29, 95)(30, 82)(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) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32 ) } Outer automorphisms :: reflexible Dual of E12.514 Graph:: simple bipartite v = 24 e = 64 f = 18 degree seq :: [ 4^16, 8^8 ] E12.510 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = D32 (small group id <32, 18>) Aut = C2 x D32 (small group id <64, 186>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y2, Y3^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y3^-1 * Y1)^2, (Y2 * Y1)^2, Y2^4, Y2^-1 * Y3^4, Y2^-2 * Y3^-1 * Y2^-2 * Y3 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 9, 41)(4, 36, 10, 42)(5, 37, 7, 39)(6, 38, 8, 40)(11, 43, 18, 50)(12, 44, 23, 55)(13, 45, 22, 54)(14, 46, 24, 56)(15, 47, 20, 52)(16, 48, 19, 51)(17, 49, 21, 53)(25, 57, 30, 62)(26, 58, 29, 61)(27, 59, 32, 64)(28, 60, 31, 63)(65, 97, 67, 99, 75, 107, 69, 101)(66, 98, 71, 103, 82, 114, 73, 105)(68, 100, 76, 108, 89, 121, 79, 111)(70, 102, 77, 109, 90, 122, 80, 112)(72, 104, 83, 115, 93, 125, 86, 118)(74, 106, 84, 116, 94, 126, 87, 119)(78, 110, 91, 123, 92, 124, 81, 113)(85, 117, 95, 127, 96, 128, 88, 120) L = (1, 68)(2, 72)(3, 76)(4, 78)(5, 79)(6, 65)(7, 83)(8, 85)(9, 86)(10, 66)(11, 89)(12, 91)(13, 67)(14, 77)(15, 81)(16, 69)(17, 70)(18, 93)(19, 95)(20, 71)(21, 84)(22, 88)(23, 73)(24, 74)(25, 92)(26, 75)(27, 90)(28, 80)(29, 96)(30, 82)(31, 94)(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) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32 ) } Outer automorphisms :: reflexible Dual of E12.513 Graph:: simple bipartite v = 24 e = 64 f = 18 degree seq :: [ 4^16, 8^8 ] E12.511 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = QD32 (small group id <32, 19>) Aut = (C2 x D16) : C2 (small group id <64, 190>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, Y2 * Y1 * Y2, (Y3 * Y1)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3)^2, Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 5, 37)(4, 36, 6, 38)(7, 39, 10, 42)(8, 40, 9, 41)(11, 43, 12, 44)(13, 45, 14, 46)(15, 47, 16, 48)(17, 49, 18, 50)(19, 51, 20, 52)(21, 53, 22, 54)(23, 55, 24, 56)(25, 57, 26, 58)(27, 59, 28, 60)(29, 61, 30, 62)(31, 63, 32, 64)(65, 97, 67, 99, 66, 98, 69, 101)(68, 100, 72, 104, 70, 102, 73, 105)(71, 103, 75, 107, 74, 106, 76, 108)(77, 109, 81, 113, 78, 110, 82, 114)(79, 111, 83, 115, 80, 112, 84, 116)(85, 117, 89, 121, 86, 118, 90, 122)(87, 119, 91, 123, 88, 120, 92, 124)(93, 125, 96, 128, 94, 126, 95, 127) L = (1, 68)(2, 70)(3, 71)(4, 65)(5, 74)(6, 66)(7, 67)(8, 77)(9, 78)(10, 69)(11, 79)(12, 80)(13, 72)(14, 73)(15, 75)(16, 76)(17, 85)(18, 86)(19, 87)(20, 88)(21, 81)(22, 82)(23, 83)(24, 84)(25, 93)(26, 94)(27, 95)(28, 96)(29, 89)(30, 90)(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) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32 ) } Outer automorphisms :: reflexible Dual of E12.516 Graph:: bipartite v = 24 e = 64 f = 18 degree seq :: [ 4^16, 8^8 ] E12.512 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = QD32 (small group id <32, 19>) Aut = (C2 x D16) : C2 (small group id <64, 190>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, (Y1 * Y3)^2, Y2^4, Y1 * Y2^2 * Y3, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3)^2, Y2^-1 * R * Y1 * Y3 * R * Y2^-1, Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y3 * Y2 * Y1 * Y2 * Y1, Y2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 9, 41)(4, 36, 7, 39)(5, 37, 10, 42)(6, 38, 11, 43)(8, 40, 12, 44)(13, 45, 17, 49)(14, 46, 18, 50)(15, 47, 19, 51)(16, 48, 20, 52)(21, 53, 25, 57)(22, 54, 26, 58)(23, 55, 27, 59)(24, 56, 28, 60)(29, 61, 32, 64)(30, 62, 31, 63)(65, 97, 67, 99, 71, 103, 69, 101)(66, 98, 70, 102, 68, 100, 72, 104)(73, 105, 77, 109, 74, 106, 78, 110)(75, 107, 79, 111, 76, 108, 80, 112)(81, 113, 85, 117, 82, 114, 86, 118)(83, 115, 87, 119, 84, 116, 88, 120)(89, 121, 93, 125, 90, 122, 94, 126)(91, 123, 95, 127, 92, 124, 96, 128) L = (1, 68)(2, 71)(3, 74)(4, 65)(5, 73)(6, 76)(7, 66)(8, 75)(9, 69)(10, 67)(11, 72)(12, 70)(13, 82)(14, 81)(15, 84)(16, 83)(17, 78)(18, 77)(19, 80)(20, 79)(21, 90)(22, 89)(23, 92)(24, 91)(25, 86)(26, 85)(27, 88)(28, 87)(29, 95)(30, 96)(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) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32 ) } Outer automorphisms :: reflexible Dual of E12.515 Graph:: bipartite v = 24 e = 64 f = 18 degree seq :: [ 4^16, 8^8 ] E12.513 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = D32 (small group id <32, 18>) Aut = C2 x D32 (small group id <64, 186>) |r| :: 2 Presentation :: [ Y2^2, R^2, Y3^2 * Y1^-1 * Y3, (R * Y1)^2, (Y3 * Y2)^2, (Y2 * Y1)^2, (Y3^-1, Y1^-1), (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y1^-5, (Y1^3 * Y3^-1)^2 ] Map:: non-degenerate R = (1, 33, 2, 34, 7, 39, 17, 49, 16, 48, 6, 38, 10, 42, 20, 52, 28, 60, 26, 58, 14, 46, 4, 36, 9, 41, 19, 51, 15, 47, 5, 37)(3, 35, 11, 43, 23, 55, 30, 62, 22, 54, 13, 45, 25, 57, 31, 63, 32, 64, 29, 61, 21, 53, 12, 44, 24, 56, 27, 59, 18, 50, 8, 40)(65, 97, 67, 99)(66, 98, 72, 104)(68, 100, 77, 109)(69, 101, 75, 107)(70, 102, 76, 108)(71, 103, 82, 114)(73, 105, 86, 118)(74, 106, 85, 117)(78, 110, 89, 121)(79, 111, 87, 119)(80, 112, 88, 120)(81, 113, 91, 123)(83, 115, 94, 126)(84, 116, 93, 125)(90, 122, 95, 127)(92, 124, 96, 128) L = (1, 68)(2, 73)(3, 76)(4, 74)(5, 78)(6, 65)(7, 83)(8, 85)(9, 84)(10, 66)(11, 88)(12, 89)(13, 67)(14, 70)(15, 90)(16, 69)(17, 79)(18, 93)(19, 92)(20, 71)(21, 77)(22, 72)(23, 91)(24, 95)(25, 75)(26, 80)(27, 96)(28, 81)(29, 86)(30, 82)(31, 87)(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) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 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 E12.510 Graph:: bipartite v = 18 e = 64 f = 24 degree seq :: [ 4^16, 32^2 ] E12.514 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = D32 (small group id <32, 18>) Aut = C2 x D32 (small group id <64, 186>) |r| :: 2 Presentation :: [ Y2^2, R^2, Y3 * Y1^-3, (R * Y1)^2, (Y3 * Y2)^2, (Y3^-1, Y1^-1), (Y2 * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y3 * Y1 * Y3^4 ] Map:: non-degenerate R = (1, 33, 2, 34, 7, 39, 4, 36, 9, 41, 18, 50, 14, 46, 21, 53, 28, 60, 26, 58, 16, 48, 22, 54, 15, 47, 6, 38, 10, 42, 5, 37)(3, 35, 11, 43, 19, 51, 12, 44, 23, 55, 29, 61, 24, 56, 31, 63, 32, 64, 30, 62, 25, 57, 27, 59, 20, 52, 13, 45, 17, 49, 8, 40)(65, 97, 67, 99)(66, 98, 72, 104)(68, 100, 77, 109)(69, 101, 75, 107)(70, 102, 76, 108)(71, 103, 81, 113)(73, 105, 84, 116)(74, 106, 83, 115)(78, 110, 89, 121)(79, 111, 87, 119)(80, 112, 88, 120)(82, 114, 91, 123)(85, 117, 94, 126)(86, 118, 93, 125)(90, 122, 95, 127)(92, 124, 96, 128) L = (1, 68)(2, 73)(3, 76)(4, 78)(5, 71)(6, 65)(7, 82)(8, 83)(9, 85)(10, 66)(11, 87)(12, 88)(13, 67)(14, 90)(15, 69)(16, 70)(17, 75)(18, 92)(19, 93)(20, 72)(21, 80)(22, 74)(23, 95)(24, 94)(25, 77)(26, 79)(27, 81)(28, 86)(29, 96)(30, 84)(31, 89)(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) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 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 E12.509 Graph:: bipartite v = 18 e = 64 f = 24 degree seq :: [ 4^16, 32^2 ] E12.515 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = QD32 (small group id <32, 19>) Aut = (C2 x D16) : C2 (small group id <64, 190>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (R * Y2)^2, (R * Y1)^2, (Y3 * Y2)^2, (R * Y3)^2, Y1^-1 * Y2 * Y1 * Y2, Y2 * Y1 * Y3 * Y1 * Y3, Y1^8 * Y2 ] Map:: non-degenerate R = (1, 33, 2, 34, 6, 38, 15, 47, 23, 55, 27, 59, 19, 51, 10, 42, 3, 35, 7, 39, 16, 48, 24, 56, 30, 62, 22, 54, 14, 46, 5, 37)(4, 36, 11, 43, 20, 52, 28, 60, 32, 64, 25, 57, 18, 50, 8, 40, 9, 41, 13, 45, 21, 53, 29, 61, 31, 63, 26, 58, 17, 49, 12, 44)(65, 97, 67, 99)(66, 98, 71, 103)(68, 100, 73, 105)(69, 101, 74, 106)(70, 102, 80, 112)(72, 104, 76, 108)(75, 107, 77, 109)(78, 110, 83, 115)(79, 111, 88, 120)(81, 113, 82, 114)(84, 116, 85, 117)(86, 118, 91, 123)(87, 119, 94, 126)(89, 121, 90, 122)(92, 124, 93, 125)(95, 127, 96, 128) L = (1, 68)(2, 72)(3, 73)(4, 65)(5, 77)(6, 81)(7, 76)(8, 66)(9, 67)(10, 75)(11, 74)(12, 71)(13, 69)(14, 84)(15, 89)(16, 82)(17, 70)(18, 80)(19, 85)(20, 78)(21, 83)(22, 93)(23, 95)(24, 90)(25, 79)(26, 88)(27, 92)(28, 91)(29, 86)(30, 96)(31, 87)(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) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 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 E12.512 Graph:: bipartite v = 18 e = 64 f = 24 degree seq :: [ 4^16, 32^2 ] E12.516 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = QD32 (small group id <32, 19>) Aut = (C2 x D16) : C2 (small group id <64, 190>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y3)^2, Y1^-1 * Y2 * Y1^-1 * Y3, (R * Y1)^2, Y3 * Y2 * Y1^8, Y1^-1 * Y3 * Y1^3 * Y3 * Y1^-4 ] Map:: non-degenerate R = (1, 33, 2, 34, 6, 38, 13, 45, 21, 53, 29, 61, 26, 58, 18, 50, 10, 42, 16, 48, 24, 56, 32, 64, 28, 60, 20, 52, 12, 44, 5, 37)(3, 35, 9, 41, 17, 49, 25, 57, 31, 63, 22, 54, 15, 47, 7, 39, 4, 36, 11, 43, 19, 51, 27, 59, 30, 62, 23, 55, 14, 46, 8, 40)(65, 97, 67, 99)(66, 98, 71, 103)(68, 100, 74, 106)(69, 101, 75, 107)(70, 102, 78, 110)(72, 104, 80, 112)(73, 105, 82, 114)(76, 108, 81, 113)(77, 109, 86, 118)(79, 111, 88, 120)(83, 115, 90, 122)(84, 116, 91, 123)(85, 117, 94, 126)(87, 119, 96, 128)(89, 121, 93, 125)(92, 124, 95, 127) L = (1, 68)(2, 72)(3, 74)(4, 65)(5, 73)(6, 79)(7, 80)(8, 66)(9, 69)(10, 67)(11, 82)(12, 83)(13, 87)(14, 88)(15, 70)(16, 71)(17, 90)(18, 75)(19, 76)(20, 89)(21, 95)(22, 96)(23, 77)(24, 78)(25, 84)(26, 81)(27, 93)(28, 94)(29, 91)(30, 92)(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) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 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 E12.511 Graph:: bipartite v = 18 e = 64 f = 24 degree seq :: [ 4^16, 32^2 ] E12.517 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = QD32 (small group id <32, 19>) Aut = (C2 x D16) : C2 (small group id <64, 190>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-1, (Y3 * Y2^-1)^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, (Y1^-1 * Y2^-1)^2, Y1^4, (Y2^-1 * Y1)^2, (R * Y2 * Y3^-1)^2, Y2^-2 * R * Y2^2 * R, Y1^-1 * Y2^-8 * Y1^-1 ] Map:: non-degenerate R = (1, 33, 2, 34, 6, 38, 4, 36)(3, 35, 9, 41, 13, 45, 8, 40)(5, 37, 11, 43, 14, 46, 7, 39)(10, 42, 16, 48, 21, 53, 17, 49)(12, 44, 15, 47, 22, 54, 19, 51)(18, 50, 25, 57, 29, 61, 24, 56)(20, 52, 27, 59, 30, 62, 23, 55)(26, 58, 32, 64, 28, 60, 31, 63)(65, 97, 67, 99, 74, 106, 82, 114, 90, 122, 94, 126, 86, 118, 78, 110, 70, 102, 77, 109, 85, 117, 93, 125, 92, 124, 84, 116, 76, 108, 69, 101)(66, 98, 71, 103, 79, 111, 87, 119, 95, 127, 89, 121, 81, 113, 73, 105, 68, 100, 75, 107, 83, 115, 91, 123, 96, 128, 88, 120, 80, 112, 72, 104) L = (1, 66)(2, 70)(3, 73)(4, 65)(5, 75)(6, 68)(7, 69)(8, 67)(9, 77)(10, 80)(11, 78)(12, 79)(13, 72)(14, 71)(15, 86)(16, 85)(17, 74)(18, 89)(19, 76)(20, 91)(21, 81)(22, 83)(23, 84)(24, 82)(25, 93)(26, 96)(27, 94)(28, 95)(29, 88)(30, 87)(31, 90)(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) :: { ( 4^8 ), ( 4^32 ) } Outer automorphisms :: reflexible Dual of E12.508 Graph:: bipartite v = 10 e = 64 f = 32 degree seq :: [ 8^8, 32^2 ] E12.518 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 32, 32}) Quotient :: edge Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1, T1^-1), T2^8 * T1, (T1^-1 * T2^-1)^32 ] Map:: non-degenerate R = (1, 3, 9, 17, 25, 27, 19, 11, 4, 10, 18, 26, 32, 30, 22, 14, 6, 13, 21, 29, 31, 24, 16, 8, 2, 7, 15, 23, 28, 20, 12, 5)(33, 34, 38, 36)(35, 39, 45, 42)(37, 40, 46, 43)(41, 47, 53, 50)(44, 48, 54, 51)(49, 55, 61, 58)(52, 56, 62, 59)(57, 60, 63, 64) L = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 64^4 ), ( 64^32 ) } Outer automorphisms :: reflexible Dual of E12.522 Transitivity :: ET+ Graph:: bipartite v = 9 e = 32 f = 1 degree seq :: [ 4^8, 32 ] E12.519 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 32, 32}) Quotient :: edge Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1, T1^-1), T2^8 * T1^-1, (T1^-1 * T2^-1)^32 ] Map:: non-degenerate R = (1, 3, 9, 17, 25, 24, 16, 8, 2, 7, 15, 23, 31, 30, 22, 14, 6, 13, 21, 29, 32, 27, 19, 11, 4, 10, 18, 26, 28, 20, 12, 5)(33, 34, 38, 36)(35, 39, 45, 42)(37, 40, 46, 43)(41, 47, 53, 50)(44, 48, 54, 51)(49, 55, 61, 58)(52, 56, 62, 59)(57, 63, 64, 60) L = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 64^4 ), ( 64^32 ) } Outer automorphisms :: reflexible Dual of E12.521 Transitivity :: ET+ Graph:: bipartite v = 9 e = 32 f = 1 degree seq :: [ 4^8, 32 ] E12.520 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 32, 32}) Quotient :: edge Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1), T2^4 * T1^4, T2^5 * T1^-3, T1^-7 * T2 ] Map:: non-degenerate R = (1, 3, 9, 19, 28, 14, 27, 24, 12, 4, 10, 20, 30, 16, 6, 15, 29, 23, 11, 21, 32, 18, 8, 2, 7, 17, 31, 22, 26, 25, 13, 5)(33, 34, 38, 46, 58, 53, 42, 35, 39, 47, 59, 57, 64, 52, 41, 49, 61, 56, 45, 50, 62, 51, 63, 55, 44, 37, 40, 48, 60, 54, 43, 36) L = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64) local type(s) :: { ( 8^32 ) } Outer automorphisms :: reflexible Dual of E12.523 Transitivity :: ET+ Graph:: bipartite v = 2 e = 32 f = 8 degree seq :: [ 32^2 ] E12.521 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 32, 32}) Quotient :: loop Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1, T1^-1), T2^8 * T1, (T1^-1 * T2^-1)^32 ] Map:: non-degenerate R = (1, 33, 3, 35, 9, 41, 17, 49, 25, 57, 27, 59, 19, 51, 11, 43, 4, 36, 10, 42, 18, 50, 26, 58, 32, 64, 30, 62, 22, 54, 14, 46, 6, 38, 13, 45, 21, 53, 29, 61, 31, 63, 24, 56, 16, 48, 8, 40, 2, 34, 7, 39, 15, 47, 23, 55, 28, 60, 20, 52, 12, 44, 5, 37) L = (1, 34)(2, 38)(3, 39)(4, 33)(5, 40)(6, 36)(7, 45)(8, 46)(9, 47)(10, 35)(11, 37)(12, 48)(13, 42)(14, 43)(15, 53)(16, 54)(17, 55)(18, 41)(19, 44)(20, 56)(21, 50)(22, 51)(23, 61)(24, 62)(25, 60)(26, 49)(27, 52)(28, 63)(29, 58)(30, 59)(31, 64)(32, 57) 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 ) } Outer automorphisms :: reflexible Dual of E12.519 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 32 f = 9 degree seq :: [ 64 ] E12.522 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 32, 32}) Quotient :: loop Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1, T1^-1), T2^8 * T1^-1, (T1^-1 * T2^-1)^32 ] Map:: non-degenerate R = (1, 33, 3, 35, 9, 41, 17, 49, 25, 57, 24, 56, 16, 48, 8, 40, 2, 34, 7, 39, 15, 47, 23, 55, 31, 63, 30, 62, 22, 54, 14, 46, 6, 38, 13, 45, 21, 53, 29, 61, 32, 64, 27, 59, 19, 51, 11, 43, 4, 36, 10, 42, 18, 50, 26, 58, 28, 60, 20, 52, 12, 44, 5, 37) L = (1, 34)(2, 38)(3, 39)(4, 33)(5, 40)(6, 36)(7, 45)(8, 46)(9, 47)(10, 35)(11, 37)(12, 48)(13, 42)(14, 43)(15, 53)(16, 54)(17, 55)(18, 41)(19, 44)(20, 56)(21, 50)(22, 51)(23, 61)(24, 62)(25, 63)(26, 49)(27, 52)(28, 57)(29, 58)(30, 59)(31, 64)(32, 60) 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 ) } Outer automorphisms :: reflexible Dual of E12.518 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 32 f = 9 degree seq :: [ 64 ] E12.523 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 32, 32}) Quotient :: loop Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, T2^4, (F * T2)^2, (T2^-1, T1^-1), T2 * T1^8, T1^2 * T2^-2 * T1^-3 * T2^-2 * T1, (T1^-1 * T2^-1)^32 ] Map:: non-degenerate R = (1, 33, 3, 35, 9, 41, 5, 37)(2, 34, 7, 39, 16, 48, 8, 40)(4, 36, 10, 42, 17, 49, 12, 44)(6, 38, 14, 46, 24, 56, 15, 47)(11, 43, 18, 50, 25, 57, 20, 52)(13, 45, 22, 54, 30, 62, 23, 55)(19, 51, 26, 58, 31, 63, 28, 60)(21, 53, 27, 59, 32, 64, 29, 61) L = (1, 34)(2, 38)(3, 39)(4, 33)(5, 40)(6, 45)(7, 46)(8, 47)(9, 48)(10, 35)(11, 36)(12, 37)(13, 53)(14, 54)(15, 55)(16, 56)(17, 41)(18, 42)(19, 43)(20, 44)(21, 60)(22, 59)(23, 61)(24, 62)(25, 49)(26, 50)(27, 51)(28, 52)(29, 63)(30, 64)(31, 57)(32, 58) local type(s) :: { ( 32^8 ) } Outer automorphisms :: reflexible Dual of E12.520 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 8 e = 32 f = 2 degree seq :: [ 8^8 ] E12.524 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 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^-1, (R * Y1)^2, Y1^4, (R * Y2)^2, (Y2, Y1^-1), (R * Y3)^2, (Y3^-1, Y2^-1), Y2^-8 * 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 ] Map:: R = (1, 33, 2, 34, 6, 38, 4, 36)(3, 35, 7, 39, 13, 45, 10, 42)(5, 37, 8, 40, 14, 46, 11, 43)(9, 41, 15, 47, 21, 53, 18, 50)(12, 44, 16, 48, 22, 54, 19, 51)(17, 49, 23, 55, 29, 61, 26, 58)(20, 52, 24, 56, 30, 62, 27, 59)(25, 57, 31, 63, 32, 64, 28, 60)(65, 97, 67, 99, 73, 105, 81, 113, 89, 121, 88, 120, 80, 112, 72, 104, 66, 98, 71, 103, 79, 111, 87, 119, 95, 127, 94, 126, 86, 118, 78, 110, 70, 102, 77, 109, 85, 117, 93, 125, 96, 128, 91, 123, 83, 115, 75, 107, 68, 100, 74, 106, 82, 114, 90, 122, 92, 124, 84, 116, 76, 108, 69, 101) L = (1, 68)(2, 65)(3, 74)(4, 70)(5, 75)(6, 66)(7, 67)(8, 69)(9, 82)(10, 77)(11, 78)(12, 83)(13, 71)(14, 72)(15, 73)(16, 76)(17, 90)(18, 85)(19, 86)(20, 91)(21, 79)(22, 80)(23, 81)(24, 84)(25, 92)(26, 93)(27, 94)(28, 96)(29, 87)(30, 88)(31, 89)(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) :: { ( 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 E12.528 Graph:: bipartite v = 9 e = 64 f = 33 degree seq :: [ 8^8, 64 ] E12.525 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 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^-1, Y1^4, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y3^-1, Y2^-1), (Y2, Y1^-1), Y2^8 * 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 ] Map:: R = (1, 33, 2, 34, 6, 38, 4, 36)(3, 35, 7, 39, 13, 45, 10, 42)(5, 37, 8, 40, 14, 46, 11, 43)(9, 41, 15, 47, 21, 53, 18, 50)(12, 44, 16, 48, 22, 54, 19, 51)(17, 49, 23, 55, 29, 61, 26, 58)(20, 52, 24, 56, 30, 62, 27, 59)(25, 57, 28, 60, 31, 63, 32, 64)(65, 97, 67, 99, 73, 105, 81, 113, 89, 121, 91, 123, 83, 115, 75, 107, 68, 100, 74, 106, 82, 114, 90, 122, 96, 128, 94, 126, 86, 118, 78, 110, 70, 102, 77, 109, 85, 117, 93, 125, 95, 127, 88, 120, 80, 112, 72, 104, 66, 98, 71, 103, 79, 111, 87, 119, 92, 124, 84, 116, 76, 108, 69, 101) L = (1, 68)(2, 65)(3, 74)(4, 70)(5, 75)(6, 66)(7, 67)(8, 69)(9, 82)(10, 77)(11, 78)(12, 83)(13, 71)(14, 72)(15, 73)(16, 76)(17, 90)(18, 85)(19, 86)(20, 91)(21, 79)(22, 80)(23, 81)(24, 84)(25, 96)(26, 93)(27, 94)(28, 89)(29, 87)(30, 88)(31, 92)(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) :: { ( 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 E12.529 Graph:: bipartite v = 9 e = 64 f = 33 degree seq :: [ 8^8, 64 ] E12.526 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 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^-1, (R * Y1)^2, R * Y2 * R * Y3, (Y2^-1, Y1^-1), Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1^2, Y2^4 * Y1^4, Y2^3 * Y1^-5, Y2^6 * Y1^-1 * Y2, (Y3^-1 * Y1^-1)^4 ] Map:: R = (1, 33, 2, 34, 6, 38, 14, 46, 26, 58, 19, 51, 31, 63, 23, 55, 12, 44, 5, 37, 8, 40, 16, 48, 28, 60, 20, 52, 9, 41, 17, 49, 29, 61, 24, 56, 13, 45, 18, 50, 30, 62, 21, 53, 10, 42, 3, 35, 7, 39, 15, 47, 27, 59, 25, 57, 32, 64, 22, 54, 11, 43, 4, 36)(65, 97, 67, 99, 73, 105, 83, 115, 96, 128, 82, 114, 72, 104, 66, 98, 71, 103, 81, 113, 95, 127, 86, 118, 94, 126, 80, 112, 70, 102, 79, 111, 93, 125, 87, 119, 75, 107, 85, 117, 92, 124, 78, 110, 91, 123, 88, 120, 76, 108, 68, 100, 74, 106, 84, 116, 90, 122, 89, 121, 77, 109, 69, 101) L = (1, 67)(2, 71)(3, 73)(4, 74)(5, 65)(6, 79)(7, 81)(8, 66)(9, 83)(10, 84)(11, 85)(12, 68)(13, 69)(14, 91)(15, 93)(16, 70)(17, 95)(18, 72)(19, 96)(20, 90)(21, 92)(22, 94)(23, 75)(24, 76)(25, 77)(26, 89)(27, 88)(28, 78)(29, 87)(30, 80)(31, 86)(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) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 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 E12.527 Graph:: bipartite v = 2 e = 64 f = 40 degree seq :: [ 64^2 ] E12.527 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y2, Y3^-1), Y2^4, Y2 * Y3^8, 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^-1 * Y1^-1)^32 ] Map:: R = (1, 33)(2, 34)(3, 35)(4, 36)(5, 37)(6, 38)(7, 39)(8, 40)(9, 41)(10, 42)(11, 43)(12, 44)(13, 45)(14, 46)(15, 47)(16, 48)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22, 54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32, 64)(65, 97, 66, 98, 70, 102, 68, 100)(67, 99, 71, 103, 77, 109, 74, 106)(69, 101, 72, 104, 78, 110, 75, 107)(73, 105, 79, 111, 85, 117, 82, 114)(76, 108, 80, 112, 86, 118, 83, 115)(81, 113, 87, 119, 93, 125, 90, 122)(84, 116, 88, 120, 94, 126, 91, 123)(89, 121, 92, 124, 95, 127, 96, 128) L = (1, 67)(2, 71)(3, 73)(4, 74)(5, 65)(6, 77)(7, 79)(8, 66)(9, 81)(10, 82)(11, 68)(12, 69)(13, 85)(14, 70)(15, 87)(16, 72)(17, 89)(18, 90)(19, 75)(20, 76)(21, 93)(22, 78)(23, 92)(24, 80)(25, 91)(26, 96)(27, 83)(28, 84)(29, 95)(30, 86)(31, 88)(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, 64 ), ( 64^8 ) } Outer automorphisms :: reflexible Dual of E12.526 Graph:: simple bipartite v = 40 e = 64 f = 2 degree seq :: [ 2^32, 8^8 ] E12.528 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1^-1), (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^4, Y1^4 * Y3 * Y1^4, Y1^2 * Y3^-1 * Y1^3 * Y3^-1 * Y1^2 * Y3^-1 * Y1, (Y1^-1 * Y3^-1)^32 ] Map:: R = (1, 33, 2, 34, 6, 38, 13, 45, 21, 53, 28, 60, 20, 52, 12, 44, 5, 37, 8, 40, 15, 47, 23, 55, 29, 61, 31, 63, 25, 57, 17, 49, 9, 41, 16, 48, 24, 56, 30, 62, 32, 64, 26, 58, 18, 50, 10, 42, 3, 35, 7, 39, 14, 46, 22, 54, 27, 59, 19, 51, 11, 43, 4, 36)(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)(91, 123)(92, 124)(93, 125)(94, 126)(95, 127)(96, 128) L = (1, 67)(2, 71)(3, 73)(4, 74)(5, 65)(6, 78)(7, 80)(8, 66)(9, 69)(10, 81)(11, 82)(12, 68)(13, 86)(14, 88)(15, 70)(16, 72)(17, 76)(18, 89)(19, 90)(20, 75)(21, 91)(22, 94)(23, 77)(24, 79)(25, 84)(26, 95)(27, 96)(28, 83)(29, 85)(30, 87)(31, 92)(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 ) } Outer automorphisms :: reflexible Dual of E12.524 Graph:: bipartite v = 33 e = 64 f = 9 degree seq :: [ 2^32, 64 ] E12.529 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, Y3^4, (Y3^-1, Y1^-1), (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^4, Y3^-1 * Y1^8, (Y1^-1 * Y3^-1)^32 ] Map:: R = (1, 33, 2, 34, 6, 38, 13, 45, 21, 53, 26, 58, 18, 50, 10, 42, 3, 35, 7, 39, 14, 46, 22, 54, 29, 61, 31, 63, 25, 57, 17, 49, 9, 41, 16, 48, 24, 56, 30, 62, 32, 64, 28, 60, 20, 52, 12, 44, 5, 37, 8, 40, 15, 47, 23, 55, 27, 59, 19, 51, 11, 43, 4, 36)(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)(91, 123)(92, 124)(93, 125)(94, 126)(95, 127)(96, 128) L = (1, 67)(2, 71)(3, 73)(4, 74)(5, 65)(6, 78)(7, 80)(8, 66)(9, 69)(10, 81)(11, 82)(12, 68)(13, 86)(14, 88)(15, 70)(16, 72)(17, 76)(18, 89)(19, 90)(20, 75)(21, 93)(22, 94)(23, 77)(24, 79)(25, 84)(26, 95)(27, 85)(28, 83)(29, 96)(30, 87)(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, 64 ), ( 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 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 E12.525 Graph:: bipartite v = 33 e = 64 f = 9 degree seq :: [ 2^32, 64 ] E12.530 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {5, 7, 35}) Quotient :: edge Aut^+ = C35 (small group id <35, 1>) Aut = D70 (small group id <70, 3>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^5, T2^7 ] Map:: non-degenerate R = (1, 3, 9, 18, 23, 13, 5)(2, 7, 16, 26, 27, 17, 8)(4, 10, 19, 28, 31, 22, 12)(6, 14, 24, 32, 33, 25, 15)(11, 20, 29, 34, 35, 30, 21)(36, 37, 41, 46, 39)(38, 42, 49, 55, 45)(40, 43, 50, 56, 47)(44, 51, 59, 64, 54)(48, 52, 60, 65, 57)(53, 61, 67, 69, 63)(58, 62, 68, 70, 66) L = (1, 36)(2, 37)(3, 38)(4, 39)(5, 40)(6, 41)(7, 42)(8, 43)(9, 44)(10, 45)(11, 46)(12, 47)(13, 48)(14, 49)(15, 50)(16, 51)(17, 52)(18, 53)(19, 54)(20, 55)(21, 56)(22, 57)(23, 58)(24, 59)(25, 60)(26, 61)(27, 62)(28, 63)(29, 64)(30, 65)(31, 66)(32, 67)(33, 68)(34, 69)(35, 70) local type(s) :: { ( 70^5 ), ( 70^7 ) } Outer automorphisms :: reflexible Dual of E12.534 Transitivity :: ET+ Graph:: simple bipartite v = 12 e = 35 f = 1 degree seq :: [ 5^7, 7^5 ] E12.531 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {5, 7, 35}) Quotient :: edge Aut^+ = C35 (small group id <35, 1>) Aut = D70 (small group id <70, 3>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-5 * T1^2, T1^7, (T1^-1 * T2^-1)^5 ] Map:: non-degenerate R = (1, 3, 9, 19, 16, 6, 15, 28, 35, 31, 22, 30, 33, 24, 12, 4, 10, 20, 18, 8, 2, 7, 17, 29, 27, 14, 26, 34, 32, 23, 11, 21, 25, 13, 5)(36, 37, 41, 49, 57, 46, 39)(38, 42, 50, 61, 65, 56, 45)(40, 43, 51, 62, 66, 58, 47)(44, 52, 63, 69, 68, 60, 55)(48, 53, 54, 64, 70, 67, 59) L = (1, 36)(2, 37)(3, 38)(4, 39)(5, 40)(6, 41)(7, 42)(8, 43)(9, 44)(10, 45)(11, 46)(12, 47)(13, 48)(14, 49)(15, 50)(16, 51)(17, 52)(18, 53)(19, 54)(20, 55)(21, 56)(22, 57)(23, 58)(24, 59)(25, 60)(26, 61)(27, 62)(28, 63)(29, 64)(30, 65)(31, 66)(32, 67)(33, 68)(34, 69)(35, 70) local type(s) :: { ( 10^7 ), ( 10^35 ) } Outer automorphisms :: reflexible Dual of E12.535 Transitivity :: ET+ Graph:: bipartite v = 6 e = 35 f = 7 degree seq :: [ 7^5, 35 ] E12.532 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {5, 7, 35}) Quotient :: edge Aut^+ = C35 (small group id <35, 1>) Aut = D70 (small group id <70, 3>) |r| :: 2 Presentation :: [ F^2, (T1, T2^-1), (F * T1)^2, (F * T2)^2, T2^-5, T2^-2 * T1^-7, T2^-1 * T1^3 * T2^-2 * T1^4 ] Map:: non-degenerate R = (1, 3, 9, 13, 5)(2, 7, 17, 18, 8)(4, 10, 19, 23, 12)(6, 15, 27, 28, 16)(11, 20, 29, 33, 22)(14, 25, 31, 35, 26)(21, 30, 34, 24, 32)(36, 37, 41, 49, 59, 68, 58, 48, 53, 63, 70, 65, 55, 45, 38, 42, 50, 60, 67, 57, 47, 40, 43, 51, 61, 69, 64, 54, 44, 52, 62, 66, 56, 46, 39) L = (1, 36)(2, 37)(3, 38)(4, 39)(5, 40)(6, 41)(7, 42)(8, 43)(9, 44)(10, 45)(11, 46)(12, 47)(13, 48)(14, 49)(15, 50)(16, 51)(17, 52)(18, 53)(19, 54)(20, 55)(21, 56)(22, 57)(23, 58)(24, 59)(25, 60)(26, 61)(27, 62)(28, 63)(29, 64)(30, 65)(31, 66)(32, 67)(33, 68)(34, 69)(35, 70) local type(s) :: { ( 14^5 ), ( 14^35 ) } Outer automorphisms :: reflexible Dual of E12.533 Transitivity :: ET+ Graph:: bipartite v = 8 e = 35 f = 5 degree seq :: [ 5^7, 35 ] E12.533 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {5, 7, 35}) Quotient :: loop Aut^+ = C35 (small group id <35, 1>) Aut = D70 (small group id <70, 3>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T1^5, T2^7 ] Map:: non-degenerate R = (1, 36, 3, 38, 9, 44, 18, 53, 23, 58, 13, 48, 5, 40)(2, 37, 7, 42, 16, 51, 26, 61, 27, 62, 17, 52, 8, 43)(4, 39, 10, 45, 19, 54, 28, 63, 31, 66, 22, 57, 12, 47)(6, 41, 14, 49, 24, 59, 32, 67, 33, 68, 25, 60, 15, 50)(11, 46, 20, 55, 29, 64, 34, 69, 35, 70, 30, 65, 21, 56) L = (1, 37)(2, 41)(3, 42)(4, 36)(5, 43)(6, 46)(7, 49)(8, 50)(9, 51)(10, 38)(11, 39)(12, 40)(13, 52)(14, 55)(15, 56)(16, 59)(17, 60)(18, 61)(19, 44)(20, 45)(21, 47)(22, 48)(23, 62)(24, 64)(25, 65)(26, 67)(27, 68)(28, 53)(29, 54)(30, 57)(31, 58)(32, 69)(33, 70)(34, 63)(35, 66) local type(s) :: { ( 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35, 5, 35 ) } Outer automorphisms :: reflexible Dual of E12.532 Transitivity :: ET+ VT+ AT Graph:: v = 5 e = 35 f = 8 degree seq :: [ 14^5 ] E12.534 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {5, 7, 35}) Quotient :: loop Aut^+ = C35 (small group id <35, 1>) Aut = D70 (small group id <70, 3>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-5 * T1^2, T1^7, (T1^-1 * T2^-1)^5 ] Map:: non-degenerate R = (1, 36, 3, 38, 9, 44, 19, 54, 16, 51, 6, 41, 15, 50, 28, 63, 35, 70, 31, 66, 22, 57, 30, 65, 33, 68, 24, 59, 12, 47, 4, 39, 10, 45, 20, 55, 18, 53, 8, 43, 2, 37, 7, 42, 17, 52, 29, 64, 27, 62, 14, 49, 26, 61, 34, 69, 32, 67, 23, 58, 11, 46, 21, 56, 25, 60, 13, 48, 5, 40) L = (1, 37)(2, 41)(3, 42)(4, 36)(5, 43)(6, 49)(7, 50)(8, 51)(9, 52)(10, 38)(11, 39)(12, 40)(13, 53)(14, 57)(15, 61)(16, 62)(17, 63)(18, 54)(19, 64)(20, 44)(21, 45)(22, 46)(23, 47)(24, 48)(25, 55)(26, 65)(27, 66)(28, 69)(29, 70)(30, 56)(31, 58)(32, 59)(33, 60)(34, 68)(35, 67) local type(s) :: { ( 5, 7, 5, 7, 5, 7, 5, 7, 5, 7, 5, 7, 5, 7, 5, 7, 5, 7, 5, 7, 5, 7, 5, 7, 5, 7, 5, 7, 5, 7, 5, 7, 5, 7, 5, 7, 5, 7, 5, 7, 5, 7, 5, 7, 5, 7, 5, 7, 5, 7, 5, 7, 5, 7, 5, 7, 5, 7, 5, 7, 5, 7, 5, 7, 5, 7, 5, 7, 5, 7 ) } Outer automorphisms :: reflexible Dual of E12.530 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 35 f = 12 degree seq :: [ 70 ] E12.535 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {5, 7, 35}) Quotient :: loop Aut^+ = C35 (small group id <35, 1>) Aut = D70 (small group id <70, 3>) |r| :: 2 Presentation :: [ F^2, (T1, T2^-1), (F * T1)^2, (F * T2)^2, T2^-5, T2^-2 * T1^-7, T2^-1 * T1^3 * T2^-2 * T1^4 ] Map:: non-degenerate R = (1, 36, 3, 38, 9, 44, 13, 48, 5, 40)(2, 37, 7, 42, 17, 52, 18, 53, 8, 43)(4, 39, 10, 45, 19, 54, 23, 58, 12, 47)(6, 41, 15, 50, 27, 62, 28, 63, 16, 51)(11, 46, 20, 55, 29, 64, 33, 68, 22, 57)(14, 49, 25, 60, 31, 66, 35, 70, 26, 61)(21, 56, 30, 65, 34, 69, 24, 59, 32, 67) L = (1, 37)(2, 41)(3, 42)(4, 36)(5, 43)(6, 49)(7, 50)(8, 51)(9, 52)(10, 38)(11, 39)(12, 40)(13, 53)(14, 59)(15, 60)(16, 61)(17, 62)(18, 63)(19, 44)(20, 45)(21, 46)(22, 47)(23, 48)(24, 68)(25, 67)(26, 69)(27, 66)(28, 70)(29, 54)(30, 55)(31, 56)(32, 57)(33, 58)(34, 64)(35, 65) local type(s) :: { ( 7, 35, 7, 35, 7, 35, 7, 35, 7, 35 ) } Outer automorphisms :: reflexible Dual of E12.531 Transitivity :: ET+ VT+ AT Graph:: v = 7 e = 35 f = 6 degree seq :: [ 10^7 ] E12.536 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 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^-1, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y2^-1, Y1^-1), (Y3^-1, Y2^-1), Y1^5, Y2^7, Y3^35 ] Map:: R = (1, 36, 2, 37, 6, 41, 11, 46, 4, 39)(3, 38, 7, 42, 14, 49, 20, 55, 10, 45)(5, 40, 8, 43, 15, 50, 21, 56, 12, 47)(9, 44, 16, 51, 24, 59, 29, 64, 19, 54)(13, 48, 17, 52, 25, 60, 30, 65, 22, 57)(18, 53, 26, 61, 32, 67, 34, 69, 28, 63)(23, 58, 27, 62, 33, 68, 35, 70, 31, 66)(71, 106, 73, 108, 79, 114, 88, 123, 93, 128, 83, 118, 75, 110)(72, 107, 77, 112, 86, 121, 96, 131, 97, 132, 87, 122, 78, 113)(74, 109, 80, 115, 89, 124, 98, 133, 101, 136, 92, 127, 82, 117)(76, 111, 84, 119, 94, 129, 102, 137, 103, 138, 95, 130, 85, 120)(81, 116, 90, 125, 99, 134, 104, 139, 105, 140, 100, 135, 91, 126) L = (1, 74)(2, 71)(3, 80)(4, 81)(5, 82)(6, 72)(7, 73)(8, 75)(9, 89)(10, 90)(11, 76)(12, 91)(13, 92)(14, 77)(15, 78)(16, 79)(17, 83)(18, 98)(19, 99)(20, 84)(21, 85)(22, 100)(23, 101)(24, 86)(25, 87)(26, 88)(27, 93)(28, 104)(29, 94)(30, 95)(31, 105)(32, 96)(33, 97)(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) :: { ( 2, 70, 2, 70, 2, 70, 2, 70, 2, 70 ), ( 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70, 2, 70 ) } Outer automorphisms :: reflexible Dual of E12.539 Graph:: bipartite v = 12 e = 70 f = 36 degree seq :: [ 10^7, 14^5 ] E12.537 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 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^-1, (R * Y1)^2, R * Y2 * R * Y3, (Y1, Y2^-1), Y1^-2 * Y2^5, Y1^7, (Y3^-1 * Y1^-1)^5 ] Map:: R = (1, 36, 2, 37, 6, 41, 14, 49, 22, 57, 11, 46, 4, 39)(3, 38, 7, 42, 15, 50, 26, 61, 30, 65, 21, 56, 10, 45)(5, 40, 8, 43, 16, 51, 27, 62, 31, 66, 23, 58, 12, 47)(9, 44, 17, 52, 28, 63, 34, 69, 33, 68, 25, 60, 20, 55)(13, 48, 18, 53, 19, 54, 29, 64, 35, 70, 32, 67, 24, 59)(71, 106, 73, 108, 79, 114, 89, 124, 86, 121, 76, 111, 85, 120, 98, 133, 105, 140, 101, 136, 92, 127, 100, 135, 103, 138, 94, 129, 82, 117, 74, 109, 80, 115, 90, 125, 88, 123, 78, 113, 72, 107, 77, 112, 87, 122, 99, 134, 97, 132, 84, 119, 96, 131, 104, 139, 102, 137, 93, 128, 81, 116, 91, 126, 95, 130, 83, 118, 75, 110) L = (1, 73)(2, 77)(3, 79)(4, 80)(5, 71)(6, 85)(7, 87)(8, 72)(9, 89)(10, 90)(11, 91)(12, 74)(13, 75)(14, 96)(15, 98)(16, 76)(17, 99)(18, 78)(19, 86)(20, 88)(21, 95)(22, 100)(23, 81)(24, 82)(25, 83)(26, 104)(27, 84)(28, 105)(29, 97)(30, 103)(31, 92)(32, 93)(33, 94)(34, 102)(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) :: { ( 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, 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, 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 E12.538 Graph:: bipartite v = 6 e = 70 f = 42 degree seq :: [ 14^5, 70 ] E12.538 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 7, 35}) Quotient :: dipole Aut^+ = C35 (small group id <35, 1>) Aut = D70 (small group id <70, 3>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y2, Y3^-1), Y2^5, Y2^5, Y2^2 * Y3^-7, Y2^-1 * Y3^-3 * Y2^-1 * Y3^-4 * Y2^-1, (Y3^-1 * Y1^-1)^35 ] Map:: R = (1, 36)(2, 37)(3, 38)(4, 39)(5, 40)(6, 41)(7, 42)(8, 43)(9, 44)(10, 45)(11, 46)(12, 47)(13, 48)(14, 49)(15, 50)(16, 51)(17, 52)(18, 53)(19, 54)(20, 55)(21, 56)(22, 57)(23, 58)(24, 59)(25, 60)(26, 61)(27, 62)(28, 63)(29, 64)(30, 65)(31, 66)(32, 67)(33, 68)(34, 69)(35, 70)(71, 106, 72, 107, 76, 111, 81, 116, 74, 109)(73, 108, 77, 112, 84, 119, 90, 125, 80, 115)(75, 110, 78, 113, 85, 120, 91, 126, 82, 117)(79, 114, 86, 121, 94, 129, 100, 135, 89, 124)(83, 118, 87, 122, 95, 130, 101, 136, 92, 127)(88, 123, 96, 131, 104, 139, 103, 138, 99, 134)(93, 128, 97, 132, 98, 133, 105, 140, 102, 137) L = (1, 73)(2, 77)(3, 79)(4, 80)(5, 71)(6, 84)(7, 86)(8, 72)(9, 88)(10, 89)(11, 90)(12, 74)(13, 75)(14, 94)(15, 76)(16, 96)(17, 78)(18, 98)(19, 99)(20, 100)(21, 81)(22, 82)(23, 83)(24, 104)(25, 85)(26, 105)(27, 87)(28, 95)(29, 97)(30, 103)(31, 91)(32, 92)(33, 93)(34, 102)(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 ) } Outer automorphisms :: reflexible Dual of E12.537 Graph:: simple bipartite v = 42 e = 70 f = 6 degree seq :: [ 2^35, 10^7 ] E12.539 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 7, 35}) Quotient :: dipole Aut^+ = C35 (small group id <35, 1>) Aut = D70 (small group id <70, 3>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1^-1), (R * Y2 * Y3^-1)^2, Y1^-6 * Y3^-1 * Y1^-1 * Y3^-1, Y3^-1 * Y1^3 * Y3^-2 * Y1^4, Y3 * Y1^-1 * Y3 * Y1^-2 * Y3 * Y1^-4, (Y3 * Y2^-1)^5 ] Map:: R = (1, 36, 2, 37, 6, 41, 14, 49, 24, 59, 33, 68, 23, 58, 13, 48, 18, 53, 28, 63, 35, 70, 30, 65, 20, 55, 10, 45, 3, 38, 7, 42, 15, 50, 25, 60, 32, 67, 22, 57, 12, 47, 5, 40, 8, 43, 16, 51, 26, 61, 34, 69, 29, 64, 19, 54, 9, 44, 17, 52, 27, 62, 31, 66, 21, 56, 11, 46, 4, 39)(71, 106)(72, 107)(73, 108)(74, 109)(75, 110)(76, 111)(77, 112)(78, 113)(79, 114)(80, 115)(81, 116)(82, 117)(83, 118)(84, 119)(85, 120)(86, 121)(87, 122)(88, 123)(89, 124)(90, 125)(91, 126)(92, 127)(93, 128)(94, 129)(95, 130)(96, 131)(97, 132)(98, 133)(99, 134)(100, 135)(101, 136)(102, 137)(103, 138)(104, 139)(105, 140) L = (1, 73)(2, 77)(3, 79)(4, 80)(5, 71)(6, 85)(7, 87)(8, 72)(9, 83)(10, 89)(11, 90)(12, 74)(13, 75)(14, 95)(15, 97)(16, 76)(17, 88)(18, 78)(19, 93)(20, 99)(21, 100)(22, 81)(23, 82)(24, 102)(25, 101)(26, 84)(27, 98)(28, 86)(29, 103)(30, 104)(31, 105)(32, 91)(33, 92)(34, 94)(35, 96)(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 ) } Outer automorphisms :: reflexible Dual of E12.536 Graph:: bipartite v = 36 e = 70 f = 12 degree seq :: [ 2^35, 70 ] E12.540 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 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^-1, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y2^-1, Y1^-1), (Y3^-1, Y2^-1), Y3^5, Y1^5, Y2 * Y3^2 * Y2^-1 * Y3 * Y1^-2, Y3^-2 * Y2^7 ] Map:: R = (1, 36, 2, 37, 6, 41, 11, 46, 4, 39)(3, 38, 7, 42, 14, 49, 20, 55, 10, 45)(5, 40, 8, 43, 15, 50, 21, 56, 12, 47)(9, 44, 16, 51, 24, 59, 30, 65, 19, 54)(13, 48, 17, 52, 25, 60, 31, 66, 22, 57)(18, 53, 26, 61, 33, 68, 35, 70, 29, 64)(23, 58, 27, 62, 34, 69, 28, 63, 32, 67)(71, 106, 73, 108, 79, 114, 88, 123, 98, 133, 101, 136, 91, 126, 81, 116, 90, 125, 100, 135, 105, 140, 97, 132, 87, 122, 78, 113, 72, 107, 77, 112, 86, 121, 96, 131, 102, 137, 92, 127, 82, 117, 74, 109, 80, 115, 89, 124, 99, 134, 104, 139, 95, 130, 85, 120, 76, 111, 84, 119, 94, 129, 103, 138, 93, 128, 83, 118, 75, 110) L = (1, 74)(2, 71)(3, 80)(4, 81)(5, 82)(6, 72)(7, 73)(8, 75)(9, 89)(10, 90)(11, 76)(12, 91)(13, 92)(14, 77)(15, 78)(16, 79)(17, 83)(18, 99)(19, 100)(20, 84)(21, 85)(22, 101)(23, 102)(24, 86)(25, 87)(26, 88)(27, 93)(28, 104)(29, 105)(30, 94)(31, 95)(32, 98)(33, 96)(34, 97)(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) :: { ( 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 E12.541 Graph:: bipartite v = 8 e = 70 f = 40 degree seq :: [ 10^7, 70 ] E12.541 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 7, 35}) Quotient :: dipole Aut^+ = C35 (small group id <35, 1>) Aut = D70 (small group id <70, 3>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1^-1), (R * Y2 * Y3^-1)^2, Y3^-5 * Y1^2, Y1^7, (Y1^-1 * Y3^-1)^5, (Y3 * Y2^-1)^35 ] Map:: R = (1, 36, 2, 37, 6, 41, 14, 49, 22, 57, 11, 46, 4, 39)(3, 38, 7, 42, 15, 50, 26, 61, 30, 65, 21, 56, 10, 45)(5, 40, 8, 43, 16, 51, 27, 62, 31, 66, 23, 58, 12, 47)(9, 44, 17, 52, 28, 63, 34, 69, 33, 68, 25, 60, 20, 55)(13, 48, 18, 53, 19, 54, 29, 64, 35, 70, 32, 67, 24, 59)(71, 106)(72, 107)(73, 108)(74, 109)(75, 110)(76, 111)(77, 112)(78, 113)(79, 114)(80, 115)(81, 116)(82, 117)(83, 118)(84, 119)(85, 120)(86, 121)(87, 122)(88, 123)(89, 124)(90, 125)(91, 126)(92, 127)(93, 128)(94, 129)(95, 130)(96, 131)(97, 132)(98, 133)(99, 134)(100, 135)(101, 136)(102, 137)(103, 138)(104, 139)(105, 140) L = (1, 73)(2, 77)(3, 79)(4, 80)(5, 71)(6, 85)(7, 87)(8, 72)(9, 89)(10, 90)(11, 91)(12, 74)(13, 75)(14, 96)(15, 98)(16, 76)(17, 99)(18, 78)(19, 86)(20, 88)(21, 95)(22, 100)(23, 81)(24, 82)(25, 83)(26, 104)(27, 84)(28, 105)(29, 97)(30, 103)(31, 92)(32, 93)(33, 94)(34, 102)(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, 70 ), ( 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70, 10, 70 ) } Outer automorphisms :: reflexible Dual of E12.540 Graph:: simple bipartite v = 40 e = 70 f = 8 degree seq :: [ 2^35, 14^5 ] E12.542 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {6, 9, 9}) Quotient :: edge Aut^+ = (C2 x C2) : C9 (small group id <36, 3>) Aut = ((C2 x C2) : C9) : C2 (small group id <72, 15>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^2 * T2^-3, T1^6, T1^6, T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1 * T2^-1, T1^-2 * T2^-1 * T1^-2 * T2^-2 ] Map:: non-degenerate R = (1, 3, 10, 6, 19, 30, 13, 17, 5)(2, 7, 21, 18, 31, 14, 4, 12, 8)(9, 24, 36, 34, 23, 28, 11, 27, 25)(15, 32, 29, 26, 35, 22, 16, 33, 20)(37, 38, 42, 54, 49, 40)(39, 45, 55, 70, 53, 47)(41, 51, 46, 62, 66, 52)(43, 56, 67, 65, 48, 58)(44, 59, 57, 63, 50, 60)(61, 69, 72, 68, 64, 71) L = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 18^6 ), ( 18^9 ) } Outer automorphisms :: reflexible Dual of E12.546 Transitivity :: ET+ Graph:: bipartite v = 10 e = 36 f = 4 degree seq :: [ 6^6, 9^4 ] E12.543 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {6, 9, 9}) Quotient :: edge Aut^+ = (C2 x C2) : C9 (small group id <36, 3>) Aut = ((C2 x C2) : C9) : C2 (small group id <72, 15>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^-2 * T1^-2 * T2^-1, T1^6, T1 * T2^-1 * T1 * T2^-1 * T1^-1 * T2^-1, T1^6, T1 * T2 * T1 * T2^-2 * T1 * T2 ] Map:: non-degenerate R = (1, 3, 10, 13, 27, 19, 6, 17, 5)(2, 7, 14, 4, 12, 29, 18, 24, 8)(9, 22, 28, 11, 23, 36, 34, 31, 25)(15, 32, 30, 16, 33, 20, 26, 35, 21)(37, 38, 42, 54, 49, 40)(39, 45, 53, 70, 63, 47)(41, 51, 55, 62, 46, 52)(43, 56, 60, 66, 48, 57)(44, 58, 65, 67, 50, 59)(61, 69, 72, 68, 64, 71) L = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 18^6 ), ( 18^9 ) } Outer automorphisms :: reflexible Dual of E12.545 Transitivity :: ET+ Graph:: bipartite v = 10 e = 36 f = 4 degree seq :: [ 6^6, 9^4 ] E12.544 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {6, 9, 9}) Quotient :: edge Aut^+ = (C2 x C2) : C9 (small group id <36, 3>) Aut = ((C2 x C2) : C9) : C2 (small group id <72, 15>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1 * T2 * T1 * T2^-2, (T1^-2 * T2)^2, (T1^-2 * T2)^2, T1^3 * T2^3, T1 * T2^-1 * T1^-1 * T2^-2 * T1^-1 * T2^-1, T2^9 ] Map:: non-degenerate R = (1, 3, 10, 28, 36, 35, 18, 17, 5)(2, 7, 21, 13, 31, 30, 34, 16, 8)(4, 12, 9, 26, 24, 20, 6, 19, 14)(11, 29, 27, 32, 23, 22, 25, 33, 15)(37, 38, 42, 54, 70, 62, 64, 49, 40)(39, 45, 61, 53, 50, 68, 72, 56, 47)(41, 51, 67, 71, 58, 43, 46, 63, 52)(44, 59, 48, 66, 65, 55, 57, 69, 60) L = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 12^9 ) } Outer automorphisms :: reflexible Dual of E12.547 Transitivity :: ET+ Graph:: bipartite v = 8 e = 36 f = 6 degree seq :: [ 9^8 ] E12.545 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {6, 9, 9}) Quotient :: loop Aut^+ = (C2 x C2) : C9 (small group id <36, 3>) Aut = ((C2 x C2) : C9) : C2 (small group id <72, 15>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^2 * T2^-3, T1^6, T1^6, T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1 * T2^-1, T1^-2 * T2^-1 * T1^-2 * T2^-2 ] Map:: non-degenerate R = (1, 37, 3, 39, 10, 46, 6, 42, 19, 55, 30, 66, 13, 49, 17, 53, 5, 41)(2, 38, 7, 43, 21, 57, 18, 54, 31, 67, 14, 50, 4, 40, 12, 48, 8, 44)(9, 45, 24, 60, 36, 72, 34, 70, 23, 59, 28, 64, 11, 47, 27, 63, 25, 61)(15, 51, 32, 68, 29, 65, 26, 62, 35, 71, 22, 58, 16, 52, 33, 69, 20, 56) L = (1, 38)(2, 42)(3, 45)(4, 37)(5, 51)(6, 54)(7, 56)(8, 59)(9, 55)(10, 62)(11, 39)(12, 58)(13, 40)(14, 60)(15, 46)(16, 41)(17, 47)(18, 49)(19, 70)(20, 67)(21, 63)(22, 43)(23, 57)(24, 44)(25, 69)(26, 66)(27, 50)(28, 71)(29, 48)(30, 52)(31, 65)(32, 64)(33, 72)(34, 53)(35, 61)(36, 68) local type(s) :: { ( 6, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9 ) } Outer automorphisms :: reflexible Dual of E12.543 Transitivity :: ET+ VT+ AT Graph:: v = 4 e = 36 f = 10 degree seq :: [ 18^4 ] E12.546 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {6, 9, 9}) Quotient :: loop Aut^+ = (C2 x C2) : C9 (small group id <36, 3>) Aut = ((C2 x C2) : C9) : C2 (small group id <72, 15>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^-2 * T1^-2 * T2^-1, T1^6, T1 * T2^-1 * T1 * T2^-1 * T1^-1 * T2^-1, T1^6, T1 * T2 * T1 * T2^-2 * T1 * T2 ] Map:: non-degenerate R = (1, 37, 3, 39, 10, 46, 13, 49, 27, 63, 19, 55, 6, 42, 17, 53, 5, 41)(2, 38, 7, 43, 14, 50, 4, 40, 12, 48, 29, 65, 18, 54, 24, 60, 8, 44)(9, 45, 22, 58, 28, 64, 11, 47, 23, 59, 36, 72, 34, 70, 31, 67, 25, 61)(15, 51, 32, 68, 30, 66, 16, 52, 33, 69, 20, 56, 26, 62, 35, 71, 21, 57) L = (1, 38)(2, 42)(3, 45)(4, 37)(5, 51)(6, 54)(7, 56)(8, 58)(9, 53)(10, 52)(11, 39)(12, 57)(13, 40)(14, 59)(15, 55)(16, 41)(17, 70)(18, 49)(19, 62)(20, 60)(21, 43)(22, 65)(23, 44)(24, 66)(25, 69)(26, 46)(27, 47)(28, 71)(29, 67)(30, 48)(31, 50)(32, 64)(33, 72)(34, 63)(35, 61)(36, 68) local type(s) :: { ( 6, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9, 6, 9 ) } Outer automorphisms :: reflexible Dual of E12.542 Transitivity :: ET+ VT+ AT Graph:: v = 4 e = 36 f = 10 degree seq :: [ 18^4 ] E12.547 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {6, 9, 9}) Quotient :: loop Aut^+ = (C2 x C2) : C9 (small group id <36, 3>) Aut = ((C2 x C2) : C9) : C2 (small group id <72, 15>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^-1 * T1^3 * T2^-1, T2 * T1 * T2^-1 * T1 * T2 * T1, T2^6, T2^-2 * T1^-2 * T2^-2 * T1^-1 ] Map:: non-degenerate R = (1, 37, 3, 39, 10, 46, 27, 63, 17, 53, 5, 41)(2, 38, 7, 43, 20, 56, 30, 66, 13, 49, 8, 44)(4, 40, 12, 48, 6, 42, 18, 54, 32, 68, 14, 50)(9, 45, 25, 61, 34, 70, 33, 69, 15, 51, 26, 62)(11, 47, 28, 64, 24, 60, 22, 58, 16, 52, 19, 55)(21, 57, 31, 67, 36, 72, 29, 65, 23, 59, 35, 71) L = (1, 38)(2, 42)(3, 45)(4, 37)(5, 51)(6, 46)(7, 55)(8, 58)(9, 60)(10, 56)(11, 39)(12, 65)(13, 40)(14, 67)(15, 47)(16, 41)(17, 49)(18, 71)(19, 72)(20, 68)(21, 43)(22, 57)(23, 44)(24, 63)(25, 48)(26, 50)(27, 70)(28, 59)(29, 69)(30, 64)(31, 61)(32, 53)(33, 54)(34, 52)(35, 62)(36, 66) local type(s) :: { ( 9^12 ) } Outer automorphisms :: reflexible Dual of E12.544 Transitivity :: ET+ VT+ AT Graph:: v = 6 e = 36 f = 8 degree seq :: [ 12^6 ] E12.548 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {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 * Y1, (R * Y3)^2, (R * Y1)^2, Y2^2 * Y1 * Y3^-1 * Y2, Y2 * Y3 * Y1^-1 * Y2^-1 * Y3^-1 * Y1, Y3 * Y2^-1 * Y1 * Y2^-1 * Y3^-1 * Y2^-1, Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1, (Y1^-1 * Y3)^3, (R * Y2^-1 * Y3^-1)^2, Y1 * Y2^-1 * Y3 * Y2^-1 * Y3^-1 * Y2^-1, Y2^-1 * Y1^2 * Y2 * Y1^-2, Y1^6, Y2^-1 * Y1^2 * Y2^-2 * Y3^-1 * Y1, Y2^2 * Y3 * Y2^2 * Y3^-1 * Y2^-1 * Y1^-1, Y1 * Y2^-1 * Y3 * Y2^2 * Y3^-1 * Y2^-1 * Y1 * Y3^-1 ] 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, 76)(2, 73)(3, 83)(4, 85)(5, 88)(6, 74)(7, 93)(8, 95)(9, 75)(10, 98)(11, 99)(12, 102)(13, 90)(14, 103)(15, 77)(16, 82)(17, 81)(18, 78)(19, 87)(20, 79)(21, 84)(22, 80)(23, 86)(24, 92)(25, 107)(26, 91)(27, 106)(28, 104)(29, 94)(30, 96)(31, 101)(32, 108)(33, 97)(34, 89)(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) :: { ( 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 E12.552 Graph:: bipartite v = 10 e = 72 f = 40 degree seq :: [ 12^6, 18^4 ] E12.549 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {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, Y1^-1 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y2^2 * Y3 * Y1^-1 * Y2, (R * Y2 * Y3^-1)^2, Y1 * Y2 * Y3^-1 * Y2 * Y3 * Y2, Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1, (Y3 * Y1^-1 * Y3)^2, Y1^3 * Y3^-1 * Y1 * Y3^-1, Y2^-1 * Y3^2 * Y2 * Y3^-2, Y2 * Y1^2 * Y2^-1 * Y1^-2, Y2 * Y1^2 * Y2 * Y1 * Y3^-1 * Y2, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^2 * Y3^-1, Y2 * Y1 * Y2^-1 * Y3^-1 * Y2 * Y3 * Y2^-1 * Y1^-1, Y2 * Y3 * Y2 * Y3 * Y2 * Y3^3 ] 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, 76)(2, 73)(3, 83)(4, 85)(5, 88)(6, 74)(7, 94)(8, 96)(9, 75)(10, 87)(11, 89)(12, 101)(13, 90)(14, 99)(15, 77)(16, 102)(17, 106)(18, 78)(19, 81)(20, 79)(21, 95)(22, 84)(23, 80)(24, 86)(25, 107)(26, 82)(27, 93)(28, 104)(29, 103)(30, 98)(31, 92)(32, 108)(33, 97)(34, 91)(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) :: { ( 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 E12.553 Graph:: bipartite v = 10 e = 72 f = 40 degree seq :: [ 12^6, 18^4 ] E12.550 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {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, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y1 * Y2 * Y1^-2 * Y2, (Y1 * Y2^-2)^2, (Y2^-1 * Y1 * Y2^-1)^2, Y1 * Y2^3 * Y1^2, Y1^9, Y2^9, (Y3^-1 * Y1^-1)^6 ] Map:: R = (1, 37, 2, 38, 6, 42, 18, 54, 35, 71, 36, 72, 27, 63, 13, 49, 4, 40)(3, 39, 9, 45, 24, 60, 17, 53, 30, 66, 33, 69, 32, 68, 14, 50, 11, 47)(5, 41, 15, 51, 7, 43, 20, 56, 29, 65, 23, 59, 10, 46, 26, 62, 16, 52)(8, 44, 22, 58, 19, 55, 34, 70, 28, 64, 25, 61, 21, 57, 31, 67, 12, 48)(73, 109, 75, 111, 82, 118, 99, 135, 104, 140, 92, 128, 90, 126, 89, 125, 77, 113)(74, 110, 79, 115, 93, 129, 85, 121, 88, 124, 106, 142, 107, 143, 95, 131, 80, 116)(76, 112, 84, 120, 102, 138, 108, 144, 97, 133, 81, 117, 78, 114, 91, 127, 86, 122)(83, 119, 100, 136, 87, 123, 105, 141, 94, 130, 98, 134, 96, 132, 103, 139, 101, 137) L = (1, 75)(2, 79)(3, 82)(4, 84)(5, 73)(6, 91)(7, 93)(8, 74)(9, 78)(10, 99)(11, 100)(12, 102)(13, 88)(14, 76)(15, 105)(16, 106)(17, 77)(18, 89)(19, 86)(20, 90)(21, 85)(22, 98)(23, 80)(24, 103)(25, 81)(26, 96)(27, 104)(28, 87)(29, 83)(30, 108)(31, 101)(32, 92)(33, 94)(34, 107)(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) :: { ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12 ) } Outer automorphisms :: reflexible Dual of E12.551 Graph:: bipartite v = 8 e = 72 f = 42 degree seq :: [ 18^8 ] E12.551 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {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 :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, Y3^-2 * Y2^2 * Y3^-1, (R * Y2 * Y3^-1)^2, Y2 * Y3 * Y2^-1 * Y3 * Y2 * Y3, Y2^6, Y2 * Y3^-1 * Y2 * Y3^2 * Y2 * Y3^-1, (Y3^-1 * Y1^-1)^9 ] Map:: R = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72)(73, 109, 74, 110, 78, 114, 90, 126, 85, 121, 76, 112)(75, 111, 81, 117, 91, 127, 106, 142, 89, 125, 83, 119)(77, 113, 87, 123, 82, 118, 98, 134, 102, 138, 88, 124)(79, 115, 92, 128, 103, 139, 101, 137, 84, 120, 94, 130)(80, 116, 95, 131, 93, 129, 99, 135, 86, 122, 96, 132)(97, 133, 105, 141, 108, 144, 104, 140, 100, 136, 107, 143) L = (1, 75)(2, 79)(3, 82)(4, 84)(5, 73)(6, 91)(7, 93)(8, 74)(9, 96)(10, 78)(11, 99)(12, 80)(13, 89)(14, 76)(15, 104)(16, 105)(17, 77)(18, 103)(19, 102)(20, 87)(21, 90)(22, 88)(23, 100)(24, 108)(25, 81)(26, 107)(27, 97)(28, 83)(29, 98)(30, 85)(31, 86)(32, 101)(33, 92)(34, 95)(35, 94)(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) :: { ( 18, 18 ), ( 18^12 ) } Outer automorphisms :: reflexible Dual of E12.550 Graph:: simple bipartite v = 42 e = 72 f = 8 degree seq :: [ 2^36, 12^6 ] E12.552 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {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 :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, Y3^-1 * Y1^3 * Y3^-1, (R * Y2 * Y3^-1)^2, Y3^6, Y3 * Y1 * Y3^-1 * Y1 * Y3 * Y1, Y3^-2 * Y1^-2 * Y3^-2 * Y1^-1, (Y3 * Y2^-1)^6 ] Map:: R = (1, 37, 2, 38, 6, 42, 10, 46, 20, 56, 32, 68, 17, 53, 13, 49, 4, 40)(3, 39, 9, 45, 24, 60, 27, 63, 34, 70, 16, 52, 5, 41, 15, 51, 11, 47)(7, 43, 19, 55, 36, 72, 30, 66, 28, 64, 23, 59, 8, 44, 22, 58, 21, 57)(12, 48, 29, 65, 33, 69, 18, 54, 35, 71, 26, 62, 14, 50, 31, 67, 25, 61)(73, 109)(74, 110)(75, 111)(76, 112)(77, 113)(78, 114)(79, 115)(80, 116)(81, 117)(82, 118)(83, 119)(84, 120)(85, 121)(86, 122)(87, 123)(88, 124)(89, 125)(90, 126)(91, 127)(92, 128)(93, 129)(94, 130)(95, 131)(96, 132)(97, 133)(98, 134)(99, 135)(100, 136)(101, 137)(102, 138)(103, 139)(104, 140)(105, 141)(106, 142)(107, 143)(108, 144) L = (1, 75)(2, 79)(3, 82)(4, 84)(5, 73)(6, 90)(7, 92)(8, 74)(9, 97)(10, 99)(11, 100)(12, 78)(13, 80)(14, 76)(15, 98)(16, 91)(17, 77)(18, 104)(19, 83)(20, 102)(21, 103)(22, 88)(23, 107)(24, 94)(25, 106)(26, 81)(27, 89)(28, 96)(29, 95)(30, 85)(31, 108)(32, 86)(33, 87)(34, 105)(35, 93)(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) :: { ( 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 E12.548 Graph:: simple bipartite v = 40 e = 72 f = 10 degree seq :: [ 2^36, 18^4 ] E12.553 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {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 :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, Y1^3 * Y3^2, (R * Y2 * Y3^-1)^2, Y3 * Y1^-1 * Y3 * Y1^-1 * Y3^-1 * Y1^-1, Y3^6, Y3 * Y1 * Y3 * Y1^-2 * Y3 * Y1, (Y3 * Y2^-1)^6 ] Map:: R = (1, 37, 2, 38, 6, 42, 17, 53, 23, 59, 27, 63, 10, 46, 13, 49, 4, 40)(3, 39, 9, 45, 16, 52, 5, 41, 15, 51, 33, 69, 26, 62, 28, 64, 11, 47)(7, 43, 19, 55, 22, 58, 8, 44, 21, 57, 36, 72, 30, 66, 34, 70, 20, 56)(12, 48, 29, 65, 32, 68, 14, 50, 31, 67, 24, 60, 18, 54, 35, 71, 25, 61)(73, 109)(74, 110)(75, 111)(76, 112)(77, 113)(78, 114)(79, 115)(80, 116)(81, 117)(82, 118)(83, 119)(84, 120)(85, 121)(86, 122)(87, 123)(88, 124)(89, 125)(90, 126)(91, 127)(92, 128)(93, 129)(94, 130)(95, 131)(96, 132)(97, 133)(98, 134)(99, 135)(100, 136)(101, 137)(102, 138)(103, 139)(104, 140)(105, 141)(106, 142)(107, 143)(108, 144) L = (1, 75)(2, 79)(3, 82)(4, 84)(5, 73)(6, 86)(7, 85)(8, 74)(9, 96)(10, 98)(11, 91)(12, 99)(13, 102)(14, 76)(15, 97)(16, 93)(17, 77)(18, 78)(19, 105)(20, 103)(21, 83)(22, 107)(23, 80)(24, 100)(25, 81)(26, 89)(27, 90)(28, 104)(29, 94)(30, 95)(31, 108)(32, 87)(33, 106)(34, 88)(35, 92)(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) :: { ( 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 E12.549 Graph:: simple bipartite v = 40 e = 72 f = 10 degree seq :: [ 2^36, 18^4 ] E12.554 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 3, 18}) Quotient :: halfedge^2 Aut^+ = D36 (small group id <36, 4>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (Y2 * Y1^-1)^2, (R * Y1)^2, (Y3 * Y1)^2, Y3 * Y2 * Y1^-1 * Y3 * Y2 * Y1^-3, (Y2 * Y1 * Y3)^3, Y1^18 ] Map:: non-degenerate R = (1, 38, 2, 42, 6, 50, 14, 62, 26, 70, 34, 56, 20, 46, 10, 53, 17, 65, 29, 59, 23, 48, 12, 54, 18, 66, 30, 72, 36, 61, 25, 49, 13, 41, 5, 37)(3, 45, 9, 55, 19, 69, 33, 64, 28, 52, 16, 44, 8, 40, 4, 47, 11, 58, 22, 67, 31, 57, 21, 71, 35, 68, 32, 60, 24, 63, 27, 51, 15, 43, 7, 39) 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, 36)(32, 34)(37, 40)(38, 44)(39, 46)(41, 47)(42, 52)(43, 53)(45, 56)(48, 60)(49, 58)(50, 64)(51, 65)(54, 68)(55, 70)(57, 72)(59, 63)(61, 67)(62, 69)(66, 71) local type(s) :: { ( 6^36 ) } Outer automorphisms :: reflexible Dual of E12.555 Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 36 f = 12 degree seq :: [ 36^2 ] E12.555 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 3, 18}) Quotient :: halfedge^2 Aut^+ = D36 (small group id <36, 4>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y1^3, R * Y3 * R * Y2, (R * Y1)^2, (Y2 * Y1^-1)^2, (Y3 * Y1)^2, Y2 * Y3 * Y2 * Y3 * Y2 * Y1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3, (Y2 * Y1 * Y3)^18 ] Map:: non-degenerate R = (1, 38, 2, 41, 5, 37)(3, 44, 8, 42, 6, 39)(4, 46, 10, 43, 7, 40)(9, 48, 12, 50, 14, 45)(11, 49, 13, 52, 16, 47)(15, 56, 20, 54, 18, 51)(17, 58, 22, 55, 19, 53)(21, 60, 24, 62, 26, 57)(23, 61, 25, 64, 28, 59)(27, 68, 32, 66, 30, 63)(29, 70, 34, 67, 31, 65)(33, 72, 36, 71, 35, 69) L = (1, 3)(2, 6)(4, 11)(5, 8)(7, 13)(9, 15)(10, 16)(12, 18)(14, 20)(17, 23)(19, 25)(21, 27)(22, 28)(24, 30)(26, 32)(29, 35)(31, 33)(34, 36)(37, 40)(38, 43)(39, 45)(41, 46)(42, 48)(44, 50)(47, 53)(49, 55)(51, 57)(52, 58)(54, 60)(56, 62)(59, 65)(61, 67)(63, 69)(64, 70)(66, 72)(68, 71) local type(s) :: { ( 36^6 ) } Outer automorphisms :: reflexible Dual of E12.554 Transitivity :: VT+ AT Graph:: bipartite v = 12 e = 36 f = 2 degree seq :: [ 6^12 ] E12.556 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 3, 18}) Quotient :: edge^2 Aut^+ = D36 (small group id <36, 4>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^3, (R * Y3)^2, R * Y1 * R * Y2, (Y3^-1 * Y1)^2, (Y3 * Y2)^2, Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y3^-1 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2, (Y3 * Y1 * Y2)^18 ] Map:: R = (1, 37, 4, 40, 5, 41)(2, 38, 7, 43, 8, 44)(3, 39, 10, 46, 11, 47)(6, 42, 13, 49, 14, 50)(9, 45, 16, 52, 17, 53)(12, 48, 19, 55, 20, 56)(15, 51, 22, 58, 23, 59)(18, 54, 25, 61, 26, 62)(21, 57, 28, 64, 29, 65)(24, 60, 31, 67, 32, 68)(27, 63, 34, 70, 35, 71)(30, 66, 36, 72, 33, 69)(73, 74)(75, 81)(76, 80)(77, 79)(78, 84)(82, 89)(83, 88)(85, 92)(86, 91)(87, 93)(90, 96)(94, 101)(95, 100)(97, 104)(98, 103)(99, 105)(102, 107)(106, 108)(109, 111)(110, 114)(112, 119)(113, 118)(115, 122)(116, 121)(117, 123)(120, 126)(124, 131)(125, 130)(127, 134)(128, 133)(129, 135)(132, 138)(136, 143)(137, 142)(139, 141)(140, 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) :: { ( 72, 72 ), ( 72^6 ) } Outer automorphisms :: reflexible Dual of E12.559 Graph:: simple bipartite v = 48 e = 72 f = 2 degree seq :: [ 2^36, 6^12 ] E12.557 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 3, 18}) Quotient :: edge^2 Aut^+ = D36 (small group id <36, 4>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y1)^2, (Y3 * Y2)^2, Y2 * Y1 * Y3 * Y2 * Y3^-3 * Y1, Y1 * Y2 * Y1 * Y3^-2 * Y2 * Y1 * Y3^-1 * Y2, Y3^18 ] Map:: R = (1, 37, 4, 40, 12, 48, 24, 60, 26, 62, 35, 71, 21, 57, 9, 45, 20, 56, 30, 66, 16, 52, 6, 42, 15, 51, 29, 65, 33, 69, 25, 61, 13, 49, 5, 41)(2, 38, 7, 43, 17, 53, 31, 67, 19, 55, 34, 70, 28, 64, 14, 50, 27, 63, 23, 59, 11, 47, 3, 39, 10, 46, 22, 58, 36, 72, 32, 68, 18, 54, 8, 44)(73, 74)(75, 81)(76, 80)(77, 79)(78, 86)(82, 93)(83, 92)(84, 90)(85, 89)(87, 100)(88, 99)(91, 105)(94, 107)(95, 102)(96, 104)(97, 103)(98, 108)(101, 106)(109, 111)(110, 114)(112, 119)(113, 118)(115, 124)(116, 123)(117, 127)(120, 131)(121, 130)(122, 134)(125, 138)(126, 137)(128, 139)(129, 142)(132, 135)(133, 144)(136, 143)(140, 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) :: { ( 12, 12 ), ( 12^36 ) } Outer automorphisms :: reflexible Dual of E12.558 Graph:: simple bipartite v = 38 e = 72 f = 12 degree seq :: [ 2^36, 36^2 ] E12.558 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 3, 18}) Quotient :: loop^2 Aut^+ = D36 (small group id <36, 4>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^3, (R * Y3)^2, R * Y1 * R * Y2, (Y3^-1 * Y1)^2, (Y3 * Y2)^2, Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y3^-1 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2, (Y3 * Y1 * Y2)^18 ] Map:: R = (1, 37, 73, 109, 4, 40, 76, 112, 5, 41, 77, 113)(2, 38, 74, 110, 7, 43, 79, 115, 8, 44, 80, 116)(3, 39, 75, 111, 10, 46, 82, 118, 11, 47, 83, 119)(6, 42, 78, 114, 13, 49, 85, 121, 14, 50, 86, 122)(9, 45, 81, 117, 16, 52, 88, 124, 17, 53, 89, 125)(12, 48, 84, 120, 19, 55, 91, 127, 20, 56, 92, 128)(15, 51, 87, 123, 22, 58, 94, 130, 23, 59, 95, 131)(18, 54, 90, 126, 25, 61, 97, 133, 26, 62, 98, 134)(21, 57, 93, 129, 28, 64, 100, 136, 29, 65, 101, 137)(24, 60, 96, 132, 31, 67, 103, 139, 32, 68, 104, 140)(27, 63, 99, 135, 34, 70, 106, 142, 35, 71, 107, 143)(30, 66, 102, 138, 36, 72, 108, 144, 33, 69, 105, 141) L = (1, 38)(2, 37)(3, 45)(4, 44)(5, 43)(6, 48)(7, 41)(8, 40)(9, 39)(10, 53)(11, 52)(12, 42)(13, 56)(14, 55)(15, 57)(16, 47)(17, 46)(18, 60)(19, 50)(20, 49)(21, 51)(22, 65)(23, 64)(24, 54)(25, 68)(26, 67)(27, 69)(28, 59)(29, 58)(30, 71)(31, 62)(32, 61)(33, 63)(34, 72)(35, 66)(36, 70)(73, 111)(74, 114)(75, 109)(76, 119)(77, 118)(78, 110)(79, 122)(80, 121)(81, 123)(82, 113)(83, 112)(84, 126)(85, 116)(86, 115)(87, 117)(88, 131)(89, 130)(90, 120)(91, 134)(92, 133)(93, 135)(94, 125)(95, 124)(96, 138)(97, 128)(98, 127)(99, 129)(100, 143)(101, 142)(102, 132)(103, 141)(104, 144)(105, 139)(106, 137)(107, 136)(108, 140) local type(s) :: { ( 2, 36, 2, 36, 2, 36, 2, 36, 2, 36, 2, 36 ) } Outer automorphisms :: reflexible Dual of E12.557 Transitivity :: VT+ Graph:: bipartite v = 12 e = 72 f = 38 degree seq :: [ 12^12 ] E12.559 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 3, 18}) Quotient :: loop^2 Aut^+ = D36 (small group id <36, 4>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y1)^2, (Y3 * Y2)^2, Y2 * Y1 * Y3 * Y2 * Y3^-3 * Y1, Y1 * Y2 * Y1 * Y3^-2 * Y2 * Y1 * Y3^-1 * Y2, Y3^18 ] Map:: R = (1, 37, 73, 109, 4, 40, 76, 112, 12, 48, 84, 120, 24, 60, 96, 132, 26, 62, 98, 134, 35, 71, 107, 143, 21, 57, 93, 129, 9, 45, 81, 117, 20, 56, 92, 128, 30, 66, 102, 138, 16, 52, 88, 124, 6, 42, 78, 114, 15, 51, 87, 123, 29, 65, 101, 137, 33, 69, 105, 141, 25, 61, 97, 133, 13, 49, 85, 121, 5, 41, 77, 113)(2, 38, 74, 110, 7, 43, 79, 115, 17, 53, 89, 125, 31, 67, 103, 139, 19, 55, 91, 127, 34, 70, 106, 142, 28, 64, 100, 136, 14, 50, 86, 122, 27, 63, 99, 135, 23, 59, 95, 131, 11, 47, 83, 119, 3, 39, 75, 111, 10, 46, 82, 118, 22, 58, 94, 130, 36, 72, 108, 144, 32, 68, 104, 140, 18, 54, 90, 126, 8, 44, 80, 116) L = (1, 38)(2, 37)(3, 45)(4, 44)(5, 43)(6, 50)(7, 41)(8, 40)(9, 39)(10, 57)(11, 56)(12, 54)(13, 53)(14, 42)(15, 64)(16, 63)(17, 49)(18, 48)(19, 69)(20, 47)(21, 46)(22, 71)(23, 66)(24, 68)(25, 67)(26, 72)(27, 52)(28, 51)(29, 70)(30, 59)(31, 61)(32, 60)(33, 55)(34, 65)(35, 58)(36, 62)(73, 111)(74, 114)(75, 109)(76, 119)(77, 118)(78, 110)(79, 124)(80, 123)(81, 127)(82, 113)(83, 112)(84, 131)(85, 130)(86, 134)(87, 116)(88, 115)(89, 138)(90, 137)(91, 117)(92, 139)(93, 142)(94, 121)(95, 120)(96, 135)(97, 144)(98, 122)(99, 132)(100, 143)(101, 126)(102, 125)(103, 128)(104, 141)(105, 140)(106, 129)(107, 136)(108, 133) 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 ) } Outer automorphisms :: reflexible Dual of E12.556 Transitivity :: VT+ Graph:: bipartite v = 2 e = 72 f = 48 degree seq :: [ 72^2 ] E12.560 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 18}) Quotient :: dipole Aut^+ = D36 (small group id <36, 4>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^3, (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y2^-1), (R * Y2)^2, (Y3^-1 * Y1)^2, (Y2 * Y1)^2, Y3^6 * 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 * Y3^-1 * Y2 ] Map:: non-degenerate R = (1, 37, 2, 38)(3, 39, 9, 45)(4, 40, 10, 46)(5, 41, 7, 43)(6, 42, 8, 44)(11, 47, 21, 57)(12, 48, 20, 56)(13, 49, 22, 58)(14, 50, 18, 54)(15, 51, 17, 53)(16, 52, 19, 55)(23, 59, 33, 69)(24, 60, 32, 68)(25, 61, 34, 70)(26, 62, 30, 66)(27, 63, 29, 65)(28, 64, 31, 67)(35, 71, 36, 72)(73, 109, 75, 111, 77, 113)(74, 110, 79, 115, 81, 117)(76, 112, 83, 119, 86, 122)(78, 114, 84, 120, 87, 123)(80, 116, 89, 125, 92, 128)(82, 118, 90, 126, 93, 129)(85, 121, 95, 131, 98, 134)(88, 124, 96, 132, 99, 135)(91, 127, 101, 137, 104, 140)(94, 130, 102, 138, 105, 141)(97, 133, 100, 136, 107, 143)(103, 139, 106, 142, 108, 144) L = (1, 76)(2, 80)(3, 83)(4, 85)(5, 86)(6, 73)(7, 89)(8, 91)(9, 92)(10, 74)(11, 95)(12, 75)(13, 97)(14, 98)(15, 77)(16, 78)(17, 101)(18, 79)(19, 103)(20, 104)(21, 81)(22, 82)(23, 100)(24, 84)(25, 99)(26, 107)(27, 87)(28, 88)(29, 106)(30, 90)(31, 105)(32, 108)(33, 93)(34, 94)(35, 96)(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) :: { ( 4, 36, 4, 36 ), ( 4, 36, 4, 36, 4, 36 ) } Outer automorphisms :: reflexible Dual of E12.563 Graph:: simple bipartite v = 30 e = 72 f = 20 degree seq :: [ 4^18, 6^12 ] E12.561 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 18}) Quotient :: dipole Aut^+ = D36 (small group id <36, 4>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^3, (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y2^-1), (R * Y2)^2, (Y3^-1 * Y1)^2, (Y2 * Y1)^2, Y3^6 * 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 * Y3^2 ] Map:: non-degenerate R = (1, 37, 2, 38)(3, 39, 9, 45)(4, 40, 10, 46)(5, 41, 7, 43)(6, 42, 8, 44)(11, 47, 21, 57)(12, 48, 20, 56)(13, 49, 22, 58)(14, 50, 18, 54)(15, 51, 17, 53)(16, 52, 19, 55)(23, 59, 33, 69)(24, 60, 32, 68)(25, 61, 34, 70)(26, 62, 30, 66)(27, 63, 29, 65)(28, 64, 31, 67)(35, 71, 36, 72)(73, 109, 75, 111, 77, 113)(74, 110, 79, 115, 81, 117)(76, 112, 83, 119, 86, 122)(78, 114, 84, 120, 87, 123)(80, 116, 89, 125, 92, 128)(82, 118, 90, 126, 93, 129)(85, 121, 95, 131, 98, 134)(88, 124, 96, 132, 99, 135)(91, 127, 101, 137, 104, 140)(94, 130, 102, 138, 105, 141)(97, 133, 107, 143, 100, 136)(103, 139, 108, 144, 106, 142) L = (1, 76)(2, 80)(3, 83)(4, 85)(5, 86)(6, 73)(7, 89)(8, 91)(9, 92)(10, 74)(11, 95)(12, 75)(13, 97)(14, 98)(15, 77)(16, 78)(17, 101)(18, 79)(19, 103)(20, 104)(21, 81)(22, 82)(23, 107)(24, 84)(25, 96)(26, 100)(27, 87)(28, 88)(29, 108)(30, 90)(31, 102)(32, 106)(33, 93)(34, 94)(35, 99)(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) :: { ( 4, 36, 4, 36 ), ( 4, 36, 4, 36, 4, 36 ) } Outer automorphisms :: reflexible Dual of E12.562 Graph:: simple bipartite v = 30 e = 72 f = 20 degree seq :: [ 4^18, 6^12 ] E12.562 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 18}) Quotient :: dipole Aut^+ = D36 (small group id <36, 4>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ Y2^2, R^2, (Y1^-1, Y3^-1), (Y3^-1, Y1), (R * Y1)^2, (Y3 * Y2)^2, (Y2 * Y1)^2, (R * Y3)^2, Y1 * Y3 * Y1 * Y3^2 * Y1, (R * Y2 * Y3^-1)^2, Y3^3 * Y1^-1 * Y3^2 ] Map:: non-degenerate R = (1, 37, 2, 38, 7, 43, 19, 55, 14, 50, 25, 61, 17, 53, 6, 42, 10, 46, 22, 58, 15, 51, 4, 40, 9, 45, 21, 57, 18, 54, 26, 62, 16, 52, 5, 41)(3, 39, 11, 47, 27, 63, 35, 71, 30, 66, 34, 70, 24, 60, 13, 49, 29, 65, 33, 69, 23, 59, 12, 48, 28, 64, 36, 72, 31, 67, 32, 68, 20, 56, 8, 44)(73, 109, 75, 111)(74, 110, 80, 116)(76, 112, 85, 121)(77, 113, 83, 119)(78, 114, 84, 120)(79, 115, 92, 128)(81, 117, 96, 132)(82, 118, 95, 131)(86, 122, 103, 139)(87, 123, 101, 137)(88, 124, 99, 135)(89, 125, 100, 136)(90, 126, 102, 138)(91, 127, 104, 140)(93, 129, 106, 142)(94, 130, 105, 141)(97, 133, 108, 144)(98, 134, 107, 143) L = (1, 76)(2, 81)(3, 84)(4, 86)(5, 87)(6, 73)(7, 93)(8, 95)(9, 97)(10, 74)(11, 100)(12, 102)(13, 75)(14, 98)(15, 91)(16, 94)(17, 77)(18, 78)(19, 90)(20, 105)(21, 89)(22, 79)(23, 107)(24, 80)(25, 88)(26, 82)(27, 108)(28, 106)(29, 83)(30, 104)(31, 85)(32, 101)(33, 99)(34, 92)(35, 103)(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) :: { ( 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 E12.561 Graph:: bipartite v = 20 e = 72 f = 30 degree seq :: [ 4^18, 36^2 ] E12.563 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 18}) Quotient :: dipole Aut^+ = D36 (small group id <36, 4>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ Y2^2, R^2, (R * Y1)^2, (Y3 * Y2)^2, (Y3^-1, Y1^-1), (R * Y3)^2, (Y2 * Y1)^2, Y1^-1 * Y3^4 * Y1^-1, (R * Y2 * Y3^-1)^2, Y3^-3 * Y1^-3, (Y1^-1 * Y3^-1)^3 ] Map:: non-degenerate R = (1, 37, 2, 38, 7, 43, 19, 55, 15, 51, 4, 40, 9, 45, 21, 57, 18, 54, 26, 62, 14, 50, 25, 61, 17, 53, 6, 42, 10, 46, 22, 58, 16, 52, 5, 41)(3, 39, 11, 47, 27, 63, 33, 69, 23, 59, 12, 48, 28, 64, 36, 72, 31, 67, 35, 71, 30, 66, 34, 70, 24, 60, 13, 49, 29, 65, 32, 68, 20, 56, 8, 44)(73, 109, 75, 111)(74, 110, 80, 116)(76, 112, 85, 121)(77, 113, 83, 119)(78, 114, 84, 120)(79, 115, 92, 128)(81, 117, 96, 132)(82, 118, 95, 131)(86, 122, 103, 139)(87, 123, 101, 137)(88, 124, 99, 135)(89, 125, 100, 136)(90, 126, 102, 138)(91, 127, 104, 140)(93, 129, 106, 142)(94, 130, 105, 141)(97, 133, 108, 144)(98, 134, 107, 143) L = (1, 76)(2, 81)(3, 84)(4, 86)(5, 87)(6, 73)(7, 93)(8, 95)(9, 97)(10, 74)(11, 100)(12, 102)(13, 75)(14, 94)(15, 98)(16, 91)(17, 77)(18, 78)(19, 90)(20, 105)(21, 89)(22, 79)(23, 107)(24, 80)(25, 88)(26, 82)(27, 108)(28, 106)(29, 83)(30, 104)(31, 85)(32, 99)(33, 103)(34, 92)(35, 101)(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) :: { ( 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 E12.560 Graph:: bipartite v = 20 e = 72 f = 30 degree seq :: [ 4^18, 36^2 ] E12.564 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 9, 36}) Quotient :: edge Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1, T1^-1), T2^9 ] Map:: non-degenerate R = (1, 3, 9, 17, 25, 28, 20, 12, 5)(2, 7, 15, 23, 31, 32, 24, 16, 8)(4, 10, 18, 26, 33, 34, 27, 19, 11)(6, 13, 21, 29, 35, 36, 30, 22, 14)(37, 38, 42, 40)(39, 43, 49, 46)(41, 44, 50, 47)(45, 51, 57, 54)(48, 52, 58, 55)(53, 59, 65, 62)(56, 60, 66, 63)(61, 67, 71, 69)(64, 68, 72, 70) L = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 72^4 ), ( 72^9 ) } Outer automorphisms :: reflexible Dual of E12.568 Transitivity :: ET+ Graph:: simple bipartite v = 13 e = 36 f = 1 degree seq :: [ 4^9, 9^4 ] E12.565 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 9, 36}) Quotient :: edge Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-4 * T1^-4, T1^-1 * T2^8, T2^-1 * T1 * T2^-2 * T1^3 * T2^-1 * T1, T1^9 ] Map:: non-degenerate R = (1, 3, 9, 19, 33, 32, 18, 8, 2, 7, 17, 31, 22, 36, 30, 16, 6, 15, 29, 23, 11, 21, 35, 28, 14, 27, 24, 12, 4, 10, 20, 34, 26, 25, 13, 5)(37, 38, 42, 50, 62, 69, 58, 47, 40)(39, 43, 51, 63, 61, 68, 72, 57, 46)(41, 44, 52, 64, 70, 55, 67, 59, 48)(45, 53, 65, 60, 49, 54, 66, 71, 56) L = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 8^9 ), ( 8^36 ) } Outer automorphisms :: reflexible Dual of E12.569 Transitivity :: ET+ Graph:: bipartite v = 5 e = 36 f = 9 degree seq :: [ 9^4, 36 ] E12.566 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 9, 36}) Quotient :: edge Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^4, (T2^-1, T1^-1), T2^-1 * T1^-9, (T1^-1 * T2^-1)^9 ] 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, 36, 31)(27, 34, 35, 29)(37, 38, 42, 49, 57, 65, 64, 56, 48, 41, 44, 51, 59, 67, 71, 69, 61, 53, 45, 52, 60, 68, 72, 70, 62, 54, 46, 39, 43, 50, 58, 66, 63, 55, 47, 40) L = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 18^4 ), ( 18^36 ) } Outer automorphisms :: reflexible Dual of E12.567 Transitivity :: ET+ Graph:: bipartite v = 10 e = 36 f = 4 degree seq :: [ 4^9, 36 ] E12.567 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 9, 36}) Quotient :: loop Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1, T1^-1), T2^9 ] Map:: non-degenerate R = (1, 37, 3, 39, 9, 45, 17, 53, 25, 61, 28, 64, 20, 56, 12, 48, 5, 41)(2, 38, 7, 43, 15, 51, 23, 59, 31, 67, 32, 68, 24, 60, 16, 52, 8, 44)(4, 40, 10, 46, 18, 54, 26, 62, 33, 69, 34, 70, 27, 63, 19, 55, 11, 47)(6, 42, 13, 49, 21, 57, 29, 65, 35, 71, 36, 72, 30, 66, 22, 58, 14, 50) L = (1, 38)(2, 42)(3, 43)(4, 37)(5, 44)(6, 40)(7, 49)(8, 50)(9, 51)(10, 39)(11, 41)(12, 52)(13, 46)(14, 47)(15, 57)(16, 58)(17, 59)(18, 45)(19, 48)(20, 60)(21, 54)(22, 55)(23, 65)(24, 66)(25, 67)(26, 53)(27, 56)(28, 68)(29, 62)(30, 63)(31, 71)(32, 72)(33, 61)(34, 64)(35, 69)(36, 70) local type(s) :: { ( 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36, 4, 36 ) } Outer automorphisms :: reflexible Dual of E12.566 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 4 e = 36 f = 10 degree seq :: [ 18^4 ] E12.568 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 9, 36}) Quotient :: loop Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-4 * T1^-4, T1^-1 * T2^8, T2^-1 * T1 * T2^-2 * T1^3 * T2^-1 * T1, T1^9 ] Map:: non-degenerate R = (1, 37, 3, 39, 9, 45, 19, 55, 33, 69, 32, 68, 18, 54, 8, 44, 2, 38, 7, 43, 17, 53, 31, 67, 22, 58, 36, 72, 30, 66, 16, 52, 6, 42, 15, 51, 29, 65, 23, 59, 11, 47, 21, 57, 35, 71, 28, 64, 14, 50, 27, 63, 24, 60, 12, 48, 4, 40, 10, 46, 20, 56, 34, 70, 26, 62, 25, 61, 13, 49, 5, 41) L = (1, 38)(2, 42)(3, 43)(4, 37)(5, 44)(6, 50)(7, 51)(8, 52)(9, 53)(10, 39)(11, 40)(12, 41)(13, 54)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 45)(21, 46)(22, 47)(23, 48)(24, 49)(25, 68)(26, 69)(27, 61)(28, 70)(29, 60)(30, 71)(31, 59)(32, 72)(33, 58)(34, 55)(35, 56)(36, 57) local type(s) :: { ( 4, 9, 4, 9, 4, 9, 4, 9, 4, 9, 4, 9, 4, 9, 4, 9, 4, 9, 4, 9, 4, 9, 4, 9, 4, 9, 4, 9, 4, 9, 4, 9, 4, 9, 4, 9, 4, 9, 4, 9, 4, 9, 4, 9, 4, 9, 4, 9, 4, 9, 4, 9, 4, 9, 4, 9, 4, 9, 4, 9, 4, 9, 4, 9, 4, 9, 4, 9, 4, 9, 4, 9 ) } Outer automorphisms :: reflexible Dual of E12.564 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 36 f = 13 degree seq :: [ 72 ] E12.569 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 9, 36}) Quotient :: loop Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^4, (T2^-1, T1^-1), T2^-1 * T1^-9, (T1^-1 * T2^-1)^9 ] Map:: non-degenerate R = (1, 37, 3, 39, 9, 45, 5, 41)(2, 38, 7, 43, 16, 52, 8, 44)(4, 40, 10, 46, 17, 53, 12, 48)(6, 42, 14, 50, 24, 60, 15, 51)(11, 47, 18, 54, 25, 61, 20, 56)(13, 49, 22, 58, 32, 68, 23, 59)(19, 55, 26, 62, 33, 69, 28, 64)(21, 57, 30, 66, 36, 72, 31, 67)(27, 63, 34, 70, 35, 71, 29, 65) L = (1, 38)(2, 42)(3, 43)(4, 37)(5, 44)(6, 49)(7, 50)(8, 51)(9, 52)(10, 39)(11, 40)(12, 41)(13, 57)(14, 58)(15, 59)(16, 60)(17, 45)(18, 46)(19, 47)(20, 48)(21, 65)(22, 66)(23, 67)(24, 68)(25, 53)(26, 54)(27, 55)(28, 56)(29, 64)(30, 63)(31, 71)(32, 72)(33, 61)(34, 62)(35, 69)(36, 70) local type(s) :: { ( 9, 36, 9, 36, 9, 36, 9, 36 ) } Outer automorphisms :: reflexible Dual of E12.565 Transitivity :: ET+ VT+ AT Graph:: v = 9 e = 36 f = 5 degree seq :: [ 8^9 ] E12.570 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 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 * Y1^-1, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y1^4, (Y2, Y1^-1), (Y3^-1, Y2^-1), Y2^9, Y3^36 ] 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, 100, 136, 92, 128, 84, 120, 77, 113)(74, 110, 79, 115, 87, 123, 95, 131, 103, 139, 104, 140, 96, 132, 88, 124, 80, 116)(76, 112, 82, 118, 90, 126, 98, 134, 105, 141, 106, 142, 99, 135, 91, 127, 83, 119)(78, 114, 85, 121, 93, 129, 101, 137, 107, 143, 108, 144, 102, 138, 94, 130, 86, 122) L = (1, 76)(2, 73)(3, 82)(4, 78)(5, 83)(6, 74)(7, 75)(8, 77)(9, 90)(10, 85)(11, 86)(12, 91)(13, 79)(14, 80)(15, 81)(16, 84)(17, 98)(18, 93)(19, 94)(20, 99)(21, 87)(22, 88)(23, 89)(24, 92)(25, 105)(26, 101)(27, 102)(28, 106)(29, 95)(30, 96)(31, 97)(32, 100)(33, 107)(34, 108)(35, 103)(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) :: { ( 2, 72, 2, 72, 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 E12.573 Graph:: bipartite v = 13 e = 72 f = 37 degree seq :: [ 8^9, 18^4 ] E12.571 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 9, 36}) Quotient :: dipole Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-1, (R * Y1)^2, R * Y2 * R * Y3, (Y1^-1, Y2^-1), Y1^-4 * Y2^-4, (Y3^-1 * Y1^-1)^4, Y1^-1 * Y2^8, Y1^9 ] Map:: R = (1, 37, 2, 38, 6, 42, 14, 50, 26, 62, 33, 69, 22, 58, 11, 47, 4, 40)(3, 39, 7, 43, 15, 51, 27, 63, 25, 61, 32, 68, 36, 72, 21, 57, 10, 46)(5, 41, 8, 44, 16, 52, 28, 64, 34, 70, 19, 55, 31, 67, 23, 59, 12, 48)(9, 45, 17, 53, 29, 65, 24, 60, 13, 49, 18, 54, 30, 66, 35, 71, 20, 56)(73, 109, 75, 111, 81, 117, 91, 127, 105, 141, 104, 140, 90, 126, 80, 116, 74, 110, 79, 115, 89, 125, 103, 139, 94, 130, 108, 144, 102, 138, 88, 124, 78, 114, 87, 123, 101, 137, 95, 131, 83, 119, 93, 129, 107, 143, 100, 136, 86, 122, 99, 135, 96, 132, 84, 120, 76, 112, 82, 118, 92, 128, 106, 142, 98, 134, 97, 133, 85, 121, 77, 113) L = (1, 75)(2, 79)(3, 81)(4, 82)(5, 73)(6, 87)(7, 89)(8, 74)(9, 91)(10, 92)(11, 93)(12, 76)(13, 77)(14, 99)(15, 101)(16, 78)(17, 103)(18, 80)(19, 105)(20, 106)(21, 107)(22, 108)(23, 83)(24, 84)(25, 85)(26, 97)(27, 96)(28, 86)(29, 95)(30, 88)(31, 94)(32, 90)(33, 104)(34, 98)(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) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 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 E12.572 Graph:: bipartite v = 5 e = 72 f = 45 degree seq :: [ 18^4, 72 ] E12.572 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 9, 36}) Quotient :: dipole Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2^4, (Y2, Y3^-1), Y2^-1 * Y3^9, 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^-1 * Y1^-1)^36 ] Map:: R = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72)(73, 109, 74, 110, 78, 114, 76, 112)(75, 111, 79, 115, 85, 121, 82, 118)(77, 113, 80, 116, 86, 122, 83, 119)(81, 117, 87, 123, 93, 129, 90, 126)(84, 120, 88, 124, 94, 130, 91, 127)(89, 125, 95, 131, 101, 137, 98, 134)(92, 128, 96, 132, 102, 138, 99, 135)(97, 133, 103, 139, 107, 143, 105, 141)(100, 136, 104, 140, 108, 144, 106, 142) L = (1, 75)(2, 79)(3, 81)(4, 82)(5, 73)(6, 85)(7, 87)(8, 74)(9, 89)(10, 90)(11, 76)(12, 77)(13, 93)(14, 78)(15, 95)(16, 80)(17, 97)(18, 98)(19, 83)(20, 84)(21, 101)(22, 86)(23, 103)(24, 88)(25, 104)(26, 105)(27, 91)(28, 92)(29, 107)(30, 94)(31, 108)(32, 96)(33, 100)(34, 99)(35, 106)(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 ) } Outer automorphisms :: reflexible Dual of E12.571 Graph:: simple bipartite v = 45 e = 72 f = 5 degree seq :: [ 2^36, 8^9 ] E12.573 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 9, 36}) Quotient :: dipole Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1^-1), (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^4, Y1^-2 * Y3^-1 * Y1^-7, Y1 * Y3^-1 * Y1^4 * Y3^-1 * Y1^3 * Y3^-1 * Y1, (Y1^-1 * Y3^-1)^9 ] Map:: R = (1, 37, 2, 38, 6, 42, 13, 49, 21, 57, 29, 65, 28, 64, 20, 56, 12, 48, 5, 41, 8, 44, 15, 51, 23, 59, 31, 67, 35, 71, 33, 69, 25, 61, 17, 53, 9, 45, 16, 52, 24, 60, 32, 68, 36, 72, 34, 70, 26, 62, 18, 54, 10, 46, 3, 39, 7, 43, 14, 50, 22, 58, 30, 66, 27, 63, 19, 55, 11, 47, 4, 40)(73, 109)(74, 110)(75, 111)(76, 112)(77, 113)(78, 114)(79, 115)(80, 116)(81, 117)(82, 118)(83, 119)(84, 120)(85, 121)(86, 122)(87, 123)(88, 124)(89, 125)(90, 126)(91, 127)(92, 128)(93, 129)(94, 130)(95, 131)(96, 132)(97, 133)(98, 134)(99, 135)(100, 136)(101, 137)(102, 138)(103, 139)(104, 140)(105, 141)(106, 142)(107, 143)(108, 144) L = (1, 75)(2, 79)(3, 81)(4, 82)(5, 73)(6, 86)(7, 88)(8, 74)(9, 77)(10, 89)(11, 90)(12, 76)(13, 94)(14, 96)(15, 78)(16, 80)(17, 84)(18, 97)(19, 98)(20, 83)(21, 102)(22, 104)(23, 85)(24, 87)(25, 92)(26, 105)(27, 106)(28, 91)(29, 99)(30, 108)(31, 93)(32, 95)(33, 100)(34, 107)(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, 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 E12.570 Graph:: bipartite v = 37 e = 72 f = 13 degree seq :: [ 2^36, 72 ] E12.574 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 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 * Y1^-1, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y3^4, Y1^4, (Y2, Y1^-1), (Y3^-1, Y2^-1), Y3 * 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 ] 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, 76)(2, 73)(3, 82)(4, 78)(5, 83)(6, 74)(7, 75)(8, 77)(9, 90)(10, 85)(11, 86)(12, 91)(13, 79)(14, 80)(15, 81)(16, 84)(17, 98)(18, 93)(19, 94)(20, 99)(21, 87)(22, 88)(23, 89)(24, 92)(25, 106)(26, 101)(27, 102)(28, 105)(29, 95)(30, 96)(31, 97)(32, 100)(33, 108)(34, 107)(35, 103)(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) :: { ( 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 E12.575 Graph:: bipartite v = 10 e = 72 f = 40 degree seq :: [ 8^9, 72 ] E12.575 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 9, 36}) Quotient :: dipole Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1^-1), (R * Y2 * Y3^-1)^2, Y3^-4 * Y1^-4, Y1^-1 * Y3^8, Y1 * Y3^-1 * Y1 * Y3^-1 * Y1^2 * Y3^-2 * Y1, Y1^9, (Y3 * Y2^-1)^36 ] Map:: R = (1, 37, 2, 38, 6, 42, 14, 50, 26, 62, 33, 69, 22, 58, 11, 47, 4, 40)(3, 39, 7, 43, 15, 51, 27, 63, 25, 61, 32, 68, 36, 72, 21, 57, 10, 46)(5, 41, 8, 44, 16, 52, 28, 64, 34, 70, 19, 55, 31, 67, 23, 59, 12, 48)(9, 45, 17, 53, 29, 65, 24, 60, 13, 49, 18, 54, 30, 66, 35, 71, 20, 56)(73, 109)(74, 110)(75, 111)(76, 112)(77, 113)(78, 114)(79, 115)(80, 116)(81, 117)(82, 118)(83, 119)(84, 120)(85, 121)(86, 122)(87, 123)(88, 124)(89, 125)(90, 126)(91, 127)(92, 128)(93, 129)(94, 130)(95, 131)(96, 132)(97, 133)(98, 134)(99, 135)(100, 136)(101, 137)(102, 138)(103, 139)(104, 140)(105, 141)(106, 142)(107, 143)(108, 144) L = (1, 75)(2, 79)(3, 81)(4, 82)(5, 73)(6, 87)(7, 89)(8, 74)(9, 91)(10, 92)(11, 93)(12, 76)(13, 77)(14, 99)(15, 101)(16, 78)(17, 103)(18, 80)(19, 105)(20, 106)(21, 107)(22, 108)(23, 83)(24, 84)(25, 85)(26, 97)(27, 96)(28, 86)(29, 95)(30, 88)(31, 94)(32, 90)(33, 104)(34, 98)(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) :: { ( 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 E12.574 Graph:: simple bipartite v = 40 e = 72 f = 10 degree seq :: [ 2^36, 18^4 ] E12.576 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 36, 36}) Quotient :: edge Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, (T2^-1, T1^-1), T2^-12 * T1, (T1^-1 * T2^-1)^36 ] Map:: non-degenerate R = (1, 3, 8, 14, 20, 26, 32, 31, 25, 19, 13, 7, 2, 6, 12, 18, 24, 30, 36, 34, 28, 22, 16, 10, 4, 9, 15, 21, 27, 33, 35, 29, 23, 17, 11, 5)(37, 38, 40)(39, 42, 45)(41, 43, 46)(44, 48, 51)(47, 49, 52)(50, 54, 57)(53, 55, 58)(56, 60, 63)(59, 61, 64)(62, 66, 69)(65, 67, 70)(68, 72, 71) L = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 72^3 ), ( 72^36 ) } Outer automorphisms :: reflexible Dual of E12.580 Transitivity :: ET+ Graph:: bipartite v = 13 e = 36 f = 1 degree seq :: [ 3^12, 36 ] E12.577 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 36, 36}) Quotient :: edge Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, (T2^-1, T1^-1), T2^12 * T1, (T1^-1 * T2^-1)^36 ] Map:: non-degenerate R = (1, 3, 8, 14, 20, 26, 32, 34, 28, 22, 16, 10, 4, 9, 15, 21, 27, 33, 36, 31, 25, 19, 13, 7, 2, 6, 12, 18, 24, 30, 35, 29, 23, 17, 11, 5)(37, 38, 40)(39, 42, 45)(41, 43, 46)(44, 48, 51)(47, 49, 52)(50, 54, 57)(53, 55, 58)(56, 60, 63)(59, 61, 64)(62, 66, 69)(65, 67, 70)(68, 71, 72) L = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 72^3 ), ( 72^36 ) } Outer automorphisms :: reflexible Dual of E12.579 Transitivity :: ET+ Graph:: bipartite v = 13 e = 36 f = 1 degree seq :: [ 3^12, 36 ] E12.578 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 36, 36}) Quotient :: edge Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ F^2, (T2, T1), (F * T1)^2, (F * T2)^2, T2^-3 * T1^-3, T2^7 * T1^-5, T1^22 * T2^-2, T2 * T1^25, T1^36 ] Map:: non-degenerate R = (1, 3, 9, 19, 25, 31, 35, 28, 24, 16, 6, 15, 12, 4, 10, 20, 26, 32, 36, 29, 22, 18, 8, 2, 7, 17, 11, 21, 27, 33, 34, 30, 23, 14, 13, 5)(37, 38, 42, 50, 58, 64, 70, 68, 61, 57, 46, 39, 43, 51, 49, 54, 60, 66, 72, 67, 63, 56, 45, 53, 48, 41, 44, 52, 59, 65, 71, 69, 62, 55, 47, 40) L = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72) local type(s) :: { ( 6^36 ) } Outer automorphisms :: reflexible Dual of E12.581 Transitivity :: ET+ Graph:: bipartite v = 2 e = 36 f = 12 degree seq :: [ 36^2 ] E12.579 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 36, 36}) Quotient :: loop Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, (T2^-1, T1^-1), T2^-12 * T1, (T1^-1 * T2^-1)^36 ] Map:: non-degenerate R = (1, 37, 3, 39, 8, 44, 14, 50, 20, 56, 26, 62, 32, 68, 31, 67, 25, 61, 19, 55, 13, 49, 7, 43, 2, 38, 6, 42, 12, 48, 18, 54, 24, 60, 30, 66, 36, 72, 34, 70, 28, 64, 22, 58, 16, 52, 10, 46, 4, 40, 9, 45, 15, 51, 21, 57, 27, 63, 33, 69, 35, 71, 29, 65, 23, 59, 17, 53, 11, 47, 5, 41) L = (1, 38)(2, 40)(3, 42)(4, 37)(5, 43)(6, 45)(7, 46)(8, 48)(9, 39)(10, 41)(11, 49)(12, 51)(13, 52)(14, 54)(15, 44)(16, 47)(17, 55)(18, 57)(19, 58)(20, 60)(21, 50)(22, 53)(23, 61)(24, 63)(25, 64)(26, 66)(27, 56)(28, 59)(29, 67)(30, 69)(31, 70)(32, 72)(33, 62)(34, 65)(35, 68)(36, 71) local type(s) :: { ( 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36 ) } Outer automorphisms :: reflexible Dual of E12.577 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 36 f = 13 degree seq :: [ 72 ] E12.580 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 36, 36}) Quotient :: loop Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, (T2^-1, T1^-1), T2^12 * T1, (T1^-1 * T2^-1)^36 ] Map:: non-degenerate R = (1, 37, 3, 39, 8, 44, 14, 50, 20, 56, 26, 62, 32, 68, 34, 70, 28, 64, 22, 58, 16, 52, 10, 46, 4, 40, 9, 45, 15, 51, 21, 57, 27, 63, 33, 69, 36, 72, 31, 67, 25, 61, 19, 55, 13, 49, 7, 43, 2, 38, 6, 42, 12, 48, 18, 54, 24, 60, 30, 66, 35, 71, 29, 65, 23, 59, 17, 53, 11, 47, 5, 41) L = (1, 38)(2, 40)(3, 42)(4, 37)(5, 43)(6, 45)(7, 46)(8, 48)(9, 39)(10, 41)(11, 49)(12, 51)(13, 52)(14, 54)(15, 44)(16, 47)(17, 55)(18, 57)(19, 58)(20, 60)(21, 50)(22, 53)(23, 61)(24, 63)(25, 64)(26, 66)(27, 56)(28, 59)(29, 67)(30, 69)(31, 70)(32, 71)(33, 62)(34, 65)(35, 72)(36, 68) local type(s) :: { ( 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36, 3, 36 ) } Outer automorphisms :: reflexible Dual of E12.576 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 36 f = 13 degree seq :: [ 72 ] E12.581 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 36, 36}) Quotient :: loop Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ F^2, T2^3, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-1 * T1^12, (T1^-1 * T2^-1)^36 ] Map:: non-degenerate R = (1, 37, 3, 39, 5, 41)(2, 38, 7, 43, 8, 44)(4, 40, 9, 45, 11, 47)(6, 42, 13, 49, 14, 50)(10, 46, 15, 51, 17, 53)(12, 48, 19, 55, 20, 56)(16, 52, 21, 57, 23, 59)(18, 54, 25, 61, 26, 62)(22, 58, 27, 63, 29, 65)(24, 60, 31, 67, 32, 68)(28, 64, 33, 69, 35, 71)(30, 66, 36, 72, 34, 70) L = (1, 38)(2, 42)(3, 43)(4, 37)(5, 44)(6, 48)(7, 49)(8, 50)(9, 39)(10, 40)(11, 41)(12, 54)(13, 55)(14, 56)(15, 45)(16, 46)(17, 47)(18, 60)(19, 61)(20, 62)(21, 51)(22, 52)(23, 53)(24, 66)(25, 67)(26, 68)(27, 57)(28, 58)(29, 59)(30, 69)(31, 72)(32, 70)(33, 63)(34, 64)(35, 65)(36, 71) local type(s) :: { ( 36^6 ) } Outer automorphisms :: reflexible Dual of E12.578 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 12 e = 36 f = 2 degree seq :: [ 6^12 ] E12.582 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 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^-1, Y3 * Y1^-2, Y1^3, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y3^-1, Y2^-1), (Y2, Y1^-1), Y2^12 * 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 ] Map:: R = (1, 37, 2, 38, 4, 40)(3, 39, 6, 42, 9, 45)(5, 41, 7, 43, 10, 46)(8, 44, 12, 48, 15, 51)(11, 47, 13, 49, 16, 52)(14, 50, 18, 54, 21, 57)(17, 53, 19, 55, 22, 58)(20, 56, 24, 60, 27, 63)(23, 59, 25, 61, 28, 64)(26, 62, 30, 66, 33, 69)(29, 65, 31, 67, 34, 70)(32, 68, 35, 71, 36, 72)(73, 109, 75, 111, 80, 116, 86, 122, 92, 128, 98, 134, 104, 140, 106, 142, 100, 136, 94, 130, 88, 124, 82, 118, 76, 112, 81, 117, 87, 123, 93, 129, 99, 135, 105, 141, 108, 144, 103, 139, 97, 133, 91, 127, 85, 121, 79, 115, 74, 110, 78, 114, 84, 120, 90, 126, 96, 132, 102, 138, 107, 143, 101, 137, 95, 131, 89, 125, 83, 119, 77, 113) L = (1, 76)(2, 73)(3, 81)(4, 74)(5, 82)(6, 75)(7, 77)(8, 87)(9, 78)(10, 79)(11, 88)(12, 80)(13, 83)(14, 93)(15, 84)(16, 85)(17, 94)(18, 86)(19, 89)(20, 99)(21, 90)(22, 91)(23, 100)(24, 92)(25, 95)(26, 105)(27, 96)(28, 97)(29, 106)(30, 98)(31, 101)(32, 108)(33, 102)(34, 103)(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) :: { ( 2, 72, 2, 72, 2, 72 ), ( 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 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 E12.586 Graph:: bipartite v = 13 e = 72 f = 37 degree seq :: [ 6^12, 72 ] E12.583 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 36, 36}) Quotient :: dipole Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, Y3^3, Y1^3, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y3^-1, Y2^-1), (Y2, Y1^-1), Y3 * Y2^12, 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 ] Map:: R = (1, 37, 2, 38, 4, 40)(3, 39, 6, 42, 9, 45)(5, 41, 7, 43, 10, 46)(8, 44, 12, 48, 15, 51)(11, 47, 13, 49, 16, 52)(14, 50, 18, 54, 21, 57)(17, 53, 19, 55, 22, 58)(20, 56, 24, 60, 27, 63)(23, 59, 25, 61, 28, 64)(26, 62, 30, 66, 33, 69)(29, 65, 31, 67, 34, 70)(32, 68, 36, 72, 35, 71)(73, 109, 75, 111, 80, 116, 86, 122, 92, 128, 98, 134, 104, 140, 103, 139, 97, 133, 91, 127, 85, 121, 79, 115, 74, 110, 78, 114, 84, 120, 90, 126, 96, 132, 102, 138, 108, 144, 106, 142, 100, 136, 94, 130, 88, 124, 82, 118, 76, 112, 81, 117, 87, 123, 93, 129, 99, 135, 105, 141, 107, 143, 101, 137, 95, 131, 89, 125, 83, 119, 77, 113) L = (1, 76)(2, 73)(3, 81)(4, 74)(5, 82)(6, 75)(7, 77)(8, 87)(9, 78)(10, 79)(11, 88)(12, 80)(13, 83)(14, 93)(15, 84)(16, 85)(17, 94)(18, 86)(19, 89)(20, 99)(21, 90)(22, 91)(23, 100)(24, 92)(25, 95)(26, 105)(27, 96)(28, 97)(29, 106)(30, 98)(31, 101)(32, 107)(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) :: { ( 2, 72, 2, 72, 2, 72 ), ( 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 2, 72, 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 E12.587 Graph:: bipartite v = 13 e = 72 f = 37 degree seq :: [ 6^12, 72 ] E12.584 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 36, 36}) Quotient :: dipole Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-1, (R * Y1)^2, R * Y2 * R * Y3, (Y1, Y2^-1), Y1^-2 * Y2^-1 * Y1^-1 * Y2^-2, (Y3^-1 * Y1^-1)^3, Y2^4 * Y1^4 * Y2^-1 * Y1^-1, Y1^8 * Y2^-1 * Y1 * Y2^-1 * Y1, Y1 * Y2^2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2^2 ] Map:: R = (1, 37, 2, 38, 6, 42, 14, 50, 22, 58, 28, 64, 34, 70, 31, 67, 27, 63, 20, 56, 9, 45, 17, 53, 12, 48, 5, 41, 8, 44, 16, 52, 23, 59, 29, 65, 35, 71, 32, 68, 25, 61, 21, 57, 10, 46, 3, 39, 7, 43, 15, 51, 13, 49, 18, 54, 24, 60, 30, 66, 36, 72, 33, 69, 26, 62, 19, 55, 11, 47, 4, 40)(73, 109, 75, 111, 81, 117, 91, 127, 97, 133, 103, 139, 108, 144, 101, 137, 94, 130, 90, 126, 80, 116, 74, 110, 79, 115, 89, 125, 83, 119, 93, 129, 99, 135, 105, 141, 107, 143, 100, 136, 96, 132, 88, 124, 78, 114, 87, 123, 84, 120, 76, 112, 82, 118, 92, 128, 98, 134, 104, 140, 106, 142, 102, 138, 95, 131, 86, 122, 85, 121, 77, 113) L = (1, 75)(2, 79)(3, 81)(4, 82)(5, 73)(6, 87)(7, 89)(8, 74)(9, 91)(10, 92)(11, 93)(12, 76)(13, 77)(14, 85)(15, 84)(16, 78)(17, 83)(18, 80)(19, 97)(20, 98)(21, 99)(22, 90)(23, 86)(24, 88)(25, 103)(26, 104)(27, 105)(28, 96)(29, 94)(30, 95)(31, 108)(32, 106)(33, 107)(34, 102)(35, 100)(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) :: { ( 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 E12.585 Graph:: bipartite v = 2 e = 72 f = 48 degree seq :: [ 72^2 ] E12.585 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 36, 36}) Quotient :: dipole Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ Y1, R^2, Y2^3, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y2, Y3^-1), Y2^-1 * Y3^12, 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 * Y3^2, (Y3^-1 * Y1^-1)^36 ] Map:: R = (1, 37)(2, 38)(3, 39)(4, 40)(5, 41)(6, 42)(7, 43)(8, 44)(9, 45)(10, 46)(11, 47)(12, 48)(13, 49)(14, 50)(15, 51)(16, 52)(17, 53)(18, 54)(19, 55)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 61)(26, 62)(27, 63)(28, 64)(29, 65)(30, 66)(31, 67)(32, 68)(33, 69)(34, 70)(35, 71)(36, 72)(73, 109, 74, 110, 76, 112)(75, 111, 78, 114, 81, 117)(77, 113, 79, 115, 82, 118)(80, 116, 84, 120, 87, 123)(83, 119, 85, 121, 88, 124)(86, 122, 90, 126, 93, 129)(89, 125, 91, 127, 94, 130)(92, 128, 96, 132, 99, 135)(95, 131, 97, 133, 100, 136)(98, 134, 102, 138, 105, 141)(101, 137, 103, 139, 106, 142)(104, 140, 108, 144, 107, 143) L = (1, 75)(2, 78)(3, 80)(4, 81)(5, 73)(6, 84)(7, 74)(8, 86)(9, 87)(10, 76)(11, 77)(12, 90)(13, 79)(14, 92)(15, 93)(16, 82)(17, 83)(18, 96)(19, 85)(20, 98)(21, 99)(22, 88)(23, 89)(24, 102)(25, 91)(26, 104)(27, 105)(28, 94)(29, 95)(30, 108)(31, 97)(32, 103)(33, 107)(34, 100)(35, 101)(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) :: { ( 72, 72 ), ( 72^6 ) } Outer automorphisms :: reflexible Dual of E12.584 Graph:: simple bipartite v = 48 e = 72 f = 2 degree seq :: [ 2^36, 6^12 ] E12.586 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 36, 36}) Quotient :: dipole Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^3, (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y1^-1), (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^3, Y3^-1 * Y1^12, (Y1^-1 * Y3^-1)^36 ] Map:: R = (1, 37, 2, 38, 6, 42, 12, 48, 18, 54, 24, 60, 30, 66, 33, 69, 27, 63, 21, 57, 15, 51, 9, 45, 3, 39, 7, 43, 13, 49, 19, 55, 25, 61, 31, 67, 36, 72, 35, 71, 29, 65, 23, 59, 17, 53, 11, 47, 5, 41, 8, 44, 14, 50, 20, 56, 26, 62, 32, 68, 34, 70, 28, 64, 22, 58, 16, 52, 10, 46, 4, 40)(73, 109)(74, 110)(75, 111)(76, 112)(77, 113)(78, 114)(79, 115)(80, 116)(81, 117)(82, 118)(83, 119)(84, 120)(85, 121)(86, 122)(87, 123)(88, 124)(89, 125)(90, 126)(91, 127)(92, 128)(93, 129)(94, 130)(95, 131)(96, 132)(97, 133)(98, 134)(99, 135)(100, 136)(101, 137)(102, 138)(103, 139)(104, 140)(105, 141)(106, 142)(107, 143)(108, 144) L = (1, 75)(2, 79)(3, 77)(4, 81)(5, 73)(6, 85)(7, 80)(8, 74)(9, 83)(10, 87)(11, 76)(12, 91)(13, 86)(14, 78)(15, 89)(16, 93)(17, 82)(18, 97)(19, 92)(20, 84)(21, 95)(22, 99)(23, 88)(24, 103)(25, 98)(26, 90)(27, 101)(28, 105)(29, 94)(30, 108)(31, 104)(32, 96)(33, 107)(34, 102)(35, 100)(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) :: { ( 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 E12.582 Graph:: bipartite v = 37 e = 72 f = 13 degree seq :: [ 2^36, 72 ] E12.587 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 36, 36}) Quotient :: dipole Aut^+ = C36 (small group id <36, 2>) Aut = D72 (small group id <72, 6>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^3, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1^-1), (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^3, Y3 * Y1^12, (Y1^-1 * Y3^-1)^36 ] Map:: R = (1, 37, 2, 38, 6, 42, 12, 48, 18, 54, 24, 60, 30, 66, 35, 71, 29, 65, 23, 59, 17, 53, 11, 47, 5, 41, 8, 44, 14, 50, 20, 56, 26, 62, 32, 68, 36, 72, 33, 69, 27, 63, 21, 57, 15, 51, 9, 45, 3, 39, 7, 43, 13, 49, 19, 55, 25, 61, 31, 67, 34, 70, 28, 64, 22, 58, 16, 52, 10, 46, 4, 40)(73, 109)(74, 110)(75, 111)(76, 112)(77, 113)(78, 114)(79, 115)(80, 116)(81, 117)(82, 118)(83, 119)(84, 120)(85, 121)(86, 122)(87, 123)(88, 124)(89, 125)(90, 126)(91, 127)(92, 128)(93, 129)(94, 130)(95, 131)(96, 132)(97, 133)(98, 134)(99, 135)(100, 136)(101, 137)(102, 138)(103, 139)(104, 140)(105, 141)(106, 142)(107, 143)(108, 144) L = (1, 75)(2, 79)(3, 77)(4, 81)(5, 73)(6, 85)(7, 80)(8, 74)(9, 83)(10, 87)(11, 76)(12, 91)(13, 86)(14, 78)(15, 89)(16, 93)(17, 82)(18, 97)(19, 92)(20, 84)(21, 95)(22, 99)(23, 88)(24, 103)(25, 98)(26, 90)(27, 101)(28, 105)(29, 94)(30, 106)(31, 104)(32, 96)(33, 107)(34, 108)(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, 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 E12.583 Graph:: bipartite v = 37 e = 72 f = 13 degree seq :: [ 2^36, 72 ] E12.588 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 13, 39}) Quotient :: edge Aut^+ = C39 (small group id <39, 2>) Aut = D78 (small group id <78, 5>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, (T2^-1, T1^-1), T2^13 ] Map:: non-degenerate R = (1, 3, 8, 14, 20, 26, 32, 35, 29, 23, 17, 11, 5)(2, 6, 12, 18, 24, 30, 36, 37, 31, 25, 19, 13, 7)(4, 9, 15, 21, 27, 33, 38, 39, 34, 28, 22, 16, 10)(40, 41, 43)(42, 45, 48)(44, 46, 49)(47, 51, 54)(50, 52, 55)(53, 57, 60)(56, 58, 61)(59, 63, 66)(62, 64, 67)(65, 69, 72)(68, 70, 73)(71, 75, 77)(74, 76, 78) L = (1, 40)(2, 41)(3, 42)(4, 43)(5, 44)(6, 45)(7, 46)(8, 47)(9, 48)(10, 49)(11, 50)(12, 51)(13, 52)(14, 53)(15, 54)(16, 55)(17, 56)(18, 57)(19, 58)(20, 59)(21, 60)(22, 61)(23, 62)(24, 63)(25, 64)(26, 65)(27, 66)(28, 67)(29, 68)(30, 69)(31, 70)(32, 71)(33, 72)(34, 73)(35, 74)(36, 75)(37, 76)(38, 77)(39, 78) local type(s) :: { ( 78^3 ), ( 78^13 ) } Outer automorphisms :: reflexible Dual of E12.592 Transitivity :: ET+ Graph:: simple bipartite v = 16 e = 39 f = 1 degree seq :: [ 3^13, 13^3 ] E12.589 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 13, 39}) Quotient :: edge Aut^+ = C39 (small group id <39, 2>) Aut = D78 (small group id <78, 5>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^3 * T1^3, T1^-1 * T2^12, T1^3 * T2^-1 * T1 * T2^-1 * T1^2 * T2^-4 * T1, T1^13 ] Map:: non-degenerate R = (1, 3, 9, 19, 25, 31, 37, 36, 29, 22, 18, 8, 2, 7, 17, 11, 21, 27, 33, 39, 35, 28, 24, 16, 6, 15, 12, 4, 10, 20, 26, 32, 38, 34, 30, 23, 14, 13, 5)(40, 41, 45, 53, 61, 67, 73, 76, 72, 65, 58, 50, 43)(42, 46, 54, 52, 57, 63, 69, 75, 78, 71, 64, 60, 49)(44, 47, 55, 62, 68, 74, 77, 70, 66, 59, 48, 56, 51) L = (1, 40)(2, 41)(3, 42)(4, 43)(5, 44)(6, 45)(7, 46)(8, 47)(9, 48)(10, 49)(11, 50)(12, 51)(13, 52)(14, 53)(15, 54)(16, 55)(17, 56)(18, 57)(19, 58)(20, 59)(21, 60)(22, 61)(23, 62)(24, 63)(25, 64)(26, 65)(27, 66)(28, 67)(29, 68)(30, 69)(31, 70)(32, 71)(33, 72)(34, 73)(35, 74)(36, 75)(37, 76)(38, 77)(39, 78) local type(s) :: { ( 6^13 ), ( 6^39 ) } Outer automorphisms :: reflexible Dual of E12.593 Transitivity :: ET+ Graph:: bipartite v = 4 e = 39 f = 13 degree seq :: [ 13^3, 39 ] E12.590 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 13, 39}) Quotient :: edge Aut^+ = C39 (small group id <39, 2>) Aut = D78 (small group id <78, 5>) |r| :: 2 Presentation :: [ F^2, T2^3, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-1 * T1^-13, (T1^-1 * T2^-1)^13 ] 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, 36)(40, 41, 45, 51, 57, 63, 69, 75, 74, 68, 62, 56, 50, 44, 47, 53, 59, 65, 71, 77, 78, 72, 66, 60, 54, 48, 42, 46, 52, 58, 64, 70, 76, 73, 67, 61, 55, 49, 43) L = (1, 40)(2, 41)(3, 42)(4, 43)(5, 44)(6, 45)(7, 46)(8, 47)(9, 48)(10, 49)(11, 50)(12, 51)(13, 52)(14, 53)(15, 54)(16, 55)(17, 56)(18, 57)(19, 58)(20, 59)(21, 60)(22, 61)(23, 62)(24, 63)(25, 64)(26, 65)(27, 66)(28, 67)(29, 68)(30, 69)(31, 70)(32, 71)(33, 72)(34, 73)(35, 74)(36, 75)(37, 76)(38, 77)(39, 78) local type(s) :: { ( 26^3 ), ( 26^39 ) } Outer automorphisms :: reflexible Dual of E12.591 Transitivity :: ET+ Graph:: bipartite v = 14 e = 39 f = 3 degree seq :: [ 3^13, 39 ] E12.591 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 13, 39}) Quotient :: loop Aut^+ = C39 (small group id <39, 2>) Aut = D78 (small group id <78, 5>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, (T2^-1, T1^-1), T2^13 ] Map:: non-degenerate R = (1, 40, 3, 42, 8, 47, 14, 53, 20, 59, 26, 65, 32, 71, 35, 74, 29, 68, 23, 62, 17, 56, 11, 50, 5, 44)(2, 41, 6, 45, 12, 51, 18, 57, 24, 63, 30, 69, 36, 75, 37, 76, 31, 70, 25, 64, 19, 58, 13, 52, 7, 46)(4, 43, 9, 48, 15, 54, 21, 60, 27, 66, 33, 72, 38, 77, 39, 78, 34, 73, 28, 67, 22, 61, 16, 55, 10, 49) L = (1, 41)(2, 43)(3, 45)(4, 40)(5, 46)(6, 48)(7, 49)(8, 51)(9, 42)(10, 44)(11, 52)(12, 54)(13, 55)(14, 57)(15, 47)(16, 50)(17, 58)(18, 60)(19, 61)(20, 63)(21, 53)(22, 56)(23, 64)(24, 66)(25, 67)(26, 69)(27, 59)(28, 62)(29, 70)(30, 72)(31, 73)(32, 75)(33, 65)(34, 68)(35, 76)(36, 77)(37, 78)(38, 71)(39, 74) local type(s) :: { ( 3, 39, 3, 39, 3, 39, 3, 39, 3, 39, 3, 39, 3, 39, 3, 39, 3, 39, 3, 39, 3, 39, 3, 39, 3, 39 ) } Outer automorphisms :: reflexible Dual of E12.590 Transitivity :: ET+ VT+ AT Graph:: v = 3 e = 39 f = 14 degree seq :: [ 26^3 ] E12.592 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 13, 39}) Quotient :: loop Aut^+ = C39 (small group id <39, 2>) Aut = D78 (small group id <78, 5>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^3 * T1^3, T1^-1 * T2^12, T1^3 * T2^-1 * T1 * T2^-1 * T1^2 * T2^-4 * T1, T1^13 ] Map:: non-degenerate R = (1, 40, 3, 42, 9, 48, 19, 58, 25, 64, 31, 70, 37, 76, 36, 75, 29, 68, 22, 61, 18, 57, 8, 47, 2, 41, 7, 46, 17, 56, 11, 50, 21, 60, 27, 66, 33, 72, 39, 78, 35, 74, 28, 67, 24, 63, 16, 55, 6, 45, 15, 54, 12, 51, 4, 43, 10, 49, 20, 59, 26, 65, 32, 71, 38, 77, 34, 73, 30, 69, 23, 62, 14, 53, 13, 52, 5, 44) L = (1, 41)(2, 45)(3, 46)(4, 40)(5, 47)(6, 53)(7, 54)(8, 55)(9, 56)(10, 42)(11, 43)(12, 44)(13, 57)(14, 61)(15, 52)(16, 62)(17, 51)(18, 63)(19, 50)(20, 48)(21, 49)(22, 67)(23, 68)(24, 69)(25, 60)(26, 58)(27, 59)(28, 73)(29, 74)(30, 75)(31, 66)(32, 64)(33, 65)(34, 76)(35, 77)(36, 78)(37, 72)(38, 70)(39, 71) local type(s) :: { ( 3, 13, 3, 13, 3, 13, 3, 13, 3, 13, 3, 13, 3, 13, 3, 13, 3, 13, 3, 13, 3, 13, 3, 13, 3, 13, 3, 13, 3, 13, 3, 13, 3, 13, 3, 13, 3, 13, 3, 13, 3, 13, 3, 13, 3, 13, 3, 13, 3, 13, 3, 13, 3, 13, 3, 13, 3, 13, 3, 13, 3, 13, 3, 13, 3, 13, 3, 13, 3, 13, 3, 13, 3, 13, 3, 13, 3, 13 ) } Outer automorphisms :: reflexible Dual of E12.588 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 39 f = 16 degree seq :: [ 78 ] E12.593 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 13, 39}) Quotient :: loop Aut^+ = C39 (small group id <39, 2>) Aut = D78 (small group id <78, 5>) |r| :: 2 Presentation :: [ F^2, T2^3, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^-1 * T1^-13, (T1^-1 * T2^-1)^13 ] Map:: non-degenerate R = (1, 40, 3, 42, 5, 44)(2, 41, 7, 46, 8, 47)(4, 43, 9, 48, 11, 50)(6, 45, 13, 52, 14, 53)(10, 49, 15, 54, 17, 56)(12, 51, 19, 58, 20, 59)(16, 55, 21, 60, 23, 62)(18, 57, 25, 64, 26, 65)(22, 61, 27, 66, 29, 68)(24, 63, 31, 70, 32, 71)(28, 67, 33, 72, 35, 74)(30, 69, 37, 76, 38, 77)(34, 73, 39, 78, 36, 75) L = (1, 41)(2, 45)(3, 46)(4, 40)(5, 47)(6, 51)(7, 52)(8, 53)(9, 42)(10, 43)(11, 44)(12, 57)(13, 58)(14, 59)(15, 48)(16, 49)(17, 50)(18, 63)(19, 64)(20, 65)(21, 54)(22, 55)(23, 56)(24, 69)(25, 70)(26, 71)(27, 60)(28, 61)(29, 62)(30, 75)(31, 76)(32, 77)(33, 66)(34, 67)(35, 68)(36, 74)(37, 73)(38, 78)(39, 72) local type(s) :: { ( 13, 39, 13, 39, 13, 39 ) } Outer automorphisms :: reflexible Dual of E12.589 Transitivity :: ET+ VT+ AT Graph:: v = 13 e = 39 f = 4 degree seq :: [ 6^13 ] E12.594 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 13, 39}) Quotient :: dipole Aut^+ = C39 (small group id <39, 2>) Aut = D78 (small group id <78, 5>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y1^3, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y3^-1, Y2^-1), (Y2, Y1^-1), Y2^13, Y3^39 ] Map:: R = (1, 40, 2, 41, 4, 43)(3, 42, 6, 45, 9, 48)(5, 44, 7, 46, 10, 49)(8, 47, 12, 51, 15, 54)(11, 50, 13, 52, 16, 55)(14, 53, 18, 57, 21, 60)(17, 56, 19, 58, 22, 61)(20, 59, 24, 63, 27, 66)(23, 62, 25, 64, 28, 67)(26, 65, 30, 69, 33, 72)(29, 68, 31, 70, 34, 73)(32, 71, 36, 75, 38, 77)(35, 74, 37, 76, 39, 78)(79, 118, 81, 120, 86, 125, 92, 131, 98, 137, 104, 143, 110, 149, 113, 152, 107, 146, 101, 140, 95, 134, 89, 128, 83, 122)(80, 119, 84, 123, 90, 129, 96, 135, 102, 141, 108, 147, 114, 153, 115, 154, 109, 148, 103, 142, 97, 136, 91, 130, 85, 124)(82, 121, 87, 126, 93, 132, 99, 138, 105, 144, 111, 150, 116, 155, 117, 156, 112, 151, 106, 145, 100, 139, 94, 133, 88, 127) L = (1, 82)(2, 79)(3, 87)(4, 80)(5, 88)(6, 81)(7, 83)(8, 93)(9, 84)(10, 85)(11, 94)(12, 86)(13, 89)(14, 99)(15, 90)(16, 91)(17, 100)(18, 92)(19, 95)(20, 105)(21, 96)(22, 97)(23, 106)(24, 98)(25, 101)(26, 111)(27, 102)(28, 103)(29, 112)(30, 104)(31, 107)(32, 116)(33, 108)(34, 109)(35, 117)(36, 110)(37, 113)(38, 114)(39, 115)(40, 118)(41, 119)(42, 120)(43, 121)(44, 122)(45, 123)(46, 124)(47, 125)(48, 126)(49, 127)(50, 128)(51, 129)(52, 130)(53, 131)(54, 132)(55, 133)(56, 134)(57, 135)(58, 136)(59, 137)(60, 138)(61, 139)(62, 140)(63, 141)(64, 142)(65, 143)(66, 144)(67, 145)(68, 146)(69, 147)(70, 148)(71, 149)(72, 150)(73, 151)(74, 152)(75, 153)(76, 154)(77, 155)(78, 156) local type(s) :: { ( 2, 78, 2, 78, 2, 78 ), ( 2, 78, 2, 78, 2, 78, 2, 78, 2, 78, 2, 78, 2, 78, 2, 78, 2, 78, 2, 78, 2, 78, 2, 78, 2, 78 ) } Outer automorphisms :: reflexible Dual of E12.597 Graph:: bipartite v = 16 e = 78 f = 40 degree seq :: [ 6^13, 26^3 ] E12.595 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 13, 39}) Quotient :: dipole Aut^+ = C39 (small group id <39, 2>) Aut = D78 (small group id <78, 5>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-1, (R * Y1)^2, R * Y2 * R * Y3, (Y1, Y2^-1), Y2^3 * Y1^3, (Y3^-1 * Y1^-1)^3, Y1^-1 * Y2^12, Y1^13 ] Map:: R = (1, 40, 2, 41, 6, 45, 14, 53, 22, 61, 28, 67, 34, 73, 37, 76, 33, 72, 26, 65, 19, 58, 11, 50, 4, 43)(3, 42, 7, 46, 15, 54, 13, 52, 18, 57, 24, 63, 30, 69, 36, 75, 39, 78, 32, 71, 25, 64, 21, 60, 10, 49)(5, 44, 8, 47, 16, 55, 23, 62, 29, 68, 35, 74, 38, 77, 31, 70, 27, 66, 20, 59, 9, 48, 17, 56, 12, 51)(79, 118, 81, 120, 87, 126, 97, 136, 103, 142, 109, 148, 115, 154, 114, 153, 107, 146, 100, 139, 96, 135, 86, 125, 80, 119, 85, 124, 95, 134, 89, 128, 99, 138, 105, 144, 111, 150, 117, 156, 113, 152, 106, 145, 102, 141, 94, 133, 84, 123, 93, 132, 90, 129, 82, 121, 88, 127, 98, 137, 104, 143, 110, 149, 116, 155, 112, 151, 108, 147, 101, 140, 92, 131, 91, 130, 83, 122) L = (1, 81)(2, 85)(3, 87)(4, 88)(5, 79)(6, 93)(7, 95)(8, 80)(9, 97)(10, 98)(11, 99)(12, 82)(13, 83)(14, 91)(15, 90)(16, 84)(17, 89)(18, 86)(19, 103)(20, 104)(21, 105)(22, 96)(23, 92)(24, 94)(25, 109)(26, 110)(27, 111)(28, 102)(29, 100)(30, 101)(31, 115)(32, 116)(33, 117)(34, 108)(35, 106)(36, 107)(37, 114)(38, 112)(39, 113)(40, 118)(41, 119)(42, 120)(43, 121)(44, 122)(45, 123)(46, 124)(47, 125)(48, 126)(49, 127)(50, 128)(51, 129)(52, 130)(53, 131)(54, 132)(55, 133)(56, 134)(57, 135)(58, 136)(59, 137)(60, 138)(61, 139)(62, 140)(63, 141)(64, 142)(65, 143)(66, 144)(67, 145)(68, 146)(69, 147)(70, 148)(71, 149)(72, 150)(73, 151)(74, 152)(75, 153)(76, 154)(77, 155)(78, 156) 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 ) } Outer automorphisms :: reflexible Dual of E12.596 Graph:: bipartite v = 4 e = 78 f = 52 degree seq :: [ 26^3, 78 ] E12.596 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 13, 39}) Quotient :: dipole Aut^+ = C39 (small group id <39, 2>) Aut = D78 (small group id <78, 5>) |r| :: 2 Presentation :: [ Y1, R^2, Y2^3, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y2, Y3^-1), Y2^-1 * Y3^13, 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 * Y3^2, (Y3^-1 * Y1^-1)^39 ] Map:: R = (1, 40)(2, 41)(3, 42)(4, 43)(5, 44)(6, 45)(7, 46)(8, 47)(9, 48)(10, 49)(11, 50)(12, 51)(13, 52)(14, 53)(15, 54)(16, 55)(17, 56)(18, 57)(19, 58)(20, 59)(21, 60)(22, 61)(23, 62)(24, 63)(25, 64)(26, 65)(27, 66)(28, 67)(29, 68)(30, 69)(31, 70)(32, 71)(33, 72)(34, 73)(35, 74)(36, 75)(37, 76)(38, 77)(39, 78)(79, 118, 80, 119, 82, 121)(81, 120, 84, 123, 87, 126)(83, 122, 85, 124, 88, 127)(86, 125, 90, 129, 93, 132)(89, 128, 91, 130, 94, 133)(92, 131, 96, 135, 99, 138)(95, 134, 97, 136, 100, 139)(98, 137, 102, 141, 105, 144)(101, 140, 103, 142, 106, 145)(104, 143, 108, 147, 111, 150)(107, 146, 109, 148, 112, 151)(110, 149, 114, 153, 116, 155)(113, 152, 115, 154, 117, 156) 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, 115)(33, 116)(34, 106)(35, 107)(36, 117)(37, 109)(38, 113)(39, 112)(40, 118)(41, 119)(42, 120)(43, 121)(44, 122)(45, 123)(46, 124)(47, 125)(48, 126)(49, 127)(50, 128)(51, 129)(52, 130)(53, 131)(54, 132)(55, 133)(56, 134)(57, 135)(58, 136)(59, 137)(60, 138)(61, 139)(62, 140)(63, 141)(64, 142)(65, 143)(66, 144)(67, 145)(68, 146)(69, 147)(70, 148)(71, 149)(72, 150)(73, 151)(74, 152)(75, 153)(76, 154)(77, 155)(78, 156) local type(s) :: { ( 26, 78 ), ( 26, 78, 26, 78, 26, 78 ) } Outer automorphisms :: reflexible Dual of E12.595 Graph:: simple bipartite v = 52 e = 78 f = 4 degree seq :: [ 2^39, 6^13 ] E12.597 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 13, 39}) Quotient :: dipole Aut^+ = C39 (small group id <39, 2>) Aut = D78 (small group id <78, 5>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^3, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1^-1), (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^3, Y3^-1 * Y1^-13, (Y1^-1 * Y3^-1)^13 ] Map:: R = (1, 40, 2, 41, 6, 45, 12, 51, 18, 57, 24, 63, 30, 69, 36, 75, 35, 74, 29, 68, 23, 62, 17, 56, 11, 50, 5, 44, 8, 47, 14, 53, 20, 59, 26, 65, 32, 71, 38, 77, 39, 78, 33, 72, 27, 66, 21, 60, 15, 54, 9, 48, 3, 42, 7, 46, 13, 52, 19, 58, 25, 64, 31, 70, 37, 76, 34, 73, 28, 67, 22, 61, 16, 55, 10, 49, 4, 43)(79, 118)(80, 119)(81, 120)(82, 121)(83, 122)(84, 123)(85, 124)(86, 125)(87, 126)(88, 127)(89, 128)(90, 129)(91, 130)(92, 131)(93, 132)(94, 133)(95, 134)(96, 135)(97, 136)(98, 137)(99, 138)(100, 139)(101, 140)(102, 141)(103, 142)(104, 143)(105, 144)(106, 145)(107, 146)(108, 147)(109, 148)(110, 149)(111, 150)(112, 151)(113, 152)(114, 153)(115, 154)(116, 155)(117, 156) L = (1, 81)(2, 85)(3, 83)(4, 87)(5, 79)(6, 91)(7, 86)(8, 80)(9, 89)(10, 93)(11, 82)(12, 97)(13, 92)(14, 84)(15, 95)(16, 99)(17, 88)(18, 103)(19, 98)(20, 90)(21, 101)(22, 105)(23, 94)(24, 109)(25, 104)(26, 96)(27, 107)(28, 111)(29, 100)(30, 115)(31, 110)(32, 102)(33, 113)(34, 117)(35, 106)(36, 112)(37, 116)(38, 108)(39, 114)(40, 118)(41, 119)(42, 120)(43, 121)(44, 122)(45, 123)(46, 124)(47, 125)(48, 126)(49, 127)(50, 128)(51, 129)(52, 130)(53, 131)(54, 132)(55, 133)(56, 134)(57, 135)(58, 136)(59, 137)(60, 138)(61, 139)(62, 140)(63, 141)(64, 142)(65, 143)(66, 144)(67, 145)(68, 146)(69, 147)(70, 148)(71, 149)(72, 150)(73, 151)(74, 152)(75, 153)(76, 154)(77, 155)(78, 156) local type(s) :: { ( 6, 26 ), ( 6, 26, 6, 26, 6, 26, 6, 26, 6, 26, 6, 26, 6, 26, 6, 26, 6, 26, 6, 26, 6, 26, 6, 26, 6, 26, 6, 26, 6, 26, 6, 26, 6, 26, 6, 26, 6, 26, 6, 26, 6, 26, 6, 26, 6, 26, 6, 26, 6, 26, 6, 26, 6, 26, 6, 26, 6, 26, 6, 26, 6, 26, 6, 26, 6, 26, 6, 26, 6, 26, 6, 26, 6, 26, 6, 26, 6, 26 ) } Outer automorphisms :: reflexible Dual of E12.594 Graph:: bipartite v = 40 e = 78 f = 16 degree seq :: [ 2^39, 78 ] E12.598 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 13, 39}) Quotient :: dipole Aut^+ = C39 (small group id <39, 2>) Aut = D78 (small group id <78, 5>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y3^3, Y1^3, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y3^-1, Y2^-1), (Y2, Y1^-1), Y3 * Y2^-13, 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 ] Map:: R = (1, 40, 2, 41, 4, 43)(3, 42, 6, 45, 9, 48)(5, 44, 7, 46, 10, 49)(8, 47, 12, 51, 15, 54)(11, 50, 13, 52, 16, 55)(14, 53, 18, 57, 21, 60)(17, 56, 19, 58, 22, 61)(20, 59, 24, 63, 27, 66)(23, 62, 25, 64, 28, 67)(26, 65, 30, 69, 33, 72)(29, 68, 31, 70, 34, 73)(32, 71, 36, 75, 39, 78)(35, 74, 37, 76, 38, 77)(79, 118, 81, 120, 86, 125, 92, 131, 98, 137, 104, 143, 110, 149, 116, 155, 112, 151, 106, 145, 100, 139, 94, 133, 88, 127, 82, 121, 87, 126, 93, 132, 99, 138, 105, 144, 111, 150, 117, 156, 115, 154, 109, 148, 103, 142, 97, 136, 91, 130, 85, 124, 80, 119, 84, 123, 90, 129, 96, 135, 102, 141, 108, 147, 114, 153, 113, 152, 107, 146, 101, 140, 95, 134, 89, 128, 83, 122) L = (1, 82)(2, 79)(3, 87)(4, 80)(5, 88)(6, 81)(7, 83)(8, 93)(9, 84)(10, 85)(11, 94)(12, 86)(13, 89)(14, 99)(15, 90)(16, 91)(17, 100)(18, 92)(19, 95)(20, 105)(21, 96)(22, 97)(23, 106)(24, 98)(25, 101)(26, 111)(27, 102)(28, 103)(29, 112)(30, 104)(31, 107)(32, 117)(33, 108)(34, 109)(35, 116)(36, 110)(37, 113)(38, 115)(39, 114)(40, 118)(41, 119)(42, 120)(43, 121)(44, 122)(45, 123)(46, 124)(47, 125)(48, 126)(49, 127)(50, 128)(51, 129)(52, 130)(53, 131)(54, 132)(55, 133)(56, 134)(57, 135)(58, 136)(59, 137)(60, 138)(61, 139)(62, 140)(63, 141)(64, 142)(65, 143)(66, 144)(67, 145)(68, 146)(69, 147)(70, 148)(71, 149)(72, 150)(73, 151)(74, 152)(75, 153)(76, 154)(77, 155)(78, 156) local type(s) :: { ( 2, 26, 2, 26, 2, 26 ), ( 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26 ) } Outer automorphisms :: reflexible Dual of E12.599 Graph:: bipartite v = 14 e = 78 f = 42 degree seq :: [ 6^13, 78 ] E12.599 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 13, 39}) Quotient :: dipole Aut^+ = C39 (small group id <39, 2>) Aut = D78 (small group id <78, 5>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1^-1), Y3^-3 * Y1^-3, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3^12, Y1^4 * Y3^-1 * Y1^2 * Y3^-5 * Y1, Y1^13, (Y3 * Y2^-1)^39 ] Map:: R = (1, 40, 2, 41, 6, 45, 14, 53, 22, 61, 28, 67, 34, 73, 37, 76, 33, 72, 26, 65, 19, 58, 11, 50, 4, 43)(3, 42, 7, 46, 15, 54, 13, 52, 18, 57, 24, 63, 30, 69, 36, 75, 39, 78, 32, 71, 25, 64, 21, 60, 10, 49)(5, 44, 8, 47, 16, 55, 23, 62, 29, 68, 35, 74, 38, 77, 31, 70, 27, 66, 20, 59, 9, 48, 17, 56, 12, 51)(79, 118)(80, 119)(81, 120)(82, 121)(83, 122)(84, 123)(85, 124)(86, 125)(87, 126)(88, 127)(89, 128)(90, 129)(91, 130)(92, 131)(93, 132)(94, 133)(95, 134)(96, 135)(97, 136)(98, 137)(99, 138)(100, 139)(101, 140)(102, 141)(103, 142)(104, 143)(105, 144)(106, 145)(107, 146)(108, 147)(109, 148)(110, 149)(111, 150)(112, 151)(113, 152)(114, 153)(115, 154)(116, 155)(117, 156) L = (1, 81)(2, 85)(3, 87)(4, 88)(5, 79)(6, 93)(7, 95)(8, 80)(9, 97)(10, 98)(11, 99)(12, 82)(13, 83)(14, 91)(15, 90)(16, 84)(17, 89)(18, 86)(19, 103)(20, 104)(21, 105)(22, 96)(23, 92)(24, 94)(25, 109)(26, 110)(27, 111)(28, 102)(29, 100)(30, 101)(31, 115)(32, 116)(33, 117)(34, 108)(35, 106)(36, 107)(37, 114)(38, 112)(39, 113)(40, 118)(41, 119)(42, 120)(43, 121)(44, 122)(45, 123)(46, 124)(47, 125)(48, 126)(49, 127)(50, 128)(51, 129)(52, 130)(53, 131)(54, 132)(55, 133)(56, 134)(57, 135)(58, 136)(59, 137)(60, 138)(61, 139)(62, 140)(63, 141)(64, 142)(65, 143)(66, 144)(67, 145)(68, 146)(69, 147)(70, 148)(71, 149)(72, 150)(73, 151)(74, 152)(75, 153)(76, 154)(77, 155)(78, 156) local type(s) :: { ( 6, 78 ), ( 6, 78, 6, 78, 6, 78, 6, 78, 6, 78, 6, 78, 6, 78, 6, 78, 6, 78, 6, 78, 6, 78, 6, 78, 6, 78 ) } Outer automorphisms :: reflexible Dual of E12.598 Graph:: simple bipartite v = 42 e = 78 f = 14 degree seq :: [ 2^39, 26^3 ] E12.600 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 5}) Quotient :: dipole Aut^+ = (C10 x C2) : C2 (small group id <40, 8>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3)^2, Y1 * Y2 * Y1 * Y3 * Y2 * Y3, (Y1 * Y2)^4, (Y3 * Y1)^5 ] Map:: polytopal non-degenerate R = (1, 41, 2, 42)(3, 43, 7, 47)(4, 44, 9, 49)(5, 45, 11, 51)(6, 46, 13, 53)(8, 48, 16, 56)(10, 50, 19, 59)(12, 52, 21, 61)(14, 54, 24, 64)(15, 55, 20, 60)(17, 57, 26, 66)(18, 58, 27, 67)(22, 62, 30, 70)(23, 63, 31, 71)(25, 65, 33, 73)(28, 68, 35, 75)(29, 69, 36, 76)(32, 72, 38, 78)(34, 74, 39, 79)(37, 77, 40, 80)(81, 121, 83, 123)(82, 122, 85, 125)(84, 124, 90, 130)(86, 126, 94, 134)(87, 127, 95, 135)(88, 128, 97, 137)(89, 129, 96, 136)(91, 131, 100, 140)(92, 132, 102, 142)(93, 133, 101, 141)(98, 138, 108, 148)(99, 139, 106, 146)(103, 143, 112, 152)(104, 144, 110, 150)(105, 145, 114, 154)(107, 147, 113, 153)(109, 149, 117, 157)(111, 151, 116, 156)(115, 155, 119, 159)(118, 158, 120, 160) L = (1, 84)(2, 86)(3, 88)(4, 81)(5, 92)(6, 82)(7, 94)(8, 83)(9, 98)(10, 91)(11, 90)(12, 85)(13, 103)(14, 87)(15, 102)(16, 105)(17, 100)(18, 89)(19, 108)(20, 97)(21, 109)(22, 95)(23, 93)(24, 112)(25, 96)(26, 114)(27, 111)(28, 99)(29, 101)(30, 117)(31, 107)(32, 104)(33, 118)(34, 106)(35, 116)(36, 115)(37, 110)(38, 113)(39, 120)(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) :: { ( 8, 10, 8, 10 ) } Outer automorphisms :: reflexible Dual of E12.605 Graph:: simple bipartite v = 40 e = 80 f = 18 degree seq :: [ 4^40 ] E12.601 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 5}) Quotient :: dipole Aut^+ = D40 (small group id <40, 6>) Aut = C2 x D40 (small group id <80, 37>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y3, Y2), (R * Y3)^2, (R * Y1)^2, Y2^4, (Y3^-1 * Y1)^2, (R * Y2)^2, (Y2^-1 * Y1)^2, Y3^5 * Y2^-1 ] Map:: polytopal non-degenerate R = (1, 41, 2, 42)(3, 43, 9, 49)(4, 44, 10, 50)(5, 45, 7, 47)(6, 46, 8, 48)(11, 51, 18, 58)(12, 52, 23, 63)(13, 53, 22, 62)(14, 54, 24, 64)(15, 55, 20, 60)(16, 56, 19, 59)(17, 57, 21, 61)(25, 65, 32, 72)(26, 66, 31, 71)(27, 67, 36, 76)(28, 68, 35, 75)(29, 69, 34, 74)(30, 70, 33, 73)(37, 77, 40, 80)(38, 78, 39, 79)(81, 121, 83, 123, 91, 131, 85, 125)(82, 122, 87, 127, 98, 138, 89, 129)(84, 124, 92, 132, 105, 145, 95, 135)(86, 126, 93, 133, 106, 146, 96, 136)(88, 128, 99, 139, 111, 151, 102, 142)(90, 130, 100, 140, 112, 152, 103, 143)(94, 134, 107, 147, 117, 157, 109, 149)(97, 137, 108, 148, 118, 158, 110, 150)(101, 141, 113, 153, 119, 159, 115, 155)(104, 144, 114, 154, 120, 160, 116, 156) 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, 108)(15, 109)(16, 85)(17, 86)(18, 111)(19, 113)(20, 87)(21, 114)(22, 115)(23, 89)(24, 90)(25, 117)(26, 91)(27, 118)(28, 93)(29, 97)(30, 96)(31, 119)(32, 98)(33, 120)(34, 100)(35, 104)(36, 103)(37, 110)(38, 106)(39, 116)(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, 10, 4, 10 ), ( 4, 10, 4, 10, 4, 10, 4, 10 ) } Outer automorphisms :: reflexible Dual of E12.603 Graph:: simple bipartite v = 30 e = 80 f = 28 degree seq :: [ 4^20, 8^10 ] E12.602 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 5}) Quotient :: dipole Aut^+ = (C10 x C2) : C2 (small group id <40, 8>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-2 * Y2^-2, Y2^4, Y3^4, (R * Y3)^2, (Y3^-1 * Y1)^2, (Y2^-1 * Y1)^2, Y3^-1 * Y2^2 * Y3^-1, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: polytopal non-degenerate R = (1, 41, 2, 42)(3, 43, 9, 49)(4, 44, 10, 50)(5, 45, 7, 47)(6, 46, 8, 48)(11, 51, 16, 56)(12, 52, 17, 57)(13, 53, 18, 58)(14, 54, 19, 59)(15, 55, 20, 60)(21, 61, 26, 66)(22, 62, 25, 65)(23, 63, 28, 68)(24, 64, 27, 67)(29, 69, 33, 73)(30, 70, 34, 74)(31, 71, 35, 75)(32, 72, 36, 76)(37, 77, 40, 80)(38, 78, 39, 79)(81, 121, 83, 123, 91, 131, 85, 125)(82, 122, 87, 127, 96, 136, 89, 129)(84, 124, 94, 134, 86, 126, 95, 135)(88, 128, 99, 139, 90, 130, 100, 140)(92, 132, 101, 141, 93, 133, 102, 142)(97, 137, 105, 145, 98, 138, 106, 146)(103, 143, 111, 151, 104, 144, 112, 152)(107, 147, 115, 155, 108, 148, 116, 156)(109, 149, 117, 157, 110, 150, 118, 158)(113, 153, 119, 159, 114, 154, 120, 160) L = (1, 84)(2, 88)(3, 92)(4, 91)(5, 93)(6, 81)(7, 97)(8, 96)(9, 98)(10, 82)(11, 86)(12, 85)(13, 83)(14, 103)(15, 104)(16, 90)(17, 89)(18, 87)(19, 107)(20, 108)(21, 109)(22, 110)(23, 95)(24, 94)(25, 113)(26, 114)(27, 100)(28, 99)(29, 102)(30, 101)(31, 117)(32, 118)(33, 106)(34, 105)(35, 119)(36, 120)(37, 112)(38, 111)(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) :: { ( 4, 10, 4, 10 ), ( 4, 10, 4, 10, 4, 10, 4, 10 ) } Outer automorphisms :: reflexible Dual of E12.604 Graph:: simple bipartite v = 30 e = 80 f = 28 degree seq :: [ 4^20, 8^10 ] E12.603 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 5}) Quotient :: dipole Aut^+ = D40 (small group id <40, 6>) Aut = C2 x D40 (small group id <80, 37>) |r| :: 2 Presentation :: [ Y2^2, R^2, (R * Y1)^2, (Y3 * Y2)^2, (Y3, Y1^-1), (Y2 * Y1)^2, (R * Y3)^2, Y3^-4 * Y1, Y1^5, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 41, 2, 42, 7, 47, 16, 56, 5, 45)(3, 43, 11, 51, 25, 65, 19, 59, 8, 48)(4, 44, 9, 49, 20, 60, 30, 70, 15, 55)(6, 46, 10, 50, 21, 61, 31, 71, 17, 57)(12, 52, 26, 66, 37, 77, 33, 73, 22, 62)(13, 53, 27, 67, 38, 78, 34, 74, 23, 63)(14, 54, 24, 64, 35, 75, 32, 72, 18, 58)(28, 68, 39, 79, 40, 80, 36, 76, 29, 69)(81, 121, 83, 123)(82, 122, 88, 128)(84, 124, 93, 133)(85, 125, 91, 131)(86, 126, 92, 132)(87, 127, 99, 139)(89, 129, 103, 143)(90, 130, 102, 142)(94, 134, 109, 149)(95, 135, 107, 147)(96, 136, 105, 145)(97, 137, 106, 146)(98, 138, 108, 148)(100, 140, 114, 154)(101, 141, 113, 153)(104, 144, 116, 156)(110, 150, 118, 158)(111, 151, 117, 157)(112, 152, 119, 159)(115, 155, 120, 160) L = (1, 84)(2, 89)(3, 92)(4, 94)(5, 95)(6, 81)(7, 100)(8, 102)(9, 104)(10, 82)(11, 106)(12, 108)(13, 83)(14, 90)(15, 98)(16, 110)(17, 85)(18, 86)(19, 113)(20, 115)(21, 87)(22, 109)(23, 88)(24, 101)(25, 117)(26, 119)(27, 91)(28, 107)(29, 93)(30, 112)(31, 96)(32, 97)(33, 116)(34, 99)(35, 111)(36, 103)(37, 120)(38, 105)(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) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E12.601 Graph:: simple bipartite v = 28 e = 80 f = 30 degree seq :: [ 4^20, 10^8 ] E12.604 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 5}) Quotient :: dipole Aut^+ = (C10 x C2) : C2 (small group id <40, 8>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ Y2^2, R^2, (R * Y1)^2, (Y3 * Y2)^2, Y3 * Y1^-1 * Y3^-1 * Y1^-1, (R * Y3)^2, (Y2 * Y1^-1)^2, Y3^4, Y1^5, (R * Y2 * Y3^-1)^2 ] Map:: polytopal non-degenerate R = (1, 41, 2, 42, 7, 47, 16, 56, 5, 45)(3, 43, 11, 51, 24, 64, 18, 58, 8, 48)(4, 44, 14, 54, 28, 68, 19, 59, 9, 49)(6, 46, 17, 57, 30, 70, 20, 60, 10, 50)(12, 52, 21, 61, 31, 71, 35, 75, 25, 65)(13, 53, 22, 62, 32, 72, 36, 76, 26, 66)(15, 55, 23, 63, 33, 73, 38, 78, 29, 69)(27, 67, 37, 77, 40, 80, 39, 79, 34, 74)(81, 121, 83, 123)(82, 122, 88, 128)(84, 124, 93, 133)(85, 125, 91, 131)(86, 126, 92, 132)(87, 127, 98, 138)(89, 129, 102, 142)(90, 130, 101, 141)(94, 134, 106, 146)(95, 135, 107, 147)(96, 136, 104, 144)(97, 137, 105, 145)(99, 139, 112, 152)(100, 140, 111, 151)(103, 143, 114, 154)(108, 148, 116, 156)(109, 149, 117, 157)(110, 150, 115, 155)(113, 153, 119, 159)(118, 158, 120, 160) L = (1, 84)(2, 89)(3, 92)(4, 95)(5, 94)(6, 81)(7, 99)(8, 101)(9, 103)(10, 82)(11, 105)(12, 107)(13, 83)(14, 109)(15, 86)(16, 108)(17, 85)(18, 111)(19, 113)(20, 87)(21, 114)(22, 88)(23, 90)(24, 115)(25, 117)(26, 91)(27, 93)(28, 118)(29, 97)(30, 96)(31, 119)(32, 98)(33, 100)(34, 102)(35, 120)(36, 104)(37, 106)(38, 110)(39, 112)(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, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E12.602 Graph:: simple bipartite v = 28 e = 80 f = 30 degree seq :: [ 4^20, 10^8 ] E12.605 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 5}) 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, R * Y2 * R * Y2^-1, (R * Y3)^2, (Y3 * Y1^-1)^2, (R * Y1)^2, (Y2^-1 * Y3)^2, Y1^-1 * Y2^-1 * Y1 * Y2^-1, Y1^4, Y2^5 ] Map:: polytopal non-degenerate R = (1, 41, 2, 42, 7, 47, 5, 45)(3, 43, 10, 50, 18, 58, 13, 53)(4, 44, 14, 54, 19, 59, 9, 49)(6, 46, 8, 48, 20, 60, 16, 56)(11, 51, 24, 64, 31, 71, 26, 66)(12, 52, 27, 67, 32, 72, 23, 63)(15, 55, 28, 68, 33, 73, 22, 62)(17, 57, 21, 61, 34, 74, 30, 70)(25, 65, 37, 77, 39, 79, 36, 76)(29, 69, 38, 78, 40, 80, 35, 75)(81, 121, 83, 123, 91, 131, 97, 137, 86, 126)(82, 122, 88, 128, 101, 141, 104, 144, 90, 130)(84, 124, 95, 135, 109, 149, 105, 145, 92, 132)(85, 125, 96, 136, 110, 150, 106, 146, 93, 133)(87, 127, 98, 138, 111, 151, 114, 154, 100, 140)(89, 129, 103, 143, 116, 156, 115, 155, 102, 142)(94, 134, 107, 147, 117, 157, 118, 158, 108, 148)(99, 139, 113, 153, 120, 160, 119, 159, 112, 152) L = (1, 84)(2, 89)(3, 92)(4, 81)(5, 94)(6, 95)(7, 99)(8, 102)(9, 82)(10, 103)(11, 105)(12, 83)(13, 107)(14, 85)(15, 86)(16, 108)(17, 109)(18, 112)(19, 87)(20, 113)(21, 115)(22, 88)(23, 90)(24, 116)(25, 91)(26, 117)(27, 93)(28, 96)(29, 97)(30, 118)(31, 119)(32, 98)(33, 100)(34, 120)(35, 101)(36, 104)(37, 106)(38, 110)(39, 111)(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) :: { ( 4^8 ), ( 4^10 ) } Outer automorphisms :: reflexible Dual of E12.600 Graph:: simple bipartite v = 18 e = 80 f = 40 degree seq :: [ 8^10, 10^8 ] E12.606 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 5}) Quotient :: dipole 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 :: [ Y1^2, R^2, Y3 * Y2^2 * Y3, Y2^4, Y3^2 * Y2^2, (Y3^-1 * Y1)^2, Y3^2 * Y2^-2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y2^-1 * Y1)^2, (Y3^-1 * Y2 * Y1)^2, (Y3^-1 * Y2)^5 ] Map:: polytopal non-degenerate R = (1, 41, 2, 42)(3, 43, 11, 51)(4, 44, 10, 50)(5, 45, 17, 57)(6, 46, 8, 48)(7, 47, 18, 58)(9, 49, 24, 64)(12, 52, 19, 59)(13, 53, 22, 62)(14, 54, 23, 63)(15, 55, 20, 60)(16, 56, 21, 61)(25, 65, 33, 73)(26, 66, 36, 76)(27, 67, 34, 74)(28, 68, 35, 75)(29, 69, 37, 77)(30, 70, 40, 80)(31, 71, 38, 78)(32, 72, 39, 79)(81, 121, 83, 123, 92, 132, 85, 125)(82, 122, 87, 127, 99, 139, 89, 129)(84, 124, 95, 135, 86, 126, 96, 136)(88, 128, 102, 142, 90, 130, 103, 143)(91, 131, 105, 145, 97, 137, 106, 146)(93, 133, 107, 147, 94, 134, 108, 148)(98, 138, 109, 149, 104, 144, 110, 150)(100, 140, 111, 151, 101, 141, 112, 152)(113, 153, 118, 158, 116, 156, 119, 159)(114, 154, 120, 160, 115, 155, 117, 157) L = (1, 84)(2, 88)(3, 93)(4, 92)(5, 94)(6, 81)(7, 100)(8, 99)(9, 101)(10, 82)(11, 103)(12, 86)(13, 85)(14, 83)(15, 98)(16, 104)(17, 102)(18, 96)(19, 90)(20, 89)(21, 87)(22, 91)(23, 97)(24, 95)(25, 114)(26, 115)(27, 113)(28, 116)(29, 118)(30, 119)(31, 117)(32, 120)(33, 108)(34, 106)(35, 105)(36, 107)(37, 112)(38, 110)(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) :: { ( 4, 10, 4, 10 ), ( 4, 10, 4, 10, 4, 10, 4, 10 ) } Outer automorphisms :: reflexible Dual of E12.607 Graph:: simple bipartite v = 30 e = 80 f = 28 degree seq :: [ 4^20, 8^10 ] E12.607 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 5}) Quotient :: dipole 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 :: [ Y2^2, R^2, (R * Y1)^2, (Y3 * Y2)^2, Y1^-1 * Y3 * Y1^-1 * Y3^-1, (R * Y3)^2, Y3^4, Y2 * Y1 * Y2 * Y1^-1, Y1^5, (R * Y2 * Y3^-1)^2 ] Map:: polytopal non-degenerate R = (1, 41, 2, 42, 7, 47, 16, 56, 5, 45)(3, 43, 8, 48, 18, 58, 26, 66, 12, 52)(4, 44, 14, 54, 28, 68, 19, 59, 9, 49)(6, 46, 17, 57, 30, 70, 20, 60, 10, 50)(11, 51, 24, 64, 35, 75, 31, 71, 21, 61)(13, 53, 27, 67, 37, 77, 32, 72, 22, 62)(15, 55, 23, 63, 33, 73, 38, 78, 29, 69)(25, 65, 34, 74, 39, 79, 40, 80, 36, 76)(81, 121, 83, 123)(82, 122, 88, 128)(84, 124, 93, 133)(85, 125, 92, 132)(86, 126, 91, 131)(87, 127, 98, 138)(89, 129, 102, 142)(90, 130, 101, 141)(94, 134, 107, 147)(95, 135, 105, 145)(96, 136, 106, 146)(97, 137, 104, 144)(99, 139, 112, 152)(100, 140, 111, 151)(103, 143, 114, 154)(108, 148, 117, 157)(109, 149, 116, 156)(110, 150, 115, 155)(113, 153, 119, 159)(118, 158, 120, 160) L = (1, 84)(2, 89)(3, 91)(4, 95)(5, 94)(6, 81)(7, 99)(8, 101)(9, 103)(10, 82)(11, 105)(12, 104)(13, 83)(14, 109)(15, 86)(16, 108)(17, 85)(18, 111)(19, 113)(20, 87)(21, 114)(22, 88)(23, 90)(24, 116)(25, 93)(26, 115)(27, 92)(28, 118)(29, 97)(30, 96)(31, 119)(32, 98)(33, 100)(34, 102)(35, 120)(36, 107)(37, 106)(38, 110)(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) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E12.606 Graph:: simple bipartite v = 28 e = 80 f = 30 degree seq :: [ 4^20, 10^8 ] E12.608 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {5, 8, 8}) Quotient :: edge Aut^+ = C5 : C8 (small group id <40, 1>) Aut = (C5 x D8) : C2 (small group id <80, 15>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2 * T1^-1 * T2^-1 * T1^-1, T1^5, T2^8 ] Map:: non-degenerate R = (1, 3, 10, 20, 30, 23, 13, 5)(2, 7, 16, 26, 35, 27, 17, 8)(4, 9, 19, 29, 37, 32, 22, 12)(6, 14, 24, 33, 39, 34, 25, 15)(11, 18, 28, 36, 40, 38, 31, 21)(41, 42, 46, 51, 44)(43, 49, 58, 54, 47)(45, 52, 61, 55, 48)(50, 56, 64, 68, 59)(53, 57, 65, 71, 62)(60, 69, 76, 73, 66)(63, 72, 78, 74, 67)(70, 75, 79, 80, 77) L = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 16^5 ), ( 16^8 ) } Outer automorphisms :: reflexible Dual of E12.609 Transitivity :: ET+ Graph:: simple bipartite v = 13 e = 40 f = 5 degree seq :: [ 5^8, 8^5 ] E12.609 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {5, 8, 8}) Quotient :: loop Aut^+ = C5 : C8 (small group id <40, 1>) Aut = (C5 x D8) : C2 (small group id <80, 15>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2 * T1^-1 * T2^-1 * T1^-1, T1^5, T2^8 ] Map:: non-degenerate R = (1, 41, 3, 43, 10, 50, 20, 60, 30, 70, 23, 63, 13, 53, 5, 45)(2, 42, 7, 47, 16, 56, 26, 66, 35, 75, 27, 67, 17, 57, 8, 48)(4, 44, 9, 49, 19, 59, 29, 69, 37, 77, 32, 72, 22, 62, 12, 52)(6, 46, 14, 54, 24, 64, 33, 73, 39, 79, 34, 74, 25, 65, 15, 55)(11, 51, 18, 58, 28, 68, 36, 76, 40, 80, 38, 78, 31, 71, 21, 61) L = (1, 42)(2, 46)(3, 49)(4, 41)(5, 52)(6, 51)(7, 43)(8, 45)(9, 58)(10, 56)(11, 44)(12, 61)(13, 57)(14, 47)(15, 48)(16, 64)(17, 65)(18, 54)(19, 50)(20, 69)(21, 55)(22, 53)(23, 72)(24, 68)(25, 71)(26, 60)(27, 63)(28, 59)(29, 76)(30, 75)(31, 62)(32, 78)(33, 66)(34, 67)(35, 79)(36, 73)(37, 70)(38, 74)(39, 80)(40, 77) local type(s) :: { ( 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8 ) } Outer automorphisms :: reflexible Dual of E12.608 Transitivity :: ET+ VT+ AT Graph:: v = 5 e = 40 f = 13 degree seq :: [ 16^5 ] E12.610 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {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^-1 * Y1^-1, (R * Y1)^2, (R * Y3)^2, Y3 * Y2 * Y1^-1 * Y2^-1, Y2 * Y3 * Y2^-1 * Y1^-1, Y1^5, (R * Y2 * Y3^-1)^2, Y2^8, (Y2^-1 * Y1)^8 ] Map:: R = (1, 41, 2, 42, 6, 46, 11, 51, 4, 44)(3, 43, 9, 49, 18, 58, 14, 54, 7, 47)(5, 45, 12, 52, 21, 61, 15, 55, 8, 48)(10, 50, 16, 56, 24, 64, 28, 68, 19, 59)(13, 53, 17, 57, 25, 65, 31, 71, 22, 62)(20, 60, 29, 69, 36, 76, 33, 73, 26, 66)(23, 63, 32, 72, 38, 78, 34, 74, 27, 67)(30, 70, 35, 75, 39, 79, 40, 80, 37, 77)(81, 121, 83, 123, 90, 130, 100, 140, 110, 150, 103, 143, 93, 133, 85, 125)(82, 122, 87, 127, 96, 136, 106, 146, 115, 155, 107, 147, 97, 137, 88, 128)(84, 124, 89, 129, 99, 139, 109, 149, 117, 157, 112, 152, 102, 142, 92, 132)(86, 126, 94, 134, 104, 144, 113, 153, 119, 159, 114, 154, 105, 145, 95, 135)(91, 131, 98, 138, 108, 148, 116, 156, 120, 160, 118, 158, 111, 151, 101, 141) L = (1, 84)(2, 81)(3, 87)(4, 91)(5, 88)(6, 82)(7, 94)(8, 95)(9, 83)(10, 99)(11, 86)(12, 85)(13, 102)(14, 98)(15, 101)(16, 90)(17, 93)(18, 89)(19, 108)(20, 106)(21, 92)(22, 111)(23, 107)(24, 96)(25, 97)(26, 113)(27, 114)(28, 104)(29, 100)(30, 117)(31, 105)(32, 103)(33, 116)(34, 118)(35, 110)(36, 109)(37, 120)(38, 112)(39, 115)(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) :: { ( 2, 16, 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 E12.611 Graph:: bipartite v = 13 e = 80 f = 45 degree seq :: [ 10^8, 16^5 ] E12.611 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {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 :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, Y3 * Y1 * Y3 * Y1^-1, (R * Y2 * Y3^-1)^2, Y1^8, (Y3 * Y2^-1)^5 ] Map:: R = (1, 41, 2, 42, 6, 46, 14, 54, 24, 64, 23, 63, 12, 52, 4, 44)(3, 43, 8, 48, 15, 55, 26, 66, 33, 73, 30, 70, 20, 60, 10, 50)(5, 45, 7, 47, 16, 56, 25, 65, 34, 74, 32, 72, 22, 62, 11, 51)(9, 49, 18, 58, 27, 67, 36, 76, 39, 79, 37, 77, 29, 69, 19, 59)(13, 53, 17, 57, 28, 68, 35, 75, 40, 80, 38, 78, 31, 71, 21, 61)(81, 121)(82, 122)(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)(99, 139)(100, 140)(101, 141)(102, 142)(103, 143)(104, 144)(105, 145)(106, 146)(107, 147)(108, 148)(109, 149)(110, 150)(111, 151)(112, 152)(113, 153)(114, 154)(115, 155)(116, 156)(117, 157)(118, 158)(119, 159)(120, 160) L = (1, 83)(2, 87)(3, 89)(4, 91)(5, 81)(6, 95)(7, 97)(8, 82)(9, 93)(10, 84)(11, 101)(12, 100)(13, 85)(14, 105)(15, 107)(16, 86)(17, 98)(18, 88)(19, 90)(20, 109)(21, 99)(22, 92)(23, 112)(24, 113)(25, 115)(26, 94)(27, 108)(28, 96)(29, 111)(30, 103)(31, 102)(32, 118)(33, 119)(34, 104)(35, 116)(36, 106)(37, 110)(38, 117)(39, 120)(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) :: { ( 10, 16 ), ( 10, 16, 10, 16, 10, 16, 10, 16, 10, 16, 10, 16, 10, 16, 10, 16 ) } Outer automorphisms :: reflexible Dual of E12.610 Graph:: simple bipartite v = 45 e = 80 f = 13 degree seq :: [ 2^40, 16^5 ] E12.612 :: Family: { 5 } :: Oriented family(ies): { E3a } Signature :: (0; {5, 8, 8}) Quotient :: edge Aut^+ = C5 : C8 (small group id <40, 3>) Aut = C5 : C8 (small group id <40, 3>) |r| :: 1 Presentation :: [ X1^5, X1 * X2 * X1 * X2^-1 * X1, X1 * X2 * X1^-2 * X2^-1, X2^8, X2^-2 * X1^-1 * X2^-3 * X1^-1 * X2^-3 * X1 ] Map:: non-degenerate R = (1, 2, 6, 13, 4)(3, 9, 7, 12, 11)(5, 15, 14, 8, 16)(10, 21, 20, 23, 18)(17, 24, 26, 25, 19)(22, 32, 31, 28, 30)(27, 36, 29, 34, 35)(33, 37, 40, 38, 39)(41, 43, 50, 62, 73, 67, 57, 45)(42, 47, 58, 68, 77, 69, 59, 48)(44, 52, 61, 71, 79, 74, 64, 54)(46, 51, 63, 72, 80, 75, 65, 55)(49, 60, 70, 78, 76, 66, 56, 53) L = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 16^5 ), ( 16^8 ) } Outer automorphisms :: chiral Transitivity :: ET+ Graph:: simple bipartite v = 13 e = 40 f = 5 degree seq :: [ 5^8, 8^5 ] E12.613 :: Family: { 5* } :: Oriented family(ies): { E3*a } Signature :: (0; {5, 8, 8}) Quotient :: loop Aut^+ = C5 : C8 (small group id <40, 3>) Aut = C5 : C8 (small group id <40, 3>) |r| :: 1 Presentation :: [ X2 * X1^-1 * X2^-3 * X1^-1, X2^-1 * X1 * X2 * X1 * X2 * X1^-1, X2^2 * X1^2 * X2^-1 * X1^-1, X1^-1 * X2 * X1^-1 * X2^5, X1^8 ] Map:: non-degenerate R = (1, 41, 2, 42, 6, 46, 18, 58, 34, 74, 30, 70, 13, 53, 4, 44)(3, 43, 9, 49, 25, 65, 8, 48, 24, 64, 40, 80, 31, 71, 11, 51)(5, 45, 15, 55, 33, 73, 38, 78, 28, 68, 12, 52, 27, 67, 16, 56)(7, 47, 21, 61, 17, 57, 20, 60, 37, 77, 29, 69, 10, 50, 23, 63)(14, 54, 19, 59, 36, 76, 26, 66, 35, 75, 32, 72, 39, 79, 22, 62) L = (1, 43)(2, 47)(3, 50)(4, 52)(5, 41)(6, 59)(7, 62)(8, 42)(9, 67)(10, 68)(11, 70)(12, 71)(13, 72)(14, 44)(15, 65)(16, 63)(17, 45)(18, 55)(19, 56)(20, 46)(21, 49)(22, 51)(23, 53)(24, 57)(25, 54)(26, 48)(27, 79)(28, 74)(29, 80)(30, 77)(31, 75)(32, 78)(33, 76)(34, 64)(35, 58)(36, 61)(37, 66)(38, 60)(39, 69)(40, 73) local type(s) :: { ( 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8, 5, 8 ) } Outer automorphisms :: chiral Transitivity :: ET+ VT+ Graph:: v = 5 e = 40 f = 13 degree seq :: [ 16^5 ] E12.614 :: Family: { 2*ex } :: Oriented family(ies): { E3c } Signature :: (0; {5, 8, 8}) Quotient :: loop Aut^+ = C5 : C8 (small group id <40, 3>) Aut = (C5 : C8) : C2 (small group id <80, 28>) |r| :: 2 Presentation :: [ F^2, F * T1 * F * T2, T2^-1 * T1 * T2 * T1 * T2 * T1^-1, T1^-1 * T2^-1 * T1^-1 * T2^-2 * T1^-1, T2 * T1^-1 * T2^-3 * T1^-1, T2 * T1^-2 * T2^-2 * T1, T1^-1 * T2 * T1^-2 * T2^2 * T1^-2, T1^-1 * T2 * T1^-1 * T2^5, T1^8 ] Map:: polytopal non-degenerate R = (1, 3, 10, 28, 34, 24, 17, 5)(2, 7, 22, 11, 30, 37, 26, 8)(4, 12, 31, 35, 18, 15, 25, 14)(6, 19, 16, 23, 13, 32, 38, 20)(9, 27, 39, 29, 40, 33, 36, 21)(41, 42, 46, 58, 74, 70, 53, 44)(43, 49, 65, 48, 64, 80, 71, 51)(45, 55, 73, 78, 68, 52, 67, 56)(47, 61, 57, 60, 77, 69, 50, 63)(54, 59, 76, 66, 75, 72, 79, 62) L = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 10^8 ) } Outer automorphisms :: reflexible Dual of E12.615 Transitivity :: ET+ VT AT Graph:: bipartite v = 10 e = 40 f = 8 degree seq :: [ 8^10 ] E12.615 :: Family: { 2ex } :: Oriented family(ies): { E3*c } Signature :: (0; {5, 8, 8}) Quotient :: edge Aut^+ = C5 : C8 (small group id <40, 3>) Aut = (C5 : C8) : C2 (small group id <80, 28>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, F * T1 * T2 * F * T1^-1, T1 * T2^2 * T1^-1 * T2^-1, T1 * T2^-1 * T1^-1 * T2^-2, T2^5, T1^8, T1^-2 * T2^-1 * T1^-3 * T2^-1 * T1^-3 * T2 ] Map:: polytopal non-degenerate R = (1, 41, 3, 43, 10, 50, 17, 57, 5, 45)(2, 42, 7, 47, 9, 49, 15, 55, 8, 48)(4, 44, 12, 52, 16, 56, 11, 51, 14, 54)(6, 46, 19, 59, 21, 61, 22, 62, 20, 60)(13, 53, 25, 65, 27, 67, 24, 64, 23, 63)(18, 58, 29, 69, 31, 71, 32, 72, 30, 70)(26, 66, 36, 76, 33, 73, 35, 75, 34, 74)(28, 68, 37, 77, 39, 79, 40, 80, 38, 78) L = (1, 42)(2, 46)(3, 49)(4, 41)(5, 55)(6, 58)(7, 61)(8, 62)(9, 60)(10, 48)(11, 43)(12, 50)(13, 44)(14, 57)(15, 59)(16, 45)(17, 47)(18, 68)(19, 71)(20, 72)(21, 70)(22, 69)(23, 51)(24, 52)(25, 56)(26, 53)(27, 54)(28, 66)(29, 79)(30, 80)(31, 78)(32, 77)(33, 63)(34, 64)(35, 65)(36, 67)(37, 73)(38, 75)(39, 74)(40, 76) local type(s) :: { ( 8^10 ) } Outer automorphisms :: reflexible Dual of E12.614 Transitivity :: ET+ VT+ Graph:: bipartite v = 8 e = 40 f = 10 degree seq :: [ 10^8 ] E12.616 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {5, 8, 8}) Quotient :: edge^2 Aut^+ = C5 : C8 (small group id <40, 3>) Aut = (C5 : C8) : C2 (small group id <80, 28>) |r| :: 2 Presentation :: [ Y3, R^2, R * Y1 * R * Y2, (R * Y3)^2, Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1^-1, Y1^-1 * Y2^-1 * Y1^-1 * Y2^-2 * Y1^-1, Y2 * Y1^-1 * Y2^-3 * Y1^-1, Y2^2 * Y1^2 * Y2^-1 * Y1^-1, Y2^8, Y1^8, (Y1^-1 * Y3^-1 * Y2^-1)^5 ] Map:: polytopal R = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80)(81, 82, 86, 98, 114, 110, 93, 84)(83, 89, 105, 88, 104, 120, 111, 91)(85, 95, 113, 118, 108, 92, 107, 96)(87, 101, 97, 100, 117, 109, 90, 103)(94, 99, 116, 106, 115, 112, 119, 102)(121, 123, 130, 148, 154, 144, 137, 125)(122, 127, 142, 131, 150, 157, 146, 128)(124, 132, 151, 155, 138, 135, 145, 134)(126, 139, 136, 143, 133, 152, 158, 140)(129, 147, 159, 149, 160, 153, 156, 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) :: { ( 20, 20 ), ( 20^8 ) } Outer automorphisms :: reflexible Dual of E12.619 Graph:: simple bipartite v = 50 e = 80 f = 8 degree seq :: [ 2^40, 8^10 ] E12.617 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {5, 8, 8}) Quotient :: edge^2 Aut^+ = C5 : C8 (small group id <40, 3>) Aut = (C5 : C8) : C2 (small group id <80, 28>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1 * Y2^-1, Y3 * Y2^-1 * Y3 * Y1^-1, Y1^-1 * Y3 * Y2^-1 * Y3, Y3^-1 * Y2 * Y3^-1 * Y1, R * Y1 * R * Y2, Y1^-1 * Y2^-1 * Y3^-2, Y2 * Y3^-1 * Y1 * Y3^-1, (R * Y3)^2, Y1^-1 * Y2^-1 * Y3^3, Y1^8, Y2^2 * Y1^-1 * Y2 * Y1^-2 * Y2 * Y1^-1, Y2^8 ] Map:: polytopal non-degenerate R = (1, 41, 4, 44, 17, 57, 12, 52, 7, 47)(2, 42, 9, 49, 6, 46, 22, 62, 11, 51)(3, 43, 5, 45, 19, 59, 16, 56, 15, 55)(8, 48, 23, 63, 10, 50, 27, 67, 21, 61)(13, 53, 14, 54, 32, 72, 18, 58, 20, 60)(24, 64, 28, 68, 25, 65, 35, 75, 26, 66)(29, 69, 30, 70, 34, 74, 31, 71, 33, 73)(36, 76, 39, 79, 37, 77, 40, 80, 38, 78)(81, 82, 88, 104, 116, 111, 100, 85)(83, 92, 89, 90, 106, 120, 113, 94)(84, 86, 101, 115, 119, 109, 98, 95)(87, 102, 103, 105, 118, 110, 93, 96)(91, 107, 108, 117, 114, 112, 99, 97)(121, 123, 133, 149, 156, 146, 143, 126)(122, 127, 139, 134, 151, 158, 148, 130)(124, 136, 140, 154, 159, 145, 128, 131)(125, 138, 153, 157, 144, 141, 129, 137)(132, 135, 152, 150, 160, 155, 147, 142) 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) :: { ( 4^8 ), ( 4^10 ) } Outer automorphisms :: reflexible Dual of E12.618 Graph:: simple bipartite v = 18 e = 80 f = 40 degree seq :: [ 8^10, 10^8 ] E12.618 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {5, 8, 8}) Quotient :: loop^2 Aut^+ = C5 : C8 (small group id <40, 3>) Aut = (C5 : C8) : C2 (small group id <80, 28>) |r| :: 2 Presentation :: [ Y3, R^2, R * Y1 * R * Y2, (R * Y3)^2, Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1^-1, Y1^-1 * Y2^-1 * Y1^-1 * Y2^-2 * Y1^-1, Y2 * Y1^-1 * Y2^-3 * Y1^-1, Y2^2 * Y1^2 * Y2^-1 * Y1^-1, Y2^8, Y1^8, (Y1^-1 * Y3^-1 * Y2^-1)^5 ] Map:: polytopal non-degenerate R = (1, 41, 81, 121)(2, 42, 82, 122)(3, 43, 83, 123)(4, 44, 84, 124)(5, 45, 85, 125)(6, 46, 86, 126)(7, 47, 87, 127)(8, 48, 88, 128)(9, 49, 89, 129)(10, 50, 90, 130)(11, 51, 91, 131)(12, 52, 92, 132)(13, 53, 93, 133)(14, 54, 94, 134)(15, 55, 95, 135)(16, 56, 96, 136)(17, 57, 97, 137)(18, 58, 98, 138)(19, 59, 99, 139)(20, 60, 100, 140)(21, 61, 101, 141)(22, 62, 102, 142)(23, 63, 103, 143)(24, 64, 104, 144)(25, 65, 105, 145)(26, 66, 106, 146)(27, 67, 107, 147)(28, 68, 108, 148)(29, 69, 109, 149)(30, 70, 110, 150)(31, 71, 111, 151)(32, 72, 112, 152)(33, 73, 113, 153)(34, 74, 114, 154)(35, 75, 115, 155)(36, 76, 116, 156)(37, 77, 117, 157)(38, 78, 118, 158)(39, 79, 119, 159)(40, 80, 120, 160) L = (1, 42)(2, 46)(3, 49)(4, 41)(5, 55)(6, 58)(7, 61)(8, 64)(9, 65)(10, 63)(11, 43)(12, 67)(13, 44)(14, 59)(15, 73)(16, 45)(17, 60)(18, 74)(19, 76)(20, 77)(21, 57)(22, 54)(23, 47)(24, 80)(25, 48)(26, 75)(27, 56)(28, 52)(29, 50)(30, 53)(31, 51)(32, 79)(33, 78)(34, 70)(35, 72)(36, 66)(37, 69)(38, 68)(39, 62)(40, 71)(81, 123)(82, 127)(83, 130)(84, 132)(85, 121)(86, 139)(87, 142)(88, 122)(89, 147)(90, 148)(91, 150)(92, 151)(93, 152)(94, 124)(95, 145)(96, 143)(97, 125)(98, 135)(99, 136)(100, 126)(101, 129)(102, 131)(103, 133)(104, 137)(105, 134)(106, 128)(107, 159)(108, 154)(109, 160)(110, 157)(111, 155)(112, 158)(113, 156)(114, 144)(115, 138)(116, 141)(117, 146)(118, 140)(119, 149)(120, 153) local type(s) :: { ( 8, 10, 8, 10 ) } Outer automorphisms :: reflexible Dual of E12.617 Transitivity :: VT+ Graph:: simple bipartite v = 40 e = 80 f = 18 degree seq :: [ 4^40 ] E12.619 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {5, 8, 8}) Quotient :: loop^2 Aut^+ = C5 : C8 (small group id <40, 3>) Aut = (C5 : C8) : C2 (small group id <80, 28>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1 * Y2^-1, Y3 * Y2^-1 * Y3 * Y1^-1, Y1^-1 * Y3 * Y2^-1 * Y3, Y3^-1 * Y2 * Y3^-1 * Y1, R * Y1 * R * Y2, Y1^-1 * Y2^-1 * Y3^-2, Y2 * Y3^-1 * Y1 * Y3^-1, (R * Y3)^2, Y1^-1 * Y2^-1 * Y3^3, Y1^8, Y2^2 * Y1^-1 * Y2 * Y1^-2 * Y2 * Y1^-1, Y2^8 ] Map:: R = (1, 41, 81, 121, 4, 44, 84, 124, 17, 57, 97, 137, 12, 52, 92, 132, 7, 47, 87, 127)(2, 42, 82, 122, 9, 49, 89, 129, 6, 46, 86, 126, 22, 62, 102, 142, 11, 51, 91, 131)(3, 43, 83, 123, 5, 45, 85, 125, 19, 59, 99, 139, 16, 56, 96, 136, 15, 55, 95, 135)(8, 48, 88, 128, 23, 63, 103, 143, 10, 50, 90, 130, 27, 67, 107, 147, 21, 61, 101, 141)(13, 53, 93, 133, 14, 54, 94, 134, 32, 72, 112, 152, 18, 58, 98, 138, 20, 60, 100, 140)(24, 64, 104, 144, 28, 68, 108, 148, 25, 65, 105, 145, 35, 75, 115, 155, 26, 66, 106, 146)(29, 69, 109, 149, 30, 70, 110, 150, 34, 74, 114, 154, 31, 71, 111, 151, 33, 73, 113, 153)(36, 76, 116, 156, 39, 79, 119, 159, 37, 77, 117, 157, 40, 80, 120, 160, 38, 78, 118, 158) L = (1, 42)(2, 48)(3, 52)(4, 46)(5, 41)(6, 61)(7, 62)(8, 64)(9, 50)(10, 66)(11, 67)(12, 49)(13, 56)(14, 43)(15, 44)(16, 47)(17, 51)(18, 55)(19, 57)(20, 45)(21, 75)(22, 63)(23, 65)(24, 76)(25, 78)(26, 80)(27, 68)(28, 77)(29, 58)(30, 53)(31, 60)(32, 59)(33, 54)(34, 72)(35, 79)(36, 71)(37, 74)(38, 70)(39, 69)(40, 73)(81, 123)(82, 127)(83, 133)(84, 136)(85, 138)(86, 121)(87, 139)(88, 131)(89, 137)(90, 122)(91, 124)(92, 135)(93, 149)(94, 151)(95, 152)(96, 140)(97, 125)(98, 153)(99, 134)(100, 154)(101, 129)(102, 132)(103, 126)(104, 141)(105, 128)(106, 143)(107, 142)(108, 130)(109, 156)(110, 160)(111, 158)(112, 150)(113, 157)(114, 159)(115, 147)(116, 146)(117, 144)(118, 148)(119, 145)(120, 155) local type(s) :: { ( 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 E12.616 Transitivity :: VT+ Graph:: bipartite v = 8 e = 80 f = 50 degree seq :: [ 20^8 ] E12.620 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 10, 10}) Quotient :: edge Aut^+ = C5 x D8 (small group id <40, 10>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T2 * T1^-1 * T2^-1 * T1^-1, T2^10 ] Map:: non-degenerate R = (1, 3, 10, 18, 26, 34, 28, 20, 12, 5)(2, 7, 15, 23, 31, 38, 32, 24, 16, 8)(4, 9, 17, 25, 33, 39, 35, 27, 19, 11)(6, 13, 21, 29, 36, 40, 37, 30, 22, 14)(41, 42, 46, 44)(43, 49, 53, 47)(45, 51, 54, 48)(50, 55, 61, 57)(52, 56, 62, 59)(58, 65, 69, 63)(60, 67, 70, 64)(66, 71, 76, 73)(68, 72, 77, 75)(74, 79, 80, 78) L = (1, 41)(2, 42)(3, 43)(4, 44)(5, 45)(6, 46)(7, 47)(8, 48)(9, 49)(10, 50)(11, 51)(12, 52)(13, 53)(14, 54)(15, 55)(16, 56)(17, 57)(18, 58)(19, 59)(20, 60)(21, 61)(22, 62)(23, 63)(24, 64)(25, 65)(26, 66)(27, 67)(28, 68)(29, 69)(30, 70)(31, 71)(32, 72)(33, 73)(34, 74)(35, 75)(36, 76)(37, 77)(38, 78)(39, 79)(40, 80) local type(s) :: { ( 20^4 ), ( 20^10 ) } Outer automorphisms :: reflexible Dual of E12.621 Transitivity :: ET+ Graph:: simple bipartite v = 14 e = 40 f = 4 degree seq :: [ 4^10, 10^4 ] E12.621 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 10, 10}) Quotient :: loop Aut^+ = C5 x D8 (small group id <40, 10>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T2 * T1^-1 * T2^-1 * T1^-1, T2^10 ] Map:: non-degenerate R = (1, 41, 3, 43, 10, 50, 18, 58, 26, 66, 34, 74, 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, 9, 49, 17, 57, 25, 65, 33, 73, 39, 79, 35, 75, 27, 67, 19, 59, 11, 51)(6, 46, 13, 53, 21, 61, 29, 69, 36, 76, 40, 80, 37, 77, 30, 70, 22, 62, 14, 54) L = (1, 42)(2, 46)(3, 49)(4, 41)(5, 51)(6, 44)(7, 43)(8, 45)(9, 53)(10, 55)(11, 54)(12, 56)(13, 47)(14, 48)(15, 61)(16, 62)(17, 50)(18, 65)(19, 52)(20, 67)(21, 57)(22, 59)(23, 58)(24, 60)(25, 69)(26, 71)(27, 70)(28, 72)(29, 63)(30, 64)(31, 76)(32, 77)(33, 66)(34, 79)(35, 68)(36, 73)(37, 75)(38, 74)(39, 80)(40, 78) local type(s) :: { ( 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 E12.620 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 4 e = 40 f = 14 degree seq :: [ 20^4 ] E12.622 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {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^-1 * Y1^-1, (R * Y3)^2, (R * Y1)^2, Y1^4, Y3 * Y2 * Y1^-1 * Y2^-1, Y2^-1 * Y1 * Y2 * Y3^-1, (R * Y2 * Y3^-1)^2, Y2^10, 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 ] 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, 84)(2, 81)(3, 87)(4, 86)(5, 88)(6, 82)(7, 93)(8, 94)(9, 83)(10, 97)(11, 85)(12, 99)(13, 89)(14, 91)(15, 90)(16, 92)(17, 101)(18, 103)(19, 102)(20, 104)(21, 95)(22, 96)(23, 109)(24, 110)(25, 98)(26, 113)(27, 100)(28, 115)(29, 105)(30, 107)(31, 106)(32, 108)(33, 116)(34, 118)(35, 117)(36, 111)(37, 112)(38, 120)(39, 114)(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) :: { ( 2, 20, 2, 20, 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 E12.623 Graph:: bipartite v = 14 e = 80 f = 44 degree seq :: [ 8^10, 20^4 ] E12.623 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {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 :: [ Y2, R^2, Y3^4, (R * Y1)^2, (R * Y3)^2, Y3 * Y1 * Y3 * Y1^-1, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^4, Y1^10 ] Map:: R = (1, 41, 2, 42, 6, 46, 13, 53, 21, 61, 29, 69, 28, 68, 20, 60, 12, 52, 4, 44)(3, 43, 8, 48, 14, 54, 23, 63, 30, 70, 37, 77, 34, 74, 26, 66, 18, 58, 10, 50)(5, 45, 7, 47, 15, 55, 22, 62, 31, 71, 36, 76, 35, 75, 27, 67, 19, 59, 11, 51)(9, 49, 16, 56, 24, 64, 32, 72, 38, 78, 40, 80, 39, 79, 33, 73, 25, 65, 17, 57)(81, 121)(82, 122)(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)(99, 139)(100, 140)(101, 141)(102, 142)(103, 143)(104, 144)(105, 145)(106, 146)(107, 147)(108, 148)(109, 149)(110, 150)(111, 151)(112, 152)(113, 153)(114, 154)(115, 155)(116, 156)(117, 157)(118, 158)(119, 159)(120, 160) L = (1, 83)(2, 87)(3, 89)(4, 91)(5, 81)(6, 94)(7, 96)(8, 82)(9, 85)(10, 84)(11, 97)(12, 98)(13, 102)(14, 104)(15, 86)(16, 88)(17, 90)(18, 105)(19, 92)(20, 107)(21, 110)(22, 112)(23, 93)(24, 95)(25, 99)(26, 100)(27, 113)(28, 114)(29, 116)(30, 118)(31, 101)(32, 103)(33, 106)(34, 119)(35, 108)(36, 120)(37, 109)(38, 111)(39, 115)(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 ) } Outer automorphisms :: reflexible Dual of E12.622 Graph:: simple bipartite v = 44 e = 80 f = 14 degree seq :: [ 2^40, 20^4 ] E12.624 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 7}) Quotient :: dipole Aut^+ = D42 (small group id <42, 5>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^-3, (R * Y3)^2, (R * Y1)^2, (Y3, Y2), (R * Y2)^2, (Y3^-1 * Y1)^2, (Y2 * Y1)^2, Y3^7 * Y2^-1 ] Map:: polytopal non-degenerate R = (1, 43, 2, 44)(3, 45, 9, 51)(4, 46, 10, 52)(5, 47, 7, 49)(6, 48, 8, 50)(11, 53, 21, 63)(12, 54, 20, 62)(13, 55, 22, 64)(14, 56, 18, 60)(15, 57, 17, 59)(16, 58, 19, 61)(23, 65, 33, 75)(24, 66, 32, 74)(25, 67, 34, 76)(26, 68, 30, 72)(27, 69, 29, 71)(28, 70, 31, 73)(35, 77, 42, 84)(36, 78, 41, 83)(37, 79, 40, 82)(38, 80, 39, 81)(85, 127, 87, 129, 89, 131)(86, 128, 91, 133, 93, 135)(88, 130, 95, 137, 98, 140)(90, 132, 96, 138, 99, 141)(92, 134, 101, 143, 104, 146)(94, 136, 102, 144, 105, 147)(97, 139, 107, 149, 110, 152)(100, 142, 108, 150, 111, 153)(103, 145, 113, 155, 116, 158)(106, 148, 114, 156, 117, 159)(109, 151, 119, 161, 121, 163)(112, 154, 120, 162, 122, 164)(115, 157, 123, 165, 125, 167)(118, 160, 124, 166, 126, 168) 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, 120)(26, 121)(27, 99)(28, 100)(29, 123)(30, 102)(31, 124)(32, 125)(33, 105)(34, 106)(35, 122)(36, 108)(37, 112)(38, 111)(39, 126)(40, 114)(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) :: { ( 4, 14, 4, 14 ), ( 4, 14, 4, 14, 4, 14 ) } Outer automorphisms :: reflexible Dual of E12.625 Graph:: simple bipartite v = 35 e = 84 f = 27 degree seq :: [ 4^21, 6^14 ] E12.625 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 3, 7}) Quotient :: dipole Aut^+ = D42 (small group id <42, 5>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ Y2^2, R^2, (R * Y1)^2, (Y3 * Y2)^2, (Y3, Y1^-1), (R * Y3)^2, (Y2 * Y1)^2, Y3^-3 * Y1^-3, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3^6, Y1^2 * Y3^-1 * Y1^2 * Y3^-2, Y1^7 ] Map:: polytopal non-degenerate R = (1, 43, 2, 44, 7, 49, 19, 61, 32, 74, 16, 58, 5, 47)(3, 45, 11, 53, 27, 69, 40, 82, 35, 77, 20, 62, 8, 50)(4, 46, 9, 51, 21, 63, 18, 60, 26, 68, 34, 76, 15, 57)(6, 48, 10, 52, 22, 64, 33, 75, 14, 56, 25, 67, 17, 59)(12, 54, 28, 70, 39, 81, 31, 73, 42, 84, 36, 78, 23, 65)(13, 55, 29, 71, 41, 83, 38, 80, 30, 72, 37, 79, 24, 66)(85, 127, 87, 129)(86, 128, 92, 134)(88, 130, 97, 139)(89, 131, 95, 137)(90, 132, 96, 138)(91, 133, 104, 146)(93, 135, 108, 150)(94, 136, 107, 149)(98, 140, 115, 157)(99, 141, 113, 155)(100, 142, 111, 153)(101, 143, 112, 154)(102, 144, 114, 156)(103, 145, 119, 161)(105, 147, 121, 163)(106, 148, 120, 162)(109, 151, 123, 165)(110, 152, 122, 164)(116, 158, 124, 166)(117, 159, 126, 168)(118, 160, 125, 167) L = (1, 88)(2, 93)(3, 96)(4, 98)(5, 99)(6, 85)(7, 105)(8, 107)(9, 109)(10, 86)(11, 112)(12, 114)(13, 87)(14, 116)(15, 117)(16, 118)(17, 89)(18, 90)(19, 102)(20, 120)(21, 101)(22, 91)(23, 122)(24, 92)(25, 100)(26, 94)(27, 123)(28, 121)(29, 95)(30, 119)(31, 97)(32, 110)(33, 103)(34, 106)(35, 126)(36, 125)(37, 104)(38, 124)(39, 108)(40, 115)(41, 111)(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, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E12.624 Graph:: simple bipartite v = 27 e = 84 f = 35 degree seq :: [ 4^21, 14^6 ] E12.626 :: Family: { 5 } :: Oriented family(ies): { E3a } Signature :: (0; {6, 6, 7}) Quotient :: edge Aut^+ = (C7 : C3) : C2 (small group id <42, 1>) Aut = (C7 : C3) : C2 (small group id <42, 1>) |r| :: 1 Presentation :: [ X1 * X2^-2 * X1^-1 * X2^-1, X2 * X1^-1 * X2^-3 * X1, X1 * X2^-1 * X1^-1 * X2^3, X2 * X1 * X2^-1 * X1^-1 * X2^2, X1^6, (X1^-1 * X2 * X1^-1)^3 ] Map:: polytopal non-degenerate R = (1, 2, 6, 18, 13, 4)(3, 9, 25, 38, 28, 11)(5, 15, 35, 37, 36, 16)(7, 21, 41, 32, 29, 22)(8, 23, 42, 31, 34, 24)(10, 27, 19, 39, 33, 14)(12, 17, 26, 20, 40, 30)(43, 45, 52, 64, 66, 59, 47)(44, 49, 57, 69, 68, 51, 50)(46, 54, 71, 53, 58, 76, 56)(48, 61, 65, 77, 67, 63, 62)(55, 73, 70, 72, 75, 78, 74)(60, 79, 82, 84, 83, 81, 80) L = (1, 43)(2, 44)(3, 45)(4, 46)(5, 47)(6, 48)(7, 49)(8, 50)(9, 51)(10, 52)(11, 53)(12, 54)(13, 55)(14, 56)(15, 57)(16, 58)(17, 59)(18, 60)(19, 61)(20, 62)(21, 63)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84) local type(s) :: { ( 12^6 ), ( 12^7 ) } Outer automorphisms :: chiral Transitivity :: ET+ Graph:: simple bipartite v = 13 e = 42 f = 7 degree seq :: [ 6^7, 7^6 ] E12.627 :: Family: { 5* } :: Oriented family(ies): { E3*a } Signature :: (0; {6, 6, 7}) Quotient :: loop Aut^+ = (C7 : C3) : C2 (small group id <42, 1>) Aut = (C7 : C3) : C2 (small group id <42, 1>) |r| :: 1 Presentation :: [ (X2 * X1^-1)^3, X2 * X1 * X2^-1 * X1 * X2 * X1^-1, X1^6, X2^6, (X2 * X1^-2)^2, X1^-1 * X2^-1 * X1^-2 * X2^-2 ] Map:: polytopal non-degenerate R = (1, 43, 2, 44, 6, 48, 18, 60, 13, 55, 4, 46)(3, 45, 9, 51, 27, 69, 39, 81, 20, 62, 11, 53)(5, 47, 15, 57, 33, 75, 40, 82, 22, 64, 16, 58)(7, 49, 21, 63, 41, 83, 30, 72, 36, 78, 23, 65)(8, 50, 24, 66, 12, 54, 31, 73, 37, 79, 25, 67)(10, 52, 29, 71, 14, 56, 34, 76, 35, 77, 26, 68)(17, 59, 32, 74, 42, 84, 28, 70, 38, 80, 19, 61) L = (1, 45)(2, 49)(3, 52)(4, 54)(5, 43)(6, 61)(7, 64)(8, 44)(9, 70)(10, 72)(11, 66)(12, 74)(13, 75)(14, 46)(15, 76)(16, 73)(17, 47)(18, 77)(19, 79)(20, 48)(21, 56)(22, 84)(23, 53)(24, 57)(25, 51)(26, 50)(27, 58)(28, 55)(29, 82)(30, 59)(31, 78)(32, 81)(33, 83)(34, 80)(35, 69)(36, 60)(37, 71)(38, 65)(39, 63)(40, 62)(41, 67)(42, 68) local type(s) :: { ( 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7 ) } Outer automorphisms :: chiral Transitivity :: ET+ VT+ Graph:: v = 7 e = 42 f = 13 degree seq :: [ 12^7 ] E12.628 :: Family: { 2*ex } :: Oriented family(ies): { E3c } Signature :: (0; {6, 6, 7}) Quotient :: loop Aut^+ = (C7 : C3) : C2 (small group id <42, 1>) Aut = C2 x ((C7 : C3) : C2) (small group id <84, 7>) |r| :: 2 Presentation :: [ F^2, F * T1 * F * T2, (T1^-1 * T2 * T1^-1)^2, T2 * T1 * T2^-1 * T1 * T2 * T1^-1, T1^6, T2^6, T1^-1 * T2^-2 * T1^-2 * T2^-1, T1^-1 * T2^-3 * T1^-1 * T2^-1 * T1^-2 ] Map:: polytopal non-degenerate R = (1, 3, 10, 30, 17, 5)(2, 7, 22, 42, 26, 8)(4, 12, 32, 37, 27, 14)(6, 19, 16, 31, 40, 20)(9, 28, 36, 18, 35, 25)(11, 24, 15, 34, 38, 23)(13, 33, 39, 21, 41, 29)(43, 44, 48, 60, 55, 46)(45, 51, 69, 81, 62, 53)(47, 57, 75, 84, 70, 58)(49, 63, 59, 74, 78, 65)(50, 66, 54, 73, 83, 67)(52, 71, 80, 61, 79, 68)(56, 76, 77, 72, 82, 64) L = (1, 43)(2, 44)(3, 45)(4, 46)(5, 47)(6, 48)(7, 49)(8, 50)(9, 51)(10, 52)(11, 53)(12, 54)(13, 55)(14, 56)(15, 57)(16, 58)(17, 59)(18, 60)(19, 61)(20, 62)(21, 63)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84) local type(s) :: { ( 14^6 ) } Outer automorphisms :: reflexible Dual of E12.630 Transitivity :: ET+ VT AT Graph:: simple bipartite v = 14 e = 42 f = 6 degree seq :: [ 6^14 ] E12.629 :: Family: { 2*ex } :: Oriented family(ies): { E3c } Signature :: (0; {6, 6, 7}) Quotient :: loop Aut^+ = C2 x (C7 : C3) (small group id <42, 2>) Aut = C2 x ((C7 : C3) : C2) (small group id <84, 7>) |r| :: 2 Presentation :: [ F^2, F * T1 * F * T2, T2^-3 * T1^3, T2^-3 * T1^-3, T2 * T1 * T2 * T1 * T2^-1 * T1^-1, (T2 * T1^-1)^3 ] Map:: polytopal non-degenerate R = (1, 3, 10, 18, 17, 5)(2, 7, 22, 13, 26, 8)(4, 12, 20, 6, 19, 14)(9, 23, 37, 31, 39, 28)(11, 24, 35, 27, 40, 32)(15, 21, 36, 29, 42, 33)(16, 34, 41, 30, 38, 25)(43, 44, 48, 60, 55, 46)(45, 51, 69, 59, 73, 53)(47, 57, 72, 52, 71, 58)(49, 63, 81, 68, 84, 65)(50, 66, 83, 64, 82, 67)(54, 74, 78, 61, 77, 75)(56, 70, 80, 62, 79, 76) L = (1, 43)(2, 44)(3, 45)(4, 46)(5, 47)(6, 48)(7, 49)(8, 50)(9, 51)(10, 52)(11, 53)(12, 54)(13, 55)(14, 56)(15, 57)(16, 58)(17, 59)(18, 60)(19, 61)(20, 62)(21, 63)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84) local type(s) :: { ( 14^6 ) } Outer automorphisms :: reflexible Dual of E12.631 Transitivity :: ET+ VT AT Graph:: bipartite v = 14 e = 42 f = 6 degree seq :: [ 6^14 ] E12.630 :: Family: { 2ex } :: Oriented family(ies): { E3*c } Signature :: (0; {6, 6, 7}) Quotient :: edge Aut^+ = (C7 : C3) : C2 (small group id <42, 1>) Aut = C2 x ((C7 : C3) : C2) (small group id <84, 7>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, F * T1 * T2 * F * T1^-1, T1 * T2 * T1^-1 * T2^2, T2 * T1 * T2^-3 * T1^-1, T1^6, (T1^-2 * T2)^3 ] Map:: polytopal non-degenerate R = (1, 43, 3, 45, 10, 52, 26, 68, 33, 75, 17, 59, 5, 47)(2, 44, 7, 49, 22, 64, 9, 51, 15, 57, 24, 66, 8, 50)(4, 46, 12, 54, 16, 58, 27, 69, 29, 71, 11, 53, 14, 56)(6, 48, 19, 61, 25, 67, 21, 63, 23, 65, 35, 77, 20, 62)(13, 55, 31, 73, 34, 76, 36, 78, 28, 70, 30, 72, 32, 74)(18, 60, 37, 79, 41, 83, 39, 81, 40, 82, 42, 84, 38, 80) L = (1, 44)(2, 48)(3, 51)(4, 43)(5, 57)(6, 60)(7, 63)(8, 65)(9, 67)(10, 50)(11, 45)(12, 68)(13, 46)(14, 75)(15, 77)(16, 47)(17, 49)(18, 55)(19, 81)(20, 82)(21, 83)(22, 62)(23, 84)(24, 61)(25, 80)(26, 64)(27, 52)(28, 53)(29, 59)(30, 54)(31, 69)(32, 71)(33, 66)(34, 56)(35, 79)(36, 58)(37, 78)(38, 70)(39, 76)(40, 72)(41, 74)(42, 73) local type(s) :: { ( 6^14 ) } Outer automorphisms :: reflexible Dual of E12.628 Transitivity :: ET+ VT+ Graph:: bipartite v = 6 e = 42 f = 14 degree seq :: [ 14^6 ] E12.631 :: Family: { 2ex } :: Oriented family(ies): { E3*c } Signature :: (0; {6, 6, 7}) Quotient :: edge Aut^+ = C2 x (C7 : C3) (small group id <42, 2>) Aut = C2 x ((C7 : C3) : C2) (small group id <84, 7>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, F * T1 * T2 * F * T1^-1, T1 * T2 * T1^-1 * T2^-2, T1^-1 * T2 * T1 * T2^3, T2 * T1 * T2^3 * T1^-1, T1 * T2^3 * T1^-1 * T2, T1^6, T1^2 * F * T1^-2 * T2 * F, T1^-2 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-2 ] Map:: polytopal non-degenerate R = (1, 43, 3, 45, 10, 52, 26, 68, 30, 72, 17, 59, 5, 47)(2, 44, 7, 49, 22, 64, 15, 57, 9, 51, 24, 66, 8, 50)(4, 46, 12, 54, 11, 53, 28, 70, 27, 69, 16, 58, 14, 56)(6, 48, 19, 61, 25, 67, 23, 65, 21, 63, 35, 77, 20, 62)(13, 55, 32, 74, 31, 73, 36, 78, 29, 71, 34, 76, 33, 75)(18, 60, 37, 79, 41, 83, 40, 82, 39, 81, 42, 84, 38, 80) L = (1, 44)(2, 48)(3, 51)(4, 43)(5, 57)(6, 60)(7, 63)(8, 65)(9, 67)(10, 49)(11, 45)(12, 72)(13, 46)(14, 68)(15, 77)(16, 47)(17, 50)(18, 55)(19, 81)(20, 82)(21, 83)(22, 61)(23, 84)(24, 62)(25, 79)(26, 66)(27, 52)(28, 59)(29, 53)(30, 64)(31, 54)(32, 69)(33, 70)(34, 56)(35, 80)(36, 58)(37, 71)(38, 78)(39, 73)(40, 76)(41, 74)(42, 75) local type(s) :: { ( 6^14 ) } Outer automorphisms :: reflexible Dual of E12.629 Transitivity :: ET+ VT+ Graph:: bipartite v = 6 e = 42 f = 14 degree seq :: [ 14^6 ] E12.632 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {6, 6, 7}) Quotient :: edge^2 Aut^+ = C2 x (C7 : C3) (small group id <42, 2>) Aut = C2 x ((C7 : C3) : C2) (small group id <84, 7>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2 * Y3, Y3^-1 * Y2^-1 * Y1^-1, R * Y2 * R * Y1, Y3^-1 * Y1^-1 * Y3 * Y2^-1, (R * Y3)^2, Y1^-2 * Y2^-2 * Y3, Y1 * Y3^-3 * Y2, Y1^2 * Y3^-1 * Y2^2, Y1^6, Y2^6, (Y2 * Y1^-1)^3 ] Map:: polytopal non-degenerate R = (1, 43, 4, 46, 17, 59, 12, 54, 21, 63, 27, 69, 7, 49)(2, 44, 9, 51, 31, 73, 25, 67, 6, 48, 23, 65, 11, 53)(3, 45, 5, 47, 16, 58, 18, 60, 39, 81, 26, 68, 15, 57)(8, 50, 29, 71, 22, 64, 35, 77, 10, 52, 33, 75, 24, 66)(13, 55, 14, 56, 19, 61, 20, 62, 41, 83, 40, 82, 37, 79)(28, 70, 36, 78, 32, 74, 38, 80, 30, 72, 42, 84, 34, 76)(85, 86, 92, 112, 104, 89)(87, 96, 107, 108, 122, 98)(88, 90, 106, 120, 97, 102)(91, 109, 117, 118, 121, 99)(93, 94, 116, 125, 110, 101)(95, 119, 126, 103, 123, 111)(100, 105, 115, 113, 114, 124)(127, 129, 139, 154, 150, 132)(128, 133, 152, 146, 160, 136)(130, 142, 167, 162, 155, 135)(131, 145, 156, 134, 137, 147)(138, 141, 166, 164, 159, 157)(140, 158, 161, 149, 143, 165)(144, 163, 168, 148, 151, 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) :: { ( 4^6 ), ( 4^14 ) } Outer automorphisms :: reflexible Dual of E12.638 Graph:: simple bipartite v = 20 e = 84 f = 42 degree seq :: [ 6^14, 14^6 ] E12.633 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {6, 6, 7}) Quotient :: edge^2 Aut^+ = (C7 : C3) : C2 (small group id <42, 1>) Aut = C2 x ((C7 : C3) : C2) (small group id <84, 7>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1^-1 * Y3^-1, R * Y1 * R * Y2, Y3 * Y1^-1 * Y3 * Y2^-1, (R * Y3)^2, Y2 * Y1 * Y2^-1 * Y3^-1 * Y1^-1, Y2^-1 * Y3^-1 * Y1^-1 * Y2 * Y1, Y3 * Y2 * Y1 * Y3^2, Y1 * Y3 * Y2 * Y1^-1 * Y2^-1, Y1^6, (Y2 * Y1^-1)^3, Y2^6 ] Map:: polytopal non-degenerate R = (1, 43, 4, 46, 17, 59, 21, 63, 12, 54, 27, 69, 7, 49)(2, 44, 9, 51, 25, 67, 6, 48, 23, 65, 35, 77, 11, 53)(3, 45, 5, 47, 19, 61, 26, 68, 36, 78, 16, 58, 15, 57)(8, 50, 29, 71, 22, 64, 10, 52, 33, 75, 24, 66, 31, 73)(13, 55, 14, 56, 38, 80, 39, 81, 40, 82, 18, 60, 20, 62)(28, 70, 41, 83, 32, 74, 30, 72, 37, 79, 34, 76, 42, 84)(85, 86, 92, 112, 104, 89)(87, 96, 119, 113, 114, 98)(88, 90, 106, 126, 123, 99)(91, 107, 108, 125, 122, 110)(93, 94, 116, 102, 100, 111)(95, 117, 118, 97, 120, 101)(103, 105, 109, 115, 121, 124)(127, 129, 139, 163, 150, 132)(128, 133, 145, 165, 160, 136)(130, 142, 166, 156, 134, 137)(131, 144, 167, 159, 161, 147)(135, 138, 141, 164, 154, 157)(140, 158, 148, 151, 143, 152)(146, 168, 155, 149, 153, 162) 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) :: { ( 4^6 ), ( 4^14 ) } Outer automorphisms :: reflexible Dual of E12.639 Graph:: simple bipartite v = 20 e = 84 f = 42 degree seq :: [ 6^14, 14^6 ] E12.634 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {6, 6, 7}) Quotient :: edge^2 Aut^+ = C2 x (C7 : C3) (small group id <42, 2>) Aut = C2 x ((C7 : C3) : C2) (small group id <84, 7>) |r| :: 2 Presentation :: [ Y3, R^2, R * Y1 * R * Y2, (R * Y3)^2, Y2^-3 * Y1^-3, Y1^6, Y2^6, Y1^-1 * Y2 * Y1 * Y2 * Y1 * Y2^-1, (Y2 * Y1^-1)^3, (Y1^-1 * Y3^-1 * Y2^-1)^7 ] Map:: polytopal R = (1, 43)(2, 44)(3, 45)(4, 46)(5, 47)(6, 48)(7, 49)(8, 50)(9, 51)(10, 52)(11, 53)(12, 54)(13, 55)(14, 56)(15, 57)(16, 58)(17, 59)(18, 60)(19, 61)(20, 62)(21, 63)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84)(85, 86, 90, 102, 97, 88)(87, 93, 111, 101, 115, 95)(89, 99, 114, 94, 113, 100)(91, 105, 123, 110, 126, 107)(92, 108, 125, 106, 124, 109)(96, 116, 120, 103, 119, 117)(98, 112, 122, 104, 121, 118)(127, 129, 136, 144, 143, 131)(128, 133, 148, 139, 152, 134)(130, 138, 146, 132, 145, 140)(135, 149, 163, 157, 165, 154)(137, 150, 161, 153, 166, 158)(141, 147, 162, 155, 168, 159)(142, 160, 167, 156, 164, 151) 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) :: { ( 28, 28 ), ( 28^6 ) } Outer automorphisms :: reflexible Dual of E12.636 Graph:: simple bipartite v = 56 e = 84 f = 6 degree seq :: [ 2^42, 6^14 ] E12.635 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {6, 6, 7}) Quotient :: edge^2 Aut^+ = (C7 : C3) : C2 (small group id <42, 1>) Aut = C2 x ((C7 : C3) : C2) (small group id <84, 7>) |r| :: 2 Presentation :: [ Y3, R^2, R * Y1 * R * Y2, (R * Y3)^2, (Y2 * Y1^-1)^3, (Y1^-1 * Y2 * Y1^-1)^2, Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1^-1, Y1^6, Y2^6, Y1^-1 * Y2^-1 * Y1^-1 * Y2^-2 * Y1^-1, Y1^-1 * Y2^-3 * Y1^-1 * Y2^-1 * Y1^-2, (Y1^-1 * Y3^-1 * Y2^-1)^7 ] Map:: polytopal R = (1, 43)(2, 44)(3, 45)(4, 46)(5, 47)(6, 48)(7, 49)(8, 50)(9, 51)(10, 52)(11, 53)(12, 54)(13, 55)(14, 56)(15, 57)(16, 58)(17, 59)(18, 60)(19, 61)(20, 62)(21, 63)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84)(85, 86, 90, 102, 97, 88)(87, 93, 111, 123, 104, 95)(89, 99, 117, 126, 112, 100)(91, 105, 101, 116, 120, 107)(92, 108, 96, 115, 125, 109)(94, 113, 122, 103, 121, 110)(98, 118, 119, 114, 124, 106)(127, 129, 136, 156, 143, 131)(128, 133, 148, 168, 152, 134)(130, 138, 158, 163, 153, 140)(132, 145, 142, 157, 166, 146)(135, 154, 162, 144, 161, 151)(137, 150, 141, 160, 164, 149)(139, 159, 165, 147, 167, 155) 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) :: { ( 28, 28 ), ( 28^6 ) } Outer automorphisms :: reflexible Dual of E12.637 Graph:: simple bipartite v = 56 e = 84 f = 6 degree seq :: [ 2^42, 6^14 ] E12.636 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {6, 6, 7}) Quotient :: loop^2 Aut^+ = C2 x (C7 : C3) (small group id <42, 2>) Aut = C2 x ((C7 : C3) : C2) (small group id <84, 7>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2 * Y3, Y3^-1 * Y2^-1 * Y1^-1, R * Y2 * R * Y1, Y3^-1 * Y1^-1 * Y3 * Y2^-1, (R * Y3)^2, Y1^-2 * Y2^-2 * Y3, Y1 * Y3^-3 * Y2, Y1^2 * Y3^-1 * Y2^2, Y1^6, Y2^6, (Y2 * Y1^-1)^3 ] Map:: R = (1, 43, 85, 127, 4, 46, 88, 130, 17, 59, 101, 143, 12, 54, 96, 138, 21, 63, 105, 147, 27, 69, 111, 153, 7, 49, 91, 133)(2, 44, 86, 128, 9, 51, 93, 135, 31, 73, 115, 157, 25, 67, 109, 151, 6, 48, 90, 132, 23, 65, 107, 149, 11, 53, 95, 137)(3, 45, 87, 129, 5, 47, 89, 131, 16, 58, 100, 142, 18, 60, 102, 144, 39, 81, 123, 165, 26, 68, 110, 152, 15, 57, 99, 141)(8, 50, 92, 134, 29, 71, 113, 155, 22, 64, 106, 148, 35, 77, 119, 161, 10, 52, 94, 136, 33, 75, 117, 159, 24, 66, 108, 150)(13, 55, 97, 139, 14, 56, 98, 140, 19, 61, 103, 145, 20, 62, 104, 146, 41, 83, 125, 167, 40, 82, 124, 166, 37, 79, 121, 163)(28, 70, 112, 154, 36, 78, 120, 162, 32, 74, 116, 158, 38, 80, 122, 164, 30, 72, 114, 156, 42, 84, 126, 168, 34, 76, 118, 160) L = (1, 44)(2, 50)(3, 54)(4, 48)(5, 43)(6, 64)(7, 67)(8, 70)(9, 52)(10, 74)(11, 77)(12, 65)(13, 60)(14, 45)(15, 49)(16, 63)(17, 51)(18, 46)(19, 81)(20, 47)(21, 73)(22, 78)(23, 66)(24, 80)(25, 75)(26, 59)(27, 53)(28, 62)(29, 72)(30, 82)(31, 71)(32, 83)(33, 76)(34, 79)(35, 84)(36, 55)(37, 57)(38, 56)(39, 69)(40, 58)(41, 68)(42, 61)(85, 129)(86, 133)(87, 139)(88, 142)(89, 145)(90, 127)(91, 152)(92, 137)(93, 130)(94, 128)(95, 147)(96, 141)(97, 154)(98, 158)(99, 166)(100, 167)(101, 165)(102, 163)(103, 156)(104, 160)(105, 131)(106, 151)(107, 143)(108, 132)(109, 153)(110, 146)(111, 144)(112, 150)(113, 135)(114, 134)(115, 138)(116, 161)(117, 157)(118, 136)(119, 149)(120, 155)(121, 168)(122, 159)(123, 140)(124, 164)(125, 162)(126, 148) 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 ) } Outer automorphisms :: reflexible Dual of E12.634 Transitivity :: VT+ Graph:: bipartite v = 6 e = 84 f = 56 degree seq :: [ 28^6 ] E12.637 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {6, 6, 7}) Quotient :: loop^2 Aut^+ = (C7 : C3) : C2 (small group id <42, 1>) Aut = C2 x ((C7 : C3) : C2) (small group id <84, 7>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1^-1 * Y3^-1, R * Y1 * R * Y2, Y3 * Y1^-1 * Y3 * Y2^-1, (R * Y3)^2, Y2 * Y1 * Y2^-1 * Y3^-1 * Y1^-1, Y2^-1 * Y3^-1 * Y1^-1 * Y2 * Y1, Y3 * Y2 * Y1 * Y3^2, Y1 * Y3 * Y2 * Y1^-1 * Y2^-1, Y1^6, (Y2 * Y1^-1)^3, Y2^6 ] Map:: R = (1, 43, 85, 127, 4, 46, 88, 130, 17, 59, 101, 143, 21, 63, 105, 147, 12, 54, 96, 138, 27, 69, 111, 153, 7, 49, 91, 133)(2, 44, 86, 128, 9, 51, 93, 135, 25, 67, 109, 151, 6, 48, 90, 132, 23, 65, 107, 149, 35, 77, 119, 161, 11, 53, 95, 137)(3, 45, 87, 129, 5, 47, 89, 131, 19, 61, 103, 145, 26, 68, 110, 152, 36, 78, 120, 162, 16, 58, 100, 142, 15, 57, 99, 141)(8, 50, 92, 134, 29, 71, 113, 155, 22, 64, 106, 148, 10, 52, 94, 136, 33, 75, 117, 159, 24, 66, 108, 150, 31, 73, 115, 157)(13, 55, 97, 139, 14, 56, 98, 140, 38, 80, 122, 164, 39, 81, 123, 165, 40, 82, 124, 166, 18, 60, 102, 144, 20, 62, 104, 146)(28, 70, 112, 154, 41, 83, 125, 167, 32, 74, 116, 158, 30, 72, 114, 156, 37, 79, 121, 163, 34, 76, 118, 160, 42, 84, 126, 168) L = (1, 44)(2, 50)(3, 54)(4, 48)(5, 43)(6, 64)(7, 65)(8, 70)(9, 52)(10, 74)(11, 75)(12, 77)(13, 78)(14, 45)(15, 46)(16, 69)(17, 53)(18, 58)(19, 63)(20, 47)(21, 67)(22, 84)(23, 66)(24, 83)(25, 73)(26, 49)(27, 51)(28, 62)(29, 72)(30, 56)(31, 79)(32, 60)(33, 76)(34, 55)(35, 71)(36, 59)(37, 82)(38, 68)(39, 57)(40, 61)(41, 80)(42, 81)(85, 129)(86, 133)(87, 139)(88, 142)(89, 144)(90, 127)(91, 145)(92, 137)(93, 138)(94, 128)(95, 130)(96, 141)(97, 163)(98, 158)(99, 164)(100, 166)(101, 152)(102, 167)(103, 165)(104, 168)(105, 131)(106, 151)(107, 153)(108, 132)(109, 143)(110, 140)(111, 162)(112, 157)(113, 149)(114, 134)(115, 135)(116, 148)(117, 161)(118, 136)(119, 147)(120, 146)(121, 150)(122, 154)(123, 160)(124, 156)(125, 159)(126, 155) 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 ) } Outer automorphisms :: reflexible Dual of E12.635 Transitivity :: VT+ Graph:: bipartite v = 6 e = 84 f = 56 degree seq :: [ 28^6 ] E12.638 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {6, 6, 7}) Quotient :: loop^2 Aut^+ = C2 x (C7 : C3) (small group id <42, 2>) Aut = C2 x ((C7 : C3) : C2) (small group id <84, 7>) |r| :: 2 Presentation :: [ Y3, R^2, R * Y1 * R * Y2, (R * Y3)^2, Y2^-3 * Y1^-3, Y1^6, Y2^6, Y1^-1 * Y2 * Y1 * Y2 * Y1 * Y2^-1, (Y2 * Y1^-1)^3, (Y1^-1 * Y3^-1 * Y2^-1)^7 ] Map:: polytopal non-degenerate R = (1, 43, 85, 127)(2, 44, 86, 128)(3, 45, 87, 129)(4, 46, 88, 130)(5, 47, 89, 131)(6, 48, 90, 132)(7, 49, 91, 133)(8, 50, 92, 134)(9, 51, 93, 135)(10, 52, 94, 136)(11, 53, 95, 137)(12, 54, 96, 138)(13, 55, 97, 139)(14, 56, 98, 140)(15, 57, 99, 141)(16, 58, 100, 142)(17, 59, 101, 143)(18, 60, 102, 144)(19, 61, 103, 145)(20, 62, 104, 146)(21, 63, 105, 147)(22, 64, 106, 148)(23, 65, 107, 149)(24, 66, 108, 150)(25, 67, 109, 151)(26, 68, 110, 152)(27, 69, 111, 153)(28, 70, 112, 154)(29, 71, 113, 155)(30, 72, 114, 156)(31, 73, 115, 157)(32, 74, 116, 158)(33, 75, 117, 159)(34, 76, 118, 160)(35, 77, 119, 161)(36, 78, 120, 162)(37, 79, 121, 163)(38, 80, 122, 164)(39, 81, 123, 165)(40, 82, 124, 166)(41, 83, 125, 167)(42, 84, 126, 168) L = (1, 44)(2, 48)(3, 51)(4, 43)(5, 57)(6, 60)(7, 63)(8, 66)(9, 69)(10, 71)(11, 45)(12, 74)(13, 46)(14, 70)(15, 72)(16, 47)(17, 73)(18, 55)(19, 77)(20, 79)(21, 81)(22, 82)(23, 49)(24, 83)(25, 50)(26, 84)(27, 59)(28, 80)(29, 58)(30, 52)(31, 53)(32, 78)(33, 54)(34, 56)(35, 75)(36, 61)(37, 76)(38, 62)(39, 68)(40, 67)(41, 64)(42, 65)(85, 129)(86, 133)(87, 136)(88, 138)(89, 127)(90, 145)(91, 148)(92, 128)(93, 149)(94, 144)(95, 150)(96, 146)(97, 152)(98, 130)(99, 147)(100, 160)(101, 131)(102, 143)(103, 140)(104, 132)(105, 162)(106, 139)(107, 163)(108, 161)(109, 142)(110, 134)(111, 166)(112, 135)(113, 168)(114, 164)(115, 165)(116, 137)(117, 141)(118, 167)(119, 153)(120, 155)(121, 157)(122, 151)(123, 154)(124, 158)(125, 156)(126, 159) local type(s) :: { ( 6, 14, 6, 14 ) } Outer automorphisms :: reflexible Dual of E12.632 Transitivity :: VT+ Graph:: simple bipartite v = 42 e = 84 f = 20 degree seq :: [ 4^42 ] E12.639 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {6, 6, 7}) Quotient :: loop^2 Aut^+ = (C7 : C3) : C2 (small group id <42, 1>) Aut = C2 x ((C7 : C3) : C2) (small group id <84, 7>) |r| :: 2 Presentation :: [ Y3, R^2, R * Y1 * R * Y2, (R * Y3)^2, (Y2 * Y1^-1)^3, (Y1^-1 * Y2 * Y1^-1)^2, Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1^-1, Y1^6, Y2^6, Y1^-1 * Y2^-1 * Y1^-1 * Y2^-2 * Y1^-1, Y1^-1 * Y2^-3 * Y1^-1 * Y2^-1 * Y1^-2, (Y1^-1 * Y3^-1 * Y2^-1)^7 ] Map:: polytopal non-degenerate R = (1, 43, 85, 127)(2, 44, 86, 128)(3, 45, 87, 129)(4, 46, 88, 130)(5, 47, 89, 131)(6, 48, 90, 132)(7, 49, 91, 133)(8, 50, 92, 134)(9, 51, 93, 135)(10, 52, 94, 136)(11, 53, 95, 137)(12, 54, 96, 138)(13, 55, 97, 139)(14, 56, 98, 140)(15, 57, 99, 141)(16, 58, 100, 142)(17, 59, 101, 143)(18, 60, 102, 144)(19, 61, 103, 145)(20, 62, 104, 146)(21, 63, 105, 147)(22, 64, 106, 148)(23, 65, 107, 149)(24, 66, 108, 150)(25, 67, 109, 151)(26, 68, 110, 152)(27, 69, 111, 153)(28, 70, 112, 154)(29, 71, 113, 155)(30, 72, 114, 156)(31, 73, 115, 157)(32, 74, 116, 158)(33, 75, 117, 159)(34, 76, 118, 160)(35, 77, 119, 161)(36, 78, 120, 162)(37, 79, 121, 163)(38, 80, 122, 164)(39, 81, 123, 165)(40, 82, 124, 166)(41, 83, 125, 167)(42, 84, 126, 168) L = (1, 44)(2, 48)(3, 51)(4, 43)(5, 57)(6, 60)(7, 63)(8, 66)(9, 69)(10, 71)(11, 45)(12, 73)(13, 46)(14, 76)(15, 75)(16, 47)(17, 74)(18, 55)(19, 79)(20, 53)(21, 59)(22, 56)(23, 49)(24, 54)(25, 50)(26, 52)(27, 81)(28, 58)(29, 80)(30, 82)(31, 83)(32, 78)(33, 84)(34, 77)(35, 72)(36, 65)(37, 68)(38, 61)(39, 62)(40, 64)(41, 67)(42, 70)(85, 129)(86, 133)(87, 136)(88, 138)(89, 127)(90, 145)(91, 148)(92, 128)(93, 154)(94, 156)(95, 150)(96, 158)(97, 159)(98, 130)(99, 160)(100, 157)(101, 131)(102, 161)(103, 142)(104, 132)(105, 167)(106, 168)(107, 137)(108, 141)(109, 135)(110, 134)(111, 140)(112, 162)(113, 139)(114, 143)(115, 166)(116, 163)(117, 165)(118, 164)(119, 151)(120, 144)(121, 153)(122, 149)(123, 147)(124, 146)(125, 155)(126, 152) local type(s) :: { ( 6, 14, 6, 14 ) } Outer automorphisms :: reflexible Dual of E12.633 Transitivity :: VT+ Graph:: simple bipartite v = 42 e = 84 f = 20 degree seq :: [ 4^42 ] E12.640 :: Family: { 5 } :: Oriented family(ies): { E3a } Signature :: (0; {6, 6, 7}) Quotient :: edge Aut^+ = C2 x (C7 : C3) (small group id <42, 2>) Aut = C2 x (C7 : C3) (small group id <42, 2>) |r| :: 1 Presentation :: [ X1 * X2^-2 * X1^-1 * X2, X2 * X1^-1 * X2^3 * X1, X1 * X2 * X1^-1 * X2^3, X1 * X2^-1 * X1^-1 * X2^-3, X1^6, (X1^-2 * X2)^3 ] Map:: non-degenerate R = (1, 2, 6, 18, 13, 4)(3, 9, 25, 37, 29, 11)(5, 15, 35, 38, 36, 16)(7, 21, 41, 32, 30, 22)(8, 23, 42, 33, 28, 24)(10, 27, 19, 39, 31, 12)(14, 17, 26, 20, 40, 34)(43, 45, 52, 66, 64, 59, 47)(44, 49, 51, 68, 69, 57, 50)(46, 54, 72, 58, 53, 70, 56)(48, 61, 63, 77, 67, 65, 62)(55, 74, 71, 76, 73, 78, 75)(60, 79, 81, 84, 83, 82, 80) L = (1, 43)(2, 44)(3, 45)(4, 46)(5, 47)(6, 48)(7, 49)(8, 50)(9, 51)(10, 52)(11, 53)(12, 54)(13, 55)(14, 56)(15, 57)(16, 58)(17, 59)(18, 60)(19, 61)(20, 62)(21, 63)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84) local type(s) :: { ( 12^6 ), ( 12^7 ) } Outer automorphisms :: chiral Transitivity :: ET+ Graph:: simple bipartite v = 13 e = 42 f = 7 degree seq :: [ 6^7, 7^6 ] E12.641 :: Family: { 5* } :: Oriented family(ies): { E3*a } Signature :: (0; {6, 6, 7}) Quotient :: loop Aut^+ = C2 x (C7 : C3) (small group id <42, 2>) Aut = C2 x (C7 : C3) (small group id <42, 2>) |r| :: 1 Presentation :: [ X1^6, X2^6, X2^2 * X1^3 * X2, (X2 * X1^-1)^3, X1^-1 * X2 * X1 * X2^-1 * X1^-1 * X2^-1 ] Map:: non-degenerate R = (1, 43, 2, 44, 6, 48, 18, 60, 13, 55, 4, 46)(3, 45, 9, 51, 27, 69, 17, 59, 31, 73, 11, 53)(5, 47, 15, 57, 30, 72, 10, 52, 29, 71, 16, 58)(7, 49, 21, 63, 39, 81, 26, 68, 42, 84, 23, 65)(8, 50, 24, 66, 41, 83, 22, 64, 40, 82, 25, 67)(12, 54, 28, 70, 36, 78, 19, 61, 35, 77, 33, 75)(14, 56, 34, 76, 38, 80, 20, 62, 37, 79, 32, 74) L = (1, 45)(2, 49)(3, 52)(4, 54)(5, 43)(6, 61)(7, 64)(8, 44)(9, 70)(10, 60)(11, 66)(12, 62)(13, 68)(14, 46)(15, 67)(16, 65)(17, 47)(18, 59)(19, 56)(20, 48)(21, 51)(22, 55)(23, 79)(24, 80)(25, 78)(26, 50)(27, 82)(28, 84)(29, 83)(30, 81)(31, 77)(32, 53)(33, 57)(34, 58)(35, 63)(36, 71)(37, 72)(38, 69)(39, 76)(40, 74)(41, 75)(42, 73) local type(s) :: { ( 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7 ) } Outer automorphisms :: chiral Transitivity :: ET+ VT+ Graph:: v = 7 e = 42 f = 13 degree seq :: [ 12^7 ] E12.642 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {6, 6, 7}) Quotient :: edge Aut^+ = C3 x D14 (small group id <42, 4>) Aut = S3 x D14 (small group id <84, 8>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T1^6, T2^7 ] Map:: non-degenerate R = (1, 3, 9, 19, 24, 13, 5)(2, 7, 17, 29, 30, 18, 8)(4, 11, 22, 33, 31, 20, 10)(6, 15, 27, 37, 38, 28, 16)(12, 21, 32, 39, 40, 34, 23)(14, 25, 35, 41, 42, 36, 26)(43, 44, 48, 56, 54, 46)(45, 50, 57, 68, 63, 52)(47, 49, 58, 67, 65, 53)(51, 60, 69, 78, 74, 62)(55, 59, 70, 77, 76, 64)(61, 72, 79, 84, 81, 73)(66, 71, 80, 83, 82, 75) L = (1, 43)(2, 44)(3, 45)(4, 46)(5, 47)(6, 48)(7, 49)(8, 50)(9, 51)(10, 52)(11, 53)(12, 54)(13, 55)(14, 56)(15, 57)(16, 58)(17, 59)(18, 60)(19, 61)(20, 62)(21, 63)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84) local type(s) :: { ( 12^6 ), ( 12^7 ) } Outer automorphisms :: reflexible Dual of E12.643 Transitivity :: ET+ Graph:: simple bipartite v = 13 e = 42 f = 7 degree seq :: [ 6^7, 7^6 ] E12.643 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {6, 6, 7}) Quotient :: loop Aut^+ = C3 x D14 (small group id <42, 4>) Aut = S3 x D14 (small group id <84, 8>) |r| :: 2 Presentation :: [ F^2, T2^2 * T1^2, (F * T1)^2, (F * T2)^2, T2^-2 * T1^4, T2^6, (T2 * T1)^7 ] Map:: non-degenerate R = (1, 43, 3, 45, 10, 52, 15, 57, 6, 48, 5, 47)(2, 44, 7, 49, 4, 46, 12, 54, 14, 56, 8, 50)(9, 51, 19, 61, 11, 53, 21, 63, 13, 55, 20, 62)(16, 58, 22, 64, 17, 59, 24, 66, 18, 60, 23, 65)(25, 67, 31, 73, 26, 68, 33, 75, 27, 69, 32, 74)(28, 70, 34, 76, 29, 71, 36, 78, 30, 72, 35, 77)(37, 79, 41, 83, 38, 80, 42, 84, 39, 81, 40, 82) L = (1, 44)(2, 48)(3, 51)(4, 43)(5, 55)(6, 56)(7, 58)(8, 60)(9, 47)(10, 46)(11, 45)(12, 59)(13, 57)(14, 52)(15, 53)(16, 50)(17, 49)(18, 54)(19, 67)(20, 69)(21, 68)(22, 70)(23, 72)(24, 71)(25, 62)(26, 61)(27, 63)(28, 65)(29, 64)(30, 66)(31, 79)(32, 81)(33, 80)(34, 82)(35, 84)(36, 83)(37, 74)(38, 73)(39, 75)(40, 77)(41, 76)(42, 78) local type(s) :: { ( 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7 ) } Outer automorphisms :: reflexible Dual of E12.642 Transitivity :: ET+ VT+ AT Graph:: v = 7 e = 42 f = 13 degree seq :: [ 12^7 ] E12.644 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 6, 7}) 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, (R * Y1)^2, (R * Y3)^2, Y1^-1 * Y2^-1 * Y1 * Y2^-1, Y1^6, Y2^7, (Y3^-1 * Y1^-1)^6 ] Map:: R = (1, 43, 2, 44, 6, 48, 14, 56, 12, 54, 4, 46)(3, 45, 8, 50, 15, 57, 26, 68, 21, 63, 10, 52)(5, 47, 7, 49, 16, 58, 25, 67, 23, 65, 11, 53)(9, 51, 18, 60, 27, 69, 36, 78, 32, 74, 20, 62)(13, 55, 17, 59, 28, 70, 35, 77, 34, 76, 22, 64)(19, 61, 30, 72, 37, 79, 42, 84, 39, 81, 31, 73)(24, 66, 29, 71, 38, 80, 41, 83, 40, 82, 33, 75)(85, 127, 87, 129, 93, 135, 103, 145, 108, 150, 97, 139, 89, 131)(86, 128, 91, 133, 101, 143, 113, 155, 114, 156, 102, 144, 92, 134)(88, 130, 95, 137, 106, 148, 117, 159, 115, 157, 104, 146, 94, 136)(90, 132, 99, 141, 111, 153, 121, 163, 122, 164, 112, 154, 100, 142)(96, 138, 105, 147, 116, 158, 123, 165, 124, 166, 118, 160, 107, 149)(98, 140, 109, 151, 119, 161, 125, 167, 126, 168, 120, 162, 110, 152) L = (1, 87)(2, 91)(3, 93)(4, 95)(5, 85)(6, 99)(7, 101)(8, 86)(9, 103)(10, 88)(11, 106)(12, 105)(13, 89)(14, 109)(15, 111)(16, 90)(17, 113)(18, 92)(19, 108)(20, 94)(21, 116)(22, 117)(23, 96)(24, 97)(25, 119)(26, 98)(27, 121)(28, 100)(29, 114)(30, 102)(31, 104)(32, 123)(33, 115)(34, 107)(35, 125)(36, 110)(37, 122)(38, 112)(39, 124)(40, 118)(41, 126)(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) :: { ( 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 E12.645 Graph:: bipartite v = 13 e = 84 f = 49 degree seq :: [ 12^7, 14^6 ] E12.645 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 6, 7}) Quotient :: dipole Aut^+ = C3 x D14 (small group id <42, 4>) Aut = S3 x D14 (small group id <84, 8>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y3^-1 * Y2 * Y3^-1, (R * Y2 * Y3^-1)^2, Y2^6, (Y3^-1 * Y1^-1)^7 ] Map:: R = (1, 43)(2, 44)(3, 45)(4, 46)(5, 47)(6, 48)(7, 49)(8, 50)(9, 51)(10, 52)(11, 53)(12, 54)(13, 55)(14, 56)(15, 57)(16, 58)(17, 59)(18, 60)(19, 61)(20, 62)(21, 63)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84)(85, 127, 86, 128, 90, 132, 98, 140, 96, 138, 88, 130)(87, 129, 92, 134, 99, 141, 110, 152, 105, 147, 94, 136)(89, 131, 91, 133, 100, 142, 109, 151, 107, 149, 95, 137)(93, 135, 102, 144, 111, 153, 120, 162, 116, 158, 104, 146)(97, 139, 101, 143, 112, 154, 119, 161, 118, 160, 106, 148)(103, 145, 114, 156, 121, 163, 126, 168, 123, 165, 115, 157)(108, 150, 113, 155, 122, 164, 125, 167, 124, 166, 117, 159) L = (1, 87)(2, 91)(3, 93)(4, 95)(5, 85)(6, 99)(7, 101)(8, 86)(9, 103)(10, 88)(11, 106)(12, 105)(13, 89)(14, 109)(15, 111)(16, 90)(17, 113)(18, 92)(19, 108)(20, 94)(21, 116)(22, 117)(23, 96)(24, 97)(25, 119)(26, 98)(27, 121)(28, 100)(29, 114)(30, 102)(31, 104)(32, 123)(33, 115)(34, 107)(35, 125)(36, 110)(37, 122)(38, 112)(39, 124)(40, 118)(41, 126)(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, 14 ), ( 12, 14, 12, 14, 12, 14, 12, 14, 12, 14, 12, 14 ) } Outer automorphisms :: reflexible Dual of E12.644 Graph:: simple bipartite v = 49 e = 84 f = 13 degree seq :: [ 2^42, 12^7 ] E12.646 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 14, 14}) Quotient :: edge Aut^+ = C7 x S3 (small group id <42, 3>) Aut = S3 x D14 (small group id <84, 8>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, T2 * T1^-1 * T2^-1 * T1^-1, T2^14 ] Map:: non-degenerate R = (1, 3, 9, 15, 21, 27, 33, 39, 35, 29, 23, 17, 11, 5)(2, 6, 12, 18, 24, 30, 36, 41, 37, 31, 25, 19, 13, 7)(4, 8, 14, 20, 26, 32, 38, 42, 40, 34, 28, 22, 16, 10)(43, 44, 46)(45, 50, 48)(47, 52, 49)(51, 54, 56)(53, 55, 58)(57, 62, 60)(59, 64, 61)(63, 66, 68)(65, 67, 70)(69, 74, 72)(71, 76, 73)(75, 78, 80)(77, 79, 82)(81, 84, 83) L = (1, 43)(2, 44)(3, 45)(4, 46)(5, 47)(6, 48)(7, 49)(8, 50)(9, 51)(10, 52)(11, 53)(12, 54)(13, 55)(14, 56)(15, 57)(16, 58)(17, 59)(18, 60)(19, 61)(20, 62)(21, 63)(22, 64)(23, 65)(24, 66)(25, 67)(26, 68)(27, 69)(28, 70)(29, 71)(30, 72)(31, 73)(32, 74)(33, 75)(34, 76)(35, 77)(36, 78)(37, 79)(38, 80)(39, 81)(40, 82)(41, 83)(42, 84) local type(s) :: { ( 28^3 ), ( 28^14 ) } Outer automorphisms :: reflexible Dual of E12.647 Transitivity :: ET+ Graph:: simple bipartite v = 17 e = 42 f = 3 degree seq :: [ 3^14, 14^3 ] E12.647 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 14, 14}) Quotient :: loop Aut^+ = C7 x S3 (small group id <42, 3>) Aut = S3 x D14 (small group id <84, 8>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, T2 * T1^-1 * T2^-1 * T1^-1, T2^14 ] Map:: non-degenerate R = (1, 43, 3, 45, 9, 51, 15, 57, 21, 63, 27, 69, 33, 75, 39, 81, 35, 77, 29, 71, 23, 65, 17, 59, 11, 53, 5, 47)(2, 44, 6, 48, 12, 54, 18, 60, 24, 66, 30, 72, 36, 78, 41, 83, 37, 79, 31, 73, 25, 67, 19, 61, 13, 55, 7, 49)(4, 46, 8, 50, 14, 56, 20, 62, 26, 68, 32, 74, 38, 80, 42, 84, 40, 82, 34, 76, 28, 70, 22, 64, 16, 58, 10, 52) L = (1, 44)(2, 46)(3, 50)(4, 43)(5, 52)(6, 45)(7, 47)(8, 48)(9, 54)(10, 49)(11, 55)(12, 56)(13, 58)(14, 51)(15, 62)(16, 53)(17, 64)(18, 57)(19, 59)(20, 60)(21, 66)(22, 61)(23, 67)(24, 68)(25, 70)(26, 63)(27, 74)(28, 65)(29, 76)(30, 69)(31, 71)(32, 72)(33, 78)(34, 73)(35, 79)(36, 80)(37, 82)(38, 75)(39, 84)(40, 77)(41, 81)(42, 83) local type(s) :: { ( 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14, 3, 14 ) } Outer automorphisms :: reflexible Dual of E12.646 Transitivity :: ET+ VT+ AT Graph:: v = 3 e = 42 f = 17 degree seq :: [ 28^3 ] E12.648 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 14, 14}) 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, Y1^3, (R * Y3)^2, (R * Y1)^2, Y3 * Y2 * Y1^-1 * Y2^-1, Y2 * Y3 * Y2^-1 * Y1^-1, (R * Y2 * Y3^-1)^2, Y2^14, (Y2^-1 * Y1)^14 ] Map:: R = (1, 43, 2, 44, 4, 46)(3, 45, 8, 50, 6, 48)(5, 47, 10, 52, 7, 49)(9, 51, 12, 54, 14, 56)(11, 53, 13, 55, 16, 58)(15, 57, 20, 62, 18, 60)(17, 59, 22, 64, 19, 61)(21, 63, 24, 66, 26, 68)(23, 65, 25, 67, 28, 70)(27, 69, 32, 74, 30, 72)(29, 71, 34, 76, 31, 73)(33, 75, 36, 78, 38, 80)(35, 77, 37, 79, 40, 82)(39, 81, 42, 84, 41, 83)(85, 127, 87, 129, 93, 135, 99, 141, 105, 147, 111, 153, 117, 159, 123, 165, 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, 92, 134, 98, 140, 104, 146, 110, 152, 116, 158, 122, 164, 126, 168, 124, 166, 118, 160, 112, 154, 106, 148, 100, 142, 94, 136) L = (1, 88)(2, 85)(3, 90)(4, 86)(5, 91)(6, 92)(7, 94)(8, 87)(9, 98)(10, 89)(11, 100)(12, 93)(13, 95)(14, 96)(15, 102)(16, 97)(17, 103)(18, 104)(19, 106)(20, 99)(21, 110)(22, 101)(23, 112)(24, 105)(25, 107)(26, 108)(27, 114)(28, 109)(29, 115)(30, 116)(31, 118)(32, 111)(33, 122)(34, 113)(35, 124)(36, 117)(37, 119)(38, 120)(39, 125)(40, 121)(41, 126)(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) :: { ( 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 E12.649 Graph:: bipartite v = 17 e = 84 f = 45 degree seq :: [ 6^14, 28^3 ] E12.649 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 14, 14}) Quotient :: dipole Aut^+ = C7 x S3 (small group id <42, 3>) Aut = S3 x D14 (small group id <84, 8>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, Y3 * Y1 * Y3 * Y1^-1, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^3, Y1^14 ] Map:: R = (1, 43, 2, 44, 6, 48, 12, 54, 18, 60, 24, 66, 30, 72, 36, 78, 35, 77, 29, 71, 23, 65, 17, 59, 11, 53, 4, 46)(3, 45, 8, 50, 13, 55, 20, 62, 25, 67, 32, 74, 37, 79, 42, 84, 39, 81, 33, 75, 27, 69, 21, 63, 15, 57, 9, 51)(5, 47, 7, 49, 14, 56, 19, 61, 26, 68, 31, 73, 38, 80, 41, 83, 40, 82, 34, 76, 28, 70, 22, 64, 16, 58, 10, 52)(85, 127)(86, 128)(87, 129)(88, 130)(89, 131)(90, 132)(91, 133)(92, 134)(93, 135)(94, 136)(95, 137)(96, 138)(97, 139)(98, 140)(99, 141)(100, 142)(101, 143)(102, 144)(103, 145)(104, 146)(105, 147)(106, 148)(107, 149)(108, 150)(109, 151)(110, 152)(111, 153)(112, 154)(113, 155)(114, 156)(115, 157)(116, 158)(117, 159)(118, 160)(119, 161)(120, 162)(121, 163)(122, 164)(123, 165)(124, 166)(125, 167)(126, 168) L = (1, 87)(2, 91)(3, 89)(4, 94)(5, 85)(6, 97)(7, 92)(8, 86)(9, 88)(10, 93)(11, 99)(12, 103)(13, 98)(14, 90)(15, 100)(16, 95)(17, 106)(18, 109)(19, 104)(20, 96)(21, 101)(22, 105)(23, 111)(24, 115)(25, 110)(26, 102)(27, 112)(28, 107)(29, 118)(30, 121)(31, 116)(32, 108)(33, 113)(34, 117)(35, 123)(36, 125)(37, 122)(38, 114)(39, 124)(40, 119)(41, 126)(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) :: { ( 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 E12.648 Graph:: simple bipartite v = 45 e = 84 f = 17 degree seq :: [ 2^42, 28^3 ] E12.650 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 6, 8}) Quotient :: edge Aut^+ = (C3 : C8) : C2 (small group id <48, 16>) Aut = (D8 x S3) : C2 (small group id <96, 118>) |r| :: 2 Presentation :: [ F^2, T1^4, T1^4, (F * T2)^2, (F * T1)^2, T1^-1 * T2 * T1^2 * T2^-1 * T1^-1, T2^6, T1^-1 * T2^-2 * T1 * T2^-2, T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 3, 10, 27, 16, 5)(2, 7, 20, 38, 24, 8)(4, 12, 31, 45, 28, 13)(6, 17, 34, 46, 35, 18)(9, 25, 14, 32, 43, 26)(11, 29, 15, 33, 44, 30)(19, 36, 22, 41, 47, 37)(21, 39, 23, 42, 48, 40)(49, 50, 54, 52)(51, 57, 65, 59)(53, 62, 66, 63)(55, 67, 60, 69)(56, 70, 61, 71)(58, 72, 82, 76)(64, 68, 83, 79)(73, 87, 77, 84)(74, 90, 78, 89)(75, 91, 94, 92)(80, 88, 81, 85)(86, 95, 93, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 16^4 ), ( 16^6 ) } Outer automorphisms :: reflexible Dual of E12.654 Transitivity :: ET+ Graph:: simple bipartite v = 20 e = 48 f = 6 degree seq :: [ 4^12, 6^8 ] E12.651 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 6, 8}) Quotient :: edge Aut^+ = (C3 : C8) : C2 (small group id <48, 16>) Aut = (D8 x S3) : C2 (small group id <96, 118>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1 * T2 * T1^2 * T2^-1 * T1, T2^3 * T1^-1 * T2^-1 * T1^-1, T2^-2 * T1^-1 * T2 * T1^-1 * T2^-1, T2^2 * T1 * T2^2 * T1^-1, T1^6, T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1 ] Map:: non-degenerate R = (1, 3, 10, 21, 41, 24, 17, 5)(2, 7, 22, 11, 31, 16, 26, 8)(4, 12, 29, 9, 28, 15, 30, 14)(6, 19, 37, 23, 42, 25, 40, 20)(13, 27, 43, 32, 44, 34, 45, 33)(18, 35, 46, 38, 48, 39, 47, 36)(49, 50, 54, 66, 61, 52)(51, 57, 75, 86, 67, 59)(53, 63, 81, 87, 68, 64)(55, 69, 60, 80, 83, 71)(56, 72, 62, 82, 84, 73)(58, 74, 85, 95, 91, 78)(65, 70, 88, 94, 93, 77)(76, 89, 79, 90, 96, 92) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8^6 ), ( 8^8 ) } Outer automorphisms :: reflexible Dual of E12.655 Transitivity :: ET+ Graph:: simple bipartite v = 14 e = 48 f = 12 degree seq :: [ 6^8, 8^6 ] E12.652 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 6, 8}) Quotient :: edge Aut^+ = (C3 : C8) : C2 (small group id <48, 16>) Aut = (D8 x S3) : C2 (small group id <96, 118>) |r| :: 2 Presentation :: [ F^2, T2^4, (F * T1)^2, (F * T2)^2, T2^4, T2^-2 * T1^-4, T2^-1 * T1^-2 * T2 * T1^-2, (T2^-1 * T1)^6 ] Map:: polytopal non-degenerate R = (1, 3, 10, 5)(2, 7, 21, 8)(4, 12, 17, 14)(6, 18, 13, 19)(9, 25, 15, 26)(11, 27, 16, 28)(20, 29, 23, 30)(22, 31, 24, 32)(33, 41, 35, 42)(34, 43, 36, 44)(37, 45, 39, 46)(38, 47, 40, 48)(49, 50, 54, 65, 58, 69, 61, 52)(51, 57, 67, 64, 53, 63, 66, 59)(55, 68, 60, 72, 56, 71, 62, 70)(73, 81, 75, 84, 74, 83, 76, 82)(77, 85, 79, 88, 78, 87, 80, 86)(89, 96, 91, 93, 90, 95, 92, 94) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 12^4 ), ( 12^8 ) } Outer automorphisms :: reflexible Dual of E12.653 Transitivity :: ET+ Graph:: bipartite v = 18 e = 48 f = 8 degree seq :: [ 4^12, 8^6 ] E12.653 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 6, 8}) Quotient :: loop Aut^+ = (C3 : C8) : C2 (small group id <48, 16>) Aut = (D8 x S3) : C2 (small group id <96, 118>) |r| :: 2 Presentation :: [ F^2, T1^4, T1^4, (F * T2)^2, (F * T1)^2, T1^-1 * T2 * T1^2 * T2^-1 * T1^-1, T2^6, T1^-1 * T2^-2 * T1 * T2^-2, T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 49, 3, 51, 10, 58, 27, 75, 16, 64, 5, 53)(2, 50, 7, 55, 20, 68, 38, 86, 24, 72, 8, 56)(4, 52, 12, 60, 31, 79, 45, 93, 28, 76, 13, 61)(6, 54, 17, 65, 34, 82, 46, 94, 35, 83, 18, 66)(9, 57, 25, 73, 14, 62, 32, 80, 43, 91, 26, 74)(11, 59, 29, 77, 15, 63, 33, 81, 44, 92, 30, 78)(19, 67, 36, 84, 22, 70, 41, 89, 47, 95, 37, 85)(21, 69, 39, 87, 23, 71, 42, 90, 48, 96, 40, 88) L = (1, 50)(2, 54)(3, 57)(4, 49)(5, 62)(6, 52)(7, 67)(8, 70)(9, 65)(10, 72)(11, 51)(12, 69)(13, 71)(14, 66)(15, 53)(16, 68)(17, 59)(18, 63)(19, 60)(20, 83)(21, 55)(22, 61)(23, 56)(24, 82)(25, 87)(26, 90)(27, 91)(28, 58)(29, 84)(30, 89)(31, 64)(32, 88)(33, 85)(34, 76)(35, 79)(36, 73)(37, 80)(38, 95)(39, 77)(40, 81)(41, 74)(42, 78)(43, 94)(44, 75)(45, 96)(46, 92)(47, 93)(48, 86) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E12.652 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 8 e = 48 f = 18 degree seq :: [ 12^8 ] E12.654 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 6, 8}) Quotient :: loop Aut^+ = (C3 : C8) : C2 (small group id <48, 16>) Aut = (D8 x S3) : C2 (small group id <96, 118>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1 * T2 * T1^2 * T2^-1 * T1, T2^3 * T1^-1 * T2^-1 * T1^-1, T2^-2 * T1^-1 * T2 * T1^-1 * T2^-1, T2^2 * T1 * T2^2 * T1^-1, T1^6, T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1 ] Map:: non-degenerate R = (1, 49, 3, 51, 10, 58, 21, 69, 41, 89, 24, 72, 17, 65, 5, 53)(2, 50, 7, 55, 22, 70, 11, 59, 31, 79, 16, 64, 26, 74, 8, 56)(4, 52, 12, 60, 29, 77, 9, 57, 28, 76, 15, 63, 30, 78, 14, 62)(6, 54, 19, 67, 37, 85, 23, 71, 42, 90, 25, 73, 40, 88, 20, 68)(13, 61, 27, 75, 43, 91, 32, 80, 44, 92, 34, 82, 45, 93, 33, 81)(18, 66, 35, 83, 46, 94, 38, 86, 48, 96, 39, 87, 47, 95, 36, 84) L = (1, 50)(2, 54)(3, 57)(4, 49)(5, 63)(6, 66)(7, 69)(8, 72)(9, 75)(10, 74)(11, 51)(12, 80)(13, 52)(14, 82)(15, 81)(16, 53)(17, 70)(18, 61)(19, 59)(20, 64)(21, 60)(22, 88)(23, 55)(24, 62)(25, 56)(26, 85)(27, 86)(28, 89)(29, 65)(30, 58)(31, 90)(32, 83)(33, 87)(34, 84)(35, 71)(36, 73)(37, 95)(38, 67)(39, 68)(40, 94)(41, 79)(42, 96)(43, 78)(44, 76)(45, 77)(46, 93)(47, 91)(48, 92) local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E12.650 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 6 e = 48 f = 20 degree seq :: [ 16^6 ] E12.655 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 6, 8}) Quotient :: loop Aut^+ = (C3 : C8) : C2 (small group id <48, 16>) Aut = (D8 x S3) : C2 (small group id <96, 118>) |r| :: 2 Presentation :: [ F^2, T2^4, (F * T1)^2, (F * T2)^2, T2^4, T2^-2 * T1^-4, T2^-1 * T1^-2 * T2 * T1^-2, (T2^-1 * T1)^6 ] Map:: non-degenerate R = (1, 49, 3, 51, 10, 58, 5, 53)(2, 50, 7, 55, 21, 69, 8, 56)(4, 52, 12, 60, 17, 65, 14, 62)(6, 54, 18, 66, 13, 61, 19, 67)(9, 57, 25, 73, 15, 63, 26, 74)(11, 59, 27, 75, 16, 64, 28, 76)(20, 68, 29, 77, 23, 71, 30, 78)(22, 70, 31, 79, 24, 72, 32, 80)(33, 81, 41, 89, 35, 83, 42, 90)(34, 82, 43, 91, 36, 84, 44, 92)(37, 85, 45, 93, 39, 87, 46, 94)(38, 86, 47, 95, 40, 88, 48, 96) L = (1, 50)(2, 54)(3, 57)(4, 49)(5, 63)(6, 65)(7, 68)(8, 71)(9, 67)(10, 69)(11, 51)(12, 72)(13, 52)(14, 70)(15, 66)(16, 53)(17, 58)(18, 59)(19, 64)(20, 60)(21, 61)(22, 55)(23, 62)(24, 56)(25, 81)(26, 83)(27, 84)(28, 82)(29, 85)(30, 87)(31, 88)(32, 86)(33, 75)(34, 73)(35, 76)(36, 74)(37, 79)(38, 77)(39, 80)(40, 78)(41, 96)(42, 95)(43, 93)(44, 94)(45, 90)(46, 89)(47, 92)(48, 91) local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E12.651 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 12 e = 48 f = 14 degree seq :: [ 8^12 ] E12.656 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 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^-1 * Y1^-1, Y3^-1 * Y1^2 * Y3^-1, Y3^4, Y1 * Y3^-2 * Y1, (R * Y3)^2, (R * Y1)^2, Y3 * Y2^-1 * Y1 * Y3^-1 * Y2 * Y1^-1, Y2 * Y3^2 * Y2^-1 * Y1^-2, (R * Y2 * Y3^-1)^2, Y2^-1 * R * Y2^2 * R * Y2^-1, Y2^2 * Y1 * Y2^2 * Y1^-1, Y3 * Y2^-2 * Y3^-1 * Y2^-2, Y2^6, Y2 * Y1 * Y2 * Y1 * Y2 * Y3^-1 * Y2 * Y1^-1, (Y3 * Y2)^8 ] Map:: 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, 24, 72, 34, 82, 28, 76)(16, 64, 20, 68, 35, 83, 31, 79)(25, 73, 39, 87, 29, 77, 36, 84)(26, 74, 42, 90, 30, 78, 41, 89)(27, 75, 43, 91, 46, 94, 44, 92)(32, 80, 40, 88, 33, 81, 37, 85)(38, 86, 47, 95, 45, 93, 48, 96)(97, 145, 99, 147, 106, 154, 123, 171, 112, 160, 101, 149)(98, 146, 103, 151, 116, 164, 134, 182, 120, 168, 104, 152)(100, 148, 108, 156, 127, 175, 141, 189, 124, 172, 109, 157)(102, 150, 113, 161, 130, 178, 142, 190, 131, 179, 114, 162)(105, 153, 121, 169, 110, 158, 128, 176, 139, 187, 122, 170)(107, 155, 125, 173, 111, 159, 129, 177, 140, 188, 126, 174)(115, 163, 132, 180, 118, 166, 137, 185, 143, 191, 133, 181)(117, 165, 135, 183, 119, 167, 138, 186, 144, 192, 136, 184) L = (1, 100)(2, 97)(3, 107)(4, 102)(5, 111)(6, 98)(7, 117)(8, 119)(9, 99)(10, 124)(11, 113)(12, 115)(13, 118)(14, 101)(15, 114)(16, 127)(17, 105)(18, 110)(19, 103)(20, 112)(21, 108)(22, 104)(23, 109)(24, 106)(25, 132)(26, 137)(27, 140)(28, 130)(29, 135)(30, 138)(31, 131)(32, 133)(33, 136)(34, 120)(35, 116)(36, 125)(37, 129)(38, 144)(39, 121)(40, 128)(41, 126)(42, 122)(43, 123)(44, 142)(45, 143)(46, 139)(47, 134)(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) :: { ( 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 E12.659 Graph:: bipartite v = 20 e = 96 f = 54 degree seq :: [ 8^12, 12^8 ] E12.657 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 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 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y1 * Y2 * Y1^2 * Y2^-1 * Y1, Y2^-2 * Y1 * Y2^-2 * Y1^-1, Y1^-1 * Y2 * Y1^-1 * Y2^-3, Y1^6, Y2^3 * Y1^-1 * Y2^-1 * Y1^-1, (Y3^-1 * Y1^-1)^4 ] Map:: R = (1, 49, 2, 50, 6, 54, 18, 66, 13, 61, 4, 52)(3, 51, 9, 57, 27, 75, 38, 86, 19, 67, 11, 59)(5, 53, 15, 63, 33, 81, 39, 87, 20, 68, 16, 64)(7, 55, 21, 69, 12, 60, 32, 80, 35, 83, 23, 71)(8, 56, 24, 72, 14, 62, 34, 82, 36, 84, 25, 73)(10, 58, 26, 74, 37, 85, 47, 95, 43, 91, 30, 78)(17, 65, 22, 70, 40, 88, 46, 94, 45, 93, 29, 77)(28, 76, 41, 89, 31, 79, 42, 90, 48, 96, 44, 92)(97, 145, 99, 147, 106, 154, 117, 165, 137, 185, 120, 168, 113, 161, 101, 149)(98, 146, 103, 151, 118, 166, 107, 155, 127, 175, 112, 160, 122, 170, 104, 152)(100, 148, 108, 156, 125, 173, 105, 153, 124, 172, 111, 159, 126, 174, 110, 158)(102, 150, 115, 163, 133, 181, 119, 167, 138, 186, 121, 169, 136, 184, 116, 164)(109, 157, 123, 171, 139, 187, 128, 176, 140, 188, 130, 178, 141, 189, 129, 177)(114, 162, 131, 179, 142, 190, 134, 182, 144, 192, 135, 183, 143, 191, 132, 180) L = (1, 99)(2, 103)(3, 106)(4, 108)(5, 97)(6, 115)(7, 118)(8, 98)(9, 124)(10, 117)(11, 127)(12, 125)(13, 123)(14, 100)(15, 126)(16, 122)(17, 101)(18, 131)(19, 133)(20, 102)(21, 137)(22, 107)(23, 138)(24, 113)(25, 136)(26, 104)(27, 139)(28, 111)(29, 105)(30, 110)(31, 112)(32, 140)(33, 109)(34, 141)(35, 142)(36, 114)(37, 119)(38, 144)(39, 143)(40, 116)(41, 120)(42, 121)(43, 128)(44, 130)(45, 129)(46, 134)(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) :: { ( 2, 8, 2, 8, 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 E12.658 Graph:: bipartite v = 14 e = 96 f = 60 degree seq :: [ 12^8, 16^6 ] E12.658 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 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 :: [ Y1, R^2, Y2^4, (R * Y3)^2, (R * Y1)^2, Y2^4, (R * Y2 * Y3^-1)^2, Y3^4 * Y2^2, Y3^2 * Y2 * Y3^2 * Y2^-1, Y3^-2 * Y2^-1 * Y3^2 * Y2^-1, (Y3^-1 * Y2^-1)^6, (Y3^-1 * Y1^-1)^8 ] Map:: R = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96)(97, 145, 98, 146, 102, 150, 100, 148)(99, 147, 105, 153, 113, 161, 107, 155)(101, 149, 110, 158, 114, 162, 111, 159)(103, 151, 115, 163, 108, 156, 117, 165)(104, 152, 118, 166, 109, 157, 119, 167)(106, 154, 120, 168, 112, 160, 116, 164)(121, 169, 129, 177, 123, 171, 130, 178)(122, 170, 131, 179, 124, 172, 132, 180)(125, 173, 133, 181, 127, 175, 134, 182)(126, 174, 135, 183, 128, 176, 136, 184)(137, 185, 144, 192, 139, 187, 142, 190)(138, 186, 143, 191, 140, 188, 141, 189) L = (1, 99)(2, 103)(3, 106)(4, 108)(5, 97)(6, 113)(7, 116)(8, 98)(9, 121)(10, 114)(11, 123)(12, 120)(13, 100)(14, 124)(15, 122)(16, 101)(17, 112)(18, 102)(19, 125)(20, 109)(21, 127)(22, 128)(23, 126)(24, 104)(25, 110)(26, 105)(27, 111)(28, 107)(29, 118)(30, 115)(31, 119)(32, 117)(33, 137)(34, 139)(35, 140)(36, 138)(37, 141)(38, 143)(39, 144)(40, 142)(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) :: { ( 12, 16 ), ( 12, 16, 12, 16, 12, 16, 12, 16 ) } Outer automorphisms :: reflexible Dual of E12.657 Graph:: simple bipartite v = 60 e = 96 f = 14 degree seq :: [ 2^48, 8^12 ] E12.659 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 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 :: [ Y2, R^2, Y3^4, (R * Y1)^2, (R * Y3)^2, Y3^4, (R * Y2 * Y3^-1)^2, Y3^-1 * Y1^-2 * Y3 * Y1^-2, Y1^-2 * Y3^-2 * Y1^-2, Y3 * Y1^2 * Y3 * Y1^-2, (Y3 * Y2^-1)^4, (Y3^-1 * Y1)^6 ] Map:: R = (1, 49, 2, 50, 6, 54, 17, 65, 10, 58, 21, 69, 13, 61, 4, 52)(3, 51, 9, 57, 19, 67, 16, 64, 5, 53, 15, 63, 18, 66, 11, 59)(7, 55, 20, 68, 12, 60, 24, 72, 8, 56, 23, 71, 14, 62, 22, 70)(25, 73, 33, 81, 27, 75, 36, 84, 26, 74, 35, 83, 28, 76, 34, 82)(29, 77, 37, 85, 31, 79, 40, 88, 30, 78, 39, 87, 32, 80, 38, 86)(41, 89, 48, 96, 43, 91, 45, 93, 42, 90, 47, 95, 44, 92, 46, 94)(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, 161)(114, 162)(115, 163)(116, 164)(117, 165)(118, 166)(119, 167)(120, 168)(121, 169)(122, 170)(123, 171)(124, 172)(125, 173)(126, 174)(127, 175)(128, 176)(129, 177)(130, 178)(131, 179)(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, 99)(2, 103)(3, 106)(4, 108)(5, 97)(6, 114)(7, 117)(8, 98)(9, 121)(10, 101)(11, 123)(12, 113)(13, 115)(14, 100)(15, 122)(16, 124)(17, 110)(18, 109)(19, 102)(20, 125)(21, 104)(22, 127)(23, 126)(24, 128)(25, 111)(26, 105)(27, 112)(28, 107)(29, 119)(30, 116)(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) :: { ( 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E12.656 Graph:: simple bipartite v = 54 e = 96 f = 20 degree seq :: [ 2^48, 16^6 ] E12.660 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 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, Y1 * Y3, Y3 * Y1, (Y3^-1, Y1^-1), (Y3 * Y1^-1)^2, Y1^-2 * Y3 * Y1^-1, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y3 * Y1^-1 * Y2^-3, (R * Y2 * Y3^-1)^2, Y2^-1 * Y3 * Y1^-1 * Y2 * Y1^2, Y2^2 * Y1 * Y2^2 * Y1^-1, (Y3 * Y2^-1)^6 ] Map:: 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, 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, 48, 96, 43, 91, 46, 94)(42, 90, 47, 95, 44, 92, 45, 93)(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, 110, 158, 124, 172, 107, 155, 123, 171, 111, 159, 122, 170)(115, 163, 125, 173, 118, 166, 128, 176, 117, 165, 127, 175, 119, 167, 126, 174)(129, 177, 137, 185, 131, 179, 140, 188, 130, 178, 139, 187, 132, 180, 138, 186)(133, 181, 141, 189, 135, 183, 144, 192, 134, 182, 143, 191, 136, 184, 142, 190) L = (1, 100)(2, 97)(3, 107)(4, 102)(5, 111)(6, 98)(7, 117)(8, 119)(9, 99)(10, 116)(11, 113)(12, 115)(13, 118)(14, 101)(15, 114)(16, 120)(17, 105)(18, 110)(19, 103)(20, 112)(21, 108)(22, 104)(23, 109)(24, 106)(25, 130)(26, 132)(27, 129)(28, 131)(29, 134)(30, 136)(31, 133)(32, 135)(33, 121)(34, 123)(35, 122)(36, 124)(37, 125)(38, 127)(39, 126)(40, 128)(41, 142)(42, 141)(43, 144)(44, 143)(45, 140)(46, 139)(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) :: { ( 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 E12.661 Graph:: bipartite v = 18 e = 96 f = 56 degree seq :: [ 8^12, 16^6 ] E12.661 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 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 :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y3 * Y1 * Y3^-3 * Y1, Y3^2 * Y1 * Y3^-1 * Y1 * Y3, Y1^6, Y3 * Y1^-2 * Y3^-1 * Y1^-2, (Y3^-1 * Y1)^4, (Y3 * Y2^-1)^8 ] Map:: polytopal R = (1, 49, 2, 50, 6, 54, 18, 66, 13, 61, 4, 52)(3, 51, 9, 57, 27, 75, 38, 86, 19, 67, 11, 59)(5, 53, 15, 63, 33, 81, 39, 87, 20, 68, 16, 64)(7, 55, 21, 69, 12, 60, 32, 80, 35, 83, 23, 71)(8, 56, 24, 72, 14, 62, 34, 82, 36, 84, 25, 73)(10, 58, 26, 74, 37, 85, 47, 95, 43, 91, 30, 78)(17, 65, 22, 70, 40, 88, 46, 94, 45, 93, 29, 77)(28, 76, 41, 89, 31, 79, 42, 90, 48, 96, 44, 92)(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, 161)(114, 162)(115, 163)(116, 164)(117, 165)(118, 166)(119, 167)(120, 168)(121, 169)(122, 170)(123, 171)(124, 172)(125, 173)(126, 174)(127, 175)(128, 176)(129, 177)(130, 178)(131, 179)(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, 99)(2, 103)(3, 106)(4, 108)(5, 97)(6, 115)(7, 118)(8, 98)(9, 124)(10, 117)(11, 127)(12, 125)(13, 123)(14, 100)(15, 126)(16, 122)(17, 101)(18, 131)(19, 133)(20, 102)(21, 137)(22, 107)(23, 138)(24, 113)(25, 136)(26, 104)(27, 139)(28, 111)(29, 105)(30, 110)(31, 112)(32, 140)(33, 109)(34, 141)(35, 142)(36, 114)(37, 119)(38, 144)(39, 143)(40, 116)(41, 120)(42, 121)(43, 128)(44, 130)(45, 129)(46, 134)(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) :: { ( 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E12.660 Graph:: simple bipartite v = 56 e = 96 f = 18 degree seq :: [ 2^48, 12^8 ] E12.662 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 6, 8}) Quotient :: edge 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 :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T1^-1 * T2^-3 * T1^-1, T2^-1 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, T2 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1^-1 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 3, 10, 6, 16, 5)(2, 7, 13, 4, 12, 8)(9, 21, 24, 11, 23, 22)(14, 25, 28, 15, 27, 26)(17, 29, 32, 18, 31, 30)(19, 33, 36, 20, 35, 34)(37, 45, 40, 38, 46, 39)(41, 47, 44, 42, 48, 43)(49, 50, 54, 52)(51, 57, 64, 59)(53, 62, 58, 63)(55, 65, 60, 66)(56, 67, 61, 68)(69, 84, 71, 82)(70, 85, 72, 86)(73, 87, 75, 88)(74, 79, 76, 77)(78, 89, 80, 90)(81, 91, 83, 92)(93, 96, 94, 95) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 16^4 ), ( 16^6 ) } Outer automorphisms :: reflexible Dual of E12.666 Transitivity :: ET+ Graph:: bipartite v = 20 e = 48 f = 6 degree seq :: [ 4^12, 6^8 ] E12.663 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 6, 8}) Quotient :: edge 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 :: [ F^2, (F * T1)^2, (F * T2)^2, T1 * T2^-1 * T1^-1 * T2^-1 * T1, T2 * T1^-1 * T2^-1 * T1^-1 * T2^2, T2 * T1 * T2^-3 * T1, T1^-1 * T2^3 * T1^-1 * T2^-1, T1^6 ] Map:: non-degenerate R = (1, 3, 10, 20, 18, 32, 17, 5)(2, 7, 21, 31, 13, 16, 23, 8)(4, 12, 25, 9, 6, 19, 33, 14)(11, 28, 42, 26, 24, 41, 45, 29)(15, 27, 43, 37, 35, 36, 46, 34)(22, 38, 47, 44, 30, 40, 48, 39)(49, 50, 54, 66, 61, 52)(51, 57, 72, 80, 62, 59)(53, 63, 55, 68, 83, 64)(56, 70, 67, 79, 78, 60)(58, 74, 84, 65, 77, 75)(69, 85, 88, 71, 82, 86)(73, 87, 89, 81, 92, 76)(90, 96, 94, 93, 95, 91) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8^6 ), ( 8^8 ) } Outer automorphisms :: reflexible Dual of E12.667 Transitivity :: ET+ Graph:: bipartite v = 14 e = 48 f = 12 degree seq :: [ 6^8, 8^6 ] E12.664 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 6, 8}) Quotient :: edge 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 :: [ F^2, (F * T1)^2, T2^4, (F * T2)^2, T1^-1 * T2^-2 * T1^-3, T2^2 * T1 * T2^2 * T1^-1, T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, T2^-1 * T1^-2 * T2 * T1^2 * T2 * T1^-2 * T2^-1 * T1^-2 ] Map:: non-degenerate R = (1, 3, 10, 5)(2, 7, 21, 8)(4, 12, 17, 14)(6, 18, 13, 19)(9, 26, 15, 27)(11, 23, 16, 20)(22, 33, 24, 31)(25, 37, 28, 38)(29, 34, 30, 32)(35, 43, 36, 44)(39, 46, 40, 45)(41, 47, 42, 48)(49, 50, 54, 65, 58, 69, 61, 52)(51, 57, 73, 64, 53, 63, 76, 59)(55, 68, 83, 72, 56, 71, 84, 70)(60, 77, 88, 75, 62, 78, 87, 74)(66, 79, 89, 82, 67, 81, 90, 80)(85, 93, 96, 92, 86, 94, 95, 91) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 12^4 ), ( 12^8 ) } Outer automorphisms :: reflexible Dual of E12.665 Transitivity :: ET+ Graph:: bipartite v = 18 e = 48 f = 8 degree seq :: [ 4^12, 8^6 ] E12.665 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 6, 8}) Quotient :: loop 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 :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T1^-1 * T2^-3 * T1^-1, T2^-1 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, T2 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1^-1 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 49, 3, 51, 10, 58, 6, 54, 16, 64, 5, 53)(2, 50, 7, 55, 13, 61, 4, 52, 12, 60, 8, 56)(9, 57, 21, 69, 24, 72, 11, 59, 23, 71, 22, 70)(14, 62, 25, 73, 28, 76, 15, 63, 27, 75, 26, 74)(17, 65, 29, 77, 32, 80, 18, 66, 31, 79, 30, 78)(19, 67, 33, 81, 36, 84, 20, 68, 35, 83, 34, 82)(37, 85, 45, 93, 40, 88, 38, 86, 46, 94, 39, 87)(41, 89, 47, 95, 44, 92, 42, 90, 48, 96, 43, 91) L = (1, 50)(2, 54)(3, 57)(4, 49)(5, 62)(6, 52)(7, 65)(8, 67)(9, 64)(10, 63)(11, 51)(12, 66)(13, 68)(14, 58)(15, 53)(16, 59)(17, 60)(18, 55)(19, 61)(20, 56)(21, 84)(22, 85)(23, 82)(24, 86)(25, 87)(26, 79)(27, 88)(28, 77)(29, 74)(30, 89)(31, 76)(32, 90)(33, 91)(34, 69)(35, 92)(36, 71)(37, 72)(38, 70)(39, 75)(40, 73)(41, 80)(42, 78)(43, 83)(44, 81)(45, 96)(46, 95)(47, 93)(48, 94) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E12.664 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 8 e = 48 f = 18 degree seq :: [ 12^8 ] E12.666 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 6, 8}) Quotient :: loop 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 :: [ F^2, (F * T1)^2, (F * T2)^2, T1 * T2^-1 * T1^-1 * T2^-1 * T1, T2 * T1^-1 * T2^-1 * T1^-1 * T2^2, T2 * T1 * T2^-3 * T1, T1^-1 * T2^3 * T1^-1 * T2^-1, T1^6 ] Map:: non-degenerate R = (1, 49, 3, 51, 10, 58, 20, 68, 18, 66, 32, 80, 17, 65, 5, 53)(2, 50, 7, 55, 21, 69, 31, 79, 13, 61, 16, 64, 23, 71, 8, 56)(4, 52, 12, 60, 25, 73, 9, 57, 6, 54, 19, 67, 33, 81, 14, 62)(11, 59, 28, 76, 42, 90, 26, 74, 24, 72, 41, 89, 45, 93, 29, 77)(15, 63, 27, 75, 43, 91, 37, 85, 35, 83, 36, 84, 46, 94, 34, 82)(22, 70, 38, 86, 47, 95, 44, 92, 30, 78, 40, 88, 48, 96, 39, 87) L = (1, 50)(2, 54)(3, 57)(4, 49)(5, 63)(6, 66)(7, 68)(8, 70)(9, 72)(10, 74)(11, 51)(12, 56)(13, 52)(14, 59)(15, 55)(16, 53)(17, 77)(18, 61)(19, 79)(20, 83)(21, 85)(22, 67)(23, 82)(24, 80)(25, 87)(26, 84)(27, 58)(28, 73)(29, 75)(30, 60)(31, 78)(32, 62)(33, 92)(34, 86)(35, 64)(36, 65)(37, 88)(38, 69)(39, 89)(40, 71)(41, 81)(42, 96)(43, 90)(44, 76)(45, 95)(46, 93)(47, 91)(48, 94) local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E12.662 Transitivity :: ET+ VT+ AT Graph:: v = 6 e = 48 f = 20 degree seq :: [ 16^6 ] E12.667 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 6, 8}) Quotient :: loop 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 :: [ F^2, (F * T1)^2, T2^4, (F * T2)^2, T1^-1 * T2^-2 * T1^-3, T2^2 * T1 * T2^2 * T1^-1, T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, T2^-1 * T1^-2 * T2 * T1^2 * T2 * T1^-2 * T2^-1 * T1^-2 ] Map:: non-degenerate R = (1, 49, 3, 51, 10, 58, 5, 53)(2, 50, 7, 55, 21, 69, 8, 56)(4, 52, 12, 60, 17, 65, 14, 62)(6, 54, 18, 66, 13, 61, 19, 67)(9, 57, 26, 74, 15, 63, 27, 75)(11, 59, 23, 71, 16, 64, 20, 68)(22, 70, 33, 81, 24, 72, 31, 79)(25, 73, 37, 85, 28, 76, 38, 86)(29, 77, 34, 82, 30, 78, 32, 80)(35, 83, 43, 91, 36, 84, 44, 92)(39, 87, 46, 94, 40, 88, 45, 93)(41, 89, 47, 95, 42, 90, 48, 96) L = (1, 50)(2, 54)(3, 57)(4, 49)(5, 63)(6, 65)(7, 68)(8, 71)(9, 73)(10, 69)(11, 51)(12, 77)(13, 52)(14, 78)(15, 76)(16, 53)(17, 58)(18, 79)(19, 81)(20, 83)(21, 61)(22, 55)(23, 84)(24, 56)(25, 64)(26, 60)(27, 62)(28, 59)(29, 88)(30, 87)(31, 89)(32, 66)(33, 90)(34, 67)(35, 72)(36, 70)(37, 93)(38, 94)(39, 74)(40, 75)(41, 82)(42, 80)(43, 85)(44, 86)(45, 96)(46, 95)(47, 91)(48, 92) local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E12.663 Transitivity :: ET+ VT+ AT Graph:: v = 12 e = 48 f = 14 degree seq :: [ 8^12 ] E12.668 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 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 * Y3, Y1^4, (R * Y3)^2, (R * Y1)^2, (Y1^-1 * Y3)^2, Y2^-2 * Y1^-1 * Y3 * Y2^-1, (R * Y2 * Y3^-1)^2, Y1 * Y2^-1 * Y1 * Y3^-1 * Y2 * Y1^-2 * Y3, Y2 * Y1 * Y2 * Y1 * Y2 * Y3^-1 * Y2 * Y1^-1, Y2^-1 * Y1 * Y2 * R * Y2^2 * Y3 * Y2^-1 * R * Y2^-1, Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y3^-1 * Y2 * Y1^-1 * Y2^-1 * Y1^-1, (Y3 * Y2^-1)^8 ] Map:: R = (1, 49, 2, 50, 6, 54, 4, 52)(3, 51, 9, 57, 16, 64, 11, 59)(5, 53, 14, 62, 10, 58, 15, 63)(7, 55, 17, 65, 12, 60, 18, 66)(8, 56, 19, 67, 13, 61, 20, 68)(21, 69, 36, 84, 23, 71, 34, 82)(22, 70, 37, 85, 24, 72, 38, 86)(25, 73, 39, 87, 27, 75, 40, 88)(26, 74, 31, 79, 28, 76, 29, 77)(30, 78, 41, 89, 32, 80, 42, 90)(33, 81, 43, 91, 35, 83, 44, 92)(45, 93, 48, 96, 46, 94, 47, 95)(97, 145, 99, 147, 106, 154, 102, 150, 112, 160, 101, 149)(98, 146, 103, 151, 109, 157, 100, 148, 108, 156, 104, 152)(105, 153, 117, 165, 120, 168, 107, 155, 119, 167, 118, 166)(110, 158, 121, 169, 124, 172, 111, 159, 123, 171, 122, 170)(113, 161, 125, 173, 128, 176, 114, 162, 127, 175, 126, 174)(115, 163, 129, 177, 132, 180, 116, 164, 131, 179, 130, 178)(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, 97)(3, 107)(4, 102)(5, 111)(6, 98)(7, 114)(8, 116)(9, 99)(10, 110)(11, 112)(12, 113)(13, 115)(14, 101)(15, 106)(16, 105)(17, 103)(18, 108)(19, 104)(20, 109)(21, 130)(22, 134)(23, 132)(24, 133)(25, 136)(26, 125)(27, 135)(28, 127)(29, 124)(30, 138)(31, 122)(32, 137)(33, 140)(34, 119)(35, 139)(36, 117)(37, 118)(38, 120)(39, 121)(40, 123)(41, 126)(42, 128)(43, 129)(44, 131)(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) :: { ( 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 E12.671 Graph:: bipartite v = 20 e = 96 f = 54 degree seq :: [ 8^12, 12^8 ] E12.669 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 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 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1, Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^2, Y2 * Y1 * Y2^-3 * Y1, Y2 * Y1 * Y2^-3 * Y1, Y1^6, (Y3^-1 * Y1^-1)^4 ] Map:: R = (1, 49, 2, 50, 6, 54, 18, 66, 13, 61, 4, 52)(3, 51, 9, 57, 24, 72, 32, 80, 14, 62, 11, 59)(5, 53, 15, 63, 7, 55, 20, 68, 35, 83, 16, 64)(8, 56, 22, 70, 19, 67, 31, 79, 30, 78, 12, 60)(10, 58, 26, 74, 36, 84, 17, 65, 29, 77, 27, 75)(21, 69, 37, 85, 40, 88, 23, 71, 34, 82, 38, 86)(25, 73, 39, 87, 41, 89, 33, 81, 44, 92, 28, 76)(42, 90, 48, 96, 46, 94, 45, 93, 47, 95, 43, 91)(97, 145, 99, 147, 106, 154, 116, 164, 114, 162, 128, 176, 113, 161, 101, 149)(98, 146, 103, 151, 117, 165, 127, 175, 109, 157, 112, 160, 119, 167, 104, 152)(100, 148, 108, 156, 121, 169, 105, 153, 102, 150, 115, 163, 129, 177, 110, 158)(107, 155, 124, 172, 138, 186, 122, 170, 120, 168, 137, 185, 141, 189, 125, 173)(111, 159, 123, 171, 139, 187, 133, 181, 131, 179, 132, 180, 142, 190, 130, 178)(118, 166, 134, 182, 143, 191, 140, 188, 126, 174, 136, 184, 144, 192, 135, 183) L = (1, 99)(2, 103)(3, 106)(4, 108)(5, 97)(6, 115)(7, 117)(8, 98)(9, 102)(10, 116)(11, 124)(12, 121)(13, 112)(14, 100)(15, 123)(16, 119)(17, 101)(18, 128)(19, 129)(20, 114)(21, 127)(22, 134)(23, 104)(24, 137)(25, 105)(26, 120)(27, 139)(28, 138)(29, 107)(30, 136)(31, 109)(32, 113)(33, 110)(34, 111)(35, 132)(36, 142)(37, 131)(38, 143)(39, 118)(40, 144)(41, 141)(42, 122)(43, 133)(44, 126)(45, 125)(46, 130)(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) :: { ( 2, 8, 2, 8, 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 E12.670 Graph:: bipartite v = 14 e = 96 f = 60 degree seq :: [ 12^8, 16^6 ] E12.670 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 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 :: [ Y1, R^2, Y2^4, (R * Y3)^2, (R * Y1)^2, Y2^4, (R * Y2 * Y3^-1)^2, Y3^4 * Y2^2, Y3 * Y2^-1 * Y3 * Y2 * Y3 * Y2^-1, Y3^2 * Y2 * Y3^2 * Y2^-1 * Y3^-1 * Y2^-1 * Y3 * Y2^-1 * Y3^-1 * Y2^-1, (Y3^-1 * Y1^-1)^8 ] Map:: R = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96)(97, 145, 98, 146, 102, 150, 100, 148)(99, 147, 105, 153, 113, 161, 107, 155)(101, 149, 110, 158, 114, 162, 111, 159)(103, 151, 115, 163, 108, 156, 117, 165)(104, 152, 118, 166, 109, 157, 119, 167)(106, 154, 122, 170, 112, 160, 123, 171)(116, 164, 128, 176, 120, 168, 129, 177)(121, 169, 133, 181, 124, 172, 134, 182)(125, 173, 135, 183, 126, 174, 136, 184)(127, 175, 137, 185, 130, 178, 138, 186)(131, 179, 139, 187, 132, 180, 140, 188)(141, 189, 144, 192, 142, 190, 143, 191) L = (1, 99)(2, 103)(3, 106)(4, 108)(5, 97)(6, 113)(7, 116)(8, 98)(9, 118)(10, 114)(11, 119)(12, 120)(13, 100)(14, 125)(15, 126)(16, 101)(17, 112)(18, 102)(19, 111)(20, 109)(21, 110)(22, 131)(23, 132)(24, 104)(25, 105)(26, 133)(27, 134)(28, 107)(29, 127)(30, 130)(31, 115)(32, 137)(33, 138)(34, 117)(35, 124)(36, 121)(37, 141)(38, 142)(39, 122)(40, 123)(41, 143)(42, 144)(43, 128)(44, 129)(45, 136)(46, 135)(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) :: { ( 12, 16 ), ( 12, 16, 12, 16, 12, 16, 12, 16 ) } Outer automorphisms :: reflexible Dual of E12.669 Graph:: simple bipartite v = 60 e = 96 f = 14 degree seq :: [ 2^48, 8^12 ] E12.671 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 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 :: [ Y2, R^2, Y3^4, (R * Y1)^2, (R * Y3)^2, Y3^4, Y1^-1 * Y3^-2 * Y1^-3, (R * Y2 * Y3^-1)^2, Y3^2 * Y1 * Y3^2 * Y1^-1, Y3 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1, (Y3 * Y2^-1)^4, Y3^-1 * Y1^-2 * Y3 * Y1^2 * Y3 * Y1^-2 * Y3^-1 * Y1^-2 ] Map:: R = (1, 49, 2, 50, 6, 54, 17, 65, 10, 58, 21, 69, 13, 61, 4, 52)(3, 51, 9, 57, 25, 73, 16, 64, 5, 53, 15, 63, 28, 76, 11, 59)(7, 55, 20, 68, 35, 83, 24, 72, 8, 56, 23, 71, 36, 84, 22, 70)(12, 60, 29, 77, 40, 88, 27, 75, 14, 62, 30, 78, 39, 87, 26, 74)(18, 66, 31, 79, 41, 89, 34, 82, 19, 67, 33, 81, 42, 90, 32, 80)(37, 85, 45, 93, 48, 96, 44, 92, 38, 86, 46, 94, 47, 95, 43, 91)(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, 161)(114, 162)(115, 163)(116, 164)(117, 165)(118, 166)(119, 167)(120, 168)(121, 169)(122, 170)(123, 171)(124, 172)(125, 173)(126, 174)(127, 175)(128, 176)(129, 177)(130, 178)(131, 179)(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, 99)(2, 103)(3, 106)(4, 108)(5, 97)(6, 114)(7, 117)(8, 98)(9, 122)(10, 101)(11, 119)(12, 113)(13, 115)(14, 100)(15, 123)(16, 116)(17, 110)(18, 109)(19, 102)(20, 107)(21, 104)(22, 129)(23, 112)(24, 127)(25, 133)(26, 111)(27, 105)(28, 134)(29, 130)(30, 128)(31, 118)(32, 125)(33, 120)(34, 126)(35, 139)(36, 140)(37, 124)(38, 121)(39, 142)(40, 141)(41, 143)(42, 144)(43, 132)(44, 131)(45, 135)(46, 136)(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, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E12.668 Graph:: simple bipartite v = 54 e = 96 f = 20 degree seq :: [ 2^48, 16^6 ] E12.672 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 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^-1, Y3^4, Y1 * Y3^-2 * Y1, (R * Y1)^2, (R * Y3)^2, Y2 * Y3^2 * Y2^-1 * Y1^-2, (R * Y2 * Y3^-1)^2, Y3 * Y2^-1 * Y1 * Y3^-1 * Y2 * Y1^-1, Y2 * Y3^-1 * Y2 * Y1^-1 * Y2 * Y1, Y2^3 * Y1^-2 * Y2, Y3 * Y1^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1, Y2 * R * Y2^-1 * Y1^2 * R * Y2 * Y1^-1, Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1^-1 * Y2 * Y3^-1 * Y2^-1 * Y1^-1 ] Map:: 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, 26, 74, 16, 64, 27, 75)(20, 68, 32, 80, 24, 72, 33, 81)(25, 73, 37, 85, 28, 76, 38, 86)(29, 77, 40, 88, 30, 78, 39, 87)(31, 79, 41, 89, 34, 82, 42, 90)(35, 83, 44, 92, 36, 84, 43, 91)(45, 93, 48, 96, 46, 94, 47, 95)(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, 119, 167, 132, 180, 124, 172, 107, 155, 118, 166, 131, 179, 121, 169)(110, 158, 125, 173, 130, 178, 117, 165, 111, 159, 126, 174, 127, 175, 115, 163)(122, 170, 134, 182, 142, 190, 136, 184, 123, 171, 133, 181, 141, 189, 135, 183)(128, 176, 138, 186, 144, 192, 140, 188, 129, 177, 137, 185, 143, 191, 139, 187) L = (1, 100)(2, 97)(3, 107)(4, 102)(5, 111)(6, 98)(7, 117)(8, 119)(9, 99)(10, 123)(11, 113)(12, 115)(13, 118)(14, 101)(15, 114)(16, 122)(17, 105)(18, 110)(19, 103)(20, 129)(21, 108)(22, 104)(23, 109)(24, 128)(25, 134)(26, 106)(27, 112)(28, 133)(29, 135)(30, 136)(31, 138)(32, 116)(33, 120)(34, 137)(35, 139)(36, 140)(37, 121)(38, 124)(39, 126)(40, 125)(41, 127)(42, 130)(43, 132)(44, 131)(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) :: { ( 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 E12.673 Graph:: bipartite v = 18 e = 96 f = 56 degree seq :: [ 8^12, 16^6 ] E12.673 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 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 :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, Y1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1, Y3 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^2, Y3 * Y1 * Y3^-3 * Y1, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3^3 * Y1^-1 * Y3^-1, Y1^6, (Y3 * Y2^-1)^8 ] Map:: R = (1, 49, 2, 50, 6, 54, 18, 66, 13, 61, 4, 52)(3, 51, 9, 57, 24, 72, 32, 80, 14, 62, 11, 59)(5, 53, 15, 63, 7, 55, 20, 68, 35, 83, 16, 64)(8, 56, 22, 70, 19, 67, 31, 79, 30, 78, 12, 60)(10, 58, 26, 74, 36, 84, 17, 65, 29, 77, 27, 75)(21, 69, 37, 85, 40, 88, 23, 71, 34, 82, 38, 86)(25, 73, 39, 87, 41, 89, 33, 81, 44, 92, 28, 76)(42, 90, 48, 96, 46, 94, 45, 93, 47, 95, 43, 91)(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, 161)(114, 162)(115, 163)(116, 164)(117, 165)(118, 166)(119, 167)(120, 168)(121, 169)(122, 170)(123, 171)(124, 172)(125, 173)(126, 174)(127, 175)(128, 176)(129, 177)(130, 178)(131, 179)(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, 99)(2, 103)(3, 106)(4, 108)(5, 97)(6, 115)(7, 117)(8, 98)(9, 102)(10, 116)(11, 124)(12, 121)(13, 112)(14, 100)(15, 123)(16, 119)(17, 101)(18, 128)(19, 129)(20, 114)(21, 127)(22, 134)(23, 104)(24, 137)(25, 105)(26, 120)(27, 139)(28, 138)(29, 107)(30, 136)(31, 109)(32, 113)(33, 110)(34, 111)(35, 132)(36, 142)(37, 131)(38, 143)(39, 118)(40, 144)(41, 141)(42, 122)(43, 133)(44, 126)(45, 125)(46, 130)(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, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E12.672 Graph:: simple bipartite v = 56 e = 96 f = 18 degree seq :: [ 2^48, 12^8 ] E12.674 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 24}) Quotient :: dipole Aut^+ = D48 (small group id <48, 7>) Aut = C2 x D48 (small group id <96, 110>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y1)^2, (Y2 * Y1)^2, (R * Y3)^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 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 5, 53)(4, 52, 8, 56)(6, 54, 10, 58)(7, 55, 11, 59)(9, 57, 13, 61)(12, 60, 16, 64)(14, 62, 18, 66)(15, 63, 19, 67)(17, 65, 21, 69)(20, 68, 24, 72)(22, 70, 26, 74)(23, 71, 27, 75)(25, 73, 29, 77)(28, 76, 32, 80)(30, 78, 34, 82)(31, 79, 35, 83)(33, 81, 37, 85)(36, 84, 40, 88)(38, 86, 42, 90)(39, 87, 43, 91)(41, 89, 45, 93)(44, 92, 48, 96)(46, 94, 47, 95)(97, 145, 99, 147)(98, 146, 101, 149)(100, 148, 103, 151)(102, 150, 105, 153)(104, 152, 107, 155)(106, 154, 109, 157)(108, 156, 111, 159)(110, 158, 113, 161)(112, 160, 115, 163)(114, 162, 117, 165)(116, 164, 119, 167)(118, 166, 121, 169)(120, 168, 123, 171)(122, 170, 125, 173)(124, 172, 127, 175)(126, 174, 129, 177)(128, 176, 131, 179)(130, 178, 133, 181)(132, 180, 135, 183)(134, 182, 137, 185)(136, 184, 139, 187)(138, 186, 141, 189)(140, 188, 143, 191)(142, 190, 144, 192) L = (1, 100)(2, 102)(3, 103)(4, 97)(5, 105)(6, 98)(7, 99)(8, 108)(9, 101)(10, 110)(11, 111)(12, 104)(13, 113)(14, 106)(15, 107)(16, 116)(17, 109)(18, 118)(19, 119)(20, 112)(21, 121)(22, 114)(23, 115)(24, 124)(25, 117)(26, 126)(27, 127)(28, 120)(29, 129)(30, 122)(31, 123)(32, 132)(33, 125)(34, 134)(35, 135)(36, 128)(37, 137)(38, 130)(39, 131)(40, 140)(41, 133)(42, 142)(43, 143)(44, 136)(45, 144)(46, 138)(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, 48, 4, 48 ) } Outer automorphisms :: reflexible Dual of E12.675 Graph:: simple bipartite v = 48 e = 96 f = 26 degree seq :: [ 4^48 ] E12.675 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 24}) Quotient :: dipole Aut^+ = D48 (small group id <48, 7>) Aut = C2 x D48 (small group id <96, 110>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (R * Y2)^2, (R * Y3)^2, (Y3 * Y1^-1)^2, (Y3 * Y2)^2, (Y1^-1 * Y2)^2, (R * Y1)^2, Y2 * Y3 * Y1^12, Y1^-1 * Y2 * Y1^5 * Y3 * Y1^-6 ] Map:: non-degenerate R = (1, 49, 2, 50, 6, 54, 13, 61, 21, 69, 29, 77, 37, 85, 45, 93, 42, 90, 34, 82, 26, 74, 18, 66, 10, 58, 16, 64, 24, 72, 32, 80, 40, 88, 48, 96, 44, 92, 36, 84, 28, 76, 20, 68, 12, 60, 5, 53)(3, 51, 9, 57, 17, 65, 25, 73, 33, 81, 41, 89, 47, 95, 39, 87, 31, 79, 23, 71, 15, 63, 8, 56, 4, 52, 11, 59, 19, 67, 27, 75, 35, 83, 43, 91, 46, 94, 38, 86, 30, 78, 22, 70, 14, 62, 7, 55)(97, 145, 99, 147)(98, 146, 103, 151)(100, 148, 106, 154)(101, 149, 105, 153)(102, 150, 110, 158)(104, 152, 112, 160)(107, 155, 114, 162)(108, 156, 113, 161)(109, 157, 118, 166)(111, 159, 120, 168)(115, 163, 122, 170)(116, 164, 121, 169)(117, 165, 126, 174)(119, 167, 128, 176)(123, 171, 130, 178)(124, 172, 129, 177)(125, 173, 134, 182)(127, 175, 136, 184)(131, 179, 138, 186)(132, 180, 137, 185)(133, 181, 142, 190)(135, 183, 144, 192)(139, 187, 141, 189)(140, 188, 143, 191) L = (1, 100)(2, 104)(3, 106)(4, 97)(5, 107)(6, 111)(7, 112)(8, 98)(9, 114)(10, 99)(11, 101)(12, 115)(13, 119)(14, 120)(15, 102)(16, 103)(17, 122)(18, 105)(19, 108)(20, 123)(21, 127)(22, 128)(23, 109)(24, 110)(25, 130)(26, 113)(27, 116)(28, 131)(29, 135)(30, 136)(31, 117)(32, 118)(33, 138)(34, 121)(35, 124)(36, 139)(37, 143)(38, 144)(39, 125)(40, 126)(41, 141)(42, 129)(43, 132)(44, 142)(45, 137)(46, 140)(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) :: { ( 4^4 ), ( 4^48 ) } Outer automorphisms :: reflexible Dual of E12.674 Graph:: bipartite v = 26 e = 96 f = 48 degree seq :: [ 4^24, 48^2 ] E12.676 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 4, 24}) Quotient :: edge Aut^+ = C3 : Q16 (small group id <48, 8>) Aut = (C24 x C2) : C2 (small group id <96, 111>) |r| :: 2 Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, T2 * T1 * T2 * T1^-1, T2^2 * T1^-2 * T2^-2 * T1^-2, T2^10 * T1^-1 * T2^-2 * T1^-1 ] Map:: non-degenerate R = (1, 3, 9, 17, 25, 33, 41, 46, 38, 30, 22, 14, 6, 13, 21, 29, 37, 45, 44, 36, 28, 20, 12, 5)(2, 7, 15, 23, 31, 39, 47, 42, 34, 26, 18, 10, 4, 11, 19, 27, 35, 43, 48, 40, 32, 24, 16, 8)(49, 50, 54, 52)(51, 56, 61, 58)(53, 55, 62, 59)(57, 64, 69, 66)(60, 63, 70, 67)(65, 72, 77, 74)(68, 71, 78, 75)(73, 80, 85, 82)(76, 79, 86, 83)(81, 88, 93, 90)(84, 87, 94, 91)(89, 96, 92, 95) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 8^4 ), ( 8^24 ) } Outer automorphisms :: reflexible Dual of E12.677 Transitivity :: ET+ Graph:: bipartite v = 14 e = 48 f = 12 degree seq :: [ 4^12, 24^2 ] E12.677 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 4, 24}) Quotient :: loop Aut^+ = C3 : Q16 (small group id <48, 8>) Aut = (C24 x C2) : C2 (small group id <96, 111>) |r| :: 2 Presentation :: [ F^2, T1^-2 * T2^2, T1^4, (F * T2)^2, (F * T1)^2, T2^-1 * T1^-2 * T2^-1, T1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 ] Map:: non-degenerate R = (1, 49, 3, 51, 6, 54, 5, 53)(2, 50, 7, 55, 4, 52, 8, 56)(9, 57, 13, 61, 10, 58, 14, 62)(11, 59, 15, 63, 12, 60, 16, 64)(17, 65, 21, 69, 18, 66, 22, 70)(19, 67, 23, 71, 20, 68, 24, 72)(25, 73, 29, 77, 26, 74, 30, 78)(27, 75, 31, 79, 28, 76, 32, 80)(33, 81, 37, 85, 34, 82, 38, 86)(35, 83, 39, 87, 36, 84, 40, 88)(41, 89, 45, 93, 42, 90, 46, 94)(43, 91, 47, 95, 44, 92, 48, 96) L = (1, 50)(2, 54)(3, 57)(4, 49)(5, 58)(6, 52)(7, 59)(8, 60)(9, 53)(10, 51)(11, 56)(12, 55)(13, 65)(14, 66)(15, 67)(16, 68)(17, 62)(18, 61)(19, 64)(20, 63)(21, 73)(22, 74)(23, 75)(24, 76)(25, 70)(26, 69)(27, 72)(28, 71)(29, 81)(30, 82)(31, 83)(32, 84)(33, 78)(34, 77)(35, 80)(36, 79)(37, 89)(38, 90)(39, 91)(40, 92)(41, 86)(42, 85)(43, 88)(44, 87)(45, 96)(46, 95)(47, 93)(48, 94) local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E12.676 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 12 e = 48 f = 14 degree seq :: [ 8^12 ] E12.678 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 24}) Quotient :: dipole Aut^+ = C3 : Q16 (small group id <48, 8>) Aut = (C24 x C2) : C2 (small group id <96, 111>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y3)^2, Y1^4, (R * Y1)^2, Y2^-1 * Y1^-1 * Y2^-1 * Y1, Y1^-1 * Y2 * Y1^-2 * Y2^-1 * Y1^-1, (Y3^-1 * Y1^-1)^4, Y2^5 * Y1^-1 * Y2^-7 * Y1^-1 ] Map:: R = (1, 49, 2, 50, 6, 54, 4, 52)(3, 51, 8, 56, 13, 61, 10, 58)(5, 53, 7, 55, 14, 62, 11, 59)(9, 57, 16, 64, 21, 69, 18, 66)(12, 60, 15, 63, 22, 70, 19, 67)(17, 65, 24, 72, 29, 77, 26, 74)(20, 68, 23, 71, 30, 78, 27, 75)(25, 73, 32, 80, 37, 85, 34, 82)(28, 76, 31, 79, 38, 86, 35, 83)(33, 81, 40, 88, 45, 93, 42, 90)(36, 84, 39, 87, 46, 94, 43, 91)(41, 89, 48, 96, 44, 92, 47, 95)(97, 145, 99, 147, 105, 153, 113, 161, 121, 169, 129, 177, 137, 185, 142, 190, 134, 182, 126, 174, 118, 166, 110, 158, 102, 150, 109, 157, 117, 165, 125, 173, 133, 181, 141, 189, 140, 188, 132, 180, 124, 172, 116, 164, 108, 156, 101, 149)(98, 146, 103, 151, 111, 159, 119, 167, 127, 175, 135, 183, 143, 191, 138, 186, 130, 178, 122, 170, 114, 162, 106, 154, 100, 148, 107, 155, 115, 163, 123, 171, 131, 179, 139, 187, 144, 192, 136, 184, 128, 176, 120, 168, 112, 160, 104, 152) L = (1, 99)(2, 103)(3, 105)(4, 107)(5, 97)(6, 109)(7, 111)(8, 98)(9, 113)(10, 100)(11, 115)(12, 101)(13, 117)(14, 102)(15, 119)(16, 104)(17, 121)(18, 106)(19, 123)(20, 108)(21, 125)(22, 110)(23, 127)(24, 112)(25, 129)(26, 114)(27, 131)(28, 116)(29, 133)(30, 118)(31, 135)(32, 120)(33, 137)(34, 122)(35, 139)(36, 124)(37, 141)(38, 126)(39, 143)(40, 128)(41, 142)(42, 130)(43, 144)(44, 132)(45, 140)(46, 134)(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) :: { ( 2, 8, 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 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 E12.679 Graph:: bipartite v = 14 e = 96 f = 60 degree seq :: [ 8^12, 48^2 ] E12.679 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 24}) Quotient :: dipole Aut^+ = C3 : Q16 (small group id <48, 8>) Aut = (C24 x C2) : C2 (small group id <96, 111>) |r| :: 2 Presentation :: [ Y1, R^2, Y3 * Y2 * Y3 * Y2^-1, (R * Y3)^2, (R * Y1)^2, Y2^4, (R * Y2 * Y3^-1)^2, Y2^-1 * Y3^-2 * Y2^-2 * Y3^2 * Y2^-1, Y3^3 * Y2^-1 * Y3^-9 * Y2^-1, (Y3^-1 * Y1^-1)^24 ] Map:: R = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96)(97, 145, 98, 146, 102, 150, 100, 148)(99, 147, 104, 152, 109, 157, 106, 154)(101, 149, 103, 151, 110, 158, 107, 155)(105, 153, 112, 160, 117, 165, 114, 162)(108, 156, 111, 159, 118, 166, 115, 163)(113, 161, 120, 168, 125, 173, 122, 170)(116, 164, 119, 167, 126, 174, 123, 171)(121, 169, 128, 176, 133, 181, 130, 178)(124, 172, 127, 175, 134, 182, 131, 179)(129, 177, 136, 184, 141, 189, 138, 186)(132, 180, 135, 183, 142, 190, 139, 187)(137, 185, 144, 192, 140, 188, 143, 191) L = (1, 99)(2, 103)(3, 105)(4, 107)(5, 97)(6, 109)(7, 111)(8, 98)(9, 113)(10, 100)(11, 115)(12, 101)(13, 117)(14, 102)(15, 119)(16, 104)(17, 121)(18, 106)(19, 123)(20, 108)(21, 125)(22, 110)(23, 127)(24, 112)(25, 129)(26, 114)(27, 131)(28, 116)(29, 133)(30, 118)(31, 135)(32, 120)(33, 137)(34, 122)(35, 139)(36, 124)(37, 141)(38, 126)(39, 143)(40, 128)(41, 142)(42, 130)(43, 144)(44, 132)(45, 140)(46, 134)(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, 48 ), ( 8, 48, 8, 48, 8, 48, 8, 48 ) } Outer automorphisms :: reflexible Dual of E12.678 Graph:: simple bipartite v = 60 e = 96 f = 14 degree seq :: [ 2^48, 8^12 ] E12.680 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 48, 48}) Quotient :: regular Aut^+ = C48 (small group id <48, 2>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T2 * T1^24 ] Map:: R = (1, 2, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 47, 43, 39, 35, 31, 27, 23, 19, 15, 11, 7, 3, 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 48, 44, 40, 36, 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, 34)(32, 35)(33, 38)(36, 39)(37, 42)(40, 43)(41, 46)(44, 47)(45, 48) local type(s) :: { ( 48^48 ) } Outer automorphisms :: reflexible selfdual Transitivity :: ET+ VT+ AT+ REG+ Graph:: v = 1 e = 24 f = 1 degree seq :: [ 48 ] E12.681 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 48, 48}) Quotient :: edge Aut^+ = C48 (small group id <48, 2>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^24 * T1 ] Map:: R = (1, 3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 43, 47, 46, 42, 38, 34, 30, 26, 22, 18, 14, 10, 6, 2, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 48, 44, 40, 36, 32, 28, 24, 20, 16, 12, 8, 4)(49, 50)(51, 53)(52, 54)(55, 57)(56, 58)(59, 61)(60, 62)(63, 65)(64, 66)(67, 69)(68, 70)(71, 73)(72, 74)(75, 77)(76, 78)(79, 81)(80, 82)(83, 85)(84, 86)(87, 89)(88, 90)(91, 93)(92, 94)(95, 96) L = (1, 49)(2, 50)(3, 51)(4, 52)(5, 53)(6, 54)(7, 55)(8, 56)(9, 57)(10, 58)(11, 59)(12, 60)(13, 61)(14, 62)(15, 63)(16, 64)(17, 65)(18, 66)(19, 67)(20, 68)(21, 69)(22, 70)(23, 71)(24, 72)(25, 73)(26, 74)(27, 75)(28, 76)(29, 77)(30, 78)(31, 79)(32, 80)(33, 81)(34, 82)(35, 83)(36, 84)(37, 85)(38, 86)(39, 87)(40, 88)(41, 89)(42, 90)(43, 91)(44, 92)(45, 93)(46, 94)(47, 95)(48, 96) local type(s) :: { ( 96, 96 ), ( 96^48 ) } Outer automorphisms :: reflexible Dual of E12.682 Transitivity :: ET+ Graph:: bipartite v = 25 e = 48 f = 1 degree seq :: [ 2^24, 48 ] E12.682 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 48, 48}) Quotient :: loop Aut^+ = C48 (small group id <48, 2>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^24 * T1 ] Map:: R = (1, 49, 3, 51, 7, 55, 11, 59, 15, 63, 19, 67, 23, 71, 27, 75, 31, 79, 35, 83, 39, 87, 43, 91, 47, 95, 46, 94, 42, 90, 38, 86, 34, 82, 30, 78, 26, 74, 22, 70, 18, 66, 14, 62, 10, 58, 6, 54, 2, 50, 5, 53, 9, 57, 13, 61, 17, 65, 21, 69, 25, 73, 29, 77, 33, 81, 37, 85, 41, 89, 45, 93, 48, 96, 44, 92, 40, 88, 36, 84, 32, 80, 28, 76, 24, 72, 20, 68, 16, 64, 12, 60, 8, 56, 4, 52) L = (1, 50)(2, 49)(3, 53)(4, 54)(5, 51)(6, 52)(7, 57)(8, 58)(9, 55)(10, 56)(11, 61)(12, 62)(13, 59)(14, 60)(15, 65)(16, 66)(17, 63)(18, 64)(19, 69)(20, 70)(21, 67)(22, 68)(23, 73)(24, 74)(25, 71)(26, 72)(27, 77)(28, 78)(29, 75)(30, 76)(31, 81)(32, 82)(33, 79)(34, 80)(35, 85)(36, 86)(37, 83)(38, 84)(39, 89)(40, 90)(41, 87)(42, 88)(43, 93)(44, 94)(45, 91)(46, 92)(47, 96)(48, 95) local type(s) :: { ( 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 2, 48, 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 E12.681 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 48 f = 25 degree seq :: [ 96 ] E12.683 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 48, 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 * Y1, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y1 * Y2 * Y1, (R * Y2 * Y3^-1)^2, Y2^24 * Y1, (Y3 * Y2^-1)^48 ] Map:: R = (1, 49, 2, 50)(3, 51, 5, 53)(4, 52, 6, 54)(7, 55, 9, 57)(8, 56, 10, 58)(11, 59, 13, 61)(12, 60, 14, 62)(15, 63, 17, 65)(16, 64, 18, 66)(19, 67, 21, 69)(20, 68, 22, 70)(23, 71, 25, 73)(24, 72, 26, 74)(27, 75, 29, 77)(28, 76, 30, 78)(31, 79, 33, 81)(32, 80, 34, 82)(35, 83, 37, 85)(36, 84, 38, 86)(39, 87, 41, 89)(40, 88, 42, 90)(43, 91, 45, 93)(44, 92, 46, 94)(47, 95, 48, 96)(97, 145, 99, 147, 103, 151, 107, 155, 111, 159, 115, 163, 119, 167, 123, 171, 127, 175, 131, 179, 135, 183, 139, 187, 143, 191, 142, 190, 138, 186, 134, 182, 130, 178, 126, 174, 122, 170, 118, 166, 114, 162, 110, 158, 106, 154, 102, 150, 98, 146, 101, 149, 105, 153, 109, 157, 113, 161, 117, 165, 121, 169, 125, 173, 129, 177, 133, 181, 137, 185, 141, 189, 144, 192, 140, 188, 136, 184, 132, 180, 128, 176, 124, 172, 120, 168, 116, 164, 112, 160, 108, 156, 104, 152, 100, 148) L = (1, 98)(2, 97)(3, 101)(4, 102)(5, 99)(6, 100)(7, 105)(8, 106)(9, 103)(10, 104)(11, 109)(12, 110)(13, 107)(14, 108)(15, 113)(16, 114)(17, 111)(18, 112)(19, 117)(20, 118)(21, 115)(22, 116)(23, 121)(24, 122)(25, 119)(26, 120)(27, 125)(28, 126)(29, 123)(30, 124)(31, 129)(32, 130)(33, 127)(34, 128)(35, 133)(36, 134)(37, 131)(38, 132)(39, 137)(40, 138)(41, 135)(42, 136)(43, 141)(44, 142)(45, 139)(46, 140)(47, 144)(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) :: { ( 2, 96, 2, 96 ), ( 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96, 2, 96 ) } Outer automorphisms :: reflexible Dual of E12.684 Graph:: bipartite v = 25 e = 96 f = 49 degree seq :: [ 4^24, 96 ] E12.684 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 48, 48}) Quotient :: dipole Aut^+ = C48 (small group id <48, 2>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y1)^2, Y3 * Y1 * Y3 * Y1^-1, (R * Y3)^2, (Y3 * Y2^-1)^2, Y3 * Y1^24 ] Map:: R = (1, 49, 2, 50, 5, 53, 9, 57, 13, 61, 17, 65, 21, 69, 25, 73, 29, 77, 33, 81, 37, 85, 41, 89, 45, 93, 47, 95, 43, 91, 39, 87, 35, 83, 31, 79, 27, 75, 23, 71, 19, 67, 15, 63, 11, 59, 7, 55, 3, 51, 6, 54, 10, 58, 14, 62, 18, 66, 22, 70, 26, 74, 30, 78, 34, 82, 38, 86, 42, 90, 46, 94, 48, 96, 44, 92, 40, 88, 36, 84, 32, 80, 28, 76, 24, 72, 20, 68, 16, 64, 12, 60, 8, 56, 4, 52)(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, 161)(114, 162)(115, 163)(116, 164)(117, 165)(118, 166)(119, 167)(120, 168)(121, 169)(122, 170)(123, 171)(124, 172)(125, 173)(126, 174)(127, 175)(128, 176)(129, 177)(130, 178)(131, 179)(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, 99)(2, 102)(3, 97)(4, 103)(5, 106)(6, 98)(7, 100)(8, 107)(9, 110)(10, 101)(11, 104)(12, 111)(13, 114)(14, 105)(15, 108)(16, 115)(17, 118)(18, 109)(19, 112)(20, 119)(21, 122)(22, 113)(23, 116)(24, 123)(25, 126)(26, 117)(27, 120)(28, 127)(29, 130)(30, 121)(31, 124)(32, 131)(33, 134)(34, 125)(35, 128)(36, 135)(37, 138)(38, 129)(39, 132)(40, 139)(41, 142)(42, 133)(43, 136)(44, 143)(45, 144)(46, 137)(47, 140)(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, 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, 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, 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 E12.683 Graph:: bipartite v = 49 e = 96 f = 25 degree seq :: [ 2^48, 96 ] E12.685 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 25, 50}) Quotient :: regular Aut^+ = C50 (small group id <50, 2>) Aut = D100 (small group id <100, 4>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T2 * T1^-25 ] Map:: R = (1, 2, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 47, 43, 39, 35, 31, 27, 23, 19, 15, 11, 7, 3, 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50, 48, 44, 40, 36, 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, 34)(32, 35)(33, 38)(36, 39)(37, 42)(40, 43)(41, 46)(44, 47)(45, 50)(48, 49) local type(s) :: { ( 25^50 ) } Outer automorphisms :: reflexible Dual of E12.686 Transitivity :: ET+ VT+ AT+ REG+ Graph:: v = 1 e = 25 f = 2 degree seq :: [ 50 ] E12.686 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 25, 50}) Quotient :: regular Aut^+ = C50 (small group id <50, 2>) Aut = D100 (small group id <100, 4>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T1^25 ] Map:: R = (1, 2, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 48, 44, 40, 36, 32, 28, 24, 20, 16, 12, 8, 4)(3, 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 49, 50, 47, 43, 39, 35, 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, 34)(32, 35)(33, 38)(36, 39)(37, 42)(40, 43)(41, 46)(44, 47)(45, 49)(48, 50) local type(s) :: { ( 50^25 ) } Outer automorphisms :: reflexible Dual of E12.685 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 2 e = 25 f = 1 degree seq :: [ 25^2 ] E12.687 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 25, 50}) Quotient :: edge Aut^+ = C50 (small group id <50, 2>) Aut = D100 (small group id <100, 4>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^25 ] Map:: R = (1, 3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 43, 47, 48, 44, 40, 36, 32, 28, 24, 20, 16, 12, 8, 4)(2, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 50, 46, 42, 38, 34, 30, 26, 22, 18, 14, 10, 6)(51, 52)(53, 55)(54, 56)(57, 59)(58, 60)(61, 63)(62, 64)(65, 67)(66, 68)(69, 71)(70, 72)(73, 75)(74, 76)(77, 79)(78, 80)(81, 83)(82, 84)(85, 87)(86, 88)(89, 91)(90, 92)(93, 95)(94, 96)(97, 99)(98, 100) L = (1, 51)(2, 52)(3, 53)(4, 54)(5, 55)(6, 56)(7, 57)(8, 58)(9, 59)(10, 60)(11, 61)(12, 62)(13, 63)(14, 64)(15, 65)(16, 66)(17, 67)(18, 68)(19, 69)(20, 70)(21, 71)(22, 72)(23, 73)(24, 74)(25, 75)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100) local type(s) :: { ( 100, 100 ), ( 100^25 ) } Outer automorphisms :: reflexible Dual of E12.691 Transitivity :: ET+ Graph:: simple bipartite v = 27 e = 50 f = 1 degree seq :: [ 2^25, 25^2 ] E12.688 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 25, 50}) Quotient :: edge Aut^+ = C50 (small group id <50, 2>) Aut = D100 (small group id <100, 4>) |r| :: 2 Presentation :: [ F^2, T2^-2 * T1^-2, (F * T1)^2, (F * T2)^2, (T2^-1 * T1^-1)^2, T2^-2 * T1^10 * T2^-1 * T1 * T2^-11, T2^-2 * T1^23, T2^9 * T1^8 * T2^-1 * T1^11 * T2^-1 * T1^11 * T2^-1 * T1 ] Map:: non-degenerate R = (1, 3, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 48, 43, 40, 35, 32, 27, 24, 19, 16, 11, 8, 2, 7, 4, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50, 47, 44, 39, 36, 31, 28, 23, 20, 15, 12, 6, 5)(51, 52, 56, 61, 65, 69, 73, 77, 81, 85, 89, 93, 97, 99, 96, 91, 88, 83, 80, 75, 72, 67, 64, 59, 54)(53, 57, 55, 58, 62, 66, 70, 74, 78, 82, 86, 90, 94, 98, 100, 95, 92, 87, 84, 79, 76, 71, 68, 63, 60) L = (1, 51)(2, 52)(3, 53)(4, 54)(5, 55)(6, 56)(7, 57)(8, 58)(9, 59)(10, 60)(11, 61)(12, 62)(13, 63)(14, 64)(15, 65)(16, 66)(17, 67)(18, 68)(19, 69)(20, 70)(21, 71)(22, 72)(23, 73)(24, 74)(25, 75)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100) local type(s) :: { ( 4^25 ), ( 4^50 ) } Outer automorphisms :: reflexible Dual of E12.692 Transitivity :: ET+ Graph:: bipartite v = 3 e = 50 f = 25 degree seq :: [ 25^2, 50 ] E12.689 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 25, 50}) Quotient :: edge Aut^+ = C50 (small group id <50, 2>) Aut = D100 (small group id <100, 4>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T2 * T1^-25 ] 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, 34)(32, 35)(33, 38)(36, 39)(37, 42)(40, 43)(41, 46)(44, 47)(45, 50)(48, 49)(51, 52, 55, 59, 63, 67, 71, 75, 79, 83, 87, 91, 95, 99, 97, 93, 89, 85, 81, 77, 73, 69, 65, 61, 57, 53, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 98, 94, 90, 86, 82, 78, 74, 70, 66, 62, 58, 54) L = (1, 51)(2, 52)(3, 53)(4, 54)(5, 55)(6, 56)(7, 57)(8, 58)(9, 59)(10, 60)(11, 61)(12, 62)(13, 63)(14, 64)(15, 65)(16, 66)(17, 67)(18, 68)(19, 69)(20, 70)(21, 71)(22, 72)(23, 73)(24, 74)(25, 75)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100) local type(s) :: { ( 50, 50 ), ( 50^50 ) } Outer automorphisms :: reflexible Dual of E12.690 Transitivity :: ET+ Graph:: bipartite v = 26 e = 50 f = 2 degree seq :: [ 2^25, 50 ] E12.690 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 25, 50}) Quotient :: loop Aut^+ = C50 (small group id <50, 2>) Aut = D100 (small group id <100, 4>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^25 ] Map:: R = (1, 51, 3, 53, 7, 57, 11, 61, 15, 65, 19, 69, 23, 73, 27, 77, 31, 81, 35, 85, 39, 89, 43, 93, 47, 97, 48, 98, 44, 94, 40, 90, 36, 86, 32, 82, 28, 78, 24, 74, 20, 70, 16, 66, 12, 62, 8, 58, 4, 54)(2, 52, 5, 55, 9, 59, 13, 63, 17, 67, 21, 71, 25, 75, 29, 79, 33, 83, 37, 87, 41, 91, 45, 95, 49, 99, 50, 100, 46, 96, 42, 92, 38, 88, 34, 84, 30, 80, 26, 76, 22, 72, 18, 68, 14, 64, 10, 60, 6, 56) L = (1, 52)(2, 51)(3, 55)(4, 56)(5, 53)(6, 54)(7, 59)(8, 60)(9, 57)(10, 58)(11, 63)(12, 64)(13, 61)(14, 62)(15, 67)(16, 68)(17, 65)(18, 66)(19, 71)(20, 72)(21, 69)(22, 70)(23, 75)(24, 76)(25, 73)(26, 74)(27, 79)(28, 80)(29, 77)(30, 78)(31, 83)(32, 84)(33, 81)(34, 82)(35, 87)(36, 88)(37, 85)(38, 86)(39, 91)(40, 92)(41, 89)(42, 90)(43, 95)(44, 96)(45, 93)(46, 94)(47, 99)(48, 100)(49, 97)(50, 98) local type(s) :: { ( 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50 ) } Outer automorphisms :: reflexible Dual of E12.689 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 50 f = 26 degree seq :: [ 50^2 ] E12.691 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 25, 50}) Quotient :: loop Aut^+ = C50 (small group id <50, 2>) Aut = D100 (small group id <100, 4>) |r| :: 2 Presentation :: [ F^2, T2^-2 * T1^-2, (F * T1)^2, (F * T2)^2, (T2^-1 * T1^-1)^2, T2^-2 * T1^10 * T2^-1 * T1 * T2^-11, T2^-2 * T1^23, T2^9 * T1^8 * T2^-1 * T1^11 * T2^-1 * T1^11 * T2^-1 * T1 ] Map:: R = (1, 51, 3, 53, 9, 59, 13, 63, 17, 67, 21, 71, 25, 75, 29, 79, 33, 83, 37, 87, 41, 91, 45, 95, 49, 99, 48, 98, 43, 93, 40, 90, 35, 85, 32, 82, 27, 77, 24, 74, 19, 69, 16, 66, 11, 61, 8, 58, 2, 52, 7, 57, 4, 54, 10, 60, 14, 64, 18, 68, 22, 72, 26, 76, 30, 80, 34, 84, 38, 88, 42, 92, 46, 96, 50, 100, 47, 97, 44, 94, 39, 89, 36, 86, 31, 81, 28, 78, 23, 73, 20, 70, 15, 65, 12, 62, 6, 56, 5, 55) L = (1, 52)(2, 56)(3, 57)(4, 51)(5, 58)(6, 61)(7, 55)(8, 62)(9, 54)(10, 53)(11, 65)(12, 66)(13, 60)(14, 59)(15, 69)(16, 70)(17, 64)(18, 63)(19, 73)(20, 74)(21, 68)(22, 67)(23, 77)(24, 78)(25, 72)(26, 71)(27, 81)(28, 82)(29, 76)(30, 75)(31, 85)(32, 86)(33, 80)(34, 79)(35, 89)(36, 90)(37, 84)(38, 83)(39, 93)(40, 94)(41, 88)(42, 87)(43, 97)(44, 98)(45, 92)(46, 91)(47, 99)(48, 100)(49, 96)(50, 95) local type(s) :: { ( 2, 25, 2, 25, 2, 25, 2, 25, 2, 25, 2, 25, 2, 25, 2, 25, 2, 25, 2, 25, 2, 25, 2, 25, 2, 25, 2, 25, 2, 25, 2, 25, 2, 25, 2, 25, 2, 25, 2, 25, 2, 25, 2, 25, 2, 25, 2, 25, 2, 25, 2, 25, 2, 25, 2, 25, 2, 25, 2, 25, 2, 25, 2, 25, 2, 25, 2, 25, 2, 25, 2, 25, 2, 25, 2, 25, 2, 25, 2, 25, 2, 25, 2, 25, 2, 25, 2, 25, 2, 25, 2, 25, 2, 25, 2, 25, 2, 25, 2, 25 ) } Outer automorphisms :: reflexible Dual of E12.687 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 50 f = 27 degree seq :: [ 100 ] E12.692 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 25, 50}) Quotient :: loop Aut^+ = C50 (small group id <50, 2>) Aut = D100 (small group id <100, 4>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T2 * T1^-25 ] Map:: non-degenerate R = (1, 51, 3, 53)(2, 52, 6, 56)(4, 54, 7, 57)(5, 55, 10, 60)(8, 58, 11, 61)(9, 59, 14, 64)(12, 62, 15, 65)(13, 63, 18, 68)(16, 66, 19, 69)(17, 67, 22, 72)(20, 70, 23, 73)(21, 71, 26, 76)(24, 74, 27, 77)(25, 75, 30, 80)(28, 78, 31, 81)(29, 79, 34, 84)(32, 82, 35, 85)(33, 83, 38, 88)(36, 86, 39, 89)(37, 87, 42, 92)(40, 90, 43, 93)(41, 91, 46, 96)(44, 94, 47, 97)(45, 95, 50, 100)(48, 98, 49, 99) L = (1, 52)(2, 55)(3, 56)(4, 51)(5, 59)(6, 60)(7, 53)(8, 54)(9, 63)(10, 64)(11, 57)(12, 58)(13, 67)(14, 68)(15, 61)(16, 62)(17, 71)(18, 72)(19, 65)(20, 66)(21, 75)(22, 76)(23, 69)(24, 70)(25, 79)(26, 80)(27, 73)(28, 74)(29, 83)(30, 84)(31, 77)(32, 78)(33, 87)(34, 88)(35, 81)(36, 82)(37, 91)(38, 92)(39, 85)(40, 86)(41, 95)(42, 96)(43, 89)(44, 90)(45, 99)(46, 100)(47, 93)(48, 94)(49, 97)(50, 98) local type(s) :: { ( 25, 50, 25, 50 ) } Outer automorphisms :: reflexible Dual of E12.688 Transitivity :: ET+ VT+ AT Graph:: v = 25 e = 50 f = 3 degree seq :: [ 4^25 ] E12.693 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 25, 50}) Quotient :: dipole Aut^+ = C50 (small group id <50, 2>) Aut = D100 (small group id <100, 4>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y1 * Y2 * Y1, (R * Y2 * Y3^-1)^2, Y2^25, (Y3 * Y2^-1)^50 ] Map:: R = (1, 51, 2, 52)(3, 53, 5, 55)(4, 54, 6, 56)(7, 57, 9, 59)(8, 58, 10, 60)(11, 61, 13, 63)(12, 62, 14, 64)(15, 65, 17, 67)(16, 66, 18, 68)(19, 69, 21, 71)(20, 70, 22, 72)(23, 73, 25, 75)(24, 74, 26, 76)(27, 77, 29, 79)(28, 78, 30, 80)(31, 81, 33, 83)(32, 82, 34, 84)(35, 85, 37, 87)(36, 86, 38, 88)(39, 89, 41, 91)(40, 90, 42, 92)(43, 93, 45, 95)(44, 94, 46, 96)(47, 97, 49, 99)(48, 98, 50, 100)(101, 151, 103, 153, 107, 157, 111, 161, 115, 165, 119, 169, 123, 173, 127, 177, 131, 181, 135, 185, 139, 189, 143, 193, 147, 197, 148, 198, 144, 194, 140, 190, 136, 186, 132, 182, 128, 178, 124, 174, 120, 170, 116, 166, 112, 162, 108, 158, 104, 154)(102, 152, 105, 155, 109, 159, 113, 163, 117, 167, 121, 171, 125, 175, 129, 179, 133, 183, 137, 187, 141, 191, 145, 195, 149, 199, 150, 200, 146, 196, 142, 192, 138, 188, 134, 184, 130, 180, 126, 176, 122, 172, 118, 168, 114, 164, 110, 160, 106, 156) L = (1, 102)(2, 101)(3, 105)(4, 106)(5, 103)(6, 104)(7, 109)(8, 110)(9, 107)(10, 108)(11, 113)(12, 114)(13, 111)(14, 112)(15, 117)(16, 118)(17, 115)(18, 116)(19, 121)(20, 122)(21, 119)(22, 120)(23, 125)(24, 126)(25, 123)(26, 124)(27, 129)(28, 130)(29, 127)(30, 128)(31, 133)(32, 134)(33, 131)(34, 132)(35, 137)(36, 138)(37, 135)(38, 136)(39, 141)(40, 142)(41, 139)(42, 140)(43, 145)(44, 146)(45, 143)(46, 144)(47, 149)(48, 150)(49, 147)(50, 148)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) local type(s) :: { ( 2, 100, 2, 100 ), ( 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100, 2, 100 ) } Outer automorphisms :: reflexible Dual of E12.696 Graph:: bipartite v = 27 e = 100 f = 51 degree seq :: [ 4^25, 50^2 ] E12.694 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 25, 50}) Quotient :: dipole Aut^+ = C50 (small group id <50, 2>) Aut = D100 (small group id <100, 4>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-1, Y2^2 * Y1^2, (R * Y1)^2, R * Y2 * R * Y3, (Y1, Y2^-1), (Y3^-1 * Y1^-1)^2, Y1^-1 * Y2^24, Y1^25 ] Map:: R = (1, 51, 2, 52, 6, 56, 11, 61, 15, 65, 19, 69, 23, 73, 27, 77, 31, 81, 35, 85, 39, 89, 43, 93, 47, 97, 49, 99, 46, 96, 41, 91, 38, 88, 33, 83, 30, 80, 25, 75, 22, 72, 17, 67, 14, 64, 9, 59, 4, 54)(3, 53, 7, 57, 5, 55, 8, 58, 12, 62, 16, 66, 20, 70, 24, 74, 28, 78, 32, 82, 36, 86, 40, 90, 44, 94, 48, 98, 50, 100, 45, 95, 42, 92, 37, 87, 34, 84, 29, 79, 26, 76, 21, 71, 18, 68, 13, 63, 10, 60)(101, 151, 103, 153, 109, 159, 113, 163, 117, 167, 121, 171, 125, 175, 129, 179, 133, 183, 137, 187, 141, 191, 145, 195, 149, 199, 148, 198, 143, 193, 140, 190, 135, 185, 132, 182, 127, 177, 124, 174, 119, 169, 116, 166, 111, 161, 108, 158, 102, 152, 107, 157, 104, 154, 110, 160, 114, 164, 118, 168, 122, 172, 126, 176, 130, 180, 134, 184, 138, 188, 142, 192, 146, 196, 150, 200, 147, 197, 144, 194, 139, 189, 136, 186, 131, 181, 128, 178, 123, 173, 120, 170, 115, 165, 112, 162, 106, 156, 105, 155) L = (1, 103)(2, 107)(3, 109)(4, 110)(5, 101)(6, 105)(7, 104)(8, 102)(9, 113)(10, 114)(11, 108)(12, 106)(13, 117)(14, 118)(15, 112)(16, 111)(17, 121)(18, 122)(19, 116)(20, 115)(21, 125)(22, 126)(23, 120)(24, 119)(25, 129)(26, 130)(27, 124)(28, 123)(29, 133)(30, 134)(31, 128)(32, 127)(33, 137)(34, 138)(35, 132)(36, 131)(37, 141)(38, 142)(39, 136)(40, 135)(41, 145)(42, 146)(43, 140)(44, 139)(45, 149)(46, 150)(47, 144)(48, 143)(49, 148)(50, 147)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) 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 ) } Outer automorphisms :: reflexible Dual of E12.695 Graph:: bipartite v = 3 e = 100 f = 75 degree seq :: [ 50^2, 100 ] E12.695 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 25, 50}) Quotient :: dipole Aut^+ = C50 (small group id <50, 2>) Aut = D100 (small group id <100, 4>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3^-1 * Y2 * Y3 * Y2, Y3^25 * Y2, (Y3^-1 * Y1^-1)^50 ] Map:: R = (1, 51)(2, 52)(3, 53)(4, 54)(5, 55)(6, 56)(7, 57)(8, 58)(9, 59)(10, 60)(11, 61)(12, 62)(13, 63)(14, 64)(15, 65)(16, 66)(17, 67)(18, 68)(19, 69)(20, 70)(21, 71)(22, 72)(23, 73)(24, 74)(25, 75)(26, 76)(27, 77)(28, 78)(29, 79)(30, 80)(31, 81)(32, 82)(33, 83)(34, 84)(35, 85)(36, 86)(37, 87)(38, 88)(39, 89)(40, 90)(41, 91)(42, 92)(43, 93)(44, 94)(45, 95)(46, 96)(47, 97)(48, 98)(49, 99)(50, 100)(101, 151, 102, 152)(103, 153, 105, 155)(104, 154, 106, 156)(107, 157, 109, 159)(108, 158, 110, 160)(111, 161, 113, 163)(112, 162, 114, 164)(115, 165, 117, 167)(116, 166, 118, 168)(119, 169, 121, 171)(120, 170, 122, 172)(123, 173, 125, 175)(124, 174, 126, 176)(127, 177, 129, 179)(128, 178, 130, 180)(131, 181, 133, 183)(132, 182, 134, 184)(135, 185, 137, 187)(136, 186, 138, 188)(139, 189, 141, 191)(140, 190, 142, 192)(143, 193, 145, 195)(144, 194, 146, 196)(147, 197, 149, 199)(148, 198, 150, 200) L = (1, 103)(2, 105)(3, 107)(4, 101)(5, 109)(6, 102)(7, 111)(8, 104)(9, 113)(10, 106)(11, 115)(12, 108)(13, 117)(14, 110)(15, 119)(16, 112)(17, 121)(18, 114)(19, 123)(20, 116)(21, 125)(22, 118)(23, 127)(24, 120)(25, 129)(26, 122)(27, 131)(28, 124)(29, 133)(30, 126)(31, 135)(32, 128)(33, 137)(34, 130)(35, 139)(36, 132)(37, 141)(38, 134)(39, 143)(40, 136)(41, 145)(42, 138)(43, 147)(44, 140)(45, 149)(46, 142)(47, 150)(48, 144)(49, 148)(50, 146)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) local type(s) :: { ( 50, 100 ), ( 50, 100, 50, 100 ) } Outer automorphisms :: reflexible Dual of E12.694 Graph:: simple bipartite v = 75 e = 100 f = 3 degree seq :: [ 2^50, 4^25 ] E12.696 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 25, 50}) Quotient :: dipole Aut^+ = C50 (small group id <50, 2>) Aut = D100 (small group id <100, 4>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, Y3 * Y1 * Y3 * Y1^-1, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2^-1)^2, Y3 * Y1^-25 ] Map:: R = (1, 51, 2, 52, 5, 55, 9, 59, 13, 63, 17, 67, 21, 71, 25, 75, 29, 79, 33, 83, 37, 87, 41, 91, 45, 95, 49, 99, 47, 97, 43, 93, 39, 89, 35, 85, 31, 81, 27, 77, 23, 73, 19, 69, 15, 65, 11, 61, 7, 57, 3, 53, 6, 56, 10, 60, 14, 64, 18, 68, 22, 72, 26, 76, 30, 80, 34, 84, 38, 88, 42, 92, 46, 96, 50, 100, 48, 98, 44, 94, 40, 90, 36, 86, 32, 82, 28, 78, 24, 74, 20, 70, 16, 66, 12, 62, 8, 58, 4, 54)(101, 151)(102, 152)(103, 153)(104, 154)(105, 155)(106, 156)(107, 157)(108, 158)(109, 159)(110, 160)(111, 161)(112, 162)(113, 163)(114, 164)(115, 165)(116, 166)(117, 167)(118, 168)(119, 169)(120, 170)(121, 171)(122, 172)(123, 173)(124, 174)(125, 175)(126, 176)(127, 177)(128, 178)(129, 179)(130, 180)(131, 181)(132, 182)(133, 183)(134, 184)(135, 185)(136, 186)(137, 187)(138, 188)(139, 189)(140, 190)(141, 191)(142, 192)(143, 193)(144, 194)(145, 195)(146, 196)(147, 197)(148, 198)(149, 199)(150, 200) L = (1, 103)(2, 106)(3, 101)(4, 107)(5, 110)(6, 102)(7, 104)(8, 111)(9, 114)(10, 105)(11, 108)(12, 115)(13, 118)(14, 109)(15, 112)(16, 119)(17, 122)(18, 113)(19, 116)(20, 123)(21, 126)(22, 117)(23, 120)(24, 127)(25, 130)(26, 121)(27, 124)(28, 131)(29, 134)(30, 125)(31, 128)(32, 135)(33, 138)(34, 129)(35, 132)(36, 139)(37, 142)(38, 133)(39, 136)(40, 143)(41, 146)(42, 137)(43, 140)(44, 147)(45, 150)(46, 141)(47, 144)(48, 149)(49, 148)(50, 145)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) local type(s) :: { ( 4, 50 ), ( 4, 50, 4, 50, 4, 50, 4, 50, 4, 50, 4, 50, 4, 50, 4, 50, 4, 50, 4, 50, 4, 50, 4, 50, 4, 50, 4, 50, 4, 50, 4, 50, 4, 50, 4, 50, 4, 50, 4, 50, 4, 50, 4, 50, 4, 50, 4, 50, 4, 50, 4, 50, 4, 50, 4, 50, 4, 50, 4, 50, 4, 50, 4, 50, 4, 50, 4, 50, 4, 50, 4, 50, 4, 50, 4, 50, 4, 50, 4, 50, 4, 50, 4, 50, 4, 50, 4, 50, 4, 50, 4, 50, 4, 50, 4, 50, 4, 50, 4, 50 ) } Outer automorphisms :: reflexible Dual of E12.693 Graph:: bipartite v = 51 e = 100 f = 27 degree seq :: [ 2^50, 100 ] E12.697 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 25, 50}) Quotient :: dipole Aut^+ = C50 (small group id <50, 2>) Aut = D100 (small group id <100, 4>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y1 * Y2 * Y1, (R * Y2 * Y3^-1)^2, Y2^25 * Y1, (Y3 * Y2^-1)^25 ] Map:: R = (1, 51, 2, 52)(3, 53, 5, 55)(4, 54, 6, 56)(7, 57, 9, 59)(8, 58, 10, 60)(11, 61, 13, 63)(12, 62, 14, 64)(15, 65, 17, 67)(16, 66, 18, 68)(19, 69, 21, 71)(20, 70, 22, 72)(23, 73, 25, 75)(24, 74, 26, 76)(27, 77, 29, 79)(28, 78, 30, 80)(31, 81, 33, 83)(32, 82, 34, 84)(35, 85, 37, 87)(36, 86, 38, 88)(39, 89, 41, 91)(40, 90, 42, 92)(43, 93, 45, 95)(44, 94, 46, 96)(47, 97, 49, 99)(48, 98, 50, 100)(101, 151, 103, 153, 107, 157, 111, 161, 115, 165, 119, 169, 123, 173, 127, 177, 131, 181, 135, 185, 139, 189, 143, 193, 147, 197, 150, 200, 146, 196, 142, 192, 138, 188, 134, 184, 130, 180, 126, 176, 122, 172, 118, 168, 114, 164, 110, 160, 106, 156, 102, 152, 105, 155, 109, 159, 113, 163, 117, 167, 121, 171, 125, 175, 129, 179, 133, 183, 137, 187, 141, 191, 145, 195, 149, 199, 148, 198, 144, 194, 140, 190, 136, 186, 132, 182, 128, 178, 124, 174, 120, 170, 116, 166, 112, 162, 108, 158, 104, 154) L = (1, 102)(2, 101)(3, 105)(4, 106)(5, 103)(6, 104)(7, 109)(8, 110)(9, 107)(10, 108)(11, 113)(12, 114)(13, 111)(14, 112)(15, 117)(16, 118)(17, 115)(18, 116)(19, 121)(20, 122)(21, 119)(22, 120)(23, 125)(24, 126)(25, 123)(26, 124)(27, 129)(28, 130)(29, 127)(30, 128)(31, 133)(32, 134)(33, 131)(34, 132)(35, 137)(36, 138)(37, 135)(38, 136)(39, 141)(40, 142)(41, 139)(42, 140)(43, 145)(44, 146)(45, 143)(46, 144)(47, 149)(48, 150)(49, 147)(50, 148)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) local type(s) :: { ( 2, 50, 2, 50 ), ( 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50, 2, 50 ) } Outer automorphisms :: reflexible Dual of E12.698 Graph:: bipartite v = 26 e = 100 f = 52 degree seq :: [ 4^25, 100 ] E12.698 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 25, 50}) Quotient :: dipole Aut^+ = C50 (small group id <50, 2>) Aut = D100 (small group id <100, 4>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^-2 * Y1^-2, (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y1^-1), (R * Y2 * Y3^-1)^2, Y1^-1 * Y3^24, Y1^10 * Y3^-1 * Y1^2 * Y3^-11 * Y1, Y1^25, (Y3 * Y2^-1)^50 ] Map:: R = (1, 51, 2, 52, 6, 56, 11, 61, 15, 65, 19, 69, 23, 73, 27, 77, 31, 81, 35, 85, 39, 89, 43, 93, 47, 97, 49, 99, 46, 96, 41, 91, 38, 88, 33, 83, 30, 80, 25, 75, 22, 72, 17, 67, 14, 64, 9, 59, 4, 54)(3, 53, 7, 57, 5, 55, 8, 58, 12, 62, 16, 66, 20, 70, 24, 74, 28, 78, 32, 82, 36, 86, 40, 90, 44, 94, 48, 98, 50, 100, 45, 95, 42, 92, 37, 87, 34, 84, 29, 79, 26, 76, 21, 71, 18, 68, 13, 63, 10, 60)(101, 151)(102, 152)(103, 153)(104, 154)(105, 155)(106, 156)(107, 157)(108, 158)(109, 159)(110, 160)(111, 161)(112, 162)(113, 163)(114, 164)(115, 165)(116, 166)(117, 167)(118, 168)(119, 169)(120, 170)(121, 171)(122, 172)(123, 173)(124, 174)(125, 175)(126, 176)(127, 177)(128, 178)(129, 179)(130, 180)(131, 181)(132, 182)(133, 183)(134, 184)(135, 185)(136, 186)(137, 187)(138, 188)(139, 189)(140, 190)(141, 191)(142, 192)(143, 193)(144, 194)(145, 195)(146, 196)(147, 197)(148, 198)(149, 199)(150, 200) L = (1, 103)(2, 107)(3, 109)(4, 110)(5, 101)(6, 105)(7, 104)(8, 102)(9, 113)(10, 114)(11, 108)(12, 106)(13, 117)(14, 118)(15, 112)(16, 111)(17, 121)(18, 122)(19, 116)(20, 115)(21, 125)(22, 126)(23, 120)(24, 119)(25, 129)(26, 130)(27, 124)(28, 123)(29, 133)(30, 134)(31, 128)(32, 127)(33, 137)(34, 138)(35, 132)(36, 131)(37, 141)(38, 142)(39, 136)(40, 135)(41, 145)(42, 146)(43, 140)(44, 139)(45, 149)(46, 150)(47, 144)(48, 143)(49, 148)(50, 147)(51, 151)(52, 152)(53, 153)(54, 154)(55, 155)(56, 156)(57, 157)(58, 158)(59, 159)(60, 160)(61, 161)(62, 162)(63, 163)(64, 164)(65, 165)(66, 166)(67, 167)(68, 168)(69, 169)(70, 170)(71, 171)(72, 172)(73, 173)(74, 174)(75, 175)(76, 176)(77, 177)(78, 178)(79, 179)(80, 180)(81, 181)(82, 182)(83, 183)(84, 184)(85, 185)(86, 186)(87, 187)(88, 188)(89, 189)(90, 190)(91, 191)(92, 192)(93, 193)(94, 194)(95, 195)(96, 196)(97, 197)(98, 198)(99, 199)(100, 200) local type(s) :: { ( 4, 100 ), ( 4, 100, 4, 100, 4, 100, 4, 100, 4, 100, 4, 100, 4, 100, 4, 100, 4, 100, 4, 100, 4, 100, 4, 100, 4, 100, 4, 100, 4, 100, 4, 100, 4, 100, 4, 100, 4, 100, 4, 100, 4, 100, 4, 100, 4, 100, 4, 100, 4, 100 ) } Outer automorphisms :: reflexible Dual of E12.697 Graph:: simple bipartite v = 52 e = 100 f = 26 degree seq :: [ 2^50, 50^2 ] E12.699 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 13}) Quotient :: dipole Aut^+ = D52 (small group id <52, 4>) Aut = C2 x C2 x D26 (small group id <104, 13>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y1)^2, (Y2 * Y1)^2, (R * Y3)^2, (Y3 * Y1)^13 ] Map:: polytopal non-degenerate R = (1, 53, 2, 54)(3, 55, 5, 57)(4, 56, 8, 60)(6, 58, 10, 62)(7, 59, 11, 63)(9, 61, 13, 65)(12, 64, 16, 68)(14, 66, 18, 70)(15, 67, 19, 71)(17, 69, 21, 73)(20, 72, 24, 76)(22, 74, 26, 78)(23, 75, 27, 79)(25, 77, 29, 81)(28, 80, 32, 84)(30, 82, 34, 86)(31, 83, 35, 87)(33, 85, 37, 89)(36, 88, 40, 92)(38, 90, 42, 94)(39, 91, 43, 95)(41, 93, 45, 97)(44, 96, 48, 100)(46, 98, 50, 102)(47, 99, 51, 103)(49, 101, 52, 104)(105, 157, 107, 159)(106, 158, 109, 161)(108, 160, 111, 163)(110, 162, 113, 165)(112, 164, 115, 167)(114, 166, 117, 169)(116, 168, 119, 171)(118, 170, 121, 173)(120, 172, 123, 175)(122, 174, 125, 177)(124, 176, 127, 179)(126, 178, 129, 181)(128, 180, 131, 183)(130, 182, 133, 185)(132, 184, 135, 187)(134, 186, 137, 189)(136, 188, 139, 191)(138, 190, 141, 193)(140, 192, 143, 195)(142, 194, 145, 197)(144, 196, 147, 199)(146, 198, 149, 201)(148, 200, 151, 203)(150, 202, 153, 205)(152, 204, 155, 207)(154, 206, 156, 208) L = (1, 108)(2, 110)(3, 111)(4, 105)(5, 113)(6, 106)(7, 107)(8, 116)(9, 109)(10, 118)(11, 119)(12, 112)(13, 121)(14, 114)(15, 115)(16, 124)(17, 117)(18, 126)(19, 127)(20, 120)(21, 129)(22, 122)(23, 123)(24, 132)(25, 125)(26, 134)(27, 135)(28, 128)(29, 137)(30, 130)(31, 131)(32, 140)(33, 133)(34, 142)(35, 143)(36, 136)(37, 145)(38, 138)(39, 139)(40, 148)(41, 141)(42, 150)(43, 151)(44, 144)(45, 153)(46, 146)(47, 147)(48, 154)(49, 149)(50, 152)(51, 156)(52, 155)(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) :: { ( 4, 26, 4, 26 ) } Outer automorphisms :: reflexible Dual of E12.700 Graph:: simple bipartite v = 52 e = 104 f = 30 degree seq :: [ 4^52 ] E12.700 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 13}) Quotient :: dipole Aut^+ = D52 (small group id <52, 4>) Aut = C2 x C2 x D26 (small group id <104, 13>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (R * Y2)^2, (R * Y3)^2, (Y3 * Y1^-1)^2, (Y3 * Y2)^2, (Y1^-1 * Y2)^2, (R * Y1)^2, Y1^13 ] Map:: polytopal non-degenerate R = (1, 53, 2, 54, 6, 58, 13, 65, 21, 73, 29, 81, 37, 89, 44, 96, 36, 88, 28, 80, 20, 72, 12, 64, 5, 57)(3, 55, 9, 61, 17, 69, 25, 77, 33, 85, 41, 93, 48, 100, 45, 97, 38, 90, 30, 82, 22, 74, 14, 66, 7, 59)(4, 56, 11, 63, 19, 71, 27, 79, 35, 87, 43, 95, 50, 102, 46, 98, 39, 91, 31, 83, 23, 75, 15, 67, 8, 60)(10, 62, 16, 68, 24, 76, 32, 84, 40, 92, 47, 99, 51, 103, 52, 104, 49, 101, 42, 94, 34, 86, 26, 78, 18, 70)(105, 157, 107, 159)(106, 158, 111, 163)(108, 160, 114, 166)(109, 161, 113, 165)(110, 162, 118, 170)(112, 164, 120, 172)(115, 167, 122, 174)(116, 168, 121, 173)(117, 169, 126, 178)(119, 171, 128, 180)(123, 175, 130, 182)(124, 176, 129, 181)(125, 177, 134, 186)(127, 179, 136, 188)(131, 183, 138, 190)(132, 184, 137, 189)(133, 185, 142, 194)(135, 187, 144, 196)(139, 191, 146, 198)(140, 192, 145, 197)(141, 193, 149, 201)(143, 195, 151, 203)(147, 199, 153, 205)(148, 200, 152, 204)(150, 202, 155, 207)(154, 206, 156, 208) L = (1, 108)(2, 112)(3, 114)(4, 105)(5, 115)(6, 119)(7, 120)(8, 106)(9, 122)(10, 107)(11, 109)(12, 123)(13, 127)(14, 128)(15, 110)(16, 111)(17, 130)(18, 113)(19, 116)(20, 131)(21, 135)(22, 136)(23, 117)(24, 118)(25, 138)(26, 121)(27, 124)(28, 139)(29, 143)(30, 144)(31, 125)(32, 126)(33, 146)(34, 129)(35, 132)(36, 147)(37, 150)(38, 151)(39, 133)(40, 134)(41, 153)(42, 137)(43, 140)(44, 154)(45, 155)(46, 141)(47, 142)(48, 156)(49, 145)(50, 148)(51, 149)(52, 152)(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) :: { ( 4^4 ), ( 4^26 ) } Outer automorphisms :: reflexible Dual of E12.699 Graph:: simple bipartite v = 30 e = 104 f = 52 degree seq :: [ 4^26, 26^4 ] E12.701 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 4, 13}) Quotient :: edge Aut^+ = C13 : C4 (small group id <52, 1>) Aut = (C26 x C2) : C2 (small group id <104, 8>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T2 * T1 * T2 * T1^-1, T2^13 ] Map:: non-degenerate R = (1, 3, 9, 17, 25, 33, 41, 44, 36, 28, 20, 12, 5)(2, 7, 15, 23, 31, 39, 47, 48, 40, 32, 24, 16, 8)(4, 11, 19, 27, 35, 43, 50, 49, 42, 34, 26, 18, 10)(6, 13, 21, 29, 37, 45, 51, 52, 46, 38, 30, 22, 14)(53, 54, 58, 56)(55, 60, 65, 62)(57, 59, 66, 63)(61, 68, 73, 70)(64, 67, 74, 71)(69, 76, 81, 78)(72, 75, 82, 79)(77, 84, 89, 86)(80, 83, 90, 87)(85, 92, 97, 94)(88, 91, 98, 95)(93, 100, 103, 101)(96, 99, 104, 102) L = (1, 53)(2, 54)(3, 55)(4, 56)(5, 57)(6, 58)(7, 59)(8, 60)(9, 61)(10, 62)(11, 63)(12, 64)(13, 65)(14, 66)(15, 67)(16, 68)(17, 69)(18, 70)(19, 71)(20, 72)(21, 73)(22, 74)(23, 75)(24, 76)(25, 77)(26, 78)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104) local type(s) :: { ( 8^4 ), ( 8^13 ) } Outer automorphisms :: reflexible Dual of E12.702 Transitivity :: ET+ Graph:: simple bipartite v = 17 e = 52 f = 13 degree seq :: [ 4^13, 13^4 ] E12.702 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 4, 13}) Quotient :: loop Aut^+ = C13 : C4 (small group id <52, 1>) Aut = (C26 x C2) : C2 (small group id <104, 8>) |r| :: 2 Presentation :: [ F^2, T2^-2 * T1^-2, T2^-2 * T1^2, (F * T2)^2, (F * T1)^2, T2^4, (T2 * T1)^13 ] 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) 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) local type(s) :: { ( 4, 13, 4, 13, 4, 13, 4, 13 ) } Outer automorphisms :: reflexible Dual of E12.701 Transitivity :: ET+ VT+ AT Graph:: v = 13 e = 52 f = 17 degree seq :: [ 8^13 ] E12.703 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 13}) Quotient :: dipole Aut^+ = C13 : C4 (small group id <52, 1>) Aut = (C26 x C2) : C2 (small group id <104, 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, Y2^13 ] Map:: R = (1, 53, 2, 54, 6, 58, 4, 56)(3, 55, 8, 60, 13, 65, 10, 62)(5, 57, 7, 59, 14, 66, 11, 63)(9, 61, 16, 68, 21, 73, 18, 70)(12, 64, 15, 67, 22, 74, 19, 71)(17, 69, 24, 76, 29, 81, 26, 78)(20, 72, 23, 75, 30, 82, 27, 79)(25, 77, 32, 84, 37, 89, 34, 86)(28, 80, 31, 83, 38, 90, 35, 87)(33, 85, 40, 92, 45, 97, 42, 94)(36, 88, 39, 91, 46, 98, 43, 95)(41, 93, 48, 100, 51, 103, 49, 101)(44, 96, 47, 99, 52, 104, 50, 102)(105, 157, 107, 159, 113, 165, 121, 173, 129, 181, 137, 189, 145, 197, 148, 200, 140, 192, 132, 184, 124, 176, 116, 168, 109, 161)(106, 158, 111, 163, 119, 171, 127, 179, 135, 187, 143, 195, 151, 203, 152, 204, 144, 196, 136, 188, 128, 180, 120, 172, 112, 164)(108, 160, 115, 167, 123, 175, 131, 183, 139, 191, 147, 199, 154, 206, 153, 205, 146, 198, 138, 190, 130, 182, 122, 174, 114, 166)(110, 162, 117, 169, 125, 177, 133, 185, 141, 193, 149, 201, 155, 207, 156, 208, 150, 202, 142, 194, 134, 186, 126, 178, 118, 170) L = (1, 107)(2, 111)(3, 113)(4, 115)(5, 105)(6, 117)(7, 119)(8, 106)(9, 121)(10, 108)(11, 123)(12, 109)(13, 125)(14, 110)(15, 127)(16, 112)(17, 129)(18, 114)(19, 131)(20, 116)(21, 133)(22, 118)(23, 135)(24, 120)(25, 137)(26, 122)(27, 139)(28, 124)(29, 141)(30, 126)(31, 143)(32, 128)(33, 145)(34, 130)(35, 147)(36, 132)(37, 149)(38, 134)(39, 151)(40, 136)(41, 148)(42, 138)(43, 154)(44, 140)(45, 155)(46, 142)(47, 152)(48, 144)(49, 146)(50, 153)(51, 156)(52, 150)(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) :: { ( 2, 8, 2, 8, 2, 8, 2, 8 ), ( 2, 8, 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 E12.704 Graph:: bipartite v = 17 e = 104 f = 65 degree seq :: [ 8^13, 26^4 ] E12.704 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 13}) Quotient :: dipole Aut^+ = C13 : C4 (small group id <52, 1>) Aut = (C26 x C2) : C2 (small group id <104, 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, (Y3^-1 * Y1^-1)^13 ] Map:: R = (1, 53)(2, 54)(3, 55)(4, 56)(5, 57)(6, 58)(7, 59)(8, 60)(9, 61)(10, 62)(11, 63)(12, 64)(13, 65)(14, 66)(15, 67)(16, 68)(17, 69)(18, 70)(19, 71)(20, 72)(21, 73)(22, 74)(23, 75)(24, 76)(25, 77)(26, 78)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104)(105, 157, 106, 158, 110, 162, 108, 160)(107, 159, 112, 164, 117, 169, 114, 166)(109, 161, 111, 163, 118, 170, 115, 167)(113, 165, 120, 172, 125, 177, 122, 174)(116, 168, 119, 171, 126, 178, 123, 175)(121, 173, 128, 180, 133, 185, 130, 182)(124, 176, 127, 179, 134, 186, 131, 183)(129, 181, 136, 188, 141, 193, 138, 190)(132, 184, 135, 187, 142, 194, 139, 191)(137, 189, 144, 196, 149, 201, 146, 198)(140, 192, 143, 195, 150, 202, 147, 199)(145, 197, 152, 204, 155, 207, 153, 205)(148, 200, 151, 203, 156, 208, 154, 206) L = (1, 107)(2, 111)(3, 113)(4, 115)(5, 105)(6, 117)(7, 119)(8, 106)(9, 121)(10, 108)(11, 123)(12, 109)(13, 125)(14, 110)(15, 127)(16, 112)(17, 129)(18, 114)(19, 131)(20, 116)(21, 133)(22, 118)(23, 135)(24, 120)(25, 137)(26, 122)(27, 139)(28, 124)(29, 141)(30, 126)(31, 143)(32, 128)(33, 145)(34, 130)(35, 147)(36, 132)(37, 149)(38, 134)(39, 151)(40, 136)(41, 148)(42, 138)(43, 154)(44, 140)(45, 155)(46, 142)(47, 152)(48, 144)(49, 146)(50, 153)(51, 156)(52, 150)(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, 26 ), ( 8, 26, 8, 26, 8, 26, 8, 26 ) } Outer automorphisms :: reflexible Dual of E12.703 Graph:: simple bipartite v = 65 e = 104 f = 17 degree seq :: [ 2^52, 8^13 ] E12.705 :: Family: { 5 } :: Oriented family(ies): { E3a } Signature :: (0; {4, 4, 13}) Quotient :: edge Aut^+ = C13 : C4 (small group id <52, 3>) Aut = C13 : C4 (small group id <52, 3>) |r| :: 1 Presentation :: [ X1^4, (X2^-1 * X1^-2)^2, X1 * X2^-3 * X1^-1 * X2^2, X1 * X2^-2 * X1^-1 * X2^-3, (X2^-1 * X1 * X2 * X1)^2, X2 * X1 * X2 * X1^-1 * X2^-1 * X1 * X2^-1 * X1^-1, X2^13 ] Map:: polytopal non-degenerate R = (1, 2, 6, 4)(3, 9, 18, 11)(5, 14, 17, 15)(7, 19, 13, 21)(8, 22, 12, 23)(10, 27, 42, 29)(16, 38, 41, 39)(20, 45, 33, 40)(24, 52, 32, 28)(25, 44, 31, 46)(26, 49, 30, 50)(34, 43, 37, 47)(35, 48, 36, 51)(53, 55, 62, 80, 99, 73, 98, 103, 75, 102, 92, 68, 57)(54, 59, 72, 79, 87, 66, 86, 78, 61, 77, 90, 76, 60)(56, 64, 84, 91, 83, 63, 82, 89, 67, 88, 81, 85, 65)(58, 69, 93, 97, 101, 74, 100, 96, 71, 95, 104, 94, 70) L = (1, 53)(2, 54)(3, 55)(4, 56)(5, 57)(6, 58)(7, 59)(8, 60)(9, 61)(10, 62)(11, 63)(12, 64)(13, 65)(14, 66)(15, 67)(16, 68)(17, 69)(18, 70)(19, 71)(20, 72)(21, 73)(22, 74)(23, 75)(24, 76)(25, 77)(26, 78)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104) local type(s) :: { ( 8^4 ), ( 8^13 ) } Outer automorphisms :: chiral Transitivity :: ET+ Graph:: simple bipartite v = 17 e = 52 f = 13 degree seq :: [ 4^13, 13^4 ] E12.706 :: Family: { 5* } :: Oriented family(ies): { E3*a } Signature :: (0; {4, 4, 13}) Quotient :: loop Aut^+ = C13 : C4 (small group id <52, 3>) Aut = C13 : C4 (small group id <52, 3>) |r| :: 1 Presentation :: [ (X2 * X1^-1)^2, X1^4, X2^4, X2^2 * X1^-2 * X2^2 * X1 * X2 * X1^-2, X2 * X1 * X2^2 * X1^-2 * X2^-1 * X1^-1 * X2^-1 * X1^-1 ] Map:: polytopal non-degenerate 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) L = (1, 55)(2, 59)(3, 62)(4, 63)(5, 53)(6, 66)(7, 69)(8, 54)(9, 71)(10, 57)(11, 75)(12, 56)(13, 73)(14, 79)(15, 58)(16, 81)(17, 60)(18, 83)(19, 86)(20, 61)(21, 88)(22, 89)(23, 64)(24, 91)(25, 65)(26, 94)(27, 67)(28, 96)(29, 99)(30, 68)(31, 101)(32, 70)(33, 103)(34, 72)(35, 97)(36, 77)(37, 102)(38, 74)(39, 100)(40, 76)(41, 95)(42, 93)(43, 78)(44, 87)(45, 80)(46, 85)(47, 82)(48, 92)(49, 84)(50, 90)(51, 104)(52, 98) local type(s) :: { ( 4, 13, 4, 13, 4, 13, 4, 13 ) } Outer automorphisms :: chiral Transitivity :: ET+ VT+ Graph:: v = 13 e = 52 f = 17 degree seq :: [ 8^13 ] E12.707 :: Family: { 2*ex } :: Oriented family(ies): { E3c } Signature :: (0; {4, 4, 13}) Quotient :: loop Aut^+ = C13 : C4 (small group id <52, 3>) Aut = C2 x (C13 : C4) (small group id <104, 12>) |r| :: 2 Presentation :: [ F^2, F * T2 * F * T1, (T1^-1 * T2)^2, T1^4, T2^4, T2 * T1 * T2^-2 * T1 * T2 * T1 * T2 * T1^-2, (T2^-1 * T1^-1)^13 ] Map:: polytopal non-degenerate R = (1, 3, 10, 5)(2, 7, 17, 8)(4, 11, 23, 12)(6, 14, 27, 15)(9, 19, 34, 20)(13, 21, 36, 25)(16, 29, 47, 30)(18, 31, 49, 32)(22, 37, 50, 38)(24, 39, 48, 40)(26, 42, 41, 43)(28, 44, 35, 45)(33, 51, 52, 46)(53, 54, 58, 56)(55, 61, 70, 60)(57, 63, 74, 65)(59, 68, 80, 67)(62, 73, 87, 72)(64, 66, 78, 76)(69, 83, 100, 82)(71, 85, 102, 84)(75, 91, 101, 90)(77, 89, 103, 93)(79, 96, 88, 95)(81, 98, 86, 97)(92, 94, 104, 99) L = (1, 53)(2, 54)(3, 55)(4, 56)(5, 57)(6, 58)(7, 59)(8, 60)(9, 61)(10, 62)(11, 63)(12, 64)(13, 65)(14, 66)(15, 67)(16, 68)(17, 69)(18, 70)(19, 71)(20, 72)(21, 73)(22, 74)(23, 75)(24, 76)(25, 77)(26, 78)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104) local type(s) :: { ( 26^4 ) } Outer automorphisms :: reflexible Dual of E12.708 Transitivity :: ET+ VT AT Graph:: simple bipartite v = 26 e = 52 f = 4 degree seq :: [ 4^26 ] E12.708 :: Family: { 2ex } :: Oriented family(ies): { E3*c } Signature :: (0; {4, 4, 13}) Quotient :: edge Aut^+ = C13 : C4 (small group id <52, 3>) Aut = C2 x (C13 : C4) (small group id <104, 12>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, T1^4, F * T1 * T2 * F * T1^-1, (T1 * T2^-1 * T1)^2, T2 * T1 * T2^2 * T1^-1 * T2^2, T1 * T2^3 * T1^-1 * T2^-2, (T2^-1 * T1 * F * T1^-1)^2, (T2^-1 * T1^-1)^4, T2 * T1 * T2 * T1^-1 * T2^-1 * T1 * T2^-1 * T1^-1, T2^13 ] Map:: polytopal non-degenerate R = (1, 53, 3, 55, 10, 62, 28, 80, 47, 99, 21, 73, 46, 98, 51, 103, 23, 75, 50, 102, 40, 92, 16, 68, 5, 57)(2, 54, 7, 59, 20, 72, 27, 79, 35, 87, 14, 66, 34, 86, 26, 78, 9, 61, 25, 77, 38, 90, 24, 76, 8, 60)(4, 56, 12, 64, 32, 84, 39, 91, 31, 83, 11, 63, 30, 82, 37, 89, 15, 67, 36, 88, 29, 81, 33, 85, 13, 65)(6, 58, 17, 69, 41, 93, 45, 97, 49, 101, 22, 74, 48, 100, 44, 96, 19, 71, 43, 95, 52, 104, 42, 94, 18, 70) L = (1, 54)(2, 58)(3, 61)(4, 53)(5, 66)(6, 56)(7, 71)(8, 74)(9, 70)(10, 79)(11, 55)(12, 75)(13, 73)(14, 69)(15, 57)(16, 90)(17, 67)(18, 63)(19, 65)(20, 97)(21, 59)(22, 64)(23, 60)(24, 104)(25, 96)(26, 101)(27, 94)(28, 76)(29, 62)(30, 102)(31, 98)(32, 80)(33, 92)(34, 95)(35, 100)(36, 103)(37, 99)(38, 93)(39, 68)(40, 72)(41, 91)(42, 81)(43, 89)(44, 83)(45, 85)(46, 77)(47, 86)(48, 88)(49, 82)(50, 78)(51, 87)(52, 84) local type(s) :: { ( 4^26 ) } Outer automorphisms :: reflexible Dual of E12.707 Transitivity :: ET+ VT+ Graph:: bipartite v = 4 e = 52 f = 26 degree seq :: [ 26^4 ] E12.709 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 13}) Quotient :: edge^2 Aut^+ = C13 : C4 (small group id <52, 3>) Aut = C2 x (C13 : C4) (small group id <104, 12>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y2^-1 * Y1^-1, Y2^4, Y1^4, (R * Y3)^2, (Y1 * Y2^-1)^2, R * Y2 * R * Y1, Y3^2 * Y1^-1 * Y3^2 * Y2^-1, Y3 * Y2^-1 * Y3^-3 * Y1^-1, Y1^-1 * Y2^-1 * Y3^5 ] Map:: polytopal non-degenerate R = (1, 53, 4, 56, 16, 68, 43, 95, 29, 81, 12, 64, 36, 88, 34, 86, 21, 73, 46, 98, 38, 90, 27, 79, 7, 59)(2, 54, 9, 61, 30, 82, 18, 70, 47, 99, 24, 76, 51, 103, 23, 75, 6, 58, 22, 74, 50, 102, 35, 87, 11, 63)(3, 55, 5, 57, 20, 72, 49, 101, 41, 93, 15, 67, 17, 69, 45, 97, 25, 77, 26, 78, 42, 94, 40, 92, 14, 66)(8, 60, 28, 80, 39, 91, 31, 83, 48, 100, 33, 85, 37, 89, 13, 65, 10, 62, 32, 84, 52, 104, 44, 96, 19, 71)(105, 106, 112, 109)(107, 116, 113, 114)(108, 110, 123, 121)(111, 128, 132, 130)(115, 137, 124, 125)(117, 119, 140, 126)(118, 142, 134, 135)(120, 122, 148, 144)(127, 152, 149, 150)(129, 133, 155, 136)(131, 154, 143, 145)(138, 151, 141, 146)(139, 156, 153, 147)(157, 159, 169, 162)(158, 163, 181, 166)(160, 171, 193, 174)(161, 175, 179, 177)(164, 167, 190, 182)(165, 185, 201, 187)(168, 170, 195, 178)(172, 198, 189, 191)(173, 200, 186, 202)(176, 204, 207, 199)(180, 183, 205, 188)(184, 203, 192, 197)(194, 196, 208, 206) 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) :: { ( 4^4 ), ( 4^26 ) } Outer automorphisms :: reflexible Dual of E12.712 Graph:: simple bipartite v = 30 e = 104 f = 52 degree seq :: [ 4^26, 26^4 ] E12.710 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 13}) Quotient :: edge^2 Aut^+ = C13 : C4 (small group id <52, 3>) Aut = C2 x (C13 : C4) (small group id <104, 12>) |r| :: 2 Presentation :: [ Y3, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y2 * Y1^-1)^2, Y1^4, Y2^4, Y2 * Y1 * Y2^2 * Y1^-2 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, Y2^2 * Y1^-2 * Y2^2 * Y1 * Y2 * Y1^-2, (Y1^-1 * Y3^-1 * Y2^-1)^13 ] Map:: polytopal R = (1, 53)(2, 54)(3, 55)(4, 56)(5, 57)(6, 58)(7, 59)(8, 60)(9, 61)(10, 62)(11, 63)(12, 64)(13, 65)(14, 66)(15, 67)(16, 68)(17, 69)(18, 70)(19, 71)(20, 72)(21, 73)(22, 74)(23, 75)(24, 76)(25, 77)(26, 78)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104)(105, 106, 110, 108)(107, 113, 122, 112)(109, 115, 126, 117)(111, 120, 132, 119)(114, 125, 139, 124)(116, 118, 130, 128)(121, 135, 152, 134)(123, 137, 154, 136)(127, 143, 153, 142)(129, 141, 155, 145)(131, 148, 140, 147)(133, 150, 138, 149)(144, 146, 156, 151)(157, 159, 166, 161)(158, 163, 173, 164)(160, 167, 179, 168)(162, 170, 183, 171)(165, 175, 190, 176)(169, 177, 192, 181)(172, 185, 203, 186)(174, 187, 205, 188)(178, 193, 206, 194)(180, 195, 204, 196)(182, 198, 197, 199)(184, 200, 191, 201)(189, 207, 208, 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) :: { ( 52, 52 ), ( 52^4 ) } Outer automorphisms :: reflexible Dual of E12.711 Graph:: simple bipartite v = 78 e = 104 f = 4 degree seq :: [ 2^52, 4^26 ] E12.711 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 13}) Quotient :: loop^2 Aut^+ = C13 : C4 (small group id <52, 3>) Aut = C2 x (C13 : C4) (small group id <104, 12>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y2^-1 * Y1^-1, Y2^4, Y1^4, (R * Y3)^2, (Y1 * Y2^-1)^2, R * Y2 * R * Y1, Y3^2 * Y1^-1 * Y3^2 * Y2^-1, Y3 * Y2^-1 * Y3^-3 * Y1^-1, Y1^-1 * Y2^-1 * Y3^5 ] Map:: R = (1, 53, 105, 157, 4, 56, 108, 160, 16, 68, 120, 172, 43, 95, 147, 199, 29, 81, 133, 185, 12, 64, 116, 168, 36, 88, 140, 192, 34, 86, 138, 190, 21, 73, 125, 177, 46, 98, 150, 202, 38, 90, 142, 194, 27, 79, 131, 183, 7, 59, 111, 163)(2, 54, 106, 158, 9, 61, 113, 165, 30, 82, 134, 186, 18, 70, 122, 174, 47, 99, 151, 203, 24, 76, 128, 180, 51, 103, 155, 207, 23, 75, 127, 179, 6, 58, 110, 162, 22, 74, 126, 178, 50, 102, 154, 206, 35, 87, 139, 191, 11, 63, 115, 167)(3, 55, 107, 159, 5, 57, 109, 161, 20, 72, 124, 176, 49, 101, 153, 205, 41, 93, 145, 197, 15, 67, 119, 171, 17, 69, 121, 173, 45, 97, 149, 201, 25, 77, 129, 181, 26, 78, 130, 182, 42, 94, 146, 198, 40, 92, 144, 196, 14, 66, 118, 170)(8, 60, 112, 164, 28, 80, 132, 184, 39, 91, 143, 195, 31, 83, 135, 187, 48, 100, 152, 204, 33, 85, 137, 189, 37, 89, 141, 193, 13, 65, 117, 169, 10, 62, 114, 166, 32, 84, 136, 188, 52, 104, 156, 208, 44, 96, 148, 200, 19, 71, 123, 175) L = (1, 54)(2, 60)(3, 64)(4, 58)(5, 53)(6, 71)(7, 76)(8, 57)(9, 62)(10, 55)(11, 85)(12, 61)(13, 67)(14, 90)(15, 88)(16, 70)(17, 56)(18, 96)(19, 69)(20, 73)(21, 63)(22, 65)(23, 100)(24, 80)(25, 81)(26, 59)(27, 102)(28, 78)(29, 103)(30, 83)(31, 66)(32, 77)(33, 72)(34, 99)(35, 104)(36, 74)(37, 94)(38, 82)(39, 93)(40, 68)(41, 79)(42, 86)(43, 87)(44, 92)(45, 98)(46, 75)(47, 89)(48, 97)(49, 95)(50, 91)(51, 84)(52, 101)(105, 159)(106, 163)(107, 169)(108, 171)(109, 175)(110, 157)(111, 181)(112, 167)(113, 185)(114, 158)(115, 190)(116, 170)(117, 162)(118, 195)(119, 193)(120, 198)(121, 200)(122, 160)(123, 179)(124, 204)(125, 161)(126, 168)(127, 177)(128, 183)(129, 166)(130, 164)(131, 205)(132, 203)(133, 201)(134, 202)(135, 165)(136, 180)(137, 191)(138, 182)(139, 172)(140, 197)(141, 174)(142, 196)(143, 178)(144, 208)(145, 184)(146, 189)(147, 176)(148, 186)(149, 187)(150, 173)(151, 192)(152, 207)(153, 188)(154, 194)(155, 199)(156, 206) 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 ) } Outer automorphisms :: reflexible Dual of E12.710 Transitivity :: VT+ Graph:: bipartite v = 4 e = 104 f = 78 degree seq :: [ 52^4 ] E12.712 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 13}) Quotient :: loop^2 Aut^+ = C13 : C4 (small group id <52, 3>) Aut = C2 x (C13 : C4) (small group id <104, 12>) |r| :: 2 Presentation :: [ Y3, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y2 * Y1^-1)^2, Y1^4, Y2^4, Y2 * Y1 * Y2^2 * Y1^-2 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, Y2^2 * Y1^-2 * Y2^2 * Y1 * Y2 * Y1^-2, (Y1^-1 * Y3^-1 * Y2^-1)^13 ] Map:: polytopal non-degenerate R = (1, 53, 105, 157)(2, 54, 106, 158)(3, 55, 107, 159)(4, 56, 108, 160)(5, 57, 109, 161)(6, 58, 110, 162)(7, 59, 111, 163)(8, 60, 112, 164)(9, 61, 113, 165)(10, 62, 114, 166)(11, 63, 115, 167)(12, 64, 116, 168)(13, 65, 117, 169)(14, 66, 118, 170)(15, 67, 119, 171)(16, 68, 120, 172)(17, 69, 121, 173)(18, 70, 122, 174)(19, 71, 123, 175)(20, 72, 124, 176)(21, 73, 125, 177)(22, 74, 126, 178)(23, 75, 127, 179)(24, 76, 128, 180)(25, 77, 129, 181)(26, 78, 130, 182)(27, 79, 131, 183)(28, 80, 132, 184)(29, 81, 133, 185)(30, 82, 134, 186)(31, 83, 135, 187)(32, 84, 136, 188)(33, 85, 137, 189)(34, 86, 138, 190)(35, 87, 139, 191)(36, 88, 140, 192)(37, 89, 141, 193)(38, 90, 142, 194)(39, 91, 143, 195)(40, 92, 144, 196)(41, 93, 145, 197)(42, 94, 146, 198)(43, 95, 147, 199)(44, 96, 148, 200)(45, 97, 149, 201)(46, 98, 150, 202)(47, 99, 151, 203)(48, 100, 152, 204)(49, 101, 153, 205)(50, 102, 154, 206)(51, 103, 155, 207)(52, 104, 156, 208) L = (1, 54)(2, 58)(3, 61)(4, 53)(5, 63)(6, 56)(7, 68)(8, 55)(9, 70)(10, 73)(11, 74)(12, 66)(13, 57)(14, 78)(15, 59)(16, 80)(17, 83)(18, 60)(19, 85)(20, 62)(21, 87)(22, 65)(23, 91)(24, 64)(25, 89)(26, 76)(27, 96)(28, 67)(29, 98)(30, 69)(31, 100)(32, 71)(33, 102)(34, 97)(35, 72)(36, 95)(37, 103)(38, 75)(39, 101)(40, 94)(41, 77)(42, 104)(43, 79)(44, 88)(45, 81)(46, 86)(47, 92)(48, 82)(49, 90)(50, 84)(51, 93)(52, 99)(105, 159)(106, 163)(107, 166)(108, 167)(109, 157)(110, 170)(111, 173)(112, 158)(113, 175)(114, 161)(115, 179)(116, 160)(117, 177)(118, 183)(119, 162)(120, 185)(121, 164)(122, 187)(123, 190)(124, 165)(125, 192)(126, 193)(127, 168)(128, 195)(129, 169)(130, 198)(131, 171)(132, 200)(133, 203)(134, 172)(135, 205)(136, 174)(137, 207)(138, 176)(139, 201)(140, 181)(141, 206)(142, 178)(143, 204)(144, 180)(145, 199)(146, 197)(147, 182)(148, 191)(149, 184)(150, 189)(151, 186)(152, 196)(153, 188)(154, 194)(155, 208)(156, 202) local type(s) :: { ( 4, 26, 4, 26 ) } Outer automorphisms :: reflexible Dual of E12.709 Transitivity :: VT+ Graph:: simple bipartite v = 52 e = 104 f = 30 degree seq :: [ 4^52 ] E12.713 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 26, 26}) Quotient :: regular Aut^+ = C26 x C2 (small group id <52, 5>) Aut = C2 x C2 x D26 (small group id <104, 13>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T1^26 ] Map:: R = (1, 2, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 48, 44, 40, 36, 32, 28, 24, 20, 16, 12, 8, 4)(3, 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50, 52, 51, 47, 43, 39, 35, 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, 34)(32, 35)(33, 38)(36, 39)(37, 42)(40, 43)(41, 46)(44, 47)(45, 50)(48, 51)(49, 52) local type(s) :: { ( 26^26 ) } Outer automorphisms :: reflexible selfdual Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 2 e = 26 f = 2 degree seq :: [ 26^2 ] E12.714 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 26, 26}) Quotient :: edge Aut^+ = C26 x C2 (small group id <52, 5>) Aut = C2 x C2 x D26 (small group id <104, 13>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^26 ] Map:: R = (1, 3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 43, 47, 51, 48, 44, 40, 36, 32, 28, 24, 20, 16, 12, 8, 4)(2, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 52, 50, 46, 42, 38, 34, 30, 26, 22, 18, 14, 10, 6)(53, 54)(55, 57)(56, 58)(59, 61)(60, 62)(63, 65)(64, 66)(67, 69)(68, 70)(71, 73)(72, 74)(75, 77)(76, 78)(79, 81)(80, 82)(83, 85)(84, 86)(87, 89)(88, 90)(91, 93)(92, 94)(95, 97)(96, 98)(99, 101)(100, 102)(103, 104) L = (1, 53)(2, 54)(3, 55)(4, 56)(5, 57)(6, 58)(7, 59)(8, 60)(9, 61)(10, 62)(11, 63)(12, 64)(13, 65)(14, 66)(15, 67)(16, 68)(17, 69)(18, 70)(19, 71)(20, 72)(21, 73)(22, 74)(23, 75)(24, 76)(25, 77)(26, 78)(27, 79)(28, 80)(29, 81)(30, 82)(31, 83)(32, 84)(33, 85)(34, 86)(35, 87)(36, 88)(37, 89)(38, 90)(39, 91)(40, 92)(41, 93)(42, 94)(43, 95)(44, 96)(45, 97)(46, 98)(47, 99)(48, 100)(49, 101)(50, 102)(51, 103)(52, 104) local type(s) :: { ( 52, 52 ), ( 52^26 ) } Outer automorphisms :: reflexible Dual of E12.715 Transitivity :: ET+ Graph:: simple bipartite v = 28 e = 52 f = 2 degree seq :: [ 2^26, 26^2 ] E12.715 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 26, 26}) Quotient :: loop Aut^+ = C26 x C2 (small group id <52, 5>) Aut = C2 x C2 x D26 (small group id <104, 13>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^26 ] Map:: R = (1, 53, 3, 55, 7, 59, 11, 63, 15, 67, 19, 71, 23, 75, 27, 79, 31, 83, 35, 87, 39, 91, 43, 95, 47, 99, 51, 103, 48, 100, 44, 96, 40, 92, 36, 88, 32, 84, 28, 80, 24, 76, 20, 72, 16, 68, 12, 64, 8, 60, 4, 56)(2, 54, 5, 57, 9, 61, 13, 65, 17, 69, 21, 73, 25, 77, 29, 81, 33, 85, 37, 89, 41, 93, 45, 97, 49, 101, 52, 104, 50, 102, 46, 98, 42, 94, 38, 90, 34, 86, 30, 82, 26, 78, 22, 74, 18, 70, 14, 66, 10, 62, 6, 58) L = (1, 54)(2, 53)(3, 57)(4, 58)(5, 55)(6, 56)(7, 61)(8, 62)(9, 59)(10, 60)(11, 65)(12, 66)(13, 63)(14, 64)(15, 69)(16, 70)(17, 67)(18, 68)(19, 73)(20, 74)(21, 71)(22, 72)(23, 77)(24, 78)(25, 75)(26, 76)(27, 81)(28, 82)(29, 79)(30, 80)(31, 85)(32, 86)(33, 83)(34, 84)(35, 89)(36, 90)(37, 87)(38, 88)(39, 93)(40, 94)(41, 91)(42, 92)(43, 97)(44, 98)(45, 95)(46, 96)(47, 101)(48, 102)(49, 99)(50, 100)(51, 104)(52, 103) local type(s) :: { ( 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26, 2, 26 ) } Outer automorphisms :: reflexible Dual of E12.714 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 52 f = 28 degree seq :: [ 52^2 ] E12.716 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 26, 26}) Quotient :: dipole Aut^+ = C26 x C2 (small group id <52, 5>) Aut = C2 x C2 x D26 (small group id <104, 13>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y1 * Y2 * Y1, (R * Y2 * Y3^-1)^2, Y2^26, (Y3 * Y2^-1)^26 ] Map:: R = (1, 53, 2, 54)(3, 55, 5, 57)(4, 56, 6, 58)(7, 59, 9, 61)(8, 60, 10, 62)(11, 63, 13, 65)(12, 64, 14, 66)(15, 67, 17, 69)(16, 68, 18, 70)(19, 71, 21, 73)(20, 72, 22, 74)(23, 75, 25, 77)(24, 76, 26, 78)(27, 79, 29, 81)(28, 80, 30, 82)(31, 83, 33, 85)(32, 84, 34, 86)(35, 87, 37, 89)(36, 88, 38, 90)(39, 91, 41, 93)(40, 92, 42, 94)(43, 95, 45, 97)(44, 96, 46, 98)(47, 99, 49, 101)(48, 100, 50, 102)(51, 103, 52, 104)(105, 157, 107, 159, 111, 163, 115, 167, 119, 171, 123, 175, 127, 179, 131, 183, 135, 187, 139, 191, 143, 195, 147, 199, 151, 203, 155, 207, 152, 204, 148, 200, 144, 196, 140, 192, 136, 188, 132, 184, 128, 180, 124, 176, 120, 172, 116, 168, 112, 164, 108, 160)(106, 158, 109, 161, 113, 165, 117, 169, 121, 173, 125, 177, 129, 181, 133, 185, 137, 189, 141, 193, 145, 197, 149, 201, 153, 205, 156, 208, 154, 206, 150, 202, 146, 198, 142, 194, 138, 190, 134, 186, 130, 182, 126, 178, 122, 174, 118, 170, 114, 166, 110, 162) L = (1, 106)(2, 105)(3, 109)(4, 110)(5, 107)(6, 108)(7, 113)(8, 114)(9, 111)(10, 112)(11, 117)(12, 118)(13, 115)(14, 116)(15, 121)(16, 122)(17, 119)(18, 120)(19, 125)(20, 126)(21, 123)(22, 124)(23, 129)(24, 130)(25, 127)(26, 128)(27, 133)(28, 134)(29, 131)(30, 132)(31, 137)(32, 138)(33, 135)(34, 136)(35, 141)(36, 142)(37, 139)(38, 140)(39, 145)(40, 146)(41, 143)(42, 144)(43, 149)(44, 150)(45, 147)(46, 148)(47, 153)(48, 154)(49, 151)(50, 152)(51, 156)(52, 155)(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) :: { ( 2, 52, 2, 52 ), ( 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52, 2, 52 ) } Outer automorphisms :: reflexible Dual of E12.717 Graph:: bipartite v = 28 e = 104 f = 54 degree seq :: [ 4^26, 52^2 ] E12.717 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 26, 26}) Quotient :: dipole Aut^+ = C26 x C2 (small group id <52, 5>) Aut = C2 x C2 x D26 (small group id <104, 13>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2^-1)^2, (Y3^-1, Y1^-1), (R * Y2 * Y3^-1)^2, Y3^-26, Y1^26 ] Map:: R = (1, 53, 2, 54, 5, 57, 9, 61, 13, 65, 17, 69, 21, 73, 25, 77, 29, 81, 33, 85, 37, 89, 41, 93, 45, 97, 49, 101, 48, 100, 44, 96, 40, 92, 36, 88, 32, 84, 28, 80, 24, 76, 20, 72, 16, 68, 12, 64, 8, 60, 4, 56)(3, 55, 6, 58, 10, 62, 14, 66, 18, 70, 22, 74, 26, 78, 30, 82, 34, 86, 38, 90, 42, 94, 46, 98, 50, 102, 52, 104, 51, 103, 47, 99, 43, 95, 39, 91, 35, 87, 31, 83, 27, 79, 23, 75, 19, 71, 15, 67, 11, 63, 7, 59)(105, 157)(106, 158)(107, 159)(108, 160)(109, 161)(110, 162)(111, 163)(112, 164)(113, 165)(114, 166)(115, 167)(116, 168)(117, 169)(118, 170)(119, 171)(120, 172)(121, 173)(122, 174)(123, 175)(124, 176)(125, 177)(126, 178)(127, 179)(128, 180)(129, 181)(130, 182)(131, 183)(132, 184)(133, 185)(134, 186)(135, 187)(136, 188)(137, 189)(138, 190)(139, 191)(140, 192)(141, 193)(142, 194)(143, 195)(144, 196)(145, 197)(146, 198)(147, 199)(148, 200)(149, 201)(150, 202)(151, 203)(152, 204)(153, 205)(154, 206)(155, 207)(156, 208) L = (1, 107)(2, 110)(3, 105)(4, 111)(5, 114)(6, 106)(7, 108)(8, 115)(9, 118)(10, 109)(11, 112)(12, 119)(13, 122)(14, 113)(15, 116)(16, 123)(17, 126)(18, 117)(19, 120)(20, 127)(21, 130)(22, 121)(23, 124)(24, 131)(25, 134)(26, 125)(27, 128)(28, 135)(29, 138)(30, 129)(31, 132)(32, 139)(33, 142)(34, 133)(35, 136)(36, 143)(37, 146)(38, 137)(39, 140)(40, 147)(41, 150)(42, 141)(43, 144)(44, 151)(45, 154)(46, 145)(47, 148)(48, 155)(49, 156)(50, 149)(51, 152)(52, 153)(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) :: { ( 4, 52 ), ( 4, 52, 4, 52, 4, 52, 4, 52, 4, 52, 4, 52, 4, 52, 4, 52, 4, 52, 4, 52, 4, 52, 4, 52, 4, 52, 4, 52, 4, 52, 4, 52, 4, 52, 4, 52, 4, 52, 4, 52, 4, 52, 4, 52, 4, 52, 4, 52, 4, 52, 4, 52 ) } Outer automorphisms :: reflexible Dual of E12.716 Graph:: simple bipartite v = 54 e = 104 f = 28 degree seq :: [ 2^52, 52^2 ] E12.718 :: Family: { 5 } :: Oriented family(ies): { E3a } Signature :: (0; {5, 5, 5}) Quotient :: edge Aut^+ = C11 : C5 (small group id <55, 1>) Aut = C11 : C5 (small group id <55, 1>) |r| :: 1 Presentation :: [ X1^5, X2^5, X1^2 * X2^-1 * X1^-1 * X2^-2, X1^-1 * X2^-1 * X1 * X2 * X1^-1 * X2 * X1^-1, X1 * X2^2 * X1^-1 * X2 * X1 * X2^-1 ] Map:: polytopal non-degenerate R = (1, 2, 6, 13, 4)(3, 9, 26, 31, 11)(5, 15, 27, 42, 16)(7, 20, 43, 17, 22)(8, 23, 47, 50, 24)(10, 19, 39, 53, 29)(12, 33, 30, 41, 34)(14, 37, 55, 49, 38)(18, 44, 28, 25, 45)(21, 36, 40, 54, 32)(35, 51, 48, 46, 52)(56, 58, 65, 72, 60)(57, 62, 76, 80, 63)(59, 67, 79, 86, 69)(61, 73, 93, 101, 74)(64, 82, 105, 107, 83)(66, 85, 99, 108, 87)(68, 90, 71, 96, 91)(70, 94, 92, 78, 95)(75, 102, 84, 89, 103)(77, 81, 106, 109, 104)(88, 110, 97, 100, 98) 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) :: { ( 10^5 ) } Outer automorphisms :: chiral Dual of E12.721 Transitivity :: ET+ Graph:: simple bipartite v = 22 e = 55 f = 11 degree seq :: [ 5^22 ] E12.719 :: Family: { 5 } :: Oriented family(ies): { E3a } Signature :: (0; {5, 5, 5}) Quotient :: edge Aut^+ = C11 : C5 (small group id <55, 1>) Aut = C11 : C5 (small group id <55, 1>) |r| :: 1 Presentation :: [ X2^5, X1^5, X2^5, X1^2 * X2 * X1^-1 * X2^2, X2^-2 * X1 * X2^-1 * X1^-2, X1 * X2^2 * X1^-1 * X2^-1 * X1^-1 * X2 ] Map:: polytopal non-degenerate R = (1, 2, 6, 13, 4)(3, 9, 26, 31, 11)(5, 15, 39, 34, 16)(7, 20, 47, 48, 22)(8, 23, 29, 10, 24)(12, 33, 55, 50, 35)(14, 37, 42, 32, 38)(17, 18, 28, 52, 43)(19, 45, 40, 21, 46)(25, 36, 27, 51, 41)(30, 53, 49, 44, 54)(56, 58, 65, 72, 60)(57, 62, 76, 80, 63)(59, 67, 89, 77, 69)(61, 73, 99, 90, 74)(64, 82, 75, 88, 83)(66, 85, 68, 91, 87)(70, 95, 109, 103, 81)(71, 96, 107, 100, 97)(78, 104, 93, 98, 102)(79, 105, 106, 108, 94)(84, 101, 86, 110, 92) 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) :: { ( 10^5 ) } Outer automorphisms :: chiral Dual of E12.720 Transitivity :: ET+ Graph:: simple bipartite v = 22 e = 55 f = 11 degree seq :: [ 5^22 ] E12.720 :: Family: { 5* } :: Oriented family(ies): { E3*a } Signature :: (0; {5, 5, 5}) Quotient :: loop Aut^+ = C11 : C5 (small group id <55, 1>) Aut = C11 : C5 (small group id <55, 1>) |r| :: 1 Presentation :: [ X1^5, X2^5, X1^2 * X2^-2 * X1^-1 * X2, X1 * X2^2 * X1^-2 * X2^-1, X2^-1 * X1 * X2^2 * X1^-2, X1^-1 * X2 * X1 * X2 * X1^2 * X2, X2 * X1^-1 * X2^-1 * X1^2 * X2 * X1^-2 ] Map:: polytopal non-degenerate R = (1, 56, 2, 57, 6, 61, 13, 68, 4, 59)(3, 58, 9, 64, 21, 76, 31, 86, 11, 66)(5, 60, 15, 70, 39, 94, 41, 96, 16, 71)(7, 62, 20, 75, 40, 95, 47, 102, 22, 77)(8, 63, 23, 78, 49, 104, 26, 81, 24, 79)(10, 65, 28, 83, 34, 89, 12, 67, 29, 84)(14, 69, 25, 80, 52, 107, 55, 110, 37, 92)(17, 72, 43, 98, 48, 103, 30, 85, 36, 91)(18, 73, 44, 99, 50, 105, 27, 82, 42, 97)(19, 74, 38, 93, 54, 109, 32, 87, 45, 100)(33, 88, 46, 101, 51, 106, 35, 90, 53, 108) L = (1, 58)(2, 62)(3, 65)(4, 67)(5, 56)(6, 73)(7, 76)(8, 57)(9, 81)(10, 72)(11, 85)(12, 88)(13, 90)(14, 59)(15, 74)(16, 86)(17, 60)(18, 95)(19, 61)(20, 87)(21, 80)(22, 92)(23, 91)(24, 102)(25, 63)(26, 89)(27, 64)(28, 99)(29, 96)(30, 101)(31, 108)(32, 66)(33, 93)(34, 100)(35, 105)(36, 68)(37, 83)(38, 69)(39, 104)(40, 70)(41, 106)(42, 71)(43, 107)(44, 103)(45, 82)(46, 75)(47, 84)(48, 77)(49, 109)(50, 78)(51, 79)(52, 94)(53, 110)(54, 98)(55, 97) local type(s) :: { ( 5^10 ) } Outer automorphisms :: chiral Dual of E12.719 Transitivity :: ET+ VT+ Graph:: simple v = 11 e = 55 f = 22 degree seq :: [ 10^11 ] E12.721 :: Family: { 5* } :: Oriented family(ies): { E3*a } Signature :: (0; {5, 5, 5}) Quotient :: loop Aut^+ = C11 : C5 (small group id <55, 1>) Aut = C11 : C5 (small group id <55, 1>) |r| :: 1 Presentation :: [ X2^5, X1^5, X2^2 * X1^-1 * X2^-1 * X1^-2, X1^2 * X2 * X1 * X2^-2, X1^2 * X2^-1 * X1 * X2 * X1^-1 * X2, X1 * X2^-1 * X1 * X2 * X1^2 * X2^2, X2 * X1 * X2 * X1^2 * X2 * X1^-2 ] Map:: polytopal non-degenerate R = (1, 56, 2, 57, 6, 61, 13, 68, 4, 59)(3, 58, 9, 64, 26, 81, 31, 86, 11, 66)(5, 60, 15, 70, 32, 87, 25, 80, 16, 71)(7, 62, 20, 75, 47, 102, 49, 104, 22, 77)(8, 63, 23, 78, 50, 105, 46, 101, 24, 79)(10, 65, 29, 84, 42, 97, 44, 99, 18, 73)(12, 67, 33, 88, 41, 96, 30, 85, 34, 89)(14, 69, 36, 91, 43, 98, 17, 72, 37, 92)(19, 74, 40, 95, 52, 107, 27, 82, 45, 100)(21, 76, 48, 103, 51, 106, 53, 108, 28, 83)(35, 90, 39, 94, 55, 110, 38, 93, 54, 109) L = (1, 58)(2, 62)(3, 65)(4, 67)(5, 56)(6, 73)(7, 76)(8, 57)(9, 82)(10, 72)(11, 85)(12, 75)(13, 83)(14, 59)(15, 94)(16, 96)(17, 60)(18, 88)(19, 61)(20, 93)(21, 80)(22, 86)(23, 91)(24, 81)(25, 63)(26, 98)(27, 90)(28, 64)(29, 105)(30, 100)(31, 109)(32, 66)(33, 101)(34, 106)(35, 68)(36, 95)(37, 103)(38, 69)(39, 78)(40, 70)(41, 110)(42, 71)(43, 89)(44, 104)(45, 102)(46, 74)(47, 87)(48, 107)(49, 92)(50, 77)(51, 79)(52, 99)(53, 97)(54, 84)(55, 108) local type(s) :: { ( 5^10 ) } Outer automorphisms :: chiral Dual of E12.718 Transitivity :: ET+ VT+ Graph:: simple v = 11 e = 55 f = 22 degree seq :: [ 10^11 ] E12.722 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 14, 28}) Quotient :: regular Aut^+ = C7 x D8 (small group id <56, 9>) Aut = D8 x D14 (small group id <112, 31>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1^2 * T2 * T1^-2, (T1 * T2 * T1^-1 * T2)^2, T1^-1 * T2 * T1^-3 * T2 * T1^-10 ] Map:: non-degenerate R = (1, 2, 5, 11, 20, 29, 37, 45, 53, 49, 41, 33, 25, 16, 24, 15, 23, 32, 40, 48, 56, 52, 44, 36, 28, 19, 10, 4)(3, 7, 12, 22, 30, 39, 46, 55, 51, 43, 35, 27, 18, 9, 14, 6, 13, 21, 31, 38, 47, 54, 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, 53)(52, 55) local type(s) :: { ( 14^28 ) } Outer automorphisms :: reflexible Dual of E12.723 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 2 e = 28 f = 4 degree seq :: [ 28^2 ] E12.723 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 14, 28}) Quotient :: regular Aut^+ = C7 x D8 (small group id <56, 9>) Aut = D8 x D14 (small group id <112, 31>) |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, T1^14, T1^-1 * T2 * T1^-3 * T2 * T1^-3 * T2 * T1^-3 * T2 * T1^-3 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 ] Map:: non-degenerate R = (1, 2, 5, 11, 20, 29, 37, 45, 44, 36, 28, 19, 10, 4)(3, 7, 12, 22, 30, 39, 46, 53, 50, 42, 34, 26, 17, 8)(6, 13, 21, 31, 38, 47, 52, 51, 43, 35, 27, 18, 9, 14)(15, 23, 32, 40, 48, 54, 56, 55, 49, 41, 33, 25, 16, 24) 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, 52)(47, 54)(51, 55)(53, 56) local type(s) :: { ( 28^14 ) } Outer automorphisms :: reflexible Dual of E12.722 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 4 e = 28 f = 2 degree seq :: [ 14^4 ] E12.724 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 14, 28}) Quotient :: edge Aut^+ = C7 x D8 (small group id <56, 9>) Aut = D8 x D14 (small group id <112, 31>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^2 * T1 * T2^-2 * T1, (T2 * T1 * T2^-1 * T1)^2, T2^14, T2^-1 * T1 * T2^-3 * T1 * T2^-3 * T1 * T2^-3 * T1 * T2^-4 ] Map:: R = (1, 3, 8, 17, 26, 34, 42, 50, 44, 36, 28, 19, 10, 4)(2, 5, 12, 22, 30, 38, 46, 53, 48, 40, 32, 24, 14, 6)(7, 15, 25, 33, 41, 49, 55, 51, 43, 35, 27, 18, 9, 16)(11, 20, 29, 37, 45, 52, 56, 54, 47, 39, 31, 23, 13, 21)(57, 58)(59, 63)(60, 65)(61, 67)(62, 69)(64, 68)(66, 70)(71, 76)(72, 77)(73, 81)(74, 79)(75, 83)(78, 85)(80, 87)(82, 86)(84, 88)(89, 93)(90, 97)(91, 95)(92, 99)(94, 101)(96, 103)(98, 102)(100, 104)(105, 108)(106, 111)(107, 110)(109, 112) 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 ), ( 56^14 ) } Outer automorphisms :: reflexible Dual of E12.728 Transitivity :: ET+ Graph:: simple bipartite v = 32 e = 56 f = 2 degree seq :: [ 2^28, 14^4 ] E12.725 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 14, 28}) Quotient :: edge Aut^+ = C7 x D8 (small group id <56, 9>) Aut = D8 x D14 (small group id <112, 31>) |r| :: 2 Presentation :: [ F^2, (T1 * T2)^2, (F * T1)^2, (F * T2)^2, T1^-2 * T2^-1 * T1 * T2^-1 * T1^-1, T1^-1 * T2 * T1^-1 * T2^-3, T1^-1 * T2 * T1^-1 * T2^5 * T1^-6 ] Map:: polytopal non-degenerate R = (1, 3, 10, 24, 33, 41, 49, 54, 45, 39, 32, 18, 6, 17, 30, 20, 13, 27, 36, 44, 52, 55, 48, 38, 28, 21, 15, 5)(2, 7, 19, 11, 26, 34, 43, 50, 53, 47, 40, 29, 16, 14, 23, 9, 4, 12, 25, 35, 42, 51, 56, 46, 37, 31, 22, 8)(57, 58, 62, 72, 84, 93, 101, 109, 108, 98, 89, 82, 69, 60)(59, 65, 73, 64, 77, 85, 95, 102, 111, 106, 97, 91, 83, 67)(61, 70, 74, 87, 94, 103, 110, 107, 100, 90, 80, 68, 76, 63)(66, 75, 86, 79, 71, 78, 88, 96, 104, 112, 105, 99, 92, 81) 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) :: { ( 4^14 ), ( 4^28 ) } Outer automorphisms :: reflexible Dual of E12.729 Transitivity :: ET+ Graph:: bipartite v = 6 e = 56 f = 28 degree seq :: [ 14^4, 28^2 ] E12.726 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 14, 28}) Quotient :: edge Aut^+ = C7 x D8 (small group id <56, 9>) Aut = D8 x D14 (small group id <112, 31>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1^2 * T2 * T1^-2, (T1 * T2 * T1^-1 * T2)^2, T2 * T1^-3 * T2 * T1^-11 ] Map:: R = (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, 58, 61, 67, 76, 85, 93, 101, 109, 105, 97, 89, 81, 72, 80, 71, 79, 88, 96, 104, 112, 108, 100, 92, 84, 75, 66, 60)(59, 63, 68, 78, 86, 95, 102, 111, 107, 99, 91, 83, 74, 65, 70, 62, 69, 77, 87, 94, 103, 110, 106, 98, 90, 82, 73, 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) :: { ( 28, 28 ), ( 28^28 ) } Outer automorphisms :: reflexible Dual of E12.727 Transitivity :: ET+ Graph:: simple bipartite v = 30 e = 56 f = 4 degree seq :: [ 2^28, 28^2 ] E12.727 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 14, 28}) Quotient :: loop Aut^+ = C7 x D8 (small group id <56, 9>) Aut = D8 x D14 (small group id <112, 31>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^2 * T1 * T2^-2 * T1, (T2 * T1 * T2^-1 * T1)^2, T2^14, T2^-1 * T1 * T2^-3 * T1 * T2^-3 * T1 * T2^-3 * T1 * T2^-4 ] Map:: R = (1, 57, 3, 59, 8, 64, 17, 73, 26, 82, 34, 90, 42, 98, 50, 106, 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, 53, 109, 48, 104, 40, 96, 32, 88, 24, 80, 14, 70, 6, 62)(7, 63, 15, 71, 25, 81, 33, 89, 41, 97, 49, 105, 55, 111, 51, 107, 43, 99, 35, 91, 27, 83, 18, 74, 9, 65, 16, 72)(11, 67, 20, 76, 29, 85, 37, 93, 45, 101, 52, 108, 56, 112, 54, 110, 47, 103, 39, 95, 31, 87, 23, 79, 13, 69, 21, 77) 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, 108)(50, 111)(51, 110)(52, 105)(53, 112)(54, 107)(55, 106)(56, 109) 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 ) } Outer automorphisms :: reflexible Dual of E12.726 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 4 e = 56 f = 30 degree seq :: [ 28^4 ] E12.728 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 14, 28}) Quotient :: loop Aut^+ = C7 x D8 (small group id <56, 9>) Aut = D8 x D14 (small group id <112, 31>) |r| :: 2 Presentation :: [ F^2, (T1 * T2)^2, (F * T1)^2, (F * T2)^2, T1^-2 * T2^-1 * T1 * T2^-1 * T1^-1, T1^-1 * T2 * T1^-1 * T2^-3, T1^-1 * T2 * T1^-1 * T2^5 * T1^-6 ] Map:: R = (1, 57, 3, 59, 10, 66, 24, 80, 33, 89, 41, 97, 49, 105, 54, 110, 45, 101, 39, 95, 32, 88, 18, 74, 6, 62, 17, 73, 30, 86, 20, 76, 13, 69, 27, 83, 36, 92, 44, 100, 52, 108, 55, 111, 48, 104, 38, 94, 28, 84, 21, 77, 15, 71, 5, 61)(2, 58, 7, 63, 19, 75, 11, 67, 26, 82, 34, 90, 43, 99, 50, 106, 53, 109, 47, 103, 40, 96, 29, 85, 16, 72, 14, 70, 23, 79, 9, 65, 4, 60, 12, 68, 25, 81, 35, 91, 42, 98, 51, 107, 56, 112, 46, 102, 37, 93, 31, 87, 22, 78, 8, 64) L = (1, 58)(2, 62)(3, 65)(4, 57)(5, 70)(6, 72)(7, 61)(8, 77)(9, 73)(10, 75)(11, 59)(12, 76)(13, 60)(14, 74)(15, 78)(16, 84)(17, 64)(18, 87)(19, 86)(20, 63)(21, 85)(22, 88)(23, 71)(24, 68)(25, 66)(26, 69)(27, 67)(28, 93)(29, 95)(30, 79)(31, 94)(32, 96)(33, 82)(34, 80)(35, 83)(36, 81)(37, 101)(38, 103)(39, 102)(40, 104)(41, 91)(42, 89)(43, 92)(44, 90)(45, 109)(46, 111)(47, 110)(48, 112)(49, 99)(50, 97)(51, 100)(52, 98)(53, 108)(54, 107)(55, 106)(56, 105) 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 ) } Outer automorphisms :: reflexible Dual of E12.724 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 56 f = 32 degree seq :: [ 56^2 ] E12.729 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 14, 28}) Quotient :: loop Aut^+ = C7 x D8 (small group id <56, 9>) Aut = D8 x D14 (small group id <112, 31>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1^2 * T2 * T1^-2, (T1 * T2 * T1^-1 * T2)^2, T2 * T1^-3 * T2 * T1^-11 ] Map:: polytopal non-degenerate R = (1, 57, 3, 59)(2, 58, 6, 62)(4, 60, 9, 65)(5, 61, 12, 68)(7, 63, 15, 71)(8, 64, 16, 72)(10, 66, 17, 73)(11, 67, 21, 77)(13, 69, 23, 79)(14, 70, 24, 80)(18, 74, 25, 81)(19, 75, 27, 83)(20, 76, 30, 86)(22, 78, 32, 88)(26, 82, 33, 89)(28, 84, 34, 90)(29, 85, 38, 94)(31, 87, 40, 96)(35, 91, 41, 97)(36, 92, 43, 99)(37, 93, 46, 102)(39, 95, 48, 104)(42, 98, 49, 105)(44, 100, 50, 106)(45, 101, 54, 110)(47, 103, 56, 112)(51, 107, 53, 109)(52, 108, 55, 111) L = (1, 58)(2, 61)(3, 63)(4, 57)(5, 67)(6, 69)(7, 68)(8, 59)(9, 70)(10, 60)(11, 76)(12, 78)(13, 77)(14, 62)(15, 79)(16, 80)(17, 64)(18, 65)(19, 66)(20, 85)(21, 87)(22, 86)(23, 88)(24, 71)(25, 72)(26, 73)(27, 74)(28, 75)(29, 93)(30, 95)(31, 94)(32, 96)(33, 81)(34, 82)(35, 83)(36, 84)(37, 101)(38, 103)(39, 102)(40, 104)(41, 89)(42, 90)(43, 91)(44, 92)(45, 109)(46, 111)(47, 110)(48, 112)(49, 97)(50, 98)(51, 99)(52, 100)(53, 105)(54, 106)(55, 107)(56, 108) local type(s) :: { ( 14, 28, 14, 28 ) } Outer automorphisms :: reflexible Dual of E12.725 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 28 e = 56 f = 6 degree seq :: [ 4^28 ] E12.730 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 14, 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, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y2^-1 * R * Y2^-1)^2, Y2^2 * Y1 * Y2^-2 * Y1, (Y2 * Y1 * Y2^-1 * Y1)^2, Y2^14, (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, 52, 108)(50, 106, 55, 111)(51, 107, 54, 110)(53, 109, 56, 112)(113, 169, 115, 171, 120, 176, 129, 185, 138, 194, 146, 202, 154, 210, 162, 218, 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, 165, 221, 160, 216, 152, 208, 144, 200, 136, 192, 126, 182, 118, 174)(119, 175, 127, 183, 137, 193, 145, 201, 153, 209, 161, 217, 167, 223, 163, 219, 155, 211, 147, 203, 139, 195, 130, 186, 121, 177, 128, 184)(123, 179, 132, 188, 141, 197, 149, 205, 157, 213, 164, 220, 168, 224, 166, 222, 159, 215, 151, 207, 143, 199, 135, 191, 125, 181, 133, 189) 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, 164)(50, 167)(51, 166)(52, 161)(53, 168)(54, 163)(55, 162)(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) :: { ( 2, 56, 2, 56 ), ( 2, 56, 2, 56, 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 E12.733 Graph:: bipartite v = 32 e = 112 f = 58 degree seq :: [ 4^28, 28^4 ] E12.731 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 14, 28}) Quotient :: dipole Aut^+ = C7 x D8 (small group id <56, 9>) Aut = D8 x D14 (small group id <112, 31>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, Y2 * Y1^2 * Y2^-1 * Y1^-2, Y2^2 * Y1 * Y2^-2 * Y1^-1, Y1 * Y2^2 * Y1^3 * Y2^2, Y2^6 * Y1^-1 * Y2^2 * Y1^-5, Y1^14 ] Map:: R = (1, 57, 2, 58, 6, 62, 16, 72, 28, 84, 37, 93, 45, 101, 53, 109, 52, 108, 42, 98, 33, 89, 26, 82, 13, 69, 4, 60)(3, 59, 9, 65, 17, 73, 8, 64, 21, 77, 29, 85, 39, 95, 46, 102, 55, 111, 50, 106, 41, 97, 35, 91, 27, 83, 11, 67)(5, 61, 14, 70, 18, 74, 31, 87, 38, 94, 47, 103, 54, 110, 51, 107, 44, 100, 34, 90, 24, 80, 12, 68, 20, 76, 7, 63)(10, 66, 19, 75, 30, 86, 23, 79, 15, 71, 22, 78, 32, 88, 40, 96, 48, 104, 56, 112, 49, 105, 43, 99, 36, 92, 25, 81)(113, 169, 115, 171, 122, 178, 136, 192, 145, 201, 153, 209, 161, 217, 166, 222, 157, 213, 151, 207, 144, 200, 130, 186, 118, 174, 129, 185, 142, 198, 132, 188, 125, 181, 139, 195, 148, 204, 156, 212, 164, 220, 167, 223, 160, 216, 150, 206, 140, 196, 133, 189, 127, 183, 117, 173)(114, 170, 119, 175, 131, 187, 123, 179, 138, 194, 146, 202, 155, 211, 162, 218, 165, 221, 159, 215, 152, 208, 141, 197, 128, 184, 126, 182, 135, 191, 121, 177, 116, 172, 124, 180, 137, 193, 147, 203, 154, 210, 163, 219, 168, 224, 158, 214, 149, 205, 143, 199, 134, 190, 120, 176) L = (1, 115)(2, 119)(3, 122)(4, 124)(5, 113)(6, 129)(7, 131)(8, 114)(9, 116)(10, 136)(11, 138)(12, 137)(13, 139)(14, 135)(15, 117)(16, 126)(17, 142)(18, 118)(19, 123)(20, 125)(21, 127)(22, 120)(23, 121)(24, 145)(25, 147)(26, 146)(27, 148)(28, 133)(29, 128)(30, 132)(31, 134)(32, 130)(33, 153)(34, 155)(35, 154)(36, 156)(37, 143)(38, 140)(39, 144)(40, 141)(41, 161)(42, 163)(43, 162)(44, 164)(45, 151)(46, 149)(47, 152)(48, 150)(49, 166)(50, 165)(51, 168)(52, 167)(53, 159)(54, 157)(55, 160)(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) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 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 E12.732 Graph:: bipartite v = 6 e = 112 f = 84 degree seq :: [ 28^4, 56^2 ] E12.732 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 14, 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, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, Y3^2 * Y2 * Y3^-2 * Y2, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y2 * Y3 * Y2)^2, Y3 * Y2 * Y3^3 * Y2 * Y3^10, (Y3^-1 * Y1^-1)^28 ] Map:: polytopal 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)(115, 171, 119, 175)(116, 172, 121, 177)(117, 173, 123, 179)(118, 174, 125, 181)(120, 176, 124, 180)(122, 178, 126, 182)(127, 183, 132, 188)(128, 184, 133, 189)(129, 185, 137, 193)(130, 186, 135, 191)(131, 187, 139, 195)(134, 190, 141, 197)(136, 192, 143, 199)(138, 194, 142, 198)(140, 196, 144, 200)(145, 201, 149, 205)(146, 202, 153, 209)(147, 203, 151, 207)(148, 204, 155, 211)(150, 206, 157, 213)(152, 208, 159, 215)(154, 210, 158, 214)(156, 212, 160, 216)(161, 217, 165, 221)(162, 218, 168, 224)(163, 219, 167, 223)(164, 220, 166, 222) L = (1, 115)(2, 117)(3, 120)(4, 113)(5, 124)(6, 114)(7, 127)(8, 129)(9, 128)(10, 116)(11, 132)(12, 134)(13, 133)(14, 118)(15, 137)(16, 119)(17, 138)(18, 121)(19, 122)(20, 141)(21, 123)(22, 142)(23, 125)(24, 126)(25, 145)(26, 146)(27, 130)(28, 131)(29, 149)(30, 150)(31, 135)(32, 136)(33, 153)(34, 154)(35, 139)(36, 140)(37, 157)(38, 158)(39, 143)(40, 144)(41, 161)(42, 162)(43, 147)(44, 148)(45, 165)(46, 166)(47, 151)(48, 152)(49, 168)(50, 167)(51, 155)(52, 156)(53, 164)(54, 163)(55, 159)(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) :: { ( 28, 56 ), ( 28, 56, 28, 56 ) } Outer automorphisms :: reflexible Dual of E12.731 Graph:: simple bipartite v = 84 e = 112 f = 6 degree seq :: [ 2^56, 4^28 ] E12.733 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 14, 28}) Quotient :: dipole Aut^+ = C7 x D8 (small group id <56, 9>) Aut = D8 x D14 (small group id <112, 31>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2^-1)^2, Y3^2 * Y1^-1 * Y3^2 * Y1, (R * Y2 * Y3^-1)^2, Y1 * Y3^-1 * Y1^-2 * Y3 * Y1, Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1, Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-12, 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^-1 ] Map:: R = (1, 57, 2, 58, 5, 61, 11, 67, 20, 76, 29, 85, 37, 93, 45, 101, 53, 109, 49, 105, 41, 97, 33, 89, 25, 81, 16, 72, 24, 80, 15, 71, 23, 79, 32, 88, 40, 96, 48, 104, 56, 112, 52, 108, 44, 100, 36, 92, 28, 84, 19, 75, 10, 66, 4, 60)(3, 59, 7, 63, 12, 68, 22, 78, 30, 86, 39, 95, 46, 102, 55, 111, 51, 107, 43, 99, 35, 91, 27, 83, 18, 74, 9, 65, 14, 70, 6, 62, 13, 69, 21, 77, 31, 87, 38, 94, 47, 103, 54, 110, 50, 106, 42, 98, 34, 90, 26, 82, 17, 73, 8, 64)(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, 113)(4, 121)(5, 124)(6, 114)(7, 127)(8, 128)(9, 116)(10, 129)(11, 133)(12, 117)(13, 135)(14, 136)(15, 119)(16, 120)(17, 122)(18, 137)(19, 139)(20, 142)(21, 123)(22, 144)(23, 125)(24, 126)(25, 130)(26, 145)(27, 131)(28, 146)(29, 150)(30, 132)(31, 152)(32, 134)(33, 138)(34, 140)(35, 153)(36, 155)(37, 158)(38, 141)(39, 160)(40, 143)(41, 147)(42, 161)(43, 148)(44, 162)(45, 166)(46, 149)(47, 168)(48, 151)(49, 154)(50, 156)(51, 165)(52, 167)(53, 163)(54, 157)(55, 164)(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, 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 E12.730 Graph:: simple bipartite v = 58 e = 112 f = 32 degree seq :: [ 2^56, 56^2 ] E12.734 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 14, 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, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y2^-1 * R * Y2^-1)^2, Y2^2 * Y1 * Y2^-2 * Y1, (Y2^-1 * Y1 * Y2 * Y1)^2, Y2^9 * Y1 * Y2^3 * Y1 * Y2^2, (Y3 * Y2^-1)^14 ] 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, 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, 168)(51, 167)(52, 166)(53, 161)(54, 164)(55, 163)(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, 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 E12.735 Graph:: bipartite v = 30 e = 112 f = 60 degree seq :: [ 4^28, 56^2 ] E12.735 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 14, 28}) Quotient :: dipole Aut^+ = C7 x D8 (small group id <56, 9>) Aut = D8 x D14 (small group id <112, 31>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3^-1 * Y1 * Y3^-1 * Y1^-2, Y3 * Y1^-1 * Y3^-3 * Y1^-1, Y1^-1 * Y3 * Y1^-1 * Y3^5 * Y1^-6, (Y3 * Y2^-1)^28 ] Map:: R = (1, 57, 2, 58, 6, 62, 16, 72, 28, 84, 37, 93, 45, 101, 53, 109, 52, 108, 42, 98, 33, 89, 26, 82, 13, 69, 4, 60)(3, 59, 9, 65, 17, 73, 8, 64, 21, 77, 29, 85, 39, 95, 46, 102, 55, 111, 50, 106, 41, 97, 35, 91, 27, 83, 11, 67)(5, 61, 14, 70, 18, 74, 31, 87, 38, 94, 47, 103, 54, 110, 51, 107, 44, 100, 34, 90, 24, 80, 12, 68, 20, 76, 7, 63)(10, 66, 19, 75, 30, 86, 23, 79, 15, 71, 22, 78, 32, 88, 40, 96, 48, 104, 56, 112, 49, 105, 43, 99, 36, 92, 25, 81)(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, 122)(4, 124)(5, 113)(6, 129)(7, 131)(8, 114)(9, 116)(10, 136)(11, 138)(12, 137)(13, 139)(14, 135)(15, 117)(16, 126)(17, 142)(18, 118)(19, 123)(20, 125)(21, 127)(22, 120)(23, 121)(24, 145)(25, 147)(26, 146)(27, 148)(28, 133)(29, 128)(30, 132)(31, 134)(32, 130)(33, 153)(34, 155)(35, 154)(36, 156)(37, 143)(38, 140)(39, 144)(40, 141)(41, 161)(42, 163)(43, 162)(44, 164)(45, 151)(46, 149)(47, 152)(48, 150)(49, 166)(50, 165)(51, 168)(52, 167)(53, 159)(54, 157)(55, 160)(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 ) } Outer automorphisms :: reflexible Dual of E12.734 Graph:: simple bipartite v = 60 e = 112 f = 30 degree seq :: [ 2^56, 28^4 ] E12.736 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 15, 15}) Quotient :: regular Aut^+ = C5 x A4 (small group id <60, 9>) Aut = (C5 x A4) : C2 (small group id <120, 38>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^2 * T2 * T1^-1 * T2 * T1^-1 * T2, T1 * T2 * T1 * T2 * T1^-2 * T2, T1^15, T1^-4 * T2 * T1^-4 * T2 * T1^-4 * T2 * T1^-3 ] Map:: non-degenerate R = (1, 2, 5, 11, 23, 31, 39, 47, 54, 46, 38, 30, 22, 10, 4)(3, 7, 15, 24, 33, 42, 48, 56, 58, 51, 43, 35, 27, 18, 8)(6, 13, 26, 32, 41, 50, 55, 60, 53, 45, 37, 29, 21, 17, 14)(9, 19, 16, 12, 25, 34, 40, 49, 57, 59, 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, 55)(49, 50)(52, 53)(54, 59)(56, 57)(58, 60) local type(s) :: { ( 15^15 ) } Outer automorphisms :: reflexible selfdual Transitivity :: ET+ VT+ AT+ REG+ Graph:: v = 4 e = 30 f = 4 degree seq :: [ 15^4 ] E12.737 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 15, 15}) Quotient :: edge Aut^+ = C5 x A4 (small group id <60, 9>) Aut = (C5 x A4) : C2 (small group id <120, 38>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T1 * T2 * T1 * T2 * T1 * T2^-2, T1 * T2^-1 * T1 * T2^2 * T1 * T2^-1, T2^15, T2^-4 * T1 * T2^-4 * T1 * T2^-4 * T1 * T2^-3 ] Map:: R = (1, 3, 8, 18, 27, 35, 43, 51, 54, 46, 38, 30, 22, 10, 4)(2, 5, 12, 23, 31, 39, 47, 55, 56, 48, 40, 32, 24, 14, 6)(7, 15, 25, 33, 41, 49, 57, 60, 53, 45, 37, 29, 21, 13, 16)(9, 19, 11, 17, 26, 34, 42, 50, 58, 59, 52, 44, 36, 28, 20)(61, 62)(63, 67)(64, 69)(65, 71)(66, 73)(68, 77)(70, 81)(72, 75)(74, 80)(76, 79)(78, 83)(82, 84)(85, 86)(87, 93)(88, 89)(90, 96)(91, 94)(92, 97)(95, 102)(98, 105)(99, 101)(100, 104)(103, 107)(106, 108)(109, 110)(111, 117)(112, 113)(114, 119)(115, 118)(116, 120) 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, 30 ), ( 30^15 ) } Outer automorphisms :: reflexible Dual of E12.738 Transitivity :: ET+ Graph:: simple bipartite v = 34 e = 60 f = 4 degree seq :: [ 2^30, 15^4 ] E12.738 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 15, 15}) Quotient :: loop Aut^+ = C5 x A4 (small group id <60, 9>) Aut = (C5 x A4) : C2 (small group id <120, 38>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T1 * T2 * T1 * T2 * T1 * T2^-2, T1 * T2^-1 * T1 * T2^2 * T1 * T2^-1, T2^15, T2^-4 * T1 * T2^-4 * T1 * T2^-4 * T1 * T2^-3 ] Map:: R = (1, 61, 3, 63, 8, 68, 18, 78, 27, 87, 35, 95, 43, 103, 51, 111, 54, 114, 46, 106, 38, 98, 30, 90, 22, 82, 10, 70, 4, 64)(2, 62, 5, 65, 12, 72, 23, 83, 31, 91, 39, 99, 47, 107, 55, 115, 56, 116, 48, 108, 40, 100, 32, 92, 24, 84, 14, 74, 6, 66)(7, 67, 15, 75, 25, 85, 33, 93, 41, 101, 49, 109, 57, 117, 60, 120, 53, 113, 45, 105, 37, 97, 29, 89, 21, 81, 13, 73, 16, 76)(9, 69, 19, 79, 11, 71, 17, 77, 26, 86, 34, 94, 42, 102, 50, 110, 58, 118, 59, 119, 52, 112, 44, 104, 36, 96, 28, 88, 20, 80) L = (1, 62)(2, 61)(3, 67)(4, 69)(5, 71)(6, 73)(7, 63)(8, 77)(9, 64)(10, 81)(11, 65)(12, 75)(13, 66)(14, 80)(15, 72)(16, 79)(17, 68)(18, 83)(19, 76)(20, 74)(21, 70)(22, 84)(23, 78)(24, 82)(25, 86)(26, 85)(27, 93)(28, 89)(29, 88)(30, 96)(31, 94)(32, 97)(33, 87)(34, 91)(35, 102)(36, 90)(37, 92)(38, 105)(39, 101)(40, 104)(41, 99)(42, 95)(43, 107)(44, 100)(45, 98)(46, 108)(47, 103)(48, 106)(49, 110)(50, 109)(51, 117)(52, 113)(53, 112)(54, 119)(55, 118)(56, 120)(57, 111)(58, 115)(59, 114)(60, 116) local type(s) :: { ( 2, 15, 2, 15, 2, 15, 2, 15, 2, 15, 2, 15, 2, 15, 2, 15, 2, 15, 2, 15, 2, 15, 2, 15, 2, 15, 2, 15, 2, 15 ) } Outer automorphisms :: reflexible Dual of E12.737 Transitivity :: ET+ VT+ AT Graph:: v = 4 e = 60 f = 34 degree seq :: [ 30^4 ] E12.739 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {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 :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1 * Y2^-1 * R * Y2^-2 * R * Y2^-1, Y1 * Y2^2 * Y1 * Y2^-1 * Y1 * Y2^-1, Y1 * Y2 * Y1 * Y2^-2 * Y1 * Y2, 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, 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, 179)(55, 178)(56, 180)(57, 171)(58, 175)(59, 174)(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 ) } Outer automorphisms :: reflexible Dual of E12.740 Graph:: bipartite v = 34 e = 120 f = 64 degree seq :: [ 4^30, 30^4 ] E12.740 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {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 :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2^-1)^2, Y1^2 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3, Y1^15, Y1^-3 * Y3 * Y1^-4 * Y3 * Y1^-4 * Y3 * Y1^-4 ] Map:: R = (1, 61, 2, 62, 5, 65, 11, 71, 23, 83, 31, 91, 39, 99, 47, 107, 54, 114, 46, 106, 38, 98, 30, 90, 22, 82, 10, 70, 4, 64)(3, 63, 7, 67, 15, 75, 24, 84, 33, 93, 42, 102, 48, 108, 56, 116, 58, 118, 51, 111, 43, 103, 35, 95, 27, 87, 18, 78, 8, 68)(6, 66, 13, 73, 26, 86, 32, 92, 41, 101, 50, 110, 55, 115, 60, 120, 53, 113, 45, 105, 37, 97, 29, 89, 21, 81, 17, 77, 14, 74)(9, 69, 19, 79, 16, 76, 12, 72, 25, 85, 34, 94, 40, 100, 49, 109, 57, 117, 59, 119, 52, 112, 44, 104, 36, 96, 28, 88, 20, 80)(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, 126)(3, 121)(4, 129)(5, 132)(6, 122)(7, 136)(8, 137)(9, 124)(10, 141)(11, 144)(12, 125)(13, 135)(14, 139)(15, 133)(16, 127)(17, 128)(18, 140)(19, 134)(20, 138)(21, 130)(22, 147)(23, 152)(24, 131)(25, 146)(26, 145)(27, 142)(28, 149)(29, 148)(30, 156)(31, 160)(32, 143)(33, 154)(34, 153)(35, 157)(36, 150)(37, 155)(38, 165)(39, 168)(40, 151)(41, 162)(42, 161)(43, 164)(44, 163)(45, 158)(46, 171)(47, 175)(48, 159)(49, 170)(50, 169)(51, 166)(52, 173)(53, 172)(54, 179)(55, 167)(56, 177)(57, 176)(58, 180)(59, 174)(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, 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 Dual of E12.739 Graph:: simple bipartite v = 64 e = 120 f = 34 degree seq :: [ 2^60, 30^4 ] E12.741 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 10, 30}) Quotient :: regular Aut^+ = C10 x S3 (small group id <60, 11>) Aut = C2 x S3 x D10 (small group id <120, 42>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^-3 * T2 * T1^3 * T2, T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1, (T1^-2 * T2 * T1^-3)^2 ] Map:: non-degenerate R = (1, 2, 5, 11, 23, 39, 53, 48, 34, 46, 32, 16, 28, 43, 57, 60, 59, 47, 33, 17, 29, 44, 31, 45, 58, 52, 38, 22, 10, 4)(3, 7, 15, 24, 41, 56, 51, 37, 21, 30, 14, 6, 13, 27, 40, 55, 50, 36, 20, 9, 19, 26, 12, 25, 42, 54, 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, 53)(52, 56)(55, 60) local type(s) :: { ( 10^30 ) } Outer automorphisms :: reflexible Dual of E12.742 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 2 e = 30 f = 6 degree seq :: [ 30^2 ] E12.742 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 10, 30}) Quotient :: regular Aut^+ = C10 x S3 (small group id <60, 11>) Aut = C2 x S3 x D10 (small group id <120, 42>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1^2 * T2 * T1^-1, T1^10, T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1, T1^-3 * 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^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 ] Map:: non-degenerate R = (1, 2, 5, 11, 20, 32, 31, 19, 10, 4)(3, 7, 12, 22, 33, 47, 43, 28, 17, 8)(6, 13, 21, 34, 46, 45, 30, 18, 9, 14)(15, 25, 35, 49, 56, 54, 42, 27, 16, 26)(23, 36, 48, 57, 55, 44, 29, 38, 24, 37)(39, 50, 58, 60, 59, 53, 41, 52, 40, 51) 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, 46)(34, 48)(36, 50)(37, 51)(38, 52)(44, 53)(45, 55)(47, 56)(49, 58)(54, 59)(57, 60) local type(s) :: { ( 30^10 ) } Outer automorphisms :: reflexible Dual of E12.741 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 6 e = 30 f = 2 degree seq :: [ 10^6 ] E12.743 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 10, 30}) Quotient :: edge Aut^+ = C10 x S3 (small group id <60, 11>) Aut = C2 x S3 x D10 (small group id <120, 42>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^2 * T1 * T2^-2 * T1, T2^10, T2^-1 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1, (T2^-1 * T1)^30 ] Map:: R = (1, 3, 8, 17, 28, 43, 31, 19, 10, 4)(2, 5, 12, 22, 35, 50, 38, 24, 14, 6)(7, 15, 26, 41, 54, 45, 30, 18, 9, 16)(11, 20, 33, 48, 57, 52, 37, 23, 13, 21)(25, 39, 53, 59, 55, 44, 29, 42, 27, 40)(32, 46, 56, 60, 58, 51, 36, 49, 34, 47)(61, 62)(63, 67)(64, 69)(65, 71)(66, 73)(68, 72)(70, 74)(75, 85)(76, 87)(77, 86)(78, 89)(79, 90)(80, 92)(81, 94)(82, 93)(83, 96)(84, 97)(88, 95)(91, 98)(99, 106)(100, 107)(101, 113)(102, 109)(103, 114)(104, 111)(105, 115)(108, 116)(110, 117)(112, 118)(119, 120) 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, 60 ), ( 60^10 ) } Outer automorphisms :: reflexible Dual of E12.747 Transitivity :: ET+ Graph:: simple bipartite v = 36 e = 60 f = 2 degree seq :: [ 2^30, 10^6 ] E12.744 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 10, 30}) Quotient :: edge Aut^+ = C10 x S3 (small group id <60, 11>) Aut = C2 x S3 x D10 (small group id <120, 42>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1 * T1^-1)^2, T1^-3 * T2^-1 * T1 * T2^-1, T2^2 * T1^-1 * T2^-4 * T1^-1, (T2^4 * T1^-1)^2, T2^-1 * T1 * T2^-1 * T1^7, T2^2 * T1^-2 * T2^4 * T1^-2 ] Map:: polytopal non-degenerate R = (1, 3, 10, 25, 47, 54, 34, 21, 42, 60, 39, 20, 13, 28, 50, 59, 38, 18, 6, 17, 36, 57, 41, 30, 52, 55, 43, 33, 15, 5)(2, 7, 19, 40, 26, 49, 53, 37, 32, 45, 23, 9, 4, 12, 29, 48, 56, 35, 16, 14, 31, 46, 24, 11, 27, 51, 58, 44, 22, 8)(61, 62, 66, 76, 94, 113, 112, 87, 73, 64)(63, 69, 77, 68, 81, 95, 115, 109, 88, 71)(65, 74, 78, 97, 114, 111, 90, 72, 80, 67)(70, 84, 96, 83, 102, 82, 103, 116, 110, 86)(75, 92, 98, 118, 107, 89, 101, 79, 99, 91)(85, 100, 117, 106, 120, 105, 93, 104, 119, 108) 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) :: { ( 4^10 ), ( 4^30 ) } Outer automorphisms :: reflexible Dual of E12.748 Transitivity :: ET+ Graph:: bipartite v = 8 e = 60 f = 30 degree seq :: [ 10^6, 30^2 ] E12.745 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 10, 30}) Quotient :: edge Aut^+ = C10 x S3 (small group id <60, 11>) Aut = C2 x S3 x D10 (small group id <120, 42>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^-3 * T2 * T1^3 * T2, T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1, (T1^-1 * T2 * T1^-4)^2 ] 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, 53)(52, 56)(55, 60)(61, 62, 65, 71, 83, 99, 113, 108, 94, 106, 92, 76, 88, 103, 117, 120, 119, 107, 93, 77, 89, 104, 91, 105, 118, 112, 98, 82, 70, 64)(63, 67, 75, 84, 101, 116, 111, 97, 81, 90, 74, 66, 73, 87, 100, 115, 110, 96, 80, 69, 79, 86, 72, 85, 102, 114, 109, 95, 78, 68) 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, 20 ), ( 20^30 ) } Outer automorphisms :: reflexible Dual of E12.746 Transitivity :: ET+ Graph:: simple bipartite v = 32 e = 60 f = 6 degree seq :: [ 2^30, 30^2 ] E12.746 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 10, 30}) Quotient :: loop Aut^+ = C10 x S3 (small group id <60, 11>) Aut = C2 x S3 x D10 (small group id <120, 42>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^2 * T1 * T2^-2 * T1, T2^10, T2^-1 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1, (T2^-1 * T1)^30 ] Map:: R = (1, 61, 3, 63, 8, 68, 17, 77, 28, 88, 43, 103, 31, 91, 19, 79, 10, 70, 4, 64)(2, 62, 5, 65, 12, 72, 22, 82, 35, 95, 50, 110, 38, 98, 24, 84, 14, 74, 6, 66)(7, 67, 15, 75, 26, 86, 41, 101, 54, 114, 45, 105, 30, 90, 18, 78, 9, 69, 16, 76)(11, 71, 20, 80, 33, 93, 48, 108, 57, 117, 52, 112, 37, 97, 23, 83, 13, 73, 21, 81)(25, 85, 39, 99, 53, 113, 59, 119, 55, 115, 44, 104, 29, 89, 42, 102, 27, 87, 40, 100)(32, 92, 46, 106, 56, 116, 60, 120, 58, 118, 51, 111, 36, 96, 49, 109, 34, 94, 47, 107) L = (1, 62)(2, 61)(3, 67)(4, 69)(5, 71)(6, 73)(7, 63)(8, 72)(9, 64)(10, 74)(11, 65)(12, 68)(13, 66)(14, 70)(15, 85)(16, 87)(17, 86)(18, 89)(19, 90)(20, 92)(21, 94)(22, 93)(23, 96)(24, 97)(25, 75)(26, 77)(27, 76)(28, 95)(29, 78)(30, 79)(31, 98)(32, 80)(33, 82)(34, 81)(35, 88)(36, 83)(37, 84)(38, 91)(39, 106)(40, 107)(41, 113)(42, 109)(43, 114)(44, 111)(45, 115)(46, 99)(47, 100)(48, 116)(49, 102)(50, 117)(51, 104)(52, 118)(53, 101)(54, 103)(55, 105)(56, 108)(57, 110)(58, 112)(59, 120)(60, 119) local type(s) :: { ( 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 E12.745 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 6 e = 60 f = 32 degree seq :: [ 20^6 ] E12.747 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 10, 30}) Quotient :: loop Aut^+ = C10 x S3 (small group id <60, 11>) Aut = C2 x S3 x D10 (small group id <120, 42>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1 * T1^-1)^2, T1^-3 * T2^-1 * T1 * T2^-1, T2^2 * T1^-1 * T2^-4 * T1^-1, (T2^4 * T1^-1)^2, T2^-1 * T1 * T2^-1 * T1^7, T2^2 * T1^-2 * T2^4 * T1^-2 ] Map:: R = (1, 61, 3, 63, 10, 70, 25, 85, 47, 107, 54, 114, 34, 94, 21, 81, 42, 102, 60, 120, 39, 99, 20, 80, 13, 73, 28, 88, 50, 110, 59, 119, 38, 98, 18, 78, 6, 66, 17, 77, 36, 96, 57, 117, 41, 101, 30, 90, 52, 112, 55, 115, 43, 103, 33, 93, 15, 75, 5, 65)(2, 62, 7, 67, 19, 79, 40, 100, 26, 86, 49, 109, 53, 113, 37, 97, 32, 92, 45, 105, 23, 83, 9, 69, 4, 64, 12, 72, 29, 89, 48, 108, 56, 116, 35, 95, 16, 76, 14, 74, 31, 91, 46, 106, 24, 84, 11, 71, 27, 87, 51, 111, 58, 118, 44, 104, 22, 82, 8, 68) L = (1, 62)(2, 66)(3, 69)(4, 61)(5, 74)(6, 76)(7, 65)(8, 81)(9, 77)(10, 84)(11, 63)(12, 80)(13, 64)(14, 78)(15, 92)(16, 94)(17, 68)(18, 97)(19, 99)(20, 67)(21, 95)(22, 103)(23, 102)(24, 96)(25, 100)(26, 70)(27, 73)(28, 71)(29, 101)(30, 72)(31, 75)(32, 98)(33, 104)(34, 113)(35, 115)(36, 83)(37, 114)(38, 118)(39, 91)(40, 117)(41, 79)(42, 82)(43, 116)(44, 119)(45, 93)(46, 120)(47, 89)(48, 85)(49, 88)(50, 86)(51, 90)(52, 87)(53, 112)(54, 111)(55, 109)(56, 110)(57, 106)(58, 107)(59, 108)(60, 105) 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, 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, 2, 10, 2, 10 ) } Outer automorphisms :: reflexible Dual of E12.743 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 60 f = 36 degree seq :: [ 60^2 ] E12.748 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 10, 30}) Quotient :: loop Aut^+ = C10 x S3 (small group id <60, 11>) Aut = C2 x S3 x D10 (small group id <120, 42>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^-3 * T2 * T1^3 * T2, T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1, (T1^-1 * T2 * T1^-4)^2 ] Map:: polytopal non-degenerate R = (1, 61, 3, 63)(2, 62, 6, 66)(4, 64, 9, 69)(5, 65, 12, 72)(7, 67, 16, 76)(8, 68, 17, 77)(10, 70, 21, 81)(11, 71, 24, 84)(13, 73, 28, 88)(14, 74, 29, 89)(15, 75, 31, 91)(18, 78, 34, 94)(19, 79, 32, 92)(20, 80, 33, 93)(22, 82, 35, 95)(23, 83, 40, 100)(25, 85, 43, 103)(26, 86, 44, 104)(27, 87, 45, 105)(30, 90, 46, 106)(36, 96, 48, 108)(37, 97, 47, 107)(38, 98, 50, 110)(39, 99, 54, 114)(41, 101, 57, 117)(42, 102, 58, 118)(49, 109, 59, 119)(51, 111, 53, 113)(52, 112, 56, 116)(55, 115, 60, 120) L = (1, 62)(2, 65)(3, 67)(4, 61)(5, 71)(6, 73)(7, 75)(8, 63)(9, 79)(10, 64)(11, 83)(12, 85)(13, 87)(14, 66)(15, 84)(16, 88)(17, 89)(18, 68)(19, 86)(20, 69)(21, 90)(22, 70)(23, 99)(24, 101)(25, 102)(26, 72)(27, 100)(28, 103)(29, 104)(30, 74)(31, 105)(32, 76)(33, 77)(34, 106)(35, 78)(36, 80)(37, 81)(38, 82)(39, 113)(40, 115)(41, 116)(42, 114)(43, 117)(44, 91)(45, 118)(46, 92)(47, 93)(48, 94)(49, 95)(50, 96)(51, 97)(52, 98)(53, 108)(54, 109)(55, 110)(56, 111)(57, 120)(58, 112)(59, 107)(60, 119) local type(s) :: { ( 10, 30, 10, 30 ) } Outer automorphisms :: reflexible Dual of E12.744 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 30 e = 60 f = 8 degree seq :: [ 4^30 ] E12.749 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {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^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2^2 * Y1 * Y2^-2 * Y1, (Y2^-1 * R * Y2^-1)^2, Y2^10, Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1, (Y3 * Y2^-1)^30 ] Map:: R = (1, 61, 2, 62)(3, 63, 7, 67)(4, 64, 9, 69)(5, 65, 11, 71)(6, 66, 13, 73)(8, 68, 12, 72)(10, 70, 14, 74)(15, 75, 25, 85)(16, 76, 27, 87)(17, 77, 26, 86)(18, 78, 29, 89)(19, 79, 30, 90)(20, 80, 32, 92)(21, 81, 34, 94)(22, 82, 33, 93)(23, 83, 36, 96)(24, 84, 37, 97)(28, 88, 35, 95)(31, 91, 38, 98)(39, 99, 46, 106)(40, 100, 47, 107)(41, 101, 53, 113)(42, 102, 49, 109)(43, 103, 54, 114)(44, 104, 51, 111)(45, 105, 55, 115)(48, 108, 56, 116)(50, 110, 57, 117)(52, 112, 58, 118)(59, 119, 60, 120)(121, 181, 123, 183, 128, 188, 137, 197, 148, 208, 163, 223, 151, 211, 139, 199, 130, 190, 124, 184)(122, 182, 125, 185, 132, 192, 142, 202, 155, 215, 170, 230, 158, 218, 144, 204, 134, 194, 126, 186)(127, 187, 135, 195, 146, 206, 161, 221, 174, 234, 165, 225, 150, 210, 138, 198, 129, 189, 136, 196)(131, 191, 140, 200, 153, 213, 168, 228, 177, 237, 172, 232, 157, 217, 143, 203, 133, 193, 141, 201)(145, 205, 159, 219, 173, 233, 179, 239, 175, 235, 164, 224, 149, 209, 162, 222, 147, 207, 160, 220)(152, 212, 166, 226, 176, 236, 180, 240, 178, 238, 171, 231, 156, 216, 169, 229, 154, 214, 167, 227) 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, 166)(40, 167)(41, 173)(42, 169)(43, 174)(44, 171)(45, 175)(46, 159)(47, 160)(48, 176)(49, 162)(50, 177)(51, 164)(52, 178)(53, 161)(54, 163)(55, 165)(56, 168)(57, 170)(58, 172)(59, 180)(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, 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 E12.752 Graph:: bipartite v = 36 e = 120 f = 62 degree seq :: [ 4^30, 20^6 ] E12.750 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {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 * Y3^-1, (Y1 * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, Y1^-1 * Y2^-1 * Y1 * Y2^-1 * Y1^-2, Y2^4 * Y1 * Y2^-2 * Y1, Y2^-1 * Y1 * Y2^-1 * Y1^7 ] Map:: R = (1, 61, 2, 62, 6, 66, 16, 76, 34, 94, 53, 113, 52, 112, 27, 87, 13, 73, 4, 64)(3, 63, 9, 69, 17, 77, 8, 68, 21, 81, 35, 95, 55, 115, 49, 109, 28, 88, 11, 71)(5, 65, 14, 74, 18, 78, 37, 97, 54, 114, 51, 111, 30, 90, 12, 72, 20, 80, 7, 67)(10, 70, 24, 84, 36, 96, 23, 83, 42, 102, 22, 82, 43, 103, 56, 116, 50, 110, 26, 86)(15, 75, 32, 92, 38, 98, 58, 118, 47, 107, 29, 89, 41, 101, 19, 79, 39, 99, 31, 91)(25, 85, 40, 100, 57, 117, 46, 106, 60, 120, 45, 105, 33, 93, 44, 104, 59, 119, 48, 108)(121, 181, 123, 183, 130, 190, 145, 205, 167, 227, 174, 234, 154, 214, 141, 201, 162, 222, 180, 240, 159, 219, 140, 200, 133, 193, 148, 208, 170, 230, 179, 239, 158, 218, 138, 198, 126, 186, 137, 197, 156, 216, 177, 237, 161, 221, 150, 210, 172, 232, 175, 235, 163, 223, 153, 213, 135, 195, 125, 185)(122, 182, 127, 187, 139, 199, 160, 220, 146, 206, 169, 229, 173, 233, 157, 217, 152, 212, 165, 225, 143, 203, 129, 189, 124, 184, 132, 192, 149, 209, 168, 228, 176, 236, 155, 215, 136, 196, 134, 194, 151, 211, 166, 226, 144, 204, 131, 191, 147, 207, 171, 231, 178, 238, 164, 224, 142, 202, 128, 188) L = (1, 123)(2, 127)(3, 130)(4, 132)(5, 121)(6, 137)(7, 139)(8, 122)(9, 124)(10, 145)(11, 147)(12, 149)(13, 148)(14, 151)(15, 125)(16, 134)(17, 156)(18, 126)(19, 160)(20, 133)(21, 162)(22, 128)(23, 129)(24, 131)(25, 167)(26, 169)(27, 171)(28, 170)(29, 168)(30, 172)(31, 166)(32, 165)(33, 135)(34, 141)(35, 136)(36, 177)(37, 152)(38, 138)(39, 140)(40, 146)(41, 150)(42, 180)(43, 153)(44, 142)(45, 143)(46, 144)(47, 174)(48, 176)(49, 173)(50, 179)(51, 178)(52, 175)(53, 157)(54, 154)(55, 163)(56, 155)(57, 161)(58, 164)(59, 158)(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) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 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 E12.751 Graph:: bipartite v = 8 e = 120 f = 90 degree seq :: [ 20^6, 60^2 ] E12.751 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {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, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^3 * Y2 * Y3^-3 * Y2, Y2 * Y3^-1 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3^-1, (Y3^2 * Y2 * Y3^3)^2, (Y3^-1 * Y1^-1)^30 ] Map:: polytopal 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)(123, 183, 127, 187)(124, 184, 129, 189)(125, 185, 131, 191)(126, 186, 133, 193)(128, 188, 137, 197)(130, 190, 141, 201)(132, 192, 145, 205)(134, 194, 149, 209)(135, 195, 143, 203)(136, 196, 147, 207)(138, 198, 146, 206)(139, 199, 144, 204)(140, 200, 148, 208)(142, 202, 150, 210)(151, 211, 161, 221)(152, 212, 160, 220)(153, 213, 159, 219)(154, 214, 162, 222)(155, 215, 167, 227)(156, 216, 165, 225)(157, 217, 164, 224)(158, 218, 170, 230)(163, 223, 173, 233)(166, 226, 176, 236)(168, 228, 174, 234)(169, 229, 178, 238)(171, 231, 177, 237)(172, 232, 175, 235)(179, 239, 180, 240) L = (1, 123)(2, 125)(3, 128)(4, 121)(5, 132)(6, 122)(7, 135)(8, 138)(9, 139)(10, 124)(11, 143)(12, 146)(13, 147)(14, 126)(15, 151)(16, 127)(17, 153)(18, 155)(19, 154)(20, 129)(21, 152)(22, 130)(23, 159)(24, 131)(25, 161)(26, 163)(27, 162)(28, 133)(29, 160)(30, 134)(31, 167)(32, 136)(33, 168)(34, 137)(35, 169)(36, 140)(37, 141)(38, 142)(39, 173)(40, 144)(41, 174)(42, 145)(43, 175)(44, 148)(45, 149)(46, 150)(47, 179)(48, 178)(49, 177)(50, 156)(51, 157)(52, 158)(53, 180)(54, 172)(55, 171)(56, 164)(57, 165)(58, 166)(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) :: { ( 20, 60 ), ( 20, 60, 20, 60 ) } Outer automorphisms :: reflexible Dual of E12.750 Graph:: simple bipartite v = 90 e = 120 f = 8 degree seq :: [ 2^60, 4^30 ] E12.752 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {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 :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y1)^2, (Y3 * Y2^-1)^2, (R * Y3)^2, Y3 * Y1^-3 * Y3 * Y1^3, Y1^-1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3, (Y1^-1 * Y3 * Y1^-4)^2 ] Map:: R = (1, 61, 2, 62, 5, 65, 11, 71, 23, 83, 39, 99, 53, 113, 48, 108, 34, 94, 46, 106, 32, 92, 16, 76, 28, 88, 43, 103, 57, 117, 60, 120, 59, 119, 47, 107, 33, 93, 17, 77, 29, 89, 44, 104, 31, 91, 45, 105, 58, 118, 52, 112, 38, 98, 22, 82, 10, 70, 4, 64)(3, 63, 7, 67, 15, 75, 24, 84, 41, 101, 56, 116, 51, 111, 37, 97, 21, 81, 30, 90, 14, 74, 6, 66, 13, 73, 27, 87, 40, 100, 55, 115, 50, 110, 36, 96, 20, 80, 9, 69, 19, 79, 26, 86, 12, 72, 25, 85, 42, 102, 54, 114, 49, 109, 35, 95, 18, 78, 8, 68)(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, 126)(3, 121)(4, 129)(5, 132)(6, 122)(7, 136)(8, 137)(9, 124)(10, 141)(11, 144)(12, 125)(13, 148)(14, 149)(15, 151)(16, 127)(17, 128)(18, 154)(19, 152)(20, 153)(21, 130)(22, 155)(23, 160)(24, 131)(25, 163)(26, 164)(27, 165)(28, 133)(29, 134)(30, 166)(31, 135)(32, 139)(33, 140)(34, 138)(35, 142)(36, 168)(37, 167)(38, 170)(39, 174)(40, 143)(41, 177)(42, 178)(43, 145)(44, 146)(45, 147)(46, 150)(47, 157)(48, 156)(49, 179)(50, 158)(51, 173)(52, 176)(53, 171)(54, 159)(55, 180)(56, 172)(57, 161)(58, 162)(59, 169)(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 ) } Outer automorphisms :: reflexible Dual of E12.749 Graph:: simple bipartite v = 62 e = 120 f = 36 degree seq :: [ 2^60, 60^2 ] E12.753 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {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^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y2^-1 * R * Y2^-2)^2, Y2^-2 * Y1 * Y2^3 * Y1 * Y2^-1, Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1, Y2^8 * Y1 * Y2^2 * Y1, (Y3 * Y2^-1)^10 ] 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, 25, 85)(14, 74, 29, 89)(15, 75, 23, 83)(16, 76, 27, 87)(18, 78, 26, 86)(19, 79, 24, 84)(20, 80, 28, 88)(22, 82, 30, 90)(31, 91, 41, 101)(32, 92, 40, 100)(33, 93, 39, 99)(34, 94, 42, 102)(35, 95, 47, 107)(36, 96, 45, 105)(37, 97, 44, 104)(38, 98, 50, 110)(43, 103, 53, 113)(46, 106, 56, 116)(48, 108, 54, 114)(49, 109, 58, 118)(51, 111, 57, 117)(52, 112, 55, 115)(59, 119, 60, 120)(121, 181, 123, 183, 128, 188, 138, 198, 155, 215, 169, 229, 177, 237, 165, 225, 149, 209, 160, 220, 144, 204, 131, 191, 143, 203, 159, 219, 173, 233, 180, 240, 176, 236, 164, 224, 148, 208, 133, 193, 147, 207, 162, 222, 145, 205, 161, 221, 174, 234, 172, 232, 158, 218, 142, 202, 130, 190, 124, 184)(122, 182, 125, 185, 132, 192, 146, 206, 163, 223, 175, 235, 171, 231, 157, 217, 141, 201, 152, 212, 136, 196, 127, 187, 135, 195, 151, 211, 167, 227, 179, 239, 170, 230, 156, 216, 140, 200, 129, 189, 139, 199, 154, 214, 137, 197, 153, 213, 168, 228, 178, 238, 166, 226, 150, 210, 134, 194, 126, 186) L = (1, 122)(2, 121)(3, 127)(4, 129)(5, 131)(6, 133)(7, 123)(8, 137)(9, 124)(10, 141)(11, 125)(12, 145)(13, 126)(14, 149)(15, 143)(16, 147)(17, 128)(18, 146)(19, 144)(20, 148)(21, 130)(22, 150)(23, 135)(24, 139)(25, 132)(26, 138)(27, 136)(28, 140)(29, 134)(30, 142)(31, 161)(32, 160)(33, 159)(34, 162)(35, 167)(36, 165)(37, 164)(38, 170)(39, 153)(40, 152)(41, 151)(42, 154)(43, 173)(44, 157)(45, 156)(46, 176)(47, 155)(48, 174)(49, 178)(50, 158)(51, 177)(52, 175)(53, 163)(54, 168)(55, 172)(56, 166)(57, 171)(58, 169)(59, 180)(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, 20, 2, 20 ), ( 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 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 E12.754 Graph:: bipartite v = 32 e = 120 f = 66 degree seq :: [ 4^30, 60^2 ] E12.754 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {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 :: [ Y2, R^2, (Y3^-1 * Y1^-1)^2, (Y1 * Y3)^2, (R * Y1)^2, (R * Y3)^2, Y3^-1 * Y1^-3 * Y3^-1 * Y1, (R * Y2 * Y3^-1)^2, Y3^4 * Y1 * Y3^-2 * Y1, Y1^-1 * Y3^2 * Y1^-1 * Y3^3 * Y1^-1 * Y3 * Y1^-1, (Y3 * Y2^-1)^30 ] Map:: R = (1, 61, 2, 62, 6, 66, 16, 76, 34, 94, 53, 113, 52, 112, 27, 87, 13, 73, 4, 64)(3, 63, 9, 69, 17, 77, 8, 68, 21, 81, 35, 95, 55, 115, 49, 109, 28, 88, 11, 71)(5, 65, 14, 74, 18, 78, 37, 97, 54, 114, 51, 111, 30, 90, 12, 72, 20, 80, 7, 67)(10, 70, 24, 84, 36, 96, 23, 83, 42, 102, 22, 82, 43, 103, 56, 116, 50, 110, 26, 86)(15, 75, 32, 92, 38, 98, 58, 118, 47, 107, 29, 89, 41, 101, 19, 79, 39, 99, 31, 91)(25, 85, 40, 100, 57, 117, 46, 106, 60, 120, 45, 105, 33, 93, 44, 104, 59, 119, 48, 108)(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, 137)(7, 139)(8, 122)(9, 124)(10, 145)(11, 147)(12, 149)(13, 148)(14, 151)(15, 125)(16, 134)(17, 156)(18, 126)(19, 160)(20, 133)(21, 162)(22, 128)(23, 129)(24, 131)(25, 167)(26, 169)(27, 171)(28, 170)(29, 168)(30, 172)(31, 166)(32, 165)(33, 135)(34, 141)(35, 136)(36, 177)(37, 152)(38, 138)(39, 140)(40, 146)(41, 150)(42, 180)(43, 153)(44, 142)(45, 143)(46, 144)(47, 174)(48, 176)(49, 173)(50, 179)(51, 178)(52, 175)(53, 157)(54, 154)(55, 163)(56, 155)(57, 161)(58, 164)(59, 158)(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) :: { ( 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 E12.753 Graph:: simple bipartite v = 66 e = 120 f = 32 degree seq :: [ 2^60, 20^6 ] E12.755 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 8, 10}) Quotient :: regular Aut^+ = (C5 x D8) : C2 (small group id <80, 15>) Aut = D16 x D10 (small group id <160, 131>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-1 * T2 * T1^-1)^2, T1^10, (T1 * T2)^8 ] Map:: polytopal non-degenerate R = (1, 2, 5, 11, 20, 32, 31, 19, 10, 4)(3, 7, 15, 25, 39, 47, 33, 22, 12, 8)(6, 13, 9, 18, 29, 44, 46, 34, 21, 14)(16, 26, 17, 28, 35, 49, 60, 53, 40, 27)(23, 36, 24, 38, 48, 61, 58, 45, 30, 37)(41, 54, 42, 56, 67, 74, 62, 57, 43, 55)(50, 63, 51, 65, 59, 72, 73, 66, 52, 64)(68, 75, 69, 76, 71, 78, 80, 79, 70, 77) 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, 46)(34, 48)(36, 50)(37, 51)(38, 52)(44, 58)(45, 59)(47, 60)(49, 62)(53, 67)(54, 68)(55, 69)(56, 70)(57, 71)(61, 73)(63, 75)(64, 76)(65, 77)(66, 78)(72, 79)(74, 80) local type(s) :: { ( 8^10 ) } Outer automorphisms :: reflexible Dual of E12.756 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 8 e = 40 f = 10 degree seq :: [ 10^8 ] E12.756 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 8, 10}) Quotient :: regular Aut^+ = (C5 x D8) : C2 (small group id <80, 15>) Aut = D16 x D10 (small group id <160, 131>) |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 ] 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, 78, 74, 80, 76, 79, 75, 77) 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, 77)(70, 78)(71, 79)(72, 80) local type(s) :: { ( 10^8 ) } Outer automorphisms :: reflexible Dual of E12.755 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 10 e = 40 f = 8 degree seq :: [ 8^10 ] E12.757 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 8, 10}) Quotient :: edge Aut^+ = (C5 x D8) : C2 (small group id <80, 15>) Aut = D16 x D10 (small group id <160, 131>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, (T1 * T2^-2)^2, T2^8, (T2^-1 * T1)^10 ] 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, 77, 70, 79, 72, 80, 71, 78)(81, 82)(83, 87)(84, 89)(85, 91)(86, 93)(88, 94)(90, 92)(95, 105)(96, 106)(97, 107)(98, 109)(99, 110)(100, 111)(101, 112)(102, 113)(103, 115)(104, 116)(108, 114)(117, 127)(118, 128)(119, 129)(120, 130)(121, 131)(122, 132)(123, 133)(124, 134)(125, 135)(126, 136)(137, 145)(138, 146)(139, 147)(140, 148)(141, 149)(142, 150)(143, 151)(144, 152)(153, 158)(154, 157)(155, 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) :: { ( 20, 20 ), ( 20^8 ) } Outer automorphisms :: reflexible Dual of E12.761 Transitivity :: ET+ Graph:: simple bipartite v = 50 e = 80 f = 8 degree seq :: [ 2^40, 8^10 ] E12.758 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 8, 10}) Quotient :: edge Aut^+ = (C5 x D8) : C2 (small group id <80, 15>) Aut = D16 x D10 (small group id <160, 131>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1 * T1^-1)^2, (T2 * T1^-1)^2, T1^8, T2^10 ] Map:: polytopal non-degenerate R = (1, 3, 10, 21, 36, 52, 40, 25, 13, 5)(2, 7, 17, 31, 47, 62, 48, 32, 18, 8)(4, 11, 23, 39, 55, 65, 51, 35, 20, 9)(6, 15, 29, 45, 60, 72, 61, 46, 30, 16)(12, 19, 34, 50, 64, 74, 67, 54, 38, 22)(14, 27, 43, 58, 70, 78, 71, 59, 44, 28)(24, 37, 53, 66, 75, 79, 73, 63, 49, 33)(26, 41, 56, 68, 76, 80, 77, 69, 57, 42)(81, 82, 86, 94, 106, 104, 92, 84)(83, 89, 99, 113, 121, 108, 95, 88)(85, 91, 102, 117, 122, 107, 96, 87)(90, 98, 109, 124, 136, 129, 114, 100)(93, 97, 110, 123, 137, 133, 118, 103)(101, 115, 130, 143, 148, 139, 125, 112)(105, 119, 134, 146, 149, 138, 126, 111)(116, 128, 140, 151, 156, 153, 144, 131)(120, 127, 141, 150, 157, 155, 147, 135)(132, 145, 154, 159, 160, 158, 152, 142) 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) :: { ( 4^8 ), ( 4^10 ) } Outer automorphisms :: reflexible Dual of E12.762 Transitivity :: ET+ Graph:: simple bipartite v = 18 e = 80 f = 40 degree seq :: [ 8^10, 10^8 ] E12.759 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 8, 10}) Quotient :: edge Aut^+ = (C5 x D8) : C2 (small group id <80, 15>) Aut = D16 x D10 (small group id <160, 131>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-1 * T2 * T1^-1)^2, T1^10, (T2 * T1)^8 ] 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, 46)(34, 48)(36, 50)(37, 51)(38, 52)(44, 58)(45, 59)(47, 60)(49, 62)(53, 67)(54, 68)(55, 69)(56, 70)(57, 71)(61, 73)(63, 75)(64, 76)(65, 77)(66, 78)(72, 79)(74, 80)(81, 82, 85, 91, 100, 112, 111, 99, 90, 84)(83, 87, 95, 105, 119, 127, 113, 102, 92, 88)(86, 93, 89, 98, 109, 124, 126, 114, 101, 94)(96, 106, 97, 108, 115, 129, 140, 133, 120, 107)(103, 116, 104, 118, 128, 141, 138, 125, 110, 117)(121, 134, 122, 136, 147, 154, 142, 137, 123, 135)(130, 143, 131, 145, 139, 152, 153, 146, 132, 144)(148, 155, 149, 156, 151, 158, 160, 159, 150, 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) :: { ( 16, 16 ), ( 16^10 ) } Outer automorphisms :: reflexible Dual of E12.760 Transitivity :: ET+ Graph:: simple bipartite v = 48 e = 80 f = 10 degree seq :: [ 2^40, 10^8 ] E12.760 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 8, 10}) Quotient :: loop Aut^+ = (C5 x D8) : C2 (small group id <80, 15>) Aut = D16 x D10 (small group id <160, 131>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, (T1 * T2^-2)^2, T2^8, (T2^-1 * T1)^10 ] Map:: R = (1, 81, 3, 83, 8, 88, 17, 97, 28, 108, 19, 99, 10, 90, 4, 84)(2, 82, 5, 85, 12, 92, 22, 102, 34, 114, 24, 104, 14, 94, 6, 86)(7, 87, 15, 95, 9, 89, 18, 98, 30, 110, 40, 120, 27, 107, 16, 96)(11, 91, 20, 100, 13, 93, 23, 103, 36, 116, 45, 125, 33, 113, 21, 101)(25, 105, 37, 117, 26, 106, 39, 119, 50, 130, 41, 121, 29, 109, 38, 118)(31, 111, 42, 122, 32, 112, 44, 124, 55, 135, 46, 126, 35, 115, 43, 123)(47, 127, 57, 137, 48, 128, 59, 139, 51, 131, 60, 140, 49, 129, 58, 138)(52, 132, 61, 141, 53, 133, 63, 143, 56, 136, 64, 144, 54, 134, 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, 81)(3, 87)(4, 89)(5, 91)(6, 93)(7, 83)(8, 94)(9, 84)(10, 92)(11, 85)(12, 90)(13, 86)(14, 88)(15, 105)(16, 106)(17, 107)(18, 109)(19, 110)(20, 111)(21, 112)(22, 113)(23, 115)(24, 116)(25, 95)(26, 96)(27, 97)(28, 114)(29, 98)(30, 99)(31, 100)(32, 101)(33, 102)(34, 108)(35, 103)(36, 104)(37, 127)(38, 128)(39, 129)(40, 130)(41, 131)(42, 132)(43, 133)(44, 134)(45, 135)(46, 136)(47, 117)(48, 118)(49, 119)(50, 120)(51, 121)(52, 122)(53, 123)(54, 124)(55, 125)(56, 126)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144)(73, 158)(74, 157)(75, 160)(76, 159)(77, 154)(78, 153)(79, 156)(80, 155) local type(s) :: { ( 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10 ) } Outer automorphisms :: reflexible Dual of E12.759 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 10 e = 80 f = 48 degree seq :: [ 16^10 ] E12.761 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 8, 10}) Quotient :: loop Aut^+ = (C5 x D8) : C2 (small group id <80, 15>) Aut = D16 x D10 (small group id <160, 131>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1 * T1^-1)^2, (T2 * T1^-1)^2, T1^8, T2^10 ] Map:: R = (1, 81, 3, 83, 10, 90, 21, 101, 36, 116, 52, 132, 40, 120, 25, 105, 13, 93, 5, 85)(2, 82, 7, 87, 17, 97, 31, 111, 47, 127, 62, 142, 48, 128, 32, 112, 18, 98, 8, 88)(4, 84, 11, 91, 23, 103, 39, 119, 55, 135, 65, 145, 51, 131, 35, 115, 20, 100, 9, 89)(6, 86, 15, 95, 29, 109, 45, 125, 60, 140, 72, 152, 61, 141, 46, 126, 30, 110, 16, 96)(12, 92, 19, 99, 34, 114, 50, 130, 64, 144, 74, 154, 67, 147, 54, 134, 38, 118, 22, 102)(14, 94, 27, 107, 43, 123, 58, 138, 70, 150, 78, 158, 71, 151, 59, 139, 44, 124, 28, 108)(24, 104, 37, 117, 53, 133, 66, 146, 75, 155, 79, 159, 73, 153, 63, 143, 49, 129, 33, 113)(26, 106, 41, 121, 56, 136, 68, 148, 76, 156, 80, 160, 77, 157, 69, 149, 57, 137, 42, 122) L = (1, 82)(2, 86)(3, 89)(4, 81)(5, 91)(6, 94)(7, 85)(8, 83)(9, 99)(10, 98)(11, 102)(12, 84)(13, 97)(14, 106)(15, 88)(16, 87)(17, 110)(18, 109)(19, 113)(20, 90)(21, 115)(22, 117)(23, 93)(24, 92)(25, 119)(26, 104)(27, 96)(28, 95)(29, 124)(30, 123)(31, 105)(32, 101)(33, 121)(34, 100)(35, 130)(36, 128)(37, 122)(38, 103)(39, 134)(40, 127)(41, 108)(42, 107)(43, 137)(44, 136)(45, 112)(46, 111)(47, 141)(48, 140)(49, 114)(50, 143)(51, 116)(52, 145)(53, 118)(54, 146)(55, 120)(56, 129)(57, 133)(58, 126)(59, 125)(60, 151)(61, 150)(62, 132)(63, 148)(64, 131)(65, 154)(66, 149)(67, 135)(68, 139)(69, 138)(70, 157)(71, 156)(72, 142)(73, 144)(74, 159)(75, 147)(76, 153)(77, 155)(78, 152)(79, 160)(80, 158) local type(s) :: { ( 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 E12.757 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 8 e = 80 f = 50 degree seq :: [ 20^8 ] E12.762 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 8, 10}) Quotient :: loop Aut^+ = (C5 x D8) : C2 (small group id <80, 15>) Aut = D16 x D10 (small group id <160, 131>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-1 * T2 * T1^-1)^2, T1^10, (T2 * T1)^8 ] Map:: polytopal non-degenerate R = (1, 81, 3, 83)(2, 82, 6, 86)(4, 84, 9, 89)(5, 85, 12, 92)(7, 87, 16, 96)(8, 88, 17, 97)(10, 90, 15, 95)(11, 91, 21, 101)(13, 93, 23, 103)(14, 94, 24, 104)(18, 98, 30, 110)(19, 99, 29, 109)(20, 100, 33, 113)(22, 102, 35, 115)(25, 105, 40, 120)(26, 106, 41, 121)(27, 107, 42, 122)(28, 108, 43, 123)(31, 111, 39, 119)(32, 112, 46, 126)(34, 114, 48, 128)(36, 116, 50, 130)(37, 117, 51, 131)(38, 118, 52, 132)(44, 124, 58, 138)(45, 125, 59, 139)(47, 127, 60, 140)(49, 129, 62, 142)(53, 133, 67, 147)(54, 134, 68, 148)(55, 135, 69, 149)(56, 136, 70, 150)(57, 137, 71, 151)(61, 141, 73, 153)(63, 143, 75, 155)(64, 144, 76, 156)(65, 145, 77, 157)(66, 146, 78, 158)(72, 152, 79, 159)(74, 154, 80, 160) L = (1, 82)(2, 85)(3, 87)(4, 81)(5, 91)(6, 93)(7, 95)(8, 83)(9, 98)(10, 84)(11, 100)(12, 88)(13, 89)(14, 86)(15, 105)(16, 106)(17, 108)(18, 109)(19, 90)(20, 112)(21, 94)(22, 92)(23, 116)(24, 118)(25, 119)(26, 97)(27, 96)(28, 115)(29, 124)(30, 117)(31, 99)(32, 111)(33, 102)(34, 101)(35, 129)(36, 104)(37, 103)(38, 128)(39, 127)(40, 107)(41, 134)(42, 136)(43, 135)(44, 126)(45, 110)(46, 114)(47, 113)(48, 141)(49, 140)(50, 143)(51, 145)(52, 144)(53, 120)(54, 122)(55, 121)(56, 147)(57, 123)(58, 125)(59, 152)(60, 133)(61, 138)(62, 137)(63, 131)(64, 130)(65, 139)(66, 132)(67, 154)(68, 155)(69, 156)(70, 157)(71, 158)(72, 153)(73, 146)(74, 142)(75, 149)(76, 151)(77, 148)(78, 160)(79, 150)(80, 159) local type(s) :: { ( 8, 10, 8, 10 ) } Outer automorphisms :: reflexible Dual of E12.758 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 40 e = 80 f = 18 degree seq :: [ 4^40 ] E12.763 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 10}) Quotient :: dipole Aut^+ = (C5 x D8) : C2 (small group id <80, 15>) Aut = D16 x D10 (small group id <160, 131>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y1 * Y2^-2)^2, Y2^8, (Y3 * Y2^-1)^10 ] Map:: R = (1, 81, 2, 82)(3, 83, 7, 87)(4, 84, 9, 89)(5, 85, 11, 91)(6, 86, 13, 93)(8, 88, 14, 94)(10, 90, 12, 92)(15, 95, 25, 105)(16, 96, 26, 106)(17, 97, 27, 107)(18, 98, 29, 109)(19, 99, 30, 110)(20, 100, 31, 111)(21, 101, 32, 112)(22, 102, 33, 113)(23, 103, 35, 115)(24, 104, 36, 116)(28, 108, 34, 114)(37, 117, 47, 127)(38, 118, 48, 128)(39, 119, 49, 129)(40, 120, 50, 130)(41, 121, 51, 131)(42, 122, 52, 132)(43, 123, 53, 133)(44, 124, 54, 134)(45, 125, 55, 135)(46, 126, 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, 78, 158)(74, 154, 77, 157)(75, 155, 80, 160)(76, 156, 79, 159)(161, 241, 163, 243, 168, 248, 177, 257, 188, 268, 179, 259, 170, 250, 164, 244)(162, 242, 165, 245, 172, 252, 182, 262, 194, 274, 184, 264, 174, 254, 166, 246)(167, 247, 175, 255, 169, 249, 178, 258, 190, 270, 200, 280, 187, 267, 176, 256)(171, 251, 180, 260, 173, 253, 183, 263, 196, 276, 205, 285, 193, 273, 181, 261)(185, 265, 197, 277, 186, 266, 199, 279, 210, 290, 201, 281, 189, 269, 198, 278)(191, 271, 202, 282, 192, 272, 204, 284, 215, 295, 206, 286, 195, 275, 203, 283)(207, 287, 217, 297, 208, 288, 219, 299, 211, 291, 220, 300, 209, 289, 218, 298)(212, 292, 221, 301, 213, 293, 223, 303, 216, 296, 224, 304, 214, 294, 222, 302)(225, 305, 233, 313, 226, 306, 235, 315, 228, 308, 236, 316, 227, 307, 234, 314)(229, 309, 237, 317, 230, 310, 239, 319, 232, 312, 240, 320, 231, 311, 238, 318) 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, 238)(74, 237)(75, 240)(76, 239)(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) :: { ( 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 E12.766 Graph:: bipartite v = 50 e = 160 f = 88 degree seq :: [ 4^40, 16^10 ] E12.764 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 10}) Quotient :: dipole Aut^+ = (C5 x D8) : C2 (small group id <80, 15>) Aut = D16 x D10 (small group id <160, 131>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-1, (Y2^-1 * Y1^-1)^2, (Y3^-1 * Y1^-1)^2, R * Y2 * R * Y3, (R * Y1)^2, (Y2^-1 * Y1)^2, Y1^8, Y2^10 ] Map:: R = (1, 81, 2, 82, 6, 86, 14, 94, 26, 106, 24, 104, 12, 92, 4, 84)(3, 83, 9, 89, 19, 99, 33, 113, 41, 121, 28, 108, 15, 95, 8, 88)(5, 85, 11, 91, 22, 102, 37, 117, 42, 122, 27, 107, 16, 96, 7, 87)(10, 90, 18, 98, 29, 109, 44, 124, 56, 136, 49, 129, 34, 114, 20, 100)(13, 93, 17, 97, 30, 110, 43, 123, 57, 137, 53, 133, 38, 118, 23, 103)(21, 101, 35, 115, 50, 130, 63, 143, 68, 148, 59, 139, 45, 125, 32, 112)(25, 105, 39, 119, 54, 134, 66, 146, 69, 149, 58, 138, 46, 126, 31, 111)(36, 116, 48, 128, 60, 140, 71, 151, 76, 156, 73, 153, 64, 144, 51, 131)(40, 120, 47, 127, 61, 141, 70, 150, 77, 157, 75, 155, 67, 147, 55, 135)(52, 132, 65, 145, 74, 154, 79, 159, 80, 160, 78, 158, 72, 152, 62, 142)(161, 241, 163, 243, 170, 250, 181, 261, 196, 276, 212, 292, 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, 183, 263, 199, 279, 215, 295, 225, 305, 211, 291, 195, 275, 180, 260, 169, 249)(166, 246, 175, 255, 189, 269, 205, 285, 220, 300, 232, 312, 221, 301, 206, 286, 190, 270, 176, 256)(172, 252, 179, 259, 194, 274, 210, 290, 224, 304, 234, 314, 227, 307, 214, 294, 198, 278, 182, 262)(174, 254, 187, 267, 203, 283, 218, 298, 230, 310, 238, 318, 231, 311, 219, 299, 204, 284, 188, 268)(184, 264, 197, 277, 213, 293, 226, 306, 235, 315, 239, 319, 233, 313, 223, 303, 209, 289, 193, 273)(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, 170)(4, 171)(5, 161)(6, 175)(7, 177)(8, 162)(9, 164)(10, 181)(11, 183)(12, 179)(13, 165)(14, 187)(15, 189)(16, 166)(17, 191)(18, 168)(19, 194)(20, 169)(21, 196)(22, 172)(23, 199)(24, 197)(25, 173)(26, 201)(27, 203)(28, 174)(29, 205)(30, 176)(31, 207)(32, 178)(33, 184)(34, 210)(35, 180)(36, 212)(37, 213)(38, 182)(39, 215)(40, 185)(41, 216)(42, 186)(43, 218)(44, 188)(45, 220)(46, 190)(47, 222)(48, 192)(49, 193)(50, 224)(51, 195)(52, 200)(53, 226)(54, 198)(55, 225)(56, 228)(57, 202)(58, 230)(59, 204)(60, 232)(61, 206)(62, 208)(63, 209)(64, 234)(65, 211)(66, 235)(67, 214)(68, 236)(69, 217)(70, 238)(71, 219)(72, 221)(73, 223)(74, 227)(75, 239)(76, 240)(77, 229)(78, 231)(79, 233)(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, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 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 E12.765 Graph:: bipartite v = 18 e = 160 f = 120 degree seq :: [ 16^10, 20^8 ] E12.765 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 10}) Quotient :: dipole Aut^+ = (C5 x D8) : C2 (small group id <80, 15>) Aut = D16 x D10 (small group id <160, 131>) |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 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2, (Y3^-1 * Y1^-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, 241, 162, 242)(163, 243, 167, 247)(164, 244, 169, 249)(165, 245, 171, 251)(166, 246, 173, 253)(168, 248, 174, 254)(170, 250, 172, 252)(175, 255, 185, 265)(176, 256, 186, 266)(177, 257, 187, 267)(178, 258, 189, 269)(179, 259, 190, 270)(180, 260, 192, 272)(181, 261, 193, 273)(182, 262, 194, 274)(183, 263, 196, 276)(184, 264, 197, 277)(188, 268, 198, 278)(191, 271, 195, 275)(199, 279, 213, 293)(200, 280, 214, 294)(201, 281, 215, 295)(202, 282, 216, 296)(203, 283, 217, 297)(204, 284, 218, 298)(205, 285, 219, 299)(206, 286, 220, 300)(207, 287, 221, 301)(208, 288, 222, 302)(209, 289, 223, 303)(210, 290, 224, 304)(211, 291, 225, 305)(212, 292, 226, 306)(227, 307, 233, 313)(228, 308, 235, 315)(229, 309, 234, 314)(230, 310, 238, 318)(231, 311, 239, 319)(232, 312, 236, 316)(237, 317, 240, 320) L = (1, 163)(2, 165)(3, 168)(4, 161)(5, 172)(6, 162)(7, 175)(8, 177)(9, 178)(10, 164)(11, 180)(12, 182)(13, 183)(14, 166)(15, 169)(16, 167)(17, 188)(18, 190)(19, 170)(20, 173)(21, 171)(22, 195)(23, 197)(24, 174)(25, 199)(26, 201)(27, 176)(28, 203)(29, 200)(30, 205)(31, 179)(32, 206)(33, 208)(34, 181)(35, 210)(36, 207)(37, 212)(38, 184)(39, 186)(40, 185)(41, 216)(42, 187)(43, 191)(44, 189)(45, 217)(46, 193)(47, 192)(48, 223)(49, 194)(50, 198)(51, 196)(52, 224)(53, 227)(54, 229)(55, 228)(56, 231)(57, 202)(58, 232)(59, 204)(60, 233)(61, 235)(62, 234)(63, 237)(64, 209)(65, 238)(66, 211)(67, 214)(68, 213)(69, 218)(70, 215)(71, 219)(72, 239)(73, 221)(74, 220)(75, 225)(76, 222)(77, 226)(78, 240)(79, 230)(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) :: { ( 16, 20 ), ( 16, 20, 16, 20 ) } Outer automorphisms :: reflexible Dual of E12.764 Graph:: simple bipartite v = 120 e = 160 f = 18 degree seq :: [ 2^80, 4^40 ] E12.766 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 10}) Quotient :: dipole Aut^+ = (C5 x D8) : C2 (small group id <80, 15>) Aut = D16 x D10 (small group id <160, 131>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2^-1)^2, (R * Y2 * Y3^-1)^2, Y3 * Y1^-2 * Y3^-1 * Y1^-2, Y1^10, (Y3^-1 * Y1)^8 ] Map:: polytopal R = (1, 81, 2, 82, 5, 85, 11, 91, 20, 100, 32, 112, 31, 111, 19, 99, 10, 90, 4, 84)(3, 83, 7, 87, 15, 95, 25, 105, 39, 119, 47, 127, 33, 113, 22, 102, 12, 92, 8, 88)(6, 86, 13, 93, 9, 89, 18, 98, 29, 109, 44, 124, 46, 126, 34, 114, 21, 101, 14, 94)(16, 96, 26, 106, 17, 97, 28, 108, 35, 115, 49, 129, 60, 140, 53, 133, 40, 120, 27, 107)(23, 103, 36, 116, 24, 104, 38, 118, 48, 128, 61, 141, 58, 138, 45, 125, 30, 110, 37, 117)(41, 121, 54, 134, 42, 122, 56, 136, 67, 147, 74, 154, 62, 142, 57, 137, 43, 123, 55, 135)(50, 130, 63, 143, 51, 131, 65, 145, 59, 139, 72, 152, 73, 153, 66, 146, 52, 132, 64, 144)(68, 148, 75, 155, 69, 149, 76, 156, 71, 151, 78, 158, 80, 160, 79, 159, 70, 150, 77, 157)(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, 166)(3, 161)(4, 169)(5, 172)(6, 162)(7, 176)(8, 177)(9, 164)(10, 175)(11, 181)(12, 165)(13, 183)(14, 184)(15, 170)(16, 167)(17, 168)(18, 190)(19, 189)(20, 193)(21, 171)(22, 195)(23, 173)(24, 174)(25, 200)(26, 201)(27, 202)(28, 203)(29, 179)(30, 178)(31, 199)(32, 206)(33, 180)(34, 208)(35, 182)(36, 210)(37, 211)(38, 212)(39, 191)(40, 185)(41, 186)(42, 187)(43, 188)(44, 218)(45, 219)(46, 192)(47, 220)(48, 194)(49, 222)(50, 196)(51, 197)(52, 198)(53, 227)(54, 228)(55, 229)(56, 230)(57, 231)(58, 204)(59, 205)(60, 207)(61, 233)(62, 209)(63, 235)(64, 236)(65, 237)(66, 238)(67, 213)(68, 214)(69, 215)(70, 216)(71, 217)(72, 239)(73, 221)(74, 240)(75, 223)(76, 224)(77, 225)(78, 226)(79, 232)(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, 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 E12.763 Graph:: simple bipartite v = 88 e = 160 f = 50 degree seq :: [ 2^80, 20^8 ] E12.767 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 10}) Quotient :: dipole Aut^+ = (C5 x D8) : C2 (small group id <80, 15>) Aut = D16 x D10 (small group id <160, 131>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y2^-2 * Y1)^2, Y2^10, (Y3 * Y2^-1)^8 ] Map:: R = (1, 81, 2, 82)(3, 83, 7, 87)(4, 84, 9, 89)(5, 85, 11, 91)(6, 86, 13, 93)(8, 88, 14, 94)(10, 90, 12, 92)(15, 95, 25, 105)(16, 96, 26, 106)(17, 97, 27, 107)(18, 98, 29, 109)(19, 99, 30, 110)(20, 100, 32, 112)(21, 101, 33, 113)(22, 102, 34, 114)(23, 103, 36, 116)(24, 104, 37, 117)(28, 108, 38, 118)(31, 111, 35, 115)(39, 119, 53, 133)(40, 120, 54, 134)(41, 121, 55, 135)(42, 122, 56, 136)(43, 123, 57, 137)(44, 124, 58, 138)(45, 125, 59, 139)(46, 126, 60, 140)(47, 127, 61, 141)(48, 128, 62, 142)(49, 129, 63, 143)(50, 130, 64, 144)(51, 131, 65, 145)(52, 132, 66, 146)(67, 147, 73, 153)(68, 148, 75, 155)(69, 149, 74, 154)(70, 150, 78, 158)(71, 151, 79, 159)(72, 152, 76, 156)(77, 157, 80, 160)(161, 241, 163, 243, 168, 248, 177, 257, 188, 268, 203, 283, 191, 271, 179, 259, 170, 250, 164, 244)(162, 242, 165, 245, 172, 252, 182, 262, 195, 275, 210, 290, 198, 278, 184, 264, 174, 254, 166, 246)(167, 247, 175, 255, 169, 249, 178, 258, 190, 270, 205, 285, 217, 297, 202, 282, 187, 267, 176, 256)(171, 251, 180, 260, 173, 253, 183, 263, 197, 277, 212, 292, 224, 304, 209, 289, 194, 274, 181, 261)(185, 265, 199, 279, 186, 266, 201, 281, 216, 296, 231, 311, 219, 299, 204, 284, 189, 269, 200, 280)(192, 272, 206, 286, 193, 273, 208, 288, 223, 303, 237, 317, 226, 306, 211, 291, 196, 276, 207, 287)(213, 293, 227, 307, 214, 294, 229, 309, 218, 298, 232, 312, 239, 319, 230, 310, 215, 295, 228, 308)(220, 300, 233, 313, 221, 301, 235, 315, 225, 305, 238, 318, 240, 320, 236, 316, 222, 302, 234, 314) 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, 192)(21, 193)(22, 194)(23, 196)(24, 197)(25, 175)(26, 176)(27, 177)(28, 198)(29, 178)(30, 179)(31, 195)(32, 180)(33, 181)(34, 182)(35, 191)(36, 183)(37, 184)(38, 188)(39, 213)(40, 214)(41, 215)(42, 216)(43, 217)(44, 218)(45, 219)(46, 220)(47, 221)(48, 222)(49, 223)(50, 224)(51, 225)(52, 226)(53, 199)(54, 200)(55, 201)(56, 202)(57, 203)(58, 204)(59, 205)(60, 206)(61, 207)(62, 208)(63, 209)(64, 210)(65, 211)(66, 212)(67, 233)(68, 235)(69, 234)(70, 238)(71, 239)(72, 236)(73, 227)(74, 229)(75, 228)(76, 232)(77, 240)(78, 230)(79, 231)(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 ) } Outer automorphisms :: reflexible Dual of E12.768 Graph:: bipartite v = 48 e = 160 f = 90 degree seq :: [ 4^40, 20^8 ] E12.768 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 10}) Quotient :: dipole Aut^+ = (C5 x D8) : C2 (small group id <80, 15>) Aut = D16 x D10 (small group id <160, 131>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y1^-1)^2, (Y3^-1 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y1^8, (Y3 * Y2^-1)^10 ] Map:: polytopal R = (1, 81, 2, 82, 6, 86, 14, 94, 26, 106, 24, 104, 12, 92, 4, 84)(3, 83, 9, 89, 19, 99, 33, 113, 41, 121, 28, 108, 15, 95, 8, 88)(5, 85, 11, 91, 22, 102, 37, 117, 42, 122, 27, 107, 16, 96, 7, 87)(10, 90, 18, 98, 29, 109, 44, 124, 56, 136, 49, 129, 34, 114, 20, 100)(13, 93, 17, 97, 30, 110, 43, 123, 57, 137, 53, 133, 38, 118, 23, 103)(21, 101, 35, 115, 50, 130, 63, 143, 68, 148, 59, 139, 45, 125, 32, 112)(25, 105, 39, 119, 54, 134, 66, 146, 69, 149, 58, 138, 46, 126, 31, 111)(36, 116, 48, 128, 60, 140, 71, 151, 76, 156, 73, 153, 64, 144, 51, 131)(40, 120, 47, 127, 61, 141, 70, 150, 77, 157, 75, 155, 67, 147, 55, 135)(52, 132, 65, 145, 74, 154, 79, 159, 80, 160, 78, 158, 72, 152, 62, 142)(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, 171)(5, 161)(6, 175)(7, 177)(8, 162)(9, 164)(10, 181)(11, 183)(12, 179)(13, 165)(14, 187)(15, 189)(16, 166)(17, 191)(18, 168)(19, 194)(20, 169)(21, 196)(22, 172)(23, 199)(24, 197)(25, 173)(26, 201)(27, 203)(28, 174)(29, 205)(30, 176)(31, 207)(32, 178)(33, 184)(34, 210)(35, 180)(36, 212)(37, 213)(38, 182)(39, 215)(40, 185)(41, 216)(42, 186)(43, 218)(44, 188)(45, 220)(46, 190)(47, 222)(48, 192)(49, 193)(50, 224)(51, 195)(52, 200)(53, 226)(54, 198)(55, 225)(56, 228)(57, 202)(58, 230)(59, 204)(60, 232)(61, 206)(62, 208)(63, 209)(64, 234)(65, 211)(66, 235)(67, 214)(68, 236)(69, 217)(70, 238)(71, 219)(72, 221)(73, 223)(74, 227)(75, 239)(76, 240)(77, 229)(78, 231)(79, 233)(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) :: { ( 4, 20 ), ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) } Outer automorphisms :: reflexible Dual of E12.767 Graph:: simple bipartite v = 90 e = 160 f = 48 degree seq :: [ 2^80, 16^10 ] E12.769 :: Family: { 5 } :: Oriented family(ies): { E3a } Signature :: (0; {3, 3, 14}) Quotient :: edge Aut^+ = (C14 x C2) : C3 (small group id <84, 11>) Aut = (C14 x C2) : C3 (small group id <84, 11>) |r| :: 1 Presentation :: [ X1^3, (X2^-1 * X1^-1)^3, (X2 * X1^-1)^3, (X2^-1 * X1^-1)^3, X2^2 * X1 * X2^-4 * X1^-1, X1^-1 * X2^6 * X1 * X2^2 ] Map:: polytopal non-degenerate R = (1, 2, 4)(3, 8, 10)(5, 13, 14)(6, 16, 18)(7, 19, 20)(9, 24, 26)(11, 28, 30)(12, 31, 22)(15, 35, 36)(17, 39, 41)(21, 45, 46)(23, 49, 44)(25, 52, 54)(27, 56, 51)(29, 53, 60)(32, 62, 63)(33, 65, 42)(34, 58, 66)(37, 67, 57)(38, 68, 48)(40, 70, 71)(43, 74, 61)(47, 75, 73)(50, 77, 72)(55, 79, 78)(59, 80, 76)(64, 83, 82)(69, 84, 81)(85, 87, 93, 109, 137, 158, 130, 156, 125, 152, 146, 121, 99, 89)(86, 90, 101, 124, 108, 135, 147, 165, 144, 150, 119, 131, 105, 91)(88, 95, 113, 143, 123, 149, 120, 139, 110, 133, 129, 148, 116, 96)(92, 106, 132, 160, 136, 162, 151, 166, 145, 114, 97, 117, 134, 107)(94, 103, 127, 153, 122, 100, 98, 118, 138, 154, 161, 159, 141, 111)(102, 115, 140, 163, 142, 112, 104, 128, 155, 164, 168, 167, 157, 126) 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) :: { ( 6^3 ), ( 6^14 ) } Outer automorphisms :: chiral Transitivity :: ET+ Graph:: simple bipartite v = 34 e = 84 f = 28 degree seq :: [ 3^28, 14^6 ] E12.770 :: Family: { 5* } :: Oriented family(ies): { E3*a } Signature :: (0; {3, 3, 14}) Quotient :: loop Aut^+ = (C14 x C2) : C3 (small group id <84, 11>) Aut = (C14 x C2) : C3 (small group id <84, 11>) |r| :: 1 Presentation :: [ X1^3, X2^3, (X1^-1 * X2)^3, (X1^-1 * X2)^3, (X1^-1 * X2^-1 * X1 * X2 * X1 * X2)^2, X2 * X1 * X2 * X1 * X2^-1 * X1^-1 * X2^-1 * X1^-1 * X2^-1 * X1^-1 * X2^-1 * X1^-1 ] Map:: polytopal non-degenerate R = (1, 85, 2, 86, 4, 88)(3, 87, 8, 92, 9, 93)(5, 89, 12, 96, 13, 97)(6, 90, 14, 98, 15, 99)(7, 91, 16, 100, 17, 101)(10, 94, 21, 105, 22, 106)(11, 95, 23, 107, 24, 108)(18, 102, 33, 117, 34, 118)(19, 103, 26, 110, 35, 119)(20, 104, 36, 120, 37, 121)(25, 109, 42, 126, 43, 127)(27, 111, 44, 128, 45, 129)(28, 112, 46, 130, 47, 131)(29, 113, 31, 115, 48, 132)(30, 114, 49, 133, 50, 134)(32, 116, 51, 135, 52, 136)(38, 122, 59, 143, 60, 144)(39, 123, 40, 124, 61, 145)(41, 125, 62, 146, 63, 147)(53, 137, 76, 160, 77, 161)(54, 138, 56, 140, 68, 152)(55, 139, 78, 162, 79, 163)(57, 141, 66, 150, 70, 154)(58, 142, 80, 164, 81, 165)(64, 148, 72, 156, 74, 158)(65, 149, 75, 159, 83, 167)(67, 151, 84, 168, 73, 157)(69, 153, 71, 155, 82, 166) L = (1, 87)(2, 90)(3, 89)(4, 94)(5, 85)(6, 91)(7, 86)(8, 102)(9, 100)(10, 95)(11, 88)(12, 109)(13, 110)(14, 112)(15, 107)(16, 104)(17, 115)(18, 103)(19, 92)(20, 93)(21, 122)(22, 96)(23, 114)(24, 124)(25, 106)(26, 111)(27, 97)(28, 113)(29, 98)(30, 99)(31, 116)(32, 101)(33, 137)(34, 120)(35, 140)(36, 139)(37, 135)(38, 123)(39, 105)(40, 125)(41, 108)(42, 148)(43, 128)(44, 149)(45, 150)(46, 152)(47, 133)(48, 155)(49, 154)(50, 146)(51, 142)(52, 158)(53, 138)(54, 117)(55, 118)(56, 141)(57, 119)(58, 121)(59, 166)(60, 126)(61, 161)(62, 157)(63, 163)(64, 144)(65, 127)(66, 151)(67, 129)(68, 153)(69, 130)(70, 131)(71, 156)(72, 132)(73, 134)(74, 159)(75, 136)(76, 143)(77, 162)(78, 145)(79, 164)(80, 147)(81, 167)(82, 160)(83, 168)(84, 165) local type(s) :: { ( 3, 14, 3, 14, 3, 14 ) } Outer automorphisms :: chiral Transitivity :: ET+ VT+ Graph:: simple v = 28 e = 84 f = 34 degree seq :: [ 6^28 ] E12.771 :: Family: { 2*ex } :: Oriented family(ies): { E3c } Signature :: (0; {3, 3, 14}) Quotient :: loop Aut^+ = (C14 x C2) : C3 (small group id <84, 11>) Aut = ((C14 x C2) : C3) : C2 (small group id <168, 49>) |r| :: 2 Presentation :: [ F^2, T1^3, T2^3, F * T1 * F * T2, (T2^-1 * T1)^3, T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1 * T2 * T1 * T2 * T1^-1 * T2^-1 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 3, 5)(2, 6, 7)(4, 10, 11)(8, 18, 19)(9, 16, 20)(12, 25, 22)(13, 26, 27)(14, 28, 29)(15, 23, 30)(17, 31, 32)(21, 38, 39)(24, 40, 41)(33, 53, 54)(34, 36, 55)(35, 56, 57)(37, 51, 58)(42, 64, 60)(43, 44, 65)(45, 66, 67)(46, 68, 69)(47, 49, 70)(48, 71, 72)(50, 62, 73)(52, 74, 75)(59, 78, 80)(61, 81, 82)(63, 83, 79)(76, 77, 84)(85, 86, 88)(87, 92, 93)(89, 96, 97)(90, 98, 99)(91, 100, 101)(94, 105, 106)(95, 107, 108)(102, 117, 118)(103, 110, 119)(104, 120, 121)(109, 126, 127)(111, 128, 129)(112, 130, 131)(113, 115, 132)(114, 133, 134)(116, 135, 136)(122, 143, 144)(123, 124, 145)(125, 146, 147)(137, 154, 160)(138, 140, 157)(139, 161, 162)(141, 150, 163)(142, 164, 165)(148, 168, 152)(149, 153, 155)(151, 156, 158)(159, 166, 167) 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) :: { ( 28^3 ) } Outer automorphisms :: reflexible Dual of E12.772 Transitivity :: ET+ VT AT Graph:: simple bipartite v = 56 e = 84 f = 6 degree seq :: [ 3^56 ] E12.772 :: Family: { 2ex } :: Oriented family(ies): { E3*c } Signature :: (0; {3, 3, 14}) Quotient :: edge Aut^+ = (C14 x C2) : C3 (small group id <84, 11>) Aut = ((C14 x C2) : C3) : C2 (small group id <168, 49>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T2)^2, F * T1 * T2 * F * T1^-1, (T1^-1 * T2^-1)^3, (T2 * T1^-1)^3, (T2^-1 * T1^-1)^3, T2^-4 * T1 * T2^2 * T1^-1, T1 * T2^6 * T1^-1 * T2^2 ] Map:: polytopal non-degenerate R = (1, 85, 3, 87, 9, 93, 25, 109, 41, 125, 68, 152, 62, 146, 81, 165, 59, 143, 74, 158, 46, 130, 37, 121, 15, 99, 5, 89)(2, 86, 6, 90, 17, 101, 40, 124, 60, 144, 66, 150, 35, 119, 52, 136, 24, 108, 51, 135, 63, 147, 47, 131, 21, 105, 7, 91)(4, 88, 11, 95, 29, 113, 55, 139, 26, 110, 49, 133, 45, 129, 70, 154, 39, 123, 65, 149, 36, 120, 64, 148, 32, 116, 12, 96)(8, 92, 22, 106, 48, 132, 76, 160, 61, 145, 30, 114, 13, 97, 33, 117, 53, 137, 79, 163, 82, 166, 77, 161, 50, 134, 23, 107)(10, 94, 19, 103, 43, 127, 71, 155, 54, 138, 78, 162, 67, 151, 69, 153, 38, 122, 16, 100, 14, 98, 34, 118, 57, 141, 27, 111)(18, 102, 31, 115, 56, 140, 80, 164, 72, 156, 84, 168, 75, 159, 83, 167, 58, 142, 28, 112, 20, 104, 44, 128, 73, 157, 42, 126) L = (1, 86)(2, 88)(3, 92)(4, 85)(5, 97)(6, 100)(7, 103)(8, 94)(9, 108)(10, 87)(11, 112)(12, 115)(13, 98)(14, 89)(15, 119)(16, 102)(17, 123)(18, 90)(19, 104)(20, 91)(21, 129)(22, 96)(23, 133)(24, 110)(25, 137)(26, 93)(27, 140)(28, 114)(29, 143)(30, 95)(31, 106)(32, 146)(33, 149)(34, 142)(35, 120)(36, 99)(37, 134)(38, 152)(39, 125)(40, 155)(41, 101)(42, 117)(43, 158)(44, 107)(45, 130)(46, 105)(47, 153)(48, 122)(49, 128)(50, 151)(51, 111)(52, 162)(53, 138)(54, 109)(55, 164)(56, 135)(57, 165)(58, 150)(59, 144)(60, 113)(61, 127)(62, 147)(63, 116)(64, 167)(65, 126)(66, 118)(67, 121)(68, 132)(69, 159)(70, 168)(71, 156)(72, 124)(73, 136)(74, 145)(75, 131)(76, 154)(77, 148)(78, 157)(79, 139)(80, 163)(81, 166)(82, 141)(83, 161)(84, 160) local type(s) :: { ( 3^28 ) } Outer automorphisms :: reflexible Dual of E12.771 Transitivity :: ET+ VT+ Graph:: v = 6 e = 84 f = 56 degree seq :: [ 28^6 ] E12.773 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {3, 3, 14}) Quotient :: edge^2 Aut^+ = (C14 x C2) : C3 (small group id <84, 11>) Aut = ((C14 x C2) : C3) : C2 (small group id <168, 49>) |r| :: 2 Presentation :: [ R^2, Y2^3, Y1^-1 * Y3^-1 * Y2^-1, Y1^3, R * Y2 * R * Y1, (R * Y3)^2, Y2 * Y1^-1 * Y2^-1 * Y3 * Y2 * Y1^-1, (Y3 * Y2^-1)^3, (Y3^-1 * Y1)^3, Y3 * Y2 * Y1 * Y3^-1 * Y1^-1 * Y2^-1, Y3 * Y2 * Y3^-1 * Y1 * Y3^3 ] Map:: polytopal non-degenerate R = (1, 85, 4, 88, 15, 99, 40, 124, 47, 131, 66, 150, 68, 152, 59, 143, 60, 144, 63, 147, 35, 119, 57, 141, 23, 107, 7, 91)(2, 86, 8, 92, 25, 109, 43, 127, 17, 101, 33, 117, 36, 120, 74, 158, 79, 163, 82, 166, 55, 139, 69, 153, 31, 115, 10, 94)(3, 87, 5, 89, 18, 102, 45, 129, 62, 146, 27, 111, 53, 137, 56, 140, 39, 123, 41, 125, 49, 133, 67, 151, 37, 121, 13, 97)(6, 90, 12, 96, 34, 118, 72, 156, 42, 126, 71, 155, 73, 157, 76, 160, 44, 128, 46, 130, 21, 105, 52, 136, 51, 135, 20, 104)(9, 93, 22, 106, 54, 138, 78, 162, 61, 145, 83, 167, 77, 161, 38, 122, 14, 98, 16, 100, 29, 113, 65, 149, 64, 148, 28, 112)(11, 95, 32, 116, 70, 154, 48, 132, 19, 103, 30, 114, 50, 134, 80, 164, 81, 165, 84, 168, 75, 159, 58, 142, 24, 108, 26, 110)(169, 170, 173)(171, 179, 180)(172, 174, 184)(175, 189, 190)(176, 177, 194)(178, 197, 198)(181, 203, 204)(182, 200, 201)(183, 185, 209)(186, 187, 214)(188, 217, 218)(191, 223, 224)(192, 220, 221)(193, 195, 228)(196, 231, 202)(199, 235, 236)(205, 243, 244)(206, 225, 241)(207, 238, 239)(208, 210, 246)(211, 229, 248)(212, 233, 234)(213, 215, 247)(216, 250, 222)(219, 251, 227)(226, 237, 245)(230, 249, 240)(232, 252, 242)(253, 255, 258)(254, 259, 261)(256, 266, 269)(257, 262, 271)(260, 276, 279)(263, 265, 285)(264, 278, 280)(267, 291, 294)(268, 272, 282)(270, 296, 299)(273, 275, 305)(274, 298, 300)(277, 311, 313)(281, 283, 318)(284, 290, 323)(286, 312, 314)(287, 289, 325)(288, 315, 316)(292, 306, 331)(293, 295, 302)(297, 326, 333)(301, 303, 320)(304, 310, 335)(307, 309, 329)(308, 334, 322)(317, 328, 336)(319, 321, 327)(324, 332, 330) L = (1, 169)(2, 170)(3, 171)(4, 172)(5, 173)(6, 174)(7, 175)(8, 176)(9, 177)(10, 178)(11, 179)(12, 180)(13, 181)(14, 182)(15, 183)(16, 184)(17, 185)(18, 186)(19, 187)(20, 188)(21, 189)(22, 190)(23, 191)(24, 192)(25, 193)(26, 194)(27, 195)(28, 196)(29, 197)(30, 198)(31, 199)(32, 200)(33, 201)(34, 202)(35, 203)(36, 204)(37, 205)(38, 206)(39, 207)(40, 208)(41, 209)(42, 210)(43, 211)(44, 212)(45, 213)(46, 214)(47, 215)(48, 216)(49, 217)(50, 218)(51, 219)(52, 220)(53, 221)(54, 222)(55, 223)(56, 224)(57, 225)(58, 226)(59, 227)(60, 228)(61, 229)(62, 230)(63, 231)(64, 232)(65, 233)(66, 234)(67, 235)(68, 236)(69, 237)(70, 238)(71, 239)(72, 240)(73, 241)(74, 242)(75, 243)(76, 244)(77, 245)(78, 246)(79, 247)(80, 248)(81, 249)(82, 250)(83, 251)(84, 252)(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) :: { ( 4^3 ), ( 4^28 ) } Outer automorphisms :: reflexible Dual of E12.776 Graph:: simple bipartite v = 62 e = 168 f = 84 degree seq :: [ 3^56, 28^6 ] E12.774 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {3, 3, 14}) Quotient :: edge^2 Aut^+ = (C14 x C2) : C3 (small group id <84, 11>) Aut = ((C14 x C2) : C3) : C2 (small group id <168, 49>) |r| :: 2 Presentation :: [ Y3, R^2, Y2^3, Y1^3, (R * Y3)^2, R * Y1 * R * Y2, (Y2^-1 * Y1)^3, Y2^-1 * Y1^-1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1, Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2^-1 * Y1^-1, (Y1^-1 * Y3^-1 * Y2^-1)^14 ] Map:: polytopal 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, 170, 172)(171, 176, 177)(173, 180, 181)(174, 182, 183)(175, 184, 185)(178, 189, 190)(179, 191, 192)(186, 201, 202)(187, 194, 203)(188, 204, 205)(193, 210, 211)(195, 212, 213)(196, 214, 215)(197, 199, 216)(198, 217, 218)(200, 219, 220)(206, 227, 228)(207, 208, 229)(209, 230, 231)(221, 238, 244)(222, 224, 241)(223, 245, 246)(225, 234, 247)(226, 248, 249)(232, 252, 236)(233, 237, 239)(235, 240, 242)(243, 250, 251)(253, 255, 257)(254, 258, 259)(256, 262, 263)(260, 270, 271)(261, 268, 272)(264, 277, 274)(265, 278, 279)(266, 280, 281)(267, 275, 282)(269, 283, 284)(273, 290, 291)(276, 292, 293)(285, 305, 306)(286, 288, 307)(287, 308, 309)(289, 303, 310)(294, 316, 312)(295, 296, 317)(297, 318, 319)(298, 320, 321)(299, 301, 322)(300, 323, 324)(302, 314, 325)(304, 326, 327)(311, 330, 332)(313, 333, 334)(315, 335, 331)(328, 329, 336) L = (1, 169)(2, 170)(3, 171)(4, 172)(5, 173)(6, 174)(7, 175)(8, 176)(9, 177)(10, 178)(11, 179)(12, 180)(13, 181)(14, 182)(15, 183)(16, 184)(17, 185)(18, 186)(19, 187)(20, 188)(21, 189)(22, 190)(23, 191)(24, 192)(25, 193)(26, 194)(27, 195)(28, 196)(29, 197)(30, 198)(31, 199)(32, 200)(33, 201)(34, 202)(35, 203)(36, 204)(37, 205)(38, 206)(39, 207)(40, 208)(41, 209)(42, 210)(43, 211)(44, 212)(45, 213)(46, 214)(47, 215)(48, 216)(49, 217)(50, 218)(51, 219)(52, 220)(53, 221)(54, 222)(55, 223)(56, 224)(57, 225)(58, 226)(59, 227)(60, 228)(61, 229)(62, 230)(63, 231)(64, 232)(65, 233)(66, 234)(67, 235)(68, 236)(69, 237)(70, 238)(71, 239)(72, 240)(73, 241)(74, 242)(75, 243)(76, 244)(77, 245)(78, 246)(79, 247)(80, 248)(81, 249)(82, 250)(83, 251)(84, 252)(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, 56 ), ( 56^3 ) } Outer automorphisms :: reflexible Dual of E12.775 Graph:: simple bipartite v = 140 e = 168 f = 6 degree seq :: [ 2^84, 3^56 ] E12.775 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {3, 3, 14}) Quotient :: loop^2 Aut^+ = (C14 x C2) : C3 (small group id <84, 11>) Aut = ((C14 x C2) : C3) : C2 (small group id <168, 49>) |r| :: 2 Presentation :: [ R^2, Y2^3, Y1^-1 * Y3^-1 * Y2^-1, Y1^3, R * Y2 * R * Y1, (R * Y3)^2, Y2 * Y1^-1 * Y2^-1 * Y3 * Y2 * Y1^-1, (Y3 * Y2^-1)^3, (Y3^-1 * Y1)^3, Y3 * Y2 * Y1 * Y3^-1 * Y1^-1 * Y2^-1, Y3 * Y2 * Y3^-1 * Y1 * Y3^3 ] Map:: R = (1, 85, 169, 253, 4, 88, 172, 256, 15, 99, 183, 267, 40, 124, 208, 292, 47, 131, 215, 299, 66, 150, 234, 318, 68, 152, 236, 320, 59, 143, 227, 311, 60, 144, 228, 312, 63, 147, 231, 315, 35, 119, 203, 287, 57, 141, 225, 309, 23, 107, 191, 275, 7, 91, 175, 259)(2, 86, 170, 254, 8, 92, 176, 260, 25, 109, 193, 277, 43, 127, 211, 295, 17, 101, 185, 269, 33, 117, 201, 285, 36, 120, 204, 288, 74, 158, 242, 326, 79, 163, 247, 331, 82, 166, 250, 334, 55, 139, 223, 307, 69, 153, 237, 321, 31, 115, 199, 283, 10, 94, 178, 262)(3, 87, 171, 255, 5, 89, 173, 257, 18, 102, 186, 270, 45, 129, 213, 297, 62, 146, 230, 314, 27, 111, 195, 279, 53, 137, 221, 305, 56, 140, 224, 308, 39, 123, 207, 291, 41, 125, 209, 293, 49, 133, 217, 301, 67, 151, 235, 319, 37, 121, 205, 289, 13, 97, 181, 265)(6, 90, 174, 258, 12, 96, 180, 264, 34, 118, 202, 286, 72, 156, 240, 324, 42, 126, 210, 294, 71, 155, 239, 323, 73, 157, 241, 325, 76, 160, 244, 328, 44, 128, 212, 296, 46, 130, 214, 298, 21, 105, 189, 273, 52, 136, 220, 304, 51, 135, 219, 303, 20, 104, 188, 272)(9, 93, 177, 261, 22, 106, 190, 274, 54, 138, 222, 306, 78, 162, 246, 330, 61, 145, 229, 313, 83, 167, 251, 335, 77, 161, 245, 329, 38, 122, 206, 290, 14, 98, 182, 266, 16, 100, 184, 268, 29, 113, 197, 281, 65, 149, 233, 317, 64, 148, 232, 316, 28, 112, 196, 280)(11, 95, 179, 263, 32, 116, 200, 284, 70, 154, 238, 322, 48, 132, 216, 300, 19, 103, 187, 271, 30, 114, 198, 282, 50, 134, 218, 302, 80, 164, 248, 332, 81, 165, 249, 333, 84, 168, 252, 336, 75, 159, 243, 327, 58, 142, 226, 310, 24, 108, 192, 276, 26, 110, 194, 278) L = (1, 86)(2, 89)(3, 95)(4, 90)(5, 85)(6, 100)(7, 105)(8, 93)(9, 110)(10, 113)(11, 96)(12, 87)(13, 119)(14, 116)(15, 101)(16, 88)(17, 125)(18, 103)(19, 130)(20, 133)(21, 106)(22, 91)(23, 139)(24, 136)(25, 111)(26, 92)(27, 144)(28, 147)(29, 114)(30, 94)(31, 151)(32, 117)(33, 98)(34, 112)(35, 120)(36, 97)(37, 159)(38, 141)(39, 154)(40, 126)(41, 99)(42, 162)(43, 145)(44, 149)(45, 131)(46, 102)(47, 163)(48, 166)(49, 134)(50, 104)(51, 167)(52, 137)(53, 108)(54, 132)(55, 140)(56, 107)(57, 157)(58, 153)(59, 135)(60, 109)(61, 164)(62, 165)(63, 118)(64, 168)(65, 150)(66, 128)(67, 152)(68, 115)(69, 161)(70, 155)(71, 123)(72, 146)(73, 122)(74, 148)(75, 160)(76, 121)(77, 142)(78, 124)(79, 129)(80, 127)(81, 156)(82, 138)(83, 143)(84, 158)(169, 255)(170, 259)(171, 258)(172, 266)(173, 262)(174, 253)(175, 261)(176, 276)(177, 254)(178, 271)(179, 265)(180, 278)(181, 285)(182, 269)(183, 291)(184, 272)(185, 256)(186, 296)(187, 257)(188, 282)(189, 275)(190, 298)(191, 305)(192, 279)(193, 311)(194, 280)(195, 260)(196, 264)(197, 283)(198, 268)(199, 318)(200, 290)(201, 263)(202, 312)(203, 289)(204, 315)(205, 325)(206, 323)(207, 294)(208, 306)(209, 295)(210, 267)(211, 302)(212, 299)(213, 326)(214, 300)(215, 270)(216, 274)(217, 303)(218, 293)(219, 320)(220, 310)(221, 273)(222, 331)(223, 309)(224, 334)(225, 329)(226, 335)(227, 313)(228, 314)(229, 277)(230, 286)(231, 316)(232, 288)(233, 328)(234, 281)(235, 321)(236, 301)(237, 327)(238, 308)(239, 284)(240, 332)(241, 287)(242, 333)(243, 319)(244, 336)(245, 307)(246, 324)(247, 292)(248, 330)(249, 297)(250, 322)(251, 304)(252, 317) 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, 2, 3, 2, 3, 2, 3, 2, 3, 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 :: reflexible Dual of E12.774 Transitivity :: VT+ Graph:: v = 6 e = 168 f = 140 degree seq :: [ 56^6 ] E12.776 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {3, 3, 14}) Quotient :: loop^2 Aut^+ = (C14 x C2) : C3 (small group id <84, 11>) Aut = ((C14 x C2) : C3) : C2 (small group id <168, 49>) |r| :: 2 Presentation :: [ Y3, R^2, Y2^3, Y1^3, (R * Y3)^2, R * Y1 * R * Y2, (Y2^-1 * Y1)^3, Y2^-1 * Y1^-1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1, Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2^-1 * Y1^-1, (Y1^-1 * Y3^-1 * Y2^-1)^14 ] Map:: polytopal non-degenerate R = (1, 85, 169, 253)(2, 86, 170, 254)(3, 87, 171, 255)(4, 88, 172, 256)(5, 89, 173, 257)(6, 90, 174, 258)(7, 91, 175, 259)(8, 92, 176, 260)(9, 93, 177, 261)(10, 94, 178, 262)(11, 95, 179, 263)(12, 96, 180, 264)(13, 97, 181, 265)(14, 98, 182, 266)(15, 99, 183, 267)(16, 100, 184, 268)(17, 101, 185, 269)(18, 102, 186, 270)(19, 103, 187, 271)(20, 104, 188, 272)(21, 105, 189, 273)(22, 106, 190, 274)(23, 107, 191, 275)(24, 108, 192, 276)(25, 109, 193, 277)(26, 110, 194, 278)(27, 111, 195, 279)(28, 112, 196, 280)(29, 113, 197, 281)(30, 114, 198, 282)(31, 115, 199, 283)(32, 116, 200, 284)(33, 117, 201, 285)(34, 118, 202, 286)(35, 119, 203, 287)(36, 120, 204, 288)(37, 121, 205, 289)(38, 122, 206, 290)(39, 123, 207, 291)(40, 124, 208, 292)(41, 125, 209, 293)(42, 126, 210, 294)(43, 127, 211, 295)(44, 128, 212, 296)(45, 129, 213, 297)(46, 130, 214, 298)(47, 131, 215, 299)(48, 132, 216, 300)(49, 133, 217, 301)(50, 134, 218, 302)(51, 135, 219, 303)(52, 136, 220, 304)(53, 137, 221, 305)(54, 138, 222, 306)(55, 139, 223, 307)(56, 140, 224, 308)(57, 141, 225, 309)(58, 142, 226, 310)(59, 143, 227, 311)(60, 144, 228, 312)(61, 145, 229, 313)(62, 146, 230, 314)(63, 147, 231, 315)(64, 148, 232, 316)(65, 149, 233, 317)(66, 150, 234, 318)(67, 151, 235, 319)(68, 152, 236, 320)(69, 153, 237, 321)(70, 154, 238, 322)(71, 155, 239, 323)(72, 156, 240, 324)(73, 157, 241, 325)(74, 158, 242, 326)(75, 159, 243, 327)(76, 160, 244, 328)(77, 161, 245, 329)(78, 162, 246, 330)(79, 163, 247, 331)(80, 164, 248, 332)(81, 165, 249, 333)(82, 166, 250, 334)(83, 167, 251, 335)(84, 168, 252, 336) L = (1, 86)(2, 88)(3, 92)(4, 85)(5, 96)(6, 98)(7, 100)(8, 93)(9, 87)(10, 105)(11, 107)(12, 97)(13, 89)(14, 99)(15, 90)(16, 101)(17, 91)(18, 117)(19, 110)(20, 120)(21, 106)(22, 94)(23, 108)(24, 95)(25, 126)(26, 119)(27, 128)(28, 130)(29, 115)(30, 133)(31, 132)(32, 135)(33, 118)(34, 102)(35, 103)(36, 121)(37, 104)(38, 143)(39, 124)(40, 145)(41, 146)(42, 127)(43, 109)(44, 129)(45, 111)(46, 131)(47, 112)(48, 113)(49, 134)(50, 114)(51, 136)(52, 116)(53, 154)(54, 140)(55, 161)(56, 157)(57, 150)(58, 164)(59, 144)(60, 122)(61, 123)(62, 147)(63, 125)(64, 168)(65, 153)(66, 163)(67, 156)(68, 148)(69, 155)(70, 160)(71, 149)(72, 158)(73, 138)(74, 151)(75, 166)(76, 137)(77, 162)(78, 139)(79, 141)(80, 165)(81, 142)(82, 167)(83, 159)(84, 152)(169, 255)(170, 258)(171, 257)(172, 262)(173, 253)(174, 259)(175, 254)(176, 270)(177, 268)(178, 263)(179, 256)(180, 277)(181, 278)(182, 280)(183, 275)(184, 272)(185, 283)(186, 271)(187, 260)(188, 261)(189, 290)(190, 264)(191, 282)(192, 292)(193, 274)(194, 279)(195, 265)(196, 281)(197, 266)(198, 267)(199, 284)(200, 269)(201, 305)(202, 288)(203, 308)(204, 307)(205, 303)(206, 291)(207, 273)(208, 293)(209, 276)(210, 316)(211, 296)(212, 317)(213, 318)(214, 320)(215, 301)(216, 323)(217, 322)(218, 314)(219, 310)(220, 326)(221, 306)(222, 285)(223, 286)(224, 309)(225, 287)(226, 289)(227, 330)(228, 294)(229, 333)(230, 325)(231, 335)(232, 312)(233, 295)(234, 319)(235, 297)(236, 321)(237, 298)(238, 299)(239, 324)(240, 300)(241, 302)(242, 327)(243, 304)(244, 329)(245, 336)(246, 332)(247, 315)(248, 311)(249, 334)(250, 313)(251, 331)(252, 328) local type(s) :: { ( 3, 28, 3, 28 ) } Outer automorphisms :: reflexible Dual of E12.773 Transitivity :: VT+ Graph:: simple v = 84 e = 168 f = 62 degree seq :: [ 4^84 ] E12.777 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 6, 14}) Quotient :: regular Aut^+ = S3 x D14 (small group id <84, 8>) Aut = C2 x S3 x D14 (small group id <168, 50>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^2)^2, T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2, T1^14 ] Map:: polytopal non-degenerate R = (1, 2, 5, 11, 20, 32, 47, 61, 60, 46, 31, 19, 10, 4)(3, 7, 15, 25, 39, 55, 67, 73, 62, 49, 33, 22, 12, 8)(6, 13, 9, 18, 29, 44, 58, 70, 72, 63, 48, 34, 21, 14)(16, 26, 17, 28, 35, 51, 64, 75, 80, 77, 68, 56, 40, 27)(23, 36, 24, 38, 50, 65, 74, 81, 79, 71, 59, 45, 30, 37)(41, 53, 42, 57, 69, 78, 83, 84, 82, 76, 66, 54, 43, 52) 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, 59)(45, 57)(46, 58)(47, 62)(49, 64)(51, 66)(55, 68)(56, 69)(60, 67)(61, 72)(63, 74)(65, 76)(70, 79)(71, 78)(73, 80)(75, 82)(77, 83)(81, 84) local type(s) :: { ( 6^14 ) } Outer automorphisms :: reflexible Dual of E12.778 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 6 e = 42 f = 14 degree seq :: [ 14^6 ] E12.778 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 6, 14}) Quotient :: regular Aut^+ = S3 x D14 (small group id <84, 8>) Aut = C2 x S3 x D14 (small group id <168, 50>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1 * T2 * T1)^2, T1^6, 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 ] Map:: polytopal non-degenerate R = (1, 2, 5, 11, 10, 4)(3, 7, 15, 20, 12, 8)(6, 13, 9, 18, 19, 14)(16, 23, 17, 25, 27, 24)(21, 28, 22, 30, 26, 29)(31, 37, 32, 39, 33, 38)(34, 40, 35, 42, 36, 41)(43, 49, 44, 51, 45, 50)(46, 52, 47, 54, 48, 53)(55, 61, 56, 63, 57, 62)(58, 64, 59, 66, 60, 65)(67, 73, 68, 75, 69, 74)(70, 76, 71, 78, 72, 77)(79, 83, 80, 84, 81, 82) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 15)(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, 79)(74, 80)(75, 81)(76, 82)(77, 83)(78, 84) local type(s) :: { ( 14^6 ) } Outer automorphisms :: reflexible Dual of E12.777 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 14 e = 42 f = 6 degree seq :: [ 6^14 ] E12.779 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 6, 14}) Quotient :: edge Aut^+ = S3 x D14 (small group id <84, 8>) Aut = C2 x S3 x D14 (small group id <168, 50>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, (T2^-1 * T1 * T2^-1)^2, T2^6, (T2 * T1)^14 ] Map:: polytopal R = (1, 3, 8, 17, 10, 4)(2, 5, 12, 21, 14, 6)(7, 15, 9, 18, 25, 16)(11, 19, 13, 22, 29, 20)(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, 58, 53, 60, 54, 59)(61, 67, 62, 69, 63, 68)(64, 70, 65, 72, 66, 71)(73, 79, 74, 81, 75, 80)(76, 82, 77, 84, 78, 83)(85, 86)(87, 91)(88, 93)(89, 95)(90, 97)(92, 98)(94, 96)(99, 107)(100, 108)(101, 109)(102, 110)(103, 111)(104, 112)(105, 113)(106, 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, 157)(152, 158)(153, 159)(154, 160)(155, 161)(156, 162)(163, 167)(164, 166)(165, 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) :: { ( 28, 28 ), ( 28^6 ) } Outer automorphisms :: reflexible Dual of E12.783 Transitivity :: ET+ Graph:: simple bipartite v = 56 e = 84 f = 6 degree seq :: [ 2^42, 6^14 ] E12.780 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 6, 14}) Quotient :: edge Aut^+ = S3 x D14 (small group id <84, 8>) Aut = C2 x S3 x D14 (small group id <168, 50>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1 * T1^-1)^2, (T2 * T1^-1)^2, T1^6, T2^14 ] Map:: polytopal non-degenerate R = (1, 3, 10, 21, 33, 45, 57, 69, 60, 48, 36, 24, 13, 5)(2, 7, 17, 29, 41, 53, 65, 76, 66, 54, 42, 30, 18, 8)(4, 11, 23, 35, 47, 59, 71, 78, 68, 56, 44, 32, 20, 9)(6, 15, 27, 39, 51, 63, 74, 82, 75, 64, 52, 40, 28, 16)(12, 19, 31, 43, 55, 67, 77, 83, 79, 70, 58, 46, 34, 22)(14, 25, 37, 49, 61, 72, 80, 84, 81, 73, 62, 50, 38, 26)(85, 86, 90, 98, 96, 88)(87, 93, 103, 110, 99, 92)(89, 95, 106, 109, 100, 91)(94, 102, 111, 122, 115, 104)(97, 101, 112, 121, 118, 107)(105, 116, 127, 134, 123, 114)(108, 119, 130, 133, 124, 113)(117, 126, 135, 146, 139, 128)(120, 125, 136, 145, 142, 131)(129, 140, 151, 157, 147, 138)(132, 143, 154, 156, 148, 137)(141, 150, 158, 165, 161, 152)(144, 149, 159, 164, 163, 155)(153, 162, 167, 168, 166, 160) 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) :: { ( 4^6 ), ( 4^14 ) } Outer automorphisms :: reflexible Dual of E12.784 Transitivity :: ET+ Graph:: simple bipartite v = 20 e = 84 f = 42 degree seq :: [ 6^14, 14^6 ] E12.781 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 6, 14}) Quotient :: edge Aut^+ = S3 x D14 (small group id <84, 8>) Aut = C2 x S3 x D14 (small group id <168, 50>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^2)^2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1, T1^14 ] 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, 59)(45, 57)(46, 58)(47, 62)(49, 64)(51, 66)(55, 68)(56, 69)(60, 67)(61, 72)(63, 74)(65, 76)(70, 79)(71, 78)(73, 80)(75, 82)(77, 83)(81, 84)(85, 86, 89, 95, 104, 116, 131, 145, 144, 130, 115, 103, 94, 88)(87, 91, 99, 109, 123, 139, 151, 157, 146, 133, 117, 106, 96, 92)(90, 97, 93, 102, 113, 128, 142, 154, 156, 147, 132, 118, 105, 98)(100, 110, 101, 112, 119, 135, 148, 159, 164, 161, 152, 140, 124, 111)(107, 120, 108, 122, 134, 149, 158, 165, 163, 155, 143, 129, 114, 121)(125, 137, 126, 141, 153, 162, 167, 168, 166, 160, 150, 138, 127, 136) 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) :: { ( 12, 12 ), ( 12^14 ) } Outer automorphisms :: reflexible Dual of E12.782 Transitivity :: ET+ Graph:: simple bipartite v = 48 e = 84 f = 14 degree seq :: [ 2^42, 14^6 ] E12.782 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 6, 14}) Quotient :: loop Aut^+ = S3 x D14 (small group id <84, 8>) Aut = C2 x S3 x D14 (small group id <168, 50>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, (T2^-1 * T1 * T2^-1)^2, T2^6, (T2 * T1)^14 ] Map:: R = (1, 85, 3, 87, 8, 92, 17, 101, 10, 94, 4, 88)(2, 86, 5, 89, 12, 96, 21, 105, 14, 98, 6, 90)(7, 91, 15, 99, 9, 93, 18, 102, 25, 109, 16, 100)(11, 95, 19, 103, 13, 97, 22, 106, 29, 113, 20, 104)(23, 107, 31, 115, 24, 108, 33, 117, 26, 110, 32, 116)(27, 111, 34, 118, 28, 112, 36, 120, 30, 114, 35, 119)(37, 121, 43, 127, 38, 122, 45, 129, 39, 123, 44, 128)(40, 124, 46, 130, 41, 125, 48, 132, 42, 126, 47, 131)(49, 133, 55, 139, 50, 134, 57, 141, 51, 135, 56, 140)(52, 136, 58, 142, 53, 137, 60, 144, 54, 138, 59, 143)(61, 145, 67, 151, 62, 146, 69, 153, 63, 147, 68, 152)(64, 148, 70, 154, 65, 149, 72, 156, 66, 150, 71, 155)(73, 157, 79, 163, 74, 158, 81, 165, 75, 159, 80, 164)(76, 160, 82, 166, 77, 161, 84, 168, 78, 162, 83, 167) L = (1, 86)(2, 85)(3, 91)(4, 93)(5, 95)(6, 97)(7, 87)(8, 98)(9, 88)(10, 96)(11, 89)(12, 94)(13, 90)(14, 92)(15, 107)(16, 108)(17, 109)(18, 110)(19, 111)(20, 112)(21, 113)(22, 114)(23, 99)(24, 100)(25, 101)(26, 102)(27, 103)(28, 104)(29, 105)(30, 106)(31, 121)(32, 122)(33, 123)(34, 124)(35, 125)(36, 126)(37, 115)(38, 116)(39, 117)(40, 118)(41, 119)(42, 120)(43, 133)(44, 134)(45, 135)(46, 136)(47, 137)(48, 138)(49, 127)(50, 128)(51, 129)(52, 130)(53, 131)(54, 132)(55, 145)(56, 146)(57, 147)(58, 148)(59, 149)(60, 150)(61, 139)(62, 140)(63, 141)(64, 142)(65, 143)(66, 144)(67, 157)(68, 158)(69, 159)(70, 160)(71, 161)(72, 162)(73, 151)(74, 152)(75, 153)(76, 154)(77, 155)(78, 156)(79, 167)(80, 166)(81, 168)(82, 164)(83, 163)(84, 165) local type(s) :: { ( 2, 14, 2, 14, 2, 14, 2, 14, 2, 14, 2, 14 ) } Outer automorphisms :: reflexible Dual of E12.781 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 14 e = 84 f = 48 degree seq :: [ 12^14 ] E12.783 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 6, 14}) Quotient :: loop Aut^+ = S3 x D14 (small group id <84, 8>) Aut = C2 x S3 x D14 (small group id <168, 50>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1 * T1^-1)^2, (T2 * T1^-1)^2, T1^6, T2^14 ] Map:: R = (1, 85, 3, 87, 10, 94, 21, 105, 33, 117, 45, 129, 57, 141, 69, 153, 60, 144, 48, 132, 36, 120, 24, 108, 13, 97, 5, 89)(2, 86, 7, 91, 17, 101, 29, 113, 41, 125, 53, 137, 65, 149, 76, 160, 66, 150, 54, 138, 42, 126, 30, 114, 18, 102, 8, 92)(4, 88, 11, 95, 23, 107, 35, 119, 47, 131, 59, 143, 71, 155, 78, 162, 68, 152, 56, 140, 44, 128, 32, 116, 20, 104, 9, 93)(6, 90, 15, 99, 27, 111, 39, 123, 51, 135, 63, 147, 74, 158, 82, 166, 75, 159, 64, 148, 52, 136, 40, 124, 28, 112, 16, 100)(12, 96, 19, 103, 31, 115, 43, 127, 55, 139, 67, 151, 77, 161, 83, 167, 79, 163, 70, 154, 58, 142, 46, 130, 34, 118, 22, 106)(14, 98, 25, 109, 37, 121, 49, 133, 61, 145, 72, 156, 80, 164, 84, 168, 81, 165, 73, 157, 62, 146, 50, 134, 38, 122, 26, 110) L = (1, 86)(2, 90)(3, 93)(4, 85)(5, 95)(6, 98)(7, 89)(8, 87)(9, 103)(10, 102)(11, 106)(12, 88)(13, 101)(14, 96)(15, 92)(16, 91)(17, 112)(18, 111)(19, 110)(20, 94)(21, 116)(22, 109)(23, 97)(24, 119)(25, 100)(26, 99)(27, 122)(28, 121)(29, 108)(30, 105)(31, 104)(32, 127)(33, 126)(34, 107)(35, 130)(36, 125)(37, 118)(38, 115)(39, 114)(40, 113)(41, 136)(42, 135)(43, 134)(44, 117)(45, 140)(46, 133)(47, 120)(48, 143)(49, 124)(50, 123)(51, 146)(52, 145)(53, 132)(54, 129)(55, 128)(56, 151)(57, 150)(58, 131)(59, 154)(60, 149)(61, 142)(62, 139)(63, 138)(64, 137)(65, 159)(66, 158)(67, 157)(68, 141)(69, 162)(70, 156)(71, 144)(72, 148)(73, 147)(74, 165)(75, 164)(76, 153)(77, 152)(78, 167)(79, 155)(80, 163)(81, 161)(82, 160)(83, 168)(84, 166) 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 ) } Outer automorphisms :: reflexible Dual of E12.779 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 6 e = 84 f = 56 degree seq :: [ 28^6 ] E12.784 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 6, 14}) Quotient :: loop Aut^+ = S3 x D14 (small group id <84, 8>) Aut = C2 x S3 x D14 (small group id <168, 50>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^2)^2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1, T1^14 ] Map:: polytopal non-degenerate R = (1, 85, 3, 87)(2, 86, 6, 90)(4, 88, 9, 93)(5, 89, 12, 96)(7, 91, 16, 100)(8, 92, 17, 101)(10, 94, 15, 99)(11, 95, 21, 105)(13, 97, 23, 107)(14, 98, 24, 108)(18, 102, 30, 114)(19, 103, 29, 113)(20, 104, 33, 117)(22, 106, 35, 119)(25, 109, 40, 124)(26, 110, 41, 125)(27, 111, 42, 126)(28, 112, 43, 127)(31, 115, 39, 123)(32, 116, 48, 132)(34, 118, 50, 134)(36, 120, 52, 136)(37, 121, 53, 137)(38, 122, 54, 138)(44, 128, 59, 143)(45, 129, 57, 141)(46, 130, 58, 142)(47, 131, 62, 146)(49, 133, 64, 148)(51, 135, 66, 150)(55, 139, 68, 152)(56, 140, 69, 153)(60, 144, 67, 151)(61, 145, 72, 156)(63, 147, 74, 158)(65, 149, 76, 160)(70, 154, 79, 163)(71, 155, 78, 162)(73, 157, 80, 164)(75, 159, 82, 166)(77, 161, 83, 167)(81, 165, 84, 168) L = (1, 86)(2, 89)(3, 91)(4, 85)(5, 95)(6, 97)(7, 99)(8, 87)(9, 102)(10, 88)(11, 104)(12, 92)(13, 93)(14, 90)(15, 109)(16, 110)(17, 112)(18, 113)(19, 94)(20, 116)(21, 98)(22, 96)(23, 120)(24, 122)(25, 123)(26, 101)(27, 100)(28, 119)(29, 128)(30, 121)(31, 103)(32, 131)(33, 106)(34, 105)(35, 135)(36, 108)(37, 107)(38, 134)(39, 139)(40, 111)(41, 137)(42, 141)(43, 136)(44, 142)(45, 114)(46, 115)(47, 145)(48, 118)(49, 117)(50, 149)(51, 148)(52, 125)(53, 126)(54, 127)(55, 151)(56, 124)(57, 153)(58, 154)(59, 129)(60, 130)(61, 144)(62, 133)(63, 132)(64, 159)(65, 158)(66, 138)(67, 157)(68, 140)(69, 162)(70, 156)(71, 143)(72, 147)(73, 146)(74, 165)(75, 164)(76, 150)(77, 152)(78, 167)(79, 155)(80, 161)(81, 163)(82, 160)(83, 168)(84, 166) local type(s) :: { ( 6, 14, 6, 14 ) } Outer automorphisms :: reflexible Dual of E12.780 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 42 e = 84 f = 20 degree seq :: [ 4^42 ] E12.785 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 14}) Quotient :: dipole Aut^+ = S3 x D14 (small group id <84, 8>) Aut = C2 x S3 x D14 (small group id <168, 50>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y2^2 * Y1)^2, Y2^6, (Y3 * Y2^-1)^14 ] Map:: R = (1, 85, 2, 86)(3, 87, 7, 91)(4, 88, 9, 93)(5, 89, 11, 95)(6, 90, 13, 97)(8, 92, 14, 98)(10, 94, 12, 96)(15, 99, 23, 107)(16, 100, 24, 108)(17, 101, 25, 109)(18, 102, 26, 110)(19, 103, 27, 111)(20, 104, 28, 112)(21, 105, 29, 113)(22, 106, 30, 114)(31, 115, 37, 121)(32, 116, 38, 122)(33, 117, 39, 123)(34, 118, 40, 124)(35, 119, 41, 125)(36, 120, 42, 126)(43, 127, 49, 133)(44, 128, 50, 134)(45, 129, 51, 135)(46, 130, 52, 136)(47, 131, 53, 137)(48, 132, 54, 138)(55, 139, 61, 145)(56, 140, 62, 146)(57, 141, 63, 147)(58, 142, 64, 148)(59, 143, 65, 149)(60, 144, 66, 150)(67, 151, 73, 157)(68, 152, 74, 158)(69, 153, 75, 159)(70, 154, 76, 160)(71, 155, 77, 161)(72, 156, 78, 162)(79, 163, 83, 167)(80, 164, 82, 166)(81, 165, 84, 168)(169, 253, 171, 255, 176, 260, 185, 269, 178, 262, 172, 256)(170, 254, 173, 257, 180, 264, 189, 273, 182, 266, 174, 258)(175, 259, 183, 267, 177, 261, 186, 270, 193, 277, 184, 268)(179, 263, 187, 271, 181, 265, 190, 274, 197, 281, 188, 272)(191, 275, 199, 283, 192, 276, 201, 285, 194, 278, 200, 284)(195, 279, 202, 286, 196, 280, 204, 288, 198, 282, 203, 287)(205, 289, 211, 295, 206, 290, 213, 297, 207, 291, 212, 296)(208, 292, 214, 298, 209, 293, 216, 300, 210, 294, 215, 299)(217, 301, 223, 307, 218, 302, 225, 309, 219, 303, 224, 308)(220, 304, 226, 310, 221, 305, 228, 312, 222, 306, 227, 311)(229, 313, 235, 319, 230, 314, 237, 321, 231, 315, 236, 320)(232, 316, 238, 322, 233, 317, 240, 324, 234, 318, 239, 323)(241, 325, 247, 331, 242, 326, 249, 333, 243, 327, 248, 332)(244, 328, 250, 334, 245, 329, 252, 336, 246, 330, 251, 335) L = (1, 170)(2, 169)(3, 175)(4, 177)(5, 179)(6, 181)(7, 171)(8, 182)(9, 172)(10, 180)(11, 173)(12, 178)(13, 174)(14, 176)(15, 191)(16, 192)(17, 193)(18, 194)(19, 195)(20, 196)(21, 197)(22, 198)(23, 183)(24, 184)(25, 185)(26, 186)(27, 187)(28, 188)(29, 189)(30, 190)(31, 205)(32, 206)(33, 207)(34, 208)(35, 209)(36, 210)(37, 199)(38, 200)(39, 201)(40, 202)(41, 203)(42, 204)(43, 217)(44, 218)(45, 219)(46, 220)(47, 221)(48, 222)(49, 211)(50, 212)(51, 213)(52, 214)(53, 215)(54, 216)(55, 229)(56, 230)(57, 231)(58, 232)(59, 233)(60, 234)(61, 223)(62, 224)(63, 225)(64, 226)(65, 227)(66, 228)(67, 241)(68, 242)(69, 243)(70, 244)(71, 245)(72, 246)(73, 235)(74, 236)(75, 237)(76, 238)(77, 239)(78, 240)(79, 251)(80, 250)(81, 252)(82, 248)(83, 247)(84, 249)(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, 28, 2, 28 ), ( 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28 ) } Outer automorphisms :: reflexible Dual of E12.788 Graph:: bipartite v = 56 e = 168 f = 90 degree seq :: [ 4^42, 12^14 ] E12.786 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 14}) Quotient :: dipole Aut^+ = S3 x D14 (small group id <84, 8>) Aut = C2 x S3 x D14 (small group id <168, 50>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (Y2^-1 * Y1^-1)^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, (Y2^-1 * Y1)^2, Y1^6, Y2^14 ] Map:: R = (1, 85, 2, 86, 6, 90, 14, 98, 12, 96, 4, 88)(3, 87, 9, 93, 19, 103, 26, 110, 15, 99, 8, 92)(5, 89, 11, 95, 22, 106, 25, 109, 16, 100, 7, 91)(10, 94, 18, 102, 27, 111, 38, 122, 31, 115, 20, 104)(13, 97, 17, 101, 28, 112, 37, 121, 34, 118, 23, 107)(21, 105, 32, 116, 43, 127, 50, 134, 39, 123, 30, 114)(24, 108, 35, 119, 46, 130, 49, 133, 40, 124, 29, 113)(33, 117, 42, 126, 51, 135, 62, 146, 55, 139, 44, 128)(36, 120, 41, 125, 52, 136, 61, 145, 58, 142, 47, 131)(45, 129, 56, 140, 67, 151, 73, 157, 63, 147, 54, 138)(48, 132, 59, 143, 70, 154, 72, 156, 64, 148, 53, 137)(57, 141, 66, 150, 74, 158, 81, 165, 77, 161, 68, 152)(60, 144, 65, 149, 75, 159, 80, 164, 79, 163, 71, 155)(69, 153, 78, 162, 83, 167, 84, 168, 82, 166, 76, 160)(169, 253, 171, 255, 178, 262, 189, 273, 201, 285, 213, 297, 225, 309, 237, 321, 228, 312, 216, 300, 204, 288, 192, 276, 181, 265, 173, 257)(170, 254, 175, 259, 185, 269, 197, 281, 209, 293, 221, 305, 233, 317, 244, 328, 234, 318, 222, 306, 210, 294, 198, 282, 186, 270, 176, 260)(172, 256, 179, 263, 191, 275, 203, 287, 215, 299, 227, 311, 239, 323, 246, 330, 236, 320, 224, 308, 212, 296, 200, 284, 188, 272, 177, 261)(174, 258, 183, 267, 195, 279, 207, 291, 219, 303, 231, 315, 242, 326, 250, 334, 243, 327, 232, 316, 220, 304, 208, 292, 196, 280, 184, 268)(180, 264, 187, 271, 199, 283, 211, 295, 223, 307, 235, 319, 245, 329, 251, 335, 247, 331, 238, 322, 226, 310, 214, 298, 202, 286, 190, 274)(182, 266, 193, 277, 205, 289, 217, 301, 229, 313, 240, 324, 248, 332, 252, 336, 249, 333, 241, 325, 230, 314, 218, 302, 206, 290, 194, 278) L = (1, 171)(2, 175)(3, 178)(4, 179)(5, 169)(6, 183)(7, 185)(8, 170)(9, 172)(10, 189)(11, 191)(12, 187)(13, 173)(14, 193)(15, 195)(16, 174)(17, 197)(18, 176)(19, 199)(20, 177)(21, 201)(22, 180)(23, 203)(24, 181)(25, 205)(26, 182)(27, 207)(28, 184)(29, 209)(30, 186)(31, 211)(32, 188)(33, 213)(34, 190)(35, 215)(36, 192)(37, 217)(38, 194)(39, 219)(40, 196)(41, 221)(42, 198)(43, 223)(44, 200)(45, 225)(46, 202)(47, 227)(48, 204)(49, 229)(50, 206)(51, 231)(52, 208)(53, 233)(54, 210)(55, 235)(56, 212)(57, 237)(58, 214)(59, 239)(60, 216)(61, 240)(62, 218)(63, 242)(64, 220)(65, 244)(66, 222)(67, 245)(68, 224)(69, 228)(70, 226)(71, 246)(72, 248)(73, 230)(74, 250)(75, 232)(76, 234)(77, 251)(78, 236)(79, 238)(80, 252)(81, 241)(82, 243)(83, 247)(84, 249)(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, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 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 E12.787 Graph:: bipartite v = 20 e = 168 f = 126 degree seq :: [ 12^14, 28^6 ] E12.787 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 14}) Quotient :: dipole Aut^+ = S3 x D14 (small group id <84, 8>) Aut = C2 x S3 x D14 (small group id <168, 50>) |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 * Y2 * Y3 * Y2, (Y3^-1 * Y1^-1)^14 ] Map:: polytopal 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)(171, 255, 175, 259)(172, 256, 177, 261)(173, 257, 179, 263)(174, 258, 181, 265)(176, 260, 182, 266)(178, 262, 180, 264)(183, 267, 193, 277)(184, 268, 194, 278)(185, 269, 195, 279)(186, 270, 197, 281)(187, 271, 198, 282)(188, 272, 200, 284)(189, 273, 201, 285)(190, 274, 202, 286)(191, 275, 204, 288)(192, 276, 205, 289)(196, 280, 206, 290)(199, 283, 203, 287)(207, 291, 216, 300)(208, 292, 215, 299)(209, 293, 220, 304)(210, 294, 223, 307)(211, 295, 224, 308)(212, 296, 217, 301)(213, 297, 226, 310)(214, 298, 227, 311)(218, 302, 229, 313)(219, 303, 230, 314)(221, 305, 232, 316)(222, 306, 233, 317)(225, 309, 234, 318)(228, 312, 231, 315)(235, 319, 243, 327)(236, 320, 245, 329)(237, 321, 246, 330)(238, 322, 240, 324)(239, 323, 247, 331)(241, 325, 248, 332)(242, 326, 249, 333)(244, 328, 250, 334)(251, 335, 252, 336) L = (1, 171)(2, 173)(3, 176)(4, 169)(5, 180)(6, 170)(7, 183)(8, 185)(9, 186)(10, 172)(11, 188)(12, 190)(13, 191)(14, 174)(15, 177)(16, 175)(17, 196)(18, 198)(19, 178)(20, 181)(21, 179)(22, 203)(23, 205)(24, 182)(25, 207)(26, 209)(27, 184)(28, 211)(29, 208)(30, 213)(31, 187)(32, 215)(33, 217)(34, 189)(35, 219)(36, 216)(37, 221)(38, 192)(39, 194)(40, 193)(41, 223)(42, 195)(43, 225)(44, 197)(45, 227)(46, 199)(47, 201)(48, 200)(49, 229)(50, 202)(51, 231)(52, 204)(53, 233)(54, 206)(55, 235)(56, 210)(57, 237)(58, 212)(59, 239)(60, 214)(61, 240)(62, 218)(63, 242)(64, 220)(65, 244)(66, 222)(67, 245)(68, 224)(69, 228)(70, 226)(71, 246)(72, 248)(73, 230)(74, 234)(75, 232)(76, 249)(77, 251)(78, 236)(79, 238)(80, 252)(81, 241)(82, 243)(83, 247)(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) :: { ( 12, 28 ), ( 12, 28, 12, 28 ) } Outer automorphisms :: reflexible Dual of E12.786 Graph:: simple bipartite v = 126 e = 168 f = 20 degree seq :: [ 2^84, 4^42 ] E12.788 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 14}) Quotient :: dipole Aut^+ = S3 x D14 (small group id <84, 8>) Aut = C2 x S3 x D14 (small group id <168, 50>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2^-1)^2, (R * Y2 * Y3^-1)^2, Y3 * Y1^-2 * Y3^-1 * Y1^-2, (Y3^-1 * Y1)^6, Y1^14 ] Map:: polytopal R = (1, 85, 2, 86, 5, 89, 11, 95, 20, 104, 32, 116, 47, 131, 61, 145, 60, 144, 46, 130, 31, 115, 19, 103, 10, 94, 4, 88)(3, 87, 7, 91, 15, 99, 25, 109, 39, 123, 55, 139, 67, 151, 73, 157, 62, 146, 49, 133, 33, 117, 22, 106, 12, 96, 8, 92)(6, 90, 13, 97, 9, 93, 18, 102, 29, 113, 44, 128, 58, 142, 70, 154, 72, 156, 63, 147, 48, 132, 34, 118, 21, 105, 14, 98)(16, 100, 26, 110, 17, 101, 28, 112, 35, 119, 51, 135, 64, 148, 75, 159, 80, 164, 77, 161, 68, 152, 56, 140, 40, 124, 27, 111)(23, 107, 36, 120, 24, 108, 38, 122, 50, 134, 65, 149, 74, 158, 81, 165, 79, 163, 71, 155, 59, 143, 45, 129, 30, 114, 37, 121)(41, 125, 53, 137, 42, 126, 57, 141, 69, 153, 78, 162, 83, 167, 84, 168, 82, 166, 76, 160, 66, 150, 54, 138, 43, 127, 52, 136)(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, 174)(3, 169)(4, 177)(5, 180)(6, 170)(7, 184)(8, 185)(9, 172)(10, 183)(11, 189)(12, 173)(13, 191)(14, 192)(15, 178)(16, 175)(17, 176)(18, 198)(19, 197)(20, 201)(21, 179)(22, 203)(23, 181)(24, 182)(25, 208)(26, 209)(27, 210)(28, 211)(29, 187)(30, 186)(31, 207)(32, 216)(33, 188)(34, 218)(35, 190)(36, 220)(37, 221)(38, 222)(39, 199)(40, 193)(41, 194)(42, 195)(43, 196)(44, 227)(45, 225)(46, 226)(47, 230)(48, 200)(49, 232)(50, 202)(51, 234)(52, 204)(53, 205)(54, 206)(55, 236)(56, 237)(57, 213)(58, 214)(59, 212)(60, 235)(61, 240)(62, 215)(63, 242)(64, 217)(65, 244)(66, 219)(67, 228)(68, 223)(69, 224)(70, 247)(71, 246)(72, 229)(73, 248)(74, 231)(75, 250)(76, 233)(77, 251)(78, 239)(79, 238)(80, 241)(81, 252)(82, 243)(83, 245)(84, 249)(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) :: { ( 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 E12.785 Graph:: simple bipartite v = 90 e = 168 f = 56 degree seq :: [ 2^84, 28^6 ] E12.789 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 14}) Quotient :: dipole Aut^+ = S3 x D14 (small group id <84, 8>) Aut = C2 x S3 x D14 (small group id <168, 50>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y2^2 * Y1)^2, (Y3 * Y2^-1)^6, Y2^14 ] Map:: R = (1, 85, 2, 86)(3, 87, 7, 91)(4, 88, 9, 93)(5, 89, 11, 95)(6, 90, 13, 97)(8, 92, 14, 98)(10, 94, 12, 96)(15, 99, 25, 109)(16, 100, 26, 110)(17, 101, 27, 111)(18, 102, 29, 113)(19, 103, 30, 114)(20, 104, 32, 116)(21, 105, 33, 117)(22, 106, 34, 118)(23, 107, 36, 120)(24, 108, 37, 121)(28, 112, 38, 122)(31, 115, 35, 119)(39, 123, 48, 132)(40, 124, 47, 131)(41, 125, 52, 136)(42, 126, 55, 139)(43, 127, 56, 140)(44, 128, 49, 133)(45, 129, 58, 142)(46, 130, 59, 143)(50, 134, 61, 145)(51, 135, 62, 146)(53, 137, 64, 148)(54, 138, 65, 149)(57, 141, 66, 150)(60, 144, 63, 147)(67, 151, 75, 159)(68, 152, 77, 161)(69, 153, 78, 162)(70, 154, 72, 156)(71, 155, 79, 163)(73, 157, 80, 164)(74, 158, 81, 165)(76, 160, 82, 166)(83, 167, 84, 168)(169, 253, 171, 255, 176, 260, 185, 269, 196, 280, 211, 295, 225, 309, 237, 321, 228, 312, 214, 298, 199, 283, 187, 271, 178, 262, 172, 256)(170, 254, 173, 257, 180, 264, 190, 274, 203, 287, 219, 303, 231, 315, 242, 326, 234, 318, 222, 306, 206, 290, 192, 276, 182, 266, 174, 258)(175, 259, 183, 267, 177, 261, 186, 270, 198, 282, 213, 297, 227, 311, 239, 323, 246, 330, 236, 320, 224, 308, 210, 294, 195, 279, 184, 268)(179, 263, 188, 272, 181, 265, 191, 275, 205, 289, 221, 305, 233, 317, 244, 328, 249, 333, 241, 325, 230, 314, 218, 302, 202, 286, 189, 273)(193, 277, 207, 291, 194, 278, 209, 293, 223, 307, 235, 319, 245, 329, 251, 335, 247, 331, 238, 322, 226, 310, 212, 296, 197, 281, 208, 292)(200, 284, 215, 299, 201, 285, 217, 301, 229, 313, 240, 324, 248, 332, 252, 336, 250, 334, 243, 327, 232, 316, 220, 304, 204, 288, 216, 300) L = (1, 170)(2, 169)(3, 175)(4, 177)(5, 179)(6, 181)(7, 171)(8, 182)(9, 172)(10, 180)(11, 173)(12, 178)(13, 174)(14, 176)(15, 193)(16, 194)(17, 195)(18, 197)(19, 198)(20, 200)(21, 201)(22, 202)(23, 204)(24, 205)(25, 183)(26, 184)(27, 185)(28, 206)(29, 186)(30, 187)(31, 203)(32, 188)(33, 189)(34, 190)(35, 199)(36, 191)(37, 192)(38, 196)(39, 216)(40, 215)(41, 220)(42, 223)(43, 224)(44, 217)(45, 226)(46, 227)(47, 208)(48, 207)(49, 212)(50, 229)(51, 230)(52, 209)(53, 232)(54, 233)(55, 210)(56, 211)(57, 234)(58, 213)(59, 214)(60, 231)(61, 218)(62, 219)(63, 228)(64, 221)(65, 222)(66, 225)(67, 243)(68, 245)(69, 246)(70, 240)(71, 247)(72, 238)(73, 248)(74, 249)(75, 235)(76, 250)(77, 236)(78, 237)(79, 239)(80, 241)(81, 242)(82, 244)(83, 252)(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, 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 E12.790 Graph:: bipartite v = 48 e = 168 f = 98 degree seq :: [ 4^42, 28^6 ] E12.790 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 14}) Quotient :: dipole Aut^+ = S3 x D14 (small group id <84, 8>) Aut = C2 x S3 x D14 (small group id <168, 50>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y1^-1)^2, (Y3^-1 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y1^6, (Y3 * Y2^-1)^14 ] Map:: polytopal R = (1, 85, 2, 86, 6, 90, 14, 98, 12, 96, 4, 88)(3, 87, 9, 93, 19, 103, 26, 110, 15, 99, 8, 92)(5, 89, 11, 95, 22, 106, 25, 109, 16, 100, 7, 91)(10, 94, 18, 102, 27, 111, 38, 122, 31, 115, 20, 104)(13, 97, 17, 101, 28, 112, 37, 121, 34, 118, 23, 107)(21, 105, 32, 116, 43, 127, 50, 134, 39, 123, 30, 114)(24, 108, 35, 119, 46, 130, 49, 133, 40, 124, 29, 113)(33, 117, 42, 126, 51, 135, 62, 146, 55, 139, 44, 128)(36, 120, 41, 125, 52, 136, 61, 145, 58, 142, 47, 131)(45, 129, 56, 140, 67, 151, 73, 157, 63, 147, 54, 138)(48, 132, 59, 143, 70, 154, 72, 156, 64, 148, 53, 137)(57, 141, 66, 150, 74, 158, 81, 165, 77, 161, 68, 152)(60, 144, 65, 149, 75, 159, 80, 164, 79, 163, 71, 155)(69, 153, 78, 162, 83, 167, 84, 168, 82, 166, 76, 160)(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, 179)(5, 169)(6, 183)(7, 185)(8, 170)(9, 172)(10, 189)(11, 191)(12, 187)(13, 173)(14, 193)(15, 195)(16, 174)(17, 197)(18, 176)(19, 199)(20, 177)(21, 201)(22, 180)(23, 203)(24, 181)(25, 205)(26, 182)(27, 207)(28, 184)(29, 209)(30, 186)(31, 211)(32, 188)(33, 213)(34, 190)(35, 215)(36, 192)(37, 217)(38, 194)(39, 219)(40, 196)(41, 221)(42, 198)(43, 223)(44, 200)(45, 225)(46, 202)(47, 227)(48, 204)(49, 229)(50, 206)(51, 231)(52, 208)(53, 233)(54, 210)(55, 235)(56, 212)(57, 237)(58, 214)(59, 239)(60, 216)(61, 240)(62, 218)(63, 242)(64, 220)(65, 244)(66, 222)(67, 245)(68, 224)(69, 228)(70, 226)(71, 246)(72, 248)(73, 230)(74, 250)(75, 232)(76, 234)(77, 251)(78, 236)(79, 238)(80, 252)(81, 241)(82, 243)(83, 247)(84, 249)(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) :: { ( 4, 28 ), ( 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28 ) } Outer automorphisms :: reflexible Dual of E12.789 Graph:: simple bipartite v = 98 e = 168 f = 48 degree seq :: [ 2^84, 12^14 ] E12.791 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 4, 48}) Quotient :: regular Aut^+ = C48 : C2 (small group id <96, 7>) Aut = $<192, 467>$ (small group id <192, 467>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-2)^2, (T1 * T2)^4, (T2 * T1^10)^2, T2 * T1^-1 * T2 * T1^23 ] Map:: non-degenerate R = (1, 2, 5, 11, 20, 29, 37, 45, 53, 61, 69, 77, 85, 93, 90, 82, 74, 66, 58, 50, 42, 34, 26, 16, 23, 17, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 92, 84, 76, 68, 60, 52, 44, 36, 28, 19, 10, 4)(3, 7, 15, 25, 33, 41, 49, 57, 65, 73, 81, 89, 95, 86, 79, 70, 63, 54, 47, 38, 31, 21, 14, 6, 13, 9, 18, 27, 35, 43, 51, 59, 67, 75, 83, 91, 94, 87, 78, 71, 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, 70)(63, 72)(67, 74)(68, 75)(69, 78)(71, 80)(73, 82)(76, 81)(77, 86)(79, 88)(83, 90)(84, 91)(85, 94)(87, 96)(89, 93)(92, 95) local type(s) :: { ( 4^48 ) } Outer automorphisms :: reflexible Dual of E12.792 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 2 e = 48 f = 24 degree seq :: [ 48^2 ] E12.792 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 4, 48}) Quotient :: regular Aut^+ = C48 : C2 (small group id <96, 7>) Aut = $<192, 467>$ (small group id <192, 467>) |r| :: 2 Presentation :: [ T2^2, F^2, T1^4, (F * T1)^2, (F * T2)^2, (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^-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, 51, 32, 52)(35, 55, 38, 56)(36, 57, 37, 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)(53, 73, 54, 74)(71, 91, 72, 92)(75, 95, 76, 96)(77, 93, 78, 94)(79, 89, 80, 90)(81, 88, 82, 87)(83, 86, 84, 85) 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, 38)(34, 35)(36, 52)(37, 51)(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, 76)(74, 75)(77, 92)(78, 91)(79, 95)(80, 96)(81, 93)(82, 94)(83, 89)(84, 90)(85, 88)(86, 87) local type(s) :: { ( 48^4 ) } Outer automorphisms :: reflexible Dual of E12.791 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 24 e = 48 f = 2 degree seq :: [ 4^24 ] E12.793 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 48}) Quotient :: edge Aut^+ = C48 : C2 (small group id <96, 7>) Aut = $<192, 467>$ (small group id <192, 467>) |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^-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, 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, 53, 34, 55)(35, 57, 40, 59)(36, 61, 43, 63)(37, 64, 38, 60)(39, 67, 41, 69)(42, 72, 44, 74)(45, 77, 46, 79)(47, 81, 48, 83)(49, 85, 50, 87)(51, 89, 52, 91)(54, 94, 56, 93)(58, 90, 70, 92)(62, 86, 75, 88)(65, 95, 66, 96)(68, 84, 71, 82)(73, 80, 76, 78)(97, 98)(99, 103)(100, 105)(101, 106)(102, 108)(104, 107)(109, 113)(110, 114)(111, 115)(112, 116)(117, 121)(118, 122)(119, 123)(120, 124)(125, 129)(126, 130)(127, 133)(128, 134)(131, 151)(132, 156)(135, 153)(136, 149)(137, 155)(138, 157)(139, 160)(140, 159)(141, 163)(142, 165)(143, 168)(144, 170)(145, 173)(146, 175)(147, 177)(148, 179)(150, 181)(152, 183)(154, 189)(158, 192)(161, 185)(162, 187)(164, 186)(166, 190)(167, 188)(169, 182)(171, 191)(172, 184)(174, 180)(176, 178) 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) :: { ( 96, 96 ), ( 96^4 ) } Outer automorphisms :: reflexible Dual of E12.797 Transitivity :: ET+ Graph:: simple bipartite v = 72 e = 96 f = 2 degree seq :: [ 2^48, 4^24 ] E12.794 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 48}) Quotient :: edge Aut^+ = C48 : C2 (small group id <96, 7>) Aut = $<192, 467>$ (small group id <192, 467>) |r| :: 2 Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, (T2 * T1^-1)^2, (T2^-1 * T1^-1)^2, T2^23 * T1 * T2^-1 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 3, 10, 18, 26, 34, 42, 50, 58, 66, 74, 82, 90, 94, 86, 78, 70, 62, 54, 46, 38, 30, 22, 14, 6, 13, 21, 29, 37, 45, 53, 61, 69, 77, 85, 93, 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, 89, 81, 73, 65, 57, 49, 41, 33, 25, 17, 9, 4, 11, 19, 27, 35, 43, 51, 59, 67, 75, 83, 91, 96, 88, 80, 72, 64, 56, 48, 40, 32, 24, 16, 8)(97, 98, 102, 100)(99, 105, 109, 104)(101, 107, 110, 103)(106, 112, 117, 113)(108, 111, 118, 115)(114, 121, 125, 120)(116, 123, 126, 119)(122, 128, 133, 129)(124, 127, 134, 131)(130, 137, 141, 136)(132, 139, 142, 135)(138, 144, 149, 145)(140, 143, 150, 147)(146, 153, 157, 152)(148, 155, 158, 151)(154, 160, 165, 161)(156, 159, 166, 163)(162, 169, 173, 168)(164, 171, 174, 167)(170, 176, 181, 177)(172, 175, 182, 179)(178, 185, 189, 184)(180, 187, 190, 183)(186, 192, 188, 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) :: { ( 4^4 ), ( 4^48 ) } Outer automorphisms :: reflexible Dual of E12.798 Transitivity :: ET+ Graph:: bipartite v = 26 e = 96 f = 48 degree seq :: [ 4^24, 48^2 ] E12.795 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 48}) Quotient :: edge Aut^+ = C48 : C2 (small group id <96, 7>) Aut = $<192, 467>$ (small group id <192, 467>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-2)^2, (T2 * T1)^4, (T2 * T1^10)^2, T2 * T1^-1 * T2 * T1^23 ] 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, 70)(63, 72)(67, 74)(68, 75)(69, 78)(71, 80)(73, 82)(76, 81)(77, 86)(79, 88)(83, 90)(84, 91)(85, 94)(87, 96)(89, 93)(92, 95)(97, 98, 101, 107, 116, 125, 133, 141, 149, 157, 165, 173, 181, 189, 186, 178, 170, 162, 154, 146, 138, 130, 122, 112, 119, 113, 120, 128, 136, 144, 152, 160, 168, 176, 184, 192, 188, 180, 172, 164, 156, 148, 140, 132, 124, 115, 106, 100)(99, 103, 111, 121, 129, 137, 145, 153, 161, 169, 177, 185, 191, 182, 175, 166, 159, 150, 143, 134, 127, 117, 110, 102, 109, 105, 114, 123, 131, 139, 147, 155, 163, 171, 179, 187, 190, 183, 174, 167, 158, 151, 142, 135, 126, 118, 108, 104) 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 ), ( 8^48 ) } Outer automorphisms :: reflexible Dual of E12.796 Transitivity :: ET+ Graph:: simple bipartite v = 50 e = 96 f = 24 degree seq :: [ 2^48, 48^2 ] E12.796 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 48}) Quotient :: loop Aut^+ = C48 : C2 (small group id <96, 7>) Aut = $<192, 467>$ (small group id <192, 467>) |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^-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, 97, 3, 99, 8, 104, 4, 100)(2, 98, 5, 101, 11, 107, 6, 102)(7, 103, 13, 109, 9, 105, 14, 110)(10, 106, 15, 111, 12, 108, 16, 112)(17, 113, 21, 117, 18, 114, 22, 118)(19, 115, 23, 119, 20, 116, 24, 120)(25, 121, 29, 125, 26, 122, 30, 126)(27, 123, 31, 127, 28, 124, 32, 128)(33, 129, 35, 131, 34, 130, 38, 134)(36, 132, 52, 148, 41, 137, 51, 147)(37, 133, 58, 154, 39, 135, 55, 151)(40, 136, 61, 157, 42, 138, 56, 152)(43, 139, 59, 155, 44, 140, 57, 153)(45, 141, 62, 158, 46, 142, 60, 156)(47, 143, 64, 160, 48, 144, 63, 159)(49, 145, 66, 162, 50, 146, 65, 161)(53, 149, 68, 164, 54, 150, 67, 163)(69, 165, 71, 167, 70, 166, 72, 168)(73, 169, 75, 171, 74, 170, 76, 172)(77, 173, 92, 188, 78, 174, 91, 187)(79, 175, 96, 192, 80, 176, 95, 191)(81, 177, 93, 189, 82, 178, 94, 190)(83, 179, 90, 186, 84, 180, 89, 185)(85, 181, 88, 184, 86, 182, 87, 183) L = (1, 98)(2, 97)(3, 103)(4, 105)(5, 106)(6, 108)(7, 99)(8, 107)(9, 100)(10, 101)(11, 104)(12, 102)(13, 113)(14, 114)(15, 115)(16, 116)(17, 109)(18, 110)(19, 111)(20, 112)(21, 121)(22, 122)(23, 123)(24, 124)(25, 117)(26, 118)(27, 119)(28, 120)(29, 129)(30, 130)(31, 147)(32, 148)(33, 125)(34, 126)(35, 151)(36, 152)(37, 153)(38, 154)(39, 155)(40, 156)(41, 157)(42, 158)(43, 159)(44, 160)(45, 161)(46, 162)(47, 163)(48, 164)(49, 165)(50, 166)(51, 127)(52, 128)(53, 169)(54, 170)(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, 187)(72, 188)(73, 149)(74, 150)(75, 191)(76, 192)(77, 190)(78, 189)(79, 185)(80, 186)(81, 183)(82, 184)(83, 182)(84, 181)(85, 180)(86, 179)(87, 177)(88, 178)(89, 175)(90, 176)(91, 167)(92, 168)(93, 174)(94, 173)(95, 171)(96, 172) local type(s) :: { ( 2, 48, 2, 48, 2, 48, 2, 48 ) } Outer automorphisms :: reflexible Dual of E12.795 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 24 e = 96 f = 50 degree seq :: [ 8^24 ] E12.797 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 48}) Quotient :: loop Aut^+ = C48 : C2 (small group id <96, 7>) Aut = $<192, 467>$ (small group id <192, 467>) |r| :: 2 Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, (T2 * T1^-1)^2, (T2^-1 * T1^-1)^2, T2^23 * T1 * T2^-1 * T1^-1 ] Map:: R = (1, 97, 3, 99, 10, 106, 18, 114, 26, 122, 34, 130, 42, 138, 50, 146, 58, 154, 66, 162, 74, 170, 82, 178, 90, 186, 94, 190, 86, 182, 78, 174, 70, 166, 62, 158, 54, 150, 46, 142, 38, 134, 30, 126, 22, 118, 14, 110, 6, 102, 13, 109, 21, 117, 29, 125, 37, 133, 45, 141, 53, 149, 61, 157, 69, 165, 77, 173, 85, 181, 93, 189, 92, 188, 84, 180, 76, 172, 68, 164, 60, 156, 52, 148, 44, 140, 36, 132, 28, 124, 20, 116, 12, 108, 5, 101)(2, 98, 7, 103, 15, 111, 23, 119, 31, 127, 39, 135, 47, 143, 55, 151, 63, 159, 71, 167, 79, 175, 87, 183, 95, 191, 89, 185, 81, 177, 73, 169, 65, 161, 57, 153, 49, 145, 41, 137, 33, 129, 25, 121, 17, 113, 9, 105, 4, 100, 11, 107, 19, 115, 27, 123, 35, 131, 43, 139, 51, 147, 59, 155, 67, 163, 75, 171, 83, 179, 91, 187, 96, 192, 88, 184, 80, 176, 72, 168, 64, 160, 56, 152, 48, 144, 40, 136, 32, 128, 24, 120, 16, 112, 8, 104) L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 107)(6, 100)(7, 101)(8, 99)(9, 109)(10, 112)(11, 110)(12, 111)(13, 104)(14, 103)(15, 118)(16, 117)(17, 106)(18, 121)(19, 108)(20, 123)(21, 113)(22, 115)(23, 116)(24, 114)(25, 125)(26, 128)(27, 126)(28, 127)(29, 120)(30, 119)(31, 134)(32, 133)(33, 122)(34, 137)(35, 124)(36, 139)(37, 129)(38, 131)(39, 132)(40, 130)(41, 141)(42, 144)(43, 142)(44, 143)(45, 136)(46, 135)(47, 150)(48, 149)(49, 138)(50, 153)(51, 140)(52, 155)(53, 145)(54, 147)(55, 148)(56, 146)(57, 157)(58, 160)(59, 158)(60, 159)(61, 152)(62, 151)(63, 166)(64, 165)(65, 154)(66, 169)(67, 156)(68, 171)(69, 161)(70, 163)(71, 164)(72, 162)(73, 173)(74, 176)(75, 174)(76, 175)(77, 168)(78, 167)(79, 182)(80, 181)(81, 170)(82, 185)(83, 172)(84, 187)(85, 177)(86, 179)(87, 180)(88, 178)(89, 189)(90, 192)(91, 190)(92, 191)(93, 184)(94, 183)(95, 186)(96, 188) 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 ) } Outer automorphisms :: reflexible Dual of E12.793 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 96 f = 72 degree seq :: [ 96^2 ] E12.798 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 48}) Quotient :: loop Aut^+ = C48 : C2 (small group id <96, 7>) Aut = $<192, 467>$ (small group id <192, 467>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-2)^2, (T2 * T1)^4, (T2 * T1^10)^2, T2 * T1^-1 * T2 * T1^23 ] Map:: polytopal non-degenerate R = (1, 97, 3, 99)(2, 98, 6, 102)(4, 100, 9, 105)(5, 101, 12, 108)(7, 103, 16, 112)(8, 104, 17, 113)(10, 106, 15, 111)(11, 107, 21, 117)(13, 109, 23, 119)(14, 110, 24, 120)(18, 114, 26, 122)(19, 115, 27, 123)(20, 116, 30, 126)(22, 118, 32, 128)(25, 121, 34, 130)(28, 124, 33, 129)(29, 125, 38, 134)(31, 127, 40, 136)(35, 131, 42, 138)(36, 132, 43, 139)(37, 133, 46, 142)(39, 135, 48, 144)(41, 137, 50, 146)(44, 140, 49, 145)(45, 141, 54, 150)(47, 143, 56, 152)(51, 147, 58, 154)(52, 148, 59, 155)(53, 149, 62, 158)(55, 151, 64, 160)(57, 153, 66, 162)(60, 156, 65, 161)(61, 157, 70, 166)(63, 159, 72, 168)(67, 163, 74, 170)(68, 164, 75, 171)(69, 165, 78, 174)(71, 167, 80, 176)(73, 169, 82, 178)(76, 172, 81, 177)(77, 173, 86, 182)(79, 175, 88, 184)(83, 179, 90, 186)(84, 180, 91, 187)(85, 181, 94, 190)(87, 183, 96, 192)(89, 185, 93, 189)(92, 188, 95, 191) L = (1, 98)(2, 101)(3, 103)(4, 97)(5, 107)(6, 109)(7, 111)(8, 99)(9, 114)(10, 100)(11, 116)(12, 104)(13, 105)(14, 102)(15, 121)(16, 119)(17, 120)(18, 123)(19, 106)(20, 125)(21, 110)(22, 108)(23, 113)(24, 128)(25, 129)(26, 112)(27, 131)(28, 115)(29, 133)(30, 118)(31, 117)(32, 136)(33, 137)(34, 122)(35, 139)(36, 124)(37, 141)(38, 127)(39, 126)(40, 144)(41, 145)(42, 130)(43, 147)(44, 132)(45, 149)(46, 135)(47, 134)(48, 152)(49, 153)(50, 138)(51, 155)(52, 140)(53, 157)(54, 143)(55, 142)(56, 160)(57, 161)(58, 146)(59, 163)(60, 148)(61, 165)(62, 151)(63, 150)(64, 168)(65, 169)(66, 154)(67, 171)(68, 156)(69, 173)(70, 159)(71, 158)(72, 176)(73, 177)(74, 162)(75, 179)(76, 164)(77, 181)(78, 167)(79, 166)(80, 184)(81, 185)(82, 170)(83, 187)(84, 172)(85, 189)(86, 175)(87, 174)(88, 192)(89, 191)(90, 178)(91, 190)(92, 180)(93, 186)(94, 183)(95, 182)(96, 188) local type(s) :: { ( 4, 48, 4, 48 ) } Outer automorphisms :: reflexible Dual of E12.794 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 48 e = 96 f = 26 degree seq :: [ 4^48 ] E12.799 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 48}) Quotient :: dipole Aut^+ = C48 : C2 (small group id <96, 7>) Aut = $<192, 467>$ (small group id <192, 467>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^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^-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)^48 ] Map:: R = (1, 97, 2, 98)(3, 99, 7, 103)(4, 100, 9, 105)(5, 101, 10, 106)(6, 102, 12, 108)(8, 104, 11, 107)(13, 109, 17, 113)(14, 110, 18, 114)(15, 111, 19, 115)(16, 112, 20, 116)(21, 117, 25, 121)(22, 118, 26, 122)(23, 119, 27, 123)(24, 120, 28, 124)(29, 125, 33, 129)(30, 126, 34, 130)(31, 127, 40, 136)(32, 128, 35, 131)(36, 132, 54, 150)(37, 133, 53, 149)(38, 134, 55, 151)(39, 135, 56, 152)(41, 137, 57, 153)(42, 138, 58, 154)(43, 139, 59, 155)(44, 140, 60, 156)(45, 141, 61, 157)(46, 142, 62, 158)(47, 143, 63, 159)(48, 144, 64, 160)(49, 145, 65, 161)(50, 146, 66, 162)(51, 147, 67, 163)(52, 148, 68, 164)(69, 165, 73, 169)(70, 166, 74, 170)(71, 167, 76, 172)(72, 168, 75, 171)(77, 173, 94, 190)(78, 174, 93, 189)(79, 175, 95, 191)(80, 176, 96, 192)(81, 177, 91, 187)(82, 178, 92, 188)(83, 179, 89, 185)(84, 180, 90, 186)(85, 181, 88, 184)(86, 182, 87, 183)(193, 289, 195, 291, 200, 296, 196, 292)(194, 290, 197, 293, 203, 299, 198, 294)(199, 295, 205, 301, 201, 297, 206, 302)(202, 298, 207, 303, 204, 300, 208, 304)(209, 305, 213, 309, 210, 306, 214, 310)(211, 307, 215, 311, 212, 308, 216, 312)(217, 313, 221, 317, 218, 314, 222, 318)(219, 315, 223, 319, 220, 316, 224, 320)(225, 321, 245, 341, 226, 322, 246, 342)(227, 323, 247, 343, 232, 328, 248, 344)(228, 324, 249, 345, 229, 325, 250, 346)(230, 326, 251, 347, 231, 327, 252, 348)(233, 329, 253, 349, 234, 330, 254, 350)(235, 331, 255, 351, 236, 332, 256, 352)(237, 333, 257, 353, 238, 334, 258, 354)(239, 335, 259, 355, 240, 336, 260, 356)(241, 337, 261, 357, 242, 338, 262, 358)(243, 339, 263, 359, 244, 340, 264, 360)(265, 361, 285, 381, 266, 362, 286, 382)(267, 363, 287, 383, 268, 364, 288, 384)(269, 365, 283, 379, 270, 366, 284, 380)(271, 367, 281, 377, 272, 368, 282, 378)(273, 369, 280, 376, 274, 370, 279, 375)(275, 371, 278, 374, 276, 372, 277, 373) L = (1, 194)(2, 193)(3, 199)(4, 201)(5, 202)(6, 204)(7, 195)(8, 203)(9, 196)(10, 197)(11, 200)(12, 198)(13, 209)(14, 210)(15, 211)(16, 212)(17, 205)(18, 206)(19, 207)(20, 208)(21, 217)(22, 218)(23, 219)(24, 220)(25, 213)(26, 214)(27, 215)(28, 216)(29, 225)(30, 226)(31, 232)(32, 227)(33, 221)(34, 222)(35, 224)(36, 246)(37, 245)(38, 247)(39, 248)(40, 223)(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, 229)(54, 228)(55, 230)(56, 231)(57, 233)(58, 234)(59, 235)(60, 236)(61, 237)(62, 238)(63, 239)(64, 240)(65, 241)(66, 242)(67, 243)(68, 244)(69, 265)(70, 266)(71, 268)(72, 267)(73, 261)(74, 262)(75, 264)(76, 263)(77, 286)(78, 285)(79, 287)(80, 288)(81, 283)(82, 284)(83, 281)(84, 282)(85, 280)(86, 279)(87, 278)(88, 277)(89, 275)(90, 276)(91, 273)(92, 274)(93, 270)(94, 269)(95, 271)(96, 272)(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, 96, 2, 96 ), ( 2, 96, 2, 96, 2, 96, 2, 96 ) } Outer automorphisms :: reflexible Dual of E12.802 Graph:: bipartite v = 72 e = 192 f = 98 degree seq :: [ 4^48, 8^24 ] E12.800 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 48}) Quotient :: dipole Aut^+ = C48 : C2 (small group id <96, 7>) Aut = $<192, 467>$ (small group id <192, 467>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (Y2^-1 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, (Y2^-1 * Y1)^2, (Y3^-1 * Y1^-1)^2, Y1^4, Y1^-1 * Y2^-24 * Y1^-1 ] Map:: R = (1, 97, 2, 98, 6, 102, 4, 100)(3, 99, 9, 105, 13, 109, 8, 104)(5, 101, 11, 107, 14, 110, 7, 103)(10, 106, 16, 112, 21, 117, 17, 113)(12, 108, 15, 111, 22, 118, 19, 115)(18, 114, 25, 121, 29, 125, 24, 120)(20, 116, 27, 123, 30, 126, 23, 119)(26, 122, 32, 128, 37, 133, 33, 129)(28, 124, 31, 127, 38, 134, 35, 131)(34, 130, 41, 137, 45, 141, 40, 136)(36, 132, 43, 139, 46, 142, 39, 135)(42, 138, 48, 144, 53, 149, 49, 145)(44, 140, 47, 143, 54, 150, 51, 147)(50, 146, 57, 153, 61, 157, 56, 152)(52, 148, 59, 155, 62, 158, 55, 151)(58, 154, 64, 160, 69, 165, 65, 161)(60, 156, 63, 159, 70, 166, 67, 163)(66, 162, 73, 169, 77, 173, 72, 168)(68, 164, 75, 171, 78, 174, 71, 167)(74, 170, 80, 176, 85, 181, 81, 177)(76, 172, 79, 175, 86, 182, 83, 179)(82, 178, 89, 185, 93, 189, 88, 184)(84, 180, 91, 187, 94, 190, 87, 183)(90, 186, 96, 192, 92, 188, 95, 191)(193, 289, 195, 291, 202, 298, 210, 306, 218, 314, 226, 322, 234, 330, 242, 338, 250, 346, 258, 354, 266, 362, 274, 370, 282, 378, 286, 382, 278, 374, 270, 366, 262, 358, 254, 350, 246, 342, 238, 334, 230, 326, 222, 318, 214, 310, 206, 302, 198, 294, 205, 301, 213, 309, 221, 317, 229, 325, 237, 333, 245, 341, 253, 349, 261, 357, 269, 365, 277, 373, 285, 381, 284, 380, 276, 372, 268, 364, 260, 356, 252, 348, 244, 340, 236, 332, 228, 324, 220, 316, 212, 308, 204, 300, 197, 293)(194, 290, 199, 295, 207, 303, 215, 311, 223, 319, 231, 327, 239, 335, 247, 343, 255, 351, 263, 359, 271, 367, 279, 375, 287, 383, 281, 377, 273, 369, 265, 361, 257, 353, 249, 345, 241, 337, 233, 329, 225, 321, 217, 313, 209, 305, 201, 297, 196, 292, 203, 299, 211, 307, 219, 315, 227, 323, 235, 331, 243, 339, 251, 347, 259, 355, 267, 363, 275, 371, 283, 379, 288, 384, 280, 376, 272, 368, 264, 360, 256, 352, 248, 344, 240, 336, 232, 328, 224, 320, 216, 312, 208, 304, 200, 296) L = (1, 195)(2, 199)(3, 202)(4, 203)(5, 193)(6, 205)(7, 207)(8, 194)(9, 196)(10, 210)(11, 211)(12, 197)(13, 213)(14, 198)(15, 215)(16, 200)(17, 201)(18, 218)(19, 219)(20, 204)(21, 221)(22, 206)(23, 223)(24, 208)(25, 209)(26, 226)(27, 227)(28, 212)(29, 229)(30, 214)(31, 231)(32, 216)(33, 217)(34, 234)(35, 235)(36, 220)(37, 237)(38, 222)(39, 239)(40, 224)(41, 225)(42, 242)(43, 243)(44, 228)(45, 245)(46, 230)(47, 247)(48, 232)(49, 233)(50, 250)(51, 251)(52, 236)(53, 253)(54, 238)(55, 255)(56, 240)(57, 241)(58, 258)(59, 259)(60, 244)(61, 261)(62, 246)(63, 263)(64, 248)(65, 249)(66, 266)(67, 267)(68, 252)(69, 269)(70, 254)(71, 271)(72, 256)(73, 257)(74, 274)(75, 275)(76, 260)(77, 277)(78, 262)(79, 279)(80, 264)(81, 265)(82, 282)(83, 283)(84, 268)(85, 285)(86, 270)(87, 287)(88, 272)(89, 273)(90, 286)(91, 288)(92, 276)(93, 284)(94, 278)(95, 281)(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, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 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 E12.801 Graph:: bipartite v = 26 e = 192 f = 144 degree seq :: [ 8^24, 96^2 ] E12.801 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 48}) Quotient :: dipole Aut^+ = C48 : C2 (small group id <96, 7>) Aut = $<192, 467>$ (small group id <192, 467>) |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, Y3^21 * Y2 * Y3^-3 * Y2, (Y3^-1 * Y1^-1)^48 ] 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)(195, 291, 199, 295)(196, 292, 201, 297)(197, 293, 203, 299)(198, 294, 205, 301)(200, 296, 206, 302)(202, 298, 204, 300)(207, 303, 212, 308)(208, 304, 215, 311)(209, 305, 217, 313)(210, 306, 213, 309)(211, 307, 219, 315)(214, 310, 221, 317)(216, 312, 223, 319)(218, 314, 224, 320)(220, 316, 222, 318)(225, 321, 231, 327)(226, 322, 233, 329)(227, 323, 229, 325)(228, 324, 235, 331)(230, 326, 237, 333)(232, 328, 239, 335)(234, 330, 240, 336)(236, 332, 238, 334)(241, 337, 247, 343)(242, 338, 249, 345)(243, 339, 245, 341)(244, 340, 251, 347)(246, 342, 253, 349)(248, 344, 255, 351)(250, 346, 256, 352)(252, 348, 254, 350)(257, 353, 263, 359)(258, 354, 265, 361)(259, 355, 261, 357)(260, 356, 267, 363)(262, 358, 269, 365)(264, 360, 271, 367)(266, 362, 272, 368)(268, 364, 270, 366)(273, 369, 279, 375)(274, 370, 281, 377)(275, 371, 277, 373)(276, 372, 283, 379)(278, 374, 285, 381)(280, 376, 287, 383)(282, 378, 288, 384)(284, 380, 286, 382) L = (1, 195)(2, 197)(3, 200)(4, 193)(5, 204)(6, 194)(7, 207)(8, 209)(9, 210)(10, 196)(11, 212)(12, 214)(13, 215)(14, 198)(15, 201)(16, 199)(17, 218)(18, 219)(19, 202)(20, 205)(21, 203)(22, 222)(23, 223)(24, 206)(25, 208)(26, 226)(27, 227)(28, 211)(29, 213)(30, 230)(31, 231)(32, 216)(33, 217)(34, 234)(35, 235)(36, 220)(37, 221)(38, 238)(39, 239)(40, 224)(41, 225)(42, 242)(43, 243)(44, 228)(45, 229)(46, 246)(47, 247)(48, 232)(49, 233)(50, 250)(51, 251)(52, 236)(53, 237)(54, 254)(55, 255)(56, 240)(57, 241)(58, 258)(59, 259)(60, 244)(61, 245)(62, 262)(63, 263)(64, 248)(65, 249)(66, 266)(67, 267)(68, 252)(69, 253)(70, 270)(71, 271)(72, 256)(73, 257)(74, 274)(75, 275)(76, 260)(77, 261)(78, 278)(79, 279)(80, 264)(81, 265)(82, 282)(83, 283)(84, 268)(85, 269)(86, 286)(87, 287)(88, 272)(89, 273)(90, 285)(91, 288)(92, 276)(93, 277)(94, 281)(95, 284)(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, 96 ), ( 8, 96, 8, 96 ) } Outer automorphisms :: reflexible Dual of E12.800 Graph:: simple bipartite v = 144 e = 192 f = 26 degree seq :: [ 2^96, 4^48 ] E12.802 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 48}) Quotient :: dipole Aut^+ = C48 : C2 (small group id <96, 7>) Aut = $<192, 467>$ (small group id <192, 467>) |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^-2)^2, (Y3 * Y1)^4, Y3 * Y1^-1 * Y3 * Y1^23, Y1^-2 * Y3 * Y1^11 * Y3 * Y1^-11 ] Map:: R = (1, 97, 2, 98, 5, 101, 11, 107, 20, 116, 29, 125, 37, 133, 45, 141, 53, 149, 61, 157, 69, 165, 77, 173, 85, 181, 93, 189, 90, 186, 82, 178, 74, 170, 66, 162, 58, 154, 50, 146, 42, 138, 34, 130, 26, 122, 16, 112, 23, 119, 17, 113, 24, 120, 32, 128, 40, 136, 48, 144, 56, 152, 64, 160, 72, 168, 80, 176, 88, 184, 96, 192, 92, 188, 84, 180, 76, 172, 68, 164, 60, 156, 52, 148, 44, 140, 36, 132, 28, 124, 19, 115, 10, 106, 4, 100)(3, 99, 7, 103, 15, 111, 25, 121, 33, 129, 41, 137, 49, 145, 57, 153, 65, 161, 73, 169, 81, 177, 89, 185, 95, 191, 86, 182, 79, 175, 70, 166, 63, 159, 54, 150, 47, 143, 38, 134, 31, 127, 21, 117, 14, 110, 6, 102, 13, 109, 9, 105, 18, 114, 27, 123, 35, 131, 43, 139, 51, 147, 59, 155, 67, 163, 75, 171, 83, 179, 91, 187, 94, 190, 87, 183, 78, 174, 71, 167, 62, 158, 55, 151, 46, 142, 39, 135, 30, 126, 22, 118, 12, 108, 8, 104)(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, 198)(3, 193)(4, 201)(5, 204)(6, 194)(7, 208)(8, 209)(9, 196)(10, 207)(11, 213)(12, 197)(13, 215)(14, 216)(15, 202)(16, 199)(17, 200)(18, 218)(19, 219)(20, 222)(21, 203)(22, 224)(23, 205)(24, 206)(25, 226)(26, 210)(27, 211)(28, 225)(29, 230)(30, 212)(31, 232)(32, 214)(33, 220)(34, 217)(35, 234)(36, 235)(37, 238)(38, 221)(39, 240)(40, 223)(41, 242)(42, 227)(43, 228)(44, 241)(45, 246)(46, 229)(47, 248)(48, 231)(49, 236)(50, 233)(51, 250)(52, 251)(53, 254)(54, 237)(55, 256)(56, 239)(57, 258)(58, 243)(59, 244)(60, 257)(61, 262)(62, 245)(63, 264)(64, 247)(65, 252)(66, 249)(67, 266)(68, 267)(69, 270)(70, 253)(71, 272)(72, 255)(73, 274)(74, 259)(75, 260)(76, 273)(77, 278)(78, 261)(79, 280)(80, 263)(81, 268)(82, 265)(83, 282)(84, 283)(85, 286)(86, 269)(87, 288)(88, 271)(89, 285)(90, 275)(91, 276)(92, 287)(93, 281)(94, 277)(95, 284)(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, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 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 E12.799 Graph:: simple bipartite v = 98 e = 192 f = 72 degree seq :: [ 2^96, 96^2 ] E12.803 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 48}) Quotient :: dipole Aut^+ = C48 : C2 (small group id <96, 7>) Aut = $<192, 467>$ (small group id <192, 467>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y2^2 * Y1)^2, (Y3 * Y2^-1)^4, Y2^3 * Y1 * Y2^-21 * Y1 ] Map:: R = (1, 97, 2, 98)(3, 99, 7, 103)(4, 100, 9, 105)(5, 101, 11, 107)(6, 102, 13, 109)(8, 104, 14, 110)(10, 106, 12, 108)(15, 111, 20, 116)(16, 112, 23, 119)(17, 113, 25, 121)(18, 114, 21, 117)(19, 115, 27, 123)(22, 118, 29, 125)(24, 120, 31, 127)(26, 122, 32, 128)(28, 124, 30, 126)(33, 129, 39, 135)(34, 130, 41, 137)(35, 131, 37, 133)(36, 132, 43, 139)(38, 134, 45, 141)(40, 136, 47, 143)(42, 138, 48, 144)(44, 140, 46, 142)(49, 145, 55, 151)(50, 146, 57, 153)(51, 147, 53, 149)(52, 148, 59, 155)(54, 150, 61, 157)(56, 152, 63, 159)(58, 154, 64, 160)(60, 156, 62, 158)(65, 161, 71, 167)(66, 162, 73, 169)(67, 163, 69, 165)(68, 164, 75, 171)(70, 166, 77, 173)(72, 168, 79, 175)(74, 170, 80, 176)(76, 172, 78, 174)(81, 177, 87, 183)(82, 178, 89, 185)(83, 179, 85, 181)(84, 180, 91, 187)(86, 182, 93, 189)(88, 184, 95, 191)(90, 186, 96, 192)(92, 188, 94, 190)(193, 289, 195, 291, 200, 296, 209, 305, 218, 314, 226, 322, 234, 330, 242, 338, 250, 346, 258, 354, 266, 362, 274, 370, 282, 378, 285, 381, 277, 373, 269, 365, 261, 357, 253, 349, 245, 341, 237, 333, 229, 325, 221, 317, 213, 309, 203, 299, 212, 308, 205, 301, 215, 311, 223, 319, 231, 327, 239, 335, 247, 343, 255, 351, 263, 359, 271, 367, 279, 375, 287, 383, 284, 380, 276, 372, 268, 364, 260, 356, 252, 348, 244, 340, 236, 332, 228, 324, 220, 316, 211, 307, 202, 298, 196, 292)(194, 290, 197, 293, 204, 300, 214, 310, 222, 318, 230, 326, 238, 334, 246, 342, 254, 350, 262, 358, 270, 366, 278, 374, 286, 382, 281, 377, 273, 369, 265, 361, 257, 353, 249, 345, 241, 337, 233, 329, 225, 321, 217, 313, 208, 304, 199, 295, 207, 303, 201, 297, 210, 306, 219, 315, 227, 323, 235, 331, 243, 339, 251, 347, 259, 355, 267, 363, 275, 371, 283, 379, 288, 384, 280, 376, 272, 368, 264, 360, 256, 352, 248, 344, 240, 336, 232, 328, 224, 320, 216, 312, 206, 302, 198, 294) L = (1, 194)(2, 193)(3, 199)(4, 201)(5, 203)(6, 205)(7, 195)(8, 206)(9, 196)(10, 204)(11, 197)(12, 202)(13, 198)(14, 200)(15, 212)(16, 215)(17, 217)(18, 213)(19, 219)(20, 207)(21, 210)(22, 221)(23, 208)(24, 223)(25, 209)(26, 224)(27, 211)(28, 222)(29, 214)(30, 220)(31, 216)(32, 218)(33, 231)(34, 233)(35, 229)(36, 235)(37, 227)(38, 237)(39, 225)(40, 239)(41, 226)(42, 240)(43, 228)(44, 238)(45, 230)(46, 236)(47, 232)(48, 234)(49, 247)(50, 249)(51, 245)(52, 251)(53, 243)(54, 253)(55, 241)(56, 255)(57, 242)(58, 256)(59, 244)(60, 254)(61, 246)(62, 252)(63, 248)(64, 250)(65, 263)(66, 265)(67, 261)(68, 267)(69, 259)(70, 269)(71, 257)(72, 271)(73, 258)(74, 272)(75, 260)(76, 270)(77, 262)(78, 268)(79, 264)(80, 266)(81, 279)(82, 281)(83, 277)(84, 283)(85, 275)(86, 285)(87, 273)(88, 287)(89, 274)(90, 288)(91, 276)(92, 286)(93, 278)(94, 284)(95, 280)(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, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 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 E12.804 Graph:: bipartite v = 50 e = 192 f = 120 degree seq :: [ 4^48, 96^2 ] E12.804 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 48}) Quotient :: dipole Aut^+ = C48 : C2 (small group id <96, 7>) Aut = $<192, 467>$ (small group id <192, 467>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, Y1^4, (Y3^-1 * Y1)^2, (Y3^-1 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3^-24 * Y1^-1, (Y3 * Y2^-1)^48 ] Map:: R = (1, 97, 2, 98, 6, 102, 4, 100)(3, 99, 9, 105, 13, 109, 8, 104)(5, 101, 11, 107, 14, 110, 7, 103)(10, 106, 16, 112, 21, 117, 17, 113)(12, 108, 15, 111, 22, 118, 19, 115)(18, 114, 25, 121, 29, 125, 24, 120)(20, 116, 27, 123, 30, 126, 23, 119)(26, 122, 32, 128, 37, 133, 33, 129)(28, 124, 31, 127, 38, 134, 35, 131)(34, 130, 41, 137, 45, 141, 40, 136)(36, 132, 43, 139, 46, 142, 39, 135)(42, 138, 48, 144, 53, 149, 49, 145)(44, 140, 47, 143, 54, 150, 51, 147)(50, 146, 57, 153, 61, 157, 56, 152)(52, 148, 59, 155, 62, 158, 55, 151)(58, 154, 64, 160, 69, 165, 65, 161)(60, 156, 63, 159, 70, 166, 67, 163)(66, 162, 73, 169, 77, 173, 72, 168)(68, 164, 75, 171, 78, 174, 71, 167)(74, 170, 80, 176, 85, 181, 81, 177)(76, 172, 79, 175, 86, 182, 83, 179)(82, 178, 89, 185, 93, 189, 88, 184)(84, 180, 91, 187, 94, 190, 87, 183)(90, 186, 96, 192, 92, 188, 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, 203)(5, 193)(6, 205)(7, 207)(8, 194)(9, 196)(10, 210)(11, 211)(12, 197)(13, 213)(14, 198)(15, 215)(16, 200)(17, 201)(18, 218)(19, 219)(20, 204)(21, 221)(22, 206)(23, 223)(24, 208)(25, 209)(26, 226)(27, 227)(28, 212)(29, 229)(30, 214)(31, 231)(32, 216)(33, 217)(34, 234)(35, 235)(36, 220)(37, 237)(38, 222)(39, 239)(40, 224)(41, 225)(42, 242)(43, 243)(44, 228)(45, 245)(46, 230)(47, 247)(48, 232)(49, 233)(50, 250)(51, 251)(52, 236)(53, 253)(54, 238)(55, 255)(56, 240)(57, 241)(58, 258)(59, 259)(60, 244)(61, 261)(62, 246)(63, 263)(64, 248)(65, 249)(66, 266)(67, 267)(68, 252)(69, 269)(70, 254)(71, 271)(72, 256)(73, 257)(74, 274)(75, 275)(76, 260)(77, 277)(78, 262)(79, 279)(80, 264)(81, 265)(82, 282)(83, 283)(84, 268)(85, 285)(86, 270)(87, 287)(88, 272)(89, 273)(90, 286)(91, 288)(92, 276)(93, 284)(94, 278)(95, 281)(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, 96 ), ( 4, 96, 4, 96, 4, 96, 4, 96 ) } Outer automorphisms :: reflexible Dual of E12.803 Graph:: simple bipartite v = 120 e = 192 f = 50 degree seq :: [ 2^96, 8^24 ] E12.805 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 4, 26}) Quotient :: regular Aut^+ = (C26 x C2) : C2 (small group id <104, 8>) Aut = D8 x D26 (small group id <208, 39>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-2 * T2)^2, (T1 * T2)^4, T1^26 ] Map:: polytopal non-degenerate R = (1, 2, 5, 11, 20, 29, 37, 45, 53, 61, 69, 77, 85, 93, 92, 84, 76, 68, 60, 52, 44, 36, 28, 19, 10, 4)(3, 7, 15, 25, 33, 41, 49, 57, 65, 73, 81, 89, 97, 101, 94, 87, 78, 71, 62, 55, 46, 39, 30, 22, 12, 8)(6, 13, 9, 18, 27, 35, 43, 51, 59, 67, 75, 83, 91, 99, 100, 95, 86, 79, 70, 63, 54, 47, 38, 31, 21, 14)(16, 23, 17, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 102, 104, 103, 98, 90, 82, 74, 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, 70)(63, 72)(67, 74)(68, 75)(69, 78)(71, 80)(73, 82)(76, 81)(77, 86)(79, 88)(83, 90)(84, 91)(85, 94)(87, 96)(89, 98)(92, 97)(93, 100)(95, 102)(99, 103)(101, 104) local type(s) :: { ( 4^26 ) } Outer automorphisms :: reflexible Dual of E12.806 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 4 e = 52 f = 26 degree seq :: [ 26^4 ] E12.806 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 4, 26}) Quotient :: regular Aut^+ = (C26 x C2) : C2 (small group id <104, 8>) Aut = D8 x D26 (small group id <208, 39>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^4, (T1^-1 * T2 * T1^-1)^2, (T1 * T2)^26 ] 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, 61, 32, 63)(35, 65, 39, 68)(36, 69, 38, 72)(37, 73, 44, 75)(40, 80, 43, 82)(41, 78, 42, 66)(45, 76, 46, 70)(47, 93, 48, 95)(49, 97, 50, 99)(51, 85, 52, 83)(53, 91, 54, 89)(55, 100, 56, 98)(57, 94, 58, 96)(59, 81, 60, 87)(62, 88, 64, 74)(67, 103, 79, 104)(71, 102, 77, 101)(84, 92, 86, 90) 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, 66)(36, 70)(37, 72)(38, 76)(39, 78)(40, 65)(41, 83)(42, 85)(43, 68)(44, 69)(45, 89)(46, 91)(47, 73)(48, 75)(49, 80)(50, 82)(51, 63)(52, 61)(55, 93)(56, 95)(57, 97)(58, 99)(59, 100)(60, 98)(62, 94)(64, 96)(67, 90)(71, 86)(74, 101)(77, 84)(79, 92)(81, 103)(87, 104)(88, 102) local type(s) :: { ( 26^4 ) } Outer automorphisms :: reflexible Dual of E12.805 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 26 e = 52 f = 4 degree seq :: [ 4^26 ] E12.807 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 26}) Quotient :: edge Aut^+ = (C26 x C2) : C2 (small group id <104, 8>) Aut = D8 x D26 (small group id <208, 39>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T1)^2, (F * T2)^2, T2^4, (T2^-1 * T1 * T2^-1)^2, (T2 * T1)^26 ] 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, 53, 34, 54)(35, 55, 40, 56)(36, 57, 37, 58)(38, 59, 39, 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, 92, 86, 91)(87, 90, 88, 89)(105, 106)(107, 111)(108, 113)(109, 114)(110, 116)(112, 115)(117, 121)(118, 122)(119, 123)(120, 124)(125, 129)(126, 130)(127, 131)(128, 132)(133, 137)(134, 138)(135, 144)(136, 139)(140, 158)(141, 157)(142, 159)(143, 160)(145, 161)(146, 162)(147, 163)(148, 164)(149, 165)(150, 166)(151, 167)(152, 168)(153, 169)(154, 170)(155, 171)(156, 172)(173, 177)(174, 178)(175, 180)(176, 179)(181, 198)(182, 197)(183, 199)(184, 200)(185, 201)(186, 202)(187, 203)(188, 204)(189, 205)(190, 206)(191, 207)(192, 208)(193, 196)(194, 195) 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) :: { ( 52, 52 ), ( 52^4 ) } Outer automorphisms :: reflexible Dual of E12.811 Transitivity :: ET+ Graph:: simple bipartite v = 78 e = 104 f = 4 degree seq :: [ 2^52, 4^26 ] E12.808 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 26}) Quotient :: edge Aut^+ = (C26 x C2) : C2 (small group id <104, 8>) Aut = D8 x D26 (small group id <208, 39>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1 * T1^-1)^2, (T2 * T1^-1)^2, T2^26 ] Map:: polytopal non-degenerate R = (1, 3, 10, 18, 26, 34, 42, 50, 58, 66, 74, 82, 90, 98, 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, 102, 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, 103, 97, 89, 81, 73, 65, 57, 49, 41, 33, 25, 17, 9)(6, 13, 21, 29, 37, 45, 53, 61, 69, 77, 85, 93, 100, 104, 101, 94, 86, 78, 70, 62, 54, 46, 38, 30, 22, 14)(105, 106, 110, 108)(107, 113, 117, 112)(109, 115, 118, 111)(114, 120, 125, 121)(116, 119, 126, 123)(122, 129, 133, 128)(124, 131, 134, 127)(130, 136, 141, 137)(132, 135, 142, 139)(138, 145, 149, 144)(140, 147, 150, 143)(146, 152, 157, 153)(148, 151, 158, 155)(154, 161, 165, 160)(156, 163, 166, 159)(162, 168, 173, 169)(164, 167, 174, 171)(170, 177, 181, 176)(172, 179, 182, 175)(178, 184, 189, 185)(180, 183, 190, 187)(186, 193, 197, 192)(188, 195, 198, 191)(194, 200, 204, 201)(196, 199, 205, 203)(202, 207, 208, 206) 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) :: { ( 4^4 ), ( 4^26 ) } Outer automorphisms :: reflexible Dual of E12.812 Transitivity :: ET+ Graph:: simple bipartite v = 30 e = 104 f = 52 degree seq :: [ 4^26, 26^4 ] E12.809 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 26}) Quotient :: edge Aut^+ = (C26 x C2) : C2 (small group id <104, 8>) Aut = D8 x D26 (small group id <208, 39>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-2 * T2)^2, (T2 * T1)^4, T1^26 ] 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, 70)(63, 72)(67, 74)(68, 75)(69, 78)(71, 80)(73, 82)(76, 81)(77, 86)(79, 88)(83, 90)(84, 91)(85, 94)(87, 96)(89, 98)(92, 97)(93, 100)(95, 102)(99, 103)(101, 104)(105, 106, 109, 115, 124, 133, 141, 149, 157, 165, 173, 181, 189, 197, 196, 188, 180, 172, 164, 156, 148, 140, 132, 123, 114, 108)(107, 111, 119, 129, 137, 145, 153, 161, 169, 177, 185, 193, 201, 205, 198, 191, 182, 175, 166, 159, 150, 143, 134, 126, 116, 112)(110, 117, 113, 122, 131, 139, 147, 155, 163, 171, 179, 187, 195, 203, 204, 199, 190, 183, 174, 167, 158, 151, 142, 135, 125, 118)(120, 127, 121, 128, 136, 144, 152, 160, 168, 176, 184, 192, 200, 206, 208, 207, 202, 194, 186, 178, 170, 162, 154, 146, 138, 130) 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 ), ( 8^26 ) } Outer automorphisms :: reflexible Dual of E12.810 Transitivity :: ET+ Graph:: simple bipartite v = 56 e = 104 f = 26 degree seq :: [ 2^52, 26^4 ] E12.810 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 26}) Quotient :: loop Aut^+ = (C26 x C2) : C2 (small group id <104, 8>) Aut = D8 x D26 (small group id <208, 39>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T1)^2, (F * T2)^2, T2^4, (T2^-1 * T1 * T2^-1)^2, (T2 * T1)^26 ] 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, 46, 150, 34, 138, 44, 148)(35, 139, 62, 166, 42, 146, 64, 168)(36, 140, 66, 170, 45, 149, 68, 172)(37, 141, 70, 174, 38, 142, 65, 169)(39, 143, 75, 179, 40, 144, 61, 165)(41, 145, 57, 161, 43, 147, 59, 163)(47, 151, 72, 176, 48, 152, 69, 173)(49, 153, 77, 181, 50, 154, 74, 178)(51, 155, 87, 191, 52, 156, 85, 189)(53, 157, 91, 195, 54, 158, 89, 193)(55, 159, 95, 199, 56, 160, 93, 197)(58, 162, 99, 203, 60, 164, 97, 201)(63, 167, 94, 198, 80, 184, 96, 200)(67, 171, 98, 202, 83, 187, 100, 204)(71, 175, 92, 196, 73, 177, 90, 194)(76, 180, 88, 192, 78, 182, 86, 190)(79, 183, 102, 206, 81, 185, 104, 208)(82, 186, 101, 205, 84, 188, 103, 207) 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, 161)(32, 163)(33, 133)(34, 134)(35, 165)(36, 169)(37, 173)(38, 176)(39, 178)(40, 181)(41, 166)(42, 179)(43, 168)(44, 170)(45, 174)(46, 172)(47, 189)(48, 191)(49, 193)(50, 195)(51, 197)(52, 199)(53, 201)(54, 203)(55, 205)(56, 207)(57, 135)(58, 206)(59, 136)(60, 208)(61, 139)(62, 145)(63, 190)(64, 147)(65, 140)(66, 148)(67, 194)(68, 150)(69, 141)(70, 149)(71, 182)(72, 142)(73, 180)(74, 143)(75, 146)(76, 177)(77, 144)(78, 175)(79, 198)(80, 192)(81, 200)(82, 202)(83, 196)(84, 204)(85, 151)(86, 167)(87, 152)(88, 184)(89, 153)(90, 171)(91, 154)(92, 187)(93, 155)(94, 183)(95, 156)(96, 185)(97, 157)(98, 186)(99, 158)(100, 188)(101, 159)(102, 162)(103, 160)(104, 164) local type(s) :: { ( 2, 26, 2, 26, 2, 26, 2, 26 ) } Outer automorphisms :: reflexible Dual of E12.809 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 26 e = 104 f = 56 degree seq :: [ 8^26 ] E12.811 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 26}) Quotient :: loop Aut^+ = (C26 x C2) : C2 (small group id <104, 8>) Aut = D8 x D26 (small group id <208, 39>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1 * T1^-1)^2, (T2 * T1^-1)^2, T2^26 ] Map:: R = (1, 105, 3, 107, 10, 114, 18, 122, 26, 130, 34, 138, 42, 146, 50, 154, 58, 162, 66, 170, 74, 178, 82, 186, 90, 194, 98, 202, 92, 196, 84, 188, 76, 180, 68, 172, 60, 164, 52, 156, 44, 148, 36, 140, 28, 132, 20, 124, 12, 116, 5, 109)(2, 106, 7, 111, 15, 119, 23, 127, 31, 135, 39, 143, 47, 151, 55, 159, 63, 167, 71, 175, 79, 183, 87, 191, 95, 199, 102, 206, 96, 200, 88, 192, 80, 184, 72, 176, 64, 168, 56, 160, 48, 152, 40, 144, 32, 136, 24, 128, 16, 120, 8, 112)(4, 108, 11, 115, 19, 123, 27, 131, 35, 139, 43, 147, 51, 155, 59, 163, 67, 171, 75, 179, 83, 187, 91, 195, 99, 203, 103, 207, 97, 201, 89, 193, 81, 185, 73, 177, 65, 169, 57, 161, 49, 153, 41, 145, 33, 137, 25, 129, 17, 121, 9, 113)(6, 110, 13, 117, 21, 125, 29, 133, 37, 141, 45, 149, 53, 157, 61, 165, 69, 173, 77, 181, 85, 189, 93, 197, 100, 204, 104, 208, 101, 205, 94, 198, 86, 190, 78, 182, 70, 174, 62, 166, 54, 158, 46, 150, 38, 142, 30, 134, 22, 126, 14, 118) L = (1, 106)(2, 110)(3, 113)(4, 105)(5, 115)(6, 108)(7, 109)(8, 107)(9, 117)(10, 120)(11, 118)(12, 119)(13, 112)(14, 111)(15, 126)(16, 125)(17, 114)(18, 129)(19, 116)(20, 131)(21, 121)(22, 123)(23, 124)(24, 122)(25, 133)(26, 136)(27, 134)(28, 135)(29, 128)(30, 127)(31, 142)(32, 141)(33, 130)(34, 145)(35, 132)(36, 147)(37, 137)(38, 139)(39, 140)(40, 138)(41, 149)(42, 152)(43, 150)(44, 151)(45, 144)(46, 143)(47, 158)(48, 157)(49, 146)(50, 161)(51, 148)(52, 163)(53, 153)(54, 155)(55, 156)(56, 154)(57, 165)(58, 168)(59, 166)(60, 167)(61, 160)(62, 159)(63, 174)(64, 173)(65, 162)(66, 177)(67, 164)(68, 179)(69, 169)(70, 171)(71, 172)(72, 170)(73, 181)(74, 184)(75, 182)(76, 183)(77, 176)(78, 175)(79, 190)(80, 189)(81, 178)(82, 193)(83, 180)(84, 195)(85, 185)(86, 187)(87, 188)(88, 186)(89, 197)(90, 200)(91, 198)(92, 199)(93, 192)(94, 191)(95, 205)(96, 204)(97, 194)(98, 207)(99, 196)(100, 201)(101, 203)(102, 202)(103, 208)(104, 206) 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 ) } Outer automorphisms :: reflexible Dual of E12.807 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 4 e = 104 f = 78 degree seq :: [ 52^4 ] E12.812 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 26}) Quotient :: loop Aut^+ = (C26 x C2) : C2 (small group id <104, 8>) Aut = D8 x D26 (small group id <208, 39>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-2 * T2)^2, (T2 * T1)^4, T1^26 ] Map:: polytopal non-degenerate R = (1, 105, 3, 107)(2, 106, 6, 110)(4, 108, 9, 113)(5, 109, 12, 116)(7, 111, 16, 120)(8, 112, 17, 121)(10, 114, 15, 119)(11, 115, 21, 125)(13, 117, 23, 127)(14, 118, 24, 128)(18, 122, 26, 130)(19, 123, 27, 131)(20, 124, 30, 134)(22, 126, 32, 136)(25, 129, 34, 138)(28, 132, 33, 137)(29, 133, 38, 142)(31, 135, 40, 144)(35, 139, 42, 146)(36, 140, 43, 147)(37, 141, 46, 150)(39, 143, 48, 152)(41, 145, 50, 154)(44, 148, 49, 153)(45, 149, 54, 158)(47, 151, 56, 160)(51, 155, 58, 162)(52, 156, 59, 163)(53, 157, 62, 166)(55, 159, 64, 168)(57, 161, 66, 170)(60, 164, 65, 169)(61, 165, 70, 174)(63, 167, 72, 176)(67, 171, 74, 178)(68, 172, 75, 179)(69, 173, 78, 182)(71, 175, 80, 184)(73, 177, 82, 186)(76, 180, 81, 185)(77, 181, 86, 190)(79, 183, 88, 192)(83, 187, 90, 194)(84, 188, 91, 195)(85, 189, 94, 198)(87, 191, 96, 200)(89, 193, 98, 202)(92, 196, 97, 201)(93, 197, 100, 204)(95, 199, 102, 206)(99, 203, 103, 207)(101, 205, 104, 208) L = (1, 106)(2, 109)(3, 111)(4, 105)(5, 115)(6, 117)(7, 119)(8, 107)(9, 122)(10, 108)(11, 124)(12, 112)(13, 113)(14, 110)(15, 129)(16, 127)(17, 128)(18, 131)(19, 114)(20, 133)(21, 118)(22, 116)(23, 121)(24, 136)(25, 137)(26, 120)(27, 139)(28, 123)(29, 141)(30, 126)(31, 125)(32, 144)(33, 145)(34, 130)(35, 147)(36, 132)(37, 149)(38, 135)(39, 134)(40, 152)(41, 153)(42, 138)(43, 155)(44, 140)(45, 157)(46, 143)(47, 142)(48, 160)(49, 161)(50, 146)(51, 163)(52, 148)(53, 165)(54, 151)(55, 150)(56, 168)(57, 169)(58, 154)(59, 171)(60, 156)(61, 173)(62, 159)(63, 158)(64, 176)(65, 177)(66, 162)(67, 179)(68, 164)(69, 181)(70, 167)(71, 166)(72, 184)(73, 185)(74, 170)(75, 187)(76, 172)(77, 189)(78, 175)(79, 174)(80, 192)(81, 193)(82, 178)(83, 195)(84, 180)(85, 197)(86, 183)(87, 182)(88, 200)(89, 201)(90, 186)(91, 203)(92, 188)(93, 196)(94, 191)(95, 190)(96, 206)(97, 205)(98, 194)(99, 204)(100, 199)(101, 198)(102, 208)(103, 202)(104, 207) local type(s) :: { ( 4, 26, 4, 26 ) } Outer automorphisms :: reflexible Dual of E12.808 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 52 e = 104 f = 30 degree seq :: [ 4^52 ] E12.813 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 26}) 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^-1 * Y1, (R * Y3)^2, (R * Y1)^2, Y2^4, (R * Y2 * Y3^-1)^2, (Y2^-1 * Y1 * Y2^-1)^2, (Y3 * Y2^-1)^26 ] 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, 38, 142)(32, 136, 37, 141)(35, 139, 53, 157)(36, 140, 60, 164)(39, 143, 57, 161)(40, 144, 55, 159)(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, 94, 198)(62, 166, 101, 205)(65, 169, 91, 195)(66, 170, 89, 193)(68, 172, 98, 202)(70, 174, 93, 197)(71, 175, 97, 201)(73, 177, 102, 206)(75, 179, 100, 204)(76, 180, 99, 203)(78, 182, 104, 208)(80, 184, 103, 207)(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, 310, 414, 283, 387, 307, 411)(273, 377, 308, 412, 274, 378, 309, 413)(276, 380, 312, 416, 279, 383, 311, 415)(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, 210)(2, 209)(3, 215)(4, 217)(5, 218)(6, 220)(7, 211)(8, 219)(9, 212)(10, 213)(11, 216)(12, 214)(13, 225)(14, 226)(15, 227)(16, 228)(17, 221)(18, 222)(19, 223)(20, 224)(21, 233)(22, 234)(23, 235)(24, 236)(25, 229)(26, 230)(27, 231)(28, 232)(29, 241)(30, 242)(31, 246)(32, 245)(33, 237)(34, 238)(35, 261)(36, 268)(37, 240)(38, 239)(39, 265)(40, 263)(41, 267)(42, 269)(43, 272)(44, 271)(45, 275)(46, 277)(47, 280)(48, 282)(49, 285)(50, 287)(51, 289)(52, 291)(53, 243)(54, 293)(55, 248)(56, 295)(57, 247)(58, 302)(59, 249)(60, 244)(61, 250)(62, 309)(63, 252)(64, 251)(65, 299)(66, 297)(67, 253)(68, 306)(69, 254)(70, 301)(71, 305)(72, 255)(73, 310)(74, 256)(75, 308)(76, 307)(77, 257)(78, 312)(79, 258)(80, 311)(81, 259)(82, 303)(83, 260)(84, 304)(85, 262)(86, 300)(87, 264)(88, 298)(89, 274)(90, 296)(91, 273)(92, 294)(93, 278)(94, 266)(95, 290)(96, 292)(97, 279)(98, 276)(99, 284)(100, 283)(101, 270)(102, 281)(103, 288)(104, 286)(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) :: { ( 2, 52, 2, 52 ), ( 2, 52, 2, 52, 2, 52, 2, 52 ) } Outer automorphisms :: reflexible Dual of E12.816 Graph:: bipartite v = 78 e = 208 f = 108 degree seq :: [ 4^52, 8^26 ] E12.814 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 26}) Quotient :: dipole 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 * Y3^-1, (Y2^-1 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, (Y2^-1 * Y1)^2, (Y3^-1 * Y1^-1)^2, Y1^4, Y2^26 ] Map:: R = (1, 105, 2, 106, 6, 110, 4, 108)(3, 107, 9, 113, 13, 117, 8, 112)(5, 109, 11, 115, 14, 118, 7, 111)(10, 114, 16, 120, 21, 125, 17, 121)(12, 116, 15, 119, 22, 126, 19, 123)(18, 122, 25, 129, 29, 133, 24, 128)(20, 124, 27, 131, 30, 134, 23, 127)(26, 130, 32, 136, 37, 141, 33, 137)(28, 132, 31, 135, 38, 142, 35, 139)(34, 138, 41, 145, 45, 149, 40, 144)(36, 140, 43, 147, 46, 150, 39, 143)(42, 146, 48, 152, 53, 157, 49, 153)(44, 148, 47, 151, 54, 158, 51, 155)(50, 154, 57, 161, 61, 165, 56, 160)(52, 156, 59, 163, 62, 166, 55, 159)(58, 162, 64, 168, 69, 173, 65, 169)(60, 164, 63, 167, 70, 174, 67, 171)(66, 170, 73, 177, 77, 181, 72, 176)(68, 172, 75, 179, 78, 182, 71, 175)(74, 178, 80, 184, 85, 189, 81, 185)(76, 180, 79, 183, 86, 190, 83, 187)(82, 186, 89, 193, 93, 197, 88, 192)(84, 188, 91, 195, 94, 198, 87, 191)(90, 194, 96, 200, 100, 204, 97, 201)(92, 196, 95, 199, 101, 205, 99, 203)(98, 202, 103, 207, 104, 208, 102, 206)(209, 313, 211, 315, 218, 322, 226, 330, 234, 338, 242, 346, 250, 354, 258, 362, 266, 370, 274, 378, 282, 386, 290, 394, 298, 402, 306, 410, 300, 404, 292, 396, 284, 388, 276, 380, 268, 372, 260, 364, 252, 356, 244, 348, 236, 340, 228, 332, 220, 324, 213, 317)(210, 314, 215, 319, 223, 327, 231, 335, 239, 343, 247, 351, 255, 359, 263, 367, 271, 375, 279, 383, 287, 391, 295, 399, 303, 407, 310, 414, 304, 408, 296, 400, 288, 392, 280, 384, 272, 376, 264, 368, 256, 360, 248, 352, 240, 344, 232, 336, 224, 328, 216, 320)(212, 316, 219, 323, 227, 331, 235, 339, 243, 347, 251, 355, 259, 363, 267, 371, 275, 379, 283, 387, 291, 395, 299, 403, 307, 411, 311, 415, 305, 409, 297, 401, 289, 393, 281, 385, 273, 377, 265, 369, 257, 361, 249, 353, 241, 345, 233, 337, 225, 329, 217, 321)(214, 318, 221, 325, 229, 333, 237, 341, 245, 349, 253, 357, 261, 365, 269, 373, 277, 381, 285, 389, 293, 397, 301, 405, 308, 412, 312, 416, 309, 413, 302, 406, 294, 398, 286, 390, 278, 382, 270, 374, 262, 366, 254, 358, 246, 350, 238, 342, 230, 334, 222, 326) L = (1, 211)(2, 215)(3, 218)(4, 219)(5, 209)(6, 221)(7, 223)(8, 210)(9, 212)(10, 226)(11, 227)(12, 213)(13, 229)(14, 214)(15, 231)(16, 216)(17, 217)(18, 234)(19, 235)(20, 220)(21, 237)(22, 222)(23, 239)(24, 224)(25, 225)(26, 242)(27, 243)(28, 228)(29, 245)(30, 230)(31, 247)(32, 232)(33, 233)(34, 250)(35, 251)(36, 236)(37, 253)(38, 238)(39, 255)(40, 240)(41, 241)(42, 258)(43, 259)(44, 244)(45, 261)(46, 246)(47, 263)(48, 248)(49, 249)(50, 266)(51, 267)(52, 252)(53, 269)(54, 254)(55, 271)(56, 256)(57, 257)(58, 274)(59, 275)(60, 260)(61, 277)(62, 262)(63, 279)(64, 264)(65, 265)(66, 282)(67, 283)(68, 268)(69, 285)(70, 270)(71, 287)(72, 272)(73, 273)(74, 290)(75, 291)(76, 276)(77, 293)(78, 278)(79, 295)(80, 280)(81, 281)(82, 298)(83, 299)(84, 284)(85, 301)(86, 286)(87, 303)(88, 288)(89, 289)(90, 306)(91, 307)(92, 292)(93, 308)(94, 294)(95, 310)(96, 296)(97, 297)(98, 300)(99, 311)(100, 312)(101, 302)(102, 304)(103, 305)(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) :: { ( 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 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 E12.815 Graph:: bipartite v = 30 e = 208 f = 156 degree seq :: [ 8^26, 52^4 ] E12.815 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 26}) 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, 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^-1 * Y1^-1)^26 ] Map:: polytopal R = (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)(209, 313, 210, 314)(211, 315, 215, 319)(212, 316, 217, 321)(213, 317, 219, 323)(214, 318, 221, 325)(216, 320, 222, 326)(218, 322, 220, 324)(223, 327, 228, 332)(224, 328, 231, 335)(225, 329, 233, 337)(226, 330, 229, 333)(227, 331, 235, 339)(230, 334, 237, 341)(232, 336, 239, 343)(234, 338, 240, 344)(236, 340, 238, 342)(241, 345, 247, 351)(242, 346, 249, 353)(243, 347, 245, 349)(244, 348, 251, 355)(246, 350, 253, 357)(248, 352, 255, 359)(250, 354, 256, 360)(252, 356, 254, 358)(257, 361, 263, 367)(258, 362, 265, 369)(259, 363, 261, 365)(260, 364, 267, 371)(262, 366, 269, 373)(264, 368, 271, 375)(266, 370, 272, 376)(268, 372, 270, 374)(273, 377, 279, 383)(274, 378, 281, 385)(275, 379, 277, 381)(276, 380, 283, 387)(278, 382, 285, 389)(280, 384, 287, 391)(282, 386, 288, 392)(284, 388, 286, 390)(289, 393, 295, 399)(290, 394, 297, 401)(291, 395, 293, 397)(292, 396, 299, 403)(294, 398, 301, 405)(296, 400, 303, 407)(298, 402, 304, 408)(300, 404, 302, 406)(305, 409, 310, 414)(306, 410, 311, 415)(307, 411, 308, 412)(309, 413, 312, 416) L = (1, 211)(2, 213)(3, 216)(4, 209)(5, 220)(6, 210)(7, 223)(8, 225)(9, 226)(10, 212)(11, 228)(12, 230)(13, 231)(14, 214)(15, 217)(16, 215)(17, 234)(18, 235)(19, 218)(20, 221)(21, 219)(22, 238)(23, 239)(24, 222)(25, 224)(26, 242)(27, 243)(28, 227)(29, 229)(30, 246)(31, 247)(32, 232)(33, 233)(34, 250)(35, 251)(36, 236)(37, 237)(38, 254)(39, 255)(40, 240)(41, 241)(42, 258)(43, 259)(44, 244)(45, 245)(46, 262)(47, 263)(48, 248)(49, 249)(50, 266)(51, 267)(52, 252)(53, 253)(54, 270)(55, 271)(56, 256)(57, 257)(58, 274)(59, 275)(60, 260)(61, 261)(62, 278)(63, 279)(64, 264)(65, 265)(66, 282)(67, 283)(68, 268)(69, 269)(70, 286)(71, 287)(72, 272)(73, 273)(74, 290)(75, 291)(76, 276)(77, 277)(78, 294)(79, 295)(80, 280)(81, 281)(82, 298)(83, 299)(84, 284)(85, 285)(86, 302)(87, 303)(88, 288)(89, 289)(90, 306)(91, 307)(92, 292)(93, 293)(94, 309)(95, 310)(96, 296)(97, 297)(98, 300)(99, 311)(100, 301)(101, 304)(102, 312)(103, 305)(104, 308)(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, 52 ), ( 8, 52, 8, 52 ) } Outer automorphisms :: reflexible Dual of E12.814 Graph:: simple bipartite v = 156 e = 208 f = 30 degree seq :: [ 2^104, 4^52 ] E12.816 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 26}) Quotient :: dipole Aut^+ = (C26 x C2) : C2 (small group id <104, 8>) Aut = D8 x D26 (small group id <208, 39>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2^-1)^2, (R * Y2 * Y3^-1)^2, Y3 * Y1^-2 * Y3^-1 * Y1^-2, (Y3^-1 * Y1)^4, Y1^26 ] Map:: polytopal R = (1, 105, 2, 106, 5, 109, 11, 115, 20, 124, 29, 133, 37, 141, 45, 149, 53, 157, 61, 165, 69, 173, 77, 181, 85, 189, 93, 197, 92, 196, 84, 188, 76, 180, 68, 172, 60, 164, 52, 156, 44, 148, 36, 140, 28, 132, 19, 123, 10, 114, 4, 108)(3, 107, 7, 111, 15, 119, 25, 129, 33, 137, 41, 145, 49, 153, 57, 161, 65, 169, 73, 177, 81, 185, 89, 193, 97, 201, 101, 205, 94, 198, 87, 191, 78, 182, 71, 175, 62, 166, 55, 159, 46, 150, 39, 143, 30, 134, 22, 126, 12, 116, 8, 112)(6, 110, 13, 117, 9, 113, 18, 122, 27, 131, 35, 139, 43, 147, 51, 155, 59, 163, 67, 171, 75, 179, 83, 187, 91, 195, 99, 203, 100, 204, 95, 199, 86, 190, 79, 183, 70, 174, 63, 167, 54, 158, 47, 151, 38, 142, 31, 135, 21, 125, 14, 118)(16, 120, 23, 127, 17, 121, 24, 128, 32, 136, 40, 144, 48, 152, 56, 160, 64, 168, 72, 176, 80, 184, 88, 192, 96, 200, 102, 206, 104, 208, 103, 207, 98, 202, 90, 194, 82, 186, 74, 178, 66, 170, 58, 162, 50, 154, 42, 146, 34, 138, 26, 130)(209, 313)(210, 314)(211, 315)(212, 316)(213, 317)(214, 318)(215, 319)(216, 320)(217, 321)(218, 322)(219, 323)(220, 324)(221, 325)(222, 326)(223, 327)(224, 328)(225, 329)(226, 330)(227, 331)(228, 332)(229, 333)(230, 334)(231, 335)(232, 336)(233, 337)(234, 338)(235, 339)(236, 340)(237, 341)(238, 342)(239, 343)(240, 344)(241, 345)(242, 346)(243, 347)(244, 348)(245, 349)(246, 350)(247, 351)(248, 352)(249, 353)(250, 354)(251, 355)(252, 356)(253, 357)(254, 358)(255, 359)(256, 360)(257, 361)(258, 362)(259, 363)(260, 364)(261, 365)(262, 366)(263, 367)(264, 368)(265, 369)(266, 370)(267, 371)(268, 372)(269, 373)(270, 374)(271, 375)(272, 376)(273, 377)(274, 378)(275, 379)(276, 380)(277, 381)(278, 382)(279, 383)(280, 384)(281, 385)(282, 386)(283, 387)(284, 388)(285, 389)(286, 390)(287, 391)(288, 392)(289, 393)(290, 394)(291, 395)(292, 396)(293, 397)(294, 398)(295, 399)(296, 400)(297, 401)(298, 402)(299, 403)(300, 404)(301, 405)(302, 406)(303, 407)(304, 408)(305, 409)(306, 410)(307, 411)(308, 412)(309, 413)(310, 414)(311, 415)(312, 416) L = (1, 211)(2, 214)(3, 209)(4, 217)(5, 220)(6, 210)(7, 224)(8, 225)(9, 212)(10, 223)(11, 229)(12, 213)(13, 231)(14, 232)(15, 218)(16, 215)(17, 216)(18, 234)(19, 235)(20, 238)(21, 219)(22, 240)(23, 221)(24, 222)(25, 242)(26, 226)(27, 227)(28, 241)(29, 246)(30, 228)(31, 248)(32, 230)(33, 236)(34, 233)(35, 250)(36, 251)(37, 254)(38, 237)(39, 256)(40, 239)(41, 258)(42, 243)(43, 244)(44, 257)(45, 262)(46, 245)(47, 264)(48, 247)(49, 252)(50, 249)(51, 266)(52, 267)(53, 270)(54, 253)(55, 272)(56, 255)(57, 274)(58, 259)(59, 260)(60, 273)(61, 278)(62, 261)(63, 280)(64, 263)(65, 268)(66, 265)(67, 282)(68, 283)(69, 286)(70, 269)(71, 288)(72, 271)(73, 290)(74, 275)(75, 276)(76, 289)(77, 294)(78, 277)(79, 296)(80, 279)(81, 284)(82, 281)(83, 298)(84, 299)(85, 302)(86, 285)(87, 304)(88, 287)(89, 306)(90, 291)(91, 292)(92, 305)(93, 308)(94, 293)(95, 310)(96, 295)(97, 300)(98, 297)(99, 311)(100, 301)(101, 312)(102, 303)(103, 307)(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, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 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 E12.813 Graph:: simple bipartite v = 108 e = 208 f = 78 degree seq :: [ 2^104, 52^4 ] E12.817 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 26}) 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^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y2^-1 * Y1 * Y2^-1)^2, (Y3 * Y2^-1)^4, Y2^26 ] Map:: R = (1, 105, 2, 106)(3, 107, 7, 111)(4, 108, 9, 113)(5, 109, 11, 115)(6, 110, 13, 117)(8, 112, 14, 118)(10, 114, 12, 116)(15, 119, 20, 124)(16, 120, 23, 127)(17, 121, 25, 129)(18, 122, 21, 125)(19, 123, 27, 131)(22, 126, 29, 133)(24, 128, 31, 135)(26, 130, 32, 136)(28, 132, 30, 134)(33, 137, 39, 143)(34, 138, 41, 145)(35, 139, 37, 141)(36, 140, 43, 147)(38, 142, 45, 149)(40, 144, 47, 151)(42, 146, 48, 152)(44, 148, 46, 150)(49, 153, 55, 159)(50, 154, 57, 161)(51, 155, 53, 157)(52, 156, 59, 163)(54, 158, 61, 165)(56, 160, 63, 167)(58, 162, 64, 168)(60, 164, 62, 166)(65, 169, 71, 175)(66, 170, 73, 177)(67, 171, 69, 173)(68, 172, 75, 179)(70, 174, 77, 181)(72, 176, 79, 183)(74, 178, 80, 184)(76, 180, 78, 182)(81, 185, 87, 191)(82, 186, 89, 193)(83, 187, 85, 189)(84, 188, 91, 195)(86, 190, 93, 197)(88, 192, 95, 199)(90, 194, 96, 200)(92, 196, 94, 198)(97, 201, 102, 206)(98, 202, 103, 207)(99, 203, 100, 204)(101, 205, 104, 208)(209, 313, 211, 315, 216, 320, 225, 329, 234, 338, 242, 346, 250, 354, 258, 362, 266, 370, 274, 378, 282, 386, 290, 394, 298, 402, 306, 410, 300, 404, 292, 396, 284, 388, 276, 380, 268, 372, 260, 364, 252, 356, 244, 348, 236, 340, 227, 331, 218, 322, 212, 316)(210, 314, 213, 317, 220, 324, 230, 334, 238, 342, 246, 350, 254, 358, 262, 366, 270, 374, 278, 382, 286, 390, 294, 398, 302, 406, 309, 413, 304, 408, 296, 400, 288, 392, 280, 384, 272, 376, 264, 368, 256, 360, 248, 352, 240, 344, 232, 336, 222, 326, 214, 318)(215, 319, 223, 327, 217, 321, 226, 330, 235, 339, 243, 347, 251, 355, 259, 363, 267, 371, 275, 379, 283, 387, 291, 395, 299, 403, 307, 411, 311, 415, 305, 409, 297, 401, 289, 393, 281, 385, 273, 377, 265, 369, 257, 361, 249, 353, 241, 345, 233, 337, 224, 328)(219, 323, 228, 332, 221, 325, 231, 335, 239, 343, 247, 351, 255, 359, 263, 367, 271, 375, 279, 383, 287, 391, 295, 399, 303, 407, 310, 414, 312, 416, 308, 412, 301, 405, 293, 397, 285, 389, 277, 381, 269, 373, 261, 365, 253, 357, 245, 349, 237, 341, 229, 333) L = (1, 210)(2, 209)(3, 215)(4, 217)(5, 219)(6, 221)(7, 211)(8, 222)(9, 212)(10, 220)(11, 213)(12, 218)(13, 214)(14, 216)(15, 228)(16, 231)(17, 233)(18, 229)(19, 235)(20, 223)(21, 226)(22, 237)(23, 224)(24, 239)(25, 225)(26, 240)(27, 227)(28, 238)(29, 230)(30, 236)(31, 232)(32, 234)(33, 247)(34, 249)(35, 245)(36, 251)(37, 243)(38, 253)(39, 241)(40, 255)(41, 242)(42, 256)(43, 244)(44, 254)(45, 246)(46, 252)(47, 248)(48, 250)(49, 263)(50, 265)(51, 261)(52, 267)(53, 259)(54, 269)(55, 257)(56, 271)(57, 258)(58, 272)(59, 260)(60, 270)(61, 262)(62, 268)(63, 264)(64, 266)(65, 279)(66, 281)(67, 277)(68, 283)(69, 275)(70, 285)(71, 273)(72, 287)(73, 274)(74, 288)(75, 276)(76, 286)(77, 278)(78, 284)(79, 280)(80, 282)(81, 295)(82, 297)(83, 293)(84, 299)(85, 291)(86, 301)(87, 289)(88, 303)(89, 290)(90, 304)(91, 292)(92, 302)(93, 294)(94, 300)(95, 296)(96, 298)(97, 310)(98, 311)(99, 308)(100, 307)(101, 312)(102, 305)(103, 306)(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) :: { ( 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 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 E12.818 Graph:: bipartite v = 56 e = 208 f = 130 degree seq :: [ 4^52, 52^4 ] E12.818 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 26}) Quotient :: dipole Aut^+ = (C26 x C2) : C2 (small group id <104, 8>) Aut = D8 x D26 (small group id <208, 39>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, Y1^4, (Y3^-1 * Y1)^2, (Y3^-1 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^26 ] Map:: polytopal R = (1, 105, 2, 106, 6, 110, 4, 108)(3, 107, 9, 113, 13, 117, 8, 112)(5, 109, 11, 115, 14, 118, 7, 111)(10, 114, 16, 120, 21, 125, 17, 121)(12, 116, 15, 119, 22, 126, 19, 123)(18, 122, 25, 129, 29, 133, 24, 128)(20, 124, 27, 131, 30, 134, 23, 127)(26, 130, 32, 136, 37, 141, 33, 137)(28, 132, 31, 135, 38, 142, 35, 139)(34, 138, 41, 145, 45, 149, 40, 144)(36, 140, 43, 147, 46, 150, 39, 143)(42, 146, 48, 152, 53, 157, 49, 153)(44, 148, 47, 151, 54, 158, 51, 155)(50, 154, 57, 161, 61, 165, 56, 160)(52, 156, 59, 163, 62, 166, 55, 159)(58, 162, 64, 168, 69, 173, 65, 169)(60, 164, 63, 167, 70, 174, 67, 171)(66, 170, 73, 177, 77, 181, 72, 176)(68, 172, 75, 179, 78, 182, 71, 175)(74, 178, 80, 184, 85, 189, 81, 185)(76, 180, 79, 183, 86, 190, 83, 187)(82, 186, 89, 193, 93, 197, 88, 192)(84, 188, 91, 195, 94, 198, 87, 191)(90, 194, 96, 200, 100, 204, 97, 201)(92, 196, 95, 199, 101, 205, 99, 203)(98, 202, 103, 207, 104, 208, 102, 206)(209, 313)(210, 314)(211, 315)(212, 316)(213, 317)(214, 318)(215, 319)(216, 320)(217, 321)(218, 322)(219, 323)(220, 324)(221, 325)(222, 326)(223, 327)(224, 328)(225, 329)(226, 330)(227, 331)(228, 332)(229, 333)(230, 334)(231, 335)(232, 336)(233, 337)(234, 338)(235, 339)(236, 340)(237, 341)(238, 342)(239, 343)(240, 344)(241, 345)(242, 346)(243, 347)(244, 348)(245, 349)(246, 350)(247, 351)(248, 352)(249, 353)(250, 354)(251, 355)(252, 356)(253, 357)(254, 358)(255, 359)(256, 360)(257, 361)(258, 362)(259, 363)(260, 364)(261, 365)(262, 366)(263, 367)(264, 368)(265, 369)(266, 370)(267, 371)(268, 372)(269, 373)(270, 374)(271, 375)(272, 376)(273, 377)(274, 378)(275, 379)(276, 380)(277, 381)(278, 382)(279, 383)(280, 384)(281, 385)(282, 386)(283, 387)(284, 388)(285, 389)(286, 390)(287, 391)(288, 392)(289, 393)(290, 394)(291, 395)(292, 396)(293, 397)(294, 398)(295, 399)(296, 400)(297, 401)(298, 402)(299, 403)(300, 404)(301, 405)(302, 406)(303, 407)(304, 408)(305, 409)(306, 410)(307, 411)(308, 412)(309, 413)(310, 414)(311, 415)(312, 416) L = (1, 211)(2, 215)(3, 218)(4, 219)(5, 209)(6, 221)(7, 223)(8, 210)(9, 212)(10, 226)(11, 227)(12, 213)(13, 229)(14, 214)(15, 231)(16, 216)(17, 217)(18, 234)(19, 235)(20, 220)(21, 237)(22, 222)(23, 239)(24, 224)(25, 225)(26, 242)(27, 243)(28, 228)(29, 245)(30, 230)(31, 247)(32, 232)(33, 233)(34, 250)(35, 251)(36, 236)(37, 253)(38, 238)(39, 255)(40, 240)(41, 241)(42, 258)(43, 259)(44, 244)(45, 261)(46, 246)(47, 263)(48, 248)(49, 249)(50, 266)(51, 267)(52, 252)(53, 269)(54, 254)(55, 271)(56, 256)(57, 257)(58, 274)(59, 275)(60, 260)(61, 277)(62, 262)(63, 279)(64, 264)(65, 265)(66, 282)(67, 283)(68, 268)(69, 285)(70, 270)(71, 287)(72, 272)(73, 273)(74, 290)(75, 291)(76, 276)(77, 293)(78, 278)(79, 295)(80, 280)(81, 281)(82, 298)(83, 299)(84, 284)(85, 301)(86, 286)(87, 303)(88, 288)(89, 289)(90, 306)(91, 307)(92, 292)(93, 308)(94, 294)(95, 310)(96, 296)(97, 297)(98, 300)(99, 311)(100, 312)(101, 302)(102, 304)(103, 305)(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, 52 ), ( 4, 52, 4, 52, 4, 52, 4, 52 ) } Outer automorphisms :: reflexible Dual of E12.817 Graph:: simple bipartite v = 130 e = 208 f = 56 degree seq :: [ 2^104, 8^26 ] E12.819 :: Family: { 2Pex } :: Oriented family(ies): { E1a } Signature :: (0; {2, 5, 10}) Quotient :: halfedge Aut^+ = (C11 : C5) : C2 (small group id <110, 1>) Aut = (C11 : C5) : C2 (small group id <110, 1>) |r| :: 1 Presentation :: [ X2^2, X1^-1 * X2 * X1^2 * X2 * X1 * X2 * X1^-1 * X2 * X1^-1, X1^-1 * X2 * X1 * X2 * X1^-2 * X2 * X1^-3, X1^10, (X1^-1 * X2)^5, X2 * X1 * X2 * X1^3 * X2 * X1^-3 * X2 * X1^-1 ] Map:: polytopal non-degenerate R = (1, 2, 5, 11, 23, 47, 46, 22, 10, 4)(3, 7, 15, 31, 61, 84, 53, 38, 18, 8)(6, 13, 27, 55, 85, 105, 80, 62, 30, 14)(9, 19, 39, 71, 37, 60, 29, 59, 42, 20)(12, 25, 51, 82, 106, 97, 102, 86, 54, 26)(16, 33, 65, 87, 109, 89, 103, 78, 48, 34)(17, 35, 68, 44, 21, 43, 67, 96, 70, 36)(24, 49, 40, 73, 92, 63, 91, 69, 81, 50)(28, 57, 88, 107, 98, 72, 94, 101, 77, 58)(32, 52, 83, 108, 99, 75, 90, 110, 93, 64)(41, 74, 100, 76, 45, 56, 79, 104, 95, 66) 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, 63)(33, 66)(34, 67)(35, 69)(36, 57)(38, 72)(39, 58)(42, 70)(43, 51)(44, 75)(46, 64)(47, 77)(49, 79)(50, 80)(54, 85)(55, 87)(59, 89)(60, 83)(62, 90)(65, 94)(68, 95)(71, 97)(73, 99)(74, 86)(76, 98)(78, 102)(81, 106)(82, 107)(84, 104)(88, 110)(91, 101)(92, 103)(93, 109)(96, 105)(100, 108) local type(s) :: { ( 5^10 ) } Outer automorphisms :: chiral Transitivity :: ET+ VT+ AT+ REG+ Graph:: simple v = 11 e = 55 f = 22 degree seq :: [ 10^11 ] E12.820 :: Family: { 2Pex } :: Oriented family(ies): { E1a } Signature :: (0; {2, 5, 10}) Quotient :: halfedge Aut^+ = (C11 : C5) : C2 (small group id <110, 1>) Aut = (C11 : C5) : C2 (small group id <110, 1>) |r| :: 1 Presentation :: [ X2^2, X2 * X1^-1 * X2 * X1 * X2 * X1^5, (X1^-1 * X2)^5, X1^-1 * X2 * X1 * X2 * X1^-1 * X2 * X1^3 * X2 * X1^-2 ] Map:: polytopal non-degenerate R = (1, 2, 5, 11, 23, 47, 46, 22, 10, 4)(3, 7, 15, 31, 63, 40, 74, 38, 18, 8)(6, 13, 27, 55, 34, 16, 33, 62, 30, 14)(9, 19, 39, 75, 102, 80, 92, 78, 42, 20)(12, 25, 51, 87, 58, 28, 57, 93, 54, 26)(17, 35, 69, 96, 56, 95, 107, 105, 70, 36)(21, 43, 79, 103, 73, 101, 61, 100, 81, 44)(24, 49, 84, 76, 90, 52, 89, 68, 86, 50)(29, 59, 98, 64, 88, 110, 104, 77, 99, 60)(32, 65, 85, 109, 97, 67, 41, 48, 83, 66)(37, 71, 91, 53, 45, 82, 94, 108, 106, 72) 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, 64)(33, 67)(34, 68)(35, 47)(36, 57)(38, 73)(39, 76)(42, 77)(43, 80)(44, 50)(46, 59)(49, 85)(51, 88)(54, 92)(55, 94)(58, 97)(60, 89)(62, 102)(63, 93)(65, 99)(66, 103)(69, 104)(70, 90)(71, 95)(72, 98)(74, 86)(75, 96)(78, 106)(79, 87)(81, 105)(82, 101)(83, 107)(84, 108)(91, 109)(100, 110) local type(s) :: { ( 5^10 ) } Outer automorphisms :: chiral Dual of E12.822 Transitivity :: ET+ VT+ AT+ REG+ Graph:: simple v = 11 e = 55 f = 22 degree seq :: [ 10^11 ] E12.821 :: Family: { 2Pex } :: Oriented family(ies): { E1a } Signature :: (0; {2, 5, 10}) Quotient :: halfedge Aut^+ = (C11 : C5) : C2 (small group id <110, 1>) Aut = (C11 : C5) : C2 (small group id <110, 1>) |r| :: 1 Presentation :: [ X2^2, X1^5, X2 * X1^-1 * X2 * X1 * X2 * X1^2 * X2 * X1^-2, (X2 * X1 * X2 * X1 * X2 * X1^-2)^2, X2 * X1^2 * X2 * X1 * X2 * X1 * X2 * X1^-1 * X2 * X1^-1 * X2 * X1^-2, (X1^-1 * X2)^10 ] 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, 43, 53, 29)(16, 30, 54, 56, 31)(20, 37, 63, 65, 38)(24, 44, 66, 72, 45)(25, 46, 73, 75, 47)(27, 49, 60, 34, 50)(32, 57, 87, 89, 58)(35, 48, 76, 94, 61)(40, 67, 96, 99, 68)(41, 62, 95, 101, 69)(51, 79, 92, 100, 80)(52, 81, 102, 70, 82)(55, 83, 108, 109, 85)(59, 90, 97, 64, 91)(71, 93, 77, 98, 103)(74, 104, 78, 86, 106)(84, 105, 110, 88, 107) 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, 51)(29, 52)(30, 42)(31, 55)(33, 59)(36, 62)(37, 64)(38, 58)(39, 66)(44, 70)(45, 71)(46, 65)(47, 74)(49, 77)(50, 78)(53, 83)(54, 84)(56, 86)(57, 88)(60, 92)(61, 93)(63, 96)(67, 98)(68, 85)(69, 100)(72, 104)(73, 105)(75, 79)(76, 107)(80, 99)(81, 89)(82, 101)(87, 103)(90, 102)(91, 108)(94, 109)(95, 110)(97, 106) local type(s) :: { ( 10^5 ) } Outer automorphisms :: chiral Transitivity :: ET+ VT+ AT+ REG+ Graph:: simple bipartite v = 22 e = 55 f = 11 degree seq :: [ 5^22 ] E12.822 :: Family: { 2Pex } :: Oriented family(ies): { E1a } Signature :: (0; {2, 5, 10}) Quotient :: halfedge Aut^+ = (C11 : C5) : C2 (small group id <110, 1>) Aut = (C11 : C5) : C2 (small group id <110, 1>) |r| :: 1 Presentation :: [ X2^2, X1^5, X2 * X1 * X2 * X1^-1 * X2 * X1^2 * X2 * X1^-2, X1 * X2 * X1 * X2 * X1 * X2 * X1 * X2 * X1^2 * X2 * X1^-1 * X2 ] 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, 50, 52, 29)(16, 30, 53, 56, 31)(20, 37, 63, 65, 38)(24, 44, 71, 73, 45)(25, 46, 27, 49, 47)(32, 57, 86, 88, 58)(34, 59, 89, 76, 48)(35, 60, 91, 94, 61)(40, 67, 99, 95, 62)(41, 68, 43, 70, 69)(51, 79, 92, 101, 80)(54, 82, 103, 72, 81)(55, 83, 107, 108, 84)(64, 96, 66, 98, 97)(74, 93, 78, 100, 104)(75, 105, 90, 87, 106)(77, 102, 110, 109, 85) 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, 51)(29, 42)(30, 54)(31, 55)(33, 53)(36, 62)(37, 57)(38, 64)(39, 66)(44, 72)(45, 65)(46, 74)(47, 75)(49, 77)(50, 78)(52, 81)(56, 85)(58, 87)(59, 90)(60, 92)(61, 93)(63, 91)(67, 100)(68, 84)(69, 101)(70, 102)(71, 83)(73, 104)(76, 79)(80, 88)(82, 97)(86, 107)(89, 103)(94, 109)(95, 108)(96, 106)(98, 110)(99, 105) local type(s) :: { ( 10^5 ) } Outer automorphisms :: chiral Dual of E12.820 Transitivity :: ET+ VT+ AT+ REG+ Graph:: simple bipartite v = 22 e = 55 f = 11 degree seq :: [ 5^22 ] E12.823 :: Family: { 5 } :: Oriented family(ies): { E3a } Signature :: (0; {2, 5, 10}) Quotient :: edge Aut^+ = (C11 : C5) : C2 (small group id <110, 1>) Aut = (C11 : C5) : C2 (small group id <110, 1>) |r| :: 1 Presentation :: [ X1^2, X2^5, X1 * X2^-1 * X1 * X2 * X1 * X2^2 * X1 * X2^-2, (X2 * X1 * X2^-2 * X1 * X2 * X1)^2, X2 * X1 * X2 * X1 * X2^-1 * X1 * X2^-1 * X1 * X2^-2 * X1 * X2^2 * X1, (X2^-1 * X1)^10 ] Map:: polytopal R = (1, 2)(3, 7)(4, 9)(5, 11)(6, 13)(8, 17)(10, 20)(12, 23)(14, 26)(15, 27)(16, 29)(18, 33)(19, 35)(21, 39)(22, 41)(24, 45)(25, 47)(28, 40)(30, 55)(31, 56)(32, 58)(34, 60)(36, 62)(37, 63)(38, 50)(42, 70)(43, 71)(44, 72)(46, 73)(48, 75)(49, 76)(51, 79)(52, 81)(53, 65)(54, 84)(57, 80)(59, 90)(61, 93)(64, 97)(66, 85)(67, 98)(68, 78)(69, 101)(74, 88)(77, 110)(82, 104)(83, 105)(86, 106)(87, 103)(89, 99)(91, 100)(92, 102)(94, 107)(95, 109)(96, 108)(111, 113, 118, 120, 114)(112, 115, 122, 124, 116)(117, 125, 138, 140, 126)(119, 128, 144, 146, 129)(121, 131, 150, 152, 132)(123, 134, 156, 158, 135)(127, 141, 167, 155, 142)(130, 147, 174, 175, 148)(133, 153, 169, 143, 154)(136, 159, 187, 188, 160)(137, 161, 190, 192, 162)(139, 163, 193, 195, 164)(145, 165, 196, 204, 171)(149, 176, 200, 209, 177)(151, 178, 210, 189, 179)(157, 180, 212, 217, 184)(166, 197, 207, 208, 198)(168, 172, 205, 211, 199)(170, 201, 206, 173, 202)(181, 213, 220, 191, 203)(182, 185, 218, 194, 214)(183, 215, 219, 186, 216) 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) :: { ( 20, 20 ), ( 20^5 ) } Outer automorphisms :: chiral Transitivity :: ET+ Graph:: simple bipartite v = 77 e = 110 f = 11 degree seq :: [ 2^55, 5^22 ] E12.824 :: Family: { 5 } :: Oriented family(ies): { E3a } Signature :: (0; {2, 5, 10}) Quotient :: edge Aut^+ = (C11 : C5) : C2 (small group id <110, 1>) Aut = (C11 : C5) : C2 (small group id <110, 1>) |r| :: 1 Presentation :: [ X1^2, X2^5, X2^-1 * X1 * X2 * X1 * X2^-1 * X1 * X2^2 * X1 * X2^-1, X2 * X1 * X2^-1 * X1 * X2^2 * X1 * X2^-2 * X1, X1 * X2^2 * X1 * X2^-1 * X1 * X2 * X1 * X2 * X1 * X2 * X1 * X2 ] Map:: polytopal R = (1, 2)(3, 7)(4, 9)(5, 11)(6, 13)(8, 17)(10, 20)(12, 23)(14, 26)(15, 27)(16, 29)(18, 33)(19, 35)(21, 39)(22, 41)(24, 45)(25, 47)(28, 53)(30, 55)(31, 56)(32, 58)(34, 46)(36, 62)(37, 49)(38, 64)(40, 68)(42, 69)(43, 70)(44, 71)(48, 75)(50, 77)(51, 79)(52, 65)(54, 84)(57, 87)(59, 89)(60, 91)(61, 93)(63, 92)(66, 85)(67, 78)(72, 97)(73, 80)(74, 83)(76, 103)(81, 101)(82, 100)(86, 99)(88, 98)(90, 102)(94, 105)(95, 104)(96, 106)(107, 108)(109, 110)(111, 113, 118, 120, 114)(112, 115, 122, 124, 116)(117, 125, 138, 140, 126)(119, 128, 144, 146, 129)(121, 131, 150, 152, 132)(123, 134, 156, 158, 135)(127, 141, 167, 151, 142)(130, 147, 173, 175, 148)(133, 153, 164, 139, 154)(136, 159, 186, 188, 160)(137, 161, 190, 191, 162)(143, 169, 200, 195, 165)(145, 170, 202, 204, 171)(149, 176, 201, 208, 177)(155, 182, 212, 189, 179)(157, 183, 213, 214, 184)(163, 192, 198, 168, 193)(166, 196, 218, 205, 172)(174, 206, 197, 219, 207)(178, 209, 211, 181, 203)(180, 210, 220, 215, 185)(187, 216, 194, 217, 199) 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) :: { ( 20, 20 ), ( 20^5 ) } Outer automorphisms :: chiral Dual of E12.834 Transitivity :: ET+ Graph:: simple bipartite v = 77 e = 110 f = 11 degree seq :: [ 2^55, 5^22 ] E12.825 :: Family: { 5 } :: Oriented family(ies): { E3a } Signature :: (0; {2, 5, 10}) Quotient :: edge Aut^+ = (C11 : C5) : C2 (small group id <110, 1>) Aut = (C11 : C5) : C2 (small group id <110, 1>) |r| :: 1 Presentation :: [ (X1^-1 * X2^-1)^2, X1^5, X2 * X1^-1 * X2^-2 * X1 * X2^-1 * X1^-2, X2^2 * X1 * X2^-1 * X1^-1 * X2 * X1^-1 * X2^2, X2 * X1^-2 * X2 * X1^-1 * X2 * X1^-1 * X2^-1 * X1, X2^2 * X1^-2 * X2^-1 * X1 * X2^-3 * X1^-1, (X2^3 * X1^-2)^2, X2^10 ] Map:: polyhedral non-degenerate R = (1, 2, 6, 13, 4)(3, 9, 22, 28, 11)(5, 14, 33, 19, 7)(8, 20, 46, 39, 16)(10, 24, 55, 60, 26)(12, 29, 65, 70, 31)(15, 36, 48, 73, 34)(17, 40, 80, 62, 32)(18, 42, 85, 89, 44)(21, 49, 82, 57, 47)(23, 53, 35, 74, 51)(25, 56, 75, 84, 58)(27, 61, 100, 92, 63)(30, 45, 71, 98, 68)(37, 77, 102, 107, 76)(38, 69, 106, 108, 78)(41, 83, 104, 87, 81)(43, 86, 90, 59, 88)(50, 72, 67, 105, 91)(52, 93, 103, 66, 64)(54, 95, 79, 97, 94)(96, 109, 110, 101, 99)(111, 113, 120, 135, 167, 207, 188, 147, 125, 115)(112, 117, 128, 153, 197, 217, 202, 160, 131, 118)(114, 122, 140, 177, 183, 196, 154, 164, 133, 119)(116, 126, 148, 189, 203, 215, 178, 194, 151, 127)(121, 137, 172, 152, 129, 155, 141, 179, 149, 134)(123, 142, 173, 212, 184, 166, 136, 169, 176, 139)(124, 144, 182, 210, 220, 216, 180, 193, 185, 145)(130, 157, 168, 208, 211, 171, 138, 174, 200, 158)(132, 161, 187, 218, 219, 195, 190, 159, 201, 162)(143, 163, 204, 192, 150, 191, 198, 170, 209, 181)(146, 186, 214, 175, 213, 205, 199, 206, 165, 156) 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) :: { ( 4^5 ), ( 4^10 ) } Outer automorphisms :: chiral Dual of E12.829 Transitivity :: ET+ Graph:: simple bipartite v = 33 e = 110 f = 55 degree seq :: [ 5^22, 10^11 ] E12.826 :: Family: { 5 } :: Oriented family(ies): { E3a } Signature :: (0; {2, 5, 10}) Quotient :: edge Aut^+ = (C11 : C5) : C2 (small group id <110, 1>) Aut = (C11 : C5) : C2 (small group id <110, 1>) |r| :: 1 Presentation :: [ (X1 * X2)^2, X1^5, X1^-1 * X2^-1 * X1^-1 * X2 * X1 * X2 * X1 * X2^-1, X2 * X1^-1 * X2 * X1^2 * X2^2 * X1^-2, X2^2 * X1^-2 * X2 * X1^-2 * X2^-1 * X1, X1 * X2^-1 * X1^-1 * X2 * X1 * X2^-4, (X2^-1 * X1 * X2^-2 * X1)^2, X2^10 ] Map:: polyhedral non-degenerate R = (1, 2, 6, 13, 4)(3, 9, 22, 28, 11)(5, 14, 33, 19, 7)(8, 20, 46, 39, 16)(10, 24, 55, 61, 26)(12, 29, 66, 72, 31)(15, 36, 81, 78, 34)(17, 40, 77, 74, 32)(18, 42, 65, 52, 44)(21, 49, 98, 71, 47)(23, 53, 103, 85, 51)(25, 57, 83, 89, 59)(27, 62, 41, 88, 64)(30, 68, 109, 87, 70)(35, 79, 38, 58, 75)(37, 84, 56, 106, 82)(43, 90, 100, 63, 92)(45, 76, 67, 108, 94)(48, 96, 73, 91, 95)(50, 101, 69, 110, 99)(54, 105, 86, 107, 104)(60, 93, 102, 80, 97)(111, 113, 120, 135, 168, 149, 195, 147, 125, 115)(112, 117, 128, 153, 201, 184, 188, 160, 131, 118)(114, 122, 140, 179, 152, 129, 155, 164, 133, 119)(116, 126, 148, 196, 178, 141, 181, 199, 151, 127)(121, 137, 173, 177, 139, 123, 142, 183, 166, 134)(124, 144, 187, 219, 215, 204, 216, 206, 190, 145)(130, 157, 182, 165, 194, 213, 220, 180, 207, 158)(132, 161, 156, 205, 202, 174, 217, 189, 212, 162)(136, 170, 197, 150, 172, 138, 175, 211, 191, 167)(143, 185, 169, 208, 200, 154, 203, 171, 176, 186)(146, 192, 218, 210, 159, 209, 163, 214, 198, 193) 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) :: { ( 4^5 ), ( 4^10 ) } Outer automorphisms :: chiral Dual of E12.830 Transitivity :: ET+ Graph:: simple bipartite v = 33 e = 110 f = 55 degree seq :: [ 5^22, 10^11 ] E12.827 :: Family: { 5 } :: Oriented family(ies): { E3a } Signature :: (0; {2, 5, 10}) Quotient :: edge Aut^+ = (C11 : C5) : C2 (small group id <110, 1>) Aut = (C11 : C5) : C2 (small group id <110, 1>) |r| :: 1 Presentation :: [ X2^2, X1^-1 * X2 * X1^2 * X2 * X1 * X2 * X1^-1 * X2 * X1^-1, (X2 * X1^-1)^5, X1^-1 * X2 * X1 * X2 * X1^-2 * X2 * X1^-3, X1^10, X2 * X1 * X2 * X1^3 * X2 * X1^-3 * X2 * X1^-1 ] Map:: polytopal R = (1, 2, 5, 11, 23, 47, 46, 22, 10, 4)(3, 7, 15, 31, 61, 84, 53, 38, 18, 8)(6, 13, 27, 55, 85, 105, 80, 62, 30, 14)(9, 19, 39, 71, 37, 60, 29, 59, 42, 20)(12, 25, 51, 82, 106, 97, 102, 86, 54, 26)(16, 33, 65, 87, 109, 89, 103, 78, 48, 34)(17, 35, 68, 44, 21, 43, 67, 96, 70, 36)(24, 49, 40, 73, 92, 63, 91, 69, 81, 50)(28, 57, 88, 107, 98, 72, 94, 101, 77, 58)(32, 52, 83, 108, 99, 75, 90, 110, 93, 64)(41, 74, 100, 76, 45, 56, 79, 104, 95, 66)(111, 113)(112, 116)(114, 119)(115, 122)(117, 126)(118, 127)(120, 131)(121, 134)(123, 138)(124, 139)(125, 142)(128, 147)(129, 150)(130, 151)(132, 155)(133, 158)(135, 162)(136, 163)(137, 166)(140, 171)(141, 173)(143, 176)(144, 177)(145, 179)(146, 167)(148, 182)(149, 168)(152, 180)(153, 161)(154, 185)(156, 174)(157, 187)(159, 189)(160, 190)(164, 195)(165, 197)(169, 199)(170, 193)(172, 200)(175, 204)(178, 205)(181, 207)(183, 209)(184, 196)(186, 208)(188, 212)(191, 216)(192, 217)(194, 214)(198, 220)(201, 211)(202, 213)(203, 219)(206, 215)(210, 218) 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) :: { ( 10, 10 ), ( 10^10 ) } Outer automorphisms :: chiral Transitivity :: ET+ Graph:: simple bipartite v = 66 e = 110 f = 22 degree seq :: [ 2^55, 10^11 ] E12.828 :: Family: { 5 } :: Oriented family(ies): { E3a } Signature :: (0; {2, 5, 10}) Quotient :: edge Aut^+ = (C11 : C5) : C2 (small group id <110, 1>) Aut = (C11 : C5) : C2 (small group id <110, 1>) |r| :: 1 Presentation :: [ X2^2, X2 * X1^-1 * X2 * X1 * X2 * X1^5, (X2 * X1^-1)^5, X1^-1 * X2 * X1 * X2 * X1^-1 * X2 * X1^3 * X2 * X1^-2, X2 * X1^-2 * X2 * X1^3 * X2 * X1 * X2 * X1^-2 ] Map:: polytopal R = (1, 2, 5, 11, 23, 47, 46, 22, 10, 4)(3, 7, 15, 31, 63, 40, 74, 38, 18, 8)(6, 13, 27, 55, 34, 16, 33, 62, 30, 14)(9, 19, 39, 75, 102, 80, 92, 78, 42, 20)(12, 25, 51, 87, 58, 28, 57, 93, 54, 26)(17, 35, 69, 96, 56, 95, 107, 105, 70, 36)(21, 43, 79, 103, 73, 101, 61, 100, 81, 44)(24, 49, 84, 76, 90, 52, 89, 68, 86, 50)(29, 59, 98, 64, 88, 110, 104, 77, 99, 60)(32, 65, 85, 109, 97, 67, 41, 48, 83, 66)(37, 71, 91, 53, 45, 82, 94, 108, 106, 72)(111, 113)(112, 116)(114, 119)(115, 122)(117, 126)(118, 127)(120, 131)(121, 134)(123, 138)(124, 139)(125, 142)(128, 147)(129, 150)(130, 151)(132, 155)(133, 158)(135, 162)(136, 163)(137, 166)(140, 171)(141, 174)(143, 177)(144, 178)(145, 157)(146, 167)(148, 183)(149, 186)(152, 187)(153, 190)(154, 160)(156, 169)(159, 195)(161, 198)(164, 202)(165, 204)(168, 207)(170, 199)(172, 212)(173, 203)(175, 209)(176, 213)(179, 214)(180, 200)(181, 205)(182, 208)(184, 196)(185, 206)(188, 216)(189, 197)(191, 215)(192, 211)(193, 217)(194, 218)(201, 219)(210, 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) :: { ( 10, 10 ), ( 10^10 ) } Outer automorphisms :: chiral Dual of E12.832 Transitivity :: ET+ Graph:: simple bipartite v = 66 e = 110 f = 22 degree seq :: [ 2^55, 10^11 ] E12.829 :: Family: { 5* } :: Oriented family(ies): { E3*a } Signature :: (0; {2, 5, 10}) Quotient :: loop Aut^+ = (C11 : C5) : C2 (small group id <110, 1>) Aut = (C11 : C5) : C2 (small group id <110, 1>) |r| :: 1 Presentation :: [ X1^2, X2^5, X1 * X2^-1 * X1 * X2 * X1 * X2^2 * X1 * X2^-2, (X2 * X1 * X2^-2 * X1 * X2 * X1)^2, X2 * X1 * X2 * X1 * X2^-1 * X1 * X2^-1 * X1 * X2^-2 * X1 * X2^2 * X1, (X2^-1 * X1)^10 ] Map:: polyhedral non-degenerate R = (1, 111, 2, 112)(3, 113, 7, 117)(4, 114, 9, 119)(5, 115, 11, 121)(6, 116, 13, 123)(8, 118, 17, 127)(10, 120, 20, 130)(12, 122, 23, 133)(14, 124, 26, 136)(15, 125, 27, 137)(16, 126, 29, 139)(18, 128, 33, 143)(19, 129, 35, 145)(21, 131, 39, 149)(22, 132, 41, 151)(24, 134, 45, 155)(25, 135, 47, 157)(28, 138, 40, 150)(30, 140, 55, 165)(31, 141, 56, 166)(32, 142, 58, 168)(34, 144, 60, 170)(36, 146, 62, 172)(37, 147, 63, 173)(38, 148, 50, 160)(42, 152, 70, 180)(43, 153, 71, 181)(44, 154, 72, 182)(46, 156, 73, 183)(48, 158, 75, 185)(49, 159, 76, 186)(51, 161, 79, 189)(52, 162, 81, 191)(53, 163, 65, 175)(54, 164, 84, 194)(57, 167, 80, 190)(59, 169, 90, 200)(61, 171, 93, 203)(64, 174, 97, 207)(66, 176, 85, 195)(67, 177, 98, 208)(68, 178, 78, 188)(69, 179, 101, 211)(74, 184, 88, 198)(77, 187, 110, 220)(82, 192, 104, 214)(83, 193, 105, 215)(86, 196, 106, 216)(87, 197, 103, 213)(89, 199, 99, 209)(91, 201, 100, 210)(92, 202, 102, 212)(94, 204, 107, 217)(95, 205, 109, 219)(96, 206, 108, 218) L = (1, 113)(2, 115)(3, 118)(4, 111)(5, 122)(6, 112)(7, 125)(8, 120)(9, 128)(10, 114)(11, 131)(12, 124)(13, 134)(14, 116)(15, 138)(16, 117)(17, 141)(18, 144)(19, 119)(20, 147)(21, 150)(22, 121)(23, 153)(24, 156)(25, 123)(26, 159)(27, 161)(28, 140)(29, 163)(30, 126)(31, 167)(32, 127)(33, 154)(34, 146)(35, 165)(36, 129)(37, 174)(38, 130)(39, 176)(40, 152)(41, 178)(42, 132)(43, 169)(44, 133)(45, 142)(46, 158)(47, 180)(48, 135)(49, 187)(50, 136)(51, 190)(52, 137)(53, 193)(54, 139)(55, 196)(56, 197)(57, 155)(58, 172)(59, 143)(60, 201)(61, 145)(62, 205)(63, 202)(64, 175)(65, 148)(66, 200)(67, 149)(68, 210)(69, 151)(70, 212)(71, 213)(72, 185)(73, 215)(74, 157)(75, 218)(76, 216)(77, 188)(78, 160)(79, 179)(80, 192)(81, 203)(82, 162)(83, 195)(84, 214)(85, 164)(86, 204)(87, 207)(88, 166)(89, 168)(90, 209)(91, 206)(92, 170)(93, 181)(94, 171)(95, 211)(96, 173)(97, 208)(98, 198)(99, 177)(100, 189)(101, 199)(102, 217)(103, 220)(104, 182)(105, 219)(106, 183)(107, 184)(108, 194)(109, 186)(110, 191) local type(s) :: { ( 5, 10, 5, 10 ) } Outer automorphisms :: chiral Dual of E12.825 Transitivity :: ET+ VT+ Graph:: simple v = 55 e = 110 f = 33 degree seq :: [ 4^55 ] E12.830 :: Family: { 5* } :: Oriented family(ies): { E3*a } Signature :: (0; {2, 5, 10}) Quotient :: loop Aut^+ = (C11 : C5) : C2 (small group id <110, 1>) Aut = (C11 : C5) : C2 (small group id <110, 1>) |r| :: 1 Presentation :: [ X1^2, X2^5, X2^-1 * X1 * X2 * X1 * X2^-1 * X1 * X2^2 * X1 * X2^-1, X2 * X1 * X2^-1 * X1 * X2^2 * X1 * X2^-2 * X1, X1 * X2^2 * X1 * X2^-1 * X1 * X2 * X1 * X2 * X1 * X2 * X1 * X2 ] Map:: polyhedral non-degenerate R = (1, 111, 2, 112)(3, 113, 7, 117)(4, 114, 9, 119)(5, 115, 11, 121)(6, 116, 13, 123)(8, 118, 17, 127)(10, 120, 20, 130)(12, 122, 23, 133)(14, 124, 26, 136)(15, 125, 27, 137)(16, 126, 29, 139)(18, 128, 33, 143)(19, 129, 35, 145)(21, 131, 39, 149)(22, 132, 41, 151)(24, 134, 45, 155)(25, 135, 47, 157)(28, 138, 53, 163)(30, 140, 55, 165)(31, 141, 56, 166)(32, 142, 58, 168)(34, 144, 46, 156)(36, 146, 62, 172)(37, 147, 49, 159)(38, 148, 64, 174)(40, 150, 68, 178)(42, 152, 69, 179)(43, 153, 70, 180)(44, 154, 71, 181)(48, 158, 75, 185)(50, 160, 77, 187)(51, 161, 79, 189)(52, 162, 65, 175)(54, 164, 84, 194)(57, 167, 87, 197)(59, 169, 89, 199)(60, 170, 91, 201)(61, 171, 93, 203)(63, 173, 92, 202)(66, 176, 85, 195)(67, 177, 78, 188)(72, 182, 97, 207)(73, 183, 80, 190)(74, 184, 83, 193)(76, 186, 103, 213)(81, 191, 101, 211)(82, 192, 100, 210)(86, 196, 99, 209)(88, 198, 98, 208)(90, 200, 102, 212)(94, 204, 105, 215)(95, 205, 104, 214)(96, 206, 106, 216)(107, 217, 108, 218)(109, 219, 110, 220) L = (1, 113)(2, 115)(3, 118)(4, 111)(5, 122)(6, 112)(7, 125)(8, 120)(9, 128)(10, 114)(11, 131)(12, 124)(13, 134)(14, 116)(15, 138)(16, 117)(17, 141)(18, 144)(19, 119)(20, 147)(21, 150)(22, 121)(23, 153)(24, 156)(25, 123)(26, 159)(27, 161)(28, 140)(29, 154)(30, 126)(31, 167)(32, 127)(33, 169)(34, 146)(35, 170)(36, 129)(37, 173)(38, 130)(39, 176)(40, 152)(41, 142)(42, 132)(43, 164)(44, 133)(45, 182)(46, 158)(47, 183)(48, 135)(49, 186)(50, 136)(51, 190)(52, 137)(53, 192)(54, 139)(55, 143)(56, 196)(57, 151)(58, 193)(59, 200)(60, 202)(61, 145)(62, 166)(63, 175)(64, 206)(65, 148)(66, 201)(67, 149)(68, 209)(69, 155)(70, 210)(71, 203)(72, 212)(73, 213)(74, 157)(75, 180)(76, 188)(77, 216)(78, 160)(79, 179)(80, 191)(81, 162)(82, 198)(83, 163)(84, 217)(85, 165)(86, 218)(87, 219)(88, 168)(89, 187)(90, 195)(91, 208)(92, 204)(93, 178)(94, 171)(95, 172)(96, 197)(97, 174)(98, 177)(99, 211)(100, 220)(101, 181)(102, 189)(103, 214)(104, 184)(105, 185)(106, 194)(107, 199)(108, 205)(109, 207)(110, 215) local type(s) :: { ( 5, 10, 5, 10 ) } Outer automorphisms :: chiral Dual of E12.826 Transitivity :: ET+ VT+ Graph:: simple v = 55 e = 110 f = 33 degree seq :: [ 4^55 ] E12.831 :: Family: { 5* } :: Oriented family(ies): { E3*a } Signature :: (0; {2, 5, 10}) Quotient :: loop Aut^+ = (C11 : C5) : C2 (small group id <110, 1>) Aut = (C11 : C5) : C2 (small group id <110, 1>) |r| :: 1 Presentation :: [ (X1^-1 * X2^-1)^2, X1^5, X2 * X1^-1 * X2^-2 * X1 * X2^-1 * X1^-2, X2^2 * X1 * X2^-1 * X1^-1 * X2 * X1^-1 * X2^2, X2 * X1^-2 * X2 * X1^-1 * X2 * X1^-1 * X2^-1 * X1, X2^2 * X1^-2 * X2^-1 * X1 * X2^-3 * X1^-1, (X2^3 * X1^-2)^2, X2^10 ] Map:: R = (1, 111, 2, 112, 6, 116, 13, 123, 4, 114)(3, 113, 9, 119, 22, 132, 28, 138, 11, 121)(5, 115, 14, 124, 33, 143, 19, 129, 7, 117)(8, 118, 20, 130, 46, 156, 39, 149, 16, 126)(10, 120, 24, 134, 55, 165, 60, 170, 26, 136)(12, 122, 29, 139, 65, 175, 70, 180, 31, 141)(15, 125, 36, 146, 48, 158, 73, 183, 34, 144)(17, 127, 40, 150, 80, 190, 62, 172, 32, 142)(18, 128, 42, 152, 85, 195, 89, 199, 44, 154)(21, 131, 49, 159, 82, 192, 57, 167, 47, 157)(23, 133, 53, 163, 35, 145, 74, 184, 51, 161)(25, 135, 56, 166, 75, 185, 84, 194, 58, 168)(27, 137, 61, 171, 100, 210, 92, 202, 63, 173)(30, 140, 45, 155, 71, 181, 98, 208, 68, 178)(37, 147, 77, 187, 102, 212, 107, 217, 76, 186)(38, 148, 69, 179, 106, 216, 108, 218, 78, 188)(41, 151, 83, 193, 104, 214, 87, 197, 81, 191)(43, 153, 86, 196, 90, 200, 59, 169, 88, 198)(50, 160, 72, 182, 67, 177, 105, 215, 91, 201)(52, 162, 93, 203, 103, 213, 66, 176, 64, 174)(54, 164, 95, 205, 79, 189, 97, 207, 94, 204)(96, 206, 109, 219, 110, 220, 101, 211, 99, 209) L = (1, 113)(2, 117)(3, 120)(4, 122)(5, 111)(6, 126)(7, 128)(8, 112)(9, 114)(10, 135)(11, 137)(12, 140)(13, 142)(14, 144)(15, 115)(16, 148)(17, 116)(18, 153)(19, 155)(20, 157)(21, 118)(22, 161)(23, 119)(24, 121)(25, 167)(26, 169)(27, 172)(28, 174)(29, 123)(30, 177)(31, 179)(32, 173)(33, 163)(34, 182)(35, 124)(36, 186)(37, 125)(38, 189)(39, 134)(40, 191)(41, 127)(42, 129)(43, 197)(44, 164)(45, 141)(46, 146)(47, 168)(48, 130)(49, 201)(50, 131)(51, 187)(52, 132)(53, 204)(54, 133)(55, 156)(56, 136)(57, 207)(58, 208)(59, 176)(60, 209)(61, 138)(62, 152)(63, 212)(64, 200)(65, 213)(66, 139)(67, 183)(68, 194)(69, 149)(70, 193)(71, 143)(72, 210)(73, 196)(74, 166)(75, 145)(76, 214)(77, 218)(78, 147)(79, 203)(80, 159)(81, 198)(82, 150)(83, 185)(84, 151)(85, 190)(86, 154)(87, 217)(88, 170)(89, 206)(90, 158)(91, 162)(92, 160)(93, 215)(94, 192)(95, 199)(96, 165)(97, 188)(98, 211)(99, 181)(100, 220)(101, 171)(102, 184)(103, 205)(104, 175)(105, 178)(106, 180)(107, 202)(108, 219)(109, 195)(110, 216) local type(s) :: { ( 2, 10, 2, 10, 2, 10, 2, 10, 2, 10 ) } Outer automorphisms :: chiral Transitivity :: ET+ VT+ Graph:: bipartite v = 22 e = 110 f = 66 degree seq :: [ 10^22 ] E12.832 :: Family: { 5* } :: Oriented family(ies): { E3*a } Signature :: (0; {2, 5, 10}) Quotient :: loop Aut^+ = (C11 : C5) : C2 (small group id <110, 1>) Aut = (C11 : C5) : C2 (small group id <110, 1>) |r| :: 1 Presentation :: [ (X1 * X2)^2, X1^5, X1^-1 * X2^-1 * X1^-1 * X2 * X1 * X2 * X1 * X2^-1, X2 * X1^-1 * X2 * X1^2 * X2^2 * X1^-2, X2^2 * X1^-2 * X2 * X1^-2 * X2^-1 * X1, X1 * X2^-1 * X1^-1 * X2 * X1 * X2^-4, (X2^-1 * X1 * X2^-2 * X1)^2, X2^10 ] Map:: R = (1, 111, 2, 112, 6, 116, 13, 123, 4, 114)(3, 113, 9, 119, 22, 132, 28, 138, 11, 121)(5, 115, 14, 124, 33, 143, 19, 129, 7, 117)(8, 118, 20, 130, 46, 156, 39, 149, 16, 126)(10, 120, 24, 134, 55, 165, 61, 171, 26, 136)(12, 122, 29, 139, 66, 176, 72, 182, 31, 141)(15, 125, 36, 146, 81, 191, 78, 188, 34, 144)(17, 127, 40, 150, 77, 187, 74, 184, 32, 142)(18, 128, 42, 152, 65, 175, 52, 162, 44, 154)(21, 131, 49, 159, 98, 208, 71, 181, 47, 157)(23, 133, 53, 163, 103, 213, 85, 195, 51, 161)(25, 135, 57, 167, 83, 193, 89, 199, 59, 169)(27, 137, 62, 172, 41, 151, 88, 198, 64, 174)(30, 140, 68, 178, 109, 219, 87, 197, 70, 180)(35, 145, 79, 189, 38, 148, 58, 168, 75, 185)(37, 147, 84, 194, 56, 166, 106, 216, 82, 192)(43, 153, 90, 200, 100, 210, 63, 173, 92, 202)(45, 155, 76, 186, 67, 177, 108, 218, 94, 204)(48, 158, 96, 206, 73, 183, 91, 201, 95, 205)(50, 160, 101, 211, 69, 179, 110, 220, 99, 209)(54, 164, 105, 215, 86, 196, 107, 217, 104, 214)(60, 170, 93, 203, 102, 212, 80, 190, 97, 207) L = (1, 113)(2, 117)(3, 120)(4, 122)(5, 111)(6, 126)(7, 128)(8, 112)(9, 114)(10, 135)(11, 137)(12, 140)(13, 142)(14, 144)(15, 115)(16, 148)(17, 116)(18, 153)(19, 155)(20, 157)(21, 118)(22, 161)(23, 119)(24, 121)(25, 168)(26, 170)(27, 173)(28, 175)(29, 123)(30, 179)(31, 181)(32, 183)(33, 185)(34, 187)(35, 124)(36, 192)(37, 125)(38, 196)(39, 195)(40, 172)(41, 127)(42, 129)(43, 201)(44, 203)(45, 164)(46, 205)(47, 182)(48, 130)(49, 209)(50, 131)(51, 156)(52, 132)(53, 214)(54, 133)(55, 194)(56, 134)(57, 136)(58, 149)(59, 208)(60, 197)(61, 176)(62, 138)(63, 177)(64, 217)(65, 211)(66, 186)(67, 139)(68, 141)(69, 152)(70, 207)(71, 199)(72, 165)(73, 166)(74, 188)(75, 169)(76, 143)(77, 219)(78, 160)(79, 212)(80, 145)(81, 167)(82, 218)(83, 146)(84, 213)(85, 147)(86, 178)(87, 150)(88, 193)(89, 151)(90, 154)(91, 184)(92, 174)(93, 171)(94, 216)(95, 202)(96, 190)(97, 158)(98, 200)(99, 163)(100, 159)(101, 191)(102, 162)(103, 220)(104, 198)(105, 204)(106, 206)(107, 189)(108, 210)(109, 215)(110, 180) local type(s) :: { ( 2, 10, 2, 10, 2, 10, 2, 10, 2, 10 ) } Outer automorphisms :: chiral Dual of E12.828 Transitivity :: ET+ VT+ Graph:: bipartite v = 22 e = 110 f = 66 degree seq :: [ 10^22 ] E12.833 :: Family: { 5* } :: Oriented family(ies): { E3*a } Signature :: (0; {2, 5, 10}) Quotient :: loop Aut^+ = (C11 : C5) : C2 (small group id <110, 1>) Aut = (C11 : C5) : C2 (small group id <110, 1>) |r| :: 1 Presentation :: [ X2^2, X1^-1 * X2 * X1^2 * X2 * X1 * X2 * X1^-1 * X2 * X1^-1, (X2 * X1^-1)^5, X1^-1 * X2 * X1 * X2 * X1^-2 * X2 * X1^-3, X1^10, X2 * X1 * X2 * X1^3 * X2 * X1^-3 * X2 * X1^-1 ] Map:: R = (1, 111, 2, 112, 5, 115, 11, 121, 23, 133, 47, 157, 46, 156, 22, 132, 10, 120, 4, 114)(3, 113, 7, 117, 15, 125, 31, 141, 61, 171, 84, 194, 53, 163, 38, 148, 18, 128, 8, 118)(6, 116, 13, 123, 27, 137, 55, 165, 85, 195, 105, 215, 80, 190, 62, 172, 30, 140, 14, 124)(9, 119, 19, 129, 39, 149, 71, 181, 37, 147, 60, 170, 29, 139, 59, 169, 42, 152, 20, 130)(12, 122, 25, 135, 51, 161, 82, 192, 106, 216, 97, 207, 102, 212, 86, 196, 54, 164, 26, 136)(16, 126, 33, 143, 65, 175, 87, 197, 109, 219, 89, 199, 103, 213, 78, 188, 48, 158, 34, 144)(17, 127, 35, 145, 68, 178, 44, 154, 21, 131, 43, 153, 67, 177, 96, 206, 70, 180, 36, 146)(24, 134, 49, 159, 40, 150, 73, 183, 92, 202, 63, 173, 91, 201, 69, 179, 81, 191, 50, 160)(28, 138, 57, 167, 88, 198, 107, 217, 98, 208, 72, 182, 94, 204, 101, 211, 77, 187, 58, 168)(32, 142, 52, 162, 83, 193, 108, 218, 99, 209, 75, 185, 90, 200, 110, 220, 93, 203, 64, 174)(41, 151, 74, 184, 100, 210, 76, 186, 45, 155, 56, 166, 79, 189, 104, 214, 95, 205, 66, 176) L = (1, 113)(2, 116)(3, 111)(4, 119)(5, 122)(6, 112)(7, 126)(8, 127)(9, 114)(10, 131)(11, 134)(12, 115)(13, 138)(14, 139)(15, 142)(16, 117)(17, 118)(18, 147)(19, 150)(20, 151)(21, 120)(22, 155)(23, 158)(24, 121)(25, 162)(26, 163)(27, 166)(28, 123)(29, 124)(30, 171)(31, 173)(32, 125)(33, 176)(34, 177)(35, 179)(36, 167)(37, 128)(38, 182)(39, 168)(40, 129)(41, 130)(42, 180)(43, 161)(44, 185)(45, 132)(46, 174)(47, 187)(48, 133)(49, 189)(50, 190)(51, 153)(52, 135)(53, 136)(54, 195)(55, 197)(56, 137)(57, 146)(58, 149)(59, 199)(60, 193)(61, 140)(62, 200)(63, 141)(64, 156)(65, 204)(66, 143)(67, 144)(68, 205)(69, 145)(70, 152)(71, 207)(72, 148)(73, 209)(74, 196)(75, 154)(76, 208)(77, 157)(78, 212)(79, 159)(80, 160)(81, 216)(82, 217)(83, 170)(84, 214)(85, 164)(86, 184)(87, 165)(88, 220)(89, 169)(90, 172)(91, 211)(92, 213)(93, 219)(94, 175)(95, 178)(96, 215)(97, 181)(98, 186)(99, 183)(100, 218)(101, 201)(102, 188)(103, 202)(104, 194)(105, 206)(106, 191)(107, 192)(108, 210)(109, 203)(110, 198) local type(s) :: { ( 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5 ) } Outer automorphisms :: chiral Transitivity :: ET+ VT+ Graph:: v = 11 e = 110 f = 77 degree seq :: [ 20^11 ] E12.834 :: Family: { 5* } :: Oriented family(ies): { E3*a } Signature :: (0; {2, 5, 10}) Quotient :: loop Aut^+ = (C11 : C5) : C2 (small group id <110, 1>) Aut = (C11 : C5) : C2 (small group id <110, 1>) |r| :: 1 Presentation :: [ X2^2, X2 * X1^-1 * X2 * X1 * X2 * X1^5, (X2 * X1^-1)^5, X1^-1 * X2 * X1 * X2 * X1^-1 * X2 * X1^3 * X2 * X1^-2, X2 * X1^-2 * X2 * X1^3 * X2 * X1 * X2 * X1^-2 ] Map:: R = (1, 111, 2, 112, 5, 115, 11, 121, 23, 133, 47, 157, 46, 156, 22, 132, 10, 120, 4, 114)(3, 113, 7, 117, 15, 125, 31, 141, 63, 173, 40, 150, 74, 184, 38, 148, 18, 128, 8, 118)(6, 116, 13, 123, 27, 137, 55, 165, 34, 144, 16, 126, 33, 143, 62, 172, 30, 140, 14, 124)(9, 119, 19, 129, 39, 149, 75, 185, 102, 212, 80, 190, 92, 202, 78, 188, 42, 152, 20, 130)(12, 122, 25, 135, 51, 161, 87, 197, 58, 168, 28, 138, 57, 167, 93, 203, 54, 164, 26, 136)(17, 127, 35, 145, 69, 179, 96, 206, 56, 166, 95, 205, 107, 217, 105, 215, 70, 180, 36, 146)(21, 131, 43, 153, 79, 189, 103, 213, 73, 183, 101, 211, 61, 171, 100, 210, 81, 191, 44, 154)(24, 134, 49, 159, 84, 194, 76, 186, 90, 200, 52, 162, 89, 199, 68, 178, 86, 196, 50, 160)(29, 139, 59, 169, 98, 208, 64, 174, 88, 198, 110, 220, 104, 214, 77, 187, 99, 209, 60, 170)(32, 142, 65, 175, 85, 195, 109, 219, 97, 207, 67, 177, 41, 151, 48, 158, 83, 193, 66, 176)(37, 147, 71, 181, 91, 201, 53, 163, 45, 155, 82, 192, 94, 204, 108, 218, 106, 216, 72, 182) L = (1, 113)(2, 116)(3, 111)(4, 119)(5, 122)(6, 112)(7, 126)(8, 127)(9, 114)(10, 131)(11, 134)(12, 115)(13, 138)(14, 139)(15, 142)(16, 117)(17, 118)(18, 147)(19, 150)(20, 151)(21, 120)(22, 155)(23, 158)(24, 121)(25, 162)(26, 163)(27, 166)(28, 123)(29, 124)(30, 171)(31, 174)(32, 125)(33, 177)(34, 178)(35, 157)(36, 167)(37, 128)(38, 183)(39, 186)(40, 129)(41, 130)(42, 187)(43, 190)(44, 160)(45, 132)(46, 169)(47, 145)(48, 133)(49, 195)(50, 154)(51, 198)(52, 135)(53, 136)(54, 202)(55, 204)(56, 137)(57, 146)(58, 207)(59, 156)(60, 199)(61, 140)(62, 212)(63, 203)(64, 141)(65, 209)(66, 213)(67, 143)(68, 144)(69, 214)(70, 200)(71, 205)(72, 208)(73, 148)(74, 196)(75, 206)(76, 149)(77, 152)(78, 216)(79, 197)(80, 153)(81, 215)(82, 211)(83, 217)(84, 218)(85, 159)(86, 184)(87, 189)(88, 161)(89, 170)(90, 180)(91, 219)(92, 164)(93, 173)(94, 165)(95, 181)(96, 185)(97, 168)(98, 182)(99, 175)(100, 220)(101, 192)(102, 172)(103, 176)(104, 179)(105, 191)(106, 188)(107, 193)(108, 194)(109, 201)(110, 210) local type(s) :: { ( 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5 ) } Outer automorphisms :: chiral Dual of E12.824 Transitivity :: ET+ VT+ Graph:: v = 11 e = 110 f = 77 degree seq :: [ 20^11 ] E12.835 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 4, 15}) Quotient :: regular 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 :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-2 * T2 * T1^-1)^2, (T1^-1 * T2)^4, T1^15 ] Map:: polytopal non-degenerate R = (1, 2, 5, 11, 23, 41, 61, 80, 96, 79, 60, 40, 22, 10, 4)(3, 7, 15, 31, 51, 71, 89, 104, 98, 81, 65, 43, 24, 18, 8)(6, 13, 27, 21, 39, 59, 78, 95, 110, 97, 84, 63, 42, 30, 14)(9, 19, 37, 57, 76, 93, 108, 100, 82, 62, 46, 26, 12, 25, 20)(16, 33, 53, 36, 45, 67, 86, 99, 112, 115, 107, 91, 72, 55, 34)(17, 35, 50, 64, 85, 102, 111, 116, 105, 90, 73, 52, 32, 48, 28)(29, 49, 68, 83, 101, 113, 118, 109, 94, 77, 58, 38, 47, 66, 44)(54, 75, 92, 106, 117, 120, 119, 114, 103, 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, 97)(82, 99)(84, 102)(85, 103)(91, 106)(93, 107)(95, 105)(96, 108)(98, 111)(100, 113)(101, 114)(104, 115)(109, 117)(110, 118)(112, 119)(116, 120) local type(s) :: { ( 4^15 ) } Outer automorphisms :: reflexible Dual of E12.836 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 8 e = 60 f = 30 degree seq :: [ 15^8 ] E12.836 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 4, 15}) Quotient :: regular 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 :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^4, (T1^-1 * T2 * T1 * T2 * T1^-1)^2, (T1^-1 * T2)^15 ] 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, 81, 76, 82)(74, 83, 75, 84)(77, 85, 80, 86)(78, 87, 79, 88)(89, 97, 92, 98)(90, 99, 91, 100)(93, 101, 96, 102)(94, 103, 95, 104)(105, 113, 108, 114)(106, 115, 107, 116)(109, 117, 112, 118)(110, 119, 111, 120) 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, 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, 120)(114, 117)(115, 118)(116, 119) local type(s) :: { ( 15^4 ) } Outer automorphisms :: reflexible Dual of E12.835 Transitivity :: ET+ VT+ AT+ REG+ Graph:: simple v = 30 e = 60 f = 8 degree seq :: [ 4^30 ] E12.837 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 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 :: [ T1^2, F^2, T2^4, (F * T1)^2, (F * T2)^2, (T2^-1 * T1 * T2^-1 * T1 * T2^-1)^2, (T2 * T1)^15 ] 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, 77, 72, 78)(70, 79, 71, 80)(81, 89, 84, 90)(82, 91, 83, 92)(85, 93, 88, 94)(86, 95, 87, 96)(97, 105, 100, 106)(98, 107, 99, 108)(101, 109, 104, 110)(102, 111, 103, 112)(113, 118, 116, 119)(114, 120, 115, 117)(121, 122)(123, 127)(124, 129)(125, 130)(126, 132)(128, 135)(131, 140)(133, 143)(134, 145)(136, 148)(137, 150)(138, 151)(139, 153)(141, 156)(142, 158)(144, 155)(146, 157)(147, 152)(149, 154)(159, 169)(160, 170)(161, 171)(162, 172)(163, 168)(164, 173)(165, 174)(166, 175)(167, 176)(177, 185)(178, 186)(179, 187)(180, 188)(181, 189)(182, 190)(183, 191)(184, 192)(193, 201)(194, 202)(195, 203)(196, 204)(197, 205)(198, 206)(199, 207)(200, 208)(209, 217)(210, 218)(211, 219)(212, 220)(213, 221)(214, 222)(215, 223)(216, 224)(225, 233)(226, 234)(227, 235)(228, 236)(229, 237)(230, 238)(231, 239)(232, 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) :: { ( 30, 30 ), ( 30^4 ) } Outer automorphisms :: reflexible Dual of E12.841 Transitivity :: ET+ Graph:: simple bipartite v = 90 e = 120 f = 8 degree seq :: [ 2^60, 4^30 ] E12.838 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 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^-1)^2, (F * T2)^2, (F * T1)^2, T1^4, (T2 * T1^-1 * T2)^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, 17, 35, 54, 70, 86, 102, 104, 88, 72, 56, 38, 20, 8)(4, 12, 26, 45, 62, 78, 94, 109, 106, 90, 74, 58, 41, 22, 9)(6, 15, 30, 49, 66, 82, 98, 112, 114, 100, 84, 68, 52, 33, 16)(11, 25, 13, 28, 46, 63, 79, 95, 110, 107, 91, 75, 59, 42, 23)(18, 36, 19, 37, 55, 71, 87, 103, 116, 115, 101, 85, 69, 53, 34)(21, 39, 57, 73, 89, 105, 117, 118, 108, 93, 77, 61, 44, 27, 40)(31, 50, 32, 51, 67, 83, 99, 113, 120, 119, 111, 97, 81, 65, 48)(121, 122, 126, 124)(123, 129, 141, 131)(125, 133, 138, 127)(128, 139, 151, 135)(130, 143, 157, 140)(132, 136, 152, 147)(134, 146, 164, 148)(137, 154, 171, 153)(142, 150, 168, 159)(144, 158, 169, 161)(145, 160, 170, 156)(149, 155, 172, 165)(162, 177, 185, 175)(163, 178, 193, 179)(166, 181, 187, 173)(167, 183, 189, 174)(176, 191, 201, 186)(180, 195, 207, 192)(182, 188, 203, 197)(184, 198, 213, 199)(190, 205, 219, 204)(194, 202, 217, 209)(196, 208, 218, 210)(200, 206, 220, 214)(211, 225, 231, 223)(212, 226, 237, 227)(215, 228, 233, 221)(216, 230, 235, 222)(224, 236, 239, 232)(229, 234, 240, 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) :: { ( 4^4 ), ( 4^15 ) } Outer automorphisms :: reflexible Dual of E12.842 Transitivity :: ET+ Graph:: simple bipartite v = 38 e = 120 f = 60 degree seq :: [ 4^30, 15^8 ] E12.839 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 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 :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-1)^4, (T2 * T1^-3)^2, T1^15 ] 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, 97)(82, 99)(84, 102)(85, 103)(91, 106)(93, 107)(95, 105)(96, 108)(98, 111)(100, 113)(101, 114)(104, 115)(109, 117)(110, 118)(112, 119)(116, 120)(121, 122, 125, 131, 143, 161, 181, 200, 216, 199, 180, 160, 142, 130, 124)(123, 127, 135, 151, 171, 191, 209, 224, 218, 201, 185, 163, 144, 138, 128)(126, 133, 147, 141, 159, 179, 198, 215, 230, 217, 204, 183, 162, 150, 134)(129, 139, 157, 177, 196, 213, 228, 220, 202, 182, 166, 146, 132, 145, 140)(136, 153, 173, 156, 165, 187, 206, 219, 232, 235, 227, 211, 192, 175, 154)(137, 155, 170, 184, 205, 222, 231, 236, 225, 210, 193, 172, 152, 168, 148)(149, 169, 188, 203, 221, 233, 238, 229, 214, 197, 178, 158, 167, 186, 164)(174, 195, 212, 226, 237, 240, 239, 234, 223, 208, 190, 176, 194, 207, 189) 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, 8 ), ( 8^15 ) } Outer automorphisms :: reflexible Dual of E12.840 Transitivity :: ET+ Graph:: simple bipartite v = 68 e = 120 f = 30 degree seq :: [ 2^60, 15^8 ] E12.840 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 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 :: [ T1^2, F^2, T2^4, (F * T1)^2, (F * T2)^2, (T2^-1 * T1 * T2^-1 * T1 * T2^-1)^2, (T2 * T1)^15 ] Map:: R = (1, 121, 3, 123, 8, 128, 4, 124)(2, 122, 5, 125, 11, 131, 6, 126)(7, 127, 13, 133, 24, 144, 14, 134)(9, 129, 16, 136, 29, 149, 17, 137)(10, 130, 18, 138, 32, 152, 19, 139)(12, 132, 21, 141, 37, 157, 22, 142)(15, 135, 26, 146, 43, 163, 27, 147)(20, 140, 34, 154, 48, 168, 35, 155)(23, 143, 39, 159, 30, 150, 40, 160)(25, 145, 41, 161, 28, 148, 42, 162)(31, 151, 44, 164, 38, 158, 45, 165)(33, 153, 46, 166, 36, 156, 47, 167)(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, 118, 238, 116, 236, 119, 239)(114, 234, 120, 240, 115, 235, 117, 237) L = (1, 122)(2, 121)(3, 127)(4, 129)(5, 130)(6, 132)(7, 123)(8, 135)(9, 124)(10, 125)(11, 140)(12, 126)(13, 143)(14, 145)(15, 128)(16, 148)(17, 150)(18, 151)(19, 153)(20, 131)(21, 156)(22, 158)(23, 133)(24, 155)(25, 134)(26, 157)(27, 152)(28, 136)(29, 154)(30, 137)(31, 138)(32, 147)(33, 139)(34, 149)(35, 144)(36, 141)(37, 146)(38, 142)(39, 169)(40, 170)(41, 171)(42, 172)(43, 168)(44, 173)(45, 174)(46, 175)(47, 176)(48, 163)(49, 159)(50, 160)(51, 161)(52, 162)(53, 164)(54, 165)(55, 166)(56, 167)(57, 185)(58, 186)(59, 187)(60, 188)(61, 189)(62, 190)(63, 191)(64, 192)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 225)(114, 226)(115, 227)(116, 228)(117, 229)(118, 230)(119, 231)(120, 232) local type(s) :: { ( 2, 15, 2, 15, 2, 15, 2, 15 ) } Outer automorphisms :: reflexible Dual of E12.839 Transitivity :: ET+ VT+ AT Graph:: v = 30 e = 120 f = 68 degree seq :: [ 8^30 ] E12.841 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 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, (T2^-1 * T1^-1)^2, (F * T2)^2, (F * T1)^2, T1^4, (T2 * T1^-1 * T2)^2, T2^15 ] Map:: R = (1, 121, 3, 123, 10, 130, 24, 144, 43, 163, 60, 180, 76, 196, 92, 212, 96, 216, 80, 200, 64, 184, 47, 167, 29, 149, 14, 134, 5, 125)(2, 122, 7, 127, 17, 137, 35, 155, 54, 174, 70, 190, 86, 206, 102, 222, 104, 224, 88, 208, 72, 192, 56, 176, 38, 158, 20, 140, 8, 128)(4, 124, 12, 132, 26, 146, 45, 165, 62, 182, 78, 198, 94, 214, 109, 229, 106, 226, 90, 210, 74, 194, 58, 178, 41, 161, 22, 142, 9, 129)(6, 126, 15, 135, 30, 150, 49, 169, 66, 186, 82, 202, 98, 218, 112, 232, 114, 234, 100, 220, 84, 204, 68, 188, 52, 172, 33, 153, 16, 136)(11, 131, 25, 145, 13, 133, 28, 148, 46, 166, 63, 183, 79, 199, 95, 215, 110, 230, 107, 227, 91, 211, 75, 195, 59, 179, 42, 162, 23, 143)(18, 138, 36, 156, 19, 139, 37, 157, 55, 175, 71, 191, 87, 207, 103, 223, 116, 236, 115, 235, 101, 221, 85, 205, 69, 189, 53, 173, 34, 154)(21, 141, 39, 159, 57, 177, 73, 193, 89, 209, 105, 225, 117, 237, 118, 238, 108, 228, 93, 213, 77, 197, 61, 181, 44, 164, 27, 147, 40, 160)(31, 151, 50, 170, 32, 152, 51, 171, 67, 187, 83, 203, 99, 219, 113, 233, 120, 240, 119, 239, 111, 231, 97, 217, 81, 201, 65, 185, 48, 168) L = (1, 122)(2, 126)(3, 129)(4, 121)(5, 133)(6, 124)(7, 125)(8, 139)(9, 141)(10, 143)(11, 123)(12, 136)(13, 138)(14, 146)(15, 128)(16, 152)(17, 154)(18, 127)(19, 151)(20, 130)(21, 131)(22, 150)(23, 157)(24, 158)(25, 160)(26, 164)(27, 132)(28, 134)(29, 155)(30, 168)(31, 135)(32, 147)(33, 137)(34, 171)(35, 172)(36, 145)(37, 140)(38, 169)(39, 142)(40, 170)(41, 144)(42, 177)(43, 178)(44, 148)(45, 149)(46, 181)(47, 183)(48, 159)(49, 161)(50, 156)(51, 153)(52, 165)(53, 166)(54, 167)(55, 162)(56, 191)(57, 185)(58, 193)(59, 163)(60, 195)(61, 187)(62, 188)(63, 189)(64, 198)(65, 175)(66, 176)(67, 173)(68, 203)(69, 174)(70, 205)(71, 201)(72, 180)(73, 179)(74, 202)(75, 207)(76, 208)(77, 182)(78, 213)(79, 184)(80, 206)(81, 186)(82, 217)(83, 197)(84, 190)(85, 219)(86, 220)(87, 192)(88, 218)(89, 194)(90, 196)(91, 225)(92, 226)(93, 199)(94, 200)(95, 228)(96, 230)(97, 209)(98, 210)(99, 204)(100, 214)(101, 215)(102, 216)(103, 211)(104, 236)(105, 231)(106, 237)(107, 212)(108, 233)(109, 234)(110, 235)(111, 223)(112, 224)(113, 221)(114, 240)(115, 222)(116, 239)(117, 227)(118, 229)(119, 232)(120, 238) 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 ) } Outer automorphisms :: reflexible Dual of E12.837 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 8 e = 120 f = 90 degree seq :: [ 30^8 ] E12.842 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 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 :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-1)^4, (T2 * T1^-3)^2, T1^15 ] 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, 32, 152)(18, 138, 36, 156)(19, 139, 38, 158)(20, 140, 33, 153)(22, 142, 31, 151)(23, 143, 42, 162)(25, 145, 44, 164)(26, 146, 45, 165)(27, 147, 47, 167)(30, 150, 50, 170)(34, 154, 54, 174)(35, 155, 56, 176)(37, 157, 55, 175)(39, 159, 52, 172)(40, 160, 57, 177)(41, 161, 62, 182)(43, 163, 64, 184)(46, 166, 68, 188)(48, 168, 69, 189)(49, 169, 70, 190)(51, 171, 72, 192)(53, 173, 74, 194)(58, 178, 75, 195)(59, 179, 77, 197)(60, 180, 78, 198)(61, 181, 81, 201)(63, 183, 83, 203)(65, 185, 86, 206)(66, 186, 87, 207)(67, 187, 88, 208)(71, 191, 90, 210)(73, 193, 92, 212)(76, 196, 94, 214)(79, 199, 89, 209)(80, 200, 97, 217)(82, 202, 99, 219)(84, 204, 102, 222)(85, 205, 103, 223)(91, 211, 106, 226)(93, 213, 107, 227)(95, 215, 105, 225)(96, 216, 108, 228)(98, 218, 111, 231)(100, 220, 113, 233)(101, 221, 114, 234)(104, 224, 115, 235)(109, 229, 117, 237)(110, 230, 118, 238)(112, 232, 119, 239)(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, 151)(16, 153)(17, 155)(18, 128)(19, 157)(20, 129)(21, 159)(22, 130)(23, 161)(24, 138)(25, 140)(26, 132)(27, 141)(28, 137)(29, 169)(30, 134)(31, 171)(32, 168)(33, 173)(34, 136)(35, 170)(36, 165)(37, 177)(38, 167)(39, 179)(40, 142)(41, 181)(42, 150)(43, 144)(44, 149)(45, 187)(46, 146)(47, 186)(48, 148)(49, 188)(50, 184)(51, 191)(52, 152)(53, 156)(54, 195)(55, 154)(56, 194)(57, 196)(58, 158)(59, 198)(60, 160)(61, 200)(62, 166)(63, 162)(64, 205)(65, 163)(66, 164)(67, 206)(68, 203)(69, 174)(70, 176)(71, 209)(72, 175)(73, 172)(74, 207)(75, 212)(76, 213)(77, 178)(78, 215)(79, 180)(80, 216)(81, 185)(82, 182)(83, 221)(84, 183)(85, 222)(86, 219)(87, 189)(88, 190)(89, 224)(90, 193)(91, 192)(92, 226)(93, 228)(94, 197)(95, 230)(96, 199)(97, 204)(98, 201)(99, 232)(100, 202)(101, 233)(102, 231)(103, 208)(104, 218)(105, 210)(106, 237)(107, 211)(108, 220)(109, 214)(110, 217)(111, 236)(112, 235)(113, 238)(114, 223)(115, 227)(116, 225)(117, 240)(118, 229)(119, 234)(120, 239) local type(s) :: { ( 4, 15, 4, 15 ) } Outer automorphisms :: reflexible Dual of E12.838 Transitivity :: ET+ VT+ AT Graph:: simple v = 60 e = 120 f = 38 degree seq :: [ 4^60 ] E12.843 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 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 :: [ Y1^2, R^2, Y3^-1 * Y1, Y2^4, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1)^2, (Y3 * Y2^-1)^15 ] Map:: 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, 248, 368, 244, 364)(242, 362, 245, 365, 251, 371, 246, 366)(247, 367, 253, 373, 264, 384, 254, 374)(249, 369, 256, 376, 269, 389, 257, 377)(250, 370, 258, 378, 272, 392, 259, 379)(252, 372, 261, 381, 277, 397, 262, 382)(255, 375, 266, 386, 283, 403, 267, 387)(260, 380, 274, 394, 288, 408, 275, 395)(263, 383, 279, 399, 270, 390, 280, 400)(265, 385, 281, 401, 268, 388, 282, 402)(271, 391, 284, 404, 278, 398, 285, 405)(273, 393, 286, 406, 276, 396, 287, 407)(289, 409, 297, 417, 292, 412, 298, 418)(290, 410, 299, 419, 291, 411, 300, 420)(293, 413, 301, 421, 296, 416, 302, 422)(294, 414, 303, 423, 295, 415, 304, 424)(305, 425, 313, 433, 308, 428, 314, 434)(306, 426, 315, 435, 307, 427, 316, 436)(309, 429, 317, 437, 312, 432, 318, 438)(310, 430, 319, 439, 311, 431, 320, 440)(321, 441, 329, 449, 324, 444, 330, 450)(322, 442, 331, 451, 323, 443, 332, 452)(325, 445, 333, 453, 328, 448, 334, 454)(326, 446, 335, 455, 327, 447, 336, 456)(337, 457, 345, 465, 340, 460, 346, 466)(338, 458, 347, 467, 339, 459, 348, 468)(341, 461, 349, 469, 344, 464, 350, 470)(342, 462, 351, 471, 343, 463, 352, 472)(353, 473, 358, 478, 356, 476, 359, 479)(354, 474, 360, 480, 355, 475, 357, 477) 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, 321)(74, 322)(75, 323)(76, 324)(77, 325)(78, 326)(79, 327)(80, 328)(81, 313)(82, 314)(83, 315)(84, 316)(85, 317)(86, 318)(87, 319)(88, 320)(89, 337)(90, 338)(91, 339)(92, 340)(93, 341)(94, 342)(95, 343)(96, 344)(97, 329)(98, 330)(99, 331)(100, 332)(101, 333)(102, 334)(103, 335)(104, 336)(105, 353)(106, 354)(107, 355)(108, 356)(109, 357)(110, 358)(111, 359)(112, 360)(113, 345)(114, 346)(115, 347)(116, 348)(117, 349)(118, 350)(119, 351)(120, 352)(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, 30, 2, 30 ), ( 2, 30, 2, 30, 2, 30, 2, 30 ) } Outer automorphisms :: reflexible Dual of E12.846 Graph:: bipartite v = 90 e = 240 f = 128 degree seq :: [ 4^60, 8^30 ] E12.844 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 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, Y3 * Y2^-1, (Y3^-1 * Y1^-1)^2, R * Y2 * R * Y3, (R * Y1)^2, (Y2^-1 * Y1^-1)^2, Y1^4, (Y2^-2 * Y1)^2, Y2^15 ] Map:: R = (1, 121, 2, 122, 6, 126, 4, 124)(3, 123, 9, 129, 21, 141, 11, 131)(5, 125, 13, 133, 18, 138, 7, 127)(8, 128, 19, 139, 31, 151, 15, 135)(10, 130, 23, 143, 37, 157, 20, 140)(12, 132, 16, 136, 32, 152, 27, 147)(14, 134, 26, 146, 44, 164, 28, 148)(17, 137, 34, 154, 51, 171, 33, 153)(22, 142, 30, 150, 48, 168, 39, 159)(24, 144, 38, 158, 49, 169, 41, 161)(25, 145, 40, 160, 50, 170, 36, 156)(29, 149, 35, 155, 52, 172, 45, 165)(42, 162, 57, 177, 65, 185, 55, 175)(43, 163, 58, 178, 73, 193, 59, 179)(46, 166, 61, 181, 67, 187, 53, 173)(47, 167, 63, 183, 69, 189, 54, 174)(56, 176, 71, 191, 81, 201, 66, 186)(60, 180, 75, 195, 87, 207, 72, 192)(62, 182, 68, 188, 83, 203, 77, 197)(64, 184, 78, 198, 93, 213, 79, 199)(70, 190, 85, 205, 99, 219, 84, 204)(74, 194, 82, 202, 97, 217, 89, 209)(76, 196, 88, 208, 98, 218, 90, 210)(80, 200, 86, 206, 100, 220, 94, 214)(91, 211, 105, 225, 111, 231, 103, 223)(92, 212, 106, 226, 117, 237, 107, 227)(95, 215, 108, 228, 113, 233, 101, 221)(96, 216, 110, 230, 115, 235, 102, 222)(104, 224, 116, 236, 119, 239, 112, 232)(109, 229, 114, 234, 120, 240, 118, 238)(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, 257, 377, 275, 395, 294, 414, 310, 430, 326, 446, 342, 462, 344, 464, 328, 448, 312, 432, 296, 416, 278, 398, 260, 380, 248, 368)(244, 364, 252, 372, 266, 386, 285, 405, 302, 422, 318, 438, 334, 454, 349, 469, 346, 466, 330, 450, 314, 434, 298, 418, 281, 401, 262, 382, 249, 369)(246, 366, 255, 375, 270, 390, 289, 409, 306, 426, 322, 442, 338, 458, 352, 472, 354, 474, 340, 460, 324, 444, 308, 428, 292, 412, 273, 393, 256, 376)(251, 371, 265, 385, 253, 373, 268, 388, 286, 406, 303, 423, 319, 439, 335, 455, 350, 470, 347, 467, 331, 451, 315, 435, 299, 419, 282, 402, 263, 383)(258, 378, 276, 396, 259, 379, 277, 397, 295, 415, 311, 431, 327, 447, 343, 463, 356, 476, 355, 475, 341, 461, 325, 445, 309, 429, 293, 413, 274, 394)(261, 381, 279, 399, 297, 417, 313, 433, 329, 449, 345, 465, 357, 477, 358, 478, 348, 468, 333, 453, 317, 437, 301, 421, 284, 404, 267, 387, 280, 400)(271, 391, 290, 410, 272, 392, 291, 411, 307, 427, 323, 443, 339, 459, 353, 473, 360, 480, 359, 479, 351, 471, 337, 457, 321, 441, 305, 425, 288, 408) 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) :: { ( 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 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 E12.845 Graph:: bipartite v = 38 e = 240 f = 180 degree seq :: [ 8^30, 30^8 ] E12.845 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 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, 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^-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)(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, 268, 388)(256, 376, 272, 392)(258, 378, 270, 390)(259, 379, 277, 397)(260, 380, 263, 383)(262, 382, 266, 386)(264, 384, 282, 402)(267, 387, 287, 407)(271, 391, 291, 411)(273, 393, 288, 408)(274, 394, 293, 413)(275, 395, 289, 409)(276, 396, 294, 414)(278, 398, 283, 403)(279, 399, 285, 405)(280, 400, 298, 418)(281, 401, 301, 421)(284, 404, 303, 423)(286, 406, 304, 424)(290, 410, 308, 428)(292, 412, 307, 427)(295, 415, 312, 432)(296, 416, 314, 434)(297, 417, 302, 422)(299, 419, 316, 436)(300, 420, 318, 438)(305, 425, 321, 441)(306, 426, 323, 443)(309, 429, 325, 445)(310, 430, 327, 447)(311, 431, 320, 440)(313, 433, 329, 449)(315, 435, 328, 448)(317, 437, 333, 453)(319, 439, 324, 444)(322, 442, 337, 457)(326, 446, 341, 461)(330, 450, 342, 462)(331, 451, 343, 463)(332, 452, 346, 466)(334, 454, 338, 458)(335, 455, 339, 459)(336, 456, 349, 469)(340, 460, 352, 472)(344, 464, 355, 475)(345, 465, 354, 474)(347, 467, 357, 477)(348, 468, 351, 471)(350, 470, 358, 478)(353, 473, 359, 479)(356, 476, 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, 274)(18, 276)(19, 278)(20, 249)(21, 279)(22, 250)(23, 281)(24, 251)(25, 284)(26, 286)(27, 288)(28, 253)(29, 289)(30, 254)(31, 261)(32, 292)(33, 256)(34, 260)(35, 257)(36, 296)(37, 291)(38, 298)(39, 299)(40, 262)(41, 269)(42, 302)(43, 264)(44, 268)(45, 265)(46, 306)(47, 301)(48, 308)(49, 309)(50, 270)(51, 311)(52, 312)(53, 272)(54, 273)(55, 275)(56, 315)(57, 277)(58, 317)(59, 318)(60, 280)(61, 320)(62, 321)(63, 282)(64, 283)(65, 285)(66, 324)(67, 287)(68, 326)(69, 327)(70, 290)(71, 293)(72, 329)(73, 294)(74, 295)(75, 332)(76, 297)(77, 334)(78, 335)(79, 300)(80, 303)(81, 337)(82, 304)(83, 305)(84, 340)(85, 307)(86, 342)(87, 343)(88, 310)(89, 345)(90, 313)(91, 314)(92, 336)(93, 316)(94, 349)(95, 350)(96, 319)(97, 351)(98, 322)(99, 323)(100, 344)(101, 325)(102, 355)(103, 356)(104, 328)(105, 357)(106, 330)(107, 331)(108, 333)(109, 347)(110, 346)(111, 359)(112, 338)(113, 339)(114, 341)(115, 353)(116, 352)(117, 358)(118, 348)(119, 360)(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) :: { ( 8, 30 ), ( 8, 30, 8, 30 ) } Outer automorphisms :: reflexible Dual of E12.844 Graph:: simple bipartite v = 180 e = 240 f = 38 degree seq :: [ 2^120, 4^60 ] E12.846 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 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 :: [ Y2, R^2, (R * Y1)^2, (R * Y3)^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, Y1^15 ] Map:: polytopal R = (1, 121, 2, 122, 5, 125, 11, 131, 23, 143, 41, 161, 61, 181, 80, 200, 96, 216, 79, 199, 60, 180, 40, 160, 22, 142, 10, 130, 4, 124)(3, 123, 7, 127, 15, 135, 31, 151, 51, 171, 71, 191, 89, 209, 104, 224, 98, 218, 81, 201, 65, 185, 43, 163, 24, 144, 18, 138, 8, 128)(6, 126, 13, 133, 27, 147, 21, 141, 39, 159, 59, 179, 78, 198, 95, 215, 110, 230, 97, 217, 84, 204, 63, 183, 42, 162, 30, 150, 14, 134)(9, 129, 19, 139, 37, 157, 57, 177, 76, 196, 93, 213, 108, 228, 100, 220, 82, 202, 62, 182, 46, 166, 26, 146, 12, 132, 25, 145, 20, 140)(16, 136, 33, 153, 53, 173, 36, 156, 45, 165, 67, 187, 86, 206, 99, 219, 112, 232, 115, 235, 107, 227, 91, 211, 72, 192, 55, 175, 34, 154)(17, 137, 35, 155, 50, 170, 64, 184, 85, 205, 102, 222, 111, 231, 116, 236, 105, 225, 90, 210, 73, 193, 52, 172, 32, 152, 48, 168, 28, 148)(29, 149, 49, 169, 68, 188, 83, 203, 101, 221, 113, 233, 118, 238, 109, 229, 94, 214, 77, 197, 58, 178, 38, 158, 47, 167, 66, 186, 44, 164)(54, 174, 75, 195, 92, 212, 106, 226, 117, 237, 120, 240, 119, 239, 114, 234, 103, 223, 88, 208, 70, 190, 56, 176, 74, 194, 87, 207, 69, 189)(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, 272)(16, 247)(17, 248)(18, 276)(19, 278)(20, 273)(21, 250)(22, 271)(23, 282)(24, 251)(25, 284)(26, 285)(27, 287)(28, 253)(29, 254)(30, 290)(31, 262)(32, 255)(33, 260)(34, 294)(35, 296)(36, 258)(37, 295)(38, 259)(39, 292)(40, 297)(41, 302)(42, 263)(43, 304)(44, 265)(45, 266)(46, 308)(47, 267)(48, 309)(49, 310)(50, 270)(51, 312)(52, 279)(53, 314)(54, 274)(55, 277)(56, 275)(57, 280)(58, 315)(59, 317)(60, 318)(61, 321)(62, 281)(63, 323)(64, 283)(65, 326)(66, 327)(67, 328)(68, 286)(69, 288)(70, 289)(71, 330)(72, 291)(73, 332)(74, 293)(75, 298)(76, 334)(77, 299)(78, 300)(79, 329)(80, 337)(81, 301)(82, 339)(83, 303)(84, 342)(85, 343)(86, 305)(87, 306)(88, 307)(89, 319)(90, 311)(91, 346)(92, 313)(93, 347)(94, 316)(95, 345)(96, 348)(97, 320)(98, 351)(99, 322)(100, 353)(101, 354)(102, 324)(103, 325)(104, 355)(105, 335)(106, 331)(107, 333)(108, 336)(109, 357)(110, 358)(111, 338)(112, 359)(113, 340)(114, 341)(115, 344)(116, 360)(117, 349)(118, 350)(119, 352)(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, 8 ), ( 4, 8, 4, 8, 4, 8, 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 E12.843 Graph:: simple bipartite v = 128 e = 240 f = 90 degree seq :: [ 2^120, 30^8 ] E12.847 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 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 :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y2 * Y1)^4, (Y2^-2 * Y1 * Y2^-1)^2, (Y3 * Y2^-1)^4, Y2^15 ] 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, 28, 148)(16, 136, 32, 152)(18, 138, 30, 150)(19, 139, 37, 157)(20, 140, 23, 143)(22, 142, 26, 146)(24, 144, 42, 162)(27, 147, 47, 167)(31, 151, 51, 171)(33, 153, 48, 168)(34, 154, 53, 173)(35, 155, 49, 169)(36, 156, 54, 174)(38, 158, 43, 163)(39, 159, 45, 165)(40, 160, 58, 178)(41, 161, 61, 181)(44, 164, 63, 183)(46, 166, 64, 184)(50, 170, 68, 188)(52, 172, 67, 187)(55, 175, 72, 192)(56, 176, 74, 194)(57, 177, 62, 182)(59, 179, 76, 196)(60, 180, 78, 198)(65, 185, 81, 201)(66, 186, 83, 203)(69, 189, 85, 205)(70, 190, 87, 207)(71, 191, 80, 200)(73, 193, 89, 209)(75, 195, 88, 208)(77, 197, 93, 213)(79, 199, 84, 204)(82, 202, 97, 217)(86, 206, 101, 221)(90, 210, 102, 222)(91, 211, 103, 223)(92, 212, 106, 226)(94, 214, 98, 218)(95, 215, 99, 219)(96, 216, 109, 229)(100, 220, 112, 232)(104, 224, 115, 235)(105, 225, 114, 234)(107, 227, 117, 237)(108, 228, 111, 231)(110, 230, 118, 238)(113, 233, 119, 239)(116, 236, 120, 240)(241, 361, 243, 363, 248, 368, 258, 378, 276, 396, 296, 416, 315, 435, 332, 452, 336, 456, 319, 439, 300, 420, 280, 400, 262, 382, 250, 370, 244, 364)(242, 362, 245, 365, 252, 372, 266, 386, 286, 406, 306, 426, 324, 444, 340, 460, 344, 464, 328, 448, 310, 430, 290, 410, 270, 390, 254, 374, 246, 366)(247, 367, 255, 375, 271, 391, 261, 381, 279, 399, 299, 419, 318, 438, 335, 455, 350, 470, 346, 466, 330, 450, 313, 433, 294, 414, 273, 393, 256, 376)(249, 369, 259, 379, 278, 398, 298, 418, 317, 437, 334, 454, 349, 469, 347, 467, 331, 451, 314, 434, 295, 415, 275, 395, 257, 377, 274, 394, 260, 380)(251, 371, 263, 383, 281, 401, 269, 389, 289, 409, 309, 429, 327, 447, 343, 463, 356, 476, 352, 472, 338, 458, 322, 442, 304, 424, 283, 403, 264, 384)(253, 373, 267, 387, 288, 408, 308, 428, 326, 446, 342, 462, 355, 475, 353, 473, 339, 459, 323, 443, 305, 425, 285, 405, 265, 385, 284, 404, 268, 388)(272, 392, 292, 412, 312, 432, 329, 449, 345, 465, 357, 477, 358, 478, 348, 468, 333, 453, 316, 436, 297, 417, 277, 397, 291, 411, 311, 431, 293, 413)(282, 402, 302, 422, 321, 441, 337, 457, 351, 471, 359, 479, 360, 480, 354, 474, 341, 461, 325, 445, 307, 427, 287, 407, 301, 421, 320, 440, 303, 423) 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, 268)(16, 272)(17, 248)(18, 270)(19, 277)(20, 263)(21, 250)(22, 266)(23, 260)(24, 282)(25, 252)(26, 262)(27, 287)(28, 255)(29, 254)(30, 258)(31, 291)(32, 256)(33, 288)(34, 293)(35, 289)(36, 294)(37, 259)(38, 283)(39, 285)(40, 298)(41, 301)(42, 264)(43, 278)(44, 303)(45, 279)(46, 304)(47, 267)(48, 273)(49, 275)(50, 308)(51, 271)(52, 307)(53, 274)(54, 276)(55, 312)(56, 314)(57, 302)(58, 280)(59, 316)(60, 318)(61, 281)(62, 297)(63, 284)(64, 286)(65, 321)(66, 323)(67, 292)(68, 290)(69, 325)(70, 327)(71, 320)(72, 295)(73, 329)(74, 296)(75, 328)(76, 299)(77, 333)(78, 300)(79, 324)(80, 311)(81, 305)(82, 337)(83, 306)(84, 319)(85, 309)(86, 341)(87, 310)(88, 315)(89, 313)(90, 342)(91, 343)(92, 346)(93, 317)(94, 338)(95, 339)(96, 349)(97, 322)(98, 334)(99, 335)(100, 352)(101, 326)(102, 330)(103, 331)(104, 355)(105, 354)(106, 332)(107, 357)(108, 351)(109, 336)(110, 358)(111, 348)(112, 340)(113, 359)(114, 345)(115, 344)(116, 360)(117, 347)(118, 350)(119, 353)(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) :: { ( 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 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 E12.848 Graph:: bipartite v = 68 e = 240 f = 150 degree seq :: [ 4^60, 30^8 ] E12.848 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 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 :: [ Y2, R^2, (Y3^-1 * Y1^-1)^2, (R * Y3)^2, (R * Y1)^2, Y1^4, (R * Y2 * Y3^-1)^2, (Y3^-2 * Y1)^2, (Y3 * Y2^-1)^15 ] Map:: polytopal R = (1, 121, 2, 122, 6, 126, 4, 124)(3, 123, 9, 129, 21, 141, 11, 131)(5, 125, 13, 133, 18, 138, 7, 127)(8, 128, 19, 139, 31, 151, 15, 135)(10, 130, 23, 143, 37, 157, 20, 140)(12, 132, 16, 136, 32, 152, 27, 147)(14, 134, 26, 146, 44, 164, 28, 148)(17, 137, 34, 154, 51, 171, 33, 153)(22, 142, 30, 150, 48, 168, 39, 159)(24, 144, 38, 158, 49, 169, 41, 161)(25, 145, 40, 160, 50, 170, 36, 156)(29, 149, 35, 155, 52, 172, 45, 165)(42, 162, 57, 177, 65, 185, 55, 175)(43, 163, 58, 178, 73, 193, 59, 179)(46, 166, 61, 181, 67, 187, 53, 173)(47, 167, 63, 183, 69, 189, 54, 174)(56, 176, 71, 191, 81, 201, 66, 186)(60, 180, 75, 195, 87, 207, 72, 192)(62, 182, 68, 188, 83, 203, 77, 197)(64, 184, 78, 198, 93, 213, 79, 199)(70, 190, 85, 205, 99, 219, 84, 204)(74, 194, 82, 202, 97, 217, 89, 209)(76, 196, 88, 208, 98, 218, 90, 210)(80, 200, 86, 206, 100, 220, 94, 214)(91, 211, 105, 225, 111, 231, 103, 223)(92, 212, 106, 226, 117, 237, 107, 227)(95, 215, 108, 228, 113, 233, 101, 221)(96, 216, 110, 230, 115, 235, 102, 222)(104, 224, 116, 236, 119, 239, 112, 232)(109, 229, 114, 234, 120, 240, 118, 238)(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, 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) :: { ( 4, 30 ), ( 4, 30, 4, 30, 4, 30, 4, 30 ) } Outer automorphisms :: reflexible Dual of E12.847 Graph:: simple bipartite v = 150 e = 240 f = 68 degree seq :: [ 2^120, 8^30 ] ## Checksum: 848 records. ## Written on: Wed Oct 16 04:13:40 CEST 2019