## Begin on: Sat Oct 19 15:28:51 CEST 2019 ENUMERATION No. of records: 1216 FAMILY (oriented family) : isomorphism classes 1 [ E1b] : 19 (15 non-degenerate) 2 [ E3b] : 100 (81 non-degenerate) 2* [E3*b] : 100 (81 non-degenerate) 2ex [E3*c] : 0 2*ex [ E3c] : 0 2P [ E2] : 28 (18 non-degenerate) 2Pex [ E1a] : 0 3 [ E5a] : 768 (551 non-degenerate) 4 [ E4] : 82 (54 non-degenerate) 4* [ E4*] : 82 (54 non-degenerate) 4P [ E6] : 37 (16 non-degenerate) 5 [ E3a] : 0 5* [E3*a] : 0 5P [ E5b] : 0 E23.1 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {23, 23}) Quotient :: toric Aut^+ = C23 (small group id <23, 1>) Aut = D46 (small group id <46, 1>) |r| :: 2 Presentation :: [ B, A, B, A, B, A, A, B, A, B, A, B, A, A, B, A, B, A, B, B, A, B, A, B, A, B, B, A, B, A, B, A, A, B, A, B, A, B, A, B, A, B, A, B, B, A, S^2, S^-1 * B * S * A, S^-1 * A * S * B, S^-1 * Z * S * Z, Z^23, (Z^-1 * A * B^-1 * A^-1 * B)^23 ] Map:: R = (1, 25, 48, 71, 2, 27, 50, 73, 4, 29, 52, 75, 6, 31, 54, 77, 8, 33, 56, 79, 10, 35, 58, 81, 12, 37, 60, 83, 14, 39, 62, 85, 16, 41, 64, 87, 18, 43, 66, 89, 20, 45, 68, 91, 22, 46, 69, 92, 23, 44, 67, 90, 21, 42, 65, 88, 19, 40, 63, 86, 17, 38, 61, 84, 15, 36, 59, 82, 13, 34, 57, 80, 11, 32, 55, 78, 9, 30, 53, 76, 7, 28, 51, 74, 5, 26, 49, 72, 3, 24, 47, 70) L = (1, 47)(2, 48)(3, 49)(4, 50)(5, 51)(6, 52)(7, 53)(8, 54)(9, 55)(10, 56)(11, 57)(12, 58)(13, 59)(14, 60)(15, 61)(16, 62)(17, 63)(18, 64)(19, 65)(20, 66)(21, 67)(22, 68)(23, 69)(24, 70)(25, 71)(26, 72)(27, 73)(28, 74)(29, 75)(30, 76)(31, 77)(32, 78)(33, 79)(34, 80)(35, 81)(36, 82)(37, 83)(38, 84)(39, 85)(40, 86)(41, 87)(42, 88)(43, 89)(44, 90)(45, 91)(46, 92) local type(s) :: { ( 92^92 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 1 e = 46 f = 1 degree seq :: [ 92 ] E23.2 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {23, 23}) Quotient :: toric Aut^+ = C23 (small group id <23, 1>) Aut = D46 (small group id <46, 1>) |r| :: 2 Presentation :: [ S^2, B^-1 * A, Z^-1 * A^-1, B^-1 * Z^-1, (S * Z)^2, S * A * S * B, B^23, Z^11 * A^-12, Z^23 ] Map:: R = (1, 25, 48, 71, 2, 27, 50, 73, 4, 29, 52, 75, 6, 31, 54, 77, 8, 33, 56, 79, 10, 35, 58, 81, 12, 37, 60, 83, 14, 39, 62, 85, 16, 41, 64, 87, 18, 43, 66, 89, 20, 45, 68, 91, 22, 46, 69, 92, 23, 44, 67, 90, 21, 42, 65, 88, 19, 40, 63, 86, 17, 38, 61, 84, 15, 36, 59, 82, 13, 34, 57, 80, 11, 32, 55, 78, 9, 30, 53, 76, 7, 28, 51, 74, 5, 26, 49, 72, 3, 24, 47, 70) L = (1, 49)(2, 47)(3, 51)(4, 48)(5, 53)(6, 50)(7, 55)(8, 52)(9, 57)(10, 54)(11, 59)(12, 56)(13, 61)(14, 58)(15, 63)(16, 60)(17, 65)(18, 62)(19, 67)(20, 64)(21, 69)(22, 66)(23, 68)(24, 71)(25, 73)(26, 70)(27, 75)(28, 72)(29, 77)(30, 74)(31, 79)(32, 76)(33, 81)(34, 78)(35, 83)(36, 80)(37, 85)(38, 82)(39, 87)(40, 84)(41, 89)(42, 86)(43, 91)(44, 88)(45, 92)(46, 90) local type(s) :: { ( 92^92 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 1 e = 46 f = 1 degree seq :: [ 92 ] E23.3 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {23, 23}) Quotient :: toric Aut^+ = C23 (small group id <23, 1>) Aut = D46 (small group id <46, 1>) |r| :: 2 Presentation :: [ S^2, B^-1 * A, Z^2 * A, (S * Z)^2, S * A * S * B, A^11 * Z^-1, Z^-1 * B^11 ] Map:: R = (1, 25, 48, 71, 2, 28, 51, 74, 5, 29, 52, 75, 6, 32, 55, 78, 9, 33, 56, 79, 10, 36, 59, 82, 13, 37, 60, 83, 14, 40, 63, 86, 17, 41, 64, 87, 18, 44, 67, 90, 21, 45, 68, 91, 22, 46, 69, 92, 23, 42, 65, 88, 19, 43, 66, 89, 20, 38, 61, 84, 15, 39, 62, 85, 16, 34, 57, 80, 11, 35, 58, 81, 12, 30, 53, 76, 7, 31, 54, 77, 8, 26, 49, 72, 3, 27, 50, 73, 4, 24, 47, 70) L = (1, 49)(2, 50)(3, 53)(4, 54)(5, 47)(6, 48)(7, 57)(8, 58)(9, 51)(10, 52)(11, 61)(12, 62)(13, 55)(14, 56)(15, 65)(16, 66)(17, 59)(18, 60)(19, 68)(20, 69)(21, 63)(22, 64)(23, 67)(24, 74)(25, 75)(26, 70)(27, 71)(28, 78)(29, 79)(30, 72)(31, 73)(32, 82)(33, 83)(34, 76)(35, 77)(36, 86)(37, 87)(38, 80)(39, 81)(40, 90)(41, 91)(42, 84)(43, 85)(44, 92)(45, 88)(46, 89) local type(s) :: { ( 92^92 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 1 e = 46 f = 1 degree seq :: [ 92 ] E23.4 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {23, 23}) Quotient :: toric Aut^+ = C23 (small group id <23, 1>) Aut = D46 (small group id <46, 1>) |r| :: 2 Presentation :: [ S^2, B * A^-1, A^-1 * Z^-3, S * A * S * B, (S * Z)^2, A * Z * A^7, Z^-2 * A^2 * B * A^4, Z * A^-3 * B^-1 * Z * A^-3 ] Map:: R = (1, 25, 48, 71, 2, 29, 52, 75, 6, 28, 51, 74, 5, 31, 54, 77, 8, 35, 58, 81, 12, 34, 57, 80, 11, 37, 60, 83, 14, 41, 64, 87, 18, 40, 63, 86, 17, 43, 66, 89, 20, 44, 67, 90, 21, 46, 69, 92, 23, 45, 68, 91, 22, 38, 61, 84, 15, 42, 65, 88, 19, 39, 62, 85, 16, 32, 55, 78, 9, 36, 59, 82, 13, 33, 56, 79, 10, 26, 49, 72, 3, 30, 53, 76, 7, 27, 50, 73, 4, 24, 47, 70) L = (1, 49)(2, 53)(3, 55)(4, 56)(5, 47)(6, 50)(7, 59)(8, 48)(9, 61)(10, 62)(11, 51)(12, 52)(13, 65)(14, 54)(15, 67)(16, 68)(17, 57)(18, 58)(19, 69)(20, 60)(21, 64)(22, 66)(23, 63)(24, 74)(25, 77)(26, 70)(27, 75)(28, 80)(29, 81)(30, 71)(31, 83)(32, 72)(33, 73)(34, 86)(35, 87)(36, 76)(37, 89)(38, 78)(39, 79)(40, 92)(41, 90)(42, 82)(43, 91)(44, 84)(45, 85)(46, 88) local type(s) :: { ( 92^92 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 1 e = 46 f = 1 degree seq :: [ 92 ] E23.5 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {23, 23}) Quotient :: toric Aut^+ = C23 (small group id <23, 1>) Aut = D46 (small group id <46, 1>) |r| :: 2 Presentation :: [ S^2, B * A^-1, (Z^-1, A), (S * Z)^2, S * A * S * B, (A^-1, Z), Z * A * Z^3, Z^-1 * A^-1 * Z^-1 * A^-1 * Z^-2 * A, A^5 * Z * A ] Map:: R = (1, 25, 48, 71, 2, 29, 52, 75, 6, 35, 58, 81, 12, 28, 51, 74, 5, 31, 54, 77, 8, 37, 60, 83, 14, 43, 66, 89, 20, 36, 59, 82, 13, 39, 62, 85, 16, 45, 68, 91, 22, 40, 63, 86, 17, 44, 67, 90, 21, 46, 69, 92, 23, 41, 64, 87, 18, 32, 55, 78, 9, 38, 61, 84, 15, 42, 65, 88, 19, 33, 56, 79, 10, 26, 49, 72, 3, 30, 53, 76, 7, 34, 57, 80, 11, 27, 50, 73, 4, 24, 47, 70) L = (1, 49)(2, 53)(3, 55)(4, 56)(5, 47)(6, 57)(7, 61)(8, 48)(9, 63)(10, 64)(11, 65)(12, 50)(13, 51)(14, 52)(15, 67)(16, 54)(17, 66)(18, 68)(19, 69)(20, 58)(21, 59)(22, 60)(23, 62)(24, 74)(25, 77)(26, 70)(27, 81)(28, 82)(29, 83)(30, 71)(31, 85)(32, 72)(33, 73)(34, 75)(35, 89)(36, 90)(37, 91)(38, 76)(39, 92)(40, 78)(41, 79)(42, 80)(43, 86)(44, 84)(45, 87)(46, 88) local type(s) :: { ( 92^92 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 1 e = 46 f = 1 degree seq :: [ 92 ] E23.6 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {23, 23}) Quotient :: toric Aut^+ = C23 (small group id <23, 1>) Aut = D46 (small group id <46, 1>) |r| :: 2 Presentation :: [ S^2, A * B^-1, (A, Z^-1), S * A * S * B, A^-1 * Z * B * Z^-1, (S * Z)^2, Z^-1 * B * Z * A^-1, Z * B^-1 * A^-1 * Z^-1 * A^2, Z^-1 * B^-1 * Z^-4, Z^-3 * A^4, B^-2 * Z * B^-1 * Z * B^-1 * Z ] Map:: R = (1, 25, 48, 71, 2, 29, 52, 75, 6, 37, 60, 83, 14, 35, 58, 81, 12, 28, 51, 74, 5, 31, 54, 77, 8, 39, 62, 85, 16, 42, 65, 88, 19, 45, 68, 91, 22, 36, 59, 82, 13, 41, 64, 87, 18, 43, 66, 89, 20, 32, 55, 78, 9, 40, 63, 86, 17, 46, 69, 92, 23, 44, 67, 90, 21, 33, 56, 79, 10, 26, 49, 72, 3, 30, 53, 76, 7, 38, 61, 84, 15, 34, 57, 80, 11, 27, 50, 73, 4, 24, 47, 70) L = (1, 49)(2, 53)(3, 55)(4, 56)(5, 47)(6, 61)(7, 63)(8, 48)(9, 65)(10, 66)(11, 67)(12, 50)(13, 51)(14, 57)(15, 69)(16, 52)(17, 68)(18, 54)(19, 60)(20, 62)(21, 64)(22, 58)(23, 59)(24, 74)(25, 77)(26, 70)(27, 81)(28, 82)(29, 85)(30, 71)(31, 87)(32, 72)(33, 73)(34, 83)(35, 91)(36, 92)(37, 88)(38, 75)(39, 89)(40, 76)(41, 90)(42, 78)(43, 79)(44, 80)(45, 86)(46, 84) local type(s) :: { ( 92^92 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 1 e = 46 f = 1 degree seq :: [ 92 ] E23.7 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {23, 23}) Quotient :: toric Aut^+ = C23 (small group id <23, 1>) Aut = D46 (small group id <46, 1>) |r| :: 2 Presentation :: [ S^2, B * A^-1, (A^-1, Z^-1), (S * Z)^2, S * A * S * B, A^2 * Z * A^2, Z^3 * A * Z^3, A^-1 * Z^2 * A^-1 * Z^2 * A^-1 * Z ] Map:: R = (1, 25, 48, 71, 2, 29, 52, 75, 6, 37, 60, 83, 14, 44, 67, 90, 21, 35, 58, 81, 12, 28, 51, 74, 5, 31, 54, 77, 8, 39, 62, 85, 16, 45, 68, 91, 22, 41, 64, 87, 18, 32, 55, 78, 9, 36, 59, 82, 13, 40, 63, 86, 17, 46, 69, 92, 23, 42, 65, 88, 19, 33, 56, 79, 10, 26, 49, 72, 3, 30, 53, 76, 7, 38, 61, 84, 15, 43, 66, 89, 20, 34, 57, 80, 11, 27, 50, 73, 4, 24, 47, 70) L = (1, 49)(2, 53)(3, 55)(4, 56)(5, 47)(6, 61)(7, 59)(8, 48)(9, 58)(10, 64)(11, 65)(12, 50)(13, 51)(14, 66)(15, 63)(16, 52)(17, 54)(18, 67)(19, 68)(20, 69)(21, 57)(22, 60)(23, 62)(24, 74)(25, 77)(26, 70)(27, 81)(28, 82)(29, 85)(30, 71)(31, 86)(32, 72)(33, 73)(34, 90)(35, 78)(36, 76)(37, 91)(38, 75)(39, 92)(40, 84)(41, 79)(42, 80)(43, 83)(44, 87)(45, 88)(46, 89) local type(s) :: { ( 92^92 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 1 e = 46 f = 1 degree seq :: [ 92 ] E23.8 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {23, 23}) Quotient :: toric Aut^+ = C23 (small group id <23, 1>) Aut = D46 (small group id <46, 1>) |r| :: 2 Presentation :: [ S^2, B^-1 * A, S * B * S * A, (S * Z)^2, (A^-1, Z^-1), A * Z^-1 * A^2 * Z^-1, Z^2 * A * Z^5 ] Map:: R = (1, 25, 48, 71, 2, 29, 52, 75, 6, 37, 60, 83, 14, 43, 66, 89, 20, 41, 64, 87, 18, 35, 58, 81, 12, 28, 51, 74, 5, 31, 54, 77, 8, 32, 55, 78, 9, 39, 62, 85, 16, 45, 68, 91, 22, 46, 69, 92, 23, 42, 65, 88, 19, 36, 59, 82, 13, 33, 56, 79, 10, 26, 49, 72, 3, 30, 53, 76, 7, 38, 61, 84, 15, 44, 67, 90, 21, 40, 63, 86, 17, 34, 57, 80, 11, 27, 50, 73, 4, 24, 47, 70) L = (1, 49)(2, 53)(3, 55)(4, 56)(5, 47)(6, 61)(7, 62)(8, 48)(9, 52)(10, 54)(11, 59)(12, 50)(13, 51)(14, 67)(15, 68)(16, 60)(17, 65)(18, 57)(19, 58)(20, 63)(21, 69)(22, 66)(23, 64)(24, 74)(25, 77)(26, 70)(27, 81)(28, 82)(29, 78)(30, 71)(31, 79)(32, 72)(33, 73)(34, 87)(35, 88)(36, 80)(37, 85)(38, 75)(39, 76)(40, 89)(41, 92)(42, 86)(43, 91)(44, 83)(45, 84)(46, 90) local type(s) :: { ( 92^92 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 1 e = 46 f = 1 degree seq :: [ 92 ] E23.9 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {23, 23}) Quotient :: toric Aut^+ = C23 (small group id <23, 1>) Aut = D46 (small group id <46, 1>) |r| :: 2 Presentation :: [ S^2, A^-1 * B, A * Z * A^2, Z^-1 * A^-1 * Z * B, (S * Z)^2, S * B * S * A, Z^-1 * B * Z * A^-1, Z^6 * B^-2 * Z ] Map:: R = (1, 25, 48, 71, 2, 29, 52, 75, 6, 35, 58, 81, 12, 41, 64, 87, 18, 44, 67, 90, 21, 38, 61, 84, 15, 32, 55, 78, 9, 28, 51, 74, 5, 31, 54, 77, 8, 37, 60, 83, 14, 43, 66, 89, 20, 45, 68, 91, 22, 39, 62, 85, 16, 33, 56, 79, 10, 26, 49, 72, 3, 30, 53, 76, 7, 36, 59, 82, 13, 42, 65, 88, 19, 46, 69, 92, 23, 40, 63, 86, 17, 34, 57, 80, 11, 27, 50, 73, 4, 24, 47, 70) L = (1, 49)(2, 53)(3, 55)(4, 56)(5, 47)(6, 59)(7, 51)(8, 48)(9, 50)(10, 61)(11, 62)(12, 65)(13, 54)(14, 52)(15, 57)(16, 67)(17, 68)(18, 69)(19, 60)(20, 58)(21, 63)(22, 64)(23, 66)(24, 74)(25, 77)(26, 70)(27, 78)(28, 76)(29, 83)(30, 71)(31, 82)(32, 72)(33, 73)(34, 84)(35, 89)(36, 75)(37, 88)(38, 79)(39, 80)(40, 90)(41, 91)(42, 81)(43, 92)(44, 85)(45, 86)(46, 87) local type(s) :: { ( 92^92 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 1 e = 46 f = 1 degree seq :: [ 92 ] E23.10 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {23, 23}) Quotient :: toric Aut^+ = C23 (small group id <23, 1>) Aut = D46 (small group id <46, 1>) |r| :: 2 Presentation :: [ S^2, A * B^-1, (Z, A^-1), Z * B^-1 * Z^-1 * A, (S * Z)^2, S * A * S * B, B * Z^-1 * A^-1 * Z, A^-2 * B^-1 * Z * A^-2, Z^3 * A^2 * Z * B, Z * B * Z * B^-1 * Z * B^-1 * Z * B^-1 * Z ] Map:: R = (1, 25, 48, 71, 2, 29, 52, 75, 6, 37, 60, 83, 14, 42, 65, 88, 19, 32, 55, 78, 9, 40, 63, 86, 17, 45, 68, 91, 22, 35, 58, 81, 12, 28, 51, 74, 5, 31, 54, 77, 8, 39, 62, 85, 16, 43, 66, 89, 20, 33, 56, 79, 10, 26, 49, 72, 3, 30, 53, 76, 7, 38, 61, 84, 15, 46, 69, 92, 23, 36, 59, 82, 13, 41, 64, 87, 18, 44, 67, 90, 21, 34, 57, 80, 11, 27, 50, 73, 4, 24, 47, 70) L = (1, 49)(2, 53)(3, 55)(4, 56)(5, 47)(6, 61)(7, 63)(8, 48)(9, 64)(10, 65)(11, 66)(12, 50)(13, 51)(14, 69)(15, 68)(16, 52)(17, 67)(18, 54)(19, 59)(20, 60)(21, 62)(22, 57)(23, 58)(24, 74)(25, 77)(26, 70)(27, 81)(28, 82)(29, 85)(30, 71)(31, 87)(32, 72)(33, 73)(34, 91)(35, 92)(36, 88)(37, 89)(38, 75)(39, 90)(40, 76)(41, 78)(42, 79)(43, 80)(44, 86)(45, 84)(46, 83) local type(s) :: { ( 92^92 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 1 e = 46 f = 1 degree seq :: [ 92 ] E23.11 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {23, 23}) Quotient :: toric Aut^+ = C23 (small group id <23, 1>) Aut = D46 (small group id <46, 1>) |r| :: 2 Presentation :: [ S^2, A * B^-1, (S * Z)^2, Z * B * Z^-1 * A^-1, S * A * S * B, Z^-1 * B * Z * A^-1, Z^2 * B^-2 * Z, Z * A * B * Z^-1 * B^-1 * A^-1, B * Z * A^6, B * Z^-1 * A * B^2 * Z * B * Z * A^2 ] Map:: R = (1, 25, 48, 71, 2, 29, 52, 75, 6, 32, 55, 78, 9, 38, 61, 84, 15, 43, 66, 89, 20, 45, 68, 91, 22, 42, 65, 88, 19, 40, 63, 86, 17, 35, 58, 81, 12, 28, 51, 74, 5, 31, 54, 77, 8, 33, 56, 79, 10, 26, 49, 72, 3, 30, 53, 76, 7, 37, 60, 83, 14, 39, 62, 85, 16, 44, 67, 90, 21, 46, 69, 92, 23, 41, 64, 87, 18, 36, 59, 82, 13, 34, 57, 80, 11, 27, 50, 73, 4, 24, 47, 70) L = (1, 49)(2, 53)(3, 55)(4, 56)(5, 47)(6, 60)(7, 61)(8, 48)(9, 62)(10, 52)(11, 54)(12, 50)(13, 51)(14, 66)(15, 67)(16, 68)(17, 57)(18, 58)(19, 59)(20, 69)(21, 65)(22, 64)(23, 63)(24, 74)(25, 77)(26, 70)(27, 81)(28, 82)(29, 79)(30, 71)(31, 80)(32, 72)(33, 73)(34, 86)(35, 87)(36, 88)(37, 75)(38, 76)(39, 78)(40, 92)(41, 91)(42, 90)(43, 83)(44, 84)(45, 85)(46, 89) local type(s) :: { ( 92^92 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 1 e = 46 f = 1 degree seq :: [ 92 ] E23.12 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {12, 12}) Quotient :: toric Aut^+ = C3 x D8 (small group id <24, 10>) Aut = (C3 x D8) : C2 (small group id <48, 15>) |r| :: 2 Presentation :: [ B^2, S^2, A^2, S * B * S * A, (S * Z)^2, Z^2 * B * Z * A, Z^3 * A * B, A * Z * B * A * B * Z^-1, (A * Z^-1 * A * Z)^2 ] Map:: non-degenerate R = (1, 26, 50, 74, 2, 30, 54, 78, 6, 37, 61, 85, 13, 43, 67, 91, 19, 47, 71, 95, 23, 48, 72, 96, 24, 45, 69, 93, 21, 46, 70, 94, 22, 34, 58, 82, 10, 41, 65, 89, 17, 29, 53, 77, 5, 25, 49, 73)(3, 33, 57, 81, 9, 40, 64, 88, 16, 44, 68, 92, 20, 32, 56, 80, 8, 39, 63, 87, 15, 42, 66, 90, 18, 31, 55, 79, 7, 38, 62, 86, 14, 28, 52, 76, 4, 36, 60, 84, 12, 35, 59, 83, 11, 27, 51, 75) L = (1, 51)(2, 55)(3, 49)(4, 61)(5, 63)(6, 64)(7, 50)(8, 67)(9, 69)(10, 68)(11, 71)(12, 65)(13, 52)(14, 70)(15, 53)(16, 54)(17, 60)(18, 72)(19, 56)(20, 58)(21, 57)(22, 62)(23, 59)(24, 66)(25, 76)(26, 80)(27, 82)(28, 73)(29, 88)(30, 83)(31, 89)(32, 74)(33, 91)(34, 75)(35, 78)(36, 93)(37, 90)(38, 95)(39, 94)(40, 77)(41, 79)(42, 85)(43, 81)(44, 96)(45, 84)(46, 87)(47, 86)(48, 92) local type(s) :: { ( 48^48 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: bipartite v = 2 e = 48 f = 2 degree seq :: [ 48^2 ] E23.13 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {12, 12}) Quotient :: toric Aut^+ = C3 x D8 (small group id <24, 10>) Aut = (C3 x D8) : C2 (small group id <48, 15>) |r| :: 2 Presentation :: [ B^2, A^2, S^2, S * B * S * A, (S * Z)^2, Z^3 * B * A, Z^2 * A * Z * B, B * A * Z^-1 * B * Z * A, (B * Z * B * Z^-1)^2 ] Map:: non-degenerate R = (1, 26, 50, 74, 2, 30, 54, 78, 6, 34, 58, 82, 10, 42, 66, 90, 18, 46, 70, 94, 22, 48, 72, 96, 24, 45, 69, 93, 21, 47, 71, 95, 23, 37, 61, 85, 13, 41, 65, 89, 17, 29, 53, 77, 5, 25, 49, 73)(3, 33, 57, 81, 9, 38, 62, 86, 14, 28, 52, 76, 4, 36, 60, 84, 12, 39, 63, 87, 15, 43, 67, 91, 19, 31, 55, 79, 7, 40, 64, 88, 16, 44, 68, 92, 20, 32, 56, 80, 8, 35, 59, 83, 11, 27, 51, 75) L = (1, 51)(2, 55)(3, 49)(4, 61)(5, 63)(6, 62)(7, 50)(8, 65)(9, 69)(10, 68)(11, 70)(12, 66)(13, 52)(14, 54)(15, 53)(16, 71)(17, 56)(18, 60)(19, 72)(20, 58)(21, 57)(22, 59)(23, 64)(24, 67)(25, 76)(26, 80)(27, 82)(28, 73)(29, 88)(30, 87)(31, 90)(32, 74)(33, 89)(34, 75)(35, 95)(36, 93)(37, 91)(38, 94)(39, 78)(40, 77)(41, 81)(42, 79)(43, 85)(44, 96)(45, 84)(46, 86)(47, 83)(48, 92) local type(s) :: { ( 48^48 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: bipartite v = 2 e = 48 f = 2 degree seq :: [ 48^2 ] E23.14 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {12, 12}) Quotient :: toric Aut^+ = C3 x Q8 (small group id <24, 11>) Aut = (C3 x Q8) : C2 (small group id <48, 17>) |r| :: 2 Presentation :: [ S^2, A^4, B^-1 * A^2 * B^-1, B^-2 * A^-2, B * Z * B * Z^-1, A * Z^-1 * A * Z, S * B * S * A, (S * Z)^2, A * B * A * B^-1, B^-1 * Z^3 * A^-1, Z * A^-1 * Z^2 * B^-1 ] Map:: non-degenerate R = (1, 26, 50, 74, 2, 32, 56, 80, 8, 40, 64, 88, 16, 46, 70, 94, 22, 47, 71, 95, 23, 37, 61, 85, 13, 45, 69, 93, 21, 48, 72, 96, 24, 38, 62, 86, 14, 44, 68, 92, 20, 29, 53, 77, 5, 25, 49, 73)(3, 35, 59, 83, 11, 41, 65, 89, 17, 28, 52, 76, 4, 36, 60, 84, 12, 42, 66, 90, 18, 30, 54, 78, 6, 33, 57, 81, 9, 43, 67, 91, 19, 31, 55, 79, 7, 34, 58, 82, 10, 39, 63, 87, 15, 27, 51, 75) L = (1, 51)(2, 57)(3, 61)(4, 64)(5, 66)(6, 49)(7, 62)(8, 65)(9, 69)(10, 70)(11, 50)(12, 68)(13, 54)(14, 52)(15, 53)(16, 55)(17, 72)(18, 71)(19, 56)(20, 58)(21, 59)(22, 60)(23, 63)(24, 67)(25, 79)(26, 84)(27, 88)(28, 73)(29, 89)(30, 86)(31, 85)(32, 87)(33, 94)(34, 74)(35, 92)(36, 93)(37, 76)(38, 75)(39, 96)(40, 78)(41, 95)(42, 80)(43, 77)(44, 81)(45, 82)(46, 83)(47, 91)(48, 90) local type(s) :: { ( 48^48 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: bipartite v = 2 e = 48 f = 2 degree seq :: [ 48^2 ] E23.15 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {12, 12}) Quotient :: toric Aut^+ = C3 x Q8 (small group id <24, 11>) Aut = (C3 x Q8) : C2 (small group id <48, 17>) |r| :: 2 Presentation :: [ S^2, A^4, A^-1 * B^-1 * A^-1 * B, B * A * B * A^-1, B^2 * A^-2, B * A^2 * B, S * A * S * B, (S * Z)^2, Z * B * Z^-1 * B, A * Z^-1 * A * Z, Z * B * Z * A^-1 * Z, Z * A * Z^2 * B^-1 ] Map:: non-degenerate R = (1, 26, 50, 74, 2, 32, 56, 80, 8, 38, 62, 86, 14, 46, 70, 94, 22, 47, 71, 95, 23, 37, 61, 85, 13, 45, 69, 93, 21, 48, 72, 96, 24, 40, 64, 88, 16, 44, 68, 92, 20, 29, 53, 77, 5, 25, 49, 73)(3, 35, 59, 83, 11, 43, 67, 91, 19, 31, 55, 79, 7, 34, 58, 82, 10, 42, 66, 90, 18, 30, 54, 78, 6, 33, 57, 81, 9, 41, 65, 89, 17, 28, 52, 76, 4, 36, 60, 84, 12, 39, 63, 87, 15, 27, 51, 75) L = (1, 51)(2, 57)(3, 61)(4, 64)(5, 66)(6, 49)(7, 62)(8, 67)(9, 69)(10, 68)(11, 50)(12, 70)(13, 54)(14, 52)(15, 53)(16, 55)(17, 56)(18, 71)(19, 72)(20, 60)(21, 59)(22, 58)(23, 63)(24, 65)(25, 79)(26, 84)(27, 88)(28, 73)(29, 89)(30, 86)(31, 85)(32, 90)(33, 92)(34, 74)(35, 94)(36, 93)(37, 76)(38, 75)(39, 80)(40, 78)(41, 95)(42, 96)(43, 77)(44, 83)(45, 82)(46, 81)(47, 91)(48, 87) local type(s) :: { ( 48^48 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: bipartite v = 2 e = 48 f = 2 degree seq :: [ 48^2 ] E23.16 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {12, 12}) Quotient :: toric Aut^+ = C24 (small group id <24, 2>) Aut = C24 : C2 (small group id <48, 6>) |r| :: 2 Presentation :: [ S^2, A^-2 * B^-1 * A^-1, B^3 * A, (S * Z)^2, (Z^-1, A^-1), S * B * S * A, (Z^-1, B^-1), (B * A^-1)^2, A * Z * A * Z^2, Z * B^2 * Z^2, Z * A^-1 * Z^2 * B^-1 ] Map:: non-degenerate R = (1, 26, 50, 74, 2, 32, 56, 80, 8, 38, 62, 86, 14, 45, 69, 93, 21, 48, 72, 96, 24, 40, 64, 88, 16, 46, 70, 94, 22, 47, 71, 95, 23, 37, 61, 85, 13, 42, 66, 90, 18, 29, 53, 77, 5, 25, 49, 73)(3, 33, 57, 81, 9, 43, 67, 91, 19, 30, 54, 78, 6, 35, 59, 83, 11, 41, 65, 89, 17, 28, 52, 76, 4, 34, 58, 82, 10, 44, 68, 92, 20, 31, 55, 79, 7, 36, 60, 84, 12, 39, 63, 87, 15, 27, 51, 75) L = (1, 51)(2, 57)(3, 61)(4, 62)(5, 63)(6, 49)(7, 64)(8, 67)(9, 66)(10, 69)(11, 50)(12, 70)(13, 55)(14, 54)(15, 71)(16, 52)(17, 56)(18, 60)(19, 53)(20, 72)(21, 59)(22, 58)(23, 68)(24, 65)(25, 79)(26, 84)(27, 88)(28, 73)(29, 92)(30, 85)(31, 86)(32, 87)(33, 94)(34, 74)(35, 90)(36, 93)(37, 76)(38, 75)(39, 96)(40, 78)(41, 77)(42, 82)(43, 95)(44, 80)(45, 81)(46, 83)(47, 89)(48, 91) local type(s) :: { ( 48^48 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: bipartite v = 2 e = 48 f = 2 degree seq :: [ 48^2 ] E23.17 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {12, 12}) Quotient :: toric Aut^+ = C24 (small group id <24, 2>) Aut = C24 : C2 (small group id <48, 6>) |r| :: 2 Presentation :: [ S^2, (B * A^-1)^2, A^-2 * B^-1 * A^-1, B^-2 * A^2, (B, A^-1), S * A * S * B, (B^-1, Z^-1), (A^-1, Z), (S * Z)^2, Z^2 * A^-1 * Z * A^-1, Z * A * B * Z^2, B^-1 * Z^2 * B^-1 * Z ] Map:: non-degenerate R = (1, 26, 50, 74, 2, 32, 56, 80, 8, 37, 61, 85, 13, 45, 69, 93, 21, 48, 72, 96, 24, 40, 64, 88, 16, 46, 70, 94, 22, 47, 71, 95, 23, 38, 62, 86, 14, 42, 66, 90, 18, 29, 53, 77, 5, 25, 49, 73)(3, 33, 57, 81, 9, 44, 68, 92, 20, 31, 55, 79, 7, 36, 60, 84, 12, 41, 65, 89, 17, 28, 52, 76, 4, 34, 58, 82, 10, 43, 67, 91, 19, 30, 54, 78, 6, 35, 59, 83, 11, 39, 63, 87, 15, 27, 51, 75) L = (1, 51)(2, 57)(3, 61)(4, 62)(5, 63)(6, 49)(7, 64)(8, 68)(9, 69)(10, 66)(11, 50)(12, 70)(13, 55)(14, 54)(15, 56)(16, 52)(17, 71)(18, 59)(19, 53)(20, 72)(21, 60)(22, 58)(23, 67)(24, 65)(25, 79)(26, 84)(27, 88)(28, 73)(29, 92)(30, 85)(31, 86)(32, 89)(33, 94)(34, 74)(35, 93)(36, 90)(37, 76)(38, 75)(39, 96)(40, 78)(41, 77)(42, 81)(43, 80)(44, 95)(45, 82)(46, 83)(47, 87)(48, 91) local type(s) :: { ( 48^48 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: bipartite v = 2 e = 48 f = 2 degree seq :: [ 48^2 ] E23.18 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {12, 12}) Quotient :: toric Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ S^2, A * B^-1, Z * B^-1 * Z^-1 * A, B^-1 * Z * A * Z^-1, (S * Z)^2, S * B * S * A, Z * B^2 * Z^2, Z * A^-1 * Z * A^3 * Z, A^8 ] Map:: R = (1, 26, 50, 74, 2, 30, 54, 78, 6, 37, 61, 85, 13, 39, 63, 87, 15, 44, 68, 92, 20, 46, 70, 94, 22, 48, 72, 96, 24, 41, 65, 89, 17, 33, 57, 81, 9, 35, 59, 83, 11, 28, 52, 76, 4, 25, 49, 73)(3, 31, 55, 79, 7, 36, 60, 84, 12, 29, 53, 77, 5, 32, 56, 80, 8, 38, 62, 86, 14, 43, 67, 91, 19, 45, 69, 93, 21, 47, 71, 95, 23, 40, 64, 88, 16, 42, 66, 90, 18, 34, 58, 82, 10, 27, 51, 75) L = (1, 51)(2, 55)(3, 57)(4, 58)(5, 49)(6, 60)(7, 59)(8, 50)(9, 64)(10, 65)(11, 66)(12, 52)(13, 53)(14, 54)(15, 56)(16, 70)(17, 71)(18, 72)(19, 61)(20, 62)(21, 63)(22, 67)(23, 68)(24, 69)(25, 77)(26, 80)(27, 73)(28, 84)(29, 85)(30, 86)(31, 74)(32, 87)(33, 75)(34, 76)(35, 79)(36, 78)(37, 91)(38, 92)(39, 93)(40, 81)(41, 82)(42, 83)(43, 94)(44, 95)(45, 96)(46, 88)(47, 89)(48, 90) local type(s) :: { ( 48^48 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: bipartite v = 2 e = 48 f = 2 degree seq :: [ 48^2 ] E23.19 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {12, 12}) Quotient :: toric Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ S^2, B * A^-1, (A, Z), (S * Z)^2, S * A * S * B, Z^2 * B^-1 * A^-1 * Z, A^-1 * Z * B^-1 * Z^2, (A^-1 * B^-1)^4, A^6 * B * A ] Map:: R = (1, 26, 50, 74, 2, 30, 54, 78, 6, 33, 57, 81, 9, 39, 63, 87, 15, 44, 68, 92, 20, 46, 70, 94, 22, 47, 71, 95, 23, 42, 66, 90, 18, 37, 61, 85, 13, 35, 59, 83, 11, 28, 52, 76, 4, 25, 49, 73)(3, 31, 55, 79, 7, 38, 62, 86, 14, 40, 64, 88, 16, 45, 69, 93, 21, 48, 72, 96, 24, 43, 67, 91, 19, 41, 65, 89, 17, 36, 60, 84, 12, 29, 53, 77, 5, 32, 56, 80, 8, 34, 58, 82, 10, 27, 51, 75) L = (1, 51)(2, 55)(3, 57)(4, 58)(5, 49)(6, 62)(7, 63)(8, 50)(9, 64)(10, 54)(11, 56)(12, 52)(13, 53)(14, 68)(15, 69)(16, 70)(17, 59)(18, 60)(19, 61)(20, 72)(21, 71)(22, 67)(23, 65)(24, 66)(25, 77)(26, 80)(27, 73)(28, 84)(29, 85)(30, 82)(31, 74)(32, 83)(33, 75)(34, 76)(35, 89)(36, 90)(37, 91)(38, 78)(39, 79)(40, 81)(41, 95)(42, 96)(43, 94)(44, 86)(45, 87)(46, 88)(47, 93)(48, 92) local type(s) :: { ( 48^48 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: bipartite v = 2 e = 48 f = 2 degree seq :: [ 48^2 ] E23.20 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {12, 12}) Quotient :: toric Aut^+ = C12 x C2 (small group id <24, 9>) Aut = (C12 x C2) : C2 (small group id <48, 37>) |r| :: 2 Presentation :: [ A^2, B^2, S^2, (B * A)^2, S * A * S * B, (S * Z)^2, Z^-1 * A * Z * A, B * Z * B * Z^-1, B * A * Z^-6 ] Map:: non-degenerate R = (1, 26, 50, 74, 2, 30, 54, 78, 6, 37, 61, 85, 13, 45, 69, 93, 21, 41, 65, 89, 17, 33, 57, 81, 9, 40, 64, 88, 16, 48, 72, 96, 24, 44, 68, 92, 20, 36, 60, 84, 12, 29, 53, 77, 5, 25, 49, 73)(3, 31, 55, 79, 7, 38, 62, 86, 14, 46, 70, 94, 22, 43, 67, 91, 19, 35, 59, 83, 11, 28, 52, 76, 4, 32, 56, 80, 8, 39, 63, 87, 15, 47, 71, 95, 23, 42, 66, 90, 18, 34, 58, 82, 10, 27, 51, 75) L = (1, 51)(2, 55)(3, 49)(4, 57)(5, 58)(6, 62)(7, 50)(8, 64)(9, 52)(10, 53)(11, 65)(12, 66)(13, 70)(14, 54)(15, 72)(16, 56)(17, 59)(18, 60)(19, 69)(20, 71)(21, 67)(22, 61)(23, 68)(24, 63)(25, 76)(26, 80)(27, 81)(28, 73)(29, 83)(30, 87)(31, 88)(32, 74)(33, 75)(34, 89)(35, 77)(36, 91)(37, 95)(38, 96)(39, 78)(40, 79)(41, 82)(42, 93)(43, 84)(44, 94)(45, 90)(46, 92)(47, 85)(48, 86) local type(s) :: { ( 48^48 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: bipartite v = 2 e = 48 f = 2 degree seq :: [ 48^2 ] E23.21 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {12, 12}) Quotient :: toric Aut^+ = C12 x C2 (small group id <24, 9>) Aut = (C12 x C2) : C2 (small group id <48, 37>) |r| :: 2 Presentation :: [ S^2, B^-1 * A^-1, B * A, B * Z^-1 * A * Z, A^4, S * A * S * B, (A^-1, Z^-1), (B^-1, Z^-1), (S * Z)^2, A^-2 * Z^-6 ] Map:: non-degenerate R = (1, 26, 50, 74, 2, 30, 54, 78, 6, 37, 61, 85, 13, 45, 69, 93, 21, 41, 65, 89, 17, 33, 57, 81, 9, 40, 64, 88, 16, 48, 72, 96, 24, 44, 68, 92, 20, 36, 60, 84, 12, 29, 53, 77, 5, 25, 49, 73)(3, 31, 55, 79, 7, 38, 62, 86, 14, 46, 70, 94, 22, 43, 67, 91, 19, 35, 59, 83, 11, 28, 52, 76, 4, 32, 56, 80, 8, 39, 63, 87, 15, 47, 71, 95, 23, 42, 66, 90, 18, 34, 58, 82, 10, 27, 51, 75) L = (1, 51)(2, 55)(3, 57)(4, 49)(5, 58)(6, 62)(7, 64)(8, 50)(9, 52)(10, 65)(11, 53)(12, 66)(13, 70)(14, 72)(15, 54)(16, 56)(17, 59)(18, 69)(19, 60)(20, 71)(21, 67)(22, 68)(23, 61)(24, 63)(25, 75)(26, 79)(27, 81)(28, 73)(29, 82)(30, 86)(31, 88)(32, 74)(33, 76)(34, 89)(35, 77)(36, 90)(37, 94)(38, 96)(39, 78)(40, 80)(41, 83)(42, 93)(43, 84)(44, 95)(45, 91)(46, 92)(47, 85)(48, 87) local type(s) :: { ( 48^48 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: bipartite v = 2 e = 48 f = 2 degree seq :: [ 48^2 ] E23.22 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {12, 12}) Quotient :: toric Aut^+ = C12 x C2 (small group id <24, 9>) Aut = (C12 x C2) : C2 (small group id <48, 37>) |r| :: 2 Presentation :: [ S^2, (A^-1, Z^-1), (A^-1, B^-1), B * A * Z^2, A * B * Z^2, (B^-1, Z^-1), S * B * S * A, Z^-1 * A^-1 * Z^-1 * B^-1, A^2 * B^-2, (S * Z)^2, Z^-2 * B^2 * Z^-2, B^-2 * Z * A^2 * Z^-1, Z * B^-1 * A^-3 * Z, (A * B)^6 ] Map:: non-degenerate R = (1, 26, 50, 74, 2, 32, 56, 80, 8, 43, 67, 91, 19, 37, 61, 85, 13, 46, 70, 94, 22, 40, 64, 88, 16, 47, 71, 95, 23, 42, 66, 90, 18, 48, 72, 96, 24, 38, 62, 86, 14, 29, 53, 77, 5, 25, 49, 73)(3, 33, 57, 81, 9, 31, 55, 79, 7, 36, 60, 84, 12, 45, 69, 93, 21, 41, 65, 89, 17, 28, 52, 76, 4, 34, 58, 82, 10, 30, 54, 78, 6, 35, 59, 83, 11, 44, 68, 92, 20, 39, 63, 87, 15, 27, 51, 75) L = (1, 51)(2, 57)(3, 61)(4, 62)(5, 63)(6, 49)(7, 64)(8, 55)(9, 70)(10, 53)(11, 50)(12, 71)(13, 69)(14, 68)(15, 67)(16, 52)(17, 72)(18, 54)(19, 60)(20, 56)(21, 66)(22, 65)(23, 58)(24, 59)(25, 79)(26, 84)(27, 88)(28, 73)(29, 81)(30, 80)(31, 90)(32, 93)(33, 95)(34, 74)(35, 91)(36, 96)(37, 76)(38, 75)(39, 94)(40, 78)(41, 77)(42, 92)(43, 89)(44, 85)(45, 86)(46, 82)(47, 83)(48, 87) local type(s) :: { ( 48^48 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: bipartite v = 2 e = 48 f = 2 degree seq :: [ 48^2 ] E23.23 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {12, 12}) Quotient :: toric Aut^+ = C3 x D8 (small group id <24, 10>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ A^2, S^2, B * A, (S * Z)^2, S * A * S * B, Z^-2 * A * Z^2 * A, (A * Z^-1 * A * Z)^2, (Z^-2 * A * Z^-1)^2 ] Map:: R = (1, 26, 50, 74, 2, 29, 53, 77, 5, 35, 59, 83, 11, 44, 68, 92, 20, 40, 64, 88, 16, 48, 72, 96, 24, 39, 63, 87, 15, 47, 71, 95, 23, 43, 67, 91, 19, 34, 58, 82, 10, 28, 52, 76, 4, 25, 49, 73)(3, 31, 55, 79, 7, 36, 60, 84, 12, 46, 70, 94, 22, 42, 66, 90, 18, 33, 57, 81, 9, 38, 62, 86, 14, 30, 54, 78, 6, 37, 61, 85, 13, 45, 69, 93, 21, 41, 65, 89, 17, 32, 56, 80, 8, 27, 51, 75) L = (1, 51)(2, 54)(3, 49)(4, 57)(5, 60)(6, 50)(7, 63)(8, 64)(9, 52)(10, 65)(11, 69)(12, 53)(13, 71)(14, 72)(15, 55)(16, 56)(17, 58)(18, 68)(19, 70)(20, 66)(21, 59)(22, 67)(23, 61)(24, 62)(25, 75)(26, 78)(27, 73)(28, 81)(29, 84)(30, 74)(31, 87)(32, 88)(33, 76)(34, 89)(35, 93)(36, 77)(37, 95)(38, 96)(39, 79)(40, 80)(41, 82)(42, 92)(43, 94)(44, 90)(45, 83)(46, 91)(47, 85)(48, 86) local type(s) :: { ( 48^48 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: bipartite v = 2 e = 48 f = 2 degree seq :: [ 48^2 ] E23.24 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {12, 12}) Quotient :: toric Aut^+ = C3 x D8 (small group id <24, 10>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ A^2, B^2, S^2, (B * A)^2, S * A * S * B, Z^-1 * A * Z * B, (S * Z)^2, B * Z * A * Z^-1, Z^-1 * A * B * Z^-5 ] Map:: non-degenerate R = (1, 26, 50, 74, 2, 30, 54, 78, 6, 37, 61, 85, 13, 45, 69, 93, 21, 41, 65, 89, 17, 33, 57, 81, 9, 40, 64, 88, 16, 48, 72, 96, 24, 44, 68, 92, 20, 36, 60, 84, 12, 29, 53, 77, 5, 25, 49, 73)(3, 32, 56, 80, 8, 38, 62, 86, 14, 47, 71, 95, 23, 43, 67, 91, 19, 35, 59, 83, 11, 28, 52, 76, 4, 31, 55, 79, 7, 39, 63, 87, 15, 46, 70, 94, 22, 42, 66, 90, 18, 34, 58, 82, 10, 27, 51, 75) L = (1, 51)(2, 55)(3, 49)(4, 57)(5, 59)(6, 62)(7, 50)(8, 64)(9, 52)(10, 65)(11, 53)(12, 66)(13, 70)(14, 54)(15, 72)(16, 56)(17, 58)(18, 60)(19, 69)(20, 71)(21, 67)(22, 61)(23, 68)(24, 63)(25, 76)(26, 80)(27, 81)(28, 73)(29, 82)(30, 87)(31, 88)(32, 74)(33, 75)(34, 77)(35, 89)(36, 91)(37, 95)(38, 96)(39, 78)(40, 79)(41, 83)(42, 93)(43, 84)(44, 94)(45, 90)(46, 92)(47, 85)(48, 86) local type(s) :: { ( 48^48 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: bipartite v = 2 e = 48 f = 2 degree seq :: [ 48^2 ] E23.25 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {12, 12}) Quotient :: toric Aut^+ = C4 x S3 (small group id <24, 5>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ A^2, S^2, B^2, B * A, S * B * S * A, (S * Z)^2, (Z^-2 * A)^2, (A * Z^-1)^4, Z^-2 * A * Z * A * Z^-3 ] Map:: R = (1, 26, 50, 74, 2, 29, 53, 77, 5, 35, 59, 83, 11, 44, 68, 92, 20, 40, 64, 88, 16, 47, 71, 95, 23, 41, 65, 89, 17, 48, 72, 96, 24, 43, 67, 91, 19, 34, 58, 82, 10, 28, 52, 76, 4, 25, 49, 73)(3, 31, 55, 79, 7, 39, 63, 87, 15, 45, 69, 93, 21, 38, 62, 86, 14, 30, 54, 78, 6, 37, 61, 85, 13, 33, 57, 81, 9, 42, 66, 90, 18, 46, 70, 94, 22, 36, 60, 84, 12, 32, 56, 80, 8, 27, 51, 75) L = (1, 51)(2, 54)(3, 49)(4, 57)(5, 60)(6, 50)(7, 64)(8, 65)(9, 52)(10, 63)(11, 69)(12, 53)(13, 71)(14, 72)(15, 58)(16, 55)(17, 56)(18, 68)(19, 70)(20, 66)(21, 59)(22, 67)(23, 61)(24, 62)(25, 75)(26, 78)(27, 73)(28, 81)(29, 84)(30, 74)(31, 88)(32, 89)(33, 76)(34, 87)(35, 93)(36, 77)(37, 95)(38, 96)(39, 82)(40, 79)(41, 80)(42, 92)(43, 94)(44, 90)(45, 83)(46, 91)(47, 85)(48, 86) local type(s) :: { ( 48^48 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: bipartite v = 2 e = 48 f = 2 degree seq :: [ 48^2 ] E23.26 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {12, 12}) Quotient :: toric Aut^+ = C4 x S3 (small group id <24, 5>) Aut = D8 x S3 (small group id <48, 38>) |r| :: 2 Presentation :: [ B^2, A^2, S^2, B * Z * A * Z^-1, S * B * S * A, A * Z^-1 * B * Z, (S * Z)^2, (B * A)^3, A * Z * A * B * A * Z^-1, Z * B * Z^-1 * B * A * B, (B * Z^-2)^2, Z^-4 * A * B, A * B * A * Z * B * Z^-1 ] Map:: non-degenerate R = (1, 26, 50, 74, 2, 30, 54, 78, 6, 40, 64, 88, 16, 34, 58, 82, 10, 44, 68, 92, 20, 48, 72, 96, 24, 47, 71, 95, 23, 36, 60, 84, 12, 45, 69, 93, 21, 39, 63, 87, 15, 29, 53, 77, 5, 25, 49, 73)(3, 33, 57, 81, 9, 42, 66, 90, 18, 37, 61, 85, 13, 28, 52, 76, 4, 31, 55, 79, 7, 43, 67, 91, 19, 38, 62, 86, 14, 46, 70, 94, 22, 32, 56, 80, 8, 41, 65, 89, 17, 35, 59, 83, 11, 27, 51, 75) L = (1, 51)(2, 55)(3, 49)(4, 60)(5, 62)(6, 65)(7, 50)(8, 69)(9, 68)(10, 70)(11, 71)(12, 52)(13, 64)(14, 53)(15, 66)(16, 61)(17, 54)(18, 63)(19, 72)(20, 57)(21, 56)(22, 58)(23, 59)(24, 67)(25, 76)(26, 80)(27, 82)(28, 73)(29, 83)(30, 90)(31, 92)(32, 74)(33, 93)(34, 75)(35, 77)(36, 94)(37, 95)(38, 88)(39, 91)(40, 86)(41, 96)(42, 78)(43, 87)(44, 79)(45, 81)(46, 84)(47, 85)(48, 89) local type(s) :: { ( 48^48 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: bipartite v = 2 e = 48 f = 2 degree seq :: [ 48^2 ] E23.27 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {12, 12}) Quotient :: toric Aut^+ = C4 x S3 (small group id <24, 5>) Aut = (C4 x S3) : C2 (small group id <48, 41>) |r| :: 2 Presentation :: [ A^2, B^2, S^2, (B * A)^2, S * A * S * B, (S * Z)^2, B * Z^-1 * A * Z^-1, Z^-2 * B * Z * B * Z^-3 ] Map:: non-degenerate R = (1, 26, 50, 74, 2, 30, 54, 78, 6, 37, 61, 85, 13, 45, 69, 93, 21, 42, 66, 90, 18, 34, 58, 82, 10, 40, 64, 88, 16, 48, 72, 96, 24, 44, 68, 92, 20, 36, 60, 84, 12, 29, 53, 77, 5, 25, 49, 73)(3, 33, 57, 81, 9, 41, 65, 89, 17, 46, 70, 94, 22, 39, 63, 87, 15, 31, 55, 79, 7, 28, 52, 76, 4, 35, 59, 83, 11, 43, 67, 91, 19, 47, 71, 95, 23, 38, 62, 86, 14, 32, 56, 80, 8, 27, 51, 75) L = (1, 51)(2, 55)(3, 49)(4, 58)(5, 59)(6, 62)(7, 50)(8, 64)(9, 66)(10, 52)(11, 53)(12, 65)(13, 70)(14, 54)(15, 72)(16, 56)(17, 60)(18, 57)(19, 69)(20, 71)(21, 67)(22, 61)(23, 68)(24, 63)(25, 76)(26, 80)(27, 82)(28, 73)(29, 81)(30, 87)(31, 88)(32, 74)(33, 77)(34, 75)(35, 90)(36, 91)(37, 95)(38, 96)(39, 78)(40, 79)(41, 93)(42, 83)(43, 84)(44, 94)(45, 89)(46, 92)(47, 85)(48, 86) local type(s) :: { ( 48^48 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: bipartite v = 2 e = 48 f = 2 degree seq :: [ 48^2 ] E23.28 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {12, 12}) Quotient :: toric Aut^+ = C4 x S3 (small group id <24, 5>) Aut = (C4 x S3) : C2 (small group id <48, 41>) |r| :: 2 Presentation :: [ A^2, B^2, S^2, A * B * Z^2, S * B * S * A, (S * Z)^2, A * Z * B * A * B * Z^-1, Z^-1 * B * Z^-5 * A, A * Z^-1 * A * B * Z^-1 * B * Z^-2 ] Map:: non-degenerate R = (1, 26, 50, 74, 2, 30, 54, 78, 6, 38, 62, 86, 14, 46, 70, 94, 22, 43, 67, 91, 19, 47, 71, 95, 23, 45, 69, 93, 21, 48, 72, 96, 24, 44, 68, 92, 20, 34, 58, 82, 10, 29, 53, 77, 5, 25, 49, 73)(3, 33, 57, 81, 9, 42, 66, 90, 18, 32, 56, 80, 8, 41, 65, 89, 17, 31, 55, 79, 7, 40, 64, 88, 16, 37, 61, 85, 13, 39, 63, 87, 15, 36, 60, 84, 12, 28, 52, 76, 4, 35, 59, 83, 11, 27, 51, 75) L = (1, 51)(2, 55)(3, 49)(4, 54)(5, 61)(6, 52)(7, 50)(8, 62)(9, 67)(10, 66)(11, 69)(12, 68)(13, 53)(14, 56)(15, 70)(16, 71)(17, 72)(18, 58)(19, 57)(20, 60)(21, 59)(22, 63)(23, 64)(24, 65)(25, 76)(26, 80)(27, 82)(28, 73)(29, 79)(30, 87)(31, 77)(32, 74)(33, 86)(34, 75)(35, 91)(36, 93)(37, 92)(38, 81)(39, 78)(40, 94)(41, 95)(42, 96)(43, 83)(44, 85)(45, 84)(46, 88)(47, 89)(48, 90) local type(s) :: { ( 48^48 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: bipartite v = 2 e = 48 f = 2 degree seq :: [ 48^2 ] E23.29 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {12, 12}) Quotient :: toric Aut^+ = C3 x Q8 (small group id <24, 11>) Aut = (C4 x S3) : C2 (small group id <48, 41>) |r| :: 2 Presentation :: [ S^2, A^-1 * B, A^-1 * B, B^4, Z^-1 * B^-1 * Z * A^-1, S * B * S * A, B^-1 * A^-2 * B^-1, Z^-1 * A * Z * B, (S * Z)^2, A * Z^-6 * A ] Map:: R = (1, 26, 50, 74, 2, 30, 54, 78, 6, 37, 61, 85, 13, 45, 69, 93, 21, 41, 65, 89, 17, 33, 57, 81, 9, 40, 64, 88, 16, 48, 72, 96, 24, 44, 68, 92, 20, 36, 60, 84, 12, 28, 52, 76, 4, 25, 49, 73)(3, 32, 56, 80, 8, 38, 62, 86, 14, 47, 71, 95, 23, 43, 67, 91, 19, 35, 59, 83, 11, 29, 53, 77, 5, 31, 55, 79, 7, 39, 63, 87, 15, 46, 70, 94, 22, 42, 66, 90, 18, 34, 58, 82, 10, 27, 51, 75) L = (1, 51)(2, 55)(3, 57)(4, 59)(5, 49)(6, 62)(7, 64)(8, 50)(9, 53)(10, 52)(11, 65)(12, 66)(13, 70)(14, 72)(15, 54)(16, 56)(17, 58)(18, 69)(19, 60)(20, 71)(21, 67)(22, 68)(23, 61)(24, 63)(25, 77)(26, 80)(27, 73)(28, 82)(29, 81)(30, 87)(31, 74)(32, 88)(33, 75)(34, 89)(35, 76)(36, 91)(37, 95)(38, 78)(39, 96)(40, 79)(41, 83)(42, 84)(43, 93)(44, 94)(45, 90)(46, 85)(47, 92)(48, 86) local type(s) :: { ( 48^48 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: bipartite v = 2 e = 48 f = 2 degree seq :: [ 48^2 ] E23.30 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {12, 12}) Quotient :: toric Aut^+ = C3 x Q8 (small group id <24, 11>) Aut = (C4 x S3) : C2 (small group id <48, 41>) |r| :: 2 Presentation :: [ S^2, B * A, B * A, (S * Z)^2, B * Z * A^-1 * Z^-1, A^4, A * Z * B^-1 * Z^-1, S * A * S * B, Z^-2 * A^-1 * Z^2 * B^-1, A^-2 * Z * A^-2 * Z^-1, Z^-1 * B * Z^-2 * A^-1 * Z^-3 ] Map:: non-degenerate R = (1, 26, 50, 74, 2, 30, 54, 78, 6, 37, 61, 85, 13, 45, 69, 93, 21, 41, 65, 89, 17, 33, 57, 81, 9, 40, 64, 88, 16, 48, 72, 96, 24, 44, 68, 92, 20, 36, 60, 84, 12, 29, 53, 77, 5, 25, 49, 73)(3, 32, 56, 80, 8, 38, 62, 86, 14, 47, 71, 95, 23, 43, 67, 91, 19, 35, 59, 83, 11, 28, 52, 76, 4, 31, 55, 79, 7, 39, 63, 87, 15, 46, 70, 94, 22, 42, 66, 90, 18, 34, 58, 82, 10, 27, 51, 75) L = (1, 51)(2, 55)(3, 57)(4, 49)(5, 59)(6, 62)(7, 64)(8, 50)(9, 52)(10, 53)(11, 65)(12, 66)(13, 70)(14, 72)(15, 54)(16, 56)(17, 58)(18, 69)(19, 60)(20, 71)(21, 67)(22, 68)(23, 61)(24, 63)(25, 75)(26, 79)(27, 81)(28, 73)(29, 83)(30, 86)(31, 88)(32, 74)(33, 76)(34, 77)(35, 89)(36, 90)(37, 94)(38, 96)(39, 78)(40, 80)(41, 82)(42, 93)(43, 84)(44, 95)(45, 91)(46, 92)(47, 85)(48, 87) local type(s) :: { ( 48^48 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: bipartite v = 2 e = 48 f = 2 degree seq :: [ 48^2 ] E23.31 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {12, 12}) Quotient :: toric Aut^+ = C12 x C2 (small group id <24, 9>) Aut = C2 x D24 (small group id <48, 36>) |r| :: 2 Presentation :: [ A^2, S^2, B^-1 * A, (S * Z)^2, Z^-1 * B * Z * A, Z^-1 * A * Z * B^-1, S * B * S * A, Z^12 ] Map:: R = (1, 26, 50, 74, 2, 29, 53, 77, 5, 33, 57, 81, 9, 37, 61, 85, 13, 41, 65, 89, 17, 45, 69, 93, 21, 44, 68, 92, 20, 40, 64, 88, 16, 36, 60, 84, 12, 32, 56, 80, 8, 28, 52, 76, 4, 25, 49, 73)(3, 30, 54, 78, 6, 34, 58, 82, 10, 38, 62, 86, 14, 42, 66, 90, 18, 46, 70, 94, 22, 48, 72, 96, 24, 47, 71, 95, 23, 43, 67, 91, 19, 39, 63, 87, 15, 35, 59, 83, 11, 31, 55, 79, 7, 27, 51, 75) L = (1, 51)(2, 54)(3, 49)(4, 55)(5, 58)(6, 50)(7, 52)(8, 59)(9, 62)(10, 53)(11, 56)(12, 63)(13, 66)(14, 57)(15, 60)(16, 67)(17, 70)(18, 61)(19, 64)(20, 71)(21, 72)(22, 65)(23, 68)(24, 69)(25, 75)(26, 78)(27, 73)(28, 79)(29, 82)(30, 74)(31, 76)(32, 83)(33, 86)(34, 77)(35, 80)(36, 87)(37, 90)(38, 81)(39, 84)(40, 91)(41, 94)(42, 85)(43, 88)(44, 95)(45, 96)(46, 89)(47, 92)(48, 93) local type(s) :: { ( 48^48 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: bipartite v = 2 e = 48 f = 2 degree seq :: [ 48^2 ] E23.32 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {12, 12}) Quotient :: toric Aut^+ = C12 x C2 (small group id <24, 9>) Aut = C2 x D24 (small group id <48, 36>) |r| :: 2 Presentation :: [ S^2, B * A^-1, B^-1 * A, (S * Z)^2, Z^-1 * A * Z * B^-1, Z^-1 * B * Z * A^-1, A^4, S * A * S * B, A^-2 * Z * A^-2 * Z^-1, Z^-1 * B * Z^-2 * A * Z^-3 ] Map:: R = (1, 26, 50, 74, 2, 30, 54, 78, 6, 37, 61, 85, 13, 45, 69, 93, 21, 41, 65, 89, 17, 33, 57, 81, 9, 40, 64, 88, 16, 48, 72, 96, 24, 43, 67, 91, 19, 35, 59, 83, 11, 28, 52, 76, 4, 25, 49, 73)(3, 31, 55, 79, 7, 38, 62, 86, 14, 46, 70, 94, 22, 44, 68, 92, 20, 36, 60, 84, 12, 29, 53, 77, 5, 32, 56, 80, 8, 39, 63, 87, 15, 47, 71, 95, 23, 42, 66, 90, 18, 34, 58, 82, 10, 27, 51, 75) L = (1, 51)(2, 55)(3, 57)(4, 58)(5, 49)(6, 62)(7, 64)(8, 50)(9, 53)(10, 65)(11, 66)(12, 52)(13, 70)(14, 72)(15, 54)(16, 56)(17, 60)(18, 69)(19, 71)(20, 59)(21, 68)(22, 67)(23, 61)(24, 63)(25, 77)(26, 80)(27, 73)(28, 84)(29, 81)(30, 87)(31, 74)(32, 88)(33, 75)(34, 76)(35, 92)(36, 89)(37, 95)(38, 78)(39, 96)(40, 79)(41, 82)(42, 83)(43, 94)(44, 93)(45, 90)(46, 85)(47, 91)(48, 86) local type(s) :: { ( 48^48 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: bipartite v = 2 e = 48 f = 2 degree seq :: [ 48^2 ] E23.33 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {12, 12}) Quotient :: toric Aut^+ = C12 x C2 (small group id <24, 9>) Aut = C2 x D24 (small group id <48, 36>) |r| :: 2 Presentation :: [ S^2, B * A^-1, (S * Z)^2, (A^-1, Z^-1), S * A * S * B, Z^-1 * A * Z^-1 * A * Z^-2, A^-2 * B^-1 * A^-3 ] Map:: R = (1, 26, 50, 74, 2, 30, 54, 78, 6, 38, 62, 86, 14, 33, 57, 81, 9, 41, 65, 89, 17, 47, 71, 95, 23, 45, 69, 93, 21, 37, 61, 85, 13, 42, 66, 90, 18, 35, 59, 83, 11, 28, 52, 76, 4, 25, 49, 73)(3, 31, 55, 79, 7, 39, 63, 87, 15, 46, 70, 94, 22, 43, 67, 91, 19, 48, 72, 96, 24, 44, 68, 92, 20, 36, 60, 84, 12, 29, 53, 77, 5, 32, 56, 80, 8, 40, 64, 88, 16, 34, 58, 82, 10, 27, 51, 75) L = (1, 51)(2, 55)(3, 57)(4, 58)(5, 49)(6, 63)(7, 65)(8, 50)(9, 67)(10, 62)(11, 64)(12, 52)(13, 53)(14, 70)(15, 71)(16, 54)(17, 72)(18, 56)(19, 61)(20, 59)(21, 60)(22, 69)(23, 68)(24, 66)(25, 77)(26, 80)(27, 73)(28, 84)(29, 85)(30, 88)(31, 74)(32, 90)(33, 75)(34, 76)(35, 92)(36, 93)(37, 91)(38, 82)(39, 78)(40, 83)(41, 79)(42, 96)(43, 81)(44, 95)(45, 94)(46, 86)(47, 87)(48, 89) local type(s) :: { ( 48^48 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: bipartite v = 2 e = 48 f = 2 degree seq :: [ 48^2 ] E23.34 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {3, 3}) Quotient :: toric Aut^+ = C33 (small group id <33, 1>) Aut = C11 x S3 (small group id <66, 1>) |r| :: 2 Presentation :: [ S^2, B^-1 * A^-1, Z^3, (Z, B^-1), S * B * S * A, (S * Z)^2, (Z, A^-1), A^6 * B^-5 ] Map:: non-degenerate R = (1, 35, 68, 101, 2, 38, 71, 104, 5, 34, 67, 100)(3, 39, 72, 105, 6, 42, 75, 108, 9, 36, 69, 102)(4, 40, 73, 106, 7, 44, 77, 110, 11, 37, 70, 103)(8, 45, 78, 111, 12, 48, 81, 114, 15, 41, 74, 107)(10, 46, 79, 112, 13, 50, 83, 116, 17, 43, 76, 109)(14, 51, 84, 117, 18, 54, 87, 120, 21, 47, 80, 113)(16, 52, 85, 118, 19, 56, 89, 122, 23, 49, 82, 115)(20, 57, 90, 123, 24, 60, 93, 126, 27, 53, 86, 119)(22, 58, 91, 124, 25, 62, 95, 128, 29, 55, 88, 121)(26, 63, 96, 129, 30, 65, 98, 131, 32, 59, 92, 125)(28, 64, 97, 130, 31, 66, 99, 132, 33, 61, 94, 127) L = (1, 69)(2, 72)(3, 74)(4, 67)(5, 75)(6, 78)(7, 68)(8, 80)(9, 81)(10, 70)(11, 71)(12, 84)(13, 73)(14, 86)(15, 87)(16, 76)(17, 77)(18, 90)(19, 79)(20, 92)(21, 93)(22, 82)(23, 83)(24, 96)(25, 85)(26, 94)(27, 98)(28, 88)(29, 89)(30, 97)(31, 91)(32, 99)(33, 95)(34, 102)(35, 105)(36, 107)(37, 100)(38, 108)(39, 111)(40, 101)(41, 113)(42, 114)(43, 103)(44, 104)(45, 117)(46, 106)(47, 119)(48, 120)(49, 109)(50, 110)(51, 123)(52, 112)(53, 125)(54, 126)(55, 115)(56, 116)(57, 129)(58, 118)(59, 127)(60, 131)(61, 121)(62, 122)(63, 130)(64, 124)(65, 132)(66, 128) local type(s) :: { ( 12^12 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 11 e = 66 f = 11 degree seq :: [ 12^11 ] E23.35 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {3, 3}) Quotient :: toric Aut^+ = C33 (small group id <33, 1>) Aut = D66 (small group id <66, 3>) |r| :: 2 Presentation :: [ S^2, B * A^-1, Z^3, S * A * S * B, (S * Z)^2, (A, Z^-1), A^11 ] Map:: R = (1, 35, 68, 101, 2, 37, 70, 103, 4, 34, 67, 100)(3, 39, 72, 105, 6, 42, 75, 108, 9, 36, 69, 102)(5, 40, 73, 106, 7, 43, 76, 109, 10, 38, 71, 104)(8, 45, 78, 111, 12, 48, 81, 114, 15, 41, 74, 107)(11, 46, 79, 112, 13, 49, 82, 115, 16, 44, 77, 110)(14, 51, 84, 117, 18, 54, 87, 120, 21, 47, 80, 113)(17, 52, 85, 118, 19, 55, 88, 121, 22, 50, 83, 116)(20, 57, 90, 123, 24, 60, 93, 126, 27, 53, 86, 119)(23, 58, 91, 124, 25, 61, 94, 127, 28, 56, 89, 122)(26, 63, 96, 129, 30, 65, 98, 131, 32, 59, 92, 125)(29, 64, 97, 130, 31, 66, 99, 132, 33, 62, 95, 128) L = (1, 69)(2, 72)(3, 74)(4, 75)(5, 67)(6, 78)(7, 68)(8, 80)(9, 81)(10, 70)(11, 71)(12, 84)(13, 73)(14, 86)(15, 87)(16, 76)(17, 77)(18, 90)(19, 79)(20, 92)(21, 93)(22, 82)(23, 83)(24, 96)(25, 85)(26, 95)(27, 98)(28, 88)(29, 89)(30, 97)(31, 91)(32, 99)(33, 94)(34, 104)(35, 106)(36, 100)(37, 109)(38, 110)(39, 101)(40, 112)(41, 102)(42, 103)(43, 115)(44, 116)(45, 105)(46, 118)(47, 107)(48, 108)(49, 121)(50, 122)(51, 111)(52, 124)(53, 113)(54, 114)(55, 127)(56, 128)(57, 117)(58, 130)(59, 119)(60, 120)(61, 132)(62, 125)(63, 123)(64, 129)(65, 126)(66, 131) local type(s) :: { ( 12^12 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: v = 11 e = 66 f = 11 degree seq :: [ 12^11 ] E23.36 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {2, 2}) Quotient :: toric Aut^+ = D44 (small group id <44, 3>) Aut = C2 x C2 x D22 (small group id <88, 11>) |r| :: 2 Presentation :: [ Z^2, S^2, A^2, B^-1 * A, S * B * S * A, (S * Z)^2, (A * Z)^22 ] Map:: R = (1, 46, 90, 134, 2, 45, 89, 133)(3, 49, 93, 137, 5, 47, 91, 135)(4, 50, 94, 138, 6, 48, 92, 136)(7, 53, 97, 141, 9, 51, 95, 139)(8, 54, 98, 142, 10, 52, 96, 140)(11, 57, 101, 145, 13, 55, 99, 143)(12, 58, 102, 146, 14, 56, 100, 144)(15, 73, 117, 161, 29, 59, 103, 147)(16, 75, 119, 163, 31, 60, 104, 148)(17, 78, 122, 166, 34, 61, 105, 149)(18, 77, 121, 165, 33, 62, 106, 150)(19, 80, 124, 168, 36, 63, 107, 151)(20, 76, 120, 164, 32, 64, 108, 152)(21, 79, 123, 167, 35, 65, 109, 153)(22, 82, 126, 170, 38, 66, 110, 154)(23, 84, 128, 172, 40, 67, 111, 155)(24, 81, 125, 169, 37, 68, 112, 156)(25, 83, 127, 171, 39, 69, 113, 157)(26, 86, 130, 174, 42, 70, 114, 158)(27, 87, 131, 175, 43, 71, 115, 159)(28, 85, 129, 173, 41, 72, 116, 160)(30, 88, 132, 176, 44, 74, 118, 162) L = (1, 91)(2, 92)(3, 89)(4, 90)(5, 95)(6, 96)(7, 93)(8, 94)(9, 99)(10, 100)(11, 97)(12, 98)(13, 103)(14, 116)(15, 101)(16, 120)(17, 123)(18, 122)(19, 119)(20, 125)(21, 127)(22, 121)(23, 124)(24, 129)(25, 117)(26, 126)(27, 128)(28, 102)(29, 113)(30, 130)(31, 107)(32, 104)(33, 110)(34, 106)(35, 105)(36, 111)(37, 108)(38, 114)(39, 109)(40, 115)(41, 112)(42, 118)(43, 132)(44, 131)(45, 135)(46, 136)(47, 133)(48, 134)(49, 139)(50, 140)(51, 137)(52, 138)(53, 143)(54, 144)(55, 141)(56, 142)(57, 147)(58, 160)(59, 145)(60, 164)(61, 167)(62, 166)(63, 163)(64, 169)(65, 171)(66, 165)(67, 168)(68, 173)(69, 161)(70, 170)(71, 172)(72, 146)(73, 157)(74, 174)(75, 151)(76, 148)(77, 154)(78, 150)(79, 149)(80, 155)(81, 152)(82, 158)(83, 153)(84, 159)(85, 156)(86, 162)(87, 176)(88, 175) local type(s) :: { ( 8^8 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: bipartite v = 22 e = 88 f = 22 degree seq :: [ 8^22 ] E23.37 :: Family: { 4P } :: Oriented family(ies): { E6 } Signature :: (1; {2, 2}) Quotient :: toric Aut^+ = D44 (small group id <44, 3>) Aut = C2 x C2 x D22 (small group id <88, 11>) |r| :: 2 Presentation :: [ Z^2, S^2, A^-1 * B^-1, (S * Z)^2, S * A * S * B, A * Z * B^-1 * Z, B^11 * A^-11 ] Map:: non-degenerate R = (1, 46, 90, 134, 2, 45, 89, 133)(3, 50, 94, 138, 6, 47, 91, 135)(4, 49, 93, 137, 5, 48, 92, 136)(7, 54, 98, 142, 10, 51, 95, 139)(8, 53, 97, 141, 9, 52, 96, 140)(11, 58, 102, 146, 14, 55, 99, 143)(12, 57, 101, 145, 13, 56, 100, 144)(15, 62, 106, 150, 18, 59, 103, 147)(16, 61, 105, 149, 17, 60, 104, 148)(19, 66, 110, 154, 22, 63, 107, 151)(20, 65, 109, 153, 21, 64, 108, 152)(23, 70, 114, 158, 26, 67, 111, 155)(24, 69, 113, 157, 25, 68, 112, 156)(27, 74, 118, 162, 30, 71, 115, 159)(28, 73, 117, 161, 29, 72, 116, 160)(31, 78, 122, 166, 34, 75, 119, 163)(32, 77, 121, 165, 33, 76, 120, 164)(35, 82, 126, 170, 38, 79, 123, 167)(36, 81, 125, 169, 37, 80, 124, 168)(39, 86, 130, 174, 42, 83, 127, 171)(40, 85, 129, 173, 41, 84, 128, 172)(43, 88, 132, 176, 44, 87, 131, 175) L = (1, 91)(2, 93)(3, 95)(4, 89)(5, 97)(6, 90)(7, 99)(8, 92)(9, 101)(10, 94)(11, 103)(12, 96)(13, 105)(14, 98)(15, 107)(16, 100)(17, 109)(18, 102)(19, 111)(20, 104)(21, 113)(22, 106)(23, 115)(24, 108)(25, 117)(26, 110)(27, 119)(28, 112)(29, 121)(30, 114)(31, 123)(32, 116)(33, 125)(34, 118)(35, 127)(36, 120)(37, 129)(38, 122)(39, 131)(40, 124)(41, 132)(42, 126)(43, 128)(44, 130)(45, 135)(46, 137)(47, 139)(48, 133)(49, 141)(50, 134)(51, 143)(52, 136)(53, 145)(54, 138)(55, 147)(56, 140)(57, 149)(58, 142)(59, 151)(60, 144)(61, 153)(62, 146)(63, 155)(64, 148)(65, 157)(66, 150)(67, 159)(68, 152)(69, 161)(70, 154)(71, 163)(72, 156)(73, 165)(74, 158)(75, 167)(76, 160)(77, 169)(78, 162)(79, 171)(80, 164)(81, 173)(82, 166)(83, 175)(84, 168)(85, 176)(86, 170)(87, 172)(88, 174) local type(s) :: { ( 8^8 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ Graph:: bipartite v = 22 e = 88 f = 22 degree seq :: [ 8^22 ] E23.38 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {24, 24, 24, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3 * Y2, Y2 * Y3 * Y1, Y3^4, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y2 * Y1^-5, Y2^5 * Y1^-1 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 19, 43, 12, 36, 3, 27, 7, 31, 10, 34, 21, 45, 23, 47, 11, 35, 13, 37, 14, 38, 16, 40, 18, 42, 22, 46, 24, 48, 15, 39, 4, 28, 6, 30, 9, 33, 20, 44, 17, 41, 5, 29)(49, 73, 51, 75, 59, 83, 70, 94, 57, 81, 50, 74, 55, 79, 61, 85, 72, 96, 68, 92, 56, 80, 58, 82, 62, 86, 63, 87, 65, 89, 67, 91, 69, 93, 64, 88, 52, 76, 53, 77, 60, 84, 71, 95, 66, 90, 54, 78) L = (1, 52)(2, 54)(3, 53)(4, 62)(5, 63)(6, 64)(7, 49)(8, 57)(9, 66)(10, 50)(11, 60)(12, 65)(13, 51)(14, 55)(15, 61)(16, 58)(17, 72)(18, 69)(19, 68)(20, 70)(21, 56)(22, 71)(23, 67)(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) :: { ( 48^48 ) } Outer automorphisms :: reflexible Dual of E23.39 Graph:: bipartite v = 2 e = 48 f = 2 degree seq :: [ 48^2 ] E23.39 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {24, 24, 24, 24}) Quotient :: dipole Aut^+ = C24 (small group id <24, 2>) Aut = D48 (small group id <48, 7>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1 * Y1, Y1^-1 * Y2^-1 * Y3, (R * Y3)^2, (R * Y1)^2, Y3^4, (R * Y2)^2, Y1^3 * Y2^-3, Y2^3 * Y3 * Y2^3, Y1 * Y3 * Y2^19 * Y3 ] Map:: non-degenerate R = (1, 25, 2, 26, 8, 32, 19, 43, 23, 47, 16, 40, 7, 31, 6, 30, 10, 34, 21, 45, 11, 35, 12, 36, 14, 38, 18, 42, 17, 41, 22, 46, 13, 37, 3, 27, 4, 28, 9, 33, 20, 44, 24, 48, 15, 39, 5, 29)(49, 73, 51, 75, 59, 83, 67, 91, 68, 92, 66, 90, 55, 79, 53, 77, 61, 85, 69, 93, 56, 80, 57, 81, 62, 86, 64, 88, 63, 87, 70, 94, 58, 82, 50, 74, 52, 76, 60, 84, 71, 95, 72, 96, 65, 89, 54, 78) L = (1, 52)(2, 57)(3, 60)(4, 62)(5, 51)(6, 50)(7, 49)(8, 68)(9, 66)(10, 56)(11, 71)(12, 64)(13, 59)(14, 55)(15, 61)(16, 53)(17, 58)(18, 54)(19, 72)(20, 65)(21, 67)(22, 69)(23, 63)(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) :: { ( 48^48 ) } Outer automorphisms :: reflexible Dual of E23.38 Graph:: bipartite v = 2 e = 48 f = 2 degree seq :: [ 48^2 ] E23.40 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 14, 14, 28}) Quotient :: dipole Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ R^2, (R * Y2)^2, (Y2^-1, Y3), (R * Y3)^2, (Y2, Y1), (R * Y1)^2, (Y3, Y1^-1), Y1^4, Y2^2 * Y3^-1 * Y2^2, Y2^2 * Y3^3, Y3^-1 * Y1 * Y3^-1 * Y2 * Y1, Y3 * Y1 * Y2^-1 * Y3 * Y1, Y3 * Y2 * Y1^-1 * Y2^2 * Y1^-1 ] Map:: non-degenerate R = (1, 29, 2, 30, 8, 36, 5, 33)(3, 31, 9, 37, 17, 45, 15, 43)(4, 32, 10, 38, 16, 44, 18, 46)(6, 34, 11, 39, 24, 52, 20, 48)(7, 35, 12, 40, 19, 47, 21, 49)(13, 41, 25, 53, 23, 51, 28, 56)(14, 42, 26, 54, 22, 50, 27, 55)(57, 85, 59, 87, 69, 97, 75, 103, 60, 88, 70, 98, 80, 108, 64, 92, 73, 101, 79, 107, 63, 91, 72, 100, 78, 106, 62, 90)(58, 86, 65, 93, 81, 109, 77, 105, 66, 94, 82, 110, 76, 104, 61, 89, 71, 99, 84, 112, 68, 96, 74, 102, 83, 111, 67, 95) L = (1, 60)(2, 66)(3, 70)(4, 73)(5, 74)(6, 75)(7, 57)(8, 72)(9, 82)(10, 71)(11, 77)(12, 58)(13, 80)(14, 79)(15, 83)(16, 59)(17, 78)(18, 65)(19, 64)(20, 68)(21, 61)(22, 69)(23, 62)(24, 63)(25, 76)(26, 84)(27, 81)(28, 67)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112) local type(s) :: { ( 28, 56, 28, 56, 28, 56, 28, 56 ), ( 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56 ) } Outer automorphisms :: reflexible Dual of E23.51 Graph:: bipartite v = 9 e = 56 f = 3 degree seq :: [ 8^7, 28^2 ] E23.41 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 14, 14, 28}) Quotient :: dipole Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ R^2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y2^-1, Y3), (Y2^-1, Y1^-1), Y1^4, (Y3, Y1^-1), Y2^-4 * Y3^-1, Y1^-1 * Y2 * Y3^2 * Y1^-1, Y3^2 * Y1 * Y2 * Y1, Y3 * Y2^-1 * Y3^2 * Y2^-1, Y3^-1 * Y2 * Y1^-1 * Y2^2 * Y1^-1, Y3^7, Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * 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, 29, 2, 30, 8, 36, 5, 33)(3, 31, 9, 37, 24, 52, 15, 43)(4, 32, 10, 38, 23, 51, 18, 46)(6, 34, 11, 39, 17, 45, 20, 48)(7, 35, 12, 40, 14, 42, 21, 49)(13, 41, 25, 53, 19, 47, 27, 55)(16, 44, 26, 54, 22, 50, 28, 56)(57, 85, 59, 87, 69, 97, 79, 107, 63, 91, 72, 100, 73, 101, 64, 92, 80, 108, 75, 103, 60, 88, 70, 98, 78, 106, 62, 90)(58, 86, 65, 93, 81, 109, 74, 102, 68, 96, 82, 110, 76, 104, 61, 89, 71, 99, 83, 111, 66, 94, 77, 105, 84, 112, 67, 95) L = (1, 60)(2, 66)(3, 70)(4, 73)(5, 74)(6, 75)(7, 57)(8, 79)(9, 77)(10, 76)(11, 83)(12, 58)(13, 78)(14, 64)(15, 68)(16, 59)(17, 69)(18, 67)(19, 72)(20, 81)(21, 61)(22, 80)(23, 62)(24, 63)(25, 84)(26, 65)(27, 82)(28, 71)(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, 56, 28, 56, 28, 56, 28, 56 ), ( 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56 ) } Outer automorphisms :: reflexible Dual of E23.53 Graph:: bipartite v = 9 e = 56 f = 3 degree seq :: [ 8^7, 28^2 ] E23.42 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 14, 14, 28}) Quotient :: dipole Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ R^2, Y3^-2 * Y2^-2, (Y3, Y2^-1), (Y3, Y1^-1), Y1^4, (R * Y2)^2, Y3^-1 * Y1^-1 * Y2^-1 * Y1^-1, Y2^-1 * Y1^-2 * Y3^-1, Y3 * Y2 * Y1^2, Y1^-1 * Y3 * Y2 * Y1^-1, (R * Y1)^2, (R * Y3)^2, Y3^7, Y3^-3 * Y2^4 ] Map:: non-degenerate R = (1, 29, 2, 30, 8, 36, 5, 33)(3, 31, 9, 37, 7, 35, 12, 40)(4, 32, 10, 38, 6, 34, 11, 39)(13, 41, 17, 45, 14, 42, 18, 46)(15, 43, 19, 47, 16, 44, 20, 48)(21, 49, 25, 53, 22, 50, 26, 54)(23, 51, 27, 55, 24, 52, 28, 56)(57, 85, 59, 87, 69, 97, 77, 105, 79, 107, 72, 100, 60, 88, 64, 92, 63, 91, 70, 98, 78, 106, 80, 108, 71, 99, 62, 90)(58, 86, 65, 93, 73, 101, 81, 109, 83, 111, 76, 104, 66, 94, 61, 89, 68, 96, 74, 102, 82, 110, 84, 112, 75, 103, 67, 95) L = (1, 60)(2, 66)(3, 64)(4, 71)(5, 67)(6, 72)(7, 57)(8, 62)(9, 61)(10, 75)(11, 76)(12, 58)(13, 63)(14, 59)(15, 79)(16, 80)(17, 68)(18, 65)(19, 83)(20, 84)(21, 70)(22, 69)(23, 78)(24, 77)(25, 74)(26, 73)(27, 82)(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) :: { ( 28, 56, 28, 56, 28, 56, 28, 56 ), ( 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56 ) } Outer automorphisms :: reflexible Dual of E23.50 Graph:: bipartite v = 9 e = 56 f = 3 degree seq :: [ 8^7, 28^2 ] E23.43 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 14, 14, 28}) Quotient :: dipole Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ R^2, Y2^2 * Y3, (Y3^-1, Y1^-1), (R * Y1)^2, Y1^4, (R * Y2)^2, (Y2^-1, Y1), (R * Y3)^2, Y2 * Y1^2 * Y3^-3, Y3^-1 * Y1^-1 * Y2 * Y3^-2 * Y1^-1, Y3^7, Y3 * 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, 29, 2, 30, 8, 36, 5, 33)(3, 31, 9, 37, 21, 49, 13, 41)(4, 32, 10, 38, 22, 50, 16, 44)(6, 34, 11, 39, 23, 51, 18, 46)(7, 35, 12, 40, 24, 52, 19, 47)(14, 42, 25, 53, 15, 43, 26, 54)(17, 45, 27, 55, 20, 48, 28, 56)(57, 85, 59, 87, 63, 91, 70, 98, 76, 104, 78, 106, 79, 107, 64, 92, 77, 105, 80, 108, 71, 99, 73, 101, 60, 88, 62, 90)(58, 86, 65, 93, 68, 96, 81, 109, 84, 112, 72, 100, 74, 102, 61, 89, 69, 97, 75, 103, 82, 110, 83, 111, 66, 94, 67, 95) L = (1, 60)(2, 66)(3, 62)(4, 71)(5, 72)(6, 73)(7, 57)(8, 78)(9, 67)(10, 82)(11, 83)(12, 58)(13, 74)(14, 59)(15, 77)(16, 81)(17, 80)(18, 84)(19, 61)(20, 63)(21, 79)(22, 70)(23, 76)(24, 64)(25, 65)(26, 69)(27, 75)(28, 68)(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, 56, 28, 56, 28, 56, 28, 56 ), ( 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56 ) } Outer automorphisms :: reflexible Dual of E23.49 Graph:: bipartite v = 9 e = 56 f = 3 degree seq :: [ 8^7, 28^2 ] E23.44 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 14, 14, 28}) Quotient :: dipole Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ R^2, Y2^-2 * Y3, (Y3^-1, Y1^-1), Y1^4, (Y2^-1, Y1^-1), (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y2 * Y3^2 * Y1^-1 * Y3 * Y1^-1, Y1^-1 * Y3^3 * Y2 * Y1^-1, Y3^-28 ] Map:: non-degenerate R = (1, 29, 2, 30, 8, 36, 5, 33)(3, 31, 9, 37, 21, 49, 14, 42)(4, 32, 10, 38, 22, 50, 16, 44)(6, 34, 11, 39, 23, 51, 17, 45)(7, 35, 12, 40, 24, 52, 18, 46)(13, 41, 25, 53, 20, 48, 28, 56)(15, 43, 26, 54, 19, 47, 27, 55)(57, 85, 59, 87, 60, 88, 69, 97, 71, 99, 80, 108, 79, 107, 64, 92, 77, 105, 78, 106, 76, 104, 75, 103, 63, 91, 62, 90)(58, 86, 65, 93, 66, 94, 81, 109, 82, 110, 74, 102, 73, 101, 61, 89, 70, 98, 72, 100, 84, 112, 83, 111, 68, 96, 67, 95) L = (1, 60)(2, 66)(3, 69)(4, 71)(5, 72)(6, 59)(7, 57)(8, 78)(9, 81)(10, 82)(11, 65)(12, 58)(13, 80)(14, 84)(15, 79)(16, 83)(17, 70)(18, 61)(19, 62)(20, 63)(21, 76)(22, 75)(23, 77)(24, 64)(25, 74)(26, 73)(27, 67)(28, 68)(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, 56, 28, 56, 28, 56, 28, 56 ), ( 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56, 28, 56 ) } Outer automorphisms :: reflexible Dual of E23.52 Graph:: bipartite v = 9 e = 56 f = 3 degree seq :: [ 8^7, 28^2 ] E23.45 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 14, 14, 28}) Quotient :: dipole Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y2 * Y3^-1, Y2^3 * Y1^-1, (Y1, Y3), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y1^-1 * Y2 * Y1^-4, Y1^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 29, 2, 30, 8, 36, 20, 48, 14, 42, 3, 31, 9, 37, 21, 49, 17, 45, 6, 34, 11, 39, 23, 51, 16, 44, 5, 33)(4, 32, 10, 38, 22, 50, 28, 56, 19, 47, 13, 41, 25, 53, 27, 55, 18, 46, 7, 35, 12, 40, 24, 52, 26, 54, 15, 43)(57, 85, 59, 87, 67, 95, 58, 86, 65, 93, 79, 107, 64, 92, 77, 105, 72, 100, 76, 104, 73, 101, 61, 89, 70, 98, 62, 90)(60, 88, 69, 97, 68, 96, 66, 94, 81, 109, 80, 108, 78, 106, 83, 111, 82, 110, 84, 112, 74, 102, 71, 99, 75, 103, 63, 91) L = (1, 60)(2, 66)(3, 69)(4, 59)(5, 71)(6, 63)(7, 57)(8, 78)(9, 81)(10, 65)(11, 68)(12, 58)(13, 67)(14, 75)(15, 70)(16, 82)(17, 74)(18, 61)(19, 62)(20, 84)(21, 83)(22, 77)(23, 80)(24, 64)(25, 79)(26, 76)(27, 72)(28, 73)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112) local type(s) :: { ( 8, 56, 8, 56, 8, 56, 8, 56, 8, 56, 8, 56, 8, 56, 8, 56, 8, 56, 8, 56, 8, 56, 8, 56, 8, 56, 8, 56 ) } Outer automorphisms :: reflexible Dual of E23.47 Graph:: bipartite v = 4 e = 56 f = 8 degree seq :: [ 28^4 ] E23.46 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 14, 14, 28}) Quotient :: dipole Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y2^-1 * Y3^-1, Y1^-1 * Y2^-3, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y1), Y3^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1, Y1^-1 * Y2^-1 * Y1^-4, (Y2 * Y1^-2)^2 ] Map:: non-degenerate R = (1, 29, 2, 30, 8, 36, 20, 48, 13, 41, 6, 34, 11, 39, 23, 51, 14, 42, 3, 31, 9, 37, 21, 49, 18, 46, 5, 33)(4, 32, 10, 38, 22, 50, 26, 54, 15, 43, 17, 45, 25, 53, 28, 56, 19, 47, 7, 35, 12, 40, 24, 52, 27, 55, 16, 44)(57, 85, 59, 87, 69, 97, 61, 89, 70, 98, 76, 104, 74, 102, 79, 107, 64, 92, 77, 105, 67, 95, 58, 86, 65, 93, 62, 90)(60, 88, 63, 91, 71, 99, 72, 100, 75, 103, 82, 110, 83, 111, 84, 112, 78, 106, 80, 108, 81, 109, 66, 94, 68, 96, 73, 101) L = (1, 60)(2, 66)(3, 63)(4, 62)(5, 72)(6, 73)(7, 57)(8, 78)(9, 68)(10, 67)(11, 81)(12, 58)(13, 71)(14, 75)(15, 59)(16, 69)(17, 65)(18, 83)(19, 61)(20, 82)(21, 80)(22, 79)(23, 84)(24, 64)(25, 77)(26, 70)(27, 76)(28, 74)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112) local type(s) :: { ( 8, 56, 8, 56, 8, 56, 8, 56, 8, 56, 8, 56, 8, 56, 8, 56, 8, 56, 8, 56, 8, 56, 8, 56, 8, 56, 8, 56 ) } Outer automorphisms :: reflexible Dual of E23.48 Graph:: bipartite v = 4 e = 56 f = 8 degree seq :: [ 28^4 ] E23.47 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 14, 14, 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, (Y2^-1, Y1), (R * Y1)^2, (R * Y3)^2, Y2^4, (R * Y2 * Y3^-1)^2, Y2 * Y1^-7, (Y3 * Y2^-1)^14, (Y3^-1 * Y1^-1)^14 ] Map:: non-degenerate R = (1, 29, 2, 30, 6, 34, 13, 41, 21, 49, 18, 46, 10, 38, 3, 31, 7, 35, 14, 42, 22, 50, 27, 55, 25, 53, 17, 45, 9, 37, 16, 44, 24, 52, 28, 56, 26, 54, 20, 48, 12, 40, 5, 33, 8, 36, 15, 43, 23, 51, 19, 47, 11, 39, 4, 32)(57, 85, 59, 87, 65, 93, 61, 89)(58, 86, 63, 91, 72, 100, 64, 92)(60, 88, 66, 94, 73, 101, 68, 96)(62, 90, 70, 98, 80, 108, 71, 99)(67, 95, 74, 102, 81, 109, 76, 104)(69, 97, 78, 106, 84, 112, 79, 107)(75, 103, 77, 105, 83, 111, 82, 110) L = (1, 58)(2, 62)(3, 63)(4, 57)(5, 64)(6, 69)(7, 70)(8, 71)(9, 72)(10, 59)(11, 60)(12, 61)(13, 77)(14, 78)(15, 79)(16, 80)(17, 65)(18, 66)(19, 67)(20, 68)(21, 74)(22, 83)(23, 75)(24, 84)(25, 73)(26, 76)(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) :: { ( 28^8 ), ( 28^56 ) } Outer automorphisms :: reflexible Dual of E23.45 Graph:: bipartite v = 8 e = 56 f = 4 degree seq :: [ 8^7, 56 ] E23.48 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 14, 14, 28}) Quotient :: dipole Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ R^2, (Y2^-1, Y1^-1), Y1^-1 * Y2^-1 * Y3 * Y1^-1, Y2^-1 * Y1^-1 * Y3 * Y1^-1, Y1 * Y2 * Y3^-1 * Y1, (R * Y1)^2, (R * Y2)^2, Y2^4, Y1^-1 * Y3^-3, (R * Y3)^2, Y2 * Y1 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3, Y1^2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1, Y2^-1 * Y3 * Y1^26 ] Map:: non-degenerate R = (1, 29, 2, 30, 8, 36, 19, 47, 27, 55, 25, 53, 15, 43, 3, 31, 9, 37, 4, 32, 10, 38, 20, 48, 18, 46, 24, 52, 13, 41, 22, 50, 14, 42, 23, 51, 17, 45, 7, 35, 12, 40, 6, 34, 11, 39, 21, 49, 28, 56, 26, 54, 16, 44, 5, 33)(57, 85, 59, 87, 69, 97, 62, 90)(58, 86, 65, 93, 78, 106, 67, 95)(60, 88, 70, 98, 77, 105, 64, 92)(61, 89, 71, 99, 80, 108, 68, 96)(63, 91, 72, 100, 81, 109, 74, 102)(66, 94, 79, 107, 84, 112, 75, 103)(73, 101, 82, 110, 83, 111, 76, 104) L = (1, 60)(2, 66)(3, 70)(4, 73)(5, 65)(6, 64)(7, 57)(8, 76)(9, 79)(10, 63)(11, 75)(12, 58)(13, 77)(14, 82)(15, 78)(16, 59)(17, 61)(18, 62)(19, 74)(20, 68)(21, 83)(22, 84)(23, 72)(24, 67)(25, 69)(26, 71)(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) :: { ( 28^8 ), ( 28^56 ) } Outer automorphisms :: reflexible Dual of E23.46 Graph:: bipartite v = 8 e = 56 f = 4 degree seq :: [ 8^7, 56 ] E23.49 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 14, 14, 28}) Quotient :: dipole Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y2^2, (Y3, Y1), (R * Y3)^2, (R * Y1)^2, (Y3, Y2^-1), (R * Y2)^2, Y3 * Y1^-4, Y1^-1 * Y3^-3 * Y1^-1, Y1 * Y3^2 * Y1 * Y3, Y1^-1 * Y3 * Y1^-3, Y1^-1 * Y3^4 * Y1^-1, Y1^-1 * Y2^-1 * Y3 * Y1^-1 * Y2^-1 * Y1^-1, (Y2^-1 * Y3)^4 ] Map:: non-degenerate R = (1, 29, 2, 30, 8, 36, 15, 43, 4, 32, 10, 38, 21, 49, 25, 53, 14, 42, 19, 47, 7, 35, 11, 39, 17, 45, 5, 33)(3, 31, 9, 37, 22, 50, 16, 44, 12, 40, 23, 51, 27, 55, 28, 56, 26, 54, 20, 48, 13, 41, 24, 52, 18, 46, 6, 34)(57, 85, 59, 87, 58, 86, 65, 93, 64, 92, 78, 106, 71, 99, 72, 100, 60, 88, 68, 96, 66, 94, 79, 107, 77, 105, 83, 111, 81, 109, 84, 112, 70, 98, 82, 110, 75, 103, 76, 104, 63, 91, 69, 97, 67, 95, 80, 108, 73, 101, 74, 102, 61, 89, 62, 90) L = (1, 60)(2, 66)(3, 68)(4, 70)(5, 71)(6, 72)(7, 57)(8, 77)(9, 79)(10, 75)(11, 58)(12, 82)(13, 59)(14, 73)(15, 81)(16, 84)(17, 64)(18, 78)(19, 61)(20, 62)(21, 63)(22, 83)(23, 76)(24, 65)(25, 67)(26, 74)(27, 69)(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) :: { ( 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28 ), ( 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28 ) } Outer automorphisms :: reflexible Dual of E23.43 Graph:: bipartite v = 3 e = 56 f = 9 degree seq :: [ 28^2, 56 ] E23.50 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 14, 14, 28}) Quotient :: dipole Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1^-1 * Y2^-1, (Y3, Y2^-1), (R * Y3)^2, (R * Y2)^2, (Y3, Y1^-1), (R * Y1)^2, Y2 * Y1^-1 * Y2 * Y1^2, Y3^3 * Y1^-2, Y3^-1 * Y1^-4, Y1 * Y3^-2 * Y1 * Y3^-1, (Y2^-1 * Y3)^4 ] Map:: non-degenerate R = (1, 29, 2, 30, 8, 36, 19, 47, 7, 35, 11, 39, 15, 43, 23, 51, 21, 49, 16, 44, 4, 32, 9, 37, 18, 46, 5, 33)(3, 31, 6, 34, 10, 38, 22, 50, 14, 42, 20, 48, 25, 53, 28, 56, 27, 55, 26, 54, 12, 40, 17, 45, 24, 52, 13, 41)(57, 85, 59, 87, 61, 89, 69, 97, 74, 102, 80, 108, 65, 93, 73, 101, 60, 88, 68, 96, 72, 100, 82, 110, 77, 105, 83, 111, 79, 107, 84, 112, 71, 99, 81, 109, 67, 95, 76, 104, 63, 91, 70, 98, 75, 103, 78, 106, 64, 92, 66, 94, 58, 86, 62, 90) L = (1, 60)(2, 65)(3, 68)(4, 71)(5, 72)(6, 73)(7, 57)(8, 74)(9, 79)(10, 80)(11, 58)(12, 81)(13, 82)(14, 59)(15, 64)(16, 67)(17, 84)(18, 77)(19, 61)(20, 62)(21, 63)(22, 69)(23, 75)(24, 83)(25, 66)(26, 76)(27, 70)(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) :: { ( 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28 ), ( 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28 ) } Outer automorphisms :: reflexible Dual of E23.42 Graph:: bipartite v = 3 e = 56 f = 9 degree seq :: [ 28^2, 56 ] E23.51 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 14, 14, 28}) Quotient :: dipole Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ R^2, (Y1, Y2^-1), Y3 * Y2^-1 * Y1 * Y2^-1, Y2 * Y3^-1 * Y1^-1 * Y2, (Y3, Y1^-1), Y1^2 * Y3^-2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y2 * Y3 * Y2 * Y1^-3, Y1 * Y2 * Y1 * Y3^2 * Y2 * Y1, Y3^2 * Y1 * Y3^3 * Y1, (Y1 * Y3)^14, Y2^28 ] Map:: non-degenerate R = (1, 29, 2, 30, 8, 36, 19, 47, 27, 55, 17, 45, 7, 35, 12, 40, 4, 32, 10, 38, 21, 49, 25, 53, 15, 43, 5, 33)(3, 31, 9, 37, 20, 48, 26, 54, 16, 44, 6, 34, 11, 39, 22, 50, 13, 41, 23, 51, 28, 56, 18, 46, 24, 52, 14, 42)(57, 85, 59, 87, 66, 94, 79, 107, 83, 111, 72, 100, 61, 89, 70, 98, 60, 88, 69, 97, 75, 103, 82, 110, 71, 99, 80, 108, 68, 96, 78, 106, 64, 92, 76, 104, 81, 109, 74, 102, 63, 91, 67, 95, 58, 86, 65, 93, 77, 105, 84, 112, 73, 101, 62, 90) L = (1, 60)(2, 66)(3, 69)(4, 64)(5, 68)(6, 70)(7, 57)(8, 77)(9, 79)(10, 75)(11, 59)(12, 58)(13, 76)(14, 78)(15, 63)(16, 80)(17, 61)(18, 62)(19, 81)(20, 84)(21, 83)(22, 65)(23, 82)(24, 67)(25, 73)(26, 74)(27, 71)(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) :: { ( 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28 ), ( 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28 ) } Outer automorphisms :: reflexible Dual of E23.40 Graph:: bipartite v = 3 e = 56 f = 9 degree seq :: [ 28^2, 56 ] E23.52 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 14, 14, 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^-2, Y1 * Y3 * Y1, Y2 * Y3 * Y2 * Y1^-1, (Y1^-1, Y2^-1), Y1^-1 * Y3 * Y2^2, Y2^-1 * Y1 * Y3^-1 * Y2^-1, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y2^-1), Y3^7, Y3^-1 * Y2^8, (Y1 * Y3^-1)^14 ] Map:: non-degenerate R = (1, 29, 2, 30, 7, 35, 10, 38, 17, 45, 19, 47, 25, 53, 27, 55, 21, 49, 22, 50, 13, 41, 14, 42, 4, 32, 5, 33)(3, 31, 8, 36, 12, 40, 18, 46, 20, 48, 26, 54, 28, 56, 23, 51, 24, 52, 15, 43, 16, 44, 6, 34, 9, 37, 11, 39)(57, 85, 59, 87, 66, 94, 74, 102, 81, 109, 84, 112, 78, 106, 71, 99, 60, 88, 65, 93, 58, 86, 64, 92, 73, 101, 76, 104, 83, 111, 79, 107, 69, 97, 72, 100, 61, 89, 67, 95, 63, 91, 68, 96, 75, 103, 82, 110, 77, 105, 80, 108, 70, 98, 62, 90) L = (1, 60)(2, 61)(3, 65)(4, 69)(5, 70)(6, 71)(7, 57)(8, 67)(9, 72)(10, 58)(11, 62)(12, 59)(13, 77)(14, 78)(15, 79)(16, 80)(17, 63)(18, 64)(19, 66)(20, 68)(21, 81)(22, 83)(23, 82)(24, 84)(25, 73)(26, 74)(27, 75)(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) :: { ( 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28 ), ( 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28 ) } Outer automorphisms :: reflexible Dual of E23.44 Graph:: bipartite v = 3 e = 56 f = 9 degree seq :: [ 28^2, 56 ] E23.53 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 14, 14, 28}) Quotient :: dipole Aut^+ = C28 (small group id <28, 2>) Aut = D56 (small group id <56, 5>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^2, Y1^-1 * Y3 * Y1^-1, (Y3^-1, Y2^-1), (R * Y1)^2, (Y1, Y2^-1), Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1, Y1 * Y2 * Y3 * Y2, (R * Y3)^2, (R * Y2)^2, Y2^2 * Y1 * Y3, Y3^7, Y3^-1 * Y2^8, (Y3^-1 * Y1^-1)^14 ] Map:: non-degenerate R = (1, 29, 2, 30, 4, 32, 9, 37, 15, 43, 18, 46, 23, 51, 26, 54, 25, 53, 21, 49, 17, 45, 11, 39, 7, 35, 5, 33)(3, 31, 8, 36, 12, 40, 6, 34, 10, 38, 16, 44, 19, 47, 24, 52, 27, 55, 28, 56, 22, 50, 20, 48, 14, 42, 13, 41)(57, 85, 59, 87, 67, 95, 76, 104, 81, 109, 83, 111, 74, 102, 72, 100, 60, 88, 68, 96, 61, 89, 69, 97, 73, 101, 78, 106, 82, 110, 80, 108, 71, 99, 66, 94, 58, 86, 64, 92, 63, 91, 70, 98, 77, 105, 84, 112, 79, 107, 75, 103, 65, 93, 62, 90) L = (1, 60)(2, 65)(3, 68)(4, 71)(5, 58)(6, 72)(7, 57)(8, 62)(9, 74)(10, 75)(11, 61)(12, 66)(13, 64)(14, 59)(15, 79)(16, 80)(17, 63)(18, 82)(19, 83)(20, 69)(21, 67)(22, 70)(23, 81)(24, 84)(25, 73)(26, 77)(27, 78)(28, 76)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112) local type(s) :: { ( 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28 ), ( 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28, 8, 28 ) } Outer automorphisms :: reflexible Dual of E23.41 Graph:: bipartite v = 3 e = 56 f = 9 degree seq :: [ 28^2, 56 ] E23.54 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 6, 10, 10}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (Y2^-1, Y1^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1^6, Y2^5 * Y1^3, (Y3^-1 * Y1^-1)^6, (Y3 * Y2^-1)^10 ] 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, 24, 54, 30, 60, 20, 50)(13, 43, 18, 48, 28, 58, 19, 49, 29, 59, 23, 53)(61, 91, 63, 93, 69, 99, 79, 109, 86, 116, 74, 104, 85, 115, 84, 114, 73, 103, 65, 95)(62, 92, 67, 97, 77, 107, 89, 119, 82, 112, 71, 101, 81, 111, 90, 120, 78, 108, 68, 98)(64, 94, 70, 100, 80, 110, 88, 118, 76, 106, 66, 96, 75, 105, 87, 117, 83, 113, 72, 102) 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) :: { ( 12, 20, 12, 20, 12, 20, 12, 20, 12, 20, 12, 20 ), ( 12, 20, 12, 20, 12, 20, 12, 20, 12, 20, 12, 20, 12, 20, 12, 20, 12, 20, 12, 20 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 8 e = 60 f = 8 degree seq :: [ 12^5, 20^3 ] E23.55 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 6, 10, 15}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^2 * Y1^-1, Y2 * Y3 * Y2 * Y1^-1, (R * Y3)^2, Y3 * Y1^-1 * Y2^2, (Y2^-1, Y1^-1), (Y3^-1, Y1^-1), (Y2, Y3^-1), (R * Y1)^2, (R * Y2)^2, Y3^3 * Y1^2, Y1^5, Y2^-1 * Y1^-2 * Y3^2 * Y2^-1, (Y3^-1 * Y1)^3 ] Map:: non-degenerate R = (1, 31, 2, 32, 8, 38, 18, 48, 5, 35)(3, 33, 9, 39, 22, 52, 28, 58, 13, 43)(4, 34, 10, 40, 21, 51, 27, 57, 16, 46)(6, 36, 11, 41, 23, 53, 30, 60, 19, 49)(7, 37, 12, 42, 24, 54, 15, 45, 20, 50)(14, 44, 25, 55, 17, 47, 26, 56, 29, 59)(61, 91, 63, 93, 72, 102, 85, 115, 76, 106, 66, 96)(62, 92, 69, 99, 84, 114, 77, 107, 64, 94, 71, 101)(65, 95, 73, 103, 67, 97, 74, 104, 87, 117, 79, 109)(68, 98, 82, 112, 75, 105, 86, 116, 70, 100, 83, 113)(78, 108, 88, 118, 80, 110, 89, 119, 81, 111, 90, 120) L = (1, 64)(2, 70)(3, 71)(4, 75)(5, 76)(6, 77)(7, 61)(8, 81)(9, 83)(10, 80)(11, 86)(12, 62)(13, 66)(14, 63)(15, 78)(16, 84)(17, 82)(18, 87)(19, 85)(20, 65)(21, 67)(22, 90)(23, 89)(24, 68)(25, 69)(26, 88)(27, 72)(28, 79)(29, 73)(30, 74)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 20, 30, 20, 30, 20, 30, 20, 30, 20, 30 ), ( 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30 ) } Outer automorphisms :: reflexible Dual of E23.64 Graph:: bipartite v = 11 e = 60 f = 5 degree seq :: [ 10^6, 12^5 ] E23.56 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 6, 10, 15}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^3, (Y3^-1, Y1^-1), (R * Y3)^2, (Y1^-1, Y2^-1), (Y2^-1, Y3^-1), (R * Y1)^2, (R * Y2)^2, Y3 * Y2 * Y1 * Y2 * Y1, Y3^-1 * Y2^2 * Y1 * Y3^-1, Y1^5, Y1^-1 * Y2 * Y3 * Y1^-2 * Y2, Y2^6 ] Map:: non-degenerate R = (1, 31, 2, 32, 8, 38, 20, 50, 5, 35)(3, 33, 9, 39, 23, 53, 28, 58, 15, 45)(4, 34, 10, 40, 22, 52, 27, 57, 18, 48)(6, 36, 11, 41, 24, 54, 14, 44, 21, 51)(7, 37, 12, 42, 25, 55, 13, 43, 17, 47)(16, 46, 19, 49, 26, 56, 29, 59, 30, 60)(61, 91, 63, 93, 73, 103, 89, 119, 82, 112, 66, 96)(62, 92, 69, 99, 77, 107, 90, 120, 87, 117, 71, 101)(64, 94, 74, 104, 80, 110, 88, 118, 72, 102, 79, 109)(65, 95, 75, 105, 85, 115, 86, 116, 70, 100, 81, 111)(67, 97, 76, 106, 78, 108, 84, 114, 68, 98, 83, 113) L = (1, 64)(2, 70)(3, 74)(4, 77)(5, 78)(6, 79)(7, 61)(8, 82)(9, 81)(10, 67)(11, 86)(12, 62)(13, 80)(14, 90)(15, 84)(16, 63)(17, 65)(18, 73)(19, 69)(20, 87)(21, 76)(22, 72)(23, 66)(24, 89)(25, 68)(26, 83)(27, 85)(28, 71)(29, 88)(30, 75)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 20, 30, 20, 30, 20, 30, 20, 30, 20, 30 ), ( 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30 ) } Outer automorphisms :: reflexible Dual of E23.66 Graph:: bipartite v = 11 e = 60 f = 5 degree seq :: [ 10^6, 12^5 ] E23.57 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 6, 10, 15}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^3, (Y1^-1, Y3), (Y1^-1, Y2), (Y3^-1, Y2^-1), (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y3 * Y1 * Y2^-1 * Y3 * Y2^-1, Y1 * Y3^-1 * Y2^-2 * Y1, Y1^5, Y2^6, (Y1^-1 * Y3^-1)^15 ] Map:: non-degenerate R = (1, 31, 2, 32, 8, 38, 19, 49, 5, 35)(3, 33, 9, 39, 24, 54, 23, 53, 15, 45)(4, 34, 10, 40, 25, 55, 22, 52, 17, 47)(6, 36, 11, 41, 14, 44, 27, 57, 20, 50)(7, 37, 12, 42, 13, 43, 26, 56, 21, 51)(16, 46, 28, 58, 29, 59, 30, 60, 18, 48)(61, 91, 63, 93, 73, 103, 89, 119, 82, 112, 66, 96)(62, 92, 69, 99, 86, 116, 90, 120, 77, 107, 71, 101)(64, 94, 74, 104, 68, 98, 84, 114, 81, 111, 78, 108)(65, 95, 75, 105, 72, 102, 88, 118, 85, 115, 80, 110)(67, 97, 76, 106, 70, 100, 87, 117, 79, 109, 83, 113) L = (1, 64)(2, 70)(3, 74)(4, 72)(5, 77)(6, 78)(7, 61)(8, 85)(9, 87)(10, 73)(11, 76)(12, 62)(13, 68)(14, 88)(15, 71)(16, 63)(17, 67)(18, 75)(19, 82)(20, 90)(21, 65)(22, 81)(23, 66)(24, 80)(25, 86)(26, 79)(27, 89)(28, 69)(29, 84)(30, 83)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 20, 30, 20, 30, 20, 30, 20, 30, 20, 30 ), ( 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30 ) } Outer automorphisms :: reflexible Dual of E23.65 Graph:: bipartite v = 11 e = 60 f = 5 degree seq :: [ 10^6, 12^5 ] E23.58 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 6, 10, 15}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1^2 * Y3^-1, Y2^-1 * Y1 * Y3^-1 * Y1, (Y3^-1, Y1), (R * Y2)^2, (R * Y1)^2, Y2^-1 * Y3^-1 * Y1^2, (R * Y3)^2, (Y3 * Y2)^3, Y3^3 * Y1^-1 * Y3^2, Y2^2 * Y3^-1 * Y2 * Y3^-1 * Y1, Y1^-1 * Y2^-1 * Y1^-2 * Y3^-1 * Y1^-1, Y3^-2 * Y1^-1 * Y3^-1 * Y2 * Y3^-1, Y2^2 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1, Y2^10, Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y3^-1 ] Map:: non-degenerate R = (1, 31, 2, 32, 8, 38, 22, 52, 17, 47, 5, 35)(3, 33, 9, 39, 23, 53, 19, 49, 7, 37, 12, 42)(4, 34, 10, 40, 24, 54, 18, 48, 6, 36, 11, 41)(13, 43, 25, 55, 21, 51, 30, 60, 14, 44, 26, 56)(15, 45, 27, 57, 20, 50, 29, 59, 16, 46, 28, 58)(61, 91, 63, 93, 73, 103, 88, 118, 70, 100, 82, 112, 79, 109, 90, 120, 80, 110, 66, 96)(62, 92, 69, 99, 85, 115, 75, 105, 84, 114, 77, 107, 67, 97, 74, 104, 89, 119, 71, 101)(64, 94, 68, 98, 83, 113, 81, 111, 87, 117, 78, 108, 65, 95, 72, 102, 86, 116, 76, 106) L = (1, 64)(2, 70)(3, 68)(4, 75)(5, 71)(6, 76)(7, 61)(8, 84)(9, 82)(10, 87)(11, 88)(12, 62)(13, 83)(14, 63)(15, 90)(16, 85)(17, 66)(18, 89)(19, 65)(20, 86)(21, 67)(22, 78)(23, 77)(24, 80)(25, 79)(26, 69)(27, 74)(28, 81)(29, 73)(30, 72)(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, 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 E23.63 Graph:: bipartite v = 8 e = 60 f = 8 degree seq :: [ 12^5, 20^3 ] E23.59 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 6, 10, 15}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y3^-3 * Y2, (Y3^-1, Y1^-1), (Y2^-1, Y1^-1), Y3 * Y1 * Y2^-2, Y3 * Y2 * Y3 * Y1^-1, Y2^2 * Y3^-1 * Y1^-1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y1^6, Y1^-1 * Y3^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1, Y3 * Y1 * Y2^8 ] Map:: non-degenerate R = (1, 31, 2, 32, 8, 38, 18, 48, 15, 45, 5, 35)(3, 33, 9, 39, 19, 49, 27, 57, 23, 53, 13, 43)(4, 34, 10, 40, 20, 50, 28, 58, 24, 54, 14, 44)(6, 36, 11, 41, 21, 51, 29, 59, 25, 55, 16, 46)(7, 37, 12, 42, 22, 52, 30, 60, 26, 56, 17, 47)(61, 91, 63, 93, 70, 100, 82, 112, 89, 119, 78, 108, 87, 117, 84, 114, 77, 107, 66, 96)(62, 92, 69, 99, 80, 110, 90, 120, 85, 115, 75, 105, 83, 113, 74, 104, 67, 97, 71, 101)(64, 94, 72, 102, 81, 111, 68, 98, 79, 109, 88, 118, 86, 116, 76, 106, 65, 95, 73, 103) L = (1, 64)(2, 70)(3, 72)(4, 71)(5, 74)(6, 73)(7, 61)(8, 80)(9, 82)(10, 81)(11, 63)(12, 62)(13, 67)(14, 66)(15, 84)(16, 83)(17, 65)(18, 88)(19, 90)(20, 89)(21, 69)(22, 68)(23, 77)(24, 76)(25, 87)(26, 75)(27, 86)(28, 85)(29, 79)(30, 78)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 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 E23.61 Graph:: bipartite v = 8 e = 60 f = 8 degree seq :: [ 12^5, 20^3 ] E23.60 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 6, 10, 15}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y3^-2 * Y1 * Y2, Y2^-2 * Y3^-1 * Y1^-1, (Y3, Y2^-1), Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1, Y3^-2 * Y2^-1 * Y3^-1, (R * Y3)^2, Y2^-1 * Y3^-1 * Y2^-1 * Y1^-1, (Y3^-1, Y1^-1), (R * Y1)^2, Y3 * Y2^-1 * Y3 * Y1^-1, (Y1, Y2^-1), (R * Y2)^2, Y1^6, Y1^-1 * Y3^-1 * Y2^8, Y1 * Y2^-2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y3 * Y2^-1 * Y1 ] Map:: non-degenerate R = (1, 31, 2, 32, 8, 38, 18, 48, 17, 47, 5, 35)(3, 33, 9, 39, 19, 49, 27, 57, 26, 56, 15, 45)(4, 34, 10, 40, 20, 50, 28, 58, 23, 53, 16, 46)(6, 36, 11, 41, 21, 51, 29, 59, 25, 55, 14, 44)(7, 37, 12, 42, 22, 52, 30, 60, 24, 54, 13, 43)(61, 91, 63, 93, 73, 103, 83, 113, 89, 119, 78, 108, 87, 117, 82, 112, 70, 100, 66, 96)(62, 92, 69, 99, 67, 97, 76, 106, 85, 115, 77, 107, 86, 116, 90, 120, 80, 110, 71, 101)(64, 94, 74, 104, 65, 95, 75, 105, 84, 114, 88, 118, 81, 111, 68, 98, 79, 109, 72, 102) L = (1, 64)(2, 70)(3, 74)(4, 69)(5, 76)(6, 72)(7, 61)(8, 80)(9, 66)(10, 79)(11, 82)(12, 62)(13, 65)(14, 67)(15, 85)(16, 63)(17, 83)(18, 88)(19, 71)(20, 87)(21, 90)(22, 68)(23, 75)(24, 77)(25, 73)(26, 89)(27, 81)(28, 86)(29, 84)(30, 78)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 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 E23.62 Graph:: bipartite v = 8 e = 60 f = 8 degree seq :: [ 12^5, 20^3 ] E23.61 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 6, 10, 15}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-1 * Y3, Y2^-1 * Y1^3, Y1^3 * Y2^-1, (Y3^-1, Y2), (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y1 * Y3 * Y1 * Y2^-1 * Y3, Y2^5 ] Map:: non-degenerate R = (1, 31, 2, 32, 8, 38, 3, 33, 9, 39, 20, 50, 12, 42, 21, 51, 27, 57, 18, 48, 23, 53, 16, 46, 6, 36, 11, 41, 5, 35)(4, 34, 10, 40, 14, 44, 13, 43, 22, 52, 25, 55, 24, 54, 30, 60, 29, 59, 26, 56, 28, 58, 19, 49, 15, 45, 17, 47, 7, 37)(61, 91, 63, 93, 72, 102, 78, 108, 66, 96)(62, 92, 69, 99, 81, 111, 83, 113, 71, 101)(64, 94, 73, 103, 84, 114, 86, 116, 75, 105)(65, 95, 68, 98, 80, 110, 87, 117, 76, 106)(67, 97, 74, 104, 85, 115, 89, 119, 79, 109)(70, 100, 82, 112, 90, 120, 88, 118, 77, 107) L = (1, 64)(2, 70)(3, 73)(4, 62)(5, 67)(6, 75)(7, 61)(8, 74)(9, 82)(10, 68)(11, 77)(12, 84)(13, 69)(14, 63)(15, 71)(16, 79)(17, 65)(18, 86)(19, 66)(20, 85)(21, 90)(22, 80)(23, 88)(24, 81)(25, 72)(26, 83)(27, 89)(28, 76)(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) :: { ( 12, 20, 12, 20, 12, 20, 12, 20, 12, 20 ), ( 12, 20, 12, 20, 12, 20, 12, 20, 12, 20, 12, 20, 12, 20, 12, 20, 12, 20, 12, 20, 12, 20, 12, 20, 12, 20, 12, 20, 12, 20 ) } Outer automorphisms :: reflexible Dual of E23.59 Graph:: bipartite v = 8 e = 60 f = 8 degree seq :: [ 10^6, 30^2 ] E23.62 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 6, 10, 15}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y3^-2 * Y1 * Y2, Y3^-2 * Y2 * Y1, (R * Y2)^2, (Y3^-1, Y2^-1), (Y3^-1, Y1^-1), (Y1, Y2^-1), (R * Y3)^2, (R * Y1)^2, Y1^3 * Y2^2, Y2^5, Y1 * Y2^-2 * Y1 * Y2^-1 * Y1, (Y1^-1 * Y3^-1)^10 ] Map:: non-degenerate R = (1, 31, 2, 32, 8, 38, 20, 50, 24, 54, 15, 45, 3, 33, 9, 39, 18, 48, 6, 36, 11, 41, 22, 52, 13, 43, 17, 47, 5, 35)(4, 34, 10, 40, 21, 51, 25, 55, 30, 60, 27, 57, 14, 44, 19, 49, 7, 37, 12, 42, 23, 53, 29, 59, 26, 56, 28, 58, 16, 46)(61, 91, 63, 93, 73, 103, 80, 110, 66, 96)(62, 92, 69, 99, 77, 107, 84, 114, 71, 101)(64, 94, 74, 104, 86, 116, 85, 115, 72, 102)(65, 95, 75, 105, 82, 112, 68, 98, 78, 108)(67, 97, 76, 106, 87, 117, 89, 119, 81, 111)(70, 100, 79, 109, 88, 118, 90, 120, 83, 113) L = (1, 64)(2, 70)(3, 74)(4, 69)(5, 76)(6, 72)(7, 61)(8, 81)(9, 79)(10, 78)(11, 83)(12, 62)(13, 86)(14, 77)(15, 87)(16, 63)(17, 88)(18, 67)(19, 65)(20, 85)(21, 66)(22, 89)(23, 68)(24, 90)(25, 71)(26, 84)(27, 73)(28, 75)(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, 20, 12, 20, 12, 20, 12, 20, 12, 20 ), ( 12, 20, 12, 20, 12, 20, 12, 20, 12, 20, 12, 20, 12, 20, 12, 20, 12, 20, 12, 20, 12, 20, 12, 20, 12, 20, 12, 20, 12, 20 ) } Outer automorphisms :: reflexible Dual of E23.60 Graph:: bipartite v = 8 e = 60 f = 8 degree seq :: [ 10^6, 30^2 ] E23.63 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 6, 10, 15}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1^-3, Y2^-1 * Y3^-1 * Y1 * Y3^-1, Y3 * Y2 * Y1^-1 * Y3, (Y2^-1, Y1^-1), (Y1, Y3^-1), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y2^5, (Y3 * Y2^-1)^6, (Y1^-1 * Y3^-1)^10 ] Map:: non-degenerate R = (1, 31, 2, 32, 8, 38, 6, 36, 11, 41, 21, 51, 19, 49, 26, 56, 27, 57, 13, 43, 23, 53, 14, 44, 3, 33, 9, 39, 5, 35)(4, 34, 10, 40, 20, 50, 17, 47, 25, 55, 28, 58, 30, 60, 29, 59, 15, 45, 24, 54, 18, 48, 7, 37, 12, 42, 22, 52, 16, 46)(61, 91, 63, 93, 73, 103, 79, 109, 66, 96)(62, 92, 69, 99, 83, 113, 86, 116, 71, 101)(64, 94, 72, 102, 84, 114, 90, 120, 77, 107)(65, 95, 74, 104, 87, 117, 81, 111, 68, 98)(67, 97, 75, 105, 88, 118, 80, 110, 76, 106)(70, 100, 82, 112, 78, 108, 89, 119, 85, 115) L = (1, 64)(2, 70)(3, 72)(4, 71)(5, 76)(6, 77)(7, 61)(8, 80)(9, 82)(10, 81)(11, 85)(12, 62)(13, 84)(14, 67)(15, 63)(16, 66)(17, 86)(18, 65)(19, 90)(20, 79)(21, 88)(22, 68)(23, 78)(24, 69)(25, 87)(26, 89)(27, 75)(28, 73)(29, 74)(30, 83)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 12, 20, 12, 20, 12, 20, 12, 20, 12, 20 ), ( 12, 20, 12, 20, 12, 20, 12, 20, 12, 20, 12, 20, 12, 20, 12, 20, 12, 20, 12, 20, 12, 20, 12, 20, 12, 20, 12, 20, 12, 20 ) } Outer automorphisms :: reflexible Dual of E23.58 Graph:: bipartite v = 8 e = 60 f = 8 degree seq :: [ 10^6, 30^2 ] E23.64 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 6, 10, 15}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y3^-1 * Y2^-1, (Y2^-1, Y1), (R * Y1)^2, (Y3^-1, Y1), (R * Y3)^2, (R * Y2)^2, Y3 * Y1^-1 * Y3 * Y1^-1 * Y3, Y1^-4 * Y2 * Y3^-1, Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y2^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 31, 2, 32, 8, 38, 22, 52, 14, 44, 26, 56, 17, 47, 28, 58, 18, 48, 5, 35)(3, 33, 9, 39, 23, 53, 30, 60, 21, 51, 16, 46, 4, 34, 10, 40, 24, 54, 13, 43)(6, 36, 11, 41, 25, 55, 20, 50, 7, 37, 12, 42, 15, 45, 27, 57, 29, 59, 19, 49)(61, 91, 63, 93, 67, 97, 74, 104, 81, 111, 89, 119, 78, 108, 84, 114, 85, 115, 68, 98, 83, 113, 75, 105, 77, 107, 64, 94, 66, 96)(62, 92, 69, 99, 72, 102, 86, 116, 76, 106, 79, 109, 65, 95, 73, 103, 80, 110, 82, 112, 90, 120, 87, 117, 88, 118, 70, 100, 71, 101) L = (1, 64)(2, 70)(3, 66)(4, 75)(5, 76)(6, 77)(7, 61)(8, 84)(9, 71)(10, 87)(11, 88)(12, 62)(13, 79)(14, 63)(15, 68)(16, 72)(17, 83)(18, 81)(19, 86)(20, 65)(21, 67)(22, 73)(23, 85)(24, 89)(25, 78)(26, 69)(27, 82)(28, 90)(29, 74)(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) :: { ( 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12 ), ( 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12 ) } Outer automorphisms :: reflexible Dual of E23.55 Graph:: bipartite v = 5 e = 60 f = 11 degree seq :: [ 20^3, 30^2 ] E23.65 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 6, 10, 15}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, (Y2, Y3^-1), Y3^-1 * Y2 * Y1^-2, Y1 * Y2^-1 * Y1 * Y3, (Y2, Y1^-1), Y1^-1 * Y2 * Y3^-1 * Y1^-1, (Y3^-1, Y2), (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y2 * Y3^-4, Y2^3 * Y1^2, Y2^-1 * Y3^-1 * Y2^-2 * Y3^-2 ] Map:: non-degenerate R = (1, 31, 2, 32, 8, 38, 22, 52, 28, 58, 30, 60, 27, 57, 29, 59, 17, 47, 5, 35)(3, 33, 9, 39, 19, 49, 25, 55, 20, 50, 26, 56, 21, 51, 16, 46, 4, 34, 10, 40)(6, 36, 11, 41, 7, 37, 12, 42, 15, 45, 24, 54, 14, 44, 23, 53, 13, 43, 18, 48)(61, 91, 63, 93, 73, 103, 77, 107, 64, 94, 74, 104, 87, 117, 81, 111, 75, 105, 88, 118, 80, 110, 67, 97, 68, 98, 79, 109, 66, 96)(62, 92, 69, 99, 78, 108, 65, 95, 70, 100, 83, 113, 89, 119, 76, 106, 84, 114, 90, 120, 86, 116, 72, 102, 82, 112, 85, 115, 71, 101) L = (1, 64)(2, 70)(3, 74)(4, 75)(5, 76)(6, 77)(7, 61)(8, 63)(9, 83)(10, 84)(11, 65)(12, 62)(13, 87)(14, 88)(15, 68)(16, 72)(17, 81)(18, 89)(19, 73)(20, 66)(21, 67)(22, 69)(23, 90)(24, 82)(25, 78)(26, 71)(27, 80)(28, 79)(29, 86)(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) :: { ( 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12 ), ( 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12 ) } Outer automorphisms :: reflexible Dual of E23.57 Graph:: bipartite v = 5 e = 60 f = 11 degree seq :: [ 20^3, 30^2 ] E23.66 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 6, 10, 15}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2 * Y3, Y1 * Y3^-1 * Y1 * Y2, (R * Y1)^2, (Y2^-1, Y1), (R * Y2)^2, Y3 * Y2^-1 * Y1^-2, (R * Y3)^2, Y2^2 * Y1^-1 * Y2^4 * Y1^-1, Y3^-1 * Y2 * Y1^-2 * Y2^2 * Y3^-1 * Y2^2, Y3 * Y2^-1 * Y1^8 ] Map:: non-degenerate R = (1, 31, 2, 32, 8, 38, 18, 48, 25, 55, 28, 58, 21, 51, 24, 54, 15, 45, 5, 35)(3, 33, 9, 39, 4, 34, 10, 40, 17, 47, 20, 50, 27, 57, 30, 60, 23, 53, 14, 44)(6, 36, 11, 41, 19, 49, 26, 56, 29, 59, 22, 52, 13, 43, 16, 46, 7, 37, 12, 42)(61, 91, 63, 93, 73, 103, 81, 111, 87, 117, 79, 109, 68, 98, 64, 94, 67, 97, 75, 105, 83, 113, 89, 119, 85, 115, 77, 107, 66, 96)(62, 92, 69, 99, 76, 106, 84, 114, 90, 120, 86, 116, 78, 108, 70, 100, 72, 102, 65, 95, 74, 104, 82, 112, 88, 118, 80, 110, 71, 101) L = (1, 64)(2, 70)(3, 67)(4, 66)(5, 69)(6, 68)(7, 61)(8, 77)(9, 72)(10, 71)(11, 78)(12, 62)(13, 75)(14, 76)(15, 63)(16, 65)(17, 79)(18, 80)(19, 85)(20, 86)(21, 83)(22, 84)(23, 73)(24, 74)(25, 87)(26, 88)(27, 89)(28, 90)(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, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12 ), ( 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12 ) } Outer automorphisms :: reflexible Dual of E23.56 Graph:: bipartite v = 5 e = 60 f = 11 degree seq :: [ 20^3, 30^2 ] E23.67 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 6, 10, 15}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y1^2 * Y2^-2, (R * Y2)^2, (R * Y1)^2, (Y3^-1, Y2^-1), (Y1, Y2), (Y3^-1, Y1^-1), (R * Y3)^2, Y3^3 * Y1^2, Y1^3 * Y2^2, Y1^-1 * Y3 * Y1^-1 * Y3^2 * Y1^-1, Y3 * Y2^-1 * Y3^2 * Y2^-1 * Y1^-1, Y2^10 ] Map:: non-degenerate R = (1, 31, 2, 32, 8, 38, 18, 48, 5, 35)(3, 33, 9, 39, 19, 49, 6, 36, 11, 41)(4, 34, 10, 40, 22, 52, 28, 58, 16, 46)(7, 37, 12, 42, 23, 53, 15, 45, 20, 50)(13, 43, 24, 54, 29, 59, 17, 47, 26, 56)(14, 44, 25, 55, 30, 60, 21, 51, 27, 57)(61, 91, 63, 93, 68, 98, 79, 109, 65, 95, 71, 101, 62, 92, 69, 99, 78, 108, 66, 96)(64, 94, 73, 103, 82, 112, 89, 119, 76, 106, 86, 116, 70, 100, 84, 114, 88, 118, 77, 107)(67, 97, 74, 104, 83, 113, 90, 120, 80, 110, 87, 117, 72, 102, 85, 115, 75, 105, 81, 111) L = (1, 64)(2, 70)(3, 73)(4, 75)(5, 76)(6, 77)(7, 61)(8, 82)(9, 84)(10, 80)(11, 86)(12, 62)(13, 81)(14, 63)(15, 78)(16, 83)(17, 85)(18, 88)(19, 89)(20, 65)(21, 66)(22, 67)(23, 68)(24, 87)(25, 69)(26, 90)(27, 71)(28, 72)(29, 74)(30, 79)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 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 E23.72 Graph:: bipartite v = 9 e = 60 f = 7 degree seq :: [ 10^6, 20^3 ] E23.68 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 6, 10, 15}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y2^2, Y3^-3 * Y1^-1, (Y3^-1, Y1^-1), (R * Y1)^2, (Y3^-1, Y2), (R * Y3)^2, (R * Y2)^2, Y3^-1 * Y2^-1 * Y3^-2 * Y2^-1, Y1^5, (Y2^-1 * Y3)^6 ] Map:: non-degenerate R = (1, 31, 2, 32, 8, 38, 17, 47, 5, 35)(3, 33, 9, 39, 20, 50, 18, 48, 6, 36)(4, 34, 10, 40, 21, 51, 27, 57, 15, 45)(7, 37, 11, 41, 22, 52, 25, 55, 14, 44)(12, 42, 23, 53, 29, 59, 28, 58, 16, 46)(13, 43, 24, 54, 30, 60, 26, 56, 19, 49)(61, 91, 63, 93, 62, 92, 69, 99, 68, 98, 80, 110, 77, 107, 78, 108, 65, 95, 66, 96)(64, 94, 72, 102, 70, 100, 83, 113, 81, 111, 89, 119, 87, 117, 88, 118, 75, 105, 76, 106)(67, 97, 73, 103, 71, 101, 84, 114, 82, 112, 90, 120, 85, 115, 86, 116, 74, 104, 79, 109) L = (1, 64)(2, 70)(3, 72)(4, 74)(5, 75)(6, 76)(7, 61)(8, 81)(9, 83)(10, 67)(11, 62)(12, 79)(13, 63)(14, 65)(15, 85)(16, 86)(17, 87)(18, 88)(19, 66)(20, 89)(21, 71)(22, 68)(23, 73)(24, 69)(25, 77)(26, 78)(27, 82)(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) :: { ( 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 E23.71 Graph:: bipartite v = 9 e = 60 f = 7 degree seq :: [ 10^6, 20^3 ] E23.69 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 6, 10, 15}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1 * Y2, Y3^3 * Y1^-1, (Y3^-1, Y2^-1), (R * Y2)^2, (R * Y1)^2, (Y1^-1, Y3^-1), (R * Y3)^2, Y1^5, Y1^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1, Y1^-1 * Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 31, 2, 32, 8, 38, 17, 47, 5, 35)(3, 33, 6, 36, 10, 40, 21, 51, 13, 43)(4, 34, 9, 39, 20, 50, 27, 57, 15, 45)(7, 37, 11, 41, 22, 52, 28, 58, 18, 48)(12, 42, 16, 46, 23, 53, 29, 59, 25, 55)(14, 44, 19, 49, 24, 54, 30, 60, 26, 56)(61, 91, 63, 93, 65, 95, 73, 103, 77, 107, 81, 111, 68, 98, 70, 100, 62, 92, 66, 96)(64, 94, 72, 102, 75, 105, 85, 115, 87, 117, 89, 119, 80, 110, 83, 113, 69, 99, 76, 106)(67, 97, 74, 104, 78, 108, 86, 116, 88, 118, 90, 120, 82, 112, 84, 114, 71, 101, 79, 109) L = (1, 64)(2, 69)(3, 72)(4, 71)(5, 75)(6, 76)(7, 61)(8, 80)(9, 82)(10, 83)(11, 62)(12, 79)(13, 85)(14, 63)(15, 67)(16, 84)(17, 87)(18, 65)(19, 66)(20, 88)(21, 89)(22, 68)(23, 90)(24, 70)(25, 74)(26, 73)(27, 78)(28, 77)(29, 86)(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) :: { ( 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 E23.70 Graph:: bipartite v = 9 e = 60 f = 7 degree seq :: [ 10^6, 20^3 ] E23.70 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 6, 10, 15}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^2, Y3 * Y1^-1 * Y2^-2, Y1 * Y2 * Y3^-1 * Y2, Y1^-1 * Y3 * Y2^-2, (Y1, Y2^-1), (Y3^-1, Y1^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y1^6, Y1^-1 * Y3^-1 * Y2^12 ] Map:: non-degenerate R = (1, 31, 2, 32, 8, 38, 18, 48, 16, 46, 5, 35)(3, 33, 9, 39, 19, 49, 27, 57, 24, 54, 14, 44)(4, 34, 10, 40, 20, 50, 28, 58, 23, 53, 13, 43)(6, 36, 11, 41, 21, 51, 29, 59, 25, 55, 15, 45)(7, 37, 12, 42, 22, 52, 30, 60, 26, 56, 17, 47)(61, 91, 63, 93, 73, 103, 77, 107, 85, 115, 76, 106, 84, 114, 88, 118, 90, 120, 81, 111, 68, 98, 79, 109, 70, 100, 72, 102, 66, 96)(62, 92, 69, 99, 64, 94, 67, 97, 75, 105, 65, 95, 74, 104, 83, 113, 86, 116, 89, 119, 78, 108, 87, 117, 80, 110, 82, 112, 71, 101) L = (1, 64)(2, 70)(3, 67)(4, 66)(5, 73)(6, 69)(7, 61)(8, 80)(9, 72)(10, 71)(11, 79)(12, 62)(13, 75)(14, 77)(15, 63)(16, 83)(17, 65)(18, 88)(19, 82)(20, 81)(21, 87)(22, 68)(23, 85)(24, 86)(25, 74)(26, 76)(27, 90)(28, 89)(29, 84)(30, 78)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 10, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20 ), ( 10, 20, 10, 20, 10, 20, 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 E23.69 Graph:: bipartite v = 7 e = 60 f = 9 degree seq :: [ 12^5, 30^2 ] E23.71 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 6, 10, 15}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y2 * Y3, Y1^-1 * Y3 * Y2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y3^-3 * Y2 * Y3^-1, Y1^6, Y1 * Y2^5 * Y1, Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-2 * Y1^-2 ] Map:: non-degenerate R = (1, 31, 2, 32, 8, 38, 20, 50, 15, 45, 5, 35)(3, 33, 9, 39, 21, 51, 28, 58, 17, 47, 7, 37)(4, 34, 10, 40, 22, 52, 27, 57, 16, 46, 6, 36)(11, 41, 23, 53, 30, 60, 26, 56, 19, 49, 12, 42)(13, 43, 24, 54, 25, 55, 29, 59, 18, 48, 14, 44)(61, 91, 63, 93, 71, 101, 85, 115, 87, 117, 75, 105, 77, 107, 79, 109, 73, 103, 70, 100, 68, 98, 81, 111, 90, 120, 78, 108, 66, 96)(62, 92, 69, 99, 83, 113, 89, 119, 76, 106, 65, 95, 67, 97, 72, 102, 84, 114, 82, 112, 80, 110, 88, 118, 86, 116, 74, 104, 64, 94) L = (1, 64)(2, 70)(3, 62)(4, 73)(5, 66)(6, 74)(7, 61)(8, 82)(9, 68)(10, 84)(11, 69)(12, 63)(13, 72)(14, 79)(15, 76)(16, 78)(17, 65)(18, 86)(19, 67)(20, 87)(21, 80)(22, 85)(23, 81)(24, 71)(25, 83)(26, 77)(27, 89)(28, 75)(29, 90)(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, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20 ), ( 10, 20, 10, 20, 10, 20, 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 E23.68 Graph:: bipartite v = 7 e = 60 f = 9 degree seq :: [ 12^5, 30^2 ] E23.72 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {5, 6, 10, 15}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, (R * Y1)^2, (Y2^-1, Y1), (R * Y2)^2, (Y3^-1, Y2), (Y1, Y3^-1), (R * Y3)^2, Y3 * Y1 * Y3^2 * Y2, Y3 * Y1 * Y2 * Y3^2, Y2^-1 * Y1^-2 * Y3^2, Y3 * Y1 * Y2^-3, Y2^-1 * Y1 * Y2^-1 * Y3 * Y2^-1, Y2 * Y1^-3 * Y2 * Y3 ] Map:: non-degenerate R = (1, 31, 2, 32, 8, 38, 26, 56, 20, 50, 5, 35)(3, 33, 9, 39, 17, 47, 24, 54, 30, 60, 15, 45)(4, 34, 10, 40, 27, 57, 23, 53, 16, 46, 18, 48)(6, 36, 11, 41, 28, 58, 14, 44, 25, 55, 21, 51)(7, 37, 12, 42, 19, 49, 13, 43, 29, 59, 22, 52)(61, 91, 63, 93, 73, 103, 70, 100, 85, 115, 80, 110, 90, 120, 72, 102, 78, 108, 88, 118, 68, 98, 77, 107, 82, 112, 83, 113, 66, 96)(62, 92, 69, 99, 89, 119, 87, 117, 81, 111, 65, 95, 75, 105, 79, 109, 64, 94, 74, 104, 86, 116, 84, 114, 67, 97, 76, 106, 71, 101) L = (1, 64)(2, 70)(3, 74)(4, 77)(5, 78)(6, 79)(7, 61)(8, 87)(9, 85)(10, 84)(11, 73)(12, 62)(13, 86)(14, 82)(15, 88)(16, 63)(17, 81)(18, 69)(19, 68)(20, 76)(21, 72)(22, 65)(23, 75)(24, 66)(25, 67)(26, 83)(27, 90)(28, 89)(29, 80)(30, 71)(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, 20, 10, 20, 10, 20, 10, 20, 10, 20, 10, 20 ), ( 10, 20, 10, 20, 10, 20, 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 E23.67 Graph:: bipartite v = 7 e = 60 f = 9 degree seq :: [ 12^5, 30^2 ] E23.73 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 10, 15, 30}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y2 * Y3, Y1^-1 * Y3 * Y2, Y1^3, Y1 * Y2 * Y1 * Y3, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y3^6 * Y2^-4, Y2^10, (Y3^-1 * Y2)^15 ] Map:: non-degenerate R = (1, 31, 2, 32, 5, 35)(3, 33, 8, 38, 7, 37)(4, 34, 9, 39, 6, 36)(10, 40, 15, 45, 11, 41)(12, 42, 14, 44, 13, 43)(16, 46, 18, 48, 17, 47)(19, 49, 21, 51, 20, 50)(22, 52, 24, 54, 23, 53)(25, 55, 27, 57, 26, 56)(28, 58, 30, 60, 29, 59)(61, 91, 63, 93, 70, 100, 76, 106, 82, 112, 88, 118, 86, 116, 79, 109, 74, 104, 66, 96)(62, 92, 68, 98, 75, 105, 78, 108, 84, 114, 90, 120, 85, 115, 81, 111, 73, 103, 64, 94)(65, 95, 67, 97, 71, 101, 77, 107, 83, 113, 89, 119, 87, 117, 80, 110, 72, 102, 69, 99) L = (1, 64)(2, 69)(3, 62)(4, 72)(5, 66)(6, 73)(7, 61)(8, 65)(9, 74)(10, 68)(11, 63)(12, 79)(13, 80)(14, 81)(15, 67)(16, 75)(17, 70)(18, 71)(19, 85)(20, 86)(21, 87)(22, 78)(23, 76)(24, 77)(25, 89)(26, 90)(27, 88)(28, 84)(29, 82)(30, 83)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 30, 60, 30, 60, 30, 60 ), ( 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60 ) } Outer automorphisms :: reflexible Dual of E23.83 Graph:: bipartite v = 13 e = 60 f = 3 degree seq :: [ 6^10, 20^3 ] E23.74 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 10, 15, 30}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y1^3, (Y3, Y1^-1), Y3^-2 * Y2 * Y3^-1, (Y2^-1, Y1^-1), (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y3^-1 * Y2^-1 * Y1 * Y2^-1, Y2^10, Y2^-1 * Y1^-3 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 31, 2, 32, 5, 35)(3, 33, 8, 38, 14, 44)(4, 34, 9, 39, 16, 46)(6, 36, 10, 40, 18, 48)(7, 37, 11, 41, 19, 49)(12, 42, 22, 52, 21, 51)(13, 43, 23, 53, 20, 50)(15, 45, 24, 54, 27, 57)(17, 47, 25, 55, 28, 58)(26, 56, 30, 60, 29, 59)(61, 91, 63, 93, 72, 102, 71, 101, 84, 114, 90, 120, 88, 118, 76, 106, 80, 110, 66, 96)(62, 92, 68, 98, 82, 112, 79, 109, 87, 117, 89, 119, 77, 107, 64, 94, 73, 103, 70, 100)(65, 95, 74, 104, 81, 111, 67, 97, 75, 105, 86, 116, 85, 115, 69, 99, 83, 113, 78, 108) L = (1, 64)(2, 69)(3, 73)(4, 75)(5, 76)(6, 77)(7, 61)(8, 83)(9, 84)(10, 85)(11, 62)(12, 70)(13, 86)(14, 80)(15, 63)(16, 87)(17, 67)(18, 88)(19, 65)(20, 89)(21, 66)(22, 78)(23, 90)(24, 68)(25, 71)(26, 72)(27, 74)(28, 79)(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) :: { ( 30, 60, 30, 60, 30, 60 ), ( 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60 ) } Outer automorphisms :: reflexible Dual of E23.84 Graph:: bipartite v = 13 e = 60 f = 3 degree seq :: [ 6^10, 20^3 ] E23.75 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 10, 15, 30}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y1^3, (Y1, Y3), (Y2^-1, Y1), (R * Y2)^2, (R * Y3)^2, Y3^-3 * Y2^-1, (Y2^-1, Y3^-1), (R * Y1)^2, Y2^3 * Y3^-1 * Y1, Y3^-1 * Y2 * Y1^-1 * Y2^2 * Y1^-1, Y2 * Y1 * Y3 * Y2 * Y1 * Y3 * Y2 * Y1 * Y3 * Y2 * Y1 * Y3^-1, (Y2 * Y3 * Y1)^15 ] Map:: non-degenerate R = (1, 31, 2, 32, 5, 35)(3, 33, 8, 38, 14, 44)(4, 34, 9, 39, 17, 47)(6, 36, 10, 40, 19, 49)(7, 37, 11, 41, 20, 50)(12, 42, 18, 48, 24, 54)(13, 43, 22, 52, 27, 57)(15, 45, 21, 51, 25, 55)(16, 46, 23, 53, 28, 58)(26, 56, 29, 59, 30, 60)(61, 91, 63, 93, 72, 102, 77, 107, 87, 117, 90, 120, 83, 113, 71, 101, 81, 111, 66, 96)(62, 92, 68, 98, 78, 108, 64, 94, 73, 103, 86, 116, 88, 118, 80, 110, 85, 115, 70, 100)(65, 95, 74, 104, 84, 114, 69, 99, 82, 112, 89, 119, 76, 106, 67, 97, 75, 105, 79, 109) L = (1, 64)(2, 69)(3, 73)(4, 76)(5, 77)(6, 78)(7, 61)(8, 82)(9, 83)(10, 84)(11, 62)(12, 86)(13, 67)(14, 87)(15, 63)(16, 66)(17, 88)(18, 89)(19, 72)(20, 65)(21, 68)(22, 71)(23, 70)(24, 90)(25, 74)(26, 75)(27, 80)(28, 79)(29, 81)(30, 85)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 30, 60, 30, 60, 30, 60 ), ( 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60, 30, 60 ) } Outer automorphisms :: reflexible Dual of E23.82 Graph:: bipartite v = 13 e = 60 f = 3 degree seq :: [ 6^10, 20^3 ] E23.76 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 10, 15, 30}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y3^-2 * Y2^-1, (Y1^-1, Y3^-1), (R * Y1)^2, (Y2^-1, Y3), (Y2^-1 * Y3^-1)^2, (R * Y3)^2, (R * Y2)^2, (Y2^-1, Y1), Y1 * Y3^-1 * Y1 * Y2 * Y3^-1, Y2^3 * Y1^2, Y3^-1 * Y1^-1 * Y2^2 * Y1^-2, Y1^10, Y3^-1 * Y1^3 * Y2^-1 * Y1^2 * Y2^-1 * Y1^2 * Y2^-1 * Y1^2 * Y2^-1 * Y1^2 * Y2^-1 * Y1^2 * Y2^-1 * Y1^2 * Y2^-1 * Y1^2 * Y2^-1 * Y1^2 * Y2^-1 * Y1^2 * Y2^-1 * Y1^2 * Y2^-1 * Y1^2 * Y2^-1 * Y1^2 * Y2^-1 ] Map:: non-degenerate R = (1, 31, 2, 32, 8, 38, 23, 53, 29, 59, 14, 44, 26, 56, 30, 60, 20, 50, 5, 35)(3, 33, 9, 39, 17, 47, 27, 57, 22, 52, 7, 37, 12, 42, 19, 49, 28, 58, 15, 45)(4, 34, 10, 40, 24, 54, 13, 43, 21, 51, 6, 36, 11, 41, 25, 55, 16, 46, 18, 48)(61, 91, 63, 93, 73, 103, 80, 110, 88, 118, 70, 100, 86, 116, 72, 102, 78, 108, 89, 119, 82, 112, 85, 115, 68, 98, 77, 107, 66, 96)(62, 92, 69, 99, 81, 111, 65, 95, 75, 105, 84, 114, 90, 120, 79, 109, 64, 94, 74, 104, 67, 97, 76, 106, 83, 113, 87, 117, 71, 101) L = (1, 64)(2, 70)(3, 74)(4, 77)(5, 78)(6, 79)(7, 61)(8, 84)(9, 86)(10, 87)(11, 88)(12, 62)(13, 67)(14, 66)(15, 89)(16, 63)(17, 90)(18, 69)(19, 68)(20, 76)(21, 72)(22, 65)(23, 73)(24, 82)(25, 75)(26, 71)(27, 80)(28, 83)(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) :: { ( 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60 ), ( 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60 ) } Outer automorphisms :: reflexible Dual of E23.81 Graph:: bipartite v = 5 e = 60 f = 11 degree seq :: [ 20^3, 30^2 ] E23.77 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 10, 15, 30}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y3^2 * Y2^-1, (Y1, Y3), (Y1, Y2^-1), (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y1^-1 * Y3^-1 * Y1^-2, Y2^3 * Y3 * Y1^-1 * Y2, Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 ] Map:: non-degenerate R = (1, 31, 2, 32, 8, 38, 21, 51, 26, 56, 30, 60, 28, 58, 14, 44, 17, 47, 5, 35)(3, 33, 9, 39, 19, 49, 7, 37, 12, 42, 23, 53, 20, 50, 25, 55, 29, 59, 15, 45)(4, 34, 10, 40, 18, 48, 6, 36, 11, 41, 22, 52, 27, 57, 13, 43, 24, 54, 16, 46)(61, 91, 63, 93, 73, 103, 86, 116, 72, 102, 70, 100, 77, 107, 89, 119, 82, 112, 68, 98, 79, 109, 76, 106, 88, 118, 80, 110, 66, 96)(62, 92, 69, 99, 84, 114, 90, 120, 83, 113, 78, 108, 65, 95, 75, 105, 87, 117, 81, 111, 67, 97, 64, 94, 74, 104, 85, 115, 71, 101) L = (1, 64)(2, 70)(3, 74)(4, 63)(5, 76)(6, 67)(7, 61)(8, 78)(9, 77)(10, 69)(11, 72)(12, 62)(13, 85)(14, 73)(15, 88)(16, 75)(17, 84)(18, 79)(19, 65)(20, 81)(21, 66)(22, 83)(23, 68)(24, 89)(25, 86)(26, 71)(27, 80)(28, 87)(29, 90)(30, 82)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60 ), ( 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60 ) } Outer automorphisms :: reflexible Dual of E23.79 Graph:: bipartite v = 5 e = 60 f = 11 degree seq :: [ 20^3, 30^2 ] E23.78 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 10, 15, 30}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y2 * Y3, Y1^-1 * Y3 * Y2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3^-2 * Y2^4, Y1^3 * Y3^3, Y2^3 * Y3^-2 * Y2, (Y3^-1 * Y1^-1)^3, (Y3 * Y2^-1)^30 ] Map:: non-degenerate R = (1, 31, 2, 32, 8, 38, 20, 50, 27, 57, 26, 56, 25, 55, 28, 58, 15, 45, 5, 35)(3, 33, 9, 39, 21, 51, 30, 60, 18, 48, 14, 44, 13, 43, 24, 54, 17, 47, 7, 37)(4, 34, 10, 40, 22, 52, 19, 49, 12, 42, 11, 41, 23, 53, 29, 59, 16, 46, 6, 36)(61, 91, 63, 93, 71, 101, 85, 115, 73, 103, 70, 100, 68, 98, 81, 111, 89, 119, 75, 105, 77, 107, 79, 109, 87, 117, 78, 108, 66, 96)(62, 92, 69, 99, 83, 113, 88, 118, 84, 114, 82, 112, 80, 110, 90, 120, 76, 106, 65, 95, 67, 97, 72, 102, 86, 116, 74, 104, 64, 94) L = (1, 64)(2, 70)(3, 62)(4, 73)(5, 66)(6, 74)(7, 61)(8, 82)(9, 68)(10, 84)(11, 69)(12, 63)(13, 88)(14, 85)(15, 76)(16, 78)(17, 65)(18, 86)(19, 67)(20, 79)(21, 80)(22, 77)(23, 81)(24, 75)(25, 83)(26, 71)(27, 72)(28, 89)(29, 90)(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) :: { ( 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60 ), ( 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60, 6, 60 ) } Outer automorphisms :: reflexible Dual of E23.80 Graph:: bipartite v = 5 e = 60 f = 11 degree seq :: [ 20^3, 30^2 ] E23.79 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 10, 15, 30}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-1, Y2^3, (R * Y3)^2, (R * Y1)^2, (Y2, Y1^-1), (R * Y2 * Y3^-1)^2, Y2^-1 * Y1^10, (Y3 * Y2^-1)^10, (Y3^-1 * Y1^-1)^15 ] Map:: non-degenerate R = (1, 31, 2, 32, 6, 36, 12, 42, 18, 48, 24, 54, 27, 57, 21, 51, 15, 45, 9, 39, 3, 33, 7, 37, 13, 43, 19, 49, 25, 55, 30, 60, 29, 59, 23, 53, 17, 47, 11, 41, 5, 35, 8, 38, 14, 44, 20, 50, 26, 56, 28, 58, 22, 52, 16, 46, 10, 40, 4, 34)(61, 91, 63, 93, 65, 95)(62, 92, 67, 97, 68, 98)(64, 94, 69, 99, 71, 101)(66, 96, 73, 103, 74, 104)(70, 100, 75, 105, 77, 107)(72, 102, 79, 109, 80, 110)(76, 106, 81, 111, 83, 113)(78, 108, 85, 115, 86, 116)(82, 112, 87, 117, 89, 119)(84, 114, 90, 120, 88, 118) L = (1, 62)(2, 66)(3, 67)(4, 61)(5, 68)(6, 72)(7, 73)(8, 74)(9, 63)(10, 64)(11, 65)(12, 78)(13, 79)(14, 80)(15, 69)(16, 70)(17, 71)(18, 84)(19, 85)(20, 86)(21, 75)(22, 76)(23, 77)(24, 87)(25, 90)(26, 88)(27, 81)(28, 82)(29, 83)(30, 89)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 20, 30, 20, 30, 20, 30 ), ( 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30 ) } Outer automorphisms :: reflexible Dual of E23.77 Graph:: bipartite v = 11 e = 60 f = 5 degree seq :: [ 6^10, 60 ] E23.80 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 10, 15, 30}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y2^3, (R * Y1)^2, (Y1^-1, Y3^-1), (Y1, Y2^-1), (R * Y2)^2, (Y2^-1, Y3), (R * Y3)^2, Y3^3 * Y1 * Y2^-1, Y2^-1 * Y1^-1 * Y3 * Y1^-2, Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y3^-1, Y3 * Y2 * Y1^-1 * Y2 * Y1^-2 ] Map:: non-degenerate R = (1, 31, 2, 32, 8, 38, 18, 48, 23, 53, 28, 58, 29, 59, 22, 52, 27, 57, 14, 44, 3, 33, 9, 39, 17, 47, 4, 34, 10, 40, 24, 54, 21, 51, 7, 37, 12, 42, 20, 50, 6, 36, 11, 41, 25, 55, 13, 43, 26, 56, 30, 60, 16, 46, 15, 45, 19, 49, 5, 35)(61, 91, 63, 93, 66, 96)(62, 92, 69, 99, 71, 101)(64, 94, 73, 103, 78, 108)(65, 95, 74, 104, 80, 110)(67, 97, 75, 105, 82, 112)(68, 98, 77, 107, 85, 115)(70, 100, 86, 116, 83, 113)(72, 102, 79, 109, 87, 117)(76, 106, 89, 119, 81, 111)(84, 114, 90, 120, 88, 118) L = (1, 64)(2, 70)(3, 73)(4, 76)(5, 77)(6, 78)(7, 61)(8, 84)(9, 86)(10, 75)(11, 83)(12, 62)(13, 89)(14, 85)(15, 63)(16, 74)(17, 90)(18, 81)(19, 69)(20, 68)(21, 65)(22, 66)(23, 67)(24, 79)(25, 88)(26, 82)(27, 71)(28, 72)(29, 80)(30, 87)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 20, 30, 20, 30, 20, 30 ), ( 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30 ) } Outer automorphisms :: reflexible Dual of E23.78 Graph:: bipartite v = 11 e = 60 f = 5 degree seq :: [ 6^10, 60 ] E23.81 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 10, 15, 30}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y2^3, (R * Y2)^2, (R * Y3)^2, (Y3, Y1), (R * Y1)^2, (Y3, Y2), (Y2^-1, Y1^-1), Y3 * Y1^-1 * Y3^2 * Y2, Y2^-1 * Y1 * Y3^-3, Y3 * Y1^3 * Y2^-1, Y1^2 * Y3 * Y1 * Y2^-1, Y1^-1 * Y3 * Y2^-1 * Y3^2 * Y2^-1, Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y1^2 ] Map:: non-degenerate R = (1, 31, 2, 32, 8, 38, 15, 45, 27, 57, 30, 60, 17, 47, 4, 34, 10, 40, 14, 44, 3, 33, 9, 39, 24, 54, 22, 52, 16, 46, 28, 58, 23, 53, 13, 43, 26, 56, 20, 50, 6, 36, 11, 41, 21, 51, 7, 37, 12, 42, 25, 55, 29, 59, 18, 48, 19, 49, 5, 35)(61, 91, 63, 93, 66, 96)(62, 92, 69, 99, 71, 101)(64, 94, 73, 103, 78, 108)(65, 95, 74, 104, 80, 110)(67, 97, 75, 105, 82, 112)(68, 98, 84, 114, 81, 111)(70, 100, 86, 116, 79, 109)(72, 102, 87, 117, 76, 106)(77, 107, 83, 113, 89, 119)(85, 115, 90, 120, 88, 118) L = (1, 64)(2, 70)(3, 73)(4, 76)(5, 77)(6, 78)(7, 61)(8, 74)(9, 86)(10, 88)(11, 79)(12, 62)(13, 72)(14, 83)(15, 63)(16, 71)(17, 82)(18, 87)(19, 90)(20, 89)(21, 65)(22, 66)(23, 67)(24, 80)(25, 68)(26, 85)(27, 69)(28, 81)(29, 75)(30, 84)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 20, 30, 20, 30, 20, 30 ), ( 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30, 20, 30 ) } Outer automorphisms :: reflexible Dual of E23.76 Graph:: bipartite v = 11 e = 60 f = 5 degree seq :: [ 6^10, 60 ] E23.82 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 10, 15, 30}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, (Y3^-1, Y2), Y1^-2 * Y2^2, (Y2^-1 * Y1)^2, (Y3^-1, Y1^-1), (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y2^-3 * Y1^-1 * Y3^-1, Y3 * Y1 * Y3^3, Y1 * Y3 * Y2 * Y1^2, Y3 * Y1^2 * Y2 * Y1, Y1 * Y3^-1 * Y2 * Y3^-1 * Y1 * Y3^-1, (Y2^-1 * Y3^-1)^10 ] Map:: non-degenerate R = (1, 31, 2, 32, 8, 38, 21, 51, 26, 56, 14, 44, 24, 54, 15, 45, 22, 52, 27, 57, 17, 47, 25, 55, 13, 43, 18, 48, 5, 35)(3, 33, 9, 39, 20, 50, 7, 37, 12, 42, 23, 53, 30, 60, 28, 58, 29, 59, 16, 46, 4, 34, 10, 40, 19, 49, 6, 36, 11, 41)(61, 91, 63, 93, 68, 98, 80, 110, 86, 116, 72, 102, 84, 114, 90, 120, 82, 112, 89, 119, 77, 107, 64, 94, 73, 103, 79, 109, 65, 95, 71, 101, 62, 92, 69, 99, 81, 111, 67, 97, 74, 104, 83, 113, 75, 105, 88, 118, 87, 117, 76, 106, 85, 115, 70, 100, 78, 108, 66, 96) L = (1, 64)(2, 70)(3, 73)(4, 75)(5, 76)(6, 77)(7, 61)(8, 79)(9, 78)(10, 82)(11, 85)(12, 62)(13, 88)(14, 63)(15, 80)(16, 84)(17, 83)(18, 89)(19, 87)(20, 65)(21, 66)(22, 67)(23, 68)(24, 69)(25, 90)(26, 71)(27, 72)(28, 86)(29, 74)(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) :: { ( 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20 ), ( 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20 ) } Outer automorphisms :: reflexible Dual of E23.75 Graph:: bipartite v = 3 e = 60 f = 13 degree seq :: [ 30^2, 60 ] E23.83 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 10, 15, 30}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1^-1 * Y2^-1, (Y3^-1, Y2), (Y1^-1, Y2), (R * Y2)^2, (Y3, Y1^-1), (Y3, Y2^-1), (R * Y3)^2, (R * Y1)^2, Y3^-3 * Y1^-1 * Y2, Y1^-1 * Y3 * Y1^-3 * Y3, Y1^-1 * Y2 * Y1^-1 * Y3 * Y2 * Y3 * Y1^-1, (Y3^-1 * Y1 * Y3^-1)^5 ] Map:: non-degenerate R = (1, 31, 2, 32, 8, 38, 22, 52, 15, 45, 14, 44, 20, 50, 26, 56, 29, 59, 12, 42, 17, 47, 21, 51, 27, 57, 18, 48, 5, 35)(3, 33, 6, 36, 10, 40, 24, 54, 28, 58, 19, 49, 7, 37, 11, 41, 25, 55, 16, 46, 4, 34, 9, 39, 23, 53, 30, 60, 13, 43)(61, 91, 63, 93, 65, 95, 73, 103, 78, 108, 90, 120, 87, 117, 83, 113, 81, 111, 69, 99, 77, 107, 64, 94, 72, 102, 76, 106, 89, 119, 85, 115, 86, 116, 71, 101, 80, 110, 67, 97, 74, 104, 79, 109, 75, 105, 88, 118, 82, 112, 84, 114, 68, 98, 70, 100, 62, 92, 66, 96) L = (1, 64)(2, 69)(3, 72)(4, 75)(5, 76)(6, 77)(7, 61)(8, 83)(9, 74)(10, 81)(11, 62)(12, 88)(13, 89)(14, 63)(15, 73)(16, 82)(17, 79)(18, 85)(19, 65)(20, 66)(21, 67)(22, 90)(23, 80)(24, 87)(25, 68)(26, 70)(27, 71)(28, 78)(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) :: { ( 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20 ), ( 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20 ) } Outer automorphisms :: reflexible Dual of E23.73 Graph:: bipartite v = 3 e = 60 f = 13 degree seq :: [ 30^2, 60 ] E23.84 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 10, 15, 30}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^2, (Y3^-1, Y2), (Y2, Y1), (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y3 * Y2^-1 * Y1 * Y2^-1, (Y1 * Y2 * Y1)^2, Y1^2 * Y3 * Y1 * Y2^-1 * Y1^2, Y1^3 * Y2 * Y1^-1 * Y3^-1 * Y2 * Y1^-1 * Y3^-1 * Y2 * Y1^-1 * Y3^-1, (Y1 * Y3)^10 ] Map:: non-degenerate R = (1, 31, 2, 32, 8, 38, 22, 52, 20, 50, 15, 45, 13, 43, 27, 57, 30, 60, 21, 51, 16, 46, 12, 42, 26, 56, 17, 47, 5, 35)(3, 33, 9, 39, 23, 53, 18, 48, 6, 36, 11, 41, 25, 55, 29, 59, 19, 49, 7, 37, 4, 34, 10, 40, 24, 54, 28, 58, 14, 44)(61, 91, 63, 93, 72, 102, 70, 100, 87, 117, 89, 119, 82, 112, 78, 108, 65, 95, 74, 104, 76, 106, 64, 94, 73, 103, 85, 115, 68, 98, 83, 113, 77, 107, 88, 118, 81, 111, 67, 97, 75, 105, 71, 101, 62, 92, 69, 99, 86, 116, 84, 114, 90, 120, 79, 109, 80, 110, 66, 96) L = (1, 64)(2, 70)(3, 73)(4, 62)(5, 67)(6, 76)(7, 61)(8, 84)(9, 87)(10, 68)(11, 72)(12, 85)(13, 69)(14, 75)(15, 63)(16, 71)(17, 79)(18, 81)(19, 65)(20, 74)(21, 66)(22, 88)(23, 90)(24, 82)(25, 86)(26, 89)(27, 83)(28, 80)(29, 77)(30, 78)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20 ), ( 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20 ) } Outer automorphisms :: reflexible Dual of E23.74 Graph:: bipartite v = 3 e = 60 f = 13 degree seq :: [ 30^2, 60 ] E23.85 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 10, 15, 30}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y1^3, Y2 * Y3^2, (Y1, Y3^-1), (Y1^-1, Y2), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y1^-1 * Y2^-5, Y3^-1 * Y2 * Y1^-1 * Y3^-1 * Y2^2 * Y1^-1 * Y2, (Y3 * Y2^-1)^10, Y2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-2 ] Map:: non-degenerate R = (1, 31, 2, 32, 5, 35)(3, 33, 8, 38, 13, 43)(4, 34, 9, 39, 15, 45)(6, 36, 10, 40, 17, 47)(7, 37, 11, 41, 18, 48)(12, 42, 20, 50, 25, 55)(14, 44, 21, 51, 27, 57)(16, 46, 22, 52, 28, 58)(19, 49, 23, 53, 24, 54)(26, 56, 29, 59, 30, 60)(61, 91, 63, 93, 72, 102, 84, 114, 77, 107, 65, 95, 73, 103, 85, 115, 83, 113, 70, 100, 62, 92, 68, 98, 80, 110, 79, 109, 66, 96)(64, 94, 67, 97, 74, 104, 86, 116, 88, 118, 75, 105, 78, 108, 87, 117, 90, 120, 82, 112, 69, 99, 71, 101, 81, 111, 89, 119, 76, 106) L = (1, 64)(2, 69)(3, 67)(4, 66)(5, 75)(6, 76)(7, 61)(8, 71)(9, 70)(10, 82)(11, 62)(12, 74)(13, 78)(14, 63)(15, 77)(16, 79)(17, 88)(18, 65)(19, 89)(20, 81)(21, 68)(22, 83)(23, 90)(24, 86)(25, 87)(26, 72)(27, 73)(28, 84)(29, 80)(30, 85)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 20, 60, 20, 60, 20, 60 ), ( 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60 ) } Outer automorphisms :: reflexible Dual of E23.89 Graph:: bipartite v = 12 e = 60 f = 4 degree seq :: [ 6^10, 30^2 ] E23.86 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 10, 15, 30}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y1^3, (Y3^-1, Y2^-1), (Y3^-1, Y1), (Y2^-1, Y1), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y3^4 * Y2^-1, Y2 * Y3 * Y2 * Y3 * Y1^-1, Y3^-1 * Y2^2 * Y3^-1 * Y2 * Y1^-1, Y2^15, Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y2^-1 ] Map:: non-degenerate R = (1, 31, 2, 32, 5, 35)(3, 33, 8, 38, 14, 44)(4, 34, 9, 39, 17, 47)(6, 36, 10, 40, 19, 49)(7, 37, 11, 41, 20, 50)(12, 42, 24, 54, 23, 53)(13, 43, 25, 55, 22, 52)(15, 45, 26, 56, 29, 59)(16, 46, 27, 57, 21, 51)(18, 48, 28, 58, 30, 60)(61, 91, 63, 93, 72, 102, 87, 117, 79, 109, 65, 95, 74, 104, 83, 113, 76, 106, 70, 100, 62, 92, 68, 98, 84, 114, 81, 111, 66, 96)(64, 94, 73, 103, 71, 101, 86, 116, 90, 120, 77, 107, 82, 112, 67, 97, 75, 105, 88, 118, 69, 99, 85, 115, 80, 110, 89, 119, 78, 108) L = (1, 64)(2, 69)(3, 73)(4, 76)(5, 77)(6, 78)(7, 61)(8, 85)(9, 87)(10, 88)(11, 62)(12, 71)(13, 70)(14, 82)(15, 63)(16, 75)(17, 81)(18, 83)(19, 90)(20, 65)(21, 89)(22, 66)(23, 67)(24, 80)(25, 79)(26, 68)(27, 86)(28, 72)(29, 74)(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, 60, 20, 60, 20, 60 ), ( 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60 ) } Outer automorphisms :: reflexible Dual of E23.90 Graph:: bipartite v = 12 e = 60 f = 4 degree seq :: [ 6^10, 30^2 ] E23.87 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 10, 15, 30}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y1^3, (Y1^-1, Y2^-1), Y1^-1 * Y3^2 * Y2^-1, Y2^-1 * Y3^2 * Y1^-1, (Y3, Y2^-1), (R * Y1)^2, Y2^-1 * Y3 * Y1^-1 * Y3, (R * Y2)^2, (R * Y3)^2, Y2^-4 * Y3^-2, (Y3^-1 * Y1^-1)^30 ] Map:: non-degenerate R = (1, 31, 2, 32, 5, 35)(3, 33, 8, 38, 14, 44)(4, 34, 9, 39, 15, 45)(6, 36, 10, 40, 16, 46)(7, 37, 11, 41, 17, 47)(12, 42, 20, 50, 26, 56)(13, 43, 21, 51, 27, 57)(18, 48, 22, 52, 24, 54)(19, 49, 23, 53, 28, 58)(25, 55, 29, 59, 30, 60)(61, 91, 63, 93, 72, 102, 84, 114, 76, 106, 65, 95, 74, 104, 86, 116, 82, 112, 70, 100, 62, 92, 68, 98, 80, 110, 78, 108, 66, 96)(64, 94, 73, 103, 85, 115, 79, 109, 67, 97, 75, 105, 87, 117, 90, 120, 88, 118, 77, 107, 69, 99, 81, 111, 89, 119, 83, 113, 71, 101) L = (1, 64)(2, 69)(3, 73)(4, 68)(5, 75)(6, 71)(7, 61)(8, 81)(9, 74)(10, 77)(11, 62)(12, 85)(13, 80)(14, 87)(15, 63)(16, 67)(17, 65)(18, 83)(19, 66)(20, 89)(21, 86)(22, 88)(23, 70)(24, 79)(25, 78)(26, 90)(27, 72)(28, 76)(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, 60, 20, 60, 20, 60 ), ( 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60, 20, 60 ) } Outer automorphisms :: reflexible Dual of E23.88 Graph:: bipartite v = 12 e = 60 f = 4 degree seq :: [ 6^10, 30^2 ] E23.88 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 10, 15, 30}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y3^-1, (R * Y1)^2, (Y3^-1, Y1^-1), R * Y2 * R * Y3^-1, Y3^-3 * Y1^-3, Y2 * Y1^-1 * Y2^2 * Y1^-2, Y2^2 * Y1 * Y2^-2 * Y1^-1, Y1^10, Y1^-1 * Y3^9, Y3^2 * Y1^-1 * Y3^2 * Y1^-3 * Y2^-2, Y2^30, (Y3 * Y2^-1)^15 ] Map:: non-degenerate R = (1, 31, 2, 32, 6, 36, 14, 44, 22, 52, 28, 58, 26, 56, 19, 49, 13, 43, 5, 35)(3, 33, 7, 37, 15, 45, 23, 53, 29, 59, 27, 57, 20, 50, 11, 41, 18, 48, 10, 40)(4, 34, 8, 38, 16, 46, 9, 39, 17, 47, 24, 54, 30, 60, 25, 55, 21, 51, 12, 42)(61, 91, 63, 93, 69, 99, 74, 104, 83, 113, 90, 120, 86, 116, 80, 110, 72, 102, 65, 95, 70, 100, 76, 106, 66, 96, 75, 105, 84, 114, 88, 118, 87, 117, 81, 111, 73, 103, 78, 108, 68, 98, 62, 92, 67, 97, 77, 107, 82, 112, 89, 119, 85, 115, 79, 109, 71, 101, 64, 94) L = (1, 64)(2, 68)(3, 61)(4, 71)(5, 72)(6, 76)(7, 62)(8, 78)(9, 63)(10, 65)(11, 79)(12, 80)(13, 81)(14, 69)(15, 66)(16, 70)(17, 67)(18, 73)(19, 85)(20, 86)(21, 87)(22, 77)(23, 74)(24, 75)(25, 89)(26, 90)(27, 88)(28, 84)(29, 82)(30, 83)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 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, 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, 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 E23.87 Graph:: bipartite v = 4 e = 60 f = 12 degree seq :: [ 20^3, 60 ] E23.89 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 10, 15, 30}) Quotient :: dipole Aut^+ = C30 (small group id <30, 4>) Aut = D60 (small group id <60, 12>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y2 * Y3 * Y1^-1, (Y2, Y1^-1), (Y3, Y1^-1), Y2^-3 * Y1^-1, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y3 * Y1^-1 * Y2 * Y1^-1, (Y3^-1, Y2), Y2^-1 * Y3^3 * Y2^-1 * Y3, Y1^-1 * Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1, Y3^-1 * Y2^-2 * Y3 * Y2^-1 * Y1^-1, Y3^-9 * Y1, Y1^10 ] Map:: non-degenerate R = (1, 31, 2, 32, 8, 38, 20, 50, 29, 59, 28, 58, 30, 60, 27, 57, 17, 47, 5, 35)(3, 33, 9, 39, 21, 51, 16, 46, 25, 55, 15, 45, 24, 54, 18, 48, 7, 37, 12, 42)(4, 34, 10, 40, 22, 52, 19, 49, 26, 56, 14, 44, 23, 53, 13, 43, 6, 36, 11, 41)(61, 91, 63, 93, 73, 103, 65, 95, 72, 102, 83, 113, 77, 107, 67, 97, 74, 104, 87, 117, 78, 108, 86, 116, 90, 120, 84, 114, 79, 109, 88, 118, 75, 105, 82, 112, 89, 119, 85, 115, 70, 100, 80, 110, 76, 106, 64, 94, 68, 98, 81, 111, 71, 101, 62, 92, 69, 99, 66, 96) L = (1, 64)(2, 70)(3, 68)(4, 75)(5, 71)(6, 76)(7, 61)(8, 82)(9, 80)(10, 84)(11, 85)(12, 62)(13, 81)(14, 63)(15, 87)(16, 88)(17, 66)(18, 65)(19, 67)(20, 79)(21, 89)(22, 78)(23, 69)(24, 77)(25, 90)(26, 72)(27, 73)(28, 74)(29, 86)(30, 83)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 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, 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, 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 E23.85 Graph:: bipartite v = 4 e = 60 f = 12 degree seq :: [ 20^3, 60 ] E23.90 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 10, 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 * Y3 * Y1^-1, Y1^-1 * Y3^2 * Y2^-1, (Y3, Y1), Y2^-1 * Y3^2 * Y1^-1, Y2^3 * Y1^-1, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y3, Y2), Y3 * Y1 * Y3^2 * Y1^2 ] Map:: non-degenerate R = (1, 31, 2, 32, 8, 38, 20, 50, 19, 49, 26, 56, 13, 43, 25, 55, 16, 46, 5, 35)(3, 33, 9, 39, 21, 51, 18, 48, 7, 37, 12, 42, 24, 54, 30, 60, 27, 57, 14, 44)(4, 34, 10, 40, 22, 52, 17, 47, 6, 36, 11, 41, 23, 53, 29, 59, 28, 58, 15, 45)(61, 91, 63, 93, 71, 101, 62, 92, 69, 99, 83, 113, 68, 98, 81, 111, 89, 119, 80, 110, 78, 108, 88, 118, 79, 109, 67, 97, 75, 105, 86, 116, 72, 102, 64, 94, 73, 103, 84, 114, 70, 100, 85, 115, 90, 120, 82, 112, 76, 106, 87, 117, 77, 107, 65, 95, 74, 104, 66, 96) L = (1, 64)(2, 70)(3, 73)(4, 69)(5, 75)(6, 72)(7, 61)(8, 82)(9, 85)(10, 81)(11, 84)(12, 62)(13, 83)(14, 86)(15, 63)(16, 88)(17, 67)(18, 65)(19, 66)(20, 77)(21, 76)(22, 78)(23, 90)(24, 68)(25, 89)(26, 71)(27, 79)(28, 74)(29, 87)(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) :: { ( 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, 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, 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 E23.86 Graph:: bipartite v = 4 e = 60 f = 12 degree seq :: [ 20^3, 60 ] E23.91 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 8, 8, 8}) Quotient :: edge^2 Aut^+ = C4 . D8 = C4 . (C4 x C2) (small group id <32, 15>) Aut = (C16 x C2) : C2 (small group id <64, 40>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1 * Y1, Y2 * Y1 * Y3, (R * Y3)^2, R * Y2 * R * Y1, Y1 * Y2^-1 * Y1 * Y2^-1 * Y3^2, Y2^8, Y3^8, Y1^8 ] Map:: non-degenerate R = (1, 33, 4, 36, 14, 46, 27, 59, 32, 64, 31, 63, 19, 51, 7, 39)(2, 34, 6, 38, 18, 50, 30, 62, 26, 58, 25, 57, 24, 56, 10, 42)(3, 35, 12, 44, 22, 54, 20, 52, 21, 53, 28, 60, 15, 47, 5, 37)(8, 40, 9, 41, 23, 55, 13, 45, 11, 43, 16, 48, 29, 61, 17, 49)(65, 66, 72, 84, 96, 90, 75, 69)(67, 71, 70, 81, 85, 91, 89, 77)(68, 74, 73, 86, 95, 94, 80, 79)(76, 83, 82, 93, 92, 78, 88, 87)(97, 99, 107, 121, 128, 117, 104, 102)(98, 100, 101, 112, 122, 127, 116, 105)(103, 108, 109, 120, 123, 124, 113, 114)(106, 110, 111, 125, 126, 115, 118, 119) 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) :: { ( 16^8 ), ( 16^16 ) } Outer automorphisms :: reflexible Dual of E23.97 Graph:: bipartite v = 12 e = 64 f = 8 degree seq :: [ 8^8, 16^4 ] E23.92 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 8, 8, 8}) Quotient :: edge^2 Aut^+ = C4 . D8 = C4 . (C4 x C2) (small group id <32, 15>) Aut = (C16 : C2) : C2 (small group id <64, 42>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1 * Y3, Y2^2 * Y1^-2, R * Y1 * R * Y2, (R * Y3)^2, Y3 * Y1 * Y2 * Y3^2, Y1 * Y3^-1 * Y2 * Y3^-2, Y2 * Y3 * Y1 * Y3^-2, Y1^8 ] Map:: non-degenerate R = (1, 33, 4, 36, 16, 48, 23, 55, 29, 61, 9, 41, 27, 59, 7, 39)(2, 34, 6, 38, 22, 54, 15, 47, 18, 50, 24, 56, 26, 58, 11, 43)(3, 35, 12, 44, 21, 53, 5, 37, 19, 51, 25, 57, 17, 49, 14, 46)(8, 40, 10, 42, 30, 62, 13, 45, 20, 52, 31, 63, 32, 64, 28, 60)(65, 66, 72, 78, 93, 82, 84, 69)(67, 71, 88, 92, 83, 87, 70, 77)(68, 79, 74, 85, 73, 75, 95, 81)(76, 80, 90, 94, 89, 91, 86, 96)(97, 99, 104, 120, 125, 115, 116, 102)(98, 105, 110, 127, 114, 100, 101, 106)(103, 121, 124, 118, 119, 108, 109, 122)(107, 112, 113, 126, 111, 123, 117, 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) :: { ( 16^8 ), ( 16^16 ) } Outer automorphisms :: reflexible Dual of E23.98 Graph:: bipartite v = 12 e = 64 f = 8 degree seq :: [ 8^8, 16^4 ] E23.93 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 8, 8, 8}) Quotient :: edge^2 Aut^+ = C4 . D8 = C4 . (C4 x C2) (small group id <32, 15>) Aut = (C16 x C2) : C2 (small group id <64, 40>) |r| :: 2 Presentation :: [ R^2, Y3^4, Y3^-1 * Y2 * Y3^-1 * Y2^-1, (R * Y3)^2, Y1^-1 * Y3^-1 * Y1 * Y3^-1, Y2 * Y1^2 * Y2, R * Y1 * R * Y2, Y1 * Y2^-1 * Y3^-1 * Y1 * Y2^-1, Y1 * Y2 * Y1 * Y3^-1 * Y2, Y2 * Y3^-2 * Y2^-1 * Y3^2, Y1^-2 * Y3^2 * Y1^-2, Y2^-3 * Y3^-2 * Y2^-1 ] Map:: non-degenerate R = (1, 33, 4, 36, 18, 50, 7, 39)(2, 34, 10, 42, 30, 62, 12, 44)(3, 35, 15, 47, 27, 59, 17, 49)(5, 37, 22, 54, 25, 57, 19, 51)(6, 38, 24, 56, 32, 64, 20, 52)(8, 40, 26, 58, 14, 46, 28, 60)(9, 41, 13, 45, 31, 63, 29, 61)(11, 43, 23, 55, 21, 53, 16, 48)(65, 66, 72, 89, 82, 94, 78, 69)(67, 77, 70, 87, 91, 93, 96, 80)(68, 76, 90, 86, 71, 74, 92, 83)(73, 88, 75, 81, 95, 84, 85, 79)(97, 99, 110, 128, 114, 123, 104, 102)(98, 105, 101, 117, 126, 127, 121, 107)(100, 113, 124, 120, 103, 111, 122, 116)(106, 125, 118, 119, 108, 109, 115, 112) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 81)(18, 82)(19, 83)(20, 84)(21, 85)(22, 86)(23, 87)(24, 88)(25, 89)(26, 90)(27, 91)(28, 92)(29, 93)(30, 94)(31, 95)(32, 96)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 32^8 ) } Outer automorphisms :: reflexible Dual of E23.95 Graph:: bipartite v = 16 e = 64 f = 4 degree seq :: [ 8^16 ] E23.94 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 8, 8, 8}) Quotient :: edge^2 Aut^+ = C4 . D8 = C4 . (C4 x C2) (small group id <32, 15>) Aut = (C16 : C2) : C2 (small group id <64, 42>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3 * Y2^-1 * Y3, Y3^4, (R * Y3)^2, Y1 * Y3^-1 * Y1^-1 * Y3^-1, R * Y1 * R * Y2, Y1^2 * Y2^-2, Y1 * Y2 * Y3 * Y1 * Y2, Y3^-1 * Y1 * Y2 * Y1^-1 * Y2^-1, Y1^-1 * Y2 * Y1^-1 * Y2 * Y3^-1, Y1^-1 * Y3^-1 * Y1^-1 * Y3 * Y1^-2, Y2^3 * Y3^2 * Y2 ] Map:: non-degenerate R = (1, 33, 4, 36, 17, 49, 7, 39)(2, 34, 10, 42, 29, 61, 12, 44)(3, 35, 14, 46, 31, 63, 16, 48)(5, 37, 20, 52, 25, 57, 18, 50)(6, 38, 23, 55, 26, 58, 19, 51)(8, 40, 27, 59, 21, 53, 28, 60)(9, 41, 24, 56, 22, 54, 13, 45)(11, 43, 30, 62, 32, 64, 15, 47)(65, 66, 72, 89, 81, 93, 85, 69)(67, 77, 90, 94, 95, 88, 70, 79)(68, 76, 91, 84, 71, 74, 92, 82)(73, 87, 96, 78, 86, 83, 75, 80)(97, 99, 104, 122, 113, 127, 117, 102)(98, 105, 121, 128, 125, 118, 101, 107)(100, 112, 123, 119, 103, 110, 124, 115)(106, 109, 114, 126, 108, 120, 116, 111) 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) :: { ( 32^8 ) } Outer automorphisms :: reflexible Dual of E23.96 Graph:: bipartite v = 16 e = 64 f = 4 degree seq :: [ 8^16 ] E23.95 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 8, 8, 8}) Quotient :: loop^2 Aut^+ = C4 . D8 = C4 . (C4 x C2) (small group id <32, 15>) Aut = (C16 x C2) : C2 (small group id <64, 40>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1 * Y1, Y2 * Y1 * Y3, (R * Y3)^2, R * Y2 * R * Y1, Y1 * Y2^-1 * Y1 * Y2^-1 * Y3^2, Y2^8, Y3^8, Y1^8 ] Map:: non-degenerate R = (1, 33, 65, 97, 4, 36, 68, 100, 14, 46, 78, 110, 27, 59, 91, 123, 32, 64, 96, 128, 31, 63, 95, 127, 19, 51, 83, 115, 7, 39, 71, 103)(2, 34, 66, 98, 6, 38, 70, 102, 18, 50, 82, 114, 30, 62, 94, 126, 26, 58, 90, 122, 25, 57, 89, 121, 24, 56, 88, 120, 10, 42, 74, 106)(3, 35, 67, 99, 12, 44, 76, 108, 22, 54, 86, 118, 20, 52, 84, 116, 21, 53, 85, 117, 28, 60, 92, 124, 15, 47, 79, 111, 5, 37, 69, 101)(8, 40, 72, 104, 9, 41, 73, 105, 23, 55, 87, 119, 13, 45, 77, 109, 11, 43, 75, 107, 16, 48, 80, 112, 29, 61, 93, 125, 17, 49, 81, 113) L = (1, 34)(2, 40)(3, 39)(4, 42)(5, 33)(6, 49)(7, 38)(8, 52)(9, 54)(10, 41)(11, 37)(12, 51)(13, 35)(14, 56)(15, 36)(16, 47)(17, 53)(18, 61)(19, 50)(20, 64)(21, 59)(22, 63)(23, 44)(24, 55)(25, 45)(26, 43)(27, 57)(28, 46)(29, 60)(30, 48)(31, 62)(32, 58)(65, 99)(66, 100)(67, 107)(68, 101)(69, 112)(70, 97)(71, 108)(72, 102)(73, 98)(74, 110)(75, 121)(76, 109)(77, 120)(78, 111)(79, 125)(80, 122)(81, 114)(82, 103)(83, 118)(84, 105)(85, 104)(86, 119)(87, 106)(88, 123)(89, 128)(90, 127)(91, 124)(92, 113)(93, 126)(94, 115)(95, 116)(96, 117) local type(s) :: { ( 8^32 ) } Outer automorphisms :: reflexible Dual of E23.93 Transitivity :: VT+ Graph:: bipartite v = 4 e = 64 f = 16 degree seq :: [ 32^4 ] E23.96 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 8, 8, 8}) Quotient :: loop^2 Aut^+ = C4 . D8 = C4 . (C4 x C2) (small group id <32, 15>) Aut = (C16 : C2) : C2 (small group id <64, 42>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1 * Y3, Y2^2 * Y1^-2, R * Y1 * R * Y2, (R * Y3)^2, Y3 * Y1 * Y2 * Y3^2, Y1 * Y3^-1 * Y2 * Y3^-2, Y2 * Y3 * Y1 * Y3^-2, Y1^8 ] Map:: non-degenerate R = (1, 33, 65, 97, 4, 36, 68, 100, 16, 48, 80, 112, 23, 55, 87, 119, 29, 61, 93, 125, 9, 41, 73, 105, 27, 59, 91, 123, 7, 39, 71, 103)(2, 34, 66, 98, 6, 38, 70, 102, 22, 54, 86, 118, 15, 47, 79, 111, 18, 50, 82, 114, 24, 56, 88, 120, 26, 58, 90, 122, 11, 43, 75, 107)(3, 35, 67, 99, 12, 44, 76, 108, 21, 53, 85, 117, 5, 37, 69, 101, 19, 51, 83, 115, 25, 57, 89, 121, 17, 49, 81, 113, 14, 46, 78, 110)(8, 40, 72, 104, 10, 42, 74, 106, 30, 62, 94, 126, 13, 45, 77, 109, 20, 52, 84, 116, 31, 63, 95, 127, 32, 64, 96, 128, 28, 60, 92, 124) L = (1, 34)(2, 40)(3, 39)(4, 47)(5, 33)(6, 45)(7, 56)(8, 46)(9, 43)(10, 53)(11, 63)(12, 48)(13, 35)(14, 61)(15, 42)(16, 58)(17, 36)(18, 52)(19, 55)(20, 37)(21, 41)(22, 64)(23, 38)(24, 60)(25, 59)(26, 62)(27, 54)(28, 51)(29, 50)(30, 57)(31, 49)(32, 44)(65, 99)(66, 105)(67, 104)(68, 101)(69, 106)(70, 97)(71, 121)(72, 120)(73, 110)(74, 98)(75, 112)(76, 109)(77, 122)(78, 127)(79, 123)(80, 113)(81, 126)(82, 100)(83, 116)(84, 102)(85, 128)(86, 119)(87, 108)(88, 125)(89, 124)(90, 103)(91, 117)(92, 118)(93, 115)(94, 111)(95, 114)(96, 107) local type(s) :: { ( 8^32 ) } Outer automorphisms :: reflexible Dual of E23.94 Transitivity :: VT+ Graph:: bipartite v = 4 e = 64 f = 16 degree seq :: [ 32^4 ] E23.97 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 8, 8, 8}) Quotient :: loop^2 Aut^+ = C4 . D8 = C4 . (C4 x C2) (small group id <32, 15>) Aut = (C16 x C2) : C2 (small group id <64, 40>) |r| :: 2 Presentation :: [ R^2, Y3^4, Y3^-1 * Y2 * Y3^-1 * Y2^-1, (R * Y3)^2, Y1^-1 * Y3^-1 * Y1 * Y3^-1, Y2 * Y1^2 * Y2, R * Y1 * R * Y2, Y1 * Y2^-1 * Y3^-1 * Y1 * Y2^-1, Y1 * Y2 * Y1 * Y3^-1 * Y2, Y2 * Y3^-2 * Y2^-1 * Y3^2, Y1^-2 * Y3^2 * Y1^-2, Y2^-3 * Y3^-2 * Y2^-1 ] Map:: non-degenerate R = (1, 33, 65, 97, 4, 36, 68, 100, 18, 50, 82, 114, 7, 39, 71, 103)(2, 34, 66, 98, 10, 42, 74, 106, 30, 62, 94, 126, 12, 44, 76, 108)(3, 35, 67, 99, 15, 47, 79, 111, 27, 59, 91, 123, 17, 49, 81, 113)(5, 37, 69, 101, 22, 54, 86, 118, 25, 57, 89, 121, 19, 51, 83, 115)(6, 38, 70, 102, 24, 56, 88, 120, 32, 64, 96, 128, 20, 52, 84, 116)(8, 40, 72, 104, 26, 58, 90, 122, 14, 46, 78, 110, 28, 60, 92, 124)(9, 41, 73, 105, 13, 45, 77, 109, 31, 63, 95, 127, 29, 61, 93, 125)(11, 43, 75, 107, 23, 55, 87, 119, 21, 53, 85, 117, 16, 48, 80, 112) L = (1, 34)(2, 40)(3, 45)(4, 44)(5, 33)(6, 55)(7, 42)(8, 57)(9, 56)(10, 60)(11, 49)(12, 58)(13, 38)(14, 37)(15, 41)(16, 35)(17, 63)(18, 62)(19, 36)(20, 53)(21, 47)(22, 39)(23, 59)(24, 43)(25, 50)(26, 54)(27, 61)(28, 51)(29, 64)(30, 46)(31, 52)(32, 48)(65, 99)(66, 105)(67, 110)(68, 113)(69, 117)(70, 97)(71, 111)(72, 102)(73, 101)(74, 125)(75, 98)(76, 109)(77, 115)(78, 128)(79, 122)(80, 106)(81, 124)(82, 123)(83, 112)(84, 100)(85, 126)(86, 119)(87, 108)(88, 103)(89, 107)(90, 116)(91, 104)(92, 120)(93, 118)(94, 127)(95, 121)(96, 114) local type(s) :: { ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E23.91 Transitivity :: VT+ Graph:: bipartite v = 8 e = 64 f = 12 degree seq :: [ 16^8 ] E23.98 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 8, 8, 8}) Quotient :: loop^2 Aut^+ = C4 . D8 = C4 . (C4 x C2) (small group id <32, 15>) Aut = (C16 : C2) : C2 (small group id <64, 42>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3 * Y2^-1 * Y3, Y3^4, (R * Y3)^2, Y1 * Y3^-1 * Y1^-1 * Y3^-1, R * Y1 * R * Y2, Y1^2 * Y2^-2, Y1 * Y2 * Y3 * Y1 * Y2, Y3^-1 * Y1 * Y2 * Y1^-1 * Y2^-1, Y1^-1 * Y2 * Y1^-1 * Y2 * Y3^-1, Y1^-1 * Y3^-1 * Y1^-1 * Y3 * Y1^-2, Y2^3 * Y3^2 * Y2 ] Map:: non-degenerate R = (1, 33, 65, 97, 4, 36, 68, 100, 17, 49, 81, 113, 7, 39, 71, 103)(2, 34, 66, 98, 10, 42, 74, 106, 29, 61, 93, 125, 12, 44, 76, 108)(3, 35, 67, 99, 14, 46, 78, 110, 31, 63, 95, 127, 16, 48, 80, 112)(5, 37, 69, 101, 20, 52, 84, 116, 25, 57, 89, 121, 18, 50, 82, 114)(6, 38, 70, 102, 23, 55, 87, 119, 26, 58, 90, 122, 19, 51, 83, 115)(8, 40, 72, 104, 27, 59, 91, 123, 21, 53, 85, 117, 28, 60, 92, 124)(9, 41, 73, 105, 24, 56, 88, 120, 22, 54, 86, 118, 13, 45, 77, 109)(11, 43, 75, 107, 30, 62, 94, 126, 32, 64, 96, 128, 15, 47, 79, 111) L = (1, 34)(2, 40)(3, 45)(4, 44)(5, 33)(6, 47)(7, 42)(8, 57)(9, 55)(10, 60)(11, 48)(12, 59)(13, 58)(14, 54)(15, 35)(16, 41)(17, 61)(18, 36)(19, 43)(20, 39)(21, 37)(22, 51)(23, 64)(24, 38)(25, 49)(26, 62)(27, 52)(28, 50)(29, 53)(30, 63)(31, 56)(32, 46)(65, 99)(66, 105)(67, 104)(68, 112)(69, 107)(70, 97)(71, 110)(72, 122)(73, 121)(74, 109)(75, 98)(76, 120)(77, 114)(78, 124)(79, 106)(80, 123)(81, 127)(82, 126)(83, 100)(84, 111)(85, 102)(86, 101)(87, 103)(88, 116)(89, 128)(90, 113)(91, 119)(92, 115)(93, 118)(94, 108)(95, 117)(96, 125) local type(s) :: { ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E23.92 Transitivity :: VT+ Graph:: bipartite v = 8 e = 64 f = 12 degree seq :: [ 16^8 ] E23.99 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 8, 8, 8}) Quotient :: dipole Aut^+ = C4 . D8 = C4 . (C4 x C2) (small group id <32, 15>) Aut = (C2 x D16) : C2 (small group id <64, 153>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^2, (R * Y3)^2, (Y1, Y2), (R * Y1)^2, Y1^4, Y2^-1 * Y1 * Y3^-1 * Y2^-1 * Y3^-1, Y2 * Y1 * Y3^-1 * Y2 * Y3^-1, Y1^2 * Y2^4, (R * Y2 * Y3^-1)^2, Y2^-2 * R * Y2^-1 * R * Y2^-1 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 9, 41, 25, 57, 14, 46)(4, 36, 7, 39, 11, 43, 17, 49)(6, 38, 10, 42, 26, 58, 19, 51)(12, 44, 27, 59, 21, 53, 28, 60)(13, 45, 15, 47, 18, 50, 24, 56)(16, 48, 23, 55, 20, 52, 22, 54)(29, 61, 30, 62, 31, 63, 32, 64)(65, 97, 67, 99, 76, 108, 90, 122, 72, 104, 89, 121, 85, 117, 70, 102)(66, 98, 73, 105, 91, 123, 83, 115, 69, 101, 78, 110, 92, 124, 74, 106)(68, 100, 80, 112, 95, 127, 77, 109, 75, 107, 84, 116, 93, 125, 82, 114)(71, 103, 87, 119, 96, 128, 79, 111, 81, 113, 86, 118, 94, 126, 88, 120) L = (1, 68)(2, 71)(3, 77)(4, 69)(5, 81)(6, 84)(7, 65)(8, 75)(9, 79)(10, 86)(11, 66)(12, 93)(13, 78)(14, 88)(15, 67)(16, 74)(17, 72)(18, 73)(19, 87)(20, 83)(21, 95)(22, 70)(23, 90)(24, 89)(25, 82)(26, 80)(27, 94)(28, 96)(29, 92)(30, 76)(31, 91)(32, 85)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 16^8 ), ( 16^16 ) } Outer automorphisms :: reflexible Dual of E23.116 Graph:: bipartite v = 12 e = 64 f = 8 degree seq :: [ 8^8, 16^4 ] E23.100 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 8, 8, 8}) Quotient :: dipole Aut^+ = C4 . D8 = C4 . (C4 x C2) (small group id <32, 15>) Aut = (C2 x D16) : C2 (small group id <64, 153>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^2, Y1^4, Y3 * Y2 * Y3 * Y2^-1, Y2^-1 * Y1 * Y2 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y2^4 * Y1^-1, Y2 * Y3^-1 * Y2 * Y1 * Y2 * Y3^-1 * Y2, (Y3^-1 * Y1^-1)^8 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 12, 44, 21, 53, 9, 41)(4, 36, 10, 42, 18, 50, 7, 39)(6, 38, 17, 49, 22, 54, 11, 43)(13, 45, 23, 55, 20, 52, 26, 58)(14, 46, 27, 59, 24, 56, 15, 47)(16, 48, 19, 51, 31, 63, 25, 57)(28, 60, 32, 64, 30, 62, 29, 61)(65, 97, 67, 99, 77, 109, 86, 118, 72, 104, 85, 117, 84, 116, 70, 102)(66, 98, 73, 105, 87, 119, 81, 113, 69, 101, 76, 108, 90, 122, 75, 107)(68, 100, 79, 111, 92, 124, 95, 127, 82, 114, 91, 123, 94, 126, 80, 112)(71, 103, 78, 110, 93, 125, 89, 121, 74, 106, 88, 120, 96, 128, 83, 115) L = (1, 68)(2, 74)(3, 78)(4, 66)(5, 71)(6, 83)(7, 65)(8, 82)(9, 79)(10, 72)(11, 80)(12, 91)(13, 92)(14, 76)(15, 67)(16, 70)(17, 95)(18, 69)(19, 81)(20, 94)(21, 88)(22, 89)(23, 96)(24, 73)(25, 75)(26, 93)(27, 85)(28, 87)(29, 77)(30, 90)(31, 86)(32, 84)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 16^8 ), ( 16^16 ) } Outer automorphisms :: reflexible Dual of E23.110 Graph:: bipartite v = 12 e = 64 f = 8 degree seq :: [ 8^8, 16^4 ] E23.101 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 8, 8, 8}) Quotient :: dipole Aut^+ = C4 . D8 = C4 . (C4 x C2) (small group id <32, 15>) Aut = (C2 x D16) : C2 (small group id <64, 153>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^2, Y3 * Y2 * Y3 * Y2^-1, Y1^4, Y2^-1 * Y1^-1 * Y2 * Y1^-1, (R * Y3)^2, Y2^-1 * Y3^-1 * Y2 * Y3^-1, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y2^4 * Y1^-1, Y2 * Y1^-1 * Y2 * Y3^-1 * Y2^2 * Y3^-1 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 12, 44, 21, 53, 9, 41)(4, 36, 7, 39, 11, 43, 16, 48)(6, 38, 18, 50, 22, 54, 10, 42)(13, 45, 23, 55, 20, 52, 26, 58)(14, 46, 15, 47, 27, 59, 24, 56)(17, 49, 30, 62, 25, 57, 19, 51)(28, 60, 29, 61, 31, 63, 32, 64)(65, 97, 67, 99, 77, 109, 86, 118, 72, 104, 85, 117, 84, 116, 70, 102)(66, 98, 73, 105, 87, 119, 82, 114, 69, 101, 76, 108, 90, 122, 74, 106)(68, 100, 79, 111, 92, 124, 89, 121, 75, 107, 88, 120, 95, 127, 81, 113)(71, 103, 78, 110, 93, 125, 94, 126, 80, 112, 91, 123, 96, 128, 83, 115) L = (1, 68)(2, 71)(3, 78)(4, 69)(5, 80)(6, 83)(7, 65)(8, 75)(9, 88)(10, 89)(11, 66)(12, 79)(13, 92)(14, 73)(15, 67)(16, 72)(17, 70)(18, 81)(19, 74)(20, 95)(21, 91)(22, 94)(23, 93)(24, 85)(25, 86)(26, 96)(27, 76)(28, 90)(29, 77)(30, 82)(31, 87)(32, 84)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 16^8 ), ( 16^16 ) } Outer automorphisms :: reflexible Dual of E23.111 Graph:: bipartite v = 12 e = 64 f = 8 degree seq :: [ 8^8, 16^4 ] E23.102 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 8, 8, 8}) Quotient :: dipole Aut^+ = C4 . D8 = C4 . (C4 x C2) (small group id <32, 15>) Aut = (C2 x D16) : C2 (small group id <64, 153>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1 * Y2, Y1^4, Y3 * Y2 * Y3 * Y2^-1, (Y3^-1, Y1^-1), (R * Y3)^2, Y1^4, (R * Y1)^2, Y3^4 * Y1^2, (R * Y2 * Y3^-1)^2, Y3 * Y1 * Y3 * Y2^-1 * Y3^-2 * Y2^-1 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 6, 38, 10, 42, 13, 45)(4, 36, 9, 41, 21, 53, 16, 48)(7, 39, 11, 43, 22, 54, 18, 50)(12, 44, 19, 51, 25, 57, 28, 60)(14, 46, 17, 49, 24, 56, 29, 61)(15, 47, 23, 55, 20, 52, 26, 58)(27, 59, 32, 64, 30, 62, 31, 63)(65, 97, 67, 99, 69, 101, 77, 109, 72, 104, 74, 106, 66, 98, 70, 102)(68, 100, 78, 110, 80, 112, 93, 125, 85, 117, 88, 120, 73, 105, 81, 113)(71, 103, 76, 108, 82, 114, 92, 124, 86, 118, 89, 121, 75, 107, 83, 115)(79, 111, 94, 126, 90, 122, 96, 128, 84, 116, 91, 123, 87, 119, 95, 127) L = (1, 68)(2, 73)(3, 76)(4, 79)(5, 80)(6, 83)(7, 65)(8, 85)(9, 87)(10, 89)(11, 66)(12, 91)(13, 92)(14, 67)(15, 86)(16, 90)(17, 70)(18, 69)(19, 96)(20, 71)(21, 84)(22, 72)(23, 82)(24, 74)(25, 94)(26, 75)(27, 88)(28, 95)(29, 77)(30, 78)(31, 81)(32, 93)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 16^8 ), ( 16^16 ) } Outer automorphisms :: reflexible Dual of E23.113 Graph:: bipartite v = 12 e = 64 f = 8 degree seq :: [ 8^8, 16^4 ] E23.103 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 8, 8, 8}) Quotient :: dipole Aut^+ = C4 . D8 = C4 . (C4 x C2) (small group id <32, 15>) Aut = (C2 x D16) : C2 (small group id <64, 153>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1^-1 * Y2, Y1^-4, (Y3^-1, Y1), Y1^4, (R * Y1)^2, Y3 * Y2^-1 * Y3 * Y2, (R * Y3)^2, Y3^-4 * Y1^2, (R * Y2 * Y3^-1)^2 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 9, 41, 17, 49, 6, 38)(4, 36, 10, 42, 21, 53, 15, 47)(7, 39, 11, 43, 22, 54, 18, 50)(12, 44, 23, 55, 31, 63, 19, 51)(13, 45, 24, 56, 30, 62, 16, 48)(14, 46, 25, 57, 20, 52, 26, 58)(27, 59, 29, 61, 28, 60, 32, 64)(65, 97, 67, 99, 66, 98, 73, 105, 72, 104, 81, 113, 69, 101, 70, 102)(68, 100, 77, 109, 74, 106, 88, 120, 85, 117, 94, 126, 79, 111, 80, 112)(71, 103, 76, 108, 75, 107, 87, 119, 86, 118, 95, 127, 82, 114, 83, 115)(78, 110, 92, 124, 89, 121, 96, 128, 84, 116, 91, 123, 90, 122, 93, 125) L = (1, 68)(2, 74)(3, 76)(4, 78)(5, 79)(6, 83)(7, 65)(8, 85)(9, 87)(10, 89)(11, 66)(12, 91)(13, 67)(14, 86)(15, 90)(16, 70)(17, 95)(18, 69)(19, 96)(20, 71)(21, 84)(22, 72)(23, 93)(24, 73)(25, 82)(26, 75)(27, 94)(28, 77)(29, 80)(30, 81)(31, 92)(32, 88)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 16^8 ), ( 16^16 ) } Outer automorphisms :: reflexible Dual of E23.112 Graph:: bipartite v = 12 e = 64 f = 8 degree seq :: [ 8^8, 16^4 ] E23.104 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 8, 8, 8}) Quotient :: dipole Aut^+ = C4 . D8 = C4 . (C4 x C2) (small group id <32, 15>) Aut = (C2 x D16) : C2 (small group id <64, 153>) |r| :: 2 Presentation :: [ R^2, Y3^2 * Y1, Y2 * Y1 * Y2^-1 * Y1, (R * Y3)^2, (R * Y1)^2, Y1^4, Y1^-1 * Y2^-1 * Y1^-1 * Y2, Y3 * Y2^-1 * Y3^-1 * Y1 * Y2, Y1^-1 * Y2 * Y3^-1 * Y2^-1 * Y3, Y2 * Y1^-1 * Y3 * Y2^-1 * Y3^-1, R * Y2 * Y1^-1 * R * Y2, (Y2 * Y1 * Y2)^2, Y3 * Y2^-3 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 12, 44, 25, 57, 9, 41)(4, 36, 7, 39, 11, 43, 17, 49)(6, 38, 19, 51, 26, 58, 10, 42)(13, 45, 27, 59, 21, 53, 28, 60)(14, 46, 15, 47, 23, 55, 16, 48)(18, 50, 20, 52, 22, 54, 24, 56)(29, 61, 30, 62, 32, 64, 31, 63)(65, 97, 67, 99, 77, 109, 90, 122, 72, 104, 89, 121, 85, 117, 70, 102)(66, 98, 73, 105, 91, 123, 83, 115, 69, 101, 76, 108, 92, 124, 74, 106)(68, 100, 80, 112, 93, 125, 86, 118, 75, 107, 79, 111, 96, 128, 82, 114)(71, 103, 87, 119, 94, 126, 84, 116, 81, 113, 78, 110, 95, 127, 88, 120) L = (1, 68)(2, 71)(3, 78)(4, 69)(5, 81)(6, 84)(7, 65)(8, 75)(9, 80)(10, 82)(11, 66)(12, 79)(13, 93)(14, 73)(15, 67)(16, 89)(17, 72)(18, 90)(19, 86)(20, 74)(21, 96)(22, 70)(23, 76)(24, 83)(25, 87)(26, 88)(27, 94)(28, 95)(29, 92)(30, 77)(31, 85)(32, 91)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 16^8 ), ( 16^16 ) } Outer automorphisms :: reflexible Dual of E23.114 Graph:: bipartite v = 12 e = 64 f = 8 degree seq :: [ 8^8, 16^4 ] E23.105 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 8, 8, 8}) Quotient :: dipole Aut^+ = C4 . D8 = C4 . (C4 x C2) (small group id <32, 15>) Aut = (C2 x D16) : C2 (small group id <64, 153>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-1 * Y3, Y2 * Y1^-1 * Y2^-1 * Y1^-1, (R * Y1)^2, Y2 * Y1^-1 * Y2^-1 * Y1^-1, Y1^4, (R * Y3)^2, Y2^-1 * Y3 * Y2 * Y1^-1 * Y3^-1, R * Y2 * Y1 * R * Y2, Y2 * Y3 * Y1 * Y2^-1 * Y3^-1, Y3 * Y2^-3 * Y3 * Y2^-1, Y3^2 * Y1 * Y2^4, (Y3^-1 * Y1^-1)^8 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 12, 44, 25, 57, 9, 41)(4, 36, 10, 42, 19, 51, 7, 39)(6, 38, 18, 50, 26, 58, 11, 43)(13, 45, 27, 59, 21, 53, 28, 60)(14, 46, 16, 48, 23, 55, 15, 47)(17, 49, 24, 56, 22, 54, 20, 52)(29, 61, 31, 63, 32, 64, 30, 62)(65, 97, 67, 99, 77, 109, 90, 122, 72, 104, 89, 121, 85, 117, 70, 102)(66, 98, 73, 105, 91, 123, 82, 114, 69, 101, 76, 108, 92, 124, 75, 107)(68, 100, 80, 112, 93, 125, 86, 118, 83, 115, 79, 111, 96, 128, 81, 113)(71, 103, 87, 119, 94, 126, 84, 116, 74, 106, 78, 110, 95, 127, 88, 120) L = (1, 68)(2, 74)(3, 78)(4, 66)(5, 71)(6, 84)(7, 65)(8, 83)(9, 79)(10, 72)(11, 86)(12, 80)(13, 93)(14, 76)(15, 67)(16, 89)(17, 90)(18, 81)(19, 69)(20, 82)(21, 96)(22, 70)(23, 73)(24, 75)(25, 87)(26, 88)(27, 95)(28, 94)(29, 91)(30, 77)(31, 85)(32, 92)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 16^8 ), ( 16^16 ) } Outer automorphisms :: reflexible Dual of E23.115 Graph:: bipartite v = 12 e = 64 f = 8 degree seq :: [ 8^8, 16^4 ] E23.106 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 8, 8, 8}) Quotient :: dipole Aut^+ = C4 . D8 = C4 . (C4 x C2) (small group id <32, 15>) Aut = (C2 x D16) : C2 (small group id <64, 153>) |r| :: 2 Presentation :: [ R^2, Y2^2 * Y1, (Y1, Y3), (R * Y1)^2, Y1^4, (R * Y3)^2, Y1^-1 * Y2 * Y3 * Y2 * Y3, Y2 * Y1^-1 * Y2 * Y1^-2, Y2 * Y1^-1 * Y3^-1 * Y2 * Y3^-1, (R * Y2 * Y3^-1)^2, Y3 * Y2^-1 * Y3^-3 * Y2, Y3^-8 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 6, 38, 10, 42, 13, 45)(4, 36, 9, 41, 25, 57, 17, 49)(7, 39, 11, 43, 26, 58, 19, 51)(12, 44, 20, 52, 22, 54, 23, 55)(14, 46, 21, 53, 15, 47, 18, 50)(16, 48, 27, 59, 24, 56, 28, 60)(29, 61, 32, 64, 30, 62, 31, 63)(65, 97, 67, 99, 69, 101, 77, 109, 72, 104, 74, 106, 66, 98, 70, 102)(68, 100, 79, 111, 81, 113, 85, 117, 89, 121, 78, 110, 73, 105, 82, 114)(71, 103, 86, 118, 83, 115, 84, 116, 90, 122, 76, 108, 75, 107, 87, 119)(80, 112, 94, 126, 92, 124, 96, 128, 88, 120, 93, 125, 91, 123, 95, 127) L = (1, 68)(2, 73)(3, 76)(4, 80)(5, 81)(6, 84)(7, 65)(8, 89)(9, 91)(10, 86)(11, 66)(12, 93)(13, 87)(14, 67)(15, 74)(16, 90)(17, 92)(18, 77)(19, 69)(20, 96)(21, 70)(22, 94)(23, 95)(24, 71)(25, 88)(26, 72)(27, 83)(28, 75)(29, 79)(30, 78)(31, 85)(32, 82)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 16^8 ), ( 16^16 ) } Outer automorphisms :: reflexible Dual of E23.108 Graph:: bipartite v = 12 e = 64 f = 8 degree seq :: [ 8^8, 16^4 ] E23.107 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 8, 8, 8}) Quotient :: dipole Aut^+ = C4 . D8 = C4 . (C4 x C2) (small group id <32, 15>) Aut = (C2 x D16) : C2 (small group id <64, 153>) |r| :: 2 Presentation :: [ R^2, Y2^2 * Y1^-1, (R * Y1)^2, Y1^4, (Y3, Y1), (R * Y3)^2, Y3 * Y2 * Y1 * Y3 * Y2, Y3 * Y2^-1 * Y1^-1 * Y3 * Y2^-1, (R * Y2 * Y3^-1)^2, Y3^-1 * Y1^-1 * Y3^-3 * Y1^-1, Y3^8 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 9, 41, 18, 50, 6, 38)(4, 36, 10, 42, 25, 57, 16, 48)(7, 39, 11, 43, 26, 58, 19, 51)(12, 44, 23, 55, 22, 54, 20, 52)(13, 45, 17, 49, 14, 46, 21, 53)(15, 47, 27, 59, 24, 56, 28, 60)(29, 61, 31, 63, 30, 62, 32, 64)(65, 97, 67, 99, 66, 98, 73, 105, 72, 104, 82, 114, 69, 101, 70, 102)(68, 100, 78, 110, 74, 106, 85, 117, 89, 121, 77, 109, 80, 112, 81, 113)(71, 103, 86, 118, 75, 107, 84, 116, 90, 122, 76, 108, 83, 115, 87, 119)(79, 111, 94, 126, 91, 123, 96, 128, 88, 120, 93, 125, 92, 124, 95, 127) L = (1, 68)(2, 74)(3, 76)(4, 79)(5, 80)(6, 84)(7, 65)(8, 89)(9, 87)(10, 91)(11, 66)(12, 93)(13, 67)(14, 82)(15, 90)(16, 92)(17, 73)(18, 86)(19, 69)(20, 96)(21, 70)(22, 94)(23, 95)(24, 71)(25, 88)(26, 72)(27, 83)(28, 75)(29, 78)(30, 77)(31, 85)(32, 81)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 16^8 ), ( 16^16 ) } Outer automorphisms :: reflexible Dual of E23.109 Graph:: bipartite v = 12 e = 64 f = 8 degree seq :: [ 8^8, 16^4 ] E23.108 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 8, 8, 8}) Quotient :: dipole Aut^+ = C4 . D8 = C4 . (C4 x C2) (small group id <32, 15>) Aut = (C2 x D16) : C2 (small group id <64, 153>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, Y1^-1 * Y2^-1 * Y1 * Y2^-1, (R * Y2 * Y3^-1)^2, Y2^3 * Y1^-1 * Y2^-1 * Y1^-3, Y2^-2 * Y1^2 * Y2^2 * Y1^-2, Y2^8, Y1^8, (Y3 * Y1)^4 ] Map:: non-degenerate R = (1, 33, 2, 34, 6, 38, 14, 46, 26, 58, 24, 56, 12, 44, 4, 36)(3, 35, 8, 40, 15, 47, 28, 60, 25, 57, 31, 63, 21, 53, 10, 42)(5, 37, 7, 39, 16, 48, 27, 59, 19, 51, 32, 64, 23, 55, 11, 43)(9, 41, 18, 50, 29, 61, 22, 54, 13, 45, 17, 49, 30, 62, 20, 52)(65, 97, 67, 99, 73, 105, 83, 115, 90, 122, 89, 121, 77, 109, 69, 101)(66, 98, 71, 103, 81, 113, 95, 127, 88, 120, 96, 128, 82, 114, 72, 104)(68, 100, 75, 107, 86, 118, 92, 124, 78, 110, 91, 123, 84, 116, 74, 106)(70, 102, 79, 111, 93, 125, 87, 119, 76, 108, 85, 117, 94, 126, 80, 112) L = (1, 66)(2, 70)(3, 72)(4, 65)(5, 71)(6, 78)(7, 80)(8, 79)(9, 82)(10, 67)(11, 69)(12, 68)(13, 81)(14, 90)(15, 92)(16, 91)(17, 94)(18, 93)(19, 96)(20, 73)(21, 74)(22, 77)(23, 75)(24, 76)(25, 95)(26, 88)(27, 83)(28, 89)(29, 86)(30, 84)(31, 85)(32, 87)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E23.106 Graph:: bipartite v = 8 e = 64 f = 12 degree seq :: [ 16^8 ] E23.109 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 8, 8, 8}) Quotient :: dipole Aut^+ = C4 . D8 = C4 . (C4 x C2) (small group id <32, 15>) Aut = (C2 x D16) : C2 (small group id <64, 153>) |r| :: 2 Presentation :: [ R^2, Y1^-3 * Y3^-1, (Y3^-1 * Y1)^2, (Y3, Y1^-1), Y3^-3 * Y1^-1, Y3 * Y2^-1 * Y3^-1 * Y2^-1, Y1^-2 * Y3^2, (R * Y1)^2, Y2^-1 * Y1 * Y2^-1 * Y1^-1, R * Y2 * R * Y2^-1, (R * Y3)^2, Y2^2 * Y3 * Y2^-1 * Y1^-1 * Y2, Y3 * Y2^-4 * Y1^-1 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 7, 39, 12, 44, 4, 36, 10, 42, 5, 37)(3, 35, 11, 43, 21, 53, 16, 48, 28, 60, 14, 46, 26, 58, 15, 47)(6, 38, 9, 41, 22, 54, 20, 52, 25, 57, 17, 49, 24, 56, 18, 50)(13, 45, 27, 59, 31, 63, 30, 62, 19, 51, 23, 55, 32, 64, 29, 61)(65, 97, 67, 99, 77, 109, 89, 121, 76, 108, 92, 124, 83, 115, 70, 102)(66, 98, 73, 105, 87, 119, 78, 110, 68, 100, 81, 113, 91, 123, 75, 107)(69, 101, 82, 114, 94, 126, 80, 112, 71, 103, 84, 116, 93, 125, 79, 111)(72, 104, 85, 117, 95, 127, 88, 120, 74, 106, 90, 122, 96, 128, 86, 118) L = (1, 68)(2, 74)(3, 78)(4, 72)(5, 76)(6, 81)(7, 65)(8, 69)(9, 88)(10, 71)(11, 90)(12, 66)(13, 87)(14, 85)(15, 92)(16, 67)(17, 86)(18, 89)(19, 91)(20, 70)(21, 79)(22, 82)(23, 95)(24, 84)(25, 73)(26, 80)(27, 96)(28, 75)(29, 83)(30, 77)(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) :: { ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E23.107 Graph:: bipartite v = 8 e = 64 f = 12 degree seq :: [ 16^8 ] E23.110 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 8, 8, 8}) Quotient :: dipole Aut^+ = C4 . D8 = C4 . (C4 x C2) (small group id <32, 15>) Aut = (C2 x D16) : C2 (small group id <64, 153>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y3 * Y1 * Y2^-1, Y3^-1 * Y1^-1 * Y2^-2, Y1^-1 * Y2 * Y1 * Y2, R * Y2 * R * Y2^-1, Y1^-2 * Y3^-2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y1^-1)^2, Y2 * Y3 * Y2 * Y3^-1, Y1^-1 * Y2^2 * Y3^3, Y1^-2 * Y3 * Y1 * Y3 * Y1^-1, Y3^-1 * Y2^-1 * Y3^-2 * Y1 * Y2, Y1^-1 * Y2^-1 * Y1^-1 * Y3 * Y2^-1 * Y1^-1, Y3^-1 * Y1^-1 * Y2^6 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 20, 52, 30, 62, 28, 60, 17, 49, 5, 37)(3, 35, 11, 43, 21, 53, 31, 63, 25, 57, 32, 64, 26, 58, 15, 47)(4, 36, 13, 45, 7, 39, 19, 51, 23, 55, 10, 42, 24, 56, 12, 44)(6, 38, 9, 41, 22, 54, 14, 46, 27, 59, 16, 48, 29, 61, 18, 50)(65, 97, 67, 99, 77, 109, 91, 123, 94, 126, 89, 121, 74, 106, 70, 102)(66, 98, 73, 105, 88, 120, 96, 128, 92, 124, 80, 112, 71, 103, 75, 107)(68, 100, 79, 111, 69, 101, 82, 114, 87, 119, 95, 127, 84, 116, 78, 110)(72, 104, 85, 117, 83, 115, 93, 125, 81, 113, 90, 122, 76, 108, 86, 118) L = (1, 68)(2, 74)(3, 78)(4, 81)(5, 83)(6, 79)(7, 65)(8, 71)(9, 89)(10, 69)(11, 70)(12, 66)(13, 84)(14, 90)(15, 93)(16, 67)(17, 88)(18, 85)(19, 92)(20, 76)(21, 80)(22, 75)(23, 72)(24, 94)(25, 82)(26, 73)(27, 95)(28, 77)(29, 96)(30, 87)(31, 86)(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, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E23.100 Graph:: bipartite v = 8 e = 64 f = 12 degree seq :: [ 16^8 ] E23.111 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 8, 8, 8}) Quotient :: dipole Aut^+ = C4 . D8 = C4 . (C4 x C2) (small group id <32, 15>) Aut = (C2 x D16) : C2 (small group id <64, 153>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y2 * Y3^-1 * Y2^-1, Y2^-2 * Y1^-1 * Y3^-1, Y3 * Y2^-2 * Y1, (R * Y3)^2, R * Y2 * R * Y2^-1, Y2^-1 * Y1^-1 * Y2^-1 * Y1, (R * Y1)^2, (Y3 * Y1^-1)^2, Y3^2 * Y1 * Y3^-2 * Y1^-1, Y3 * Y2^-1 * Y1^-1 * Y3 * Y2 * Y1^-1, Y3^8, Y1^8, Y2^-2 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1, Y1^-1 * Y3^-1 * Y2^6 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 20, 52, 30, 62, 29, 61, 17, 49, 5, 37)(3, 35, 11, 43, 21, 53, 16, 48, 28, 60, 19, 51, 27, 59, 14, 46)(4, 36, 15, 47, 7, 39, 18, 50, 23, 55, 10, 42, 24, 56, 12, 44)(6, 38, 9, 41, 22, 54, 31, 63, 25, 57, 32, 64, 26, 58, 13, 45)(65, 97, 67, 99, 74, 106, 89, 121, 94, 126, 92, 124, 79, 111, 70, 102)(66, 98, 73, 105, 71, 103, 83, 115, 93, 125, 96, 128, 88, 120, 75, 107)(68, 100, 80, 112, 84, 116, 95, 127, 87, 119, 78, 110, 69, 101, 77, 109)(72, 104, 85, 117, 76, 108, 90, 122, 81, 113, 91, 123, 82, 114, 86, 118) L = (1, 68)(2, 74)(3, 77)(4, 81)(5, 82)(6, 80)(7, 65)(8, 71)(9, 67)(10, 69)(11, 89)(12, 66)(13, 91)(14, 86)(15, 84)(16, 90)(17, 88)(18, 93)(19, 70)(20, 76)(21, 73)(22, 83)(23, 72)(24, 94)(25, 78)(26, 75)(27, 96)(28, 95)(29, 79)(30, 87)(31, 85)(32, 92)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E23.101 Graph:: bipartite v = 8 e = 64 f = 12 degree seq :: [ 16^8 ] E23.112 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 8, 8, 8}) Quotient :: dipole Aut^+ = C4 . D8 = C4 . (C4 x C2) (small group id <32, 15>) Aut = (C2 x D16) : C2 (small group id <64, 153>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-1, (R * Y1)^2, (R * Y3)^2, Y1^-1 * Y2^2 * Y1 * Y2^2, Y2^2 * Y3 * Y2^-1 * Y1^-1 * Y2, Y2 * Y1^-3 * Y2 * Y1^-1, Y2 * Y1 * Y2^-3 * Y1^-1, (R * Y2 * Y3^-1)^2, Y1^-1 * Y2^-1 * Y3^-1 * Y1^-2 * Y2^-1, Y1^-1 * Y2 * Y1^2 * Y2^-1 * Y1^-1, Y2^-2 * Y3 * Y2 * Y1^-1 * Y2^-1, (Y3^-1 * Y1^-1)^4, (Y3 * Y2^-1)^8 ] Map:: non-degenerate R = (1, 33, 2, 34, 6, 38, 18, 50, 30, 62, 27, 59, 13, 45, 4, 36)(3, 35, 9, 41, 19, 51, 14, 46, 25, 57, 8, 40, 24, 56, 11, 43)(5, 37, 15, 47, 20, 52, 12, 44, 23, 55, 7, 39, 21, 53, 16, 48)(10, 42, 26, 58, 31, 63, 29, 61, 17, 49, 22, 54, 32, 64, 28, 60)(65, 97, 67, 99, 74, 106, 87, 119, 94, 126, 89, 121, 81, 113, 69, 101)(66, 98, 71, 103, 86, 118, 73, 105, 91, 123, 79, 111, 90, 122, 72, 104)(68, 100, 76, 108, 93, 125, 75, 107, 82, 114, 80, 112, 92, 124, 78, 110)(70, 102, 83, 115, 95, 127, 85, 117, 77, 109, 88, 120, 96, 128, 84, 116) L = (1, 66)(2, 70)(3, 73)(4, 65)(5, 79)(6, 82)(7, 85)(8, 88)(9, 83)(10, 90)(11, 67)(12, 87)(13, 68)(14, 89)(15, 84)(16, 69)(17, 86)(18, 94)(19, 78)(20, 76)(21, 80)(22, 96)(23, 71)(24, 75)(25, 72)(26, 95)(27, 77)(28, 74)(29, 81)(30, 91)(31, 93)(32, 92)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E23.103 Graph:: bipartite v = 8 e = 64 f = 12 degree seq :: [ 16^8 ] E23.113 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 8, 8, 8}) Quotient :: dipole Aut^+ = C4 . D8 = C4 . (C4 x C2) (small group id <32, 15>) Aut = (C2 x D16) : C2 (small group id <64, 153>) |r| :: 2 Presentation :: [ R^2, (Y1, Y3), (R * Y3)^2, Y3^2 * Y1^-2, Y1^-2 * Y3^-1 * Y1^-1, Y3^-1 * Y1^-1 * Y3^-2, Y2^-1 * Y3 * Y2^-1 * Y1^-1, (Y3 * Y1^-1)^2, Y2^-1 * Y1 * Y2^-1 * Y3^-1, (R * Y1)^2, Y2^-1 * Y1^-1 * Y3^-1 * Y2 * Y1^-2, Y2^2 * Y3 * Y2^-2 * Y1^-1, (R * Y2 * Y3^-1)^2, Y2^8 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 7, 39, 12, 44, 4, 36, 10, 42, 5, 37)(3, 35, 13, 45, 21, 53, 16, 48, 27, 59, 11, 43, 26, 58, 15, 47)(6, 38, 17, 49, 22, 54, 18, 50, 25, 57, 9, 41, 23, 55, 19, 51)(14, 46, 28, 60, 31, 63, 30, 62, 20, 52, 24, 56, 32, 64, 29, 61)(65, 97, 67, 99, 78, 110, 89, 121, 76, 108, 91, 123, 84, 116, 70, 102)(66, 98, 73, 105, 88, 120, 77, 109, 68, 100, 81, 113, 92, 124, 75, 107)(69, 101, 82, 114, 94, 126, 79, 111, 71, 103, 83, 115, 93, 125, 80, 112)(72, 104, 85, 117, 95, 127, 87, 119, 74, 106, 90, 122, 96, 128, 86, 118) L = (1, 68)(2, 74)(3, 75)(4, 72)(5, 76)(6, 73)(7, 65)(8, 69)(9, 86)(10, 71)(11, 85)(12, 66)(13, 90)(14, 88)(15, 91)(16, 67)(17, 87)(18, 70)(19, 89)(20, 92)(21, 79)(22, 83)(23, 82)(24, 95)(25, 81)(26, 80)(27, 77)(28, 96)(29, 84)(30, 78)(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) :: { ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E23.102 Graph:: bipartite v = 8 e = 64 f = 12 degree seq :: [ 16^8 ] E23.114 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 8, 8, 8}) Quotient :: dipole Aut^+ = C4 . D8 = C4 . (C4 x C2) (small group id <32, 15>) Aut = (C2 x D16) : C2 (small group id <64, 153>) |r| :: 2 Presentation :: [ R^2, Y3^2 * Y1^2, Y2 * Y1 * Y2^-1 * Y3, Y3^-1 * Y1^-1 * Y2^2, (Y3 * Y1^-1)^2, Y2^2 * Y3 * Y1, Y3^2 * Y1^2, Y1 * Y2^-1 * Y3 * Y2, (R * Y1)^2, (R * Y3)^2, Y3 * Y1 * Y2^-1 * Y3^-1 * Y2^-1 * Y1^-1, Y3^-1 * Y2 * Y3^-1 * Y2 * Y1^2, Y2^-1 * Y1^-1 * Y2^-1 * Y1^-3, Y1^-2 * Y2 * Y3^-1 * Y1 * Y2, (R * Y2 * Y3^-1)^2, Y1 * Y2 * Y3 * Y1^-1 * Y3^-1 * Y2, Y2 * Y1 * Y2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1, (Y2^-1 * Y3 * Y2^-1 * Y3^-1)^2, Y1^8, Y3^8 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 22, 54, 32, 64, 31, 63, 18, 50, 5, 37)(3, 35, 13, 45, 23, 55, 21, 53, 27, 59, 11, 43, 29, 61, 15, 47)(4, 36, 17, 49, 7, 39, 20, 52, 25, 57, 10, 42, 30, 62, 12, 44)(6, 38, 16, 48, 24, 56, 19, 51, 28, 60, 9, 41, 26, 58, 14, 46)(65, 97, 67, 99, 74, 106, 92, 124, 96, 128, 91, 123, 81, 113, 70, 102)(66, 98, 73, 105, 71, 103, 77, 109, 95, 127, 80, 112, 94, 126, 75, 107)(68, 100, 79, 111, 86, 118, 78, 110, 89, 121, 85, 117, 69, 101, 83, 115)(72, 104, 87, 119, 76, 108, 90, 122, 82, 114, 93, 125, 84, 116, 88, 120) L = (1, 68)(2, 74)(3, 78)(4, 82)(5, 84)(6, 85)(7, 65)(8, 71)(9, 91)(10, 69)(11, 70)(12, 66)(13, 92)(14, 93)(15, 88)(16, 67)(17, 86)(18, 94)(19, 87)(20, 95)(21, 90)(22, 76)(23, 80)(24, 75)(25, 72)(26, 77)(27, 83)(28, 79)(29, 73)(30, 96)(31, 81)(32, 89)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E23.104 Graph:: bipartite v = 8 e = 64 f = 12 degree seq :: [ 16^8 ] E23.115 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 8, 8, 8}) Quotient :: dipole Aut^+ = C4 . D8 = C4 . (C4 x C2) (small group id <32, 15>) Aut = (C2 x D16) : C2 (small group id <64, 153>) |r| :: 2 Presentation :: [ R^2, Y3^-2 * Y1^-2, Y3 * Y2^-1 * Y1 * Y2, Y2^-1 * Y3 * Y1 * Y2^-1, Y1 * Y2^-2 * Y3, Y2^-1 * Y3^-1 * Y1^-1 * Y2^-1, (R * Y3)^2, Y1^-2 * Y3^-2, Y2 * Y3^-1 * Y2^-1 * Y1^-1, (R * Y1)^2, (Y3 * Y1^-1)^2, Y2^3 * Y3 * Y2 * Y1, Y1^-3 * Y2^-1 * Y1^-1 * Y2^-1, Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y1^-1, Y2^-1 * Y1 * Y3^-1 * Y1^-1 * Y2 * Y1^-1, Y2^-1 * Y1^2 * Y2 * Y1^-2, (R * Y2 * Y3^-1)^2, Y3 * Y2^-2 * Y1 * Y3 * Y1 * Y3 * Y1, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3^-1 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 22, 54, 32, 64, 31, 63, 18, 50, 5, 37)(3, 35, 13, 45, 23, 55, 17, 49, 29, 61, 11, 43, 30, 62, 16, 48)(4, 36, 14, 46, 7, 39, 20, 52, 25, 57, 10, 42, 27, 59, 12, 44)(6, 38, 21, 53, 24, 56, 15, 47, 28, 60, 9, 41, 26, 58, 19, 51)(65, 97, 67, 99, 78, 110, 92, 124, 96, 128, 93, 125, 74, 106, 70, 102)(66, 98, 73, 105, 91, 123, 77, 109, 95, 127, 85, 117, 71, 103, 75, 107)(68, 100, 81, 113, 69, 101, 79, 111, 89, 121, 80, 112, 86, 118, 83, 115)(72, 104, 87, 119, 84, 116, 90, 122, 82, 114, 94, 126, 76, 108, 88, 120) L = (1, 68)(2, 74)(3, 79)(4, 82)(5, 84)(6, 80)(7, 65)(8, 71)(9, 67)(10, 69)(11, 92)(12, 66)(13, 70)(14, 86)(15, 94)(16, 90)(17, 88)(18, 91)(19, 87)(20, 95)(21, 93)(22, 76)(23, 73)(24, 77)(25, 72)(26, 75)(27, 96)(28, 81)(29, 83)(30, 85)(31, 78)(32, 89)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E23.105 Graph:: bipartite v = 8 e = 64 f = 12 degree seq :: [ 16^8 ] E23.116 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 8, 8, 8}) Quotient :: dipole Aut^+ = C4 . D8 = C4 . (C4 x C2) (small group id <32, 15>) Aut = (C2 x D16) : C2 (small group id <64, 153>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3, Y2^-1 * Y1^-2 * Y2^-1, Y3^-1 * Y1^-1 * Y2^-2, (R * Y3)^2, (R * Y1)^2, Y2 * Y1^-1 * Y3^-1 * Y2^-1 * Y3 * Y1, Y2^-1 * R * Y1 * Y3 * R * Y2^-1, (R * Y2 * Y3^-1)^2, (Y2^-1 * Y3^-1 * Y2 * Y1^-1)^2, Y2^8, Y1^-1 * Y2 * Y1^-1 * Y3^-1 * Y1^-2 * Y2 * Y1^-1, Y2 * Y1^-1 * Y2 * Y3 * Y2 * Y3 * Y2 * Y1^-1, Y2 * R * Y2^-1 * Y1 * Y2^-1 * R * Y2^-1 * Y1^-1, Y1^8, (Y3 * Y2^-1)^8 ] Map:: non-degenerate R = (1, 33, 2, 34, 6, 38, 14, 46, 26, 58, 22, 54, 10, 42, 4, 36)(3, 35, 9, 41, 5, 37, 13, 45, 15, 47, 28, 60, 21, 53, 11, 43)(7, 39, 16, 48, 8, 40, 18, 50, 27, 59, 24, 56, 12, 44, 17, 49)(19, 51, 32, 64, 20, 52, 31, 63, 25, 57, 29, 61, 23, 55, 30, 62)(65, 97, 67, 99, 74, 106, 85, 117, 90, 122, 79, 111, 70, 102, 69, 101)(66, 98, 71, 103, 68, 100, 76, 108, 86, 118, 91, 123, 78, 110, 72, 104)(73, 105, 83, 115, 75, 107, 87, 119, 92, 124, 89, 121, 77, 109, 84, 116)(80, 112, 93, 125, 81, 113, 95, 127, 88, 120, 96, 128, 82, 114, 94, 126) L = (1, 66)(2, 70)(3, 73)(4, 65)(5, 77)(6, 78)(7, 80)(8, 82)(9, 69)(10, 68)(11, 67)(12, 81)(13, 79)(14, 90)(15, 92)(16, 72)(17, 71)(18, 91)(19, 96)(20, 95)(21, 75)(22, 74)(23, 94)(24, 76)(25, 93)(26, 86)(27, 88)(28, 85)(29, 87)(30, 83)(31, 89)(32, 84)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E23.99 Graph:: bipartite v = 8 e = 64 f = 12 degree seq :: [ 16^8 ] E23.117 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 16, 16}) Quotient :: edge^2 Aut^+ = Q32 (small group id <32, 20>) Aut = (C16 x C2) : C2 (small group id <64, 189>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y2^-1, Y1^4, R * Y2 * R * Y1, Y3^-1 * Y1 * Y3^-1 * Y1^-1, Y2^4, (R * Y3)^2, Y3^-1 * Y2 * Y3^-1 * Y2^-1, Y1^-1 * Y3 * Y2 * Y1^-1 * Y3^-1 * Y1^-1, Y3^3 * Y2 * Y3^-5 * Y1^-1 ] Map:: non-degenerate R = (1, 33, 4, 36, 11, 43, 19, 51, 27, 59, 30, 62, 22, 54, 14, 46, 6, 38, 13, 45, 21, 53, 29, 61, 28, 60, 20, 52, 12, 44, 5, 37)(2, 34, 7, 39, 15, 47, 23, 55, 31, 63, 26, 58, 18, 50, 10, 42, 3, 35, 9, 41, 17, 49, 25, 57, 32, 64, 24, 56, 16, 48, 8, 40)(65, 66, 70, 67)(68, 72, 77, 74)(69, 71, 78, 73)(75, 80, 85, 82)(76, 79, 86, 81)(83, 88, 93, 90)(84, 87, 94, 89)(91, 96, 92, 95)(97, 99, 102, 98)(100, 106, 109, 104)(101, 105, 110, 103)(107, 114, 117, 112)(108, 113, 118, 111)(115, 122, 125, 120)(116, 121, 126, 119)(123, 127, 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) :: { ( 64^4 ), ( 64^32 ) } Outer automorphisms :: reflexible Dual of E23.124 Graph:: bipartite v = 18 e = 64 f = 2 degree seq :: [ 4^16, 32^2 ] E23.118 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 16, 16}) Quotient :: edge^2 Aut^+ = Q32 (small group id <32, 20>) Aut = (C16 x C2) : C2 (small group id <64, 189>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2^-2 * Y1, Y1^-1 * Y2 * Y1^-1 * Y2^-1, Y1^2 * Y2^2, Y1^4, R * Y2 * R * Y1, Y3 * Y1 * Y3 * Y1^-1, (R * Y3)^2, Y3^-1 * Y2^-1 * Y3^-1 * Y2, Y3^4 * Y2 * Y1^-1, Y3^2 * Y1 * Y3^-2 * Y1^-2 * Y3^-2 * Y1^-2 * Y3^-2 * Y1^-2 * Y3^-2 * Y1^-2 * Y3^-2 * Y1^-2 * Y3^-2 * Y1^-2 * Y3^-2 * Y1^-1 ] Map:: non-degenerate R = (1, 33, 4, 36, 15, 47, 26, 58, 11, 43, 27, 59, 32, 64, 22, 54, 8, 40, 21, 53, 31, 63, 24, 56, 9, 41, 23, 55, 20, 52, 7, 39)(2, 34, 10, 42, 25, 57, 14, 46, 3, 35, 13, 45, 29, 61, 16, 48, 5, 37, 18, 50, 30, 62, 17, 49, 6, 38, 19, 51, 28, 60, 12, 44)(65, 66, 72, 69)(67, 75, 70, 73)(68, 76, 85, 80)(71, 74, 86, 82)(77, 90, 83, 88)(78, 91, 81, 87)(79, 92, 95, 93)(84, 89, 96, 94)(97, 99, 104, 102)(98, 105, 101, 107)(100, 110, 117, 113)(103, 109, 118, 115)(106, 120, 114, 122)(108, 119, 112, 123)(111, 121, 127, 126)(116, 125, 128, 124) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 81)(18, 82)(19, 83)(20, 84)(21, 85)(22, 86)(23, 87)(24, 88)(25, 89)(26, 90)(27, 91)(28, 92)(29, 93)(30, 94)(31, 95)(32, 96)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 64^4 ), ( 64^32 ) } Outer automorphisms :: reflexible Dual of E23.127 Graph:: bipartite v = 18 e = 64 f = 2 degree seq :: [ 4^16, 32^2 ] E23.119 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 16, 16}) Quotient :: edge^2 Aut^+ = Q32 (small group id <32, 20>) Aut = (C16 x C2) : C2 (small group id <64, 189>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1^-1, Y1^4, R * Y1 * R * Y2, (R * Y3)^2, Y3^-1 * Y1^-1 * Y3^-1 * Y1, Y2^4, Y3^7 * Y1^-1 * Y3^-1 * Y1^-1, (Y3 * Y1^-1 * Y2^-1)^16 ] Map:: non-degenerate R = (1, 33, 3, 35, 9, 41, 17, 49, 25, 57, 30, 62, 22, 54, 14, 46, 6, 38, 13, 45, 21, 53, 29, 61, 28, 60, 20, 52, 12, 44, 5, 37)(2, 34, 7, 39, 15, 47, 23, 55, 31, 63, 26, 58, 18, 50, 10, 42, 4, 36, 11, 43, 19, 51, 27, 59, 32, 64, 24, 56, 16, 48, 8, 40)(65, 66, 70, 68)(67, 72, 77, 74)(69, 71, 78, 75)(73, 80, 85, 82)(76, 79, 86, 83)(81, 88, 93, 90)(84, 87, 94, 91)(89, 96, 92, 95)(97, 98, 102, 100)(99, 104, 109, 106)(101, 103, 110, 107)(105, 112, 117, 114)(108, 111, 118, 115)(113, 120, 125, 122)(116, 119, 126, 123)(121, 128, 124, 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) :: { ( 64^4 ), ( 64^32 ) } Outer automorphisms :: reflexible Dual of E23.126 Graph:: bipartite v = 18 e = 64 f = 2 degree seq :: [ 4^16, 32^2 ] E23.120 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 16, 16}) Quotient :: edge^2 Aut^+ = Q32 (small group id <32, 20>) Aut = (C16 x C2) : C2 (small group id <64, 189>) |r| :: 2 Presentation :: [ R^2, Y1^2 * Y2^2, Y1^-1 * Y2 * Y1^-1 * Y2^-1, Y2^-1 * Y1^2 * Y2^-1, Y2^4, Y2^-1 * Y1 * Y2^-1 * Y1^-1, R * Y2 * R * Y1, (R * Y3)^2, Y3 * Y1 * Y3 * Y1^-1, Y3 * Y2^-1 * Y3 * Y2, Y3^-4 * Y2 * Y1^-1, Y3 * Y2^-2 * Y3 * Y1^-1 * Y3^-2 * Y1^-2 * Y3^-2 * Y1^-2 * Y3^-2 * Y1^-2 * Y3^-2 * Y1^-2 * Y3^-2 * Y1^-2 * Y3^-2 * Y1^-2 * Y3^-2 * Y1^-1 ] Map:: non-degenerate R = (1, 33, 4, 36, 15, 47, 24, 56, 9, 41, 23, 55, 32, 64, 22, 54, 8, 40, 21, 53, 31, 63, 26, 58, 11, 43, 27, 59, 20, 52, 7, 39)(2, 34, 10, 42, 25, 57, 17, 49, 6, 38, 19, 51, 30, 62, 16, 48, 5, 37, 18, 50, 29, 61, 14, 46, 3, 35, 13, 45, 28, 60, 12, 44)(65, 66, 72, 69)(67, 75, 70, 73)(68, 76, 85, 80)(71, 74, 86, 82)(77, 90, 83, 88)(78, 91, 81, 87)(79, 92, 95, 94)(84, 89, 96, 93)(97, 99, 104, 102)(98, 105, 101, 107)(100, 110, 117, 113)(103, 109, 118, 115)(106, 120, 114, 122)(108, 119, 112, 123)(111, 125, 127, 121)(116, 124, 128, 126) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 81)(18, 82)(19, 83)(20, 84)(21, 85)(22, 86)(23, 87)(24, 88)(25, 89)(26, 90)(27, 91)(28, 92)(29, 93)(30, 94)(31, 95)(32, 96)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 64^4 ), ( 64^32 ) } Outer automorphisms :: reflexible Dual of E23.125 Graph:: bipartite v = 18 e = 64 f = 2 degree seq :: [ 4^16, 32^2 ] E23.121 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 16, 16}) Quotient :: edge^2 Aut^+ = C16 : C2 (small group id <32, 17>) Aut = (C16 x C2) : C2 (small group id <64, 185>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1, Y1 * Y2, Y3^4, R * Y1 * R * Y2, (R * Y3)^2, Y3 * Y1^-1 * Y3 * Y2^-1, Y2^4 * Y3 * Y1^-1 * Y3^-1 * Y1^-3, Y1^16, Y2^16 ] Map:: non-degenerate 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, 32, 64, 23, 55)(17, 49, 26, 58, 29, 61, 27, 59)(21, 53, 30, 62, 25, 57, 31, 63)(65, 66, 70, 77, 85, 93, 92, 84, 76, 80, 88, 96, 89, 81, 73, 67)(68, 72, 78, 87, 94, 90, 83, 74, 69, 71, 79, 86, 95, 91, 82, 75)(97, 99, 105, 113, 121, 128, 120, 112, 108, 116, 124, 125, 117, 109, 102, 98)(100, 107, 114, 123, 127, 118, 111, 103, 101, 106, 115, 122, 126, 119, 110, 104) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 81)(18, 82)(19, 83)(20, 84)(21, 85)(22, 86)(23, 87)(24, 88)(25, 89)(26, 90)(27, 91)(28, 92)(29, 93)(30, 94)(31, 95)(32, 96)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 16^8 ), ( 16^16 ) } Outer automorphisms :: reflexible Dual of E23.128 Graph:: bipartite v = 12 e = 64 f = 8 degree seq :: [ 8^8, 16^4 ] E23.122 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 16, 16}) Quotient :: edge^2 Aut^+ = Q32 (small group id <32, 20>) Aut = (C16 x C2) : C2 (small group id <64, 189>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y2^-1, Y1 * Y2, Y3^4, (R * Y3)^2, R * Y1 * R * Y2, Y3 * Y2^-1 * Y3^-1 * Y2^-1, Y2^4 * Y3^-1 * Y2^-1 * Y3^-1 * Y1^-3, Y2^16, Y1^16 ] Map:: non-degenerate 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, 32, 64, 23, 55)(17, 49, 26, 58, 29, 61, 27, 59)(21, 53, 30, 62, 25, 57, 31, 63)(65, 66, 70, 77, 85, 93, 92, 84, 76, 80, 88, 96, 89, 81, 73, 67)(68, 74, 82, 90, 95, 87, 79, 72, 69, 75, 83, 91, 94, 86, 78, 71)(97, 99, 105, 113, 121, 128, 120, 112, 108, 116, 124, 125, 117, 109, 102, 98)(100, 103, 110, 118, 126, 123, 115, 107, 101, 104, 111, 119, 127, 122, 114, 106) 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) :: { ( 16^8 ), ( 16^16 ) } Outer automorphisms :: reflexible Dual of E23.129 Graph:: bipartite v = 12 e = 64 f = 8 degree seq :: [ 8^8, 16^4 ] E23.123 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 16, 16}) Quotient :: edge^2 Aut^+ = QD32 (small group id <32, 19>) Aut = (C16 x C2) : C2 (small group id <64, 189>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1^-1, Y1 * Y2, Y3 * Y1 * Y3 * Y2^-1, R * Y2 * R * Y1, (R * Y3)^2, Y3^-1 * Y1 * Y3^-1 * Y2^-1, Y3^4, Y2^4 * Y3 * Y1 * Y3^-1 * Y1^-3, Y1^16, Y2^16 ] Map:: non-degenerate 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, 32, 64, 23, 55)(17, 49, 26, 58, 29, 61, 27, 59)(21, 53, 30, 62, 25, 57, 31, 63)(65, 66, 70, 77, 85, 93, 92, 84, 76, 80, 88, 96, 89, 81, 73, 67)(68, 75, 82, 91, 95, 86, 79, 71, 69, 74, 83, 90, 94, 87, 78, 72)(97, 99, 105, 113, 121, 128, 120, 112, 108, 116, 124, 125, 117, 109, 102, 98)(100, 104, 110, 119, 126, 122, 115, 106, 101, 103, 111, 118, 127, 123, 114, 107) 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) :: { ( 16^8 ), ( 16^16 ) } Outer automorphisms :: reflexible Dual of E23.130 Graph:: bipartite v = 12 e = 64 f = 8 degree seq :: [ 8^8, 16^4 ] E23.124 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 16, 16}) Quotient :: loop^2 Aut^+ = Q32 (small group id <32, 20>) Aut = (C16 x C2) : C2 (small group id <64, 189>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y2^-1, Y1^4, R * Y2 * R * Y1, Y3^-1 * Y1 * Y3^-1 * Y1^-1, Y2^4, (R * Y3)^2, Y3^-1 * Y2 * Y3^-1 * Y2^-1, Y1^-1 * Y3 * Y2 * Y1^-1 * Y3^-1 * Y1^-1, Y3^3 * Y2 * Y3^-5 * Y1^-1 ] Map:: non-degenerate R = (1, 33, 65, 97, 4, 36, 68, 100, 11, 43, 75, 107, 19, 51, 83, 115, 27, 59, 91, 123, 30, 62, 94, 126, 22, 54, 86, 118, 14, 46, 78, 110, 6, 38, 70, 102, 13, 45, 77, 109, 21, 53, 85, 117, 29, 61, 93, 125, 28, 60, 92, 124, 20, 52, 84, 116, 12, 44, 76, 108, 5, 37, 69, 101)(2, 34, 66, 98, 7, 39, 71, 103, 15, 47, 79, 111, 23, 55, 87, 119, 31, 63, 95, 127, 26, 58, 90, 122, 18, 50, 82, 114, 10, 42, 74, 106, 3, 35, 67, 99, 9, 41, 73, 105, 17, 49, 81, 113, 25, 57, 89, 121, 32, 64, 96, 128, 24, 56, 88, 120, 16, 48, 80, 112, 8, 40, 72, 104) L = (1, 34)(2, 38)(3, 33)(4, 40)(5, 39)(6, 35)(7, 46)(8, 45)(9, 37)(10, 36)(11, 48)(12, 47)(13, 42)(14, 41)(15, 54)(16, 53)(17, 44)(18, 43)(19, 56)(20, 55)(21, 50)(22, 49)(23, 62)(24, 61)(25, 52)(26, 51)(27, 64)(28, 63)(29, 58)(30, 57)(31, 59)(32, 60)(65, 99)(66, 97)(67, 102)(68, 106)(69, 105)(70, 98)(71, 101)(72, 100)(73, 110)(74, 109)(75, 114)(76, 113)(77, 104)(78, 103)(79, 108)(80, 107)(81, 118)(82, 117)(83, 122)(84, 121)(85, 112)(86, 111)(87, 116)(88, 115)(89, 126)(90, 125)(91, 127)(92, 128)(93, 120)(94, 119)(95, 124)(96, 123) 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 E23.117 Transitivity :: VT+ Graph:: bipartite v = 2 e = 64 f = 18 degree seq :: [ 64^2 ] E23.125 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 16, 16}) Quotient :: loop^2 Aut^+ = Q32 (small group id <32, 20>) Aut = (C16 x C2) : C2 (small group id <64, 189>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2^-2 * Y1, Y1^-1 * Y2 * Y1^-1 * Y2^-1, Y1^2 * Y2^2, Y1^4, R * Y2 * R * Y1, Y3 * Y1 * Y3 * Y1^-1, (R * Y3)^2, Y3^-1 * Y2^-1 * Y3^-1 * Y2, Y3^4 * Y2 * Y1^-1, Y3^2 * Y1 * Y3^-2 * Y1^-2 * Y3^-2 * Y1^-2 * Y3^-2 * Y1^-2 * Y3^-2 * Y1^-2 * Y3^-2 * Y1^-2 * Y3^-2 * Y1^-2 * Y3^-2 * Y1^-1 ] Map:: non-degenerate R = (1, 33, 65, 97, 4, 36, 68, 100, 15, 47, 79, 111, 26, 58, 90, 122, 11, 43, 75, 107, 27, 59, 91, 123, 32, 64, 96, 128, 22, 54, 86, 118, 8, 40, 72, 104, 21, 53, 85, 117, 31, 63, 95, 127, 24, 56, 88, 120, 9, 41, 73, 105, 23, 55, 87, 119, 20, 52, 84, 116, 7, 39, 71, 103)(2, 34, 66, 98, 10, 42, 74, 106, 25, 57, 89, 121, 14, 46, 78, 110, 3, 35, 67, 99, 13, 45, 77, 109, 29, 61, 93, 125, 16, 48, 80, 112, 5, 37, 69, 101, 18, 50, 82, 114, 30, 62, 94, 126, 17, 49, 81, 113, 6, 38, 70, 102, 19, 51, 83, 115, 28, 60, 92, 124, 12, 44, 76, 108) L = (1, 34)(2, 40)(3, 43)(4, 44)(5, 33)(6, 41)(7, 42)(8, 37)(9, 35)(10, 54)(11, 38)(12, 53)(13, 58)(14, 59)(15, 60)(16, 36)(17, 55)(18, 39)(19, 56)(20, 57)(21, 48)(22, 50)(23, 46)(24, 45)(25, 64)(26, 51)(27, 49)(28, 63)(29, 47)(30, 52)(31, 61)(32, 62)(65, 99)(66, 105)(67, 104)(68, 110)(69, 107)(70, 97)(71, 109)(72, 102)(73, 101)(74, 120)(75, 98)(76, 119)(77, 118)(78, 117)(79, 121)(80, 123)(81, 100)(82, 122)(83, 103)(84, 125)(85, 113)(86, 115)(87, 112)(88, 114)(89, 127)(90, 106)(91, 108)(92, 116)(93, 128)(94, 111)(95, 126)(96, 124) 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 E23.120 Transitivity :: VT+ Graph:: bipartite v = 2 e = 64 f = 18 degree seq :: [ 64^2 ] E23.126 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 16, 16}) Quotient :: loop^2 Aut^+ = Q32 (small group id <32, 20>) Aut = (C16 x C2) : C2 (small group id <64, 189>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1^-1, Y1^4, R * Y1 * R * Y2, (R * Y3)^2, Y3^-1 * Y1^-1 * Y3^-1 * Y1, Y2^4, Y3^7 * Y1^-1 * Y3^-1 * Y1^-1, (Y3 * Y1^-1 * Y2^-1)^16 ] Map:: non-degenerate R = (1, 33, 65, 97, 3, 35, 67, 99, 9, 41, 73, 105, 17, 49, 81, 113, 25, 57, 89, 121, 30, 62, 94, 126, 22, 54, 86, 118, 14, 46, 78, 110, 6, 38, 70, 102, 13, 45, 77, 109, 21, 53, 85, 117, 29, 61, 93, 125, 28, 60, 92, 124, 20, 52, 84, 116, 12, 44, 76, 108, 5, 37, 69, 101)(2, 34, 66, 98, 7, 39, 71, 103, 15, 47, 79, 111, 23, 55, 87, 119, 31, 63, 95, 127, 26, 58, 90, 122, 18, 50, 82, 114, 10, 42, 74, 106, 4, 36, 68, 100, 11, 43, 75, 107, 19, 51, 83, 115, 27, 59, 91, 123, 32, 64, 96, 128, 24, 56, 88, 120, 16, 48, 80, 112, 8, 40, 72, 104) L = (1, 34)(2, 38)(3, 40)(4, 33)(5, 39)(6, 36)(7, 46)(8, 45)(9, 48)(10, 35)(11, 37)(12, 47)(13, 42)(14, 43)(15, 54)(16, 53)(17, 56)(18, 41)(19, 44)(20, 55)(21, 50)(22, 51)(23, 62)(24, 61)(25, 64)(26, 49)(27, 52)(28, 63)(29, 58)(30, 59)(31, 57)(32, 60)(65, 98)(66, 102)(67, 104)(68, 97)(69, 103)(70, 100)(71, 110)(72, 109)(73, 112)(74, 99)(75, 101)(76, 111)(77, 106)(78, 107)(79, 118)(80, 117)(81, 120)(82, 105)(83, 108)(84, 119)(85, 114)(86, 115)(87, 126)(88, 125)(89, 128)(90, 113)(91, 116)(92, 127)(93, 122)(94, 123)(95, 121)(96, 124) 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 E23.119 Transitivity :: VT+ Graph:: bipartite v = 2 e = 64 f = 18 degree seq :: [ 64^2 ] E23.127 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 16, 16}) Quotient :: loop^2 Aut^+ = Q32 (small group id <32, 20>) Aut = (C16 x C2) : C2 (small group id <64, 189>) |r| :: 2 Presentation :: [ R^2, Y1^2 * Y2^2, Y1^-1 * Y2 * Y1^-1 * Y2^-1, Y2^-1 * Y1^2 * Y2^-1, Y2^4, Y2^-1 * Y1 * Y2^-1 * Y1^-1, R * Y2 * R * Y1, (R * Y3)^2, Y3 * Y1 * Y3 * Y1^-1, Y3 * Y2^-1 * Y3 * Y2, Y3^-4 * Y2 * Y1^-1, Y3 * Y2^-2 * Y3 * Y1^-1 * Y3^-2 * Y1^-2 * Y3^-2 * Y1^-2 * Y3^-2 * Y1^-2 * Y3^-2 * Y1^-2 * Y3^-2 * Y1^-2 * Y3^-2 * Y1^-2 * Y3^-2 * Y1^-1 ] Map:: non-degenerate R = (1, 33, 65, 97, 4, 36, 68, 100, 15, 47, 79, 111, 24, 56, 88, 120, 9, 41, 73, 105, 23, 55, 87, 119, 32, 64, 96, 128, 22, 54, 86, 118, 8, 40, 72, 104, 21, 53, 85, 117, 31, 63, 95, 127, 26, 58, 90, 122, 11, 43, 75, 107, 27, 59, 91, 123, 20, 52, 84, 116, 7, 39, 71, 103)(2, 34, 66, 98, 10, 42, 74, 106, 25, 57, 89, 121, 17, 49, 81, 113, 6, 38, 70, 102, 19, 51, 83, 115, 30, 62, 94, 126, 16, 48, 80, 112, 5, 37, 69, 101, 18, 50, 82, 114, 29, 61, 93, 125, 14, 46, 78, 110, 3, 35, 67, 99, 13, 45, 77, 109, 28, 60, 92, 124, 12, 44, 76, 108) L = (1, 34)(2, 40)(3, 43)(4, 44)(5, 33)(6, 41)(7, 42)(8, 37)(9, 35)(10, 54)(11, 38)(12, 53)(13, 58)(14, 59)(15, 60)(16, 36)(17, 55)(18, 39)(19, 56)(20, 57)(21, 48)(22, 50)(23, 46)(24, 45)(25, 64)(26, 51)(27, 49)(28, 63)(29, 52)(30, 47)(31, 62)(32, 61)(65, 99)(66, 105)(67, 104)(68, 110)(69, 107)(70, 97)(71, 109)(72, 102)(73, 101)(74, 120)(75, 98)(76, 119)(77, 118)(78, 117)(79, 125)(80, 123)(81, 100)(82, 122)(83, 103)(84, 124)(85, 113)(86, 115)(87, 112)(88, 114)(89, 111)(90, 106)(91, 108)(92, 128)(93, 127)(94, 116)(95, 121)(96, 126) 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 E23.118 Transitivity :: VT+ Graph:: bipartite v = 2 e = 64 f = 18 degree seq :: [ 64^2 ] E23.128 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 16, 16}) Quotient :: loop^2 Aut^+ = C16 : C2 (small group id <32, 17>) Aut = (C16 x C2) : C2 (small group id <64, 185>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1, Y1 * Y2, Y3^4, R * Y1 * R * Y2, (R * Y3)^2, Y3 * Y1^-1 * Y3 * Y2^-1, Y2^4 * Y3 * Y1^-1 * Y3^-1 * Y1^-3, Y1^16, Y2^16 ] Map:: non-degenerate 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, 32, 64, 96, 128, 23, 55, 87, 119)(17, 49, 81, 113, 26, 58, 90, 122, 29, 61, 93, 125, 27, 59, 91, 123)(21, 53, 85, 117, 30, 62, 94, 126, 25, 57, 89, 121, 31, 63, 95, 127) L = (1, 34)(2, 38)(3, 33)(4, 40)(5, 39)(6, 45)(7, 47)(8, 46)(9, 35)(10, 37)(11, 36)(12, 48)(13, 53)(14, 55)(15, 54)(16, 56)(17, 41)(18, 43)(19, 42)(20, 44)(21, 61)(22, 63)(23, 62)(24, 64)(25, 49)(26, 51)(27, 50)(28, 52)(29, 60)(30, 58)(31, 59)(32, 57)(65, 99)(66, 97)(67, 105)(68, 107)(69, 106)(70, 98)(71, 101)(72, 100)(73, 113)(74, 115)(75, 114)(76, 116)(77, 102)(78, 104)(79, 103)(80, 108)(81, 121)(82, 123)(83, 122)(84, 124)(85, 109)(86, 111)(87, 110)(88, 112)(89, 128)(90, 126)(91, 127)(92, 125)(93, 117)(94, 119)(95, 118)(96, 120) local type(s) :: { ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E23.121 Transitivity :: VT+ Graph:: bipartite v = 8 e = 64 f = 12 degree seq :: [ 16^8 ] E23.129 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 16, 16}) Quotient :: loop^2 Aut^+ = Q32 (small group id <32, 20>) Aut = (C16 x C2) : C2 (small group id <64, 189>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y2^-1, Y1 * Y2, Y3^4, (R * Y3)^2, R * Y1 * R * Y2, Y3 * Y2^-1 * Y3^-1 * Y2^-1, Y2^4 * Y3^-1 * Y2^-1 * Y3^-1 * Y1^-3, Y2^16, Y1^16 ] Map:: non-degenerate 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, 32, 64, 96, 128, 23, 55, 87, 119)(17, 49, 81, 113, 26, 58, 90, 122, 29, 61, 93, 125, 27, 59, 91, 123)(21, 53, 85, 117, 30, 62, 94, 126, 25, 57, 89, 121, 31, 63, 95, 127) L = (1, 34)(2, 38)(3, 33)(4, 42)(5, 43)(6, 45)(7, 36)(8, 37)(9, 35)(10, 50)(11, 51)(12, 48)(13, 53)(14, 39)(15, 40)(16, 56)(17, 41)(18, 58)(19, 59)(20, 44)(21, 61)(22, 46)(23, 47)(24, 64)(25, 49)(26, 63)(27, 62)(28, 52)(29, 60)(30, 54)(31, 55)(32, 57)(65, 99)(66, 97)(67, 105)(68, 103)(69, 104)(70, 98)(71, 110)(72, 111)(73, 113)(74, 100)(75, 101)(76, 116)(77, 102)(78, 118)(79, 119)(80, 108)(81, 121)(82, 106)(83, 107)(84, 124)(85, 109)(86, 126)(87, 127)(88, 112)(89, 128)(90, 114)(91, 115)(92, 125)(93, 117)(94, 123)(95, 122)(96, 120) local type(s) :: { ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E23.122 Transitivity :: VT+ Graph:: bipartite v = 8 e = 64 f = 12 degree seq :: [ 16^8 ] E23.130 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 16, 16}) Quotient :: loop^2 Aut^+ = QD32 (small group id <32, 19>) Aut = (C16 x C2) : C2 (small group id <64, 189>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1^-1, Y1 * Y2, Y3 * Y1 * Y3 * Y2^-1, R * Y2 * R * Y1, (R * Y3)^2, Y3^-1 * Y1 * Y3^-1 * Y2^-1, Y3^4, Y2^4 * Y3 * Y1 * Y3^-1 * Y1^-3, Y1^16, Y2^16 ] Map:: non-degenerate 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, 32, 64, 96, 128, 23, 55, 87, 119)(17, 49, 81, 113, 26, 58, 90, 122, 29, 61, 93, 125, 27, 59, 91, 123)(21, 53, 85, 117, 30, 62, 94, 126, 25, 57, 89, 121, 31, 63, 95, 127) L = (1, 34)(2, 38)(3, 33)(4, 43)(5, 42)(6, 45)(7, 37)(8, 36)(9, 35)(10, 51)(11, 50)(12, 48)(13, 53)(14, 40)(15, 39)(16, 56)(17, 41)(18, 59)(19, 58)(20, 44)(21, 61)(22, 47)(23, 46)(24, 64)(25, 49)(26, 62)(27, 63)(28, 52)(29, 60)(30, 55)(31, 54)(32, 57)(65, 99)(66, 97)(67, 105)(68, 104)(69, 103)(70, 98)(71, 111)(72, 110)(73, 113)(74, 101)(75, 100)(76, 116)(77, 102)(78, 119)(79, 118)(80, 108)(81, 121)(82, 107)(83, 106)(84, 124)(85, 109)(86, 127)(87, 126)(88, 112)(89, 128)(90, 115)(91, 114)(92, 125)(93, 117)(94, 122)(95, 123)(96, 120) local type(s) :: { ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E23.123 Transitivity :: VT+ Graph:: bipartite v = 8 e = 64 f = 12 degree seq :: [ 16^8 ] E23.131 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 16, 16}) Quotient :: dipole Aut^+ = C16 x C2 (small group id <32, 16>) Aut = C2 x D32 (small group id <64, 186>) |r| :: 2 Presentation :: [ R^2, Y2^2 * Y1^2, Y1^-2 * Y2^2, (R * Y2)^2, (Y2, Y1^-1), (R * Y1)^2, (R * Y3)^2, (Y2, Y3^-1), Y2^4, Y1^4, (Y3, Y1), Y2 * Y3^4, Y2 * Y1 * Y3^-2 * Y1 * Y3^-2, Y3 * Y1 * Y3 * Y1 * Y3^2 * Y2^-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 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 9, 41, 6, 38, 11, 43)(4, 36, 10, 42, 21, 53, 16, 48)(7, 39, 12, 44, 22, 54, 18, 50)(13, 45, 23, 55, 17, 49, 26, 58)(14, 46, 24, 56, 19, 51, 27, 59)(15, 47, 25, 57, 29, 61, 30, 62)(20, 52, 28, 60, 31, 63, 32, 64)(65, 97, 67, 99, 72, 104, 70, 102)(66, 98, 73, 105, 69, 101, 75, 107)(68, 100, 77, 109, 85, 117, 81, 113)(71, 103, 78, 110, 86, 118, 83, 115)(74, 106, 87, 119, 80, 112, 90, 122)(76, 108, 88, 120, 82, 114, 91, 123)(79, 111, 84, 116, 93, 125, 95, 127)(89, 121, 92, 124, 94, 126, 96, 128) L = (1, 68)(2, 74)(3, 77)(4, 79)(5, 80)(6, 81)(7, 65)(8, 85)(9, 87)(10, 89)(11, 90)(12, 66)(13, 84)(14, 67)(15, 83)(16, 94)(17, 95)(18, 69)(19, 70)(20, 71)(21, 93)(22, 72)(23, 92)(24, 73)(25, 91)(26, 96)(27, 75)(28, 76)(29, 78)(30, 88)(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) :: { ( 32^8 ) } Outer automorphisms :: reflexible Dual of E23.146 Graph:: bipartite v = 16 e = 64 f = 4 degree seq :: [ 8^16 ] E23.132 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 16, 16}) Quotient :: dipole Aut^+ = C16 x C2 (small group id <32, 16>) Aut = C2 x D32 (small group id <64, 186>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (Y2^-1, Y1), (R * Y1)^2, (R * Y3)^2, Y1^4, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^4, Y2^8 * Y1^2, (Y3 * Y2^-1)^16 ] 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, 28, 60, 32, 64)(65, 97, 67, 99, 73, 105, 81, 113, 89, 121, 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, 91, 123, 83, 115, 75, 107, 68, 100, 74, 106, 82, 114, 90, 122, 96, 128, 88, 120, 80, 112, 72, 104) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 81)(18, 82)(19, 83)(20, 84)(21, 85)(22, 86)(23, 87)(24, 88)(25, 89)(26, 90)(27, 91)(28, 92)(29, 93)(30, 94)(31, 95)(32, 96)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8, 32, 8, 32, 8, 32, 8, 32 ), ( 8, 32, 8, 32, 8, 32, 8, 32, 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 = 10 e = 64 f = 10 degree seq :: [ 8^8, 32^2 ] E23.133 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 16, 16}) Quotient :: dipole Aut^+ = C16 x C2 (small group id <32, 16>) Aut = C2 x D32 (small group id <64, 186>) |r| :: 2 Presentation :: [ R^2, Y3^2, (R * Y2)^2, Y1^-1 * Y3 * Y1 * Y3, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y3 * Y2 * Y3, Y1^4, (Y2^-1, Y1^-1), Y1 * Y2^4 ] Map:: non-degenerate R = (1, 33, 2, 34, 7, 39, 5, 37)(3, 35, 8, 40, 18, 50, 13, 45)(4, 36, 9, 41, 19, 51, 14, 46)(6, 38, 10, 42, 20, 52, 16, 48)(11, 43, 17, 49, 23, 55, 25, 57)(12, 44, 21, 53, 29, 61, 26, 58)(15, 47, 22, 54, 30, 62, 27, 59)(24, 56, 28, 60, 31, 63, 32, 64)(65, 97, 67, 99, 75, 107, 80, 112, 69, 101, 77, 109, 89, 121, 84, 116, 71, 103, 82, 114, 87, 119, 74, 106, 66, 98, 72, 104, 81, 113, 70, 102)(68, 100, 76, 108, 88, 120, 91, 123, 78, 110, 90, 122, 96, 128, 94, 126, 83, 115, 93, 125, 95, 127, 86, 118, 73, 105, 85, 117, 92, 124, 79, 111) L = (1, 68)(2, 73)(3, 76)(4, 65)(5, 78)(6, 79)(7, 83)(8, 85)(9, 66)(10, 86)(11, 88)(12, 67)(13, 90)(14, 69)(15, 70)(16, 91)(17, 92)(18, 93)(19, 71)(20, 94)(21, 72)(22, 74)(23, 95)(24, 75)(25, 96)(26, 77)(27, 80)(28, 81)(29, 82)(30, 84)(31, 87)(32, 89)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8, 32, 8, 32, 8, 32, 8, 32 ), ( 8, 32, 8, 32, 8, 32, 8, 32, 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 E23.136 Graph:: bipartite v = 10 e = 64 f = 10 degree seq :: [ 8^8, 32^2 ] E23.134 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 16, 16}) Quotient :: dipole Aut^+ = C16 x C2 (small group id <32, 16>) Aut = C2 x D32 (small group id <64, 186>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y3 * Y2 * Y3 * Y2^-1, (R * Y2)^2, (R * Y1)^2, Y1^4, Y1^-1 * Y3 * Y1 * Y3, (Y2^-1, Y1^-1), (R * Y3)^2, Y2^4 * Y1^-1 ] Map:: non-degenerate R = (1, 33, 2, 34, 7, 39, 5, 37)(3, 35, 8, 40, 18, 50, 13, 45)(4, 36, 9, 41, 19, 51, 14, 46)(6, 38, 10, 42, 20, 52, 16, 48)(11, 43, 21, 53, 28, 60, 17, 49)(12, 44, 22, 54, 29, 61, 25, 57)(15, 47, 23, 55, 30, 62, 26, 58)(24, 56, 31, 63, 32, 64, 27, 59)(65, 97, 67, 99, 75, 107, 74, 106, 66, 98, 72, 104, 85, 117, 84, 116, 71, 103, 82, 114, 92, 124, 80, 112, 69, 101, 77, 109, 81, 113, 70, 102)(68, 100, 76, 108, 88, 120, 87, 119, 73, 105, 86, 118, 95, 127, 94, 126, 83, 115, 93, 125, 96, 128, 90, 122, 78, 110, 89, 121, 91, 123, 79, 111) L = (1, 68)(2, 73)(3, 76)(4, 65)(5, 78)(6, 79)(7, 83)(8, 86)(9, 66)(10, 87)(11, 88)(12, 67)(13, 89)(14, 69)(15, 70)(16, 90)(17, 91)(18, 93)(19, 71)(20, 94)(21, 95)(22, 72)(23, 74)(24, 75)(25, 77)(26, 80)(27, 81)(28, 96)(29, 82)(30, 84)(31, 85)(32, 92)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8, 32, 8, 32, 8, 32, 8, 32 ), ( 8, 32, 8, 32, 8, 32, 8, 32, 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 E23.135 Graph:: bipartite v = 10 e = 64 f = 10 degree seq :: [ 8^8, 32^2 ] E23.135 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 16, 16}) Quotient :: dipole Aut^+ = C16 x C2 (small group id <32, 16>) Aut = C2 x D32 (small group id <64, 186>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1^-1 * Y3 * Y1 * Y3, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y2^-1, Y1), Y1^4, Y3 * Y2 * Y3 * Y2^-1, Y3 * Y2^4 * Y1^-1 ] Map:: non-degenerate R = (1, 33, 2, 34, 7, 39, 5, 37)(3, 35, 8, 40, 18, 50, 13, 45)(4, 36, 9, 41, 19, 51, 14, 46)(6, 38, 10, 42, 20, 52, 16, 48)(11, 43, 21, 53, 29, 61, 25, 57)(12, 44, 22, 54, 30, 62, 26, 58)(15, 47, 23, 55, 31, 63, 27, 59)(17, 49, 24, 56, 32, 64, 28, 60)(65, 97, 67, 99, 75, 107, 87, 119, 73, 105, 86, 118, 96, 128, 84, 116, 71, 103, 82, 114, 93, 125, 91, 123, 78, 110, 90, 122, 81, 113, 70, 102)(66, 98, 72, 104, 85, 117, 95, 127, 83, 115, 94, 126, 92, 124, 80, 112, 69, 101, 77, 109, 89, 121, 79, 111, 68, 100, 76, 108, 88, 120, 74, 106) L = (1, 68)(2, 73)(3, 76)(4, 65)(5, 78)(6, 79)(7, 83)(8, 86)(9, 66)(10, 87)(11, 88)(12, 67)(13, 90)(14, 69)(15, 70)(16, 91)(17, 89)(18, 94)(19, 71)(20, 95)(21, 96)(22, 72)(23, 74)(24, 75)(25, 81)(26, 77)(27, 80)(28, 93)(29, 92)(30, 82)(31, 84)(32, 85)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8, 32, 8, 32, 8, 32, 8, 32 ), ( 8, 32, 8, 32, 8, 32, 8, 32, 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 E23.134 Graph:: bipartite v = 10 e = 64 f = 10 degree seq :: [ 8^8, 32^2 ] E23.136 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 16, 16}) Quotient :: dipole Aut^+ = C16 x C2 (small group id <32, 16>) Aut = C2 x D32 (small group id <64, 186>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1^-1 * Y3 * Y1 * Y3, (R * Y2)^2, (Y2, Y1^-1), Y3 * Y2^-1 * Y3 * Y2, (R * Y1)^2, Y1^4, (R * Y3)^2, Y2^-1 * Y3 * Y1^-1 * Y2^-3 ] Map:: non-degenerate R = (1, 33, 2, 34, 7, 39, 5, 37)(3, 35, 8, 40, 18, 50, 13, 45)(4, 36, 9, 41, 19, 51, 14, 46)(6, 38, 10, 42, 20, 52, 16, 48)(11, 43, 21, 53, 29, 61, 27, 59)(12, 44, 22, 54, 30, 62, 28, 60)(15, 47, 23, 55, 31, 63, 25, 57)(17, 49, 24, 56, 32, 64, 26, 58)(65, 97, 67, 99, 75, 107, 89, 121, 78, 110, 92, 124, 96, 128, 84, 116, 71, 103, 82, 114, 93, 125, 87, 119, 73, 105, 86, 118, 81, 113, 70, 102)(66, 98, 72, 104, 85, 117, 79, 111, 68, 100, 76, 108, 90, 122, 80, 112, 69, 101, 77, 109, 91, 123, 95, 127, 83, 115, 94, 126, 88, 120, 74, 106) L = (1, 68)(2, 73)(3, 76)(4, 65)(5, 78)(6, 79)(7, 83)(8, 86)(9, 66)(10, 87)(11, 90)(12, 67)(13, 92)(14, 69)(15, 70)(16, 89)(17, 85)(18, 94)(19, 71)(20, 95)(21, 81)(22, 72)(23, 74)(24, 93)(25, 80)(26, 75)(27, 96)(28, 77)(29, 88)(30, 82)(31, 84)(32, 91)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8, 32, 8, 32, 8, 32, 8, 32 ), ( 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32 ) } Outer automorphisms :: reflexible Dual of E23.133 Graph:: bipartite v = 10 e = 64 f = 10 degree seq :: [ 8^8, 32^2 ] E23.137 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 16, 16}) Quotient :: dipole Aut^+ = C16 x C2 (small group id <32, 16>) Aut = C2 x D32 (small group id <64, 186>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y3 * Y1^2, (R * Y2)^2, Y2^-1 * Y3 * Y2 * Y3, (R * Y1)^2, (R * Y3)^2, (Y2, Y1^-1), Y2^2 * Y1 * Y2^-3 * Y1^-1 * Y2, Y2^8 * Y3 ] Map:: non-degenerate R = (1, 33, 2, 34, 4, 36, 5, 37)(3, 35, 7, 39, 10, 42, 11, 43)(6, 38, 8, 40, 12, 44, 13, 45)(9, 41, 15, 47, 18, 50, 19, 51)(14, 46, 16, 48, 20, 52, 21, 53)(17, 49, 23, 55, 26, 58, 27, 59)(22, 54, 24, 56, 28, 60, 29, 61)(25, 57, 31, 63, 30, 62, 32, 64)(65, 97, 67, 99, 73, 105, 81, 113, 89, 121, 92, 124, 84, 116, 76, 108, 68, 100, 74, 106, 82, 114, 90, 122, 94, 126, 86, 118, 78, 110, 70, 102)(66, 98, 71, 103, 79, 111, 87, 119, 95, 127, 93, 125, 85, 117, 77, 109, 69, 101, 75, 107, 83, 115, 91, 123, 96, 128, 88, 120, 80, 112, 72, 104) L = (1, 68)(2, 69)(3, 74)(4, 65)(5, 66)(6, 76)(7, 75)(8, 77)(9, 82)(10, 67)(11, 71)(12, 70)(13, 72)(14, 84)(15, 83)(16, 85)(17, 90)(18, 73)(19, 79)(20, 78)(21, 80)(22, 92)(23, 91)(24, 93)(25, 94)(26, 81)(27, 87)(28, 86)(29, 88)(30, 89)(31, 96)(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) :: { ( 8, 32, 8, 32, 8, 32, 8, 32 ), ( 8, 32, 8, 32, 8, 32, 8, 32, 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 = 10 e = 64 f = 10 degree seq :: [ 8^8, 32^2 ] E23.138 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 16, 16}) Quotient :: dipole Aut^+ = Q32 (small group id <32, 20>) Aut = (C16 x C2) : C2 (small group id <64, 189>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (R * Y3)^2, Y2^-1 * Y1^-1 * Y2^-1 * Y1, Y1^4, (R * Y1)^2, Y1^-1 * Y2 * Y1^-2 * Y2^-1 * Y1^-1, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^4, Y2^3 * Y1^-1 * Y2^-5 * Y1^-1, (Y3 * Y2^-1)^16 ] Map:: R = (1, 33, 2, 34, 6, 38, 4, 36)(3, 35, 8, 40, 13, 45, 10, 42)(5, 37, 7, 39, 14, 46, 11, 43)(9, 41, 16, 48, 21, 53, 18, 50)(12, 44, 15, 47, 22, 54, 19, 51)(17, 49, 24, 56, 29, 61, 26, 58)(20, 52, 23, 55, 30, 62, 27, 59)(25, 57, 32, 64, 28, 60, 31, 63)(65, 97, 67, 99, 73, 105, 81, 113, 89, 121, 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, 90, 122, 82, 114, 74, 106, 68, 100, 75, 107, 83, 115, 91, 123, 96, 128, 88, 120, 80, 112, 72, 104) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 81)(18, 82)(19, 83)(20, 84)(21, 85)(22, 86)(23, 87)(24, 88)(25, 89)(26, 90)(27, 91)(28, 92)(29, 93)(30, 94)(31, 95)(32, 96)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8, 32, 8, 32, 8, 32, 8, 32 ), ( 8, 32, 8, 32, 8, 32, 8, 32, 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 = 10 e = 64 f = 10 degree seq :: [ 8^8, 32^2 ] E23.139 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 16, 16}) Quotient :: dipole Aut^+ = Q32 (small group id <32, 20>) Aut = (C16 x C2) : C2 (small group id <64, 189>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1^-1 * Y3 * Y1^-1, Y3 * Y1^2, (R * Y2)^2, Y1 * Y2^-1 * Y1^-1 * Y2^-1, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y3 * Y2 * Y3, Y2^8 * Y3 ] Map:: non-degenerate R = (1, 33, 2, 34, 4, 36, 5, 37)(3, 35, 8, 40, 10, 42, 11, 43)(6, 38, 7, 39, 12, 44, 13, 45)(9, 41, 16, 48, 18, 50, 19, 51)(14, 46, 15, 47, 20, 52, 21, 53)(17, 49, 24, 56, 26, 58, 27, 59)(22, 54, 23, 55, 28, 60, 29, 61)(25, 57, 32, 64, 30, 62, 31, 63)(65, 97, 67, 99, 73, 105, 81, 113, 89, 121, 92, 124, 84, 116, 76, 108, 68, 100, 74, 106, 82, 114, 90, 122, 94, 126, 86, 118, 78, 110, 70, 102)(66, 98, 71, 103, 79, 111, 87, 119, 95, 127, 91, 123, 83, 115, 75, 107, 69, 101, 77, 109, 85, 117, 93, 125, 96, 128, 88, 120, 80, 112, 72, 104) L = (1, 68)(2, 69)(3, 74)(4, 65)(5, 66)(6, 76)(7, 77)(8, 75)(9, 82)(10, 67)(11, 72)(12, 70)(13, 71)(14, 84)(15, 85)(16, 83)(17, 90)(18, 73)(19, 80)(20, 78)(21, 79)(22, 92)(23, 93)(24, 91)(25, 94)(26, 81)(27, 88)(28, 86)(29, 87)(30, 89)(31, 96)(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) :: { ( 8, 32, 8, 32, 8, 32, 8, 32 ), ( 8, 32, 8, 32, 8, 32, 8, 32, 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 = 10 e = 64 f = 10 degree seq :: [ 8^8, 32^2 ] E23.140 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 16, 16}) Quotient :: dipole Aut^+ = Q32 (small group id <32, 20>) Aut = (C16 x C2) : C2 (small group id <64, 189>) |r| :: 2 Presentation :: [ R^2, Y3^2 * Y1^-2, Y1^-1 * Y3^-2 * Y1^-1, Y3 * Y1^-1 * Y3^-1 * Y1^-1, Y1^-1 * Y3^-1 * Y1 * Y3^-1, (R * Y3)^2, Y1^4, (Y3, Y2^-1), (R * Y1)^2, Y2 * Y1 * Y2 * Y1^-1, (R * Y2)^2, Y2^2 * Y3 * Y2^2, Y2^2 * Y3^-1 * Y2^2 * Y3^-2, (Y2^-1 * Y3)^16 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 11, 43, 21, 53, 15, 47)(4, 36, 12, 44, 7, 39, 10, 42)(6, 38, 9, 41, 22, 54, 18, 50)(13, 45, 27, 59, 31, 63, 29, 61)(14, 46, 28, 60, 16, 48, 26, 58)(17, 49, 25, 57, 20, 52, 24, 56)(19, 51, 23, 55, 30, 62, 32, 64)(65, 97, 67, 99, 77, 109, 84, 116, 71, 103, 80, 112, 94, 126, 86, 118, 72, 104, 85, 117, 95, 127, 81, 113, 68, 100, 78, 110, 83, 115, 70, 102)(66, 98, 73, 105, 87, 119, 92, 124, 76, 108, 89, 121, 93, 125, 79, 111, 69, 101, 82, 114, 96, 128, 90, 122, 74, 106, 88, 120, 91, 123, 75, 107) L = (1, 68)(2, 74)(3, 78)(4, 72)(5, 76)(6, 81)(7, 65)(8, 71)(9, 88)(10, 69)(11, 90)(12, 66)(13, 83)(14, 85)(15, 92)(16, 67)(17, 86)(18, 89)(19, 95)(20, 70)(21, 80)(22, 84)(23, 91)(24, 82)(25, 73)(26, 79)(27, 96)(28, 75)(29, 87)(30, 77)(31, 94)(32, 93)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8, 32, 8, 32, 8, 32, 8, 32 ), ( 8, 32, 8, 32, 8, 32, 8, 32, 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 E23.141 Graph:: bipartite v = 10 e = 64 f = 10 degree seq :: [ 8^8, 32^2 ] E23.141 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 16, 16}) Quotient :: dipole Aut^+ = Q32 (small group id <32, 20>) Aut = (C16 x C2) : C2 (small group id <64, 189>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-2 * Y1^-1, Y3 * Y1^-1 * Y3^-1 * Y1^-1, Y3^2 * Y1^-2, Y1^-1 * Y3^-1 * Y1 * Y3^-1, (Y3^-1, Y2^-1), Y2 * Y1 * Y2 * Y1^-1, (R * Y1)^2, Y1^4, Y3^4, (R * Y2)^2, (R * Y3)^2, Y3^-1 * Y2^4, (Y2^2 * Y3)^8 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 11, 43, 21, 53, 15, 47)(4, 36, 12, 44, 7, 39, 10, 42)(6, 38, 9, 41, 22, 54, 18, 50)(13, 45, 27, 59, 32, 64, 30, 62)(14, 46, 28, 60, 16, 48, 26, 58)(17, 49, 25, 57, 20, 52, 24, 56)(19, 51, 23, 55, 29, 61, 31, 63)(65, 97, 67, 99, 77, 109, 81, 113, 68, 100, 78, 110, 93, 125, 86, 118, 72, 104, 85, 117, 96, 128, 84, 116, 71, 103, 80, 112, 83, 115, 70, 102)(66, 98, 73, 105, 87, 119, 90, 122, 74, 106, 88, 120, 94, 126, 79, 111, 69, 101, 82, 114, 95, 127, 92, 124, 76, 108, 89, 121, 91, 123, 75, 107) L = (1, 68)(2, 74)(3, 78)(4, 72)(5, 76)(6, 81)(7, 65)(8, 71)(9, 88)(10, 69)(11, 90)(12, 66)(13, 93)(14, 85)(15, 92)(16, 67)(17, 86)(18, 89)(19, 77)(20, 70)(21, 80)(22, 84)(23, 94)(24, 82)(25, 73)(26, 79)(27, 87)(28, 75)(29, 96)(30, 95)(31, 91)(32, 83)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8, 32, 8, 32, 8, 32, 8, 32 ), ( 8, 32, 8, 32, 8, 32, 8, 32, 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 E23.140 Graph:: bipartite v = 10 e = 64 f = 10 degree seq :: [ 8^8, 32^2 ] E23.142 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 16, 16}) Quotient :: dipole Aut^+ = Q32 (small group id <32, 20>) Aut = (C16 x C2) : C2 (small group id <64, 189>) |r| :: 2 Presentation :: [ R^2, Y2^2 * Y3, Y2 * Y1 * Y2 * Y1^-1, Y1 * Y2^-1 * Y1^-1 * Y2^-1, Y3 * Y1 * Y3 * Y1^-1, Y1^4, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y3^-4 * Y1^-2, Y1^2 * Y3 * Y1^2 * Y3^-1, Y3 * Y1^2 * Y2^-1 * Y3^2 * Y2^-1, (Y3 * Y2^-1)^16 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 11, 43, 21, 53, 13, 45)(4, 36, 12, 44, 22, 54, 16, 48)(6, 38, 9, 41, 23, 55, 18, 50)(7, 39, 10, 42, 24, 56, 19, 51)(14, 46, 27, 59, 31, 63, 29, 61)(15, 47, 28, 60, 20, 52, 26, 58)(17, 49, 25, 57, 30, 62, 32, 64)(65, 97, 67, 99, 71, 103, 78, 110, 84, 116, 94, 126, 86, 118, 87, 119, 72, 104, 85, 117, 88, 120, 95, 127, 79, 111, 81, 113, 68, 100, 70, 102)(66, 98, 73, 105, 76, 108, 89, 121, 92, 124, 93, 125, 83, 115, 77, 109, 69, 101, 82, 114, 80, 112, 96, 128, 90, 122, 91, 123, 74, 106, 75, 107) L = (1, 68)(2, 74)(3, 70)(4, 79)(5, 83)(6, 81)(7, 65)(8, 86)(9, 75)(10, 90)(11, 91)(12, 66)(13, 93)(14, 67)(15, 88)(16, 69)(17, 95)(18, 77)(19, 92)(20, 71)(21, 87)(22, 84)(23, 94)(24, 72)(25, 73)(26, 80)(27, 96)(28, 76)(29, 89)(30, 78)(31, 85)(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) :: { ( 8, 32, 8, 32, 8, 32, 8, 32 ), ( 8, 32, 8, 32, 8, 32, 8, 32, 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 E23.145 Graph:: bipartite v = 10 e = 64 f = 10 degree seq :: [ 8^8, 32^2 ] E23.143 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 16, 16}) Quotient :: dipole Aut^+ = Q32 (small group id <32, 20>) Aut = (C16 x C2) : C2 (small group id <64, 189>) |r| :: 2 Presentation :: [ R^2, Y2^2 * Y3^-1, Y1 * Y2^-1 * Y1^-1 * Y2^-1, Y1^4, (R * Y3)^2, Y3 * Y1 * Y3 * Y1^-1, (R * Y2)^2, (R * Y1)^2, Y1^-2 * Y2 * Y1^-2 * Y2^-1, Y1^-1 * Y3^-4 * Y1^-1 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 11, 43, 21, 53, 14, 46)(4, 36, 12, 44, 22, 54, 16, 48)(6, 38, 9, 41, 23, 55, 17, 49)(7, 39, 10, 42, 24, 56, 18, 50)(13, 45, 27, 59, 32, 64, 30, 62)(15, 47, 28, 60, 20, 52, 26, 58)(19, 51, 25, 57, 29, 61, 31, 63)(65, 97, 67, 99, 68, 100, 77, 109, 79, 111, 93, 125, 88, 120, 87, 119, 72, 104, 85, 117, 86, 118, 96, 128, 84, 116, 83, 115, 71, 103, 70, 102)(66, 98, 73, 105, 74, 106, 89, 121, 90, 122, 94, 126, 80, 112, 78, 110, 69, 101, 81, 113, 82, 114, 95, 127, 92, 124, 91, 123, 76, 108, 75, 107) L = (1, 68)(2, 74)(3, 77)(4, 79)(5, 82)(6, 67)(7, 65)(8, 86)(9, 89)(10, 90)(11, 73)(12, 66)(13, 93)(14, 81)(15, 88)(16, 69)(17, 95)(18, 92)(19, 70)(20, 71)(21, 96)(22, 84)(23, 85)(24, 72)(25, 94)(26, 80)(27, 75)(28, 76)(29, 87)(30, 78)(31, 91)(32, 83)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8, 32, 8, 32, 8, 32, 8, 32 ), ( 8, 32, 8, 32, 8, 32, 8, 32, 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 = 10 e = 64 f = 10 degree seq :: [ 8^8, 32^2 ] E23.144 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 16, 16}) Quotient :: dipole Aut^+ = Q32 (small group id <32, 20>) Aut = (C16 x C2) : C2 (small group id <64, 189>) |r| :: 2 Presentation :: [ R^2, (R * Y2)^2, (Y3^-1, Y2^-1), (R * Y3)^2, Y2 * Y1 * Y2 * Y1^-1, (R * Y1)^2, Y3^-1 * Y1 * Y3^-1 * Y1^-1, Y1^4, Y3^3 * Y2^2, Y1^-1 * Y3^-1 * Y2^2 * Y1^-1, Y3 * Y2^-2 * Y1^-2, Y2^16, 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 * Y1^2 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 11, 43, 19, 51, 15, 47)(4, 36, 12, 44, 13, 45, 18, 50)(6, 38, 9, 41, 16, 48, 20, 52)(7, 39, 10, 42, 22, 54, 21, 53)(14, 46, 27, 59, 29, 61, 30, 62)(17, 49, 28, 60, 24, 56, 26, 58)(23, 55, 25, 57, 31, 63, 32, 64)(65, 97, 67, 99, 77, 109, 93, 125, 81, 113, 87, 119, 71, 103, 80, 112, 72, 104, 83, 115, 68, 100, 78, 110, 88, 120, 95, 127, 86, 118, 70, 102)(66, 98, 73, 105, 85, 117, 96, 128, 90, 122, 91, 123, 76, 108, 79, 111, 69, 101, 84, 116, 74, 106, 89, 121, 92, 124, 94, 126, 82, 114, 75, 107) L = (1, 68)(2, 74)(3, 78)(4, 81)(5, 85)(6, 83)(7, 65)(8, 77)(9, 89)(10, 90)(11, 84)(12, 66)(13, 88)(14, 87)(15, 73)(16, 67)(17, 86)(18, 69)(19, 93)(20, 96)(21, 92)(22, 72)(23, 70)(24, 71)(25, 91)(26, 82)(27, 75)(28, 76)(29, 95)(30, 79)(31, 80)(32, 94)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8, 32, 8, 32, 8, 32, 8, 32 ), ( 8, 32, 8, 32, 8, 32, 8, 32, 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 = 10 e = 64 f = 10 degree seq :: [ 8^8, 32^2 ] E23.145 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 16, 16}) Quotient :: dipole Aut^+ = Q32 (small group id <32, 20>) Aut = (C16 x C2) : C2 (small group id <64, 189>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1 * Y2^-1 * Y1^-1, Y3^-1 * Y1 * Y3^-1 * Y1^-1, (R * Y3)^2, (Y2^-1, Y3), (R * Y1)^2, (R * Y2^-1)^2, Y1^4, Y2^2 * Y3^-3, Y2^-2 * Y3^-1 * Y1^-2, Y2^-1 * Y1^2 * Y3^-1 * Y2^-1, Y2^16 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 11, 43, 23, 55, 15, 47)(4, 36, 12, 44, 22, 54, 18, 50)(6, 38, 9, 41, 14, 46, 20, 52)(7, 39, 10, 42, 13, 45, 21, 53)(16, 48, 27, 59, 29, 61, 31, 63)(17, 49, 28, 60, 24, 56, 26, 58)(19, 51, 25, 57, 30, 62, 32, 64)(65, 97, 67, 99, 77, 109, 93, 125, 88, 120, 83, 115, 68, 100, 78, 110, 72, 104, 87, 119, 71, 103, 80, 112, 81, 113, 94, 126, 86, 118, 70, 102)(66, 98, 73, 105, 82, 114, 96, 128, 92, 124, 91, 123, 74, 106, 79, 111, 69, 101, 84, 116, 76, 108, 89, 121, 90, 122, 95, 127, 85, 117, 75, 107) L = (1, 68)(2, 74)(3, 78)(4, 81)(5, 85)(6, 83)(7, 65)(8, 86)(9, 79)(10, 90)(11, 91)(12, 66)(13, 72)(14, 94)(15, 95)(16, 67)(17, 77)(18, 69)(19, 80)(20, 75)(21, 92)(22, 88)(23, 70)(24, 71)(25, 73)(26, 82)(27, 89)(28, 76)(29, 87)(30, 93)(31, 96)(32, 84)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8, 32, 8, 32, 8, 32, 8, 32 ), ( 8, 32, 8, 32, 8, 32, 8, 32, 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 E23.142 Graph:: bipartite v = 10 e = 64 f = 10 degree seq :: [ 8^8, 32^2 ] E23.146 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 16, 16}) Quotient :: dipole Aut^+ = C16 x C2 (small group id <32, 16>) Aut = C2 x D32 (small group id <64, 186>) |r| :: 2 Presentation :: [ R^2, (Y3, Y2^-1), Y2^-1 * Y3^-1 * Y2^-2, (Y3^-1, Y1), (R * Y1)^2, Y2 * Y1^-1 * Y3 * Y1^-1, (R * Y3)^2, Y1^-1 * Y3 * Y2 * Y1^-1, (R * Y2)^2, (Y2^-1 * Y1^-1)^2, Y3^-1 * Y2 * Y3^-4, Y1^-1 * Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1, Y3 * Y2 * Y1^14 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 19, 51, 16, 48, 23, 55, 15, 47, 22, 54, 30, 62, 28, 60, 18, 50, 24, 56, 14, 46, 21, 53, 13, 45, 5, 37)(3, 35, 9, 41, 6, 38, 11, 43, 4, 36, 10, 42, 20, 52, 29, 61, 27, 59, 32, 64, 26, 58, 31, 63, 25, 57, 17, 49, 7, 39, 12, 44)(65, 97, 67, 99, 77, 109, 71, 103, 78, 110, 89, 121, 82, 114, 90, 122, 94, 126, 91, 123, 79, 111, 84, 116, 80, 112, 68, 100, 72, 104, 70, 102)(66, 98, 73, 105, 69, 101, 76, 108, 85, 117, 81, 113, 88, 120, 95, 127, 92, 124, 96, 128, 86, 118, 93, 125, 87, 119, 74, 106, 83, 115, 75, 107) L = (1, 68)(2, 74)(3, 72)(4, 79)(5, 75)(6, 80)(7, 65)(8, 84)(9, 83)(10, 86)(11, 87)(12, 66)(13, 70)(14, 67)(15, 90)(16, 91)(17, 69)(18, 71)(19, 93)(20, 94)(21, 73)(22, 95)(23, 96)(24, 76)(25, 77)(26, 78)(27, 82)(28, 81)(29, 92)(30, 89)(31, 85)(32, 88)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8^32 ) } Outer automorphisms :: reflexible Dual of E23.131 Graph:: bipartite v = 4 e = 64 f = 16 degree seq :: [ 32^4 ] E23.147 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 16, 16}) Quotient :: edge^2 Aut^+ = C16 : C2 (small group id <32, 17>) Aut = (C2 x D16) : C2 (small group id <64, 190>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2, Y1^4, R * Y2 * R * Y1, Y3^-1 * Y1 * Y3 * Y2^-1, Y2^4, (R * Y3)^2, Y3^-1 * Y2 * Y3 * Y1^-1, Y3^3 * Y1 * Y3^5 * Y1^-1 ] Map:: non-degenerate R = (1, 33, 4, 36, 11, 43, 19, 51, 27, 59, 30, 62, 22, 54, 14, 46, 6, 38, 13, 45, 21, 53, 29, 61, 28, 60, 20, 52, 12, 44, 5, 37)(2, 34, 7, 39, 15, 47, 23, 55, 31, 63, 26, 58, 18, 50, 10, 42, 3, 35, 9, 41, 17, 49, 25, 57, 32, 64, 24, 56, 16, 48, 8, 40)(65, 66, 70, 67)(68, 73, 77, 71)(69, 74, 78, 72)(75, 79, 85, 81)(76, 80, 86, 82)(83, 89, 93, 87)(84, 90, 94, 88)(91, 95, 92, 96)(97, 99, 102, 98)(100, 103, 109, 105)(101, 104, 110, 106)(107, 113, 117, 111)(108, 114, 118, 112)(115, 119, 125, 121)(116, 120, 126, 122)(123, 128, 124, 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) :: { ( 64^4 ), ( 64^32 ) } Outer automorphisms :: reflexible Dual of E23.154 Graph:: bipartite v = 18 e = 64 f = 2 degree seq :: [ 4^16, 32^2 ] E23.148 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 16, 16}) Quotient :: edge^2 Aut^+ = QD32 (small group id <32, 19>) Aut = (C2 x D16) : C2 (small group id <64, 190>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1^-1, R * Y2 * R * Y1, (Y3 * Y1^-1)^2, (Y1^-1 * Y3^-1)^2, (R * Y3)^2, Y1^4, Y2^4, Y1^-1 * Y3 * Y1^2 * Y3^-1 * Y1^-1, Y3^3 * Y1 * Y3^-5 * Y1^-1, Y3^16 ] Map:: non-degenerate R = (1, 33, 3, 35, 10, 42, 18, 50, 26, 58, 30, 62, 22, 54, 14, 46, 6, 38, 13, 45, 21, 53, 29, 61, 28, 60, 20, 52, 12, 44, 5, 37)(2, 34, 7, 39, 15, 47, 23, 55, 31, 63, 25, 57, 17, 49, 9, 41, 4, 36, 11, 43, 19, 51, 27, 59, 32, 64, 24, 56, 16, 48, 8, 40)(65, 66, 70, 68)(67, 73, 77, 72)(69, 75, 78, 71)(74, 80, 85, 81)(76, 79, 86, 83)(82, 89, 93, 88)(84, 91, 94, 87)(90, 96, 92, 95)(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, 124, 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) :: { ( 64^4 ), ( 64^32 ) } Outer automorphisms :: reflexible Dual of E23.155 Graph:: bipartite v = 18 e = 64 f = 2 degree seq :: [ 4^16, 32^2 ] E23.149 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 16, 16}) Quotient :: edge^2 Aut^+ = QD32 (small group id <32, 19>) Aut = (C2 x D16) : C2 (small group id <64, 190>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2 * Y1^-1 * Y2, Y2^-2 * Y1^2, Y1 * Y2 * Y1 * Y2^-1, Y1^-1 * Y2^-2 * Y1^-1, (Y2^-1 * Y3^-1)^2, (Y3^-1 * Y1^-1)^2, (Y3 * Y2^-1)^2, R * Y1 * R * Y2, (R * Y3)^2, (Y3 * Y1^-1)^2, Y3^-1 * Y2^-1 * Y3^3 * Y1^-1, Y3 * Y2 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1, Y1^-1 * Y3^2 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1^-1 ] Map:: non-degenerate R = (1, 33, 4, 36, 17, 49, 24, 56, 9, 41, 23, 55, 32, 64, 22, 54, 8, 40, 21, 53, 31, 63, 25, 57, 11, 43, 27, 59, 20, 52, 7, 39)(2, 34, 10, 42, 26, 58, 16, 48, 6, 38, 19, 51, 30, 62, 15, 47, 5, 37, 18, 50, 29, 61, 14, 46, 3, 35, 13, 45, 28, 60, 12, 44)(65, 66, 72, 69)(67, 75, 70, 73)(68, 79, 85, 76)(71, 82, 86, 74)(77, 88, 83, 89)(78, 87, 80, 91)(81, 92, 95, 94)(84, 90, 96, 93)(97, 99, 104, 102)(98, 105, 101, 107)(100, 112, 117, 110)(103, 115, 118, 109)(106, 121, 114, 120)(108, 123, 111, 119)(113, 125, 127, 122)(116, 124, 128, 126) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 81)(18, 82)(19, 83)(20, 84)(21, 85)(22, 86)(23, 87)(24, 88)(25, 89)(26, 90)(27, 91)(28, 92)(29, 93)(30, 94)(31, 95)(32, 96)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 64^4 ), ( 64^32 ) } Outer automorphisms :: reflexible Dual of E23.158 Graph:: bipartite v = 18 e = 64 f = 2 degree seq :: [ 4^16, 32^2 ] E23.150 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 16, 16}) Quotient :: edge^2 Aut^+ = QD32 (small group id <32, 19>) Aut = (C2 x D16) : C2 (small group id <64, 190>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1^-1, Y1^4, R * Y2 * R * Y1, Y3^-1 * Y1 * Y3^-1 * Y2^-1, Y2^4, (R * Y3)^2, Y3^-1 * Y2 * Y3^-1 * Y1^-1, Y1^-1 * Y3 * Y1 * Y2^-1 * Y3^-1 * Y1^-1, Y3^3 * Y1 * Y3^-5 * Y1^-1 ] Map:: non-degenerate R = (1, 33, 4, 36, 11, 43, 19, 51, 27, 59, 30, 62, 22, 54, 14, 46, 6, 38, 13, 45, 21, 53, 29, 61, 28, 60, 20, 52, 12, 44, 5, 37)(2, 34, 7, 39, 15, 47, 23, 55, 31, 63, 26, 58, 18, 50, 10, 42, 3, 35, 9, 41, 17, 49, 25, 57, 32, 64, 24, 56, 16, 48, 8, 40)(65, 66, 70, 67)(68, 74, 77, 72)(69, 73, 78, 71)(75, 80, 85, 82)(76, 79, 86, 81)(83, 90, 93, 88)(84, 89, 94, 87)(91, 96, 92, 95)(97, 99, 102, 98)(100, 104, 109, 106)(101, 103, 110, 105)(107, 114, 117, 112)(108, 113, 118, 111)(115, 120, 125, 122)(116, 119, 126, 121)(123, 127, 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) :: { ( 64^4 ), ( 64^32 ) } Outer automorphisms :: reflexible Dual of E23.157 Graph:: bipartite v = 18 e = 64 f = 2 degree seq :: [ 4^16, 32^2 ] E23.151 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 16, 16}) Quotient :: edge^2 Aut^+ = QD32 (small group id <32, 19>) Aut = (C2 x D16) : C2 (small group id <64, 190>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1 * Y2^-1 * Y1, Y2^4, Y2^-2 * Y1^2, (Y1^-1 * Y3^-1)^2, (Y2^-1 * Y3^-1)^2, R * Y2 * R * Y1, Y1^-1 * Y2^-2 * Y1^-1, (Y3 * Y1^-1)^2, (R * Y3)^2, (Y3 * Y2^-1)^2, Y3 * Y2^-1 * Y3^-3 * Y1^-1, Y3 * Y2 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1, Y1^-1 * Y3^2 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1^-1 ] Map:: non-degenerate R = (1, 33, 4, 36, 17, 49, 25, 57, 11, 43, 27, 59, 32, 64, 22, 54, 8, 40, 21, 53, 31, 63, 24, 56, 9, 41, 23, 55, 20, 52, 7, 39)(2, 34, 10, 42, 26, 58, 14, 46, 3, 35, 13, 45, 29, 61, 15, 47, 5, 37, 18, 50, 30, 62, 16, 48, 6, 38, 19, 51, 28, 60, 12, 44)(65, 66, 72, 69)(67, 75, 70, 73)(68, 79, 85, 76)(71, 82, 86, 74)(77, 88, 83, 89)(78, 87, 80, 91)(81, 92, 95, 93)(84, 90, 96, 94)(97, 99, 104, 102)(98, 105, 101, 107)(100, 112, 117, 110)(103, 115, 118, 109)(106, 121, 114, 120)(108, 123, 111, 119)(113, 122, 127, 126)(116, 125, 128, 124) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 81)(18, 82)(19, 83)(20, 84)(21, 85)(22, 86)(23, 87)(24, 88)(25, 89)(26, 90)(27, 91)(28, 92)(29, 93)(30, 94)(31, 95)(32, 96)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 64^4 ), ( 64^32 ) } Outer automorphisms :: reflexible Dual of E23.156 Graph:: bipartite v = 18 e = 64 f = 2 degree seq :: [ 4^16, 32^2 ] E23.152 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 16, 16}) Quotient :: edge^2 Aut^+ = QD32 (small group id <32, 19>) Aut = (C2 x D16) : C2 (small group id <64, 190>) |r| :: 2 Presentation :: [ R^2, (Y1^-1 * Y2^-1)^2, Y3^2 * Y2^-1 * Y1^-1, (Y2^-1, Y1^-1), Y3 * Y2 * Y3^-1 * Y1^-1, Y3^-1 * Y2 * Y3 * Y1^-1, Y1^-1 * Y3^-2 * Y2^-1, Y2^2 * Y1^2, (Y3 * Y2^-1)^2, R * Y1 * R * Y2, (R * Y3)^2, (Y3 * Y1)^2, Y1^-6 * Y2 * Y1^-1 ] Map:: non-degenerate R = (1, 33, 4, 36, 9, 41, 7, 39)(2, 34, 10, 42, 6, 38, 12, 44)(3, 35, 14, 46, 5, 37, 16, 48)(8, 40, 18, 50, 11, 43, 20, 52)(13, 45, 22, 54, 15, 47, 24, 56)(17, 49, 26, 58, 19, 51, 28, 60)(21, 53, 29, 61, 23, 55, 30, 62)(25, 57, 31, 63, 27, 59, 32, 64)(65, 66, 72, 81, 89, 85, 79, 67, 73, 70, 75, 83, 91, 87, 77, 69)(68, 78, 86, 93, 96, 90, 84, 74, 71, 80, 88, 94, 95, 92, 82, 76)(97, 99, 109, 117, 123, 113, 107, 98, 105, 101, 111, 119, 121, 115, 104, 102)(100, 106, 114, 122, 127, 125, 120, 110, 103, 108, 116, 124, 128, 126, 118, 112) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 81)(18, 82)(19, 83)(20, 84)(21, 85)(22, 86)(23, 87)(24, 88)(25, 89)(26, 90)(27, 91)(28, 92)(29, 93)(30, 94)(31, 95)(32, 96)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 16^8 ), ( 16^16 ) } Outer automorphisms :: reflexible Dual of E23.159 Graph:: bipartite v = 12 e = 64 f = 8 degree seq :: [ 8^8, 16^4 ] E23.153 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 16, 16}) Quotient :: edge^2 Aut^+ = Q32 (small group id <32, 20>) Aut = (C2 x Q16) : C2 (small group id <64, 191>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1^-1 * Y3^2, Y2^-1 * Y3^2 * Y1^-1, Y3^-2 * Y2^-1 * Y1^-1, Y3^-1 * Y2 * Y3^-1 * Y1^-1, Y2^2 * Y1^2, Y3^-1 * Y2^-1 * Y3 * Y2^-1, (Y2^-1, Y1^-1), Y3 * Y2 * Y3 * Y1^-1, (Y1^-1 * Y2^-1)^2, R * Y1 * R * Y2, Y3^4, (R * Y3)^2, Y1^-6 * Y2 * Y1^-1 ] Map:: non-degenerate R = (1, 33, 4, 36, 9, 41, 7, 39)(2, 34, 10, 42, 6, 38, 12, 44)(3, 35, 14, 46, 5, 37, 16, 48)(8, 40, 18, 50, 11, 43, 20, 52)(13, 45, 22, 54, 15, 47, 24, 56)(17, 49, 26, 58, 19, 51, 28, 60)(21, 53, 29, 61, 23, 55, 30, 62)(25, 57, 31, 63, 27, 59, 32, 64)(65, 66, 72, 81, 89, 85, 79, 67, 73, 70, 75, 83, 91, 87, 77, 69)(68, 80, 86, 94, 96, 92, 84, 76, 71, 78, 88, 93, 95, 90, 82, 74)(97, 99, 109, 117, 123, 113, 107, 98, 105, 101, 111, 119, 121, 115, 104, 102)(100, 108, 114, 124, 127, 126, 120, 112, 103, 106, 116, 122, 128, 125, 118, 110) 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) :: { ( 16^8 ), ( 16^16 ) } Outer automorphisms :: reflexible Dual of E23.160 Graph:: bipartite v = 12 e = 64 f = 8 degree seq :: [ 8^8, 16^4 ] E23.154 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 16, 16}) Quotient :: loop^2 Aut^+ = C16 : C2 (small group id <32, 17>) Aut = (C2 x D16) : C2 (small group id <64, 190>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2, Y1^4, R * Y2 * R * Y1, Y3^-1 * Y1 * Y3 * Y2^-1, Y2^4, (R * Y3)^2, Y3^-1 * Y2 * Y3 * Y1^-1, Y3^3 * Y1 * Y3^5 * Y1^-1 ] Map:: non-degenerate R = (1, 33, 65, 97, 4, 36, 68, 100, 11, 43, 75, 107, 19, 51, 83, 115, 27, 59, 91, 123, 30, 62, 94, 126, 22, 54, 86, 118, 14, 46, 78, 110, 6, 38, 70, 102, 13, 45, 77, 109, 21, 53, 85, 117, 29, 61, 93, 125, 28, 60, 92, 124, 20, 52, 84, 116, 12, 44, 76, 108, 5, 37, 69, 101)(2, 34, 66, 98, 7, 39, 71, 103, 15, 47, 79, 111, 23, 55, 87, 119, 31, 63, 95, 127, 26, 58, 90, 122, 18, 50, 82, 114, 10, 42, 74, 106, 3, 35, 67, 99, 9, 41, 73, 105, 17, 49, 81, 113, 25, 57, 89, 121, 32, 64, 96, 128, 24, 56, 88, 120, 16, 48, 80, 112, 8, 40, 72, 104) L = (1, 34)(2, 38)(3, 33)(4, 41)(5, 42)(6, 35)(7, 36)(8, 37)(9, 45)(10, 46)(11, 47)(12, 48)(13, 39)(14, 40)(15, 53)(16, 54)(17, 43)(18, 44)(19, 57)(20, 58)(21, 49)(22, 50)(23, 51)(24, 52)(25, 61)(26, 62)(27, 63)(28, 64)(29, 55)(30, 56)(31, 60)(32, 59)(65, 99)(66, 97)(67, 102)(68, 103)(69, 104)(70, 98)(71, 109)(72, 110)(73, 100)(74, 101)(75, 113)(76, 114)(77, 105)(78, 106)(79, 107)(80, 108)(81, 117)(82, 118)(83, 119)(84, 120)(85, 111)(86, 112)(87, 125)(88, 126)(89, 115)(90, 116)(91, 128)(92, 127)(93, 121)(94, 122)(95, 123)(96, 124) 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 E23.147 Transitivity :: VT+ Graph:: bipartite v = 2 e = 64 f = 18 degree seq :: [ 64^2 ] E23.155 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 16, 16}) Quotient :: loop^2 Aut^+ = QD32 (small group id <32, 19>) Aut = (C2 x D16) : C2 (small group id <64, 190>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1^-1, R * Y2 * R * Y1, (Y3 * Y1^-1)^2, (Y1^-1 * Y3^-1)^2, (R * Y3)^2, Y1^4, Y2^4, Y1^-1 * Y3 * Y1^2 * Y3^-1 * Y1^-1, Y3^3 * Y1 * Y3^-5 * Y1^-1, Y3^16 ] Map:: non-degenerate R = (1, 33, 65, 97, 3, 35, 67, 99, 10, 42, 74, 106, 18, 50, 82, 114, 26, 58, 90, 122, 30, 62, 94, 126, 22, 54, 86, 118, 14, 46, 78, 110, 6, 38, 70, 102, 13, 45, 77, 109, 21, 53, 85, 117, 29, 61, 93, 125, 28, 60, 92, 124, 20, 52, 84, 116, 12, 44, 76, 108, 5, 37, 69, 101)(2, 34, 66, 98, 7, 39, 71, 103, 15, 47, 79, 111, 23, 55, 87, 119, 31, 63, 95, 127, 25, 57, 89, 121, 17, 49, 81, 113, 9, 41, 73, 105, 4, 36, 68, 100, 11, 43, 75, 107, 19, 51, 83, 115, 27, 59, 91, 123, 32, 64, 96, 128, 24, 56, 88, 120, 16, 48, 80, 112, 8, 40, 72, 104) L = (1, 34)(2, 38)(3, 41)(4, 33)(5, 43)(6, 36)(7, 37)(8, 35)(9, 45)(10, 48)(11, 46)(12, 47)(13, 40)(14, 39)(15, 54)(16, 53)(17, 42)(18, 57)(19, 44)(20, 59)(21, 49)(22, 51)(23, 52)(24, 50)(25, 61)(26, 64)(27, 62)(28, 63)(29, 56)(30, 55)(31, 58)(32, 60)(65, 98)(66, 102)(67, 105)(68, 97)(69, 107)(70, 100)(71, 101)(72, 99)(73, 109)(74, 112)(75, 110)(76, 111)(77, 104)(78, 103)(79, 118)(80, 117)(81, 106)(82, 121)(83, 108)(84, 123)(85, 113)(86, 115)(87, 116)(88, 114)(89, 125)(90, 128)(91, 126)(92, 127)(93, 120)(94, 119)(95, 122)(96, 124) 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 E23.148 Transitivity :: VT+ Graph:: bipartite v = 2 e = 64 f = 18 degree seq :: [ 64^2 ] E23.156 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 16, 16}) Quotient :: loop^2 Aut^+ = QD32 (small group id <32, 19>) Aut = (C2 x D16) : C2 (small group id <64, 190>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2 * Y1^-1 * Y2, Y2^-2 * Y1^2, Y1 * Y2 * Y1 * Y2^-1, Y1^-1 * Y2^-2 * Y1^-1, (Y2^-1 * Y3^-1)^2, (Y3^-1 * Y1^-1)^2, (Y3 * Y2^-1)^2, R * Y1 * R * Y2, (R * Y3)^2, (Y3 * Y1^-1)^2, Y3^-1 * Y2^-1 * Y3^3 * Y1^-1, Y3 * Y2 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1, Y1^-1 * Y3^2 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1^-1 ] Map:: non-degenerate R = (1, 33, 65, 97, 4, 36, 68, 100, 17, 49, 81, 113, 24, 56, 88, 120, 9, 41, 73, 105, 23, 55, 87, 119, 32, 64, 96, 128, 22, 54, 86, 118, 8, 40, 72, 104, 21, 53, 85, 117, 31, 63, 95, 127, 25, 57, 89, 121, 11, 43, 75, 107, 27, 59, 91, 123, 20, 52, 84, 116, 7, 39, 71, 103)(2, 34, 66, 98, 10, 42, 74, 106, 26, 58, 90, 122, 16, 48, 80, 112, 6, 38, 70, 102, 19, 51, 83, 115, 30, 62, 94, 126, 15, 47, 79, 111, 5, 37, 69, 101, 18, 50, 82, 114, 29, 61, 93, 125, 14, 46, 78, 110, 3, 35, 67, 99, 13, 45, 77, 109, 28, 60, 92, 124, 12, 44, 76, 108) L = (1, 34)(2, 40)(3, 43)(4, 47)(5, 33)(6, 41)(7, 50)(8, 37)(9, 35)(10, 39)(11, 38)(12, 36)(13, 56)(14, 55)(15, 53)(16, 59)(17, 60)(18, 54)(19, 57)(20, 58)(21, 44)(22, 42)(23, 48)(24, 51)(25, 45)(26, 64)(27, 46)(28, 63)(29, 52)(30, 49)(31, 62)(32, 61)(65, 99)(66, 105)(67, 104)(68, 112)(69, 107)(70, 97)(71, 115)(72, 102)(73, 101)(74, 121)(75, 98)(76, 123)(77, 103)(78, 100)(79, 119)(80, 117)(81, 125)(82, 120)(83, 118)(84, 124)(85, 110)(86, 109)(87, 108)(88, 106)(89, 114)(90, 113)(91, 111)(92, 128)(93, 127)(94, 116)(95, 122)(96, 126) 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 E23.151 Transitivity :: VT+ Graph:: bipartite v = 2 e = 64 f = 18 degree seq :: [ 64^2 ] E23.157 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 16, 16}) Quotient :: loop^2 Aut^+ = QD32 (small group id <32, 19>) Aut = (C2 x D16) : C2 (small group id <64, 190>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1^-1, Y1^4, R * Y2 * R * Y1, Y3^-1 * Y1 * Y3^-1 * Y2^-1, Y2^4, (R * Y3)^2, Y3^-1 * Y2 * Y3^-1 * Y1^-1, Y1^-1 * Y3 * Y1 * Y2^-1 * Y3^-1 * Y1^-1, Y3^3 * Y1 * Y3^-5 * Y1^-1 ] Map:: non-degenerate R = (1, 33, 65, 97, 4, 36, 68, 100, 11, 43, 75, 107, 19, 51, 83, 115, 27, 59, 91, 123, 30, 62, 94, 126, 22, 54, 86, 118, 14, 46, 78, 110, 6, 38, 70, 102, 13, 45, 77, 109, 21, 53, 85, 117, 29, 61, 93, 125, 28, 60, 92, 124, 20, 52, 84, 116, 12, 44, 76, 108, 5, 37, 69, 101)(2, 34, 66, 98, 7, 39, 71, 103, 15, 47, 79, 111, 23, 55, 87, 119, 31, 63, 95, 127, 26, 58, 90, 122, 18, 50, 82, 114, 10, 42, 74, 106, 3, 35, 67, 99, 9, 41, 73, 105, 17, 49, 81, 113, 25, 57, 89, 121, 32, 64, 96, 128, 24, 56, 88, 120, 16, 48, 80, 112, 8, 40, 72, 104) L = (1, 34)(2, 38)(3, 33)(4, 42)(5, 41)(6, 35)(7, 37)(8, 36)(9, 46)(10, 45)(11, 48)(12, 47)(13, 40)(14, 39)(15, 54)(16, 53)(17, 44)(18, 43)(19, 58)(20, 57)(21, 50)(22, 49)(23, 52)(24, 51)(25, 62)(26, 61)(27, 64)(28, 63)(29, 56)(30, 55)(31, 59)(32, 60)(65, 99)(66, 97)(67, 102)(68, 104)(69, 103)(70, 98)(71, 110)(72, 109)(73, 101)(74, 100)(75, 114)(76, 113)(77, 106)(78, 105)(79, 108)(80, 107)(81, 118)(82, 117)(83, 120)(84, 119)(85, 112)(86, 111)(87, 126)(88, 125)(89, 116)(90, 115)(91, 127)(92, 128)(93, 122)(94, 121)(95, 124)(96, 123) 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 E23.150 Transitivity :: VT+ Graph:: bipartite v = 2 e = 64 f = 18 degree seq :: [ 64^2 ] E23.158 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 16, 16}) Quotient :: loop^2 Aut^+ = QD32 (small group id <32, 19>) Aut = (C2 x D16) : C2 (small group id <64, 190>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1 * Y2^-1 * Y1, Y2^4, Y2^-2 * Y1^2, (Y1^-1 * Y3^-1)^2, (Y2^-1 * Y3^-1)^2, R * Y2 * R * Y1, Y1^-1 * Y2^-2 * Y1^-1, (Y3 * Y1^-1)^2, (R * Y3)^2, (Y3 * Y2^-1)^2, Y3 * Y2^-1 * Y3^-3 * Y1^-1, Y3 * Y2 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1, Y1^-1 * Y3^2 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y1^-1 ] Map:: non-degenerate R = (1, 33, 65, 97, 4, 36, 68, 100, 17, 49, 81, 113, 25, 57, 89, 121, 11, 43, 75, 107, 27, 59, 91, 123, 32, 64, 96, 128, 22, 54, 86, 118, 8, 40, 72, 104, 21, 53, 85, 117, 31, 63, 95, 127, 24, 56, 88, 120, 9, 41, 73, 105, 23, 55, 87, 119, 20, 52, 84, 116, 7, 39, 71, 103)(2, 34, 66, 98, 10, 42, 74, 106, 26, 58, 90, 122, 14, 46, 78, 110, 3, 35, 67, 99, 13, 45, 77, 109, 29, 61, 93, 125, 15, 47, 79, 111, 5, 37, 69, 101, 18, 50, 82, 114, 30, 62, 94, 126, 16, 48, 80, 112, 6, 38, 70, 102, 19, 51, 83, 115, 28, 60, 92, 124, 12, 44, 76, 108) L = (1, 34)(2, 40)(3, 43)(4, 47)(5, 33)(6, 41)(7, 50)(8, 37)(9, 35)(10, 39)(11, 38)(12, 36)(13, 56)(14, 55)(15, 53)(16, 59)(17, 60)(18, 54)(19, 57)(20, 58)(21, 44)(22, 42)(23, 48)(24, 51)(25, 45)(26, 64)(27, 46)(28, 63)(29, 49)(30, 52)(31, 61)(32, 62)(65, 99)(66, 105)(67, 104)(68, 112)(69, 107)(70, 97)(71, 115)(72, 102)(73, 101)(74, 121)(75, 98)(76, 123)(77, 103)(78, 100)(79, 119)(80, 117)(81, 122)(82, 120)(83, 118)(84, 125)(85, 110)(86, 109)(87, 108)(88, 106)(89, 114)(90, 127)(91, 111)(92, 116)(93, 128)(94, 113)(95, 126)(96, 124) 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 E23.149 Transitivity :: VT+ Graph:: bipartite v = 2 e = 64 f = 18 degree seq :: [ 64^2 ] E23.159 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 16, 16}) Quotient :: loop^2 Aut^+ = QD32 (small group id <32, 19>) Aut = (C2 x D16) : C2 (small group id <64, 190>) |r| :: 2 Presentation :: [ R^2, (Y1^-1 * Y2^-1)^2, Y3^2 * Y2^-1 * Y1^-1, (Y2^-1, Y1^-1), Y3 * Y2 * Y3^-1 * Y1^-1, Y3^-1 * Y2 * Y3 * Y1^-1, Y1^-1 * Y3^-2 * Y2^-1, Y2^2 * Y1^2, (Y3 * Y2^-1)^2, R * Y1 * R * Y2, (R * Y3)^2, (Y3 * Y1)^2, Y1^-6 * Y2 * Y1^-1 ] Map:: non-degenerate R = (1, 33, 65, 97, 4, 36, 68, 100, 9, 41, 73, 105, 7, 39, 71, 103)(2, 34, 66, 98, 10, 42, 74, 106, 6, 38, 70, 102, 12, 44, 76, 108)(3, 35, 67, 99, 14, 46, 78, 110, 5, 37, 69, 101, 16, 48, 80, 112)(8, 40, 72, 104, 18, 50, 82, 114, 11, 43, 75, 107, 20, 52, 84, 116)(13, 45, 77, 109, 22, 54, 86, 118, 15, 47, 79, 111, 24, 56, 88, 120)(17, 49, 81, 113, 26, 58, 90, 122, 19, 51, 83, 115, 28, 60, 92, 124)(21, 53, 85, 117, 29, 61, 93, 125, 23, 55, 87, 119, 30, 62, 94, 126)(25, 57, 89, 121, 31, 63, 95, 127, 27, 59, 91, 123, 32, 64, 96, 128) L = (1, 34)(2, 40)(3, 41)(4, 46)(5, 33)(6, 43)(7, 48)(8, 49)(9, 38)(10, 39)(11, 51)(12, 36)(13, 37)(14, 54)(15, 35)(16, 56)(17, 57)(18, 44)(19, 59)(20, 42)(21, 47)(22, 61)(23, 45)(24, 62)(25, 53)(26, 52)(27, 55)(28, 50)(29, 64)(30, 63)(31, 60)(32, 58)(65, 99)(66, 105)(67, 109)(68, 106)(69, 111)(70, 97)(71, 108)(72, 102)(73, 101)(74, 114)(75, 98)(76, 116)(77, 117)(78, 103)(79, 119)(80, 100)(81, 107)(82, 122)(83, 104)(84, 124)(85, 123)(86, 112)(87, 121)(88, 110)(89, 115)(90, 127)(91, 113)(92, 128)(93, 120)(94, 118)(95, 125)(96, 126) local type(s) :: { ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E23.152 Transitivity :: VT+ Graph:: bipartite v = 8 e = 64 f = 12 degree seq :: [ 16^8 ] E23.160 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 16, 16}) Quotient :: loop^2 Aut^+ = Q32 (small group id <32, 20>) Aut = (C2 x Q16) : C2 (small group id <64, 191>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1^-1 * Y3^2, Y2^-1 * Y3^2 * Y1^-1, Y3^-2 * Y2^-1 * Y1^-1, Y3^-1 * Y2 * Y3^-1 * Y1^-1, Y2^2 * Y1^2, Y3^-1 * Y2^-1 * Y3 * Y2^-1, (Y2^-1, Y1^-1), Y3 * Y2 * Y3 * Y1^-1, (Y1^-1 * Y2^-1)^2, R * Y1 * R * Y2, Y3^4, (R * Y3)^2, Y1^-6 * Y2 * Y1^-1 ] Map:: non-degenerate R = (1, 33, 65, 97, 4, 36, 68, 100, 9, 41, 73, 105, 7, 39, 71, 103)(2, 34, 66, 98, 10, 42, 74, 106, 6, 38, 70, 102, 12, 44, 76, 108)(3, 35, 67, 99, 14, 46, 78, 110, 5, 37, 69, 101, 16, 48, 80, 112)(8, 40, 72, 104, 18, 50, 82, 114, 11, 43, 75, 107, 20, 52, 84, 116)(13, 45, 77, 109, 22, 54, 86, 118, 15, 47, 79, 111, 24, 56, 88, 120)(17, 49, 81, 113, 26, 58, 90, 122, 19, 51, 83, 115, 28, 60, 92, 124)(21, 53, 85, 117, 29, 61, 93, 125, 23, 55, 87, 119, 30, 62, 94, 126)(25, 57, 89, 121, 31, 63, 95, 127, 27, 59, 91, 123, 32, 64, 96, 128) L = (1, 34)(2, 40)(3, 41)(4, 48)(5, 33)(6, 43)(7, 46)(8, 49)(9, 38)(10, 36)(11, 51)(12, 39)(13, 37)(14, 56)(15, 35)(16, 54)(17, 57)(18, 42)(19, 59)(20, 44)(21, 47)(22, 62)(23, 45)(24, 61)(25, 53)(26, 50)(27, 55)(28, 52)(29, 63)(30, 64)(31, 58)(32, 60)(65, 99)(66, 105)(67, 109)(68, 108)(69, 111)(70, 97)(71, 106)(72, 102)(73, 101)(74, 116)(75, 98)(76, 114)(77, 117)(78, 100)(79, 119)(80, 103)(81, 107)(82, 124)(83, 104)(84, 122)(85, 123)(86, 110)(87, 121)(88, 112)(89, 115)(90, 128)(91, 113)(92, 127)(93, 118)(94, 120)(95, 126)(96, 125) local type(s) :: { ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E23.153 Transitivity :: VT+ Graph:: bipartite v = 8 e = 64 f = 12 degree seq :: [ 16^8 ] E23.161 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 16, 16}) Quotient :: dipole Aut^+ = C16 : C2 (small group id <32, 17>) Aut = (C2 x D16) : C2 (small group id <64, 190>) |r| :: 2 Presentation :: [ R^2, Y2^2 * Y1^2, Y2^-2 * Y1^2, (Y2, Y1), Y1^4, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2, Y3^-1), Y3^-1 * Y1^-1 * Y3 * Y1^-1, Y3^2 * Y2 * Y3^2, Y3 * Y1^-1 * Y2^-1 * Y3^-1 * Y1 * 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 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 9, 41, 6, 38, 11, 43)(4, 36, 15, 47, 21, 53, 10, 42)(7, 39, 18, 50, 22, 54, 12, 44)(13, 45, 26, 58, 17, 49, 23, 55)(14, 46, 27, 59, 19, 51, 24, 56)(16, 48, 25, 57, 29, 61, 30, 62)(20, 52, 28, 60, 31, 63, 32, 64)(65, 97, 67, 99, 72, 104, 70, 102)(66, 98, 73, 105, 69, 101, 75, 107)(68, 100, 77, 109, 85, 117, 81, 113)(71, 103, 78, 110, 86, 118, 83, 115)(74, 106, 87, 119, 79, 111, 90, 122)(76, 108, 88, 120, 82, 114, 91, 123)(80, 112, 84, 116, 93, 125, 95, 127)(89, 121, 92, 124, 94, 126, 96, 128) L = (1, 68)(2, 74)(3, 77)(4, 80)(5, 79)(6, 81)(7, 65)(8, 85)(9, 87)(10, 89)(11, 90)(12, 66)(13, 84)(14, 67)(15, 94)(16, 83)(17, 95)(18, 69)(19, 70)(20, 71)(21, 93)(22, 72)(23, 92)(24, 73)(25, 91)(26, 96)(27, 75)(28, 76)(29, 78)(30, 88)(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) :: { ( 32^8 ) } Outer automorphisms :: reflexible Dual of E23.176 Graph:: bipartite v = 16 e = 64 f = 4 degree seq :: [ 8^16 ] E23.162 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 16, 16}) Quotient :: dipole Aut^+ = QD32 (small group id <32, 19>) Aut = (C2 x D16) : C2 (small group id <64, 190>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (R * Y1)^2, (Y2 * Y1^-1)^2, (R * Y3)^2, Y1^4, (Y2^-1 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^4, Y1^-1 * Y2^-8 * Y1^-1, (Y3 * Y2^-1)^16 ] Map:: 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, 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) :: { ( 8, 32, 8, 32, 8, 32, 8, 32 ), ( 8, 32, 8, 32, 8, 32, 8, 32, 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 = 10 e = 64 f = 10 degree seq :: [ 8^8, 32^2 ] E23.163 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 16, 16}) Quotient :: dipole Aut^+ = C16 : C2 (small group id <32, 17>) Aut = (C2 x D16) : C2 (small group id <64, 190>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, (R * Y3)^2, (R * Y1)^2, Y2 * Y1^-1 * Y2^-1 * Y1^-1, Y1^4, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^4, Y1^-1 * Y2^8 * Y1^-1, (Y3 * Y2^-1)^16 ] Map:: R = (1, 33, 2, 34, 6, 38, 4, 36)(3, 35, 9, 41, 13, 45, 7, 39)(5, 37, 11, 43, 14, 46, 8, 40)(10, 42, 15, 47, 21, 53, 17, 49)(12, 44, 16, 48, 22, 54, 19, 51)(18, 50, 25, 57, 29, 61, 23, 55)(20, 52, 27, 59, 30, 62, 24, 56)(26, 58, 31, 63, 28, 60, 32, 64)(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, 91, 123, 83, 115, 75, 107, 68, 100, 73, 105, 81, 113, 89, 121, 96, 128, 88, 120, 80, 112, 72, 104) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 81)(18, 82)(19, 83)(20, 84)(21, 85)(22, 86)(23, 87)(24, 88)(25, 89)(26, 90)(27, 91)(28, 92)(29, 93)(30, 94)(31, 95)(32, 96)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8, 32, 8, 32, 8, 32, 8, 32 ), ( 8, 32, 8, 32, 8, 32, 8, 32, 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 = 10 e = 64 f = 10 degree seq :: [ 8^8, 32^2 ] E23.164 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 16, 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, Y3^2, Y1 * Y3 * Y1, Y1^2 * Y3, (Y2 * Y1^-1)^2, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, (Y1^-1 * Y2^-1)^2, Y2 * Y3 * Y2^-1 * Y3, Y2^8 * Y3 ] Map:: non-degenerate R = (1, 33, 2, 34, 4, 36, 5, 37)(3, 35, 9, 41, 11, 43, 8, 40)(6, 38, 13, 45, 12, 44, 7, 39)(10, 42, 16, 48, 19, 51, 17, 49)(14, 46, 15, 47, 20, 52, 21, 53)(18, 50, 25, 57, 27, 59, 24, 56)(22, 54, 29, 61, 28, 60, 23, 55)(26, 58, 32, 64, 30, 62, 31, 63)(65, 97, 67, 99, 74, 106, 82, 114, 90, 122, 92, 124, 84, 116, 76, 108, 68, 100, 75, 107, 83, 115, 91, 123, 94, 126, 86, 118, 78, 110, 70, 102)(66, 98, 71, 103, 79, 111, 87, 119, 95, 127, 89, 121, 81, 113, 73, 105, 69, 101, 77, 109, 85, 117, 93, 125, 96, 128, 88, 120, 80, 112, 72, 104) L = (1, 68)(2, 69)(3, 75)(4, 65)(5, 66)(6, 76)(7, 77)(8, 73)(9, 72)(10, 83)(11, 67)(12, 70)(13, 71)(14, 84)(15, 85)(16, 81)(17, 80)(18, 91)(19, 74)(20, 78)(21, 79)(22, 92)(23, 93)(24, 89)(25, 88)(26, 94)(27, 82)(28, 86)(29, 87)(30, 90)(31, 96)(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) :: { ( 8, 32, 8, 32, 8, 32, 8, 32 ), ( 8, 32, 8, 32, 8, 32, 8, 32, 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 = 10 e = 64 f = 10 degree seq :: [ 8^8, 32^2 ] E23.165 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 16, 16}) Quotient :: dipole Aut^+ = C16 : C2 (small group id <32, 17>) Aut = (C2 x D16) : C2 (small group id <64, 190>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1 * Y3 * Y1, Y2 * Y1^-1 * Y2^-1 * Y1^-1, Y2^-1 * Y3 * Y2 * Y3, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y2^8 * Y3, (Y2^3 * Y1 * Y2)^2 ] Map:: non-degenerate R = (1, 33, 2, 34, 4, 36, 5, 37)(3, 35, 9, 41, 11, 43, 7, 39)(6, 38, 13, 45, 12, 44, 8, 40)(10, 42, 15, 47, 19, 51, 17, 49)(14, 46, 16, 48, 20, 52, 21, 53)(18, 50, 25, 57, 27, 59, 23, 55)(22, 54, 29, 61, 28, 60, 24, 56)(26, 58, 31, 63, 30, 62, 32, 64)(65, 97, 67, 99, 74, 106, 82, 114, 90, 122, 92, 124, 84, 116, 76, 108, 68, 100, 75, 107, 83, 115, 91, 123, 94, 126, 86, 118, 78, 110, 70, 102)(66, 98, 71, 103, 79, 111, 87, 119, 95, 127, 93, 125, 85, 117, 77, 109, 69, 101, 73, 105, 81, 113, 89, 121, 96, 128, 88, 120, 80, 112, 72, 104) L = (1, 68)(2, 69)(3, 75)(4, 65)(5, 66)(6, 76)(7, 73)(8, 77)(9, 71)(10, 83)(11, 67)(12, 70)(13, 72)(14, 84)(15, 81)(16, 85)(17, 79)(18, 91)(19, 74)(20, 78)(21, 80)(22, 92)(23, 89)(24, 93)(25, 87)(26, 94)(27, 82)(28, 86)(29, 88)(30, 90)(31, 96)(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) :: { ( 8, 32, 8, 32, 8, 32, 8, 32 ), ( 8, 32, 8, 32, 8, 32, 8, 32, 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 = 10 e = 64 f = 10 degree seq :: [ 8^8, 32^2 ] E23.166 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 16, 16}) Quotient :: dipole Aut^+ = C16 : C2 (small group id <32, 17>) Aut = (C2 x D16) : C2 (small group id <64, 190>) |r| :: 2 Presentation :: [ Y3^2, R^2, (R * Y3)^2, (Y2^-1, Y1), Y1^-1 * Y3 * Y1 * Y3, Y1^4, (R * Y1)^2, Y2^4 * Y1, Y3 * Y2^-2 * Y3 * Y2^2, (R * Y2 * Y3)^2, (R * Y2^-2)^2, Y3 * Y2^-1 * Y3 * Y1^-1 * Y2 * Y1^-1, Y3 * Y1^-1 * Y2 * Y3 * Y2^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 33, 2, 34, 7, 39, 5, 37)(3, 35, 8, 40, 20, 52, 13, 45)(4, 36, 9, 41, 21, 53, 15, 47)(6, 38, 10, 42, 22, 54, 17, 49)(11, 43, 19, 51, 27, 59, 29, 61)(12, 44, 23, 55, 14, 46, 24, 56)(16, 48, 25, 57, 18, 50, 26, 58)(28, 60, 31, 63, 30, 62, 32, 64)(65, 97, 67, 99, 75, 107, 81, 113, 69, 101, 77, 109, 93, 125, 86, 118, 71, 103, 84, 116, 91, 123, 74, 106, 66, 98, 72, 104, 83, 115, 70, 102)(68, 100, 78, 110, 92, 124, 90, 122, 79, 111, 87, 119, 96, 128, 82, 114, 85, 117, 76, 108, 94, 126, 89, 121, 73, 105, 88, 120, 95, 127, 80, 112) L = (1, 68)(2, 73)(3, 76)(4, 65)(5, 79)(6, 82)(7, 85)(8, 87)(9, 66)(10, 90)(11, 92)(12, 67)(13, 88)(14, 84)(15, 69)(16, 86)(17, 89)(18, 70)(19, 95)(20, 78)(21, 71)(22, 80)(23, 72)(24, 77)(25, 81)(26, 74)(27, 94)(28, 75)(29, 96)(30, 91)(31, 83)(32, 93)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8, 32, 8, 32, 8, 32, 8, 32 ), ( 8, 32, 8, 32, 8, 32, 8, 32, 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 E23.169 Graph:: bipartite v = 10 e = 64 f = 10 degree seq :: [ 8^8, 32^2 ] E23.167 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 16, 16}) Quotient :: dipole Aut^+ = C16 : C2 (small group id <32, 17>) Aut = (C2 x D16) : C2 (small group id <64, 190>) |r| :: 2 Presentation :: [ Y3^2, R^2, (Y2^-1, Y1), Y3 * Y1 * Y3 * Y1^-1, (R * Y3)^2, (R * Y1)^2, Y1^4, Y1^-1 * Y2^4, Y2^-1 * Y3 * Y2 * Y1^-2 * Y3, (R * Y2 * Y3)^2, Y1^-1 * Y2 * Y1^-2 * Y2^-1 * Y1^-1, Y2 * Y1 * R * Y2 * R * Y1, Y1 * Y2 * Y3 * Y2^-1 * Y3 * Y1 ] Map:: non-degenerate R = (1, 33, 2, 34, 7, 39, 5, 37)(3, 35, 8, 40, 20, 52, 13, 45)(4, 36, 9, 41, 21, 53, 15, 47)(6, 38, 10, 42, 22, 54, 17, 49)(11, 43, 23, 55, 31, 63, 19, 51)(12, 44, 24, 56, 14, 46, 25, 57)(16, 48, 26, 58, 18, 50, 27, 59)(28, 60, 32, 64, 29, 61, 30, 62)(65, 97, 67, 99, 75, 107, 74, 106, 66, 98, 72, 104, 87, 119, 86, 118, 71, 103, 84, 116, 95, 127, 81, 113, 69, 101, 77, 109, 83, 115, 70, 102)(68, 100, 78, 110, 92, 124, 90, 122, 73, 105, 89, 121, 96, 128, 82, 114, 85, 117, 76, 108, 93, 125, 91, 123, 79, 111, 88, 120, 94, 126, 80, 112) L = (1, 68)(2, 73)(3, 76)(4, 65)(5, 79)(6, 82)(7, 85)(8, 88)(9, 66)(10, 91)(11, 92)(12, 67)(13, 89)(14, 84)(15, 69)(16, 86)(17, 90)(18, 70)(19, 94)(20, 78)(21, 71)(22, 80)(23, 96)(24, 72)(25, 77)(26, 81)(27, 74)(28, 75)(29, 95)(30, 83)(31, 93)(32, 87)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8, 32, 8, 32, 8, 32, 8, 32 ), ( 8, 32, 8, 32, 8, 32, 8, 32, 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 E23.168 Graph:: bipartite v = 10 e = 64 f = 10 degree seq :: [ 8^8, 32^2 ] E23.168 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 16, 16}) Quotient :: dipole Aut^+ = C16 : C2 (small group id <32, 17>) Aut = (C2 x D16) : C2 (small group id <64, 190>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-1 * Y1 * Y2 * Y1, (R * Y3)^2, Y3 * Y1^-1 * Y3 * Y1, Y1^4, (R * Y1)^2, (R * Y2 * Y3)^2, Y3 * Y2^-1 * Y3 * Y1^2 * Y2, Y3 * Y2^3 * Y1 * Y2, Y1 * Y3 * Y2^-1 * Y3 * Y2 * Y1, (Y2^-1 * Y1^-2 * Y2^-1)^8 ] Map:: non-degenerate R = (1, 33, 2, 34, 7, 39, 5, 37)(3, 35, 11, 43, 20, 52, 8, 40)(4, 36, 9, 41, 21, 53, 15, 47)(6, 38, 17, 49, 22, 54, 10, 42)(12, 44, 23, 55, 31, 63, 29, 61)(13, 45, 25, 57, 14, 46, 24, 56)(16, 48, 27, 59, 18, 50, 26, 58)(19, 51, 28, 60, 32, 64, 30, 62)(65, 97, 67, 99, 76, 108, 90, 122, 73, 105, 89, 121, 96, 128, 86, 118, 71, 103, 84, 116, 95, 127, 91, 123, 79, 111, 88, 120, 83, 115, 70, 102)(66, 98, 72, 104, 87, 119, 82, 114, 85, 117, 77, 109, 94, 126, 81, 113, 69, 101, 75, 107, 93, 125, 80, 112, 68, 100, 78, 110, 92, 124, 74, 106) L = (1, 68)(2, 73)(3, 77)(4, 65)(5, 79)(6, 82)(7, 85)(8, 88)(9, 66)(10, 91)(11, 89)(12, 92)(13, 67)(14, 84)(15, 69)(16, 86)(17, 90)(18, 70)(19, 93)(20, 78)(21, 71)(22, 80)(23, 96)(24, 72)(25, 75)(26, 81)(27, 74)(28, 76)(29, 83)(30, 95)(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) :: { ( 8, 32, 8, 32, 8, 32, 8, 32 ), ( 8, 32, 8, 32, 8, 32, 8, 32, 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 E23.167 Graph:: bipartite v = 10 e = 64 f = 10 degree seq :: [ 8^8, 32^2 ] E23.169 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 16, 16}) Quotient :: dipole Aut^+ = C16 : C2 (small group id <32, 17>) Aut = (C2 x D16) : C2 (small group id <64, 190>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y3 * Y1 * Y3 * Y1^-1, Y1^4, Y2^-1 * Y1^-1 * Y2 * Y1^-1, (R * Y1)^2, (R * Y3)^2, Y2 * Y3 * Y2^-1 * Y1^-2 * Y3, (R * Y2 * Y3)^2, Y3 * Y1^-1 * Y2^-1 * Y3 * Y2 * Y1^-1, Y2 * Y3 * Y2^2 * Y1 * Y2, Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y1^2 ] Map:: non-degenerate R = (1, 33, 2, 34, 7, 39, 5, 37)(3, 35, 11, 43, 20, 52, 8, 40)(4, 36, 9, 41, 21, 53, 15, 47)(6, 38, 17, 49, 22, 54, 10, 42)(12, 44, 23, 55, 31, 63, 29, 61)(13, 45, 25, 57, 14, 46, 24, 56)(16, 48, 27, 59, 18, 50, 26, 58)(19, 51, 28, 60, 32, 64, 30, 62)(65, 97, 67, 99, 76, 108, 91, 123, 79, 111, 88, 120, 96, 128, 86, 118, 71, 103, 84, 116, 95, 127, 90, 122, 73, 105, 89, 121, 83, 115, 70, 102)(66, 98, 72, 104, 87, 119, 80, 112, 68, 100, 78, 110, 94, 126, 81, 113, 69, 101, 75, 107, 93, 125, 82, 114, 85, 117, 77, 109, 92, 124, 74, 106) L = (1, 68)(2, 73)(3, 77)(4, 65)(5, 79)(6, 82)(7, 85)(8, 88)(9, 66)(10, 91)(11, 89)(12, 94)(13, 67)(14, 84)(15, 69)(16, 86)(17, 90)(18, 70)(19, 87)(20, 78)(21, 71)(22, 80)(23, 83)(24, 72)(25, 75)(26, 81)(27, 74)(28, 95)(29, 96)(30, 76)(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, 32, 8, 32, 8, 32, 8, 32 ), ( 8, 32, 8, 32, 8, 32, 8, 32, 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 E23.166 Graph:: bipartite v = 10 e = 64 f = 10 degree seq :: [ 8^8, 32^2 ] E23.170 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 16, 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^-1 * Y1^-1 * Y3 * Y1^-1, Y3^-2 * Y1^-2, Y1^4, Y3^-1 * Y1 * Y3^-1 * Y1^-1, (Y3^-1, Y2^-1), Y1 * Y3^-2 * Y1, (R * Y1)^2, (R * Y2)^2, (Y1^-1 * Y2^-1)^2, (R * Y3)^2, (Y2 * Y1^-1)^2, Y2^3 * Y3 * Y2, Y2^-1 * Y1^-1 * Y2 * Y3^-1 * Y2 * 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 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 13, 45, 21, 53, 11, 43)(4, 36, 12, 44, 7, 39, 10, 42)(6, 38, 18, 50, 22, 54, 9, 41)(14, 46, 27, 59, 31, 63, 29, 61)(15, 47, 26, 58, 16, 48, 28, 60)(17, 49, 24, 56, 20, 52, 25, 57)(19, 51, 23, 55, 30, 62, 32, 64)(65, 97, 67, 99, 78, 110, 84, 116, 71, 103, 80, 112, 94, 126, 86, 118, 72, 104, 85, 117, 95, 127, 81, 113, 68, 100, 79, 111, 83, 115, 70, 102)(66, 98, 73, 105, 87, 119, 92, 124, 76, 108, 89, 121, 93, 125, 77, 109, 69, 101, 82, 114, 96, 128, 90, 122, 74, 106, 88, 120, 91, 123, 75, 107) L = (1, 68)(2, 74)(3, 79)(4, 72)(5, 76)(6, 81)(7, 65)(8, 71)(9, 88)(10, 69)(11, 90)(12, 66)(13, 92)(14, 83)(15, 85)(16, 67)(17, 86)(18, 89)(19, 95)(20, 70)(21, 80)(22, 84)(23, 91)(24, 82)(25, 73)(26, 77)(27, 96)(28, 75)(29, 87)(30, 78)(31, 94)(32, 93)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8, 32, 8, 32, 8, 32, 8, 32 ), ( 8, 32, 8, 32, 8, 32, 8, 32, 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 E23.171 Graph:: bipartite v = 10 e = 64 f = 10 degree seq :: [ 8^8, 32^2 ] E23.171 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 16, 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, Y3^4, (R * Y2)^2, Y3^-1 * Y1^-1 * Y3 * Y1^-1, (Y1 * Y2)^2, Y1^2 * Y3^2, (R * Y3)^2, Y3^-1 * Y1 * Y3^-1 * Y1^-1, Y1 * Y3^-2 * Y1, (Y3^-1, Y2^-1), (R * Y1)^2, (Y2 * Y1^-1)^2, Y3^-1 * Y2^4, Y2^-1 * Y1^-1 * Y2 * Y3 * Y2 * Y1^-1 * Y2^-1 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 13, 45, 21, 53, 11, 43)(4, 36, 12, 44, 7, 39, 10, 42)(6, 38, 18, 50, 22, 54, 9, 41)(14, 46, 27, 59, 32, 64, 29, 61)(15, 47, 26, 58, 16, 48, 28, 60)(17, 49, 24, 56, 20, 52, 25, 57)(19, 51, 23, 55, 30, 62, 31, 63)(65, 97, 67, 99, 78, 110, 81, 113, 68, 100, 79, 111, 94, 126, 86, 118, 72, 104, 85, 117, 96, 128, 84, 116, 71, 103, 80, 112, 83, 115, 70, 102)(66, 98, 73, 105, 87, 119, 90, 122, 74, 106, 88, 120, 93, 125, 77, 109, 69, 101, 82, 114, 95, 127, 92, 124, 76, 108, 89, 121, 91, 123, 75, 107) L = (1, 68)(2, 74)(3, 79)(4, 72)(5, 76)(6, 81)(7, 65)(8, 71)(9, 88)(10, 69)(11, 90)(12, 66)(13, 92)(14, 94)(15, 85)(16, 67)(17, 86)(18, 89)(19, 78)(20, 70)(21, 80)(22, 84)(23, 93)(24, 82)(25, 73)(26, 77)(27, 87)(28, 75)(29, 95)(30, 96)(31, 91)(32, 83)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8, 32, 8, 32, 8, 32, 8, 32 ), ( 8, 32, 8, 32, 8, 32, 8, 32, 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 E23.170 Graph:: bipartite v = 10 e = 64 f = 10 degree seq :: [ 8^8, 32^2 ] E23.172 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 16, 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 * Y3 * Y2, Y3 * Y1 * Y3 * Y1^-1, (Y2 * Y1^-1)^2, (Y1 * Y2)^2, Y1^4, (R * Y2)^2, Y3 * Y1 * Y3 * Y1^-1, (Y2^-1 * Y1)^2, (R * Y1)^2, (R * Y3)^2, Y3^-4 * Y1^-2, Y1^2 * Y3 * Y1^2 * Y3^-1, Y3 * Y1^2 * Y2^-1 * Y3^2 * Y2^-1, (Y3 * Y2^-1)^16 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 13, 45, 21, 53, 11, 43)(4, 36, 12, 44, 22, 54, 16, 48)(6, 38, 18, 50, 23, 55, 9, 41)(7, 39, 10, 42, 24, 56, 19, 51)(14, 46, 29, 61, 31, 63, 27, 59)(15, 47, 28, 60, 20, 52, 26, 58)(17, 49, 32, 64, 30, 62, 25, 57)(65, 97, 67, 99, 71, 103, 78, 110, 84, 116, 94, 126, 86, 118, 87, 119, 72, 104, 85, 117, 88, 120, 95, 127, 79, 111, 81, 113, 68, 100, 70, 102)(66, 98, 73, 105, 76, 108, 89, 121, 92, 124, 93, 125, 83, 115, 77, 109, 69, 101, 82, 114, 80, 112, 96, 128, 90, 122, 91, 123, 74, 106, 75, 107) L = (1, 68)(2, 74)(3, 70)(4, 79)(5, 83)(6, 81)(7, 65)(8, 86)(9, 75)(10, 90)(11, 91)(12, 66)(13, 93)(14, 67)(15, 88)(16, 69)(17, 95)(18, 77)(19, 92)(20, 71)(21, 87)(22, 84)(23, 94)(24, 72)(25, 73)(26, 80)(27, 96)(28, 76)(29, 89)(30, 78)(31, 85)(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) :: { ( 8, 32, 8, 32, 8, 32, 8, 32 ), ( 8, 32, 8, 32, 8, 32, 8, 32, 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 E23.175 Graph:: bipartite v = 10 e = 64 f = 10 degree seq :: [ 8^8, 32^2 ] E23.173 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 16, 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, (Y1^-1 * Y2^-1)^2, Y1^4, Y3 * Y1 * Y3 * Y1^-1, (Y1 * Y2^-1)^2, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y3^2 * Y1^-1 * Y3^-2 * Y1^-1, Y1^-2 * Y2 * Y3^3 * Y2 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 13, 45, 21, 53, 11, 43)(4, 36, 12, 44, 22, 54, 16, 48)(6, 38, 17, 49, 23, 55, 9, 41)(7, 39, 10, 42, 24, 56, 18, 50)(14, 46, 29, 61, 32, 64, 27, 59)(15, 47, 28, 60, 20, 52, 26, 58)(19, 51, 31, 63, 30, 62, 25, 57)(65, 97, 67, 99, 68, 100, 78, 110, 79, 111, 94, 126, 88, 120, 87, 119, 72, 104, 85, 117, 86, 118, 96, 128, 84, 116, 83, 115, 71, 103, 70, 102)(66, 98, 73, 105, 74, 106, 89, 121, 90, 122, 93, 125, 80, 112, 77, 109, 69, 101, 81, 113, 82, 114, 95, 127, 92, 124, 91, 123, 76, 108, 75, 107) L = (1, 68)(2, 74)(3, 78)(4, 79)(5, 82)(6, 67)(7, 65)(8, 86)(9, 89)(10, 90)(11, 73)(12, 66)(13, 81)(14, 94)(15, 88)(16, 69)(17, 95)(18, 92)(19, 70)(20, 71)(21, 96)(22, 84)(23, 85)(24, 72)(25, 93)(26, 80)(27, 75)(28, 76)(29, 77)(30, 87)(31, 91)(32, 83)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8, 32, 8, 32, 8, 32, 8, 32 ), ( 8, 32, 8, 32, 8, 32, 8, 32, 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 = 10 e = 64 f = 10 degree seq :: [ 8^8, 32^2 ] E23.174 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 16, 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, (R * Y2)^2, (Y3^-1, Y2^-1), (Y2 * Y1^-1)^2, (Y2^-1 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, Y3 * Y1 * Y3 * Y1^-1, Y1^4, Y3^3 * Y2^2, Y2 * Y1^-1 * Y3 * Y2^-1 * Y1, Y1^-1 * Y3^-1 * Y1^-1 * Y2^-2, Y2 * Y1^-1 * Y2^-1 * Y1 * Y3^-1, Y1^-2 * Y2^2 * Y3^-1, Y2^16 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 13, 45, 19, 51, 11, 43)(4, 36, 12, 44, 14, 46, 18, 50)(6, 38, 20, 52, 16, 48, 9, 41)(7, 39, 10, 42, 22, 54, 21, 53)(15, 47, 29, 61, 30, 62, 27, 59)(17, 49, 28, 60, 24, 56, 26, 58)(23, 55, 32, 64, 31, 63, 25, 57)(65, 97, 67, 99, 78, 110, 94, 126, 81, 113, 87, 119, 71, 103, 80, 112, 72, 104, 83, 115, 68, 100, 79, 111, 88, 120, 95, 127, 86, 118, 70, 102)(66, 98, 73, 105, 85, 117, 96, 128, 90, 122, 91, 123, 76, 108, 77, 109, 69, 101, 84, 116, 74, 106, 89, 121, 92, 124, 93, 125, 82, 114, 75, 107) L = (1, 68)(2, 74)(3, 79)(4, 81)(5, 85)(6, 83)(7, 65)(8, 78)(9, 89)(10, 90)(11, 84)(12, 66)(13, 73)(14, 88)(15, 87)(16, 67)(17, 86)(18, 69)(19, 94)(20, 96)(21, 92)(22, 72)(23, 70)(24, 71)(25, 91)(26, 82)(27, 75)(28, 76)(29, 77)(30, 95)(31, 80)(32, 93)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8, 32, 8, 32, 8, 32, 8, 32 ), ( 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32, 8, 32 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 10 e = 64 f = 10 degree seq :: [ 8^8, 32^2 ] E23.175 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 16, 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, (R * Y1)^2, (Y2, Y3), (R * Y3)^2, (Y2^-1 * Y1^-1)^2, (R * Y2)^2, Y1^4, Y3^-1 * Y1 * Y3^-1 * Y1^-1, (Y2 * Y1^-1)^2, Y3^-1 * Y1 * Y2 * Y1^-1 * Y2^-1, Y2^-2 * Y3^3, Y2^-1 * Y1^-1 * Y2 * Y1 * Y3^-1, Y3 * Y1 * Y2^-2 * Y1, Y1^-2 * Y2 * Y3 * Y2, Y2^-1 * Y1^-2 * Y3^-1 * Y2^-1, Y2^16 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 5, 37)(3, 35, 13, 45, 23, 55, 11, 43)(4, 36, 12, 44, 22, 54, 18, 50)(6, 38, 20, 52, 15, 47, 9, 41)(7, 39, 10, 42, 14, 46, 21, 53)(16, 48, 29, 61, 30, 62, 27, 59)(17, 49, 28, 60, 24, 56, 26, 58)(19, 51, 32, 64, 31, 63, 25, 57)(65, 97, 67, 99, 78, 110, 94, 126, 88, 120, 83, 115, 68, 100, 79, 111, 72, 104, 87, 119, 71, 103, 80, 112, 81, 113, 95, 127, 86, 118, 70, 102)(66, 98, 73, 105, 82, 114, 96, 128, 92, 124, 91, 123, 74, 106, 77, 109, 69, 101, 84, 116, 76, 108, 89, 121, 90, 122, 93, 125, 85, 117, 75, 107) L = (1, 68)(2, 74)(3, 79)(4, 81)(5, 85)(6, 83)(7, 65)(8, 86)(9, 77)(10, 90)(11, 91)(12, 66)(13, 93)(14, 72)(15, 95)(16, 67)(17, 78)(18, 69)(19, 80)(20, 75)(21, 92)(22, 88)(23, 70)(24, 71)(25, 73)(26, 82)(27, 89)(28, 76)(29, 96)(30, 87)(31, 94)(32, 84)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8, 32, 8, 32, 8, 32, 8, 32 ), ( 8, 32, 8, 32, 8, 32, 8, 32, 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 E23.172 Graph:: bipartite v = 10 e = 64 f = 10 degree seq :: [ 8^8, 32^2 ] E23.176 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 16, 16}) Quotient :: dipole Aut^+ = C16 : C2 (small group id <32, 17>) Aut = (C2 x D16) : C2 (small group id <64, 190>) |r| :: 2 Presentation :: [ R^2, (Y3, Y2^-1), Y3^-1 * Y2^-3, Y3 * Y1^-1 * Y2 * Y1^-1, (R * Y3)^2, (R * Y1)^2, Y1^-2 * Y3^-2, (Y2^-1 * Y1^-1)^2, (R * Y2)^2, Y3^-1 * Y2 * Y1 * Y3 * Y2^-1 * Y1^-1, Y3^-1 * Y2^-1 * Y1^-1 * Y2 * Y3^-1 * Y1^-1, Y2 * Y1^4 * Y3^-1, Y3^2 * Y2 * Y1^-1 * Y3^-1 * Y1^-1, Y2^-1 * Y1^2 * Y2^-2 * Y3, (Y3 * Y2 * Y1^-2)^2 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 22, 54, 19, 51, 30, 62, 14, 46, 26, 58, 32, 64, 31, 63, 15, 47, 27, 59, 16, 48, 28, 60, 18, 50, 5, 37)(3, 35, 13, 45, 23, 55, 11, 43, 4, 36, 17, 49, 7, 39, 20, 52, 25, 57, 9, 41, 6, 38, 21, 53, 24, 56, 10, 42, 29, 61, 12, 44)(65, 97, 67, 99, 78, 110, 71, 103, 80, 112, 88, 120, 72, 104, 87, 119, 96, 128, 89, 121, 82, 114, 93, 125, 83, 115, 68, 100, 79, 111, 70, 102)(66, 98, 73, 105, 90, 122, 76, 108, 92, 124, 81, 113, 86, 118, 85, 117, 95, 127, 77, 109, 69, 101, 84, 116, 94, 126, 74, 106, 91, 123, 75, 107) L = (1, 68)(2, 74)(3, 79)(4, 82)(5, 85)(6, 83)(7, 65)(8, 71)(9, 91)(10, 69)(11, 94)(12, 66)(13, 86)(14, 70)(15, 93)(16, 67)(17, 90)(18, 87)(19, 89)(20, 95)(21, 92)(22, 76)(23, 80)(24, 78)(25, 72)(26, 75)(27, 84)(28, 73)(29, 96)(30, 77)(31, 81)(32, 88)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 8^32 ) } Outer automorphisms :: reflexible Dual of E23.161 Graph:: bipartite v = 4 e = 64 f = 16 degree seq :: [ 32^4 ] E23.177 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 16, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2 * Y3^2, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y2 * Y1 * Y2^-1 * Y1, Y3^-1 * Y1 * Y3 * Y1, Y2^8 * Y1, (Y3 * Y2^-1)^32 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 7, 39)(4, 36, 8, 40)(5, 37, 9, 41)(6, 38, 10, 42)(11, 43, 15, 47)(12, 44, 16, 48)(13, 45, 17, 49)(14, 46, 18, 50)(19, 51, 23, 55)(20, 52, 24, 56)(21, 53, 25, 57)(22, 54, 26, 58)(27, 59, 30, 62)(28, 60, 31, 63)(29, 61, 32, 64)(65, 97, 67, 99, 75, 107, 83, 115, 91, 123, 90, 122, 82, 114, 73, 105, 66, 98, 71, 103, 79, 111, 87, 119, 94, 126, 86, 118, 78, 110, 69, 101)(68, 100, 70, 102, 76, 108, 84, 116, 92, 124, 96, 128, 89, 121, 81, 113, 72, 104, 74, 106, 80, 112, 88, 120, 95, 127, 93, 125, 85, 117, 77, 109) L = (1, 68)(2, 72)(3, 70)(4, 69)(5, 77)(6, 65)(7, 74)(8, 73)(9, 81)(10, 66)(11, 76)(12, 67)(13, 78)(14, 85)(15, 80)(16, 71)(17, 82)(18, 89)(19, 84)(20, 75)(21, 86)(22, 93)(23, 88)(24, 79)(25, 90)(26, 96)(27, 92)(28, 83)(29, 94)(30, 95)(31, 87)(32, 91)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 64^4 ), ( 64^32 ) } Outer automorphisms :: reflexible Dual of E23.197 Graph:: bipartite v = 18 e = 64 f = 2 degree seq :: [ 4^16, 32^2 ] E23.178 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 16, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y1 * Y3^-1 * Y1 * Y3, (Y3, Y2), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2^-1 * Y1 * Y2 * Y1, Y2^2 * Y3 * Y2 * Y3, Y2 * Y1 * Y3^-1 * Y2^-1 * Y1 * Y3, Y3^-3 * Y1 * Y2^2 * Y3^-1, Y2^-8 * Y1 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 7, 39)(4, 36, 8, 40)(5, 37, 9, 41)(6, 38, 10, 42)(11, 43, 19, 51)(12, 44, 20, 52)(13, 45, 21, 53)(14, 46, 22, 54)(15, 47, 23, 55)(16, 48, 24, 56)(17, 49, 25, 57)(18, 50, 26, 58)(27, 59, 29, 61)(28, 60, 30, 62)(31, 63, 32, 64)(65, 97, 67, 99, 75, 107, 82, 114, 92, 124, 86, 118, 88, 120, 73, 105, 66, 98, 71, 103, 83, 115, 90, 122, 94, 126, 78, 110, 80, 112, 69, 101)(68, 100, 76, 108, 81, 113, 70, 102, 77, 109, 91, 123, 96, 128, 87, 119, 72, 104, 84, 116, 89, 121, 74, 106, 85, 117, 93, 125, 95, 127, 79, 111) L = (1, 68)(2, 72)(3, 76)(4, 78)(5, 79)(6, 65)(7, 84)(8, 86)(9, 87)(10, 66)(11, 81)(12, 80)(13, 67)(14, 93)(15, 94)(16, 95)(17, 69)(18, 70)(19, 89)(20, 88)(21, 71)(22, 91)(23, 92)(24, 96)(25, 73)(26, 74)(27, 75)(28, 77)(29, 83)(30, 85)(31, 90)(32, 82)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 64^4 ), ( 64^32 ) } Outer automorphisms :: reflexible Dual of E23.198 Graph:: bipartite v = 18 e = 64 f = 2 degree seq :: [ 4^16, 32^2 ] E23.179 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 16, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1 * Y3 * Y1, Y2^-1 * Y1 * Y2 * Y1, (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y2^-1), (R * Y2)^2, Y3^-2 * Y2^3 * Y1, Y3 * Y2^-1 * Y3 * Y2^-2 * Y1, Y2^2 * Y1 * Y3^4, Y1 * Y3 * Y2^2 * Y3^3 ] Map:: non-degenerate R = (1, 33, 2, 34)(3, 35, 7, 39)(4, 36, 8, 40)(5, 37, 9, 41)(6, 38, 10, 42)(11, 43, 19, 51)(12, 44, 20, 52)(13, 45, 21, 53)(14, 46, 22, 54)(15, 47, 23, 55)(16, 48, 24, 56)(17, 49, 25, 57)(18, 50, 26, 58)(27, 59, 32, 64)(28, 60, 31, 63)(29, 61, 30, 62)(65, 97, 67, 99, 75, 107, 86, 118, 95, 127, 82, 114, 88, 120, 73, 105, 66, 98, 71, 103, 83, 115, 78, 110, 92, 124, 90, 122, 80, 112, 69, 101)(68, 100, 76, 108, 91, 123, 94, 126, 81, 113, 70, 102, 77, 109, 87, 119, 72, 104, 84, 116, 96, 128, 93, 125, 89, 121, 74, 106, 85, 117, 79, 111) L = (1, 68)(2, 72)(3, 76)(4, 78)(5, 79)(6, 65)(7, 84)(8, 86)(9, 87)(10, 66)(11, 91)(12, 92)(13, 67)(14, 93)(15, 83)(16, 85)(17, 69)(18, 70)(19, 96)(20, 95)(21, 71)(22, 94)(23, 75)(24, 77)(25, 73)(26, 74)(27, 90)(28, 89)(29, 88)(30, 80)(31, 81)(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) :: { ( 64^4 ), ( 64^32 ) } Outer automorphisms :: reflexible Dual of E23.196 Graph:: bipartite v = 18 e = 64 f = 2 degree seq :: [ 4^16, 32^2 ] E23.180 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 16, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3 * Y2, (Y3 * Y1)^2, (Y3^-1, Y1), Y3^-2 * Y1^-2, (Y2^-1, Y1^-1), (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y3^-2 * Y1^2 * Y3^-1 * Y1 * Y3^-2, Y3^34 * Y1^2 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 19, 51, 27, 59, 23, 55, 16, 48, 4, 36, 10, 42, 7, 39, 12, 44, 21, 53, 29, 61, 24, 56, 15, 47, 5, 37)(3, 35, 9, 41, 20, 52, 28, 60, 32, 64, 25, 57, 18, 50, 6, 38, 11, 43, 14, 46, 22, 54, 30, 62, 31, 63, 26, 58, 17, 49, 13, 45)(65, 97, 67, 99, 71, 103, 78, 110, 72, 104, 84, 116, 85, 117, 94, 126, 91, 123, 96, 128, 88, 120, 90, 122, 80, 112, 82, 114, 69, 101, 77, 109, 74, 106, 75, 107, 66, 98, 73, 105, 76, 108, 86, 118, 83, 115, 92, 124, 93, 125, 95, 127, 87, 119, 89, 121, 79, 111, 81, 113, 68, 100, 70, 102) L = (1, 68)(2, 74)(3, 70)(4, 79)(5, 80)(6, 81)(7, 65)(8, 71)(9, 75)(10, 69)(11, 77)(12, 66)(13, 82)(14, 67)(15, 87)(16, 88)(17, 89)(18, 90)(19, 76)(20, 78)(21, 72)(22, 73)(23, 93)(24, 91)(25, 95)(26, 96)(27, 85)(28, 86)(29, 83)(30, 84)(31, 92)(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, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64 ), ( 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64 ) } Outer automorphisms :: reflexible Dual of E23.190 Graph:: bipartite v = 3 e = 64 f = 17 degree seq :: [ 32^2, 64 ] E23.181 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 16, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ R^2, Y2^2 * Y3^-1, (Y1, Y2^-1), (Y3^-1, Y1^-1), (Y3^-1 * Y1^-1)^2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y1 * Y3^2 * Y1, Y1^-4 * Y3 * Y1^-3, Y3^-6 * Y1 * Y3^-1 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 19, 51, 27, 59, 25, 57, 16, 48, 4, 36, 10, 42, 7, 39, 12, 44, 21, 53, 29, 61, 26, 58, 15, 47, 5, 37)(3, 35, 9, 41, 18, 50, 22, 54, 30, 62, 31, 63, 24, 56, 13, 45, 17, 49, 6, 38, 11, 43, 20, 52, 28, 60, 32, 64, 23, 55, 14, 46)(65, 97, 67, 99, 68, 100, 77, 109, 79, 111, 87, 119, 89, 121, 95, 127, 93, 125, 92, 124, 83, 115, 86, 118, 76, 108, 75, 107, 66, 98, 73, 105, 74, 106, 81, 113, 69, 101, 78, 110, 80, 112, 88, 120, 90, 122, 96, 128, 91, 123, 94, 126, 85, 117, 84, 116, 72, 104, 82, 114, 71, 103, 70, 102) L = (1, 68)(2, 74)(3, 77)(4, 79)(5, 80)(6, 67)(7, 65)(8, 71)(9, 81)(10, 69)(11, 73)(12, 66)(13, 87)(14, 88)(15, 89)(16, 90)(17, 78)(18, 70)(19, 76)(20, 82)(21, 72)(22, 75)(23, 95)(24, 96)(25, 93)(26, 91)(27, 85)(28, 86)(29, 83)(30, 84)(31, 92)(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, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64 ), ( 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64 ) } Outer automorphisms :: reflexible Dual of E23.188 Graph:: bipartite v = 3 e = 64 f = 17 degree seq :: [ 32^2, 64 ] E23.182 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 16, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ R^2, (Y3^-1, Y2^-1), (Y3^-1, Y1^-1), (Y1^-1 * Y3^-1)^2, (R * Y2)^2, (Y1^-1, Y2^-1), (R * Y3)^2, Y3^2 * Y1^2, (R * Y1)^2, Y2 * Y3 * Y2 * Y1^-1 * Y3, Y2^-2 * Y1^-1 * Y2^-2 * Y3, Y2^2 * Y1 * Y3^-1 * Y2^2, Y2 * Y1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * 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, 33, 2, 34, 8, 40, 13, 45, 25, 57, 31, 63, 18, 50, 4, 36, 10, 42, 7, 39, 12, 44, 24, 56, 30, 62, 21, 53, 17, 49, 5, 37)(3, 35, 9, 41, 23, 55, 29, 61, 19, 51, 28, 60, 22, 54, 14, 46, 26, 58, 16, 48, 27, 59, 32, 64, 20, 52, 6, 38, 11, 43, 15, 47)(65, 97, 67, 99, 77, 109, 93, 125, 82, 114, 86, 118, 71, 103, 80, 112, 94, 126, 84, 116, 69, 101, 79, 111, 72, 104, 87, 119, 95, 127, 92, 124, 74, 106, 90, 122, 88, 120, 96, 128, 81, 113, 75, 107, 66, 98, 73, 105, 89, 121, 83, 115, 68, 100, 78, 110, 76, 108, 91, 123, 85, 117, 70, 102) L = (1, 68)(2, 74)(3, 78)(4, 81)(5, 82)(6, 83)(7, 65)(8, 71)(9, 90)(10, 69)(11, 92)(12, 66)(13, 76)(14, 75)(15, 86)(16, 67)(17, 95)(18, 85)(19, 96)(20, 93)(21, 89)(22, 70)(23, 80)(24, 72)(25, 88)(26, 79)(27, 73)(28, 84)(29, 91)(30, 77)(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, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64 ), ( 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64 ) } Outer automorphisms :: reflexible Dual of E23.191 Graph:: bipartite v = 3 e = 64 f = 17 degree seq :: [ 32^2, 64 ] E23.183 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 16, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ R^2, (Y2^-1, Y1), (Y3^-1 * Y1^-1)^2, Y3^-2 * Y1^-2, (Y3, Y2^-1), (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y3^-1 * Y2^2 * Y1 * Y3^-1, Y3^-2 * Y1 * Y2^2, Y2^-2 * Y3^-1 * Y2^-2 * Y1, Y3^-5 * Y2^-2, Y2^-10 * Y1, Y2^32 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 21, 53, 27, 59, 32, 64, 18, 50, 4, 36, 10, 42, 7, 39, 12, 44, 24, 56, 29, 61, 13, 45, 17, 49, 5, 37)(3, 35, 9, 41, 20, 52, 6, 38, 11, 43, 23, 55, 31, 63, 14, 46, 25, 57, 16, 48, 19, 51, 26, 58, 22, 54, 28, 60, 30, 62, 15, 47)(65, 97, 67, 99, 77, 109, 92, 124, 76, 108, 83, 115, 68, 100, 78, 110, 91, 123, 75, 107, 66, 98, 73, 105, 81, 113, 94, 126, 88, 120, 90, 122, 74, 106, 89, 121, 96, 128, 87, 119, 72, 104, 84, 116, 69, 101, 79, 111, 93, 125, 86, 118, 71, 103, 80, 112, 82, 114, 95, 127, 85, 117, 70, 102) L = (1, 68)(2, 74)(3, 78)(4, 81)(5, 82)(6, 83)(7, 65)(8, 71)(9, 89)(10, 69)(11, 90)(12, 66)(13, 91)(14, 94)(15, 95)(16, 67)(17, 96)(18, 77)(19, 73)(20, 80)(21, 76)(22, 70)(23, 86)(24, 72)(25, 79)(26, 84)(27, 88)(28, 75)(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) :: { ( 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64 ), ( 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64 ) } Outer automorphisms :: reflexible Dual of E23.194 Graph:: bipartite v = 3 e = 64 f = 17 degree seq :: [ 32^2, 64 ] E23.184 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 16, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ R^2, (Y3^-1 * Y1^-1)^2, (Y2^-1, Y3), (Y1^-1, Y3), (R * Y3)^2, Y1^2 * Y3^2, (R * Y1)^2, (R * Y2)^2, (Y2^-1, Y1^-1), Y2^2 * Y3^-3, Y3^-1 * Y1 * Y2^2 * Y1, Y2^-1 * Y1 * Y2^-2 * Y3^-1 * Y2^-1, Y2^-6 * Y1^-1, Y3 * Y2^10 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 23, 55, 29, 61, 13, 45, 18, 50, 4, 36, 10, 42, 7, 39, 12, 44, 21, 53, 27, 59, 32, 64, 17, 49, 5, 37)(3, 35, 9, 41, 19, 51, 26, 58, 22, 54, 28, 60, 31, 63, 14, 46, 25, 57, 16, 48, 20, 52, 6, 38, 11, 43, 24, 56, 30, 62, 15, 47)(65, 97, 67, 99, 77, 109, 92, 124, 76, 108, 84, 116, 69, 101, 79, 111, 93, 125, 86, 118, 71, 103, 80, 112, 81, 113, 94, 126, 87, 119, 90, 122, 74, 106, 89, 121, 96, 128, 88, 120, 72, 104, 83, 115, 68, 100, 78, 110, 91, 123, 75, 107, 66, 98, 73, 105, 82, 114, 95, 127, 85, 117, 70, 102) L = (1, 68)(2, 74)(3, 78)(4, 81)(5, 82)(6, 83)(7, 65)(8, 71)(9, 89)(10, 69)(11, 90)(12, 66)(13, 91)(14, 94)(15, 95)(16, 67)(17, 77)(18, 96)(19, 80)(20, 73)(21, 72)(22, 70)(23, 76)(24, 86)(25, 79)(26, 84)(27, 87)(28, 75)(29, 85)(30, 92)(31, 88)(32, 93)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64 ), ( 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64 ) } Outer automorphisms :: reflexible Dual of E23.189 Graph:: bipartite v = 3 e = 64 f = 17 degree seq :: [ 32^2, 64 ] E23.185 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 16, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ R^2, (Y3^-1, Y2^-1), (Y3^-1 * Y1^-1)^2, (Y3^-1, Y1^-1), (R * Y3)^2, (Y1^-1, Y2), (R * Y1)^2, (R * Y2)^2, Y3^2 * Y1^2, Y3^-2 * Y2^-2 * Y3^-1, Y2^-1 * Y3 * Y2^-3 * Y1^-1, (Y3 * Y1^-1)^8, Y2 * Y1 * Y3^-1 * Y1 * Y3^-2 * Y1 * Y3^-2 * Y1 * Y3^-2 * Y1 * Y3^-2 * Y1 * Y3^-2 * Y1 * Y3^-2 * Y1 * Y3^-2 * Y1 * Y3^-2 * Y1 * Y3^-2 * Y1 * Y3^-2 * Y1 * Y3^-2 * Y1 * Y3^-1 * Y2 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 23, 55, 30, 62, 21, 53, 18, 50, 4, 36, 10, 42, 7, 39, 12, 44, 13, 45, 25, 57, 31, 63, 17, 49, 5, 37)(3, 35, 9, 41, 24, 56, 32, 64, 20, 52, 6, 38, 11, 43, 14, 46, 26, 58, 16, 48, 27, 59, 29, 61, 19, 51, 28, 60, 22, 54, 15, 47)(65, 97, 67, 99, 77, 109, 93, 125, 82, 114, 75, 107, 66, 98, 73, 105, 89, 121, 83, 115, 68, 100, 78, 110, 72, 104, 88, 120, 95, 127, 92, 124, 74, 106, 90, 122, 87, 119, 96, 128, 81, 113, 86, 118, 71, 103, 80, 112, 94, 126, 84, 116, 69, 101, 79, 111, 76, 108, 91, 123, 85, 117, 70, 102) L = (1, 68)(2, 74)(3, 78)(4, 81)(5, 82)(6, 83)(7, 65)(8, 71)(9, 90)(10, 69)(11, 92)(12, 66)(13, 72)(14, 86)(15, 75)(16, 67)(17, 85)(18, 95)(19, 96)(20, 93)(21, 89)(22, 70)(23, 76)(24, 80)(25, 87)(26, 79)(27, 73)(28, 84)(29, 88)(30, 77)(31, 94)(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, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64 ), ( 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64 ) } Outer automorphisms :: reflexible Dual of E23.192 Graph:: bipartite v = 3 e = 64 f = 17 degree seq :: [ 32^2, 64 ] E23.186 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 16, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1 * Y2, (Y3^-1, Y1), (Y3, Y2), (Y1^-1 * Y3^-1)^2, (R * Y3)^2, Y3^2 * Y1^2, (R * Y1)^2, (R * Y2)^2, Y1^2 * Y3^-5 * Y1, Y3^-2 * Y1 * Y2^-1 * Y3^-1 * Y1 * Y3^-2 * Y2^-1 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 19, 51, 27, 59, 25, 57, 16, 48, 4, 36, 9, 41, 7, 39, 11, 43, 21, 53, 29, 61, 26, 58, 15, 47, 5, 37)(3, 35, 6, 38, 10, 42, 20, 52, 28, 60, 31, 63, 24, 56, 12, 44, 17, 49, 14, 46, 18, 50, 22, 54, 30, 62, 32, 64, 23, 55, 13, 45)(65, 97, 67, 99, 69, 101, 77, 109, 79, 111, 87, 119, 90, 122, 96, 128, 93, 125, 94, 126, 85, 117, 86, 118, 75, 107, 82, 114, 71, 103, 78, 110, 73, 105, 81, 113, 68, 100, 76, 108, 80, 112, 88, 120, 89, 121, 95, 127, 91, 123, 92, 124, 83, 115, 84, 116, 72, 104, 74, 106, 66, 98, 70, 102) L = (1, 68)(2, 73)(3, 76)(4, 79)(5, 80)(6, 81)(7, 65)(8, 71)(9, 69)(10, 78)(11, 66)(12, 87)(13, 88)(14, 67)(15, 89)(16, 90)(17, 77)(18, 70)(19, 75)(20, 82)(21, 72)(22, 74)(23, 95)(24, 96)(25, 93)(26, 91)(27, 85)(28, 86)(29, 83)(30, 84)(31, 94)(32, 92)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64 ), ( 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64 ) } Outer automorphisms :: reflexible Dual of E23.195 Graph:: bipartite v = 3 e = 64 f = 17 degree seq :: [ 32^2, 64 ] E23.187 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 16, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1^-1 * Y2, (Y3^-1 * Y1^-1)^2, (R * Y3)^2, Y3^-2 * Y1^-2, (R * Y2)^2, (Y3, Y2), (R * Y1)^2, Y3 * Y2 * Y3 * Y2 * Y1, Y1^-2 * Y3^5 * Y1^-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 * Y1^-1 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 19, 51, 27, 59, 23, 55, 15, 47, 4, 36, 10, 42, 7, 39, 11, 43, 21, 53, 29, 61, 24, 56, 14, 46, 5, 37)(3, 35, 9, 41, 20, 52, 28, 60, 31, 63, 26, 58, 16, 48, 12, 44, 18, 50, 13, 45, 22, 54, 30, 62, 32, 64, 25, 57, 17, 49, 6, 38)(65, 97, 67, 99, 66, 98, 73, 105, 72, 104, 84, 116, 83, 115, 92, 124, 91, 123, 95, 127, 87, 119, 90, 122, 79, 111, 80, 112, 68, 100, 76, 108, 74, 106, 82, 114, 71, 103, 77, 109, 75, 107, 86, 118, 85, 117, 94, 126, 93, 125, 96, 128, 88, 120, 89, 121, 78, 110, 81, 113, 69, 101, 70, 102) L = (1, 68)(2, 74)(3, 76)(4, 78)(5, 79)(6, 80)(7, 65)(8, 71)(9, 82)(10, 69)(11, 66)(12, 81)(13, 67)(14, 87)(15, 88)(16, 89)(17, 90)(18, 70)(19, 75)(20, 77)(21, 72)(22, 73)(23, 93)(24, 91)(25, 95)(26, 96)(27, 85)(28, 86)(29, 83)(30, 84)(31, 94)(32, 92)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64 ), ( 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64 ) } Outer automorphisms :: reflexible Dual of E23.193 Graph:: bipartite v = 3 e = 64 f = 17 degree seq :: [ 32^2, 64 ] E23.188 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 16, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3 * Y1^2, Y2 * Y1 * Y2 * Y1^-1, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y3^-1 * Y2 * Y3 * Y2, Y3^8 * Y2, Y3^3 * Y2 * Y1^-1 * Y3^4 * Y1^-1 ] Map:: non-degenerate R = (1, 33, 2, 34, 6, 38, 8, 40, 14, 46, 16, 48, 22, 54, 24, 56, 30, 62, 32, 64, 25, 57, 26, 58, 17, 49, 18, 50, 9, 41, 10, 42, 3, 35, 7, 39, 11, 43, 15, 47, 19, 51, 23, 55, 27, 59, 31, 63, 28, 60, 29, 61, 20, 52, 21, 53, 12, 44, 13, 45, 4, 36, 5, 37)(65, 97, 67, 99)(66, 98, 71, 103)(68, 100, 73, 105)(69, 101, 74, 106)(70, 102, 75, 107)(72, 104, 79, 111)(76, 108, 81, 113)(77, 109, 82, 114)(78, 110, 83, 115)(80, 112, 87, 119)(84, 116, 89, 121)(85, 117, 90, 122)(86, 118, 91, 123)(88, 120, 95, 127)(92, 124, 94, 126)(93, 125, 96, 128) L = (1, 68)(2, 69)(3, 73)(4, 76)(5, 77)(6, 65)(7, 74)(8, 66)(9, 81)(10, 82)(11, 67)(12, 84)(13, 85)(14, 70)(15, 71)(16, 72)(17, 89)(18, 90)(19, 75)(20, 92)(21, 93)(22, 78)(23, 79)(24, 80)(25, 94)(26, 96)(27, 83)(28, 91)(29, 95)(30, 86)(31, 87)(32, 88)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 32, 64, 32, 64 ), ( 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64 ) } Outer automorphisms :: reflexible Dual of E23.181 Graph:: bipartite v = 17 e = 64 f = 3 degree seq :: [ 4^16, 64 ] E23.189 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 16, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y1^-2 * Y3, Y2 * Y1^-1 * Y2 * Y1, (R * Y1)^2, Y3^-1 * Y2 * Y3 * Y2, (R * Y2)^2, (R * Y3)^2, Y3^-8 * Y2, Y3^-3 * Y2 * Y1^-1 * Y3^-4 * Y1^-1, (Y3^-1 * Y1^-1)^32 ] Map:: non-degenerate R = (1, 33, 2, 34, 4, 36, 8, 40, 12, 44, 16, 48, 20, 52, 24, 56, 28, 60, 32, 64, 27, 59, 26, 58, 19, 51, 18, 50, 11, 43, 10, 42, 3, 35, 7, 39, 9, 41, 15, 47, 17, 49, 23, 55, 25, 57, 31, 63, 30, 62, 29, 61, 22, 54, 21, 53, 14, 46, 13, 45, 6, 38, 5, 37)(65, 97, 67, 99)(66, 98, 71, 103)(68, 100, 73, 105)(69, 101, 74, 106)(70, 102, 75, 107)(72, 104, 79, 111)(76, 108, 81, 113)(77, 109, 82, 114)(78, 110, 83, 115)(80, 112, 87, 119)(84, 116, 89, 121)(85, 117, 90, 122)(86, 118, 91, 123)(88, 120, 95, 127)(92, 124, 94, 126)(93, 125, 96, 128) L = (1, 68)(2, 72)(3, 73)(4, 76)(5, 66)(6, 65)(7, 79)(8, 80)(9, 81)(10, 71)(11, 67)(12, 84)(13, 69)(14, 70)(15, 87)(16, 88)(17, 89)(18, 74)(19, 75)(20, 92)(21, 77)(22, 78)(23, 95)(24, 96)(25, 94)(26, 82)(27, 83)(28, 91)(29, 85)(30, 86)(31, 93)(32, 90)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 32, 64, 32, 64 ), ( 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64 ) } Outer automorphisms :: reflexible Dual of E23.184 Graph:: bipartite v = 17 e = 64 f = 3 degree seq :: [ 4^16, 64 ] E23.190 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 16, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y1^-1, Y3^-1), (R * Y3)^2, Y1 * Y2 * Y1^-1 * Y2, (R * Y1)^2, Y2 * Y3^-1 * Y2 * Y3, (R * Y2)^2, Y1^2 * Y3^3, Y1^-4 * Y2 * Y3^2, Y3^-1 * Y1 * Y3^-1 * Y1^2 * Y2 * Y1, Y1^-7 * Y2 * Y1 * Y3^-1, Y1^32 ] Map:: non-degenerate R = (1, 33, 2, 34, 7, 39, 19, 51, 25, 57, 28, 60, 13, 45, 23, 55, 31, 63, 15, 47, 4, 36, 9, 41, 18, 50, 24, 56, 27, 59, 12, 44, 3, 35, 8, 40, 20, 52, 30, 62, 14, 46, 17, 49, 6, 38, 10, 42, 21, 53, 26, 58, 11, 43, 22, 54, 29, 61, 32, 64, 16, 48, 5, 37)(65, 97, 67, 99)(66, 98, 72, 104)(68, 100, 75, 107)(69, 101, 76, 108)(70, 102, 77, 109)(71, 103, 84, 116)(73, 105, 86, 118)(74, 106, 87, 119)(78, 110, 89, 121)(79, 111, 90, 122)(80, 112, 91, 123)(81, 113, 92, 124)(82, 114, 93, 125)(83, 115, 94, 126)(85, 117, 95, 127)(88, 120, 96, 128) L = (1, 68)(2, 73)(3, 75)(4, 78)(5, 79)(6, 65)(7, 82)(8, 86)(9, 81)(10, 66)(11, 89)(12, 90)(13, 67)(14, 80)(15, 94)(16, 95)(17, 69)(18, 70)(19, 88)(20, 93)(21, 71)(22, 92)(23, 72)(24, 74)(25, 91)(26, 83)(27, 85)(28, 76)(29, 77)(30, 96)(31, 84)(32, 87)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 32, 64, 32, 64 ), ( 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64 ) } Outer automorphisms :: reflexible Dual of E23.180 Graph:: bipartite v = 17 e = 64 f = 3 degree seq :: [ 4^16, 64 ] E23.191 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 16, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3 * Y2 * Y3^-1 * Y2, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y1 * Y2 * Y1^-1 * Y2, (Y3^-1, Y1^-1), Y3^-3 * Y1^2, Y2 * Y1^2 * Y3^2 * Y1^2, Y1 * Y3 * Y1^-5 * Y3 * Y1^2 * Y3, Y3^-1 * Y1^-10, Y3^-1 * Y1^-10, (Y1^-1 * Y3^-1)^32 ] Map:: non-degenerate R = (1, 33, 2, 34, 7, 39, 19, 51, 29, 61, 26, 58, 11, 43, 22, 54, 31, 63, 17, 49, 6, 38, 10, 42, 14, 46, 24, 56, 27, 59, 12, 44, 3, 35, 8, 40, 20, 52, 32, 64, 18, 50, 15, 47, 4, 36, 9, 41, 21, 53, 28, 60, 13, 45, 23, 55, 25, 57, 30, 62, 16, 48, 5, 37)(65, 97, 67, 99)(66, 98, 72, 104)(68, 100, 75, 107)(69, 101, 76, 108)(70, 102, 77, 109)(71, 103, 84, 116)(73, 105, 86, 118)(74, 106, 87, 119)(78, 110, 89, 121)(79, 111, 90, 122)(80, 112, 91, 123)(81, 113, 92, 124)(82, 114, 93, 125)(83, 115, 96, 128)(85, 117, 95, 127)(88, 120, 94, 126) L = (1, 68)(2, 73)(3, 75)(4, 78)(5, 79)(6, 65)(7, 85)(8, 86)(9, 88)(10, 66)(11, 89)(12, 90)(13, 67)(14, 71)(15, 74)(16, 82)(17, 69)(18, 70)(19, 92)(20, 95)(21, 91)(22, 94)(23, 72)(24, 83)(25, 84)(26, 87)(27, 93)(28, 76)(29, 77)(30, 96)(31, 80)(32, 81)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 32, 64, 32, 64 ), ( 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64 ) } Outer automorphisms :: reflexible Dual of E23.182 Graph:: bipartite v = 17 e = 64 f = 3 degree seq :: [ 4^16, 64 ] E23.192 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 16, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y1^-1, Y3), (Y1^-1, Y3^-1), Y2 * Y3 * Y2 * Y3^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y1 * Y2 * Y1^-1 * Y2, Y1 * Y3^-2 * Y2 * Y3^-1 * Y1, Y3^3 * Y2 * Y1^-2, Y2 * Y1^3 * Y3^2 * Y1 ] Map:: non-degenerate R = (1, 33, 2, 34, 7, 39, 19, 51, 29, 61, 15, 47, 4, 36, 9, 41, 21, 53, 28, 60, 13, 45, 24, 56, 14, 46, 25, 57, 27, 59, 12, 44, 3, 35, 8, 40, 20, 52, 32, 64, 18, 50, 26, 58, 11, 43, 23, 55, 31, 63, 17, 49, 6, 38, 10, 42, 22, 54, 30, 62, 16, 48, 5, 37)(65, 97, 67, 99)(66, 98, 72, 104)(68, 100, 75, 107)(69, 101, 76, 108)(70, 102, 77, 109)(71, 103, 84, 116)(73, 105, 87, 119)(74, 106, 88, 120)(78, 110, 86, 118)(79, 111, 90, 122)(80, 112, 91, 123)(81, 113, 92, 124)(82, 114, 93, 125)(83, 115, 96, 128)(85, 117, 95, 127)(89, 121, 94, 126) L = (1, 68)(2, 73)(3, 75)(4, 78)(5, 79)(6, 65)(7, 85)(8, 87)(9, 89)(10, 66)(11, 86)(12, 90)(13, 67)(14, 84)(15, 88)(16, 93)(17, 69)(18, 70)(19, 92)(20, 95)(21, 91)(22, 71)(23, 94)(24, 72)(25, 96)(26, 74)(27, 82)(28, 76)(29, 77)(30, 83)(31, 80)(32, 81)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 32, 64, 32, 64 ), ( 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64 ) } Outer automorphisms :: reflexible Dual of E23.185 Graph:: bipartite v = 17 e = 64 f = 3 degree seq :: [ 4^16, 64 ] E23.193 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 16, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y2 * Y1 * Y2 * Y1^-1, (R * Y2)^2, (Y3, Y1^-1), Y3^-1 * Y2 * Y3 * Y2, (R * Y3)^2, (R * Y1)^2, Y2 * Y1^2 * Y3^3, Y3^-3 * Y2 * Y1^-2, Y3 * Y1 * Y3 * Y1 * Y3 * Y2, Y3^-5 * Y1^2, Y3^-1 * Y1^-6 ] Map:: non-degenerate R = (1, 33, 2, 34, 7, 39, 19, 51, 27, 59, 17, 49, 6, 38, 10, 42, 22, 54, 28, 60, 11, 43, 23, 55, 18, 50, 26, 58, 29, 61, 12, 44, 3, 35, 8, 40, 20, 52, 30, 62, 14, 46, 25, 57, 13, 45, 24, 56, 31, 63, 15, 47, 4, 36, 9, 41, 21, 53, 32, 64, 16, 48, 5, 37)(65, 97, 67, 99)(66, 98, 72, 104)(68, 100, 75, 107)(69, 101, 76, 108)(70, 102, 77, 109)(71, 103, 84, 116)(73, 105, 87, 119)(74, 106, 88, 120)(78, 110, 91, 123)(79, 111, 92, 124)(80, 112, 93, 125)(81, 113, 89, 121)(82, 114, 85, 117)(83, 115, 94, 126)(86, 118, 95, 127)(90, 122, 96, 128) L = (1, 68)(2, 73)(3, 75)(4, 78)(5, 79)(6, 65)(7, 85)(8, 87)(9, 89)(10, 66)(11, 91)(12, 92)(13, 67)(14, 93)(15, 94)(16, 95)(17, 69)(18, 70)(19, 96)(20, 82)(21, 77)(22, 71)(23, 81)(24, 72)(25, 76)(26, 74)(27, 80)(28, 83)(29, 86)(30, 90)(31, 84)(32, 88)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 32, 64, 32, 64 ), ( 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64 ) } Outer automorphisms :: reflexible Dual of E23.187 Graph:: bipartite v = 17 e = 64 f = 3 degree seq :: [ 4^16, 64 ] E23.194 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 16, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y2 * Y3 * Y2 * Y3^-1, Y3^-1 * Y1 * Y2 * Y1, Y1^-1 * Y3 * Y2 * Y1^-1, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y2 * Y3^8, Y3 * Y2 * Y1^30, (Y3^-1 * Y1^-1)^32 ] Map:: non-degenerate R = (1, 33, 2, 34, 7, 39, 15, 47, 12, 44, 17, 49, 24, 56, 31, 63, 28, 60, 29, 61, 22, 54, 26, 58, 19, 51, 13, 45, 6, 38, 10, 42, 3, 35, 8, 40, 4, 36, 9, 41, 16, 48, 23, 55, 20, 52, 25, 57, 30, 62, 32, 64, 27, 59, 21, 53, 14, 46, 18, 50, 11, 43, 5, 37)(65, 97, 67, 99)(66, 98, 72, 104)(68, 100, 71, 103)(69, 101, 74, 106)(70, 102, 75, 107)(73, 105, 79, 111)(76, 108, 80, 112)(77, 109, 82, 114)(78, 110, 83, 115)(81, 113, 87, 119)(84, 116, 88, 120)(85, 117, 90, 122)(86, 118, 91, 123)(89, 121, 95, 127)(92, 124, 94, 126)(93, 125, 96, 128) L = (1, 68)(2, 73)(3, 71)(4, 76)(5, 72)(6, 65)(7, 80)(8, 79)(9, 81)(10, 66)(11, 67)(12, 84)(13, 69)(14, 70)(15, 87)(16, 88)(17, 89)(18, 74)(19, 75)(20, 92)(21, 77)(22, 78)(23, 95)(24, 94)(25, 93)(26, 82)(27, 83)(28, 91)(29, 85)(30, 86)(31, 96)(32, 90)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 32, 64, 32, 64 ), ( 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64 ) } Outer automorphisms :: reflexible Dual of E23.183 Graph:: bipartite v = 17 e = 64 f = 3 degree seq :: [ 4^16, 64 ] E23.195 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 16, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3 * Y2 * Y3^-1 * Y2, Y2 * Y1 * Y2 * Y1^-1, Y3 * Y1 * Y2 * Y1, Y1^-2 * Y3^-1 * Y2, (R * Y2)^2, (R * Y3)^2, Y3 * Y2 * Y1^2, (R * Y1)^2, Y3^8 * Y2 ] Map:: non-degenerate R = (1, 33, 2, 34, 7, 39, 15, 47, 14, 46, 18, 50, 24, 56, 31, 63, 30, 62, 29, 61, 20, 52, 25, 57, 19, 51, 13, 45, 4, 36, 9, 41, 3, 35, 8, 40, 6, 38, 10, 42, 16, 48, 23, 55, 22, 54, 26, 58, 28, 60, 32, 64, 27, 59, 21, 53, 12, 44, 17, 49, 11, 43, 5, 37)(65, 97, 67, 99)(66, 98, 72, 104)(68, 100, 75, 107)(69, 101, 73, 105)(70, 102, 71, 103)(74, 106, 79, 111)(76, 108, 83, 115)(77, 109, 81, 113)(78, 110, 80, 112)(82, 114, 87, 119)(84, 116, 91, 123)(85, 117, 89, 121)(86, 118, 88, 120)(90, 122, 95, 127)(92, 124, 94, 126)(93, 125, 96, 128) L = (1, 68)(2, 73)(3, 75)(4, 76)(5, 77)(6, 65)(7, 67)(8, 69)(9, 81)(10, 66)(11, 83)(12, 84)(13, 85)(14, 70)(15, 72)(16, 71)(17, 89)(18, 74)(19, 91)(20, 92)(21, 93)(22, 78)(23, 79)(24, 80)(25, 96)(26, 82)(27, 94)(28, 88)(29, 90)(30, 86)(31, 87)(32, 95)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 32, 64, 32, 64 ), ( 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64, 32, 64 ) } Outer automorphisms :: reflexible Dual of E23.186 Graph:: bipartite v = 17 e = 64 f = 3 degree seq :: [ 4^16, 64 ] E23.196 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 16, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-2 * Y2^-1, Y3^-1 * Y1^-1 * Y3^-1 * Y2^-1, (Y3, Y2^-1), Y2 * Y1 * Y3^2, (Y3^-1, Y1^-1), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y2^2 * Y3^-2, Y1^-1 * Y3 * Y1^-4, (Y1^-1 * Y2)^8 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 19, 51, 17, 49, 4, 36, 10, 42, 21, 53, 30, 62, 26, 58, 13, 45, 6, 38, 11, 43, 22, 54, 31, 63, 25, 57, 16, 48, 24, 56, 32, 64, 28, 60, 15, 47, 3, 35, 9, 41, 20, 52, 29, 61, 27, 59, 14, 46, 7, 39, 12, 44, 23, 55, 18, 50, 5, 37)(65, 97, 67, 99, 77, 109, 69, 101, 79, 111, 90, 122, 82, 114, 92, 124, 94, 126, 87, 119, 96, 128, 85, 117, 76, 108, 88, 120, 74, 106, 71, 103, 80, 112, 68, 100, 78, 110, 89, 121, 81, 113, 91, 123, 95, 127, 83, 115, 93, 125, 86, 118, 72, 104, 84, 116, 75, 107, 66, 98, 73, 105, 70, 102) L = (1, 68)(2, 74)(3, 78)(4, 77)(5, 81)(6, 80)(7, 65)(8, 85)(9, 71)(10, 70)(11, 88)(12, 66)(13, 89)(14, 69)(15, 91)(16, 67)(17, 90)(18, 83)(19, 94)(20, 76)(21, 75)(22, 96)(23, 72)(24, 73)(25, 79)(26, 95)(27, 82)(28, 93)(29, 87)(30, 86)(31, 92)(32, 84)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 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 E23.179 Graph:: bipartite v = 2 e = 64 f = 18 degree seq :: [ 64^2 ] E23.197 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 16, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ R^2, (Y3^-1 * Y2)^2, Y3^2 * Y2^-2, Y1^2 * Y3 * Y1, (R * Y3)^2, (R * Y1)^2, (Y2^-1, Y1^-1), (R * Y2)^2, Y2^-1 * Y3^-1 * Y1 * Y2^-1 * Y3^-1 * Y2^-1, Y3^2 * Y1 * Y2^-2 * Y1^-1, Y3^2 * Y1^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y1^-2, Y3^-1 * Y2^-2 * Y1^-1 * Y3^-8, Y3 * Y1 * Y2^-1 * Y3 * Y2^26 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 7, 39, 12, 44, 23, 55, 19, 51, 27, 59, 31, 63, 30, 62, 14, 46, 25, 57, 15, 47, 3, 35, 9, 41, 21, 53, 16, 48, 26, 58, 18, 50, 6, 38, 11, 43, 22, 54, 20, 52, 28, 60, 32, 64, 29, 61, 13, 45, 24, 56, 17, 49, 4, 36, 10, 42, 5, 37)(65, 97, 67, 99, 77, 109, 91, 123, 75, 107, 66, 98, 73, 105, 88, 120, 95, 127, 86, 118, 72, 104, 85, 117, 81, 113, 94, 126, 84, 116, 71, 103, 80, 112, 68, 100, 78, 110, 92, 124, 76, 108, 90, 122, 74, 106, 89, 121, 96, 128, 87, 119, 82, 114, 69, 101, 79, 111, 93, 125, 83, 115, 70, 102) L = (1, 68)(2, 74)(3, 78)(4, 77)(5, 81)(6, 80)(7, 65)(8, 69)(9, 89)(10, 88)(11, 90)(12, 66)(13, 92)(14, 91)(15, 94)(16, 67)(17, 93)(18, 85)(19, 71)(20, 70)(21, 79)(22, 82)(23, 72)(24, 96)(25, 95)(26, 73)(27, 76)(28, 75)(29, 84)(30, 83)(31, 87)(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, 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 E23.177 Graph:: bipartite v = 2 e = 64 f = 18 degree seq :: [ 64^2 ] E23.198 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 16, 32, 32}) Quotient :: dipole Aut^+ = C32 (small group id <32, 1>) Aut = D64 (small group id <64, 52>) |r| :: 2 Presentation :: [ R^2, (Y3, Y2), (Y3^-1 * Y2)^2, (Y2, Y1^-1), Y3 * Y1^-1 * Y2 * Y1^-1, Y1^-2 * Y3 * Y2, (R * Y2)^2, Y2^-2 * Y3^2, (R * Y1)^2, Y2 * Y3 * Y1^-2, (R * Y3)^2, Y3^-1 * Y2^-2 * Y3^-3 * Y2^-1 * Y1^-1, Y2^-1 * Y1^-1 * Y3^-2 * Y2^-1 * Y3^-2 * Y2^-1 * Y3^-2 * Y2^-1 * Y3^-2 * Y2^-2 * Y1^-1, Y2^25 * Y1^-1, (Y3^-1 * Y1^-1)^16 ] Map:: non-degenerate R = (1, 33, 2, 34, 8, 40, 19, 51, 29, 61, 27, 59, 17, 49, 7, 39, 12, 44, 3, 35, 9, 41, 20, 52, 30, 62, 28, 60, 18, 50, 24, 56, 14, 46, 23, 55, 13, 45, 22, 54, 32, 64, 26, 58, 16, 48, 6, 38, 11, 43, 4, 36, 10, 42, 21, 53, 31, 63, 25, 57, 15, 47, 5, 37)(65, 97, 67, 99, 77, 109, 85, 117, 93, 125, 92, 124, 80, 112, 69, 101, 76, 108, 87, 119, 74, 106, 83, 115, 94, 126, 90, 122, 79, 111, 71, 103, 78, 110, 68, 100, 72, 104, 84, 116, 96, 128, 89, 121, 81, 113, 88, 120, 75, 107, 66, 98, 73, 105, 86, 118, 95, 127, 91, 123, 82, 114, 70, 102) L = (1, 68)(2, 74)(3, 72)(4, 77)(5, 75)(6, 78)(7, 65)(8, 85)(9, 83)(10, 86)(11, 87)(12, 66)(13, 84)(14, 67)(15, 70)(16, 88)(17, 69)(18, 71)(19, 95)(20, 93)(21, 96)(22, 94)(23, 73)(24, 76)(25, 80)(26, 82)(27, 79)(28, 81)(29, 89)(30, 91)(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, 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 E23.178 Graph:: bipartite v = 2 e = 64 f = 18 degree seq :: [ 64^2 ] E23.199 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 6, 9}) Quotient :: edge^2 Aut^+ = C9 : C4 (small group id <36, 1>) Aut = (C18 x C2) : C2 (small group id <72, 8>) |r| :: 2 Presentation :: [ R^2, Y2^4, Y1^4, Y1 * Y3^-1 * Y1^-1 * Y3^-1, Y3^-1 * Y2 * Y3^-1 * Y2^-1, Y2^2 * Y1^-2, R * Y1 * R * Y2, (R * Y3)^2, Y1 * Y2^2 * Y1, Y3^2 * Y2^-2 * Y3, Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, (Y3 * Y1^-1 * Y2^-1)^9 ] Map:: non-degenerate R = (1, 37, 4, 40, 17, 53, 8, 44, 22, 58, 7, 43)(2, 38, 10, 46, 18, 54, 5, 41, 20, 56, 12, 48)(3, 39, 14, 50, 19, 55, 6, 42, 21, 57, 16, 52)(9, 45, 24, 60, 27, 63, 11, 47, 28, 64, 26, 62)(13, 49, 30, 66, 33, 69, 15, 51, 34, 70, 32, 68)(23, 59, 35, 71, 29, 65, 25, 61, 36, 72, 31, 67)(73, 74, 80, 77)(75, 85, 78, 87)(76, 84, 94, 90)(79, 82, 89, 92)(81, 95, 83, 97)(86, 104, 93, 105)(88, 102, 91, 106)(96, 103, 100, 101)(98, 107, 99, 108)(109, 111, 116, 114)(110, 117, 113, 119)(112, 124, 130, 127)(115, 122, 125, 129)(118, 134, 128, 135)(120, 132, 126, 136)(121, 137, 123, 139)(131, 140, 133, 141)(138, 143, 142, 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) :: { ( 36^4 ), ( 36^12 ) } Outer automorphisms :: reflexible Dual of E23.202 Graph:: bipartite v = 24 e = 72 f = 4 degree seq :: [ 4^18, 12^6 ] E23.200 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 6, 9}) Quotient :: edge^2 Aut^+ = C9 : C4 (small group id <36, 1>) Aut = (C18 x C2) : C2 (small group id <72, 8>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1^2 * Y2^-1, Y2^4, Y2^-1 * Y3^-1 * Y2 * Y3^-1, Y1^4, (R * Y3)^2, Y1 * Y2^2 * Y1, R * Y1 * R * Y2, Y3 * Y1^-1 * Y3 * Y1, Y3^-1 * Y1 * Y2 * Y1^-1 * Y2^-1, Y3 * Y1 * Y3^-3 * Y2^-1, Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2 ] Map:: non-degenerate R = (1, 37, 4, 40, 17, 53, 30, 66, 15, 51, 11, 47, 27, 63, 22, 58, 7, 43)(2, 38, 10, 46, 26, 62, 31, 67, 16, 52, 3, 39, 14, 50, 28, 64, 12, 48)(5, 41, 20, 56, 34, 70, 33, 69, 19, 55, 6, 42, 21, 57, 32, 68, 18, 54)(8, 44, 23, 59, 35, 71, 29, 65, 13, 49, 9, 45, 25, 61, 36, 72, 24, 60)(73, 74, 80, 77)(75, 85, 78, 87)(76, 84, 95, 90)(79, 82, 96, 92)(81, 91, 83, 88)(86, 101, 93, 102)(89, 100, 107, 104)(94, 98, 108, 106)(97, 105, 99, 103)(109, 111, 116, 114)(110, 117, 113, 119)(112, 124, 131, 127)(115, 122, 132, 129)(118, 121, 128, 123)(120, 133, 126, 135)(125, 139, 143, 141)(130, 136, 144, 140)(134, 137, 142, 138) L = (1, 73)(2, 74)(3, 75)(4, 76)(5, 77)(6, 78)(7, 79)(8, 80)(9, 81)(10, 82)(11, 83)(12, 84)(13, 85)(14, 86)(15, 87)(16, 88)(17, 89)(18, 90)(19, 91)(20, 92)(21, 93)(22, 94)(23, 95)(24, 96)(25, 97)(26, 98)(27, 99)(28, 100)(29, 101)(30, 102)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 24^4 ), ( 24^18 ) } Outer automorphisms :: reflexible Dual of E23.201 Graph:: simple bipartite v = 22 e = 72 f = 6 degree seq :: [ 4^18, 18^4 ] E23.201 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 6, 9}) Quotient :: loop^2 Aut^+ = C9 : C4 (small group id <36, 1>) Aut = (C18 x C2) : C2 (small group id <72, 8>) |r| :: 2 Presentation :: [ R^2, Y2^4, Y1^4, Y1 * Y3^-1 * Y1^-1 * Y3^-1, Y3^-1 * Y2 * Y3^-1 * Y2^-1, Y2^2 * Y1^-2, R * Y1 * R * Y2, (R * Y3)^2, Y1 * Y2^2 * Y1, Y3^2 * Y2^-2 * Y3, Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, (Y3 * Y1^-1 * Y2^-1)^9 ] Map:: non-degenerate R = (1, 37, 73, 109, 4, 40, 76, 112, 17, 53, 89, 125, 8, 44, 80, 116, 22, 58, 94, 130, 7, 43, 79, 115)(2, 38, 74, 110, 10, 46, 82, 118, 18, 54, 90, 126, 5, 41, 77, 113, 20, 56, 92, 128, 12, 48, 84, 120)(3, 39, 75, 111, 14, 50, 86, 122, 19, 55, 91, 127, 6, 42, 78, 114, 21, 57, 93, 129, 16, 52, 88, 124)(9, 45, 81, 117, 24, 60, 96, 132, 27, 63, 99, 135, 11, 47, 83, 119, 28, 64, 100, 136, 26, 62, 98, 134)(13, 49, 85, 121, 30, 66, 102, 138, 33, 69, 105, 141, 15, 51, 87, 123, 34, 70, 106, 142, 32, 68, 104, 140)(23, 59, 95, 131, 35, 71, 107, 143, 29, 65, 101, 137, 25, 61, 97, 133, 36, 72, 108, 144, 31, 67, 103, 139) L = (1, 38)(2, 44)(3, 49)(4, 48)(5, 37)(6, 51)(7, 46)(8, 41)(9, 59)(10, 53)(11, 61)(12, 58)(13, 42)(14, 68)(15, 39)(16, 66)(17, 56)(18, 40)(19, 70)(20, 43)(21, 69)(22, 54)(23, 47)(24, 67)(25, 45)(26, 71)(27, 72)(28, 65)(29, 60)(30, 55)(31, 64)(32, 57)(33, 50)(34, 52)(35, 63)(36, 62)(73, 111)(74, 117)(75, 116)(76, 124)(77, 119)(78, 109)(79, 122)(80, 114)(81, 113)(82, 134)(83, 110)(84, 132)(85, 137)(86, 125)(87, 139)(88, 130)(89, 129)(90, 136)(91, 112)(92, 135)(93, 115)(94, 127)(95, 140)(96, 126)(97, 141)(98, 128)(99, 118)(100, 120)(101, 123)(102, 143)(103, 121)(104, 133)(105, 131)(106, 144)(107, 142)(108, 138) 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 ) } Outer automorphisms :: reflexible Dual of E23.200 Transitivity :: VT+ Graph:: bipartite v = 6 e = 72 f = 22 degree seq :: [ 24^6 ] E23.202 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 6, 9}) Quotient :: loop^2 Aut^+ = C9 : C4 (small group id <36, 1>) Aut = (C18 x C2) : C2 (small group id <72, 8>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1^2 * Y2^-1, Y2^4, Y2^-1 * Y3^-1 * Y2 * Y3^-1, Y1^4, (R * Y3)^2, Y1 * Y2^2 * Y1, R * Y1 * R * Y2, Y3 * Y1^-1 * Y3 * Y1, Y3^-1 * Y1 * Y2 * Y1^-1 * Y2^-1, Y3 * Y1 * Y3^-3 * Y2^-1, Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2 ] Map:: non-degenerate R = (1, 37, 73, 109, 4, 40, 76, 112, 17, 53, 89, 125, 30, 66, 102, 138, 15, 51, 87, 123, 11, 47, 83, 119, 27, 63, 99, 135, 22, 58, 94, 130, 7, 43, 79, 115)(2, 38, 74, 110, 10, 46, 82, 118, 26, 62, 98, 134, 31, 67, 103, 139, 16, 52, 88, 124, 3, 39, 75, 111, 14, 50, 86, 122, 28, 64, 100, 136, 12, 48, 84, 120)(5, 41, 77, 113, 20, 56, 92, 128, 34, 70, 106, 142, 33, 69, 105, 141, 19, 55, 91, 127, 6, 42, 78, 114, 21, 57, 93, 129, 32, 68, 104, 140, 18, 54, 90, 126)(8, 44, 80, 116, 23, 59, 95, 131, 35, 71, 107, 143, 29, 65, 101, 137, 13, 49, 85, 121, 9, 45, 81, 117, 25, 61, 97, 133, 36, 72, 108, 144, 24, 60, 96, 132) L = (1, 38)(2, 44)(3, 49)(4, 48)(5, 37)(6, 51)(7, 46)(8, 41)(9, 55)(10, 60)(11, 52)(12, 59)(13, 42)(14, 65)(15, 39)(16, 45)(17, 64)(18, 40)(19, 47)(20, 43)(21, 66)(22, 62)(23, 54)(24, 56)(25, 69)(26, 72)(27, 67)(28, 71)(29, 57)(30, 50)(31, 61)(32, 53)(33, 63)(34, 58)(35, 68)(36, 70)(73, 111)(74, 117)(75, 116)(76, 124)(77, 119)(78, 109)(79, 122)(80, 114)(81, 113)(82, 121)(83, 110)(84, 133)(85, 128)(86, 132)(87, 118)(88, 131)(89, 139)(90, 135)(91, 112)(92, 123)(93, 115)(94, 136)(95, 127)(96, 129)(97, 126)(98, 137)(99, 120)(100, 144)(101, 142)(102, 134)(103, 143)(104, 130)(105, 125)(106, 138)(107, 141)(108, 140) 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 E23.199 Transitivity :: VT+ Graph:: bipartite v = 4 e = 72 f = 24 degree seq :: [ 36^4 ] E23.203 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 6, 9}) Quotient :: dipole Aut^+ = C9 : C4 (small group id <36, 1>) Aut = (C18 x C2) : C2 (small group id <72, 8>) |r| :: 2 Presentation :: [ R^2, Y3^2 * Y2^-1 * Y3, (Y3, Y2^-1), (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y2 * Y1 * Y2 * Y1^-1, Y1^4, Y3^-1 * Y1^-1 * Y3^-1 * Y1, Y2^-2 * Y1^2 * Y2^-1 ] Map:: non-degenerate R = (1, 37, 2, 38, 8, 44, 5, 41)(3, 39, 11, 47, 21, 57, 15, 51)(4, 40, 12, 48, 23, 59, 17, 53)(6, 42, 9, 45, 13, 49, 19, 55)(7, 43, 10, 46, 24, 60, 20, 56)(14, 50, 28, 64, 34, 70, 31, 67)(16, 52, 27, 63, 36, 72, 32, 68)(18, 54, 26, 62, 29, 65, 33, 69)(22, 58, 25, 61, 30, 66, 35, 71)(73, 109, 75, 111, 85, 121, 80, 116, 93, 129, 78, 114)(74, 110, 81, 117, 87, 123, 77, 113, 91, 127, 83, 119)(76, 112, 86, 122, 101, 137, 95, 131, 106, 142, 90, 126)(79, 115, 88, 124, 102, 138, 96, 132, 108, 144, 94, 130)(82, 118, 97, 133, 104, 140, 92, 128, 107, 143, 99, 135)(84, 120, 98, 134, 103, 139, 89, 125, 105, 141, 100, 136) L = (1, 76)(2, 82)(3, 86)(4, 88)(5, 92)(6, 90)(7, 73)(8, 95)(9, 97)(10, 98)(11, 99)(12, 74)(13, 101)(14, 102)(15, 104)(16, 75)(17, 77)(18, 79)(19, 107)(20, 105)(21, 106)(22, 78)(23, 108)(24, 80)(25, 103)(26, 81)(27, 84)(28, 83)(29, 96)(30, 85)(31, 87)(32, 89)(33, 91)(34, 94)(35, 100)(36, 93)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 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 E23.205 Graph:: bipartite v = 15 e = 72 f = 13 degree seq :: [ 8^9, 12^6 ] E23.204 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 6, 9}) Quotient :: dipole Aut^+ = C9 : C4 (small group id <36, 1>) Aut = (C18 x C2) : C2 (small group id <72, 8>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y2^-1 * Y3^-2, (R * Y1)^2, (R * Y2^-1)^2, Y2 * Y1 * Y2 * Y1^-1, Y3^-1 * Y1^-1 * Y3^-1 * Y1, (R * Y3)^2, Y1^4, (Y2, Y3^-1), Y2^-2 * Y1^2 * Y2^-1, Y1^-1 * Y3^2 * Y1 * Y2^-1 * Y3^-1, Y3^-1 * Y2^-1 * Y1 * Y3^-1 * Y2^-1 * Y1^-1, Y3 * Y2 * Y1 * Y3^-2 * Y1^-1, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 37, 2, 38, 8, 44, 5, 41)(3, 39, 11, 47, 22, 58, 15, 51)(4, 40, 12, 48, 23, 59, 18, 54)(6, 42, 9, 45, 13, 49, 20, 56)(7, 43, 10, 46, 24, 60, 21, 57)(14, 50, 27, 63, 36, 72, 31, 67)(16, 52, 28, 64, 34, 70, 32, 68)(17, 53, 25, 61, 30, 66, 33, 69)(19, 55, 26, 62, 29, 65, 35, 71)(73, 109, 75, 111, 85, 121, 80, 116, 94, 130, 78, 114)(74, 110, 81, 117, 87, 123, 77, 113, 92, 128, 83, 119)(76, 112, 86, 122, 101, 137, 95, 131, 108, 144, 91, 127)(79, 115, 88, 124, 102, 138, 96, 132, 106, 142, 89, 125)(82, 118, 97, 133, 104, 140, 93, 129, 105, 141, 100, 136)(84, 120, 98, 134, 103, 139, 90, 126, 107, 143, 99, 135) L = (1, 76)(2, 82)(3, 86)(4, 89)(5, 93)(6, 91)(7, 73)(8, 95)(9, 97)(10, 99)(11, 100)(12, 74)(13, 101)(14, 79)(15, 104)(16, 75)(17, 78)(18, 77)(19, 106)(20, 105)(21, 103)(22, 108)(23, 102)(24, 80)(25, 84)(26, 81)(27, 83)(28, 107)(29, 88)(30, 85)(31, 87)(32, 98)(33, 90)(34, 94)(35, 92)(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) :: { ( 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 E23.206 Graph:: bipartite v = 15 e = 72 f = 13 degree seq :: [ 8^9, 12^6 ] E23.205 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 6, 9}) Quotient :: dipole Aut^+ = C9 : C4 (small group id <36, 1>) Aut = (C18 x C2) : C2 (small group id <72, 8>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^2, Y1 * Y2 * Y1 * Y2^-1, (R * Y3)^2, (R * Y1)^2, Y3 * Y2^-1 * Y3 * Y2, Y2^4, Y1^2 * Y3 * Y1^-2 * Y3^-1, Y2^-1 * Y3^-1 * Y2^-2 * Y3 * Y2^-1, (R * Y2 * Y3^-1)^2, Y2 * Y1^-2 * Y3^-1 * Y2 * Y1^2, (Y3^-1 * Y1^-1)^6 ] Map:: non-degenerate R = (1, 37, 2, 38, 8, 44, 21, 57, 32, 68, 31, 67, 33, 69, 17, 53, 5, 41)(3, 39, 12, 48, 28, 64, 27, 63, 16, 52, 20, 56, 36, 72, 22, 58, 9, 45)(4, 40, 10, 46, 23, 59, 29, 65, 13, 49, 25, 61, 35, 71, 19, 55, 7, 43)(6, 42, 18, 54, 34, 70, 26, 62, 15, 51, 14, 50, 30, 66, 24, 60, 11, 47)(73, 109, 75, 111, 85, 121, 78, 114)(74, 110, 81, 117, 97, 133, 83, 119)(76, 112, 87, 123, 103, 139, 88, 124)(77, 113, 84, 120, 101, 137, 90, 126)(79, 115, 86, 122, 104, 140, 92, 128)(80, 116, 94, 130, 107, 143, 96, 132)(82, 118, 98, 134, 105, 141, 99, 135)(89, 125, 100, 136, 95, 131, 106, 142)(91, 127, 102, 138, 93, 129, 108, 144) L = (1, 76)(2, 82)(3, 86)(4, 74)(5, 79)(6, 92)(7, 73)(8, 95)(9, 87)(10, 80)(11, 88)(12, 102)(13, 103)(14, 84)(15, 75)(16, 78)(17, 91)(18, 108)(19, 77)(20, 90)(21, 101)(22, 98)(23, 93)(24, 99)(25, 105)(26, 81)(27, 83)(28, 96)(29, 104)(30, 100)(31, 97)(32, 85)(33, 107)(34, 94)(35, 89)(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) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E23.203 Graph:: bipartite v = 13 e = 72 f = 15 degree seq :: [ 8^9, 18^4 ] E23.206 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 6, 9}) Quotient :: dipole Aut^+ = C9 : C4 (small group id <36, 1>) Aut = (C18 x C2) : C2 (small group id <72, 8>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2 * Y1 * Y2^-1, (Y1^-1, Y3^-1), (R * Y3)^2, (R * Y1)^2, Y2 * Y3 * Y2^-1 * Y3, Y2^4, Y1^-1 * Y3^-4, Y2 * Y3^-1 * Y2 * Y1^-2, Y2^-1 * Y1^-2 * Y3 * Y2^-1, (R * Y2 * Y3^-1)^2, Y1^9 ] Map:: non-degenerate R = (1, 37, 2, 38, 8, 44, 25, 61, 17, 53, 24, 60, 29, 65, 20, 56, 5, 41)(3, 39, 13, 49, 23, 59, 35, 71, 31, 67, 32, 68, 28, 64, 19, 55, 9, 45)(4, 40, 10, 46, 26, 62, 34, 70, 22, 58, 7, 43, 12, 48, 14, 50, 18, 54)(6, 42, 21, 57, 15, 51, 30, 66, 36, 72, 33, 69, 27, 63, 16, 52, 11, 47)(73, 109, 75, 111, 86, 122, 78, 114)(74, 110, 81, 117, 90, 126, 83, 119)(76, 112, 88, 124, 80, 116, 91, 127)(77, 113, 85, 121, 84, 120, 93, 129)(79, 115, 87, 123, 92, 128, 95, 131)(82, 118, 99, 135, 97, 133, 100, 136)(89, 125, 104, 140, 98, 134, 105, 141)(94, 130, 102, 138, 101, 137, 107, 143)(96, 132, 103, 139, 106, 142, 108, 144) L = (1, 76)(2, 82)(3, 87)(4, 89)(5, 90)(6, 95)(7, 73)(8, 98)(9, 93)(10, 96)(11, 85)(12, 74)(13, 102)(14, 80)(15, 103)(16, 75)(17, 94)(18, 97)(19, 78)(20, 86)(21, 107)(22, 77)(23, 108)(24, 79)(25, 106)(26, 101)(27, 81)(28, 83)(29, 84)(30, 104)(31, 99)(32, 88)(33, 91)(34, 92)(35, 105)(36, 100)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 8, 12, 8, 12, 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E23.204 Graph:: bipartite v = 13 e = 72 f = 15 degree seq :: [ 8^9, 18^4 ] E23.207 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 18, 18}) Quotient :: dipole Aut^+ = C18 x C2 (small group id <36, 5>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y3, Y2), (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y1 * Y2 * Y1, (R * Y2)^2, Y3 * Y1 * Y3^-1 * Y1, Y3^3 * Y2^2, Y2^6 ] Map:: non-degenerate R = (1, 37, 2, 38)(3, 39, 7, 43)(4, 40, 8, 44)(5, 41, 9, 45)(6, 42, 10, 46)(11, 47, 19, 55)(12, 48, 20, 56)(13, 49, 21, 57)(14, 50, 22, 58)(15, 51, 23, 59)(16, 52, 24, 60)(17, 53, 25, 61)(18, 54, 26, 62)(27, 63, 32, 68)(28, 64, 33, 69)(29, 65, 34, 70)(30, 66, 35, 71)(31, 67, 36, 72)(73, 109, 75, 111, 83, 119, 99, 135, 88, 124, 77, 113)(74, 110, 79, 115, 91, 127, 104, 140, 96, 132, 81, 117)(76, 112, 84, 120, 90, 126, 101, 137, 103, 139, 87, 123)(78, 114, 85, 121, 100, 136, 102, 138, 86, 122, 89, 125)(80, 116, 92, 128, 98, 134, 106, 142, 108, 144, 95, 131)(82, 118, 93, 129, 105, 141, 107, 143, 94, 130, 97, 133) L = (1, 76)(2, 80)(3, 84)(4, 86)(5, 87)(6, 73)(7, 92)(8, 94)(9, 95)(10, 74)(11, 90)(12, 89)(13, 75)(14, 88)(15, 102)(16, 103)(17, 77)(18, 78)(19, 98)(20, 97)(21, 79)(22, 96)(23, 107)(24, 108)(25, 81)(26, 82)(27, 101)(28, 83)(29, 85)(30, 99)(31, 100)(32, 106)(33, 91)(34, 93)(35, 104)(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) :: { ( 36^4 ), ( 36^12 ) } Outer automorphisms :: reflexible Dual of E23.223 Graph:: simple bipartite v = 24 e = 72 f = 4 degree seq :: [ 4^18, 12^6 ] E23.208 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 18, 18}) Quotient :: dipole Aut^+ = C18 x C2 (small group id <36, 5>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y3, Y2), Y3 * Y1 * Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2^-1 * Y1 * Y2 * Y1, Y3^3 * Y2^-2, Y2^6 ] Map:: non-degenerate R = (1, 37, 2, 38)(3, 39, 7, 43)(4, 40, 8, 44)(5, 41, 9, 45)(6, 42, 10, 46)(11, 47, 19, 55)(12, 48, 20, 56)(13, 49, 21, 57)(14, 50, 22, 58)(15, 51, 23, 59)(16, 52, 24, 60)(17, 53, 25, 61)(18, 54, 26, 62)(27, 63, 32, 68)(28, 64, 33, 69)(29, 65, 34, 70)(30, 66, 35, 71)(31, 67, 36, 72)(73, 109, 75, 111, 83, 119, 99, 135, 88, 124, 77, 113)(74, 110, 79, 115, 91, 127, 104, 140, 96, 132, 81, 117)(76, 112, 84, 120, 100, 136, 103, 139, 90, 126, 87, 123)(78, 114, 85, 121, 86, 122, 101, 137, 102, 138, 89, 125)(80, 116, 92, 128, 105, 141, 108, 144, 98, 134, 95, 131)(82, 118, 93, 129, 94, 130, 106, 142, 107, 143, 97, 133) L = (1, 76)(2, 80)(3, 84)(4, 86)(5, 87)(6, 73)(7, 92)(8, 94)(9, 95)(10, 74)(11, 100)(12, 101)(13, 75)(14, 83)(15, 85)(16, 90)(17, 77)(18, 78)(19, 105)(20, 106)(21, 79)(22, 91)(23, 93)(24, 98)(25, 81)(26, 82)(27, 103)(28, 102)(29, 99)(30, 88)(31, 89)(32, 108)(33, 107)(34, 104)(35, 96)(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) :: { ( 36^4 ), ( 36^12 ) } Outer automorphisms :: reflexible Dual of E23.222 Graph:: simple bipartite v = 24 e = 72 f = 4 degree seq :: [ 4^18, 12^6 ] E23.209 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 18, 18}) Quotient :: dipole Aut^+ = C18 x C2 (small group id <36, 5>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^3 * Y1, (Y3, Y2^-1), Y3^-1 * Y1 * Y3 * Y1, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y3 * Y2^-1 * Y3^4 * Y2^-1 * Y3, Y3^2 * Y2^2 * Y3^-2 * Y2 * Y1, (Y2^-1 * Y3)^18 ] Map:: non-degenerate R = (1, 37, 2, 38)(3, 39, 7, 43)(4, 40, 8, 44)(5, 41, 9, 45)(6, 42, 10, 46)(11, 47, 17, 53)(12, 48, 18, 54)(13, 49, 19, 55)(14, 50, 20, 56)(15, 51, 21, 57)(16, 52, 22, 58)(23, 59, 29, 65)(24, 60, 30, 66)(25, 61, 31, 67)(26, 62, 32, 68)(27, 63, 33, 69)(28, 64, 34, 70)(35, 71, 36, 72)(73, 109, 75, 111, 81, 117, 74, 110, 79, 115, 77, 113)(76, 112, 83, 119, 92, 128, 80, 116, 89, 125, 86, 122)(78, 114, 84, 120, 93, 129, 82, 118, 90, 126, 87, 123)(85, 121, 95, 131, 104, 140, 91, 127, 101, 137, 98, 134)(88, 124, 96, 132, 105, 141, 94, 130, 102, 138, 99, 135)(97, 133, 106, 142, 108, 144, 103, 139, 100, 136, 107, 143) 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, 106)(24, 84)(25, 105)(26, 107)(27, 87)(28, 88)(29, 100)(30, 90)(31, 99)(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) :: { ( 36^4 ), ( 36^12 ) } Outer automorphisms :: reflexible Dual of E23.224 Graph:: bipartite v = 24 e = 72 f = 4 degree seq :: [ 4^18, 12^6 ] E23.210 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 18, 18}) Quotient :: dipole Aut^+ = C18 x C2 (small group id <36, 5>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ R^2, Y3^3, Y1 * Y3^-1 * Y1, (R * Y2)^2, (R * Y3)^2, (Y2^-1, Y1^-1), (Y2, Y3), (Y3^-1 * Y1^-1)^2, (R * Y1)^2, Y2^-1 * Y1^-1 * Y2^2 * Y1 * Y2^-1, Y2^-6 * Y3^-1, (Y2^-1 * Y3)^18 ] Map:: non-degenerate R = (1, 37, 2, 38, 4, 40, 9, 45, 7, 43, 5, 41)(3, 39, 8, 44, 12, 48, 20, 56, 14, 50, 13, 49)(6, 42, 10, 46, 15, 51, 21, 57, 18, 54, 16, 52)(11, 47, 19, 55, 24, 60, 32, 68, 26, 62, 25, 61)(17, 53, 22, 58, 27, 63, 33, 69, 30, 66, 28, 64)(23, 59, 31, 67, 29, 65, 34, 70, 36, 72, 35, 71)(73, 109, 75, 111, 83, 119, 95, 131, 102, 138, 90, 126, 79, 115, 86, 122, 98, 134, 108, 144, 99, 135, 87, 123, 76, 112, 84, 120, 96, 132, 101, 137, 89, 125, 78, 114)(74, 110, 80, 116, 91, 127, 103, 139, 100, 136, 88, 124, 77, 113, 85, 121, 97, 133, 107, 143, 105, 141, 93, 129, 81, 117, 92, 128, 104, 140, 106, 142, 94, 130, 82, 118) L = (1, 76)(2, 81)(3, 84)(4, 79)(5, 74)(6, 87)(7, 73)(8, 92)(9, 77)(10, 93)(11, 96)(12, 86)(13, 80)(14, 75)(15, 90)(16, 82)(17, 99)(18, 78)(19, 104)(20, 85)(21, 88)(22, 105)(23, 101)(24, 98)(25, 91)(26, 83)(27, 102)(28, 94)(29, 108)(30, 89)(31, 106)(32, 97)(33, 100)(34, 107)(35, 103)(36, 95)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 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 E23.216 Graph:: bipartite v = 8 e = 72 f = 20 degree seq :: [ 12^6, 36^2 ] E23.211 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 18, 18}) Quotient :: dipole Aut^+ = C18 x C2 (small group id <36, 5>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3 * Y1^-1, Y3^3, Y1 * Y3^-1 * Y1, (R * Y2)^2, (R * Y3)^2, (Y2^-1, Y1^-1), (Y3^-1 * Y1^-1)^2, (Y2, Y3), (R * Y1)^2, Y2^6 * Y3^-1, (Y2^-1 * Y3)^18 ] Map:: non-degenerate R = (1, 37, 2, 38, 4, 40, 9, 45, 7, 43, 5, 41)(3, 39, 8, 44, 12, 48, 20, 56, 14, 50, 13, 49)(6, 42, 10, 46, 15, 51, 21, 57, 18, 54, 16, 52)(11, 47, 19, 55, 24, 60, 32, 68, 26, 62, 25, 61)(17, 53, 22, 58, 27, 63, 33, 69, 30, 66, 28, 64)(23, 59, 31, 67, 35, 71, 36, 72, 29, 65, 34, 70)(73, 109, 75, 111, 83, 119, 95, 131, 99, 135, 87, 123, 76, 112, 84, 120, 96, 132, 107, 143, 102, 138, 90, 126, 79, 115, 86, 122, 98, 134, 101, 137, 89, 125, 78, 114)(74, 110, 80, 116, 91, 127, 103, 139, 105, 141, 93, 129, 81, 117, 92, 128, 104, 140, 108, 144, 100, 136, 88, 124, 77, 113, 85, 121, 97, 133, 106, 142, 94, 130, 82, 118) L = (1, 76)(2, 81)(3, 84)(4, 79)(5, 74)(6, 87)(7, 73)(8, 92)(9, 77)(10, 93)(11, 96)(12, 86)(13, 80)(14, 75)(15, 90)(16, 82)(17, 99)(18, 78)(19, 104)(20, 85)(21, 88)(22, 105)(23, 107)(24, 98)(25, 91)(26, 83)(27, 102)(28, 94)(29, 95)(30, 89)(31, 108)(32, 97)(33, 100)(34, 103)(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) :: { ( 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 E23.217 Graph:: bipartite v = 8 e = 72 f = 20 degree seq :: [ 12^6, 36^2 ] E23.212 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 18, 18}) Quotient :: dipole Aut^+ = C18 x C2 (small group id <36, 5>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ R^2, Y3^2 * Y1^2, Y2^-3 * Y1^-1, (Y1, Y2^-1), (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y2), (Y1^-1 * Y3^-1)^2, (Y3, Y1), (R * Y2)^2, Y3^3 * Y1^-1 * Y3 * Y1^-1, Y1^6, Y2 * Y3 * Y2 * Y3 * Y2 * Y1^-3, (Y1^-1 * Y2)^9 ] Map:: non-degenerate R = (1, 37, 2, 38, 8, 44, 21, 57, 17, 53, 5, 41)(3, 39, 9, 45, 22, 58, 33, 69, 31, 67, 15, 51)(4, 40, 10, 46, 7, 43, 12, 48, 24, 60, 18, 54)(6, 42, 11, 47, 23, 59, 34, 70, 30, 66, 13, 49)(14, 50, 25, 61, 16, 52, 26, 62, 35, 71, 32, 68)(19, 55, 27, 63, 20, 56, 28, 64, 36, 72, 29, 65)(73, 109, 75, 111, 85, 121, 77, 113, 87, 123, 102, 138, 89, 125, 103, 139, 106, 142, 93, 129, 105, 141, 95, 131, 80, 116, 94, 130, 83, 119, 74, 110, 81, 117, 78, 114)(76, 112, 86, 122, 101, 137, 90, 126, 104, 140, 108, 144, 96, 132, 107, 143, 100, 136, 84, 120, 98, 134, 92, 128, 79, 115, 88, 124, 99, 135, 82, 118, 97, 133, 91, 127) L = (1, 76)(2, 82)(3, 86)(4, 89)(5, 90)(6, 91)(7, 73)(8, 79)(9, 97)(10, 77)(11, 99)(12, 74)(13, 101)(14, 103)(15, 104)(16, 75)(17, 96)(18, 93)(19, 102)(20, 78)(21, 84)(22, 88)(23, 92)(24, 80)(25, 87)(26, 81)(27, 85)(28, 83)(29, 106)(30, 108)(31, 107)(32, 105)(33, 98)(34, 100)(35, 94)(36, 95)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 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 E23.218 Graph:: bipartite v = 8 e = 72 f = 20 degree seq :: [ 12^6, 36^2 ] E23.213 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 18, 18}) Quotient :: dipole Aut^+ = C18 x C2 (small group id <36, 5>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-2 * Y1^-1, (Y3 * Y1)^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y1^-1), (Y2^-1, Y1), (Y3^-1, Y2^-1), (R * Y2)^2, Y1^-1 * Y2^2 * Y3 * Y2, Y1^-1 * Y3 * Y2^3, Y1 * Y3^-4 * Y1, Y1 * Y3^-1 * Y1 * Y3^-1 * Y1^2, Y2 * Y3^-1 * Y2^2 * Y3^-2 * Y1, (Y1 * Y3^-1 * Y2)^9 ] Map:: non-degenerate R = (1, 37, 2, 38, 8, 44, 23, 59, 17, 53, 5, 41)(3, 39, 9, 45, 24, 60, 35, 71, 32, 68, 15, 51)(4, 40, 10, 46, 7, 43, 12, 48, 26, 62, 18, 54)(6, 42, 11, 47, 25, 61, 31, 67, 33, 69, 20, 56)(13, 49, 27, 63, 34, 70, 19, 55, 30, 66, 22, 58)(14, 50, 28, 64, 16, 52, 29, 65, 36, 72, 21, 57)(73, 109, 75, 111, 85, 121, 84, 120, 101, 137, 105, 141, 89, 125, 104, 140, 102, 138, 82, 118, 100, 136, 97, 133, 80, 116, 96, 132, 106, 142, 90, 126, 93, 129, 78, 114)(74, 110, 81, 117, 99, 135, 98, 134, 108, 144, 92, 128, 77, 113, 87, 123, 94, 130, 79, 115, 88, 124, 103, 139, 95, 131, 107, 143, 91, 127, 76, 112, 86, 122, 83, 119) L = (1, 76)(2, 82)(3, 86)(4, 89)(5, 90)(6, 91)(7, 73)(8, 79)(9, 100)(10, 77)(11, 102)(12, 74)(13, 83)(14, 104)(15, 93)(16, 75)(17, 98)(18, 95)(19, 105)(20, 106)(21, 107)(22, 78)(23, 84)(24, 88)(25, 94)(26, 80)(27, 97)(28, 87)(29, 81)(30, 92)(31, 85)(32, 108)(33, 99)(34, 103)(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, 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 E23.220 Graph:: bipartite v = 8 e = 72 f = 20 degree seq :: [ 12^6, 36^2 ] E23.214 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 18, 18}) Quotient :: dipole Aut^+ = C18 x C2 (small group id <36, 5>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ R^2, (Y3^-1, Y1^-1), Y1^-2 * Y3^-2, Y2^2 * Y1^-1 * Y2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, (Y2, Y3), (Y2^-1, Y1^-1), Y1^-2 * Y3^2 * Y1^-2, Y3^-1 * Y2^-1 * Y3^-1 * Y2^-2 * Y1^-1, (Y2^-1 * Y3)^18 ] Map:: non-degenerate R = (1, 37, 2, 38, 8, 44, 21, 57, 16, 52, 5, 41)(3, 39, 9, 45, 22, 58, 33, 69, 29, 65, 14, 50)(4, 40, 10, 46, 7, 43, 12, 48, 24, 60, 17, 53)(6, 42, 11, 47, 23, 59, 34, 70, 31, 67, 19, 55)(13, 49, 25, 61, 15, 51, 26, 62, 35, 71, 30, 66)(18, 54, 27, 63, 20, 56, 28, 64, 36, 72, 32, 68)(73, 109, 75, 111, 83, 119, 74, 110, 81, 117, 95, 131, 80, 116, 94, 130, 106, 142, 93, 129, 105, 141, 103, 139, 88, 124, 101, 137, 91, 127, 77, 113, 86, 122, 78, 114)(76, 112, 85, 121, 99, 135, 82, 118, 97, 133, 92, 128, 79, 115, 87, 123, 100, 136, 84, 120, 98, 134, 108, 144, 96, 132, 107, 143, 104, 140, 89, 125, 102, 138, 90, 126) L = (1, 76)(2, 82)(3, 85)(4, 88)(5, 89)(6, 90)(7, 73)(8, 79)(9, 97)(10, 77)(11, 99)(12, 74)(13, 101)(14, 102)(15, 75)(16, 96)(17, 93)(18, 103)(19, 104)(20, 78)(21, 84)(22, 87)(23, 92)(24, 80)(25, 86)(26, 81)(27, 91)(28, 83)(29, 107)(30, 105)(31, 108)(32, 106)(33, 98)(34, 100)(35, 94)(36, 95)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 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 E23.219 Graph:: bipartite v = 8 e = 72 f = 20 degree seq :: [ 12^6, 36^2 ] E23.215 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 18, 18}) Quotient :: dipole Aut^+ = C18 x C2 (small group id <36, 5>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ R^2, (Y3^-1, Y1^-1), Y1^2 * Y3^2, (R * Y2)^2, (Y1^-1, Y2), (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y3), Y3^-1 * Y1 * Y2^3, Y3^-1 * Y1^-1 * Y2 * Y3^-1 * Y1^-1 * Y2^-1, Y3^6, Y1^6, Y3^-2 * Y2^-1 * Y1 * Y3^-1 * Y2^-2 ] Map:: non-degenerate R = (1, 37, 2, 38, 8, 44, 23, 59, 17, 53, 5, 41)(3, 39, 9, 45, 24, 60, 36, 72, 33, 69, 15, 51)(4, 40, 10, 46, 7, 43, 12, 48, 26, 62, 18, 54)(6, 42, 11, 47, 25, 61, 31, 67, 35, 71, 20, 56)(13, 49, 19, 55, 28, 64, 22, 58, 30, 66, 32, 68)(14, 50, 27, 63, 16, 52, 21, 57, 29, 65, 34, 70)(73, 109, 75, 111, 85, 121, 90, 126, 106, 142, 97, 133, 80, 116, 96, 132, 100, 136, 82, 118, 99, 135, 107, 143, 89, 125, 105, 141, 102, 138, 84, 120, 93, 129, 78, 114)(74, 110, 81, 117, 91, 127, 76, 112, 86, 122, 103, 139, 95, 131, 108, 144, 94, 130, 79, 115, 88, 124, 92, 128, 77, 113, 87, 123, 104, 140, 98, 134, 101, 137, 83, 119) L = (1, 76)(2, 82)(3, 86)(4, 89)(5, 90)(6, 91)(7, 73)(8, 79)(9, 99)(10, 77)(11, 100)(12, 74)(13, 103)(14, 105)(15, 106)(16, 75)(17, 98)(18, 95)(19, 107)(20, 85)(21, 81)(22, 78)(23, 84)(24, 88)(25, 94)(26, 80)(27, 87)(28, 92)(29, 96)(30, 83)(31, 102)(32, 97)(33, 101)(34, 108)(35, 104)(36, 93)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 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 E23.221 Graph:: bipartite v = 8 e = 72 f = 20 degree seq :: [ 12^6, 36^2 ] E23.216 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 18, 18}) Quotient :: dipole Aut^+ = C18 x C2 (small group id <36, 5>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^3, (R * Y3)^2, (Y3, Y1), (R * Y1)^2, Y2 * Y1 * Y2 * Y1^-1, Y3^-1 * Y2 * Y3 * Y2, (R * Y2)^2, Y3 * Y1^6, (Y1^-1 * Y3^-1)^18 ] Map:: non-degenerate R = (1, 37, 2, 38, 7, 43, 17, 53, 28, 64, 16, 52, 6, 42, 10, 46, 20, 56, 30, 66, 26, 62, 14, 50, 4, 40, 9, 45, 19, 55, 27, 63, 15, 51, 5, 41)(3, 39, 8, 44, 18, 54, 29, 65, 35, 71, 25, 61, 13, 49, 22, 58, 32, 68, 36, 72, 33, 69, 23, 59, 11, 47, 21, 57, 31, 67, 34, 70, 24, 60, 12, 48)(73, 109, 75, 111)(74, 110, 80, 116)(76, 112, 83, 119)(77, 113, 84, 120)(78, 114, 85, 121)(79, 115, 90, 126)(81, 117, 93, 129)(82, 118, 94, 130)(86, 122, 95, 131)(87, 123, 96, 132)(88, 124, 97, 133)(89, 125, 101, 137)(91, 127, 103, 139)(92, 128, 104, 140)(98, 134, 105, 141)(99, 135, 106, 142)(100, 136, 107, 143)(102, 138, 108, 144) L = (1, 76)(2, 81)(3, 83)(4, 78)(5, 86)(6, 73)(7, 91)(8, 93)(9, 82)(10, 74)(11, 85)(12, 95)(13, 75)(14, 88)(15, 98)(16, 77)(17, 99)(18, 103)(19, 92)(20, 79)(21, 94)(22, 80)(23, 97)(24, 105)(25, 84)(26, 100)(27, 102)(28, 87)(29, 106)(30, 89)(31, 104)(32, 90)(33, 107)(34, 108)(35, 96)(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, 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 E23.210 Graph:: bipartite v = 20 e = 72 f = 8 degree seq :: [ 4^18, 36^2 ] E23.217 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 18, 18}) Quotient :: dipole Aut^+ = C18 x C2 (small group id <36, 5>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^3, (R * Y3)^2, (R * Y1)^2, (Y1, Y3^-1), Y2 * Y1 * Y2 * Y1^-1, Y3^-1 * Y2 * Y3 * Y2, (R * Y2)^2, Y1^6 * Y3^-1, (Y1^-1 * Y3^-1)^18 ] Map:: non-degenerate R = (1, 37, 2, 38, 7, 43, 17, 53, 26, 62, 14, 50, 4, 40, 9, 45, 19, 55, 30, 66, 28, 64, 16, 52, 6, 42, 10, 46, 20, 56, 27, 63, 15, 51, 5, 41)(3, 39, 8, 44, 18, 54, 29, 65, 33, 69, 23, 59, 11, 47, 21, 57, 31, 67, 36, 72, 35, 71, 25, 61, 13, 49, 22, 58, 32, 68, 34, 70, 24, 60, 12, 48)(73, 109, 75, 111)(74, 110, 80, 116)(76, 112, 83, 119)(77, 113, 84, 120)(78, 114, 85, 121)(79, 115, 90, 126)(81, 117, 93, 129)(82, 118, 94, 130)(86, 122, 95, 131)(87, 123, 96, 132)(88, 124, 97, 133)(89, 125, 101, 137)(91, 127, 103, 139)(92, 128, 104, 140)(98, 134, 105, 141)(99, 135, 106, 142)(100, 136, 107, 143)(102, 138, 108, 144) L = (1, 76)(2, 81)(3, 83)(4, 78)(5, 86)(6, 73)(7, 91)(8, 93)(9, 82)(10, 74)(11, 85)(12, 95)(13, 75)(14, 88)(15, 98)(16, 77)(17, 102)(18, 103)(19, 92)(20, 79)(21, 94)(22, 80)(23, 97)(24, 105)(25, 84)(26, 100)(27, 89)(28, 87)(29, 108)(30, 99)(31, 104)(32, 90)(33, 107)(34, 101)(35, 96)(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) :: { ( 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 E23.211 Graph:: bipartite v = 20 e = 72 f = 8 degree seq :: [ 4^18, 36^2 ] E23.218 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 18, 18}) Quotient :: dipole Aut^+ = C18 x C2 (small group id <36, 5>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^-1 * Y2 * Y3 * Y2, Y2 * Y1 * Y2 * Y1^-1, (R * Y1)^2, (R * Y2)^2, (Y3, Y1), (R * Y3)^2, Y3^-1 * Y2 * Y3^-1 * Y1^-3, Y1^-1 * Y2 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1, Y3^6, Y1^6 * Y3^-2, Y3^-1 * Y2 * Y3^-2 * Y1 * Y3^-1 * Y1^2 ] Map:: non-degenerate R = (1, 37, 2, 38, 7, 43, 19, 55, 32, 68, 30, 66, 14, 50, 25, 61, 12, 48, 3, 39, 8, 44, 20, 56, 18, 54, 26, 62, 35, 71, 27, 63, 16, 52, 5, 41)(4, 40, 9, 45, 21, 57, 13, 49, 24, 60, 34, 70, 29, 65, 36, 72, 28, 64, 11, 47, 23, 59, 17, 53, 6, 42, 10, 46, 22, 58, 33, 69, 31, 67, 15, 51)(73, 109, 75, 111)(74, 110, 80, 116)(76, 112, 83, 119)(77, 113, 84, 120)(78, 114, 85, 121)(79, 115, 92, 128)(81, 117, 95, 131)(82, 118, 96, 132)(86, 122, 99, 135)(87, 123, 100, 136)(88, 124, 97, 133)(89, 125, 93, 129)(90, 126, 91, 127)(94, 130, 106, 142)(98, 134, 104, 140)(101, 137, 105, 141)(102, 138, 107, 143)(103, 139, 108, 144) L = (1, 76)(2, 81)(3, 83)(4, 86)(5, 87)(6, 73)(7, 93)(8, 95)(9, 97)(10, 74)(11, 99)(12, 100)(13, 75)(14, 101)(15, 102)(16, 103)(17, 77)(18, 78)(19, 85)(20, 89)(21, 84)(22, 79)(23, 88)(24, 80)(25, 108)(26, 82)(27, 105)(28, 107)(29, 90)(30, 106)(31, 104)(32, 96)(33, 91)(34, 92)(35, 94)(36, 98)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 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 E23.212 Graph:: bipartite v = 20 e = 72 f = 8 degree seq :: [ 4^18, 36^2 ] E23.219 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 18, 18}) Quotient :: dipole Aut^+ = C18 x C2 (small group id <36, 5>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y2 * Y1^-1 * Y2 * Y1, (Y3^-1, Y1), (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y3 * Y2 * Y3^-1 * Y2, Y1^-1 * Y2 * Y1^-1 * Y3^2 * Y1^-1, Y1^-1 * Y3^2 * Y2 * Y1^-2, Y3^6, Y1^6 * Y3^2, Y3^-2 * Y2 * Y1^-1 * Y3^-2 * Y1^-2, Y2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 37, 2, 38, 7, 43, 19, 55, 32, 68, 31, 67, 18, 54, 26, 62, 12, 48, 3, 39, 8, 44, 20, 56, 14, 50, 25, 61, 35, 71, 28, 64, 16, 52, 5, 41)(4, 40, 9, 45, 21, 57, 33, 69, 30, 66, 17, 53, 6, 42, 10, 46, 22, 58, 11, 47, 23, 59, 34, 70, 29, 65, 36, 72, 27, 63, 13, 49, 24, 60, 15, 51)(73, 109, 75, 111)(74, 110, 80, 116)(76, 112, 83, 119)(77, 113, 84, 120)(78, 114, 85, 121)(79, 115, 92, 128)(81, 117, 95, 131)(82, 118, 96, 132)(86, 122, 91, 127)(87, 123, 94, 130)(88, 124, 98, 134)(89, 125, 99, 135)(90, 126, 100, 136)(93, 129, 106, 142)(97, 133, 104, 140)(101, 137, 105, 141)(102, 138, 108, 144)(103, 139, 107, 143) L = (1, 76)(2, 81)(3, 83)(4, 86)(5, 87)(6, 73)(7, 93)(8, 95)(9, 97)(10, 74)(11, 91)(12, 94)(13, 75)(14, 101)(15, 92)(16, 96)(17, 77)(18, 78)(19, 105)(20, 106)(21, 107)(22, 79)(23, 104)(24, 80)(25, 108)(26, 82)(27, 84)(28, 85)(29, 90)(30, 88)(31, 89)(32, 102)(33, 100)(34, 103)(35, 99)(36, 98)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 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 E23.214 Graph:: bipartite v = 20 e = 72 f = 8 degree seq :: [ 4^18, 36^2 ] E23.220 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 18, 18}) Quotient :: dipole Aut^+ = C18 x C2 (small group id <36, 5>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ R^2, Y2^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y1), Y1^-1 * Y2 * Y1 * Y2, Y3 * Y2 * Y3^-1 * Y2, Y3^-1 * Y1^3 * Y2, Y1^-1 * Y3 * Y1^-2 * Y2, Y3^-6 ] Map:: non-degenerate R = (1, 37, 2, 38, 7, 43, 11, 47, 20, 56, 27, 63, 14, 50, 21, 57, 30, 66, 33, 69, 36, 72, 29, 65, 18, 54, 22, 58, 24, 60, 13, 49, 16, 52, 5, 41)(3, 39, 8, 44, 15, 51, 4, 40, 9, 45, 19, 55, 23, 59, 31, 67, 35, 71, 26, 62, 32, 68, 34, 70, 25, 61, 28, 64, 17, 53, 6, 42, 10, 46, 12, 48)(73, 109, 75, 111)(74, 110, 80, 116)(76, 112, 83, 119)(77, 113, 84, 120)(78, 114, 85, 121)(79, 115, 87, 123)(81, 117, 92, 128)(82, 118, 88, 124)(86, 122, 95, 131)(89, 125, 96, 132)(90, 126, 97, 133)(91, 127, 99, 135)(93, 129, 103, 139)(94, 130, 100, 136)(98, 134, 105, 141)(101, 137, 106, 142)(102, 138, 107, 143)(104, 140, 108, 144) L = (1, 76)(2, 81)(3, 83)(4, 86)(5, 87)(6, 73)(7, 91)(8, 92)(9, 93)(10, 74)(11, 95)(12, 79)(13, 75)(14, 98)(15, 99)(16, 80)(17, 77)(18, 78)(19, 102)(20, 103)(21, 104)(22, 82)(23, 105)(24, 84)(25, 85)(26, 90)(27, 107)(28, 88)(29, 89)(30, 106)(31, 108)(32, 94)(33, 97)(34, 96)(35, 101)(36, 100)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 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 E23.213 Graph:: bipartite v = 20 e = 72 f = 8 degree seq :: [ 4^18, 36^2 ] E23.221 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 18, 18}) Quotient :: dipole Aut^+ = C18 x C2 (small group id <36, 5>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ R^2, Y2^2, (R * Y2)^2, (R * Y3)^2, (Y1, Y3^-1), (R * Y1)^2, Y1^-1 * Y2 * Y1 * Y2, Y3 * Y2 * Y3^-1 * Y2, Y1^2 * Y3 * Y1 * Y2, Y3^6, Y3^-1 * Y2 * Y3^-1 * Y1 * Y2 * Y3^-1 * Y1 * Y2 * Y3^-1 * Y1 * Y2 * Y3^-1 * Y1 * Y2 * Y3^-1 * Y1 * Y2 * Y3^-1 * Y1 * Y2 * Y3^-1 * Y1 * Y2 * Y3^-2 * Y1^-1 ] Map:: non-degenerate R = (1, 37, 2, 38, 7, 43, 13, 49, 20, 56, 29, 65, 18, 54, 22, 58, 30, 66, 33, 69, 36, 72, 27, 63, 14, 50, 21, 57, 24, 60, 11, 47, 16, 52, 5, 41)(3, 39, 8, 44, 17, 53, 6, 42, 10, 46, 19, 55, 25, 61, 31, 67, 35, 71, 26, 62, 32, 68, 34, 70, 23, 59, 28, 64, 15, 51, 4, 40, 9, 45, 12, 48)(73, 109, 75, 111)(74, 110, 80, 116)(76, 112, 83, 119)(77, 113, 84, 120)(78, 114, 85, 121)(79, 115, 89, 125)(81, 117, 88, 124)(82, 118, 92, 128)(86, 122, 95, 131)(87, 123, 96, 132)(90, 126, 97, 133)(91, 127, 101, 137)(93, 129, 100, 136)(94, 130, 103, 139)(98, 134, 105, 141)(99, 135, 106, 142)(102, 138, 107, 143)(104, 140, 108, 144) L = (1, 76)(2, 81)(3, 83)(4, 86)(5, 87)(6, 73)(7, 84)(8, 88)(9, 93)(10, 74)(11, 95)(12, 96)(13, 75)(14, 98)(15, 99)(16, 100)(17, 77)(18, 78)(19, 79)(20, 80)(21, 104)(22, 82)(23, 105)(24, 106)(25, 85)(26, 90)(27, 107)(28, 108)(29, 89)(30, 91)(31, 92)(32, 94)(33, 97)(34, 102)(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) :: { ( 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 E23.215 Graph:: bipartite v = 20 e = 72 f = 8 degree seq :: [ 4^18, 36^2 ] E23.222 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 18, 18}) Quotient :: dipole Aut^+ = C18 x C2 (small group id <36, 5>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ R^2, Y1^-2 * Y3, Y2^-1 * Y3^2 * Y2^-1, (Y3^-1 * Y2)^2, (Y1^-1, Y2^-1), (R * Y3)^2, Y2^-2 * Y3^2, (R * Y1)^2, (R * Y2)^2, Y2^8 * Y3, Y3^9, (Y3^-1 * Y1^-1)^6 ] Map:: non-degenerate R = (1, 37, 2, 38, 4, 40, 9, 45, 11, 47, 19, 55, 22, 58, 28, 64, 29, 65, 35, 71, 33, 69, 32, 68, 26, 62, 23, 59, 17, 53, 16, 52, 7, 43, 5, 41)(3, 39, 8, 44, 12, 48, 20, 56, 21, 57, 27, 63, 30, 66, 36, 72, 34, 70, 31, 67, 25, 61, 24, 60, 18, 54, 15, 51, 6, 42, 10, 46, 14, 50, 13, 49)(73, 109, 75, 111, 83, 119, 93, 129, 101, 137, 106, 142, 98, 134, 90, 126, 79, 115, 86, 122, 76, 112, 84, 120, 94, 130, 102, 138, 105, 141, 97, 133, 89, 125, 78, 114)(74, 110, 80, 116, 91, 127, 99, 135, 107, 143, 103, 139, 95, 131, 87, 123, 77, 113, 85, 121, 81, 117, 92, 128, 100, 136, 108, 144, 104, 140, 96, 132, 88, 124, 82, 118) L = (1, 76)(2, 81)(3, 84)(4, 83)(5, 74)(6, 86)(7, 73)(8, 92)(9, 91)(10, 85)(11, 94)(12, 93)(13, 80)(14, 75)(15, 82)(16, 77)(17, 79)(18, 78)(19, 100)(20, 99)(21, 102)(22, 101)(23, 88)(24, 87)(25, 90)(26, 89)(27, 108)(28, 107)(29, 105)(30, 106)(31, 96)(32, 95)(33, 98)(34, 97)(35, 104)(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) :: { ( 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 E23.208 Graph:: bipartite v = 4 e = 72 f = 24 degree seq :: [ 36^4 ] E23.223 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 18, 18}) Quotient :: dipole Aut^+ = C18 x C2 (small group id <36, 5>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ R^2, (Y2^-1, Y3), (Y2 * Y3^-1)^2, Y3^2 * Y2^-2, (R * Y1)^2, (Y2^-1, Y1^-1), (Y3^-1, Y1^-1), (R * Y2)^2, (R * Y3)^2, Y1^3 * Y3 * Y1, Y3^2 * Y1^-1 * Y2^2 * Y1^-1, Y1^-1 * Y2 * Y3^2 * Y2 * Y1^-1 ] Map:: non-degenerate R = (1, 37, 2, 38, 8, 44, 20, 56, 7, 43, 12, 48, 25, 61, 35, 71, 21, 57, 29, 65, 13, 49, 26, 62, 33, 69, 17, 53, 4, 40, 10, 46, 18, 54, 5, 41)(3, 39, 9, 45, 23, 59, 32, 68, 16, 52, 28, 64, 34, 70, 19, 55, 6, 42, 11, 47, 24, 60, 36, 72, 22, 58, 30, 66, 14, 50, 27, 63, 31, 67, 15, 51)(73, 109, 75, 111, 85, 121, 96, 132, 80, 116, 95, 131, 105, 141, 94, 130, 79, 115, 88, 124, 76, 112, 86, 122, 97, 133, 106, 142, 90, 126, 103, 139, 93, 129, 78, 114)(74, 110, 81, 117, 98, 134, 108, 144, 92, 128, 104, 140, 89, 125, 102, 138, 84, 120, 100, 136, 82, 118, 99, 135, 107, 143, 91, 127, 77, 113, 87, 123, 101, 137, 83, 119) L = (1, 76)(2, 82)(3, 86)(4, 85)(5, 89)(6, 88)(7, 73)(8, 90)(9, 99)(10, 98)(11, 100)(12, 74)(13, 97)(14, 96)(15, 102)(16, 75)(17, 101)(18, 105)(19, 104)(20, 77)(21, 79)(22, 78)(23, 103)(24, 106)(25, 80)(26, 107)(27, 108)(28, 81)(29, 84)(30, 83)(31, 94)(32, 87)(33, 93)(34, 95)(35, 92)(36, 91)(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, 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 E23.207 Graph:: bipartite v = 4 e = 72 f = 24 degree seq :: [ 36^4 ] E23.224 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 18, 18}) Quotient :: dipole Aut^+ = C18 x C2 (small group id <36, 5>) Aut = C2 x C2 x D18 (small group id <72, 17>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-2 * Y2, (Y2^-1, Y1^-1), (Y2 * Y3^-1)^2, (R * Y3)^2, (Y3, Y1^-1), (R * Y1)^2, (R * Y2)^2, Y2^-1 * Y1^-1 * Y2^-2 * Y1^-2, (Y1^2 * Y3^-1)^2, Y3^-1 * Y1^-3 * Y3^-1 * Y2^-1, Y3^2 * Y1^-4 ] Map:: non-degenerate R = (1, 37, 2, 38, 8, 44, 23, 59, 13, 49, 28, 64, 19, 55, 6, 42, 11, 47, 26, 62, 15, 51, 3, 39, 9, 45, 24, 60, 21, 57, 31, 67, 18, 54, 5, 41)(4, 40, 10, 46, 25, 61, 22, 58, 32, 68, 36, 72, 34, 70, 16, 52, 30, 66, 35, 71, 33, 69, 14, 50, 29, 65, 20, 56, 7, 43, 12, 48, 27, 63, 17, 53)(73, 109, 75, 111, 85, 121, 103, 139, 83, 119, 74, 110, 81, 117, 100, 136, 90, 126, 98, 134, 80, 116, 96, 132, 91, 127, 77, 113, 87, 123, 95, 131, 93, 129, 78, 114)(76, 112, 86, 122, 104, 140, 84, 120, 102, 138, 82, 118, 101, 137, 108, 144, 99, 135, 107, 143, 97, 133, 92, 128, 106, 142, 89, 125, 105, 141, 94, 130, 79, 115, 88, 124) L = (1, 76)(2, 82)(3, 86)(4, 85)(5, 89)(6, 88)(7, 73)(8, 97)(9, 101)(10, 100)(11, 102)(12, 74)(13, 104)(14, 103)(15, 105)(16, 75)(17, 95)(18, 99)(19, 106)(20, 77)(21, 79)(22, 78)(23, 94)(24, 92)(25, 91)(26, 107)(27, 80)(28, 108)(29, 90)(30, 81)(31, 84)(32, 83)(33, 93)(34, 87)(35, 96)(36, 98)(37, 109)(38, 110)(39, 111)(40, 112)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 121)(50, 122)(51, 123)(52, 124)(53, 125)(54, 126)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 141)(70, 142)(71, 143)(72, 144) local type(s) :: { ( 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 E23.209 Graph:: bipartite v = 4 e = 72 f = 24 degree seq :: [ 36^4 ] E23.225 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10, 20}) Quotient :: dipole Aut^+ = C5 x D8 (small group id <40, 10>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y2 * Y3 * Y2, Y3 * Y2^-1 * Y3^-1 * Y2^-1, (Y2^-1 * Y1)^2, Y2^4, (R * Y1)^2, R * Y2 * R * Y2^-1, (R * Y3)^2, Y2^-1 * Y3 * Y1 * Y2^-1 * Y3^-1 * Y1, Y3^-1 * Y1 * Y2^2 * Y3 * Y1, Y1 * Y3^-1 * Y1 * Y3 * Y2^-2, Y3 * Y2 * Y1 * Y3^4, (Y3^-2 * Y2^-2)^10 ] Map:: non-degenerate R = (1, 41, 2, 42)(3, 43, 9, 49)(4, 44, 14, 54)(5, 45, 7, 47)(6, 46, 18, 58)(8, 48, 23, 63)(10, 50, 27, 67)(11, 51, 20, 60)(12, 52, 21, 61)(13, 53, 22, 62)(15, 55, 24, 64)(16, 56, 25, 65)(17, 57, 26, 66)(19, 59, 28, 68)(29, 69, 36, 76)(30, 70, 33, 73)(31, 71, 39, 79)(32, 72, 37, 77)(34, 74, 38, 78)(35, 75, 40, 80)(81, 121, 83, 123, 91, 131, 85, 125)(82, 122, 87, 127, 100, 140, 89, 129)(84, 124, 95, 135, 103, 143, 92, 132)(86, 126, 97, 137, 107, 147, 93, 133)(88, 128, 104, 144, 94, 134, 101, 141)(90, 130, 106, 146, 98, 138, 102, 142)(96, 136, 109, 149, 119, 159, 112, 152)(99, 139, 110, 150, 120, 160, 114, 154)(105, 145, 117, 157, 111, 151, 116, 156)(108, 148, 118, 158, 115, 155, 113, 153) L = (1, 84)(2, 88)(3, 92)(4, 96)(5, 95)(6, 81)(7, 101)(8, 105)(9, 104)(10, 82)(11, 103)(12, 109)(13, 83)(14, 111)(15, 112)(16, 113)(17, 85)(18, 100)(19, 86)(20, 94)(21, 117)(22, 87)(23, 119)(24, 116)(25, 114)(26, 89)(27, 91)(28, 90)(29, 115)(30, 93)(31, 110)(32, 108)(33, 106)(34, 97)(35, 98)(36, 99)(37, 120)(38, 102)(39, 118)(40, 107)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 20, 40, 20, 40 ), ( 20, 40, 20, 40, 20, 40, 20, 40 ) } Outer automorphisms :: reflexible Dual of E23.239 Graph:: simple bipartite v = 30 e = 80 f = 6 degree seq :: [ 4^20, 8^10 ] E23.226 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10, 20}) Quotient :: dipole Aut^+ = C5 x D8 (small group id <40, 10>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y2 * Y1)^2, Y3 * Y2^-1 * Y3^-1 * Y2^-1, (R * Y1)^2, Y2^4, (R * Y3)^2, R * Y2 * R * Y2^-1, Y3^-1 * Y2 * Y1 * Y2^-1 * Y3 * Y1, Y3 * Y1 * Y2^2 * Y3^-1 * Y1, Y3^-2 * Y1 * Y3^2 * Y1, Y2^-1 * Y3^4 * Y1 * Y3, Y3^-1 * Y2^2 * Y3^-2 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ] Map:: non-degenerate R = (1, 41, 2, 42)(3, 43, 9, 49)(4, 44, 14, 54)(5, 45, 7, 47)(6, 46, 18, 58)(8, 48, 23, 63)(10, 50, 27, 67)(11, 51, 20, 60)(12, 52, 21, 61)(13, 53, 22, 62)(15, 55, 24, 64)(16, 56, 25, 65)(17, 57, 26, 66)(19, 59, 28, 68)(29, 69, 38, 78)(30, 70, 39, 79)(31, 71, 37, 77)(32, 72, 36, 76)(33, 73, 34, 74)(35, 75, 40, 80)(81, 121, 83, 123, 91, 131, 85, 125)(82, 122, 87, 127, 100, 140, 89, 129)(84, 124, 95, 135, 103, 143, 92, 132)(86, 126, 97, 137, 107, 147, 93, 133)(88, 128, 104, 144, 94, 134, 101, 141)(90, 130, 106, 146, 98, 138, 102, 142)(96, 136, 109, 149, 117, 157, 112, 152)(99, 139, 110, 150, 120, 160, 114, 154)(105, 145, 116, 156, 111, 151, 118, 158)(108, 148, 113, 153, 115, 155, 119, 159) L = (1, 84)(2, 88)(3, 92)(4, 96)(5, 95)(6, 81)(7, 101)(8, 105)(9, 104)(10, 82)(11, 103)(12, 109)(13, 83)(14, 111)(15, 112)(16, 113)(17, 85)(18, 100)(19, 86)(20, 94)(21, 116)(22, 87)(23, 117)(24, 118)(25, 110)(26, 89)(27, 91)(28, 90)(29, 108)(30, 93)(31, 114)(32, 115)(33, 102)(34, 97)(35, 98)(36, 99)(37, 119)(38, 120)(39, 106)(40, 107)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 20, 40, 20, 40 ), ( 20, 40, 20, 40, 20, 40, 20, 40 ) } Outer automorphisms :: reflexible Dual of E23.240 Graph:: simple bipartite v = 30 e = 80 f = 6 degree seq :: [ 4^20, 8^10 ] E23.227 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10, 20}) Quotient :: dipole Aut^+ = C4 x D10 (small group id <40, 5>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ R^2, (Y3^-1 * Y1)^2, Y3^2 * Y1^2, (R * Y3)^2, (Y3^-1, Y1^-1), Y1 * Y2^-1 * Y1^-1 * Y2^-1, (R * Y1)^2, Y3^2 * Y1^-2, (Y2, Y3), (R * Y2)^2, (Y3 * Y2 * Y1^-1)^2, Y2^-1 * Y1 * Y2^2 * Y1 * Y2^-2, Y3 * Y2^2 * Y3 * Y2^3, Y2^2 * Y3^-1 * Y2^3 * Y3^-1, (Y2^-1 * Y3)^20 ] Map:: non-degenerate R = (1, 41, 2, 42, 8, 48, 5, 45)(3, 43, 11, 51, 21, 61, 15, 55)(4, 44, 10, 50, 7, 47, 12, 52)(6, 46, 9, 49, 22, 62, 18, 58)(13, 53, 27, 67, 35, 75, 31, 71)(14, 54, 26, 66, 16, 56, 28, 68)(17, 57, 24, 64, 20, 60, 25, 65)(19, 59, 23, 63, 29, 69, 34, 74)(30, 70, 39, 79, 32, 72, 40, 80)(33, 73, 37, 77, 36, 76, 38, 78)(81, 121, 83, 123, 93, 133, 109, 149, 102, 142, 88, 128, 101, 141, 115, 155, 99, 139, 86, 126)(82, 122, 89, 129, 103, 143, 111, 151, 95, 135, 85, 125, 98, 138, 114, 154, 107, 147, 91, 131)(84, 124, 94, 134, 110, 150, 116, 156, 100, 140, 87, 127, 96, 136, 112, 152, 113, 153, 97, 137)(90, 130, 104, 144, 117, 157, 120, 160, 108, 148, 92, 132, 105, 145, 118, 158, 119, 159, 106, 146) L = (1, 84)(2, 90)(3, 94)(4, 88)(5, 92)(6, 97)(7, 81)(8, 87)(9, 104)(10, 85)(11, 106)(12, 82)(13, 110)(14, 101)(15, 108)(16, 83)(17, 102)(18, 105)(19, 113)(20, 86)(21, 96)(22, 100)(23, 117)(24, 98)(25, 89)(26, 95)(27, 119)(28, 91)(29, 116)(30, 115)(31, 120)(32, 93)(33, 109)(34, 118)(35, 112)(36, 99)(37, 114)(38, 103)(39, 111)(40, 107)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 4, 40, 4, 40, 4, 40, 4, 40 ), ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ) } Outer automorphisms :: reflexible Dual of E23.235 Graph:: bipartite v = 14 e = 80 f = 22 degree seq :: [ 8^10, 20^4 ] E23.228 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10, 20}) Quotient :: dipole Aut^+ = C4 x D10 (small group id <40, 5>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ R^2, (Y2^-1, Y3^-1), (R * Y3)^2, (Y3^-1 * Y1)^2, Y2 * Y1 * Y2 * Y1^-1, Y1^4, (Y3^-1 * Y1^-1)^2, (R * Y2)^2, (R * Y1)^2, Y3^-2 * Y2^3, Y3^-1 * Y2^-2 * Y3^-1 * Y1^-2, Y1^-2 * Y3^2 * Y2^2, Y1^-2 * Y3 * Y1^2 * Y3^-1 ] Map:: non-degenerate R = (1, 41, 2, 42, 8, 48, 5, 45)(3, 43, 11, 51, 25, 65, 15, 55)(4, 44, 17, 57, 26, 66, 12, 52)(6, 46, 9, 49, 27, 67, 20, 60)(7, 47, 21, 61, 28, 68, 10, 50)(13, 53, 34, 74, 24, 64, 32, 72)(14, 54, 30, 70, 23, 63, 35, 75)(16, 56, 37, 77, 39, 79, 33, 73)(18, 58, 36, 76, 22, 62, 29, 69)(19, 59, 38, 78, 40, 80, 31, 71)(81, 121, 83, 123, 93, 133, 98, 138, 107, 147, 88, 128, 105, 145, 104, 144, 102, 142, 86, 126)(82, 122, 89, 129, 109, 149, 112, 152, 95, 135, 85, 125, 100, 140, 116, 156, 114, 154, 91, 131)(84, 124, 94, 134, 108, 148, 119, 159, 120, 160, 106, 146, 103, 143, 87, 127, 96, 136, 99, 139)(90, 130, 110, 150, 97, 137, 118, 158, 117, 157, 101, 141, 115, 155, 92, 132, 111, 151, 113, 153) L = (1, 84)(2, 90)(3, 94)(4, 98)(5, 101)(6, 99)(7, 81)(8, 106)(9, 110)(10, 112)(11, 113)(12, 82)(13, 108)(14, 107)(15, 117)(16, 83)(17, 85)(18, 119)(19, 93)(20, 115)(21, 114)(22, 96)(23, 86)(24, 87)(25, 103)(26, 102)(27, 120)(28, 88)(29, 97)(30, 95)(31, 89)(32, 118)(33, 109)(34, 111)(35, 91)(36, 92)(37, 116)(38, 100)(39, 105)(40, 104)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 4, 40, 4, 40, 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 E23.237 Graph:: bipartite v = 14 e = 80 f = 22 degree seq :: [ 8^10, 20^4 ] E23.229 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10, 20}) Quotient :: dipole Aut^+ = C4 x D10 (small group id <40, 5>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-2, (Y1 * Y3)^2, Y1^-1 * Y2 * Y1 * Y2, (Y1 * Y3^-1)^2, Y1^4, Y1 * Y2^-1 * Y1^-1 * Y2^-1, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y1)^2, Y2^-1 * Y1 * Y2 * Y1 * Y2^-3, Y2^2 * Y3 * Y2^2 * Y1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 41, 2, 42, 8, 48, 5, 45)(3, 43, 11, 51, 21, 61, 15, 55)(4, 44, 16, 56, 22, 62, 12, 52)(6, 46, 9, 49, 23, 63, 17, 57)(7, 47, 18, 58, 24, 64, 10, 50)(13, 53, 27, 67, 35, 75, 31, 71)(14, 54, 32, 72, 37, 77, 28, 68)(19, 59, 25, 65, 29, 69, 33, 73)(20, 60, 34, 74, 38, 78, 26, 66)(30, 70, 39, 79, 36, 76, 40, 80)(81, 121, 83, 123, 93, 133, 109, 149, 103, 143, 88, 128, 101, 141, 115, 155, 99, 139, 86, 126)(82, 122, 89, 129, 105, 145, 111, 151, 95, 135, 85, 125, 97, 137, 113, 153, 107, 147, 91, 131)(84, 124, 94, 134, 110, 150, 118, 158, 104, 144, 102, 142, 117, 157, 116, 156, 100, 140, 87, 127)(90, 130, 106, 146, 119, 159, 112, 152, 96, 136, 98, 138, 114, 154, 120, 160, 108, 148, 92, 132) L = (1, 84)(2, 90)(3, 94)(4, 83)(5, 98)(6, 87)(7, 81)(8, 102)(9, 106)(10, 89)(11, 92)(12, 82)(13, 110)(14, 93)(15, 96)(16, 85)(17, 114)(18, 97)(19, 100)(20, 86)(21, 117)(22, 101)(23, 104)(24, 88)(25, 119)(26, 105)(27, 108)(28, 91)(29, 118)(30, 109)(31, 112)(32, 95)(33, 120)(34, 113)(35, 116)(36, 99)(37, 115)(38, 103)(39, 111)(40, 107)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 4, 40, 4, 40, 4, 40, 4, 40 ), ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ) } Outer automorphisms :: reflexible Dual of E23.236 Graph:: bipartite v = 14 e = 80 f = 22 degree seq :: [ 8^10, 20^4 ] E23.230 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10, 20}) Quotient :: dipole Aut^+ = C4 x D10 (small group id <40, 5>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2 * Y3, (Y1^-1 * Y3^-1)^2, Y1 * Y2^-1 * Y1^-1 * Y2^-1, (R * Y1)^2, (R * Y3)^2, Y1^4, (Y3 * Y1)^2, (Y3 * Y1^-1)^2, (R * Y2^-1)^2, Y3^-1 * Y2 * Y3^-1 * Y2^-2, (Y3^-1 * Y2 * Y1)^2, Y2 * Y1^-1 * Y2^-4 * Y1^-1, Y1 * Y2^-1 * Y1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-2 ] Map:: non-degenerate R = (1, 41, 2, 42, 8, 48, 5, 45)(3, 43, 11, 51, 21, 61, 14, 54)(4, 44, 16, 56, 22, 62, 12, 52)(6, 46, 9, 49, 23, 63, 18, 58)(7, 47, 19, 59, 24, 64, 10, 50)(13, 53, 28, 68, 36, 76, 30, 70)(15, 55, 32, 72, 37, 77, 27, 67)(17, 57, 33, 73, 38, 78, 26, 66)(20, 60, 25, 65, 29, 69, 35, 75)(31, 71, 39, 79, 34, 74, 40, 80)(81, 121, 83, 123, 93, 133, 109, 149, 103, 143, 88, 128, 101, 141, 116, 156, 100, 140, 86, 126)(82, 122, 89, 129, 105, 145, 110, 150, 94, 134, 85, 125, 98, 138, 115, 155, 108, 148, 91, 131)(84, 124, 87, 127, 95, 135, 111, 151, 118, 158, 102, 142, 104, 144, 117, 157, 114, 154, 97, 137)(90, 130, 92, 132, 106, 146, 119, 159, 112, 152, 99, 139, 96, 136, 113, 153, 120, 160, 107, 147) L = (1, 84)(2, 90)(3, 87)(4, 86)(5, 99)(6, 97)(7, 81)(8, 102)(9, 92)(10, 91)(11, 107)(12, 82)(13, 95)(14, 112)(15, 83)(16, 85)(17, 100)(18, 96)(19, 94)(20, 114)(21, 104)(22, 103)(23, 118)(24, 88)(25, 106)(26, 89)(27, 108)(28, 120)(29, 111)(30, 119)(31, 93)(32, 110)(33, 98)(34, 116)(35, 113)(36, 117)(37, 101)(38, 109)(39, 105)(40, 115)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 4, 40, 4, 40, 4, 40, 4, 40 ), ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ) } Outer automorphisms :: reflexible Dual of E23.238 Graph:: bipartite v = 14 e = 80 f = 22 degree seq :: [ 8^10, 20^4 ] E23.231 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10, 20}) Quotient :: dipole Aut^+ = C5 x D8 (small group id <40, 10>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1^4, Y2^-1 * Y1^-1 * Y2 * Y1^-1, (Y3 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, Y1^-1 * Y2 * Y3 * Y2^-1 * Y3 * Y1^-1, (R * Y1 * Y2)^2, Y3 * Y2 * Y1^2 * Y3 * Y2^-1, (R * Y2 * Y3)^2, Y1^-1 * Y2^-1 * Y1^2 * Y2 * Y1^-1, Y2 * Y1^-1 * Y2^3 * Y3 * Y2, (Y2^-1 * Y1^2 * Y2^-1)^10 ] Map:: non-degenerate R = (1, 41, 2, 42, 7, 47, 5, 45)(3, 43, 11, 51, 20, 60, 8, 48)(4, 44, 14, 54, 21, 61, 9, 49)(6, 46, 17, 57, 22, 62, 10, 50)(12, 52, 23, 63, 37, 77, 29, 69)(13, 53, 24, 64, 15, 55, 25, 65)(16, 56, 26, 66, 18, 58, 27, 67)(19, 59, 28, 68, 38, 78, 34, 74)(30, 70, 33, 73, 40, 80, 35, 75)(31, 71, 39, 79, 32, 72, 36, 76)(81, 121, 83, 123, 92, 132, 110, 150, 106, 146, 89, 129, 105, 145, 116, 156, 99, 139, 86, 126)(82, 122, 88, 128, 103, 143, 115, 155, 98, 138, 101, 141, 93, 133, 112, 152, 108, 148, 90, 130)(84, 124, 95, 135, 111, 151, 114, 154, 97, 137, 85, 125, 91, 131, 109, 149, 113, 153, 96, 136)(87, 127, 100, 140, 117, 157, 120, 160, 107, 147, 94, 134, 104, 144, 119, 159, 118, 158, 102, 142) L = (1, 84)(2, 89)(3, 93)(4, 81)(5, 94)(6, 98)(7, 101)(8, 104)(9, 82)(10, 107)(11, 105)(12, 111)(13, 83)(14, 85)(15, 100)(16, 102)(17, 106)(18, 86)(19, 113)(20, 95)(21, 87)(22, 96)(23, 116)(24, 88)(25, 91)(26, 97)(27, 90)(28, 110)(29, 119)(30, 108)(31, 92)(32, 117)(33, 99)(34, 120)(35, 118)(36, 103)(37, 112)(38, 115)(39, 109)(40, 114)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 4, 40, 4, 40, 4, 40, 4, 40 ), ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ) } Outer automorphisms :: reflexible Dual of E23.233 Graph:: bipartite v = 14 e = 80 f = 22 degree seq :: [ 8^10, 20^4 ] E23.232 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10, 20}) Quotient :: dipole Aut^+ = C5 x D8 (small group id <40, 10>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ R^2, Y3^2, (Y1 * Y3)^2, Y1^4, Y2 * Y1^-1 * Y2^-1 * Y1^-1, (R * Y3)^2, (R * Y1)^2, Y3 * Y1^-1 * Y2 * Y3 * Y2^-1 * Y1, Y3 * Y2 * Y1 * Y3 * Y1^-1 * Y2^-1, (R * Y2 * Y3)^2, Y2 * Y1^-1 * Y2^4 * Y3, (Y3 * Y2^-1)^20 ] Map:: non-degenerate R = (1, 41, 2, 42, 7, 47, 5, 45)(3, 43, 11, 51, 20, 60, 8, 48)(4, 44, 14, 54, 21, 61, 9, 49)(6, 46, 17, 57, 22, 62, 10, 50)(12, 52, 23, 63, 37, 77, 29, 69)(13, 53, 24, 64, 15, 55, 25, 65)(16, 56, 26, 66, 18, 58, 27, 67)(19, 59, 28, 68, 38, 78, 34, 74)(30, 70, 35, 75, 40, 80, 33, 73)(31, 71, 36, 76, 32, 72, 39, 79)(81, 121, 83, 123, 92, 132, 110, 150, 107, 147, 94, 134, 104, 144, 116, 156, 99, 139, 86, 126)(82, 122, 88, 128, 103, 143, 113, 153, 96, 136, 84, 124, 95, 135, 111, 151, 108, 148, 90, 130)(85, 125, 91, 131, 109, 149, 115, 155, 98, 138, 101, 141, 93, 133, 112, 152, 114, 154, 97, 137)(87, 127, 100, 140, 117, 157, 120, 160, 106, 146, 89, 129, 105, 145, 119, 159, 118, 158, 102, 142) L = (1, 84)(2, 89)(3, 93)(4, 81)(5, 94)(6, 98)(7, 101)(8, 104)(9, 82)(10, 107)(11, 105)(12, 111)(13, 83)(14, 85)(15, 100)(16, 102)(17, 106)(18, 86)(19, 113)(20, 95)(21, 87)(22, 96)(23, 119)(24, 88)(25, 91)(26, 97)(27, 90)(28, 120)(29, 116)(30, 114)(31, 92)(32, 117)(33, 99)(34, 110)(35, 118)(36, 109)(37, 112)(38, 115)(39, 103)(40, 108)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 4, 40, 4, 40, 4, 40, 4, 40 ), ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ) } Outer automorphisms :: reflexible Dual of E23.234 Graph:: bipartite v = 14 e = 80 f = 22 degree seq :: [ 8^10, 20^4 ] E23.233 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10, 20}) Quotient :: dipole Aut^+ = C5 x D8 (small group id <40, 10>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y2 * Y1^2 * Y2 * Y1^-1, (R * Y2 * Y3)^2, Y3 * Y1^-1 * Y3 * Y2 * Y1 * Y2, Y2 * Y3 * Y2 * Y1 * Y3 * Y1^-1, Y3 * Y1 * Y2 * Y1^-1 * Y3 * Y2, (Y1^-1 * R * Y2)^2, Y3 * Y1^2 * Y3 * Y1^-2, Y2 * Y1 * Y3 * Y2 * Y3 * Y1^-1, Y3 * Y1^2 * Y2 * Y1^3, (Y1^-1 * Y2 * Y1 * Y2)^2, (Y2 * Y1^-1)^10 ] Map:: non-degenerate R = (1, 41, 2, 42, 6, 46, 18, 58, 28, 68, 10, 50, 22, 62, 36, 76, 39, 79, 29, 69, 38, 78, 27, 67, 37, 77, 40, 80, 30, 70, 13, 53, 25, 65, 35, 75, 17, 57, 5, 45)(3, 43, 9, 49, 19, 59, 32, 72, 14, 54, 4, 44, 12, 52, 20, 60, 33, 73, 15, 55, 23, 63, 7, 47, 21, 61, 34, 74, 16, 56, 26, 66, 8, 48, 24, 64, 31, 71, 11, 51)(81, 121, 83, 123)(82, 122, 87, 127)(84, 124, 93, 133)(85, 125, 95, 135)(86, 126, 99, 139)(88, 128, 105, 145)(89, 129, 107, 147)(90, 130, 106, 146)(91, 131, 109, 149)(92, 132, 102, 142)(94, 134, 108, 148)(96, 136, 110, 150)(97, 137, 111, 151)(98, 138, 114, 154)(100, 140, 115, 155)(101, 141, 117, 157)(103, 143, 118, 158)(104, 144, 116, 156)(112, 152, 120, 160)(113, 153, 119, 159) L = (1, 84)(2, 88)(3, 90)(4, 81)(5, 96)(6, 100)(7, 102)(8, 82)(9, 105)(10, 83)(11, 110)(12, 107)(13, 103)(14, 109)(15, 108)(16, 85)(17, 112)(18, 111)(19, 116)(20, 86)(21, 115)(22, 87)(23, 93)(24, 117)(25, 89)(26, 118)(27, 92)(28, 95)(29, 94)(30, 91)(31, 98)(32, 97)(33, 120)(34, 119)(35, 101)(36, 99)(37, 104)(38, 106)(39, 114)(40, 113)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 8, 20, 8, 20 ), ( 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20 ) } Outer automorphisms :: reflexible Dual of E23.231 Graph:: bipartite v = 22 e = 80 f = 14 degree seq :: [ 4^20, 40^2 ] E23.234 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10, 20}) Quotient :: dipole Aut^+ = C5 x D8 (small group id <40, 10>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (R * Y3)^2, (R * Y1)^2, (Y1^-1 * R * Y2)^2, Y3 * Y2 * Y1 * Y2 * Y3 * Y1^-1, Y3 * Y1 * Y2 * Y3 * Y2 * Y1^-1, Y2 * Y3 * Y1 * Y2 * Y1^-1 * Y3, (R * Y2 * Y3)^2, Y2 * Y3 * Y2 * Y1 * Y3 * Y1^-1, Y1^2 * Y2 * Y1^-2 * Y2, Y2 * Y1^4 * Y3 * Y1, Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1 * Y2 * Y1 ] Map:: non-degenerate R = (1, 41, 2, 42, 6, 46, 18, 58, 30, 70, 13, 53, 25, 65, 36, 76, 40, 80, 29, 69, 38, 78, 27, 67, 37, 77, 39, 79, 28, 68, 10, 50, 22, 62, 35, 75, 17, 57, 5, 45)(3, 43, 9, 49, 19, 59, 34, 74, 16, 56, 26, 66, 8, 48, 24, 64, 33, 73, 15, 55, 23, 63, 7, 47, 21, 61, 32, 72, 14, 54, 4, 44, 12, 52, 20, 60, 31, 71, 11, 51)(81, 121, 83, 123)(82, 122, 87, 127)(84, 124, 93, 133)(85, 125, 95, 135)(86, 126, 99, 139)(88, 128, 105, 145)(89, 129, 107, 147)(90, 130, 106, 146)(91, 131, 109, 149)(92, 132, 102, 142)(94, 134, 108, 148)(96, 136, 110, 150)(97, 137, 111, 151)(98, 138, 112, 152)(100, 140, 116, 156)(101, 141, 117, 157)(103, 143, 118, 158)(104, 144, 115, 155)(113, 153, 120, 160)(114, 154, 119, 159) L = (1, 84)(2, 88)(3, 90)(4, 81)(5, 96)(6, 100)(7, 102)(8, 82)(9, 105)(10, 83)(11, 110)(12, 107)(13, 103)(14, 109)(15, 108)(16, 85)(17, 112)(18, 113)(19, 115)(20, 86)(21, 116)(22, 87)(23, 93)(24, 117)(25, 89)(26, 118)(27, 92)(28, 95)(29, 94)(30, 91)(31, 119)(32, 97)(33, 98)(34, 120)(35, 99)(36, 101)(37, 104)(38, 106)(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) :: { ( 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 E23.232 Graph:: bipartite v = 22 e = 80 f = 14 degree seq :: [ 4^20, 40^2 ] E23.235 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10, 20}) Quotient :: dipole Aut^+ = C4 x D10 (small group id <40, 5>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3^-1, Y1), Y2 * Y3^-1 * Y2 * Y3, (R * Y1)^2, Y3^4, (R * Y2)^2, (R * Y3)^2, Y2 * Y1 * Y3^-2 * Y2 * Y1, (Y2 * Y3^-1 * Y1^-1)^2, Y1^-5 * Y3, Y2 * Y1^-1 * Y3^-2 * Y2 * Y1^-1, Y2 * Y3 * Y1^2 * Y2 * Y3^-1 * Y1^2, Y2 * Y1 * Y2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 41, 2, 42, 7, 47, 20, 60, 16, 56, 4, 44, 9, 49, 22, 62, 36, 76, 30, 70, 15, 55, 28, 68, 40, 80, 34, 74, 19, 59, 6, 46, 10, 50, 23, 63, 18, 58, 5, 45)(3, 43, 11, 51, 29, 69, 37, 77, 27, 67, 12, 52, 31, 71, 35, 75, 26, 66, 8, 48, 24, 64, 17, 57, 33, 73, 39, 79, 25, 65, 14, 54, 32, 72, 38, 78, 21, 61, 13, 53)(81, 121, 83, 123)(82, 122, 88, 128)(84, 124, 92, 132)(85, 125, 97, 137)(86, 126, 94, 134)(87, 127, 101, 141)(89, 129, 105, 145)(90, 130, 107, 147)(91, 131, 110, 150)(93, 133, 108, 148)(95, 135, 104, 144)(96, 136, 112, 152)(98, 138, 109, 149)(99, 139, 111, 151)(100, 140, 115, 155)(102, 142, 117, 157)(103, 143, 119, 159)(106, 146, 120, 160)(113, 153, 116, 156)(114, 154, 118, 158) L = (1, 84)(2, 89)(3, 92)(4, 95)(5, 96)(6, 81)(7, 102)(8, 105)(9, 108)(10, 82)(11, 111)(12, 104)(13, 107)(14, 83)(15, 86)(16, 110)(17, 112)(18, 100)(19, 85)(20, 116)(21, 117)(22, 120)(23, 87)(24, 94)(25, 93)(26, 119)(27, 88)(28, 90)(29, 115)(30, 99)(31, 97)(32, 91)(33, 118)(34, 98)(35, 113)(36, 114)(37, 106)(38, 109)(39, 101)(40, 103)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 8, 20, 8, 20 ), ( 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20 ) } Outer automorphisms :: reflexible Dual of E23.227 Graph:: bipartite v = 22 e = 80 f = 14 degree seq :: [ 4^20, 40^2 ] E23.236 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10, 20}) Quotient :: dipole Aut^+ = C4 x D10 (small group id <40, 5>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y2 * Y1^2)^2, (Y2 * Y1^-1)^4, (Y3 * Y2)^4, Y1^-2 * Y2 * Y1 * Y2 * Y1^-7, (Y3^-1 * Y1^-1)^10 ] Map:: non-degenerate R = (1, 41, 2, 42, 5, 45, 11, 51, 20, 60, 29, 69, 37, 77, 34, 74, 26, 66, 16, 56, 23, 63, 17, 57, 24, 64, 32, 72, 40, 80, 36, 76, 28, 68, 19, 59, 10, 50, 4, 44)(3, 43, 7, 47, 15, 55, 25, 65, 33, 73, 38, 78, 31, 71, 21, 61, 14, 54, 6, 46, 13, 53, 9, 49, 18, 58, 27, 67, 35, 75, 39, 79, 30, 70, 22, 62, 12, 52, 8, 48)(81, 121, 83, 123)(82, 122, 86, 126)(84, 124, 89, 129)(85, 125, 92, 132)(87, 127, 96, 136)(88, 128, 97, 137)(90, 130, 95, 135)(91, 131, 101, 141)(93, 133, 103, 143)(94, 134, 104, 144)(98, 138, 106, 146)(99, 139, 107, 147)(100, 140, 110, 150)(102, 142, 112, 152)(105, 145, 114, 154)(108, 148, 113, 153)(109, 149, 118, 158)(111, 151, 120, 160)(115, 155, 117, 157)(116, 156, 119, 159) 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, 103)(17, 104)(18, 107)(19, 90)(20, 109)(21, 94)(22, 92)(23, 97)(24, 112)(25, 113)(26, 96)(27, 115)(28, 99)(29, 117)(30, 102)(31, 101)(32, 120)(33, 118)(34, 106)(35, 119)(36, 108)(37, 114)(38, 111)(39, 110)(40, 116)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 8, 20, 8, 20 ), ( 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20 ) } Outer automorphisms :: reflexible Dual of E23.229 Graph:: bipartite v = 22 e = 80 f = 14 degree seq :: [ 4^20, 40^2 ] E23.237 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10, 20}) Quotient :: dipole Aut^+ = C4 x D10 (small group id <40, 5>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y1^2 * Y3 * Y1, (Y3^-1, Y1^-1), (R * Y1)^2, (R * Y3)^2, (Y2 * Y3^-1 * Y1^-1)^2, Y3^-1 * Y1 * Y2 * Y3 * Y2 * Y3^-1, Y3^-1 * Y2 * Y1^2 * Y2 * Y1^-1, Y1^-1 * Y2 * Y3^-3 * Y2, R * Y2 * Y1^-1 * Y3 * R * Y2, (R * Y2 * Y3^-1)^2, (Y3 * Y2 * Y1^-1)^2, Y2 * R * Y1^-1 * Y3 * Y1^-1 * Y2 * R * Y1^-1 ] Map:: non-degenerate R = (1, 41, 2, 42, 7, 47, 6, 46, 10, 50, 22, 62, 20, 60, 30, 70, 38, 78, 31, 71, 39, 79, 35, 75, 40, 80, 33, 73, 16, 56, 28, 68, 17, 57, 4, 44, 9, 49, 5, 45)(3, 43, 11, 51, 27, 67, 14, 54, 32, 72, 37, 77, 24, 64, 19, 59, 25, 65, 8, 48, 23, 63, 18, 58, 26, 66, 15, 55, 34, 74, 36, 76, 29, 69, 12, 52, 21, 61, 13, 53)(81, 121, 83, 123)(82, 122, 88, 128)(84, 124, 95, 135)(85, 125, 98, 138)(86, 126, 99, 139)(87, 127, 101, 141)(89, 129, 107, 147)(90, 130, 109, 149)(91, 131, 111, 151)(92, 132, 113, 153)(93, 133, 115, 155)(94, 134, 110, 150)(96, 136, 104, 144)(97, 137, 112, 152)(100, 140, 114, 154)(102, 142, 117, 157)(103, 143, 119, 159)(105, 145, 120, 160)(106, 146, 118, 158)(108, 148, 116, 156) L = (1, 84)(2, 89)(3, 92)(4, 96)(5, 97)(6, 81)(7, 85)(8, 104)(9, 108)(10, 82)(11, 101)(12, 114)(13, 109)(14, 83)(15, 103)(16, 115)(17, 113)(18, 105)(19, 112)(20, 86)(21, 116)(22, 87)(23, 99)(24, 94)(25, 117)(26, 88)(27, 93)(28, 120)(29, 95)(30, 90)(31, 100)(32, 91)(33, 119)(34, 98)(35, 118)(36, 106)(37, 107)(38, 102)(39, 110)(40, 111)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 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 E23.228 Graph:: bipartite v = 22 e = 80 f = 14 degree seq :: [ 4^20, 40^2 ] E23.238 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10, 20}) Quotient :: dipole Aut^+ = C4 x D10 (small group id <40, 5>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3^-1, Y1^-1), (R * Y3)^2, (R * Y1)^2, Y3^-2 * Y1^-1 * Y3^-1, Y2 * Y1 * Y2 * Y3 * Y1^-2, (Y2 * Y3 * Y1^-1)^2, Y2 * Y3^-1 * Y2 * Y1^-3, Y3^2 * Y2 * Y3^-1 * Y1^-1 * Y2, (R * Y2 * Y3^-1)^2, (Y1^-1 * Y3^-1 * Y2)^2, Y2 * R * Y3 * Y1^-2 * R * Y2 * Y1^-1, Y2 * Y3 * Y2 * Y1^-1 * Y3 * Y1^-2 * Y3, (Y1^-1 * Y3^2)^4 ] Map:: non-degenerate R = (1, 41, 2, 42, 7, 47, 21, 61, 36, 76, 35, 75, 16, 56, 6, 46, 10, 50, 24, 64, 38, 78, 33, 73, 17, 57, 4, 44, 9, 49, 23, 63, 37, 77, 32, 72, 19, 59, 5, 45)(3, 43, 11, 51, 26, 66, 20, 60, 34, 74, 39, 79, 29, 69, 14, 54, 27, 67, 8, 48, 25, 65, 18, 58, 30, 70, 12, 52, 31, 71, 40, 80, 28, 68, 15, 55, 22, 62, 13, 53)(81, 121, 83, 123)(82, 122, 88, 128)(84, 124, 95, 135)(85, 125, 98, 138)(86, 126, 100, 140)(87, 127, 102, 142)(89, 129, 109, 149)(90, 130, 110, 150)(91, 131, 104, 144)(92, 132, 112, 152)(93, 133, 113, 153)(94, 134, 101, 141)(96, 136, 111, 151)(97, 137, 107, 147)(99, 139, 106, 146)(103, 143, 120, 160)(105, 145, 118, 158)(108, 148, 116, 156)(114, 154, 117, 157)(115, 155, 119, 159) L = (1, 84)(2, 89)(3, 92)(4, 96)(5, 97)(6, 81)(7, 103)(8, 106)(9, 86)(10, 82)(11, 111)(12, 109)(13, 110)(14, 83)(15, 105)(16, 85)(17, 115)(18, 114)(19, 113)(20, 108)(21, 117)(22, 98)(23, 90)(24, 87)(25, 100)(26, 120)(27, 91)(28, 88)(29, 93)(30, 119)(31, 94)(32, 118)(33, 116)(34, 95)(35, 99)(36, 112)(37, 104)(38, 101)(39, 102)(40, 107)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 8, 20, 8, 20 ), ( 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20 ) } Outer automorphisms :: reflexible Dual of E23.230 Graph:: bipartite v = 22 e = 80 f = 14 degree seq :: [ 4^20, 40^2 ] E23.239 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10, 20}) Quotient :: dipole Aut^+ = C5 x D8 (small group id <40, 10>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-2 * Y3^-1, (Y1^-1 * Y2^-1)^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, Y3^-1 * Y1 * Y2^-1 * Y1^2, Y3^-1 * Y1^3 * Y2^-1, Y2^2 * Y1^-1 * Y2 * Y3, Y2^-1 * Y1 * Y3^-1 * Y2^-2, Y2^-2 * Y3 * Y1 * Y3 * Y1^-1, (R * Y2 * Y3^-1)^2, Y3 * Y2^-2 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 41, 2, 42, 8, 48, 19, 59, 36, 76, 25, 65, 38, 78, 27, 67, 20, 60, 5, 45)(3, 43, 13, 53, 30, 70, 11, 51, 21, 61, 4, 44, 18, 58, 7, 47, 28, 68, 16, 56)(6, 46, 24, 64, 23, 63, 37, 77, 10, 50, 35, 75, 12, 52, 22, 62, 33, 73, 9, 49)(14, 54, 31, 71, 40, 80, 39, 79, 26, 66, 15, 55, 32, 72, 17, 57, 34, 74, 29, 69)(81, 121, 83, 123, 94, 134, 92, 132, 118, 158, 98, 138, 112, 152, 103, 143, 88, 128, 110, 150, 120, 160, 113, 153, 100, 140, 108, 148, 114, 154, 90, 130, 116, 156, 101, 141, 106, 146, 86, 126)(82, 122, 89, 129, 111, 151, 96, 136, 107, 147, 115, 155, 97, 137, 84, 124, 99, 139, 104, 144, 119, 159, 93, 133, 85, 125, 102, 142, 109, 149, 87, 127, 105, 145, 117, 157, 95, 135, 91, 131) L = (1, 84)(2, 90)(3, 95)(4, 100)(5, 103)(6, 105)(7, 81)(8, 87)(9, 112)(10, 85)(11, 118)(12, 82)(13, 116)(14, 104)(15, 108)(16, 88)(17, 83)(18, 111)(19, 92)(20, 91)(21, 109)(22, 106)(23, 107)(24, 114)(25, 113)(26, 115)(27, 86)(28, 119)(29, 110)(30, 97)(31, 101)(32, 102)(33, 99)(34, 89)(35, 120)(36, 96)(37, 94)(38, 93)(39, 98)(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, 4, 8, 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 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 E23.225 Graph:: bipartite v = 6 e = 80 f = 30 degree seq :: [ 20^4, 40^2 ] E23.240 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10, 20}) Quotient :: dipole Aut^+ = C5 x D8 (small group id <40, 10>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ R^2, (R * Y1)^2, Y3 * Y1^2 * Y3, (R * Y3)^2, (Y1^-1 * Y2^-1)^2, (Y3 * Y2^-1)^2, Y3^-2 * Y1 * Y3^-1 * Y2^-1, Y3^-1 * Y2^-1 * Y1 * Y3^-2, Y2 * Y3 * Y2 * Y1^-1 * Y2, Y2^2 * Y1^-1 * Y3 * Y2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2^2 * Y1 * Y3^-1 * Y1^-1, Y3 * Y2^-1 * Y1 * Y3 * Y2^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 41, 2, 42, 8, 48, 15, 55, 32, 72, 17, 57, 34, 74, 29, 69, 20, 60, 5, 45)(3, 43, 13, 53, 30, 70, 11, 51, 23, 63, 37, 77, 10, 50, 35, 75, 12, 52, 16, 56)(4, 44, 18, 58, 7, 47, 28, 68, 22, 62, 33, 73, 9, 49, 6, 46, 24, 64, 21, 61)(14, 54, 31, 71, 40, 80, 39, 79, 26, 66, 19, 59, 36, 76, 25, 65, 38, 78, 27, 67)(81, 121, 83, 123, 94, 134, 108, 148, 114, 154, 90, 130, 116, 156, 101, 141, 88, 128, 110, 150, 120, 160, 113, 153, 100, 140, 92, 132, 118, 158, 98, 138, 112, 152, 103, 143, 106, 146, 86, 126)(82, 122, 89, 129, 111, 151, 96, 136, 109, 149, 87, 127, 105, 145, 117, 157, 95, 135, 104, 144, 119, 159, 93, 133, 85, 125, 102, 142, 107, 147, 115, 155, 97, 137, 84, 124, 99, 139, 91, 131) L = (1, 84)(2, 90)(3, 95)(4, 100)(5, 103)(6, 105)(7, 81)(8, 87)(9, 112)(10, 85)(11, 118)(12, 82)(13, 116)(14, 91)(15, 92)(16, 106)(17, 83)(18, 111)(19, 108)(20, 104)(21, 107)(22, 88)(23, 109)(24, 114)(25, 113)(26, 115)(27, 86)(28, 119)(29, 110)(30, 97)(31, 101)(32, 102)(33, 99)(34, 89)(35, 120)(36, 96)(37, 94)(38, 93)(39, 98)(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, 4, 8, 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 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 E23.226 Graph:: bipartite v = 6 e = 80 f = 30 degree seq :: [ 20^4, 40^2 ] E23.241 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10, 20}) Quotient :: dipole Aut^+ = C4 x D10 (small group id <40, 5>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^-1 * Y3^-1 * Y2^-1 * Y3, Y3^4, R * Y2 * R * Y2^-1, (R * Y3)^2, (Y2 * Y1)^2, (R * Y1)^2, Y2^-1 * Y1 * Y3 * Y1 * Y3, Y2^-1 * Y3^-1 * Y2^3 * Y3^-1 * Y2^-1, Y2^-1 * Y3 * Y2 * Y1 * Y2^-2 * Y3^-1 * Y1 ] Map:: non-degenerate R = (1, 41, 2, 42)(3, 43, 9, 49)(4, 44, 14, 54)(5, 45, 7, 47)(6, 46, 19, 59)(8, 48, 13, 53)(10, 50, 12, 52)(11, 51, 23, 63)(15, 55, 29, 69)(16, 56, 22, 62)(17, 57, 20, 60)(18, 58, 35, 75)(21, 61, 27, 67)(24, 64, 26, 66)(25, 65, 39, 79)(28, 68, 38, 78)(30, 70, 32, 72)(31, 71, 37, 77)(33, 73, 36, 76)(34, 74, 40, 80)(81, 121, 83, 123, 91, 131, 105, 145, 112, 152, 96, 136, 108, 148, 113, 153, 97, 137, 85, 125)(82, 122, 87, 127, 100, 140, 116, 156, 118, 158, 102, 142, 110, 150, 119, 159, 103, 143, 89, 129)(84, 124, 95, 135, 111, 151, 107, 147, 93, 133, 86, 126, 98, 138, 114, 154, 106, 146, 92, 132)(88, 128, 101, 141, 117, 157, 109, 149, 94, 134, 90, 130, 104, 144, 120, 160, 115, 155, 99, 139) L = (1, 84)(2, 88)(3, 92)(4, 96)(5, 95)(6, 81)(7, 99)(8, 102)(9, 101)(10, 82)(11, 106)(12, 108)(13, 83)(14, 87)(15, 112)(16, 86)(17, 111)(18, 85)(19, 110)(20, 115)(21, 118)(22, 90)(23, 117)(24, 89)(25, 114)(26, 113)(27, 91)(28, 93)(29, 100)(30, 94)(31, 105)(32, 98)(33, 107)(34, 97)(35, 119)(36, 120)(37, 116)(38, 104)(39, 109)(40, 103)(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, 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 E23.246 Graph:: simple bipartite v = 24 e = 80 f = 12 degree seq :: [ 4^20, 20^4 ] E23.242 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10, 20}) Quotient :: dipole Aut^+ = C4 x D10 (small group id <40, 5>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3 * Y2^-1 * Y3^-1 * Y2^-1, (R * Y3)^2, (R * Y1)^2, R * Y2 * R * Y2^-1, (Y2 * Y1)^2, Y3^4, Y2 * Y1 * Y3^-1 * Y1 * Y3^-1, Y2 * Y3 * Y2^-2 * Y3 * Y2^2, Y3^-1 * Y2^-1 * Y1 * Y3 * Y2^-3 * Y1 ] Map:: non-degenerate R = (1, 41, 2, 42)(3, 43, 9, 49)(4, 44, 14, 54)(5, 45, 7, 47)(6, 46, 19, 59)(8, 48, 18, 58)(10, 50, 15, 55)(11, 51, 24, 64)(12, 52, 28, 68)(13, 53, 30, 70)(16, 56, 23, 63)(17, 57, 20, 60)(21, 61, 35, 75)(22, 62, 32, 72)(25, 65, 40, 80)(26, 66, 37, 77)(27, 67, 38, 78)(29, 69, 31, 71)(33, 73, 39, 79)(34, 74, 36, 76)(81, 121, 83, 123, 91, 131, 105, 145, 113, 153, 96, 136, 109, 149, 114, 154, 97, 137, 85, 125)(82, 122, 87, 127, 100, 140, 116, 156, 111, 151, 103, 143, 119, 159, 120, 160, 104, 144, 89, 129)(84, 124, 95, 135, 112, 152, 107, 147, 93, 133, 86, 126, 98, 138, 115, 155, 106, 146, 92, 132)(88, 128, 99, 139, 110, 150, 118, 158, 102, 142, 90, 130, 94, 134, 108, 148, 117, 157, 101, 141) L = (1, 84)(2, 88)(3, 92)(4, 96)(5, 95)(6, 81)(7, 101)(8, 103)(9, 99)(10, 82)(11, 106)(12, 109)(13, 83)(14, 89)(15, 113)(16, 86)(17, 112)(18, 85)(19, 111)(20, 117)(21, 119)(22, 87)(23, 90)(24, 110)(25, 115)(26, 114)(27, 91)(28, 104)(29, 93)(30, 116)(31, 94)(32, 105)(33, 98)(34, 107)(35, 97)(36, 108)(37, 120)(38, 100)(39, 102)(40, 118)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 8, 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 E23.247 Graph:: simple bipartite v = 24 e = 80 f = 12 degree seq :: [ 4^20, 20^4 ] E23.243 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10, 20}) Quotient :: dipole Aut^+ = C4 x D10 (small group id <40, 5>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y2^-1 * Y1)^2, Y2^-1 * Y3 * Y2^-1 * Y3^-1, (R * Y3)^2, (R * Y1)^2, Y3^4, R * Y2 * R * Y2^-1, Y3^-1 * Y1 * Y3^2 * Y1 * Y3^-1, Y2 * Y3 * Y2^-1 * Y1 * Y3^-1 * Y1, Y2 * Y3 * Y2^-2 * Y3 * Y2^2, Y2 * Y1 * Y3^-1 * Y2^2 * Y1 * Y3^-1, Y2^10 ] Map:: non-degenerate R = (1, 41, 2, 42)(3, 43, 9, 49)(4, 44, 14, 54)(5, 45, 7, 47)(6, 46, 19, 59)(8, 48, 23, 63)(10, 50, 28, 68)(11, 51, 26, 66)(12, 52, 21, 61)(13, 53, 22, 62)(15, 55, 32, 72)(16, 56, 25, 65)(17, 57, 20, 60)(18, 58, 37, 77)(24, 64, 36, 76)(27, 67, 33, 73)(29, 69, 31, 71)(30, 70, 40, 80)(34, 74, 39, 79)(35, 75, 38, 78)(81, 121, 83, 123, 91, 131, 109, 149, 114, 154, 96, 136, 110, 150, 115, 155, 97, 137, 85, 125)(82, 122, 87, 127, 100, 140, 118, 158, 120, 160, 105, 145, 119, 159, 111, 151, 106, 146, 89, 129)(84, 124, 95, 135, 113, 153, 108, 148, 93, 133, 86, 126, 98, 138, 116, 156, 103, 143, 92, 132)(88, 128, 104, 144, 117, 157, 99, 139, 102, 142, 90, 130, 107, 147, 112, 152, 94, 134, 101, 141) L = (1, 84)(2, 88)(3, 92)(4, 96)(5, 95)(6, 81)(7, 101)(8, 105)(9, 104)(10, 82)(11, 103)(12, 110)(13, 83)(14, 111)(15, 114)(16, 86)(17, 113)(18, 85)(19, 100)(20, 94)(21, 119)(22, 87)(23, 115)(24, 120)(25, 90)(26, 117)(27, 89)(28, 91)(29, 116)(30, 93)(31, 99)(32, 106)(33, 109)(34, 98)(35, 108)(36, 97)(37, 118)(38, 112)(39, 102)(40, 107)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 8, 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 E23.245 Graph:: simple bipartite v = 24 e = 80 f = 12 degree seq :: [ 4^20, 20^4 ] E23.244 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10, 20}) Quotient :: dipole Aut^+ = C4 x D10 (small group id <40, 5>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y2^-1 * Y1)^2, Y3 * Y2 * Y3^-1 * Y2, R * Y2 * R * Y2^-1, (R * Y1)^2, Y3^4, (R * Y3)^2, Y2^-1 * Y3^-2 * Y2 * Y3^-2, Y3^-1 * Y1 * Y3^2 * Y1 * Y3^-1, Y3 * Y1 * Y2^-1 * Y3^-1 * Y2 * Y1, Y1 * Y3 * Y2^-1 * Y1 * Y3 * Y2^-2, Y2^-4 * Y3^-1 * Y2 * Y3^-1 ] Map:: non-degenerate R = (1, 41, 2, 42)(3, 43, 9, 49)(4, 44, 14, 54)(5, 45, 7, 47)(6, 46, 19, 59)(8, 48, 23, 63)(10, 50, 28, 68)(11, 51, 26, 66)(12, 52, 32, 72)(13, 53, 34, 74)(15, 55, 24, 64)(16, 56, 25, 65)(17, 57, 20, 60)(18, 58, 27, 67)(21, 61, 31, 71)(22, 62, 30, 70)(29, 69, 40, 80)(33, 73, 39, 79)(35, 75, 37, 77)(36, 76, 38, 78)(81, 121, 83, 123, 91, 131, 109, 149, 116, 156, 96, 136, 113, 153, 117, 157, 97, 137, 85, 125)(82, 122, 87, 127, 100, 140, 115, 155, 119, 159, 105, 145, 118, 158, 120, 160, 106, 146, 89, 129)(84, 124, 95, 135, 103, 143, 111, 151, 93, 133, 86, 126, 98, 138, 108, 148, 110, 150, 92, 132)(88, 128, 104, 144, 94, 134, 112, 152, 102, 142, 90, 130, 107, 147, 99, 139, 114, 154, 101, 141) L = (1, 84)(2, 88)(3, 92)(4, 96)(5, 95)(6, 81)(7, 101)(8, 105)(9, 104)(10, 82)(11, 110)(12, 113)(13, 83)(14, 115)(15, 116)(16, 86)(17, 103)(18, 85)(19, 106)(20, 114)(21, 118)(22, 87)(23, 109)(24, 119)(25, 90)(26, 94)(27, 89)(28, 97)(29, 108)(30, 117)(31, 91)(32, 100)(33, 93)(34, 120)(35, 99)(36, 98)(37, 111)(38, 102)(39, 107)(40, 112)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 8, 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 E23.248 Graph:: simple bipartite v = 24 e = 80 f = 12 degree seq :: [ 4^20, 20^4 ] E23.245 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10, 20}) Quotient :: dipole Aut^+ = C4 x D10 (small group id <40, 5>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ R^2, Y1^2 * Y3^-2, (Y3 * Y1^-1)^2, Y1^4, (Y2 * Y1^-1)^2, Y3^4, (Y2, Y3^-1), (R * Y2)^2, (Y1^-1 * Y2^-1)^2, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, (R * Y1)^2, Y1^-1 * Y2^-1 * Y3^2 * Y2 * Y1^-1, Y3^-1 * Y2^-5, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-2 ] Map:: non-degenerate R = (1, 41, 2, 42, 8, 48, 5, 45)(3, 43, 13, 53, 21, 61, 11, 51)(4, 44, 10, 50, 7, 47, 12, 52)(6, 46, 18, 58, 22, 62, 9, 49)(14, 54, 27, 67, 35, 75, 29, 69)(15, 55, 28, 68, 16, 56, 26, 66)(17, 57, 25, 65, 20, 60, 24, 64)(19, 59, 23, 63, 36, 76, 34, 74)(30, 70, 39, 79, 33, 73, 38, 78)(31, 71, 40, 80, 32, 72, 37, 77)(81, 121, 83, 123, 94, 134, 110, 150, 100, 140, 87, 127, 96, 136, 112, 152, 116, 156, 102, 142, 88, 128, 101, 141, 115, 155, 113, 153, 97, 137, 84, 124, 95, 135, 111, 151, 99, 139, 86, 126)(82, 122, 89, 129, 103, 143, 117, 157, 108, 148, 92, 132, 105, 145, 119, 159, 109, 149, 93, 133, 85, 125, 98, 138, 114, 154, 120, 160, 106, 146, 90, 130, 104, 144, 118, 158, 107, 147, 91, 131) L = (1, 84)(2, 90)(3, 95)(4, 88)(5, 92)(6, 97)(7, 81)(8, 87)(9, 104)(10, 85)(11, 106)(12, 82)(13, 108)(14, 111)(15, 101)(16, 83)(17, 102)(18, 105)(19, 113)(20, 86)(21, 96)(22, 100)(23, 118)(24, 98)(25, 89)(26, 93)(27, 120)(28, 91)(29, 117)(30, 99)(31, 115)(32, 94)(33, 116)(34, 119)(35, 112)(36, 110)(37, 107)(38, 114)(39, 103)(40, 109)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 4, 20, 4, 20, 4, 20, 4, 20 ), ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 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 E23.243 Graph:: bipartite v = 12 e = 80 f = 24 degree seq :: [ 8^10, 40^2 ] E23.246 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10, 20}) Quotient :: dipole Aut^+ = C4 x D10 (small group id <40, 5>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2, (Y3^-1 * Y1^-1)^2, R * Y2 * R * Y3^-1, (R * Y1)^2, Y3 * Y1^-1 * Y2^-1 * Y1^-1, Y1^4, Y1^-1 * Y3^2 * Y1 * Y2^-2, Y2^2 * Y1 * Y3^-2 * Y1^-1, Y2 * Y3^-1 * Y1^-1 * Y3^3 * Y2^-5 * Y1^-1, (Y3 * Y2^-1)^10, Y2^20 ] Map:: non-degenerate R = (1, 41, 2, 42, 6, 46, 5, 45)(3, 43, 9, 49, 13, 53, 8, 48)(4, 44, 11, 51, 14, 54, 7, 47)(10, 50, 16, 56, 21, 61, 17, 57)(12, 52, 15, 55, 22, 62, 19, 59)(18, 58, 25, 65, 29, 69, 24, 64)(20, 60, 27, 67, 30, 70, 23, 63)(26, 66, 32, 72, 37, 77, 33, 73)(28, 68, 31, 71, 38, 78, 35, 75)(34, 74, 39, 79, 36, 76, 40, 80)(81, 121, 83, 123, 90, 130, 98, 138, 106, 146, 114, 154, 118, 158, 110, 150, 102, 142, 94, 134, 86, 126, 93, 133, 101, 141, 109, 149, 117, 157, 116, 156, 108, 148, 100, 140, 92, 132, 84, 124)(82, 122, 87, 127, 95, 135, 103, 143, 111, 151, 119, 159, 113, 153, 105, 145, 97, 137, 89, 129, 85, 125, 91, 131, 99, 139, 107, 147, 115, 155, 120, 160, 112, 152, 104, 144, 96, 136, 88, 128) L = (1, 84)(2, 88)(3, 81)(4, 92)(5, 89)(6, 94)(7, 82)(8, 96)(9, 97)(10, 83)(11, 85)(12, 100)(13, 86)(14, 102)(15, 87)(16, 104)(17, 105)(18, 90)(19, 91)(20, 108)(21, 93)(22, 110)(23, 95)(24, 112)(25, 113)(26, 98)(27, 99)(28, 116)(29, 101)(30, 118)(31, 103)(32, 120)(33, 119)(34, 106)(35, 107)(36, 117)(37, 109)(38, 114)(39, 111)(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, 20, 4, 20, 4, 20, 4, 20 ), ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 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 E23.241 Graph:: bipartite v = 12 e = 80 f = 24 degree seq :: [ 8^10, 40^2 ] E23.247 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10, 20}) Quotient :: dipole Aut^+ = C4 x D10 (small group id <40, 5>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ R^2, (Y2^-1, Y3), Y3 * Y2^-3, (R * Y3)^2, (R * Y2)^2, (Y3 * Y1^-1)^2, (Y3^-1 * Y1^-1)^2, (Y1^-1 * Y2)^2, (R * Y1)^2, (Y2^-1 * Y1^-1)^2, Y1^4, Y3^-2 * Y2^-1 * Y1 * Y3 * Y1^-1, Y1^-1 * Y3 * Y1^2 * Y3^-1 * Y1^-1, Y1^-1 * Y3^-1 * Y2^-1 * Y3^-2 * Y1^-1, Y3 * Y2^-1 * Y3^6 ] Map:: non-degenerate R = (1, 41, 2, 42, 8, 48, 5, 45)(3, 43, 13, 53, 23, 63, 11, 51)(4, 44, 17, 57, 24, 64, 12, 52)(6, 46, 19, 59, 25, 65, 9, 49)(7, 47, 20, 60, 26, 66, 10, 50)(14, 54, 29, 69, 37, 77, 34, 74)(15, 55, 31, 71, 22, 62, 30, 70)(16, 56, 27, 67, 38, 78, 33, 73)(18, 58, 32, 72, 21, 61, 28, 68)(35, 75, 39, 79, 36, 76, 40, 80)(81, 121, 83, 123, 94, 134, 84, 124, 95, 135, 115, 155, 98, 138, 106, 146, 118, 158, 105, 145, 88, 128, 103, 143, 117, 157, 104, 144, 102, 142, 116, 156, 101, 141, 87, 127, 96, 136, 86, 126)(82, 122, 89, 129, 107, 147, 90, 130, 108, 148, 119, 159, 110, 150, 97, 137, 114, 154, 93, 133, 85, 125, 99, 139, 113, 153, 100, 140, 112, 152, 120, 160, 111, 151, 92, 132, 109, 149, 91, 131) L = (1, 84)(2, 90)(3, 95)(4, 98)(5, 100)(6, 94)(7, 81)(8, 104)(9, 108)(10, 110)(11, 107)(12, 82)(13, 113)(14, 115)(15, 106)(16, 83)(17, 85)(18, 105)(19, 112)(20, 111)(21, 86)(22, 87)(23, 102)(24, 101)(25, 117)(26, 88)(27, 119)(28, 97)(29, 89)(30, 93)(31, 91)(32, 92)(33, 120)(34, 99)(35, 118)(36, 96)(37, 116)(38, 103)(39, 114)(40, 109)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 4, 20, 4, 20, 4, 20, 4, 20 ), ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 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 E23.242 Graph:: bipartite v = 12 e = 80 f = 24 degree seq :: [ 8^10, 40^2 ] E23.248 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10, 20}) Quotient :: dipole Aut^+ = C4 x D10 (small group id <40, 5>) Aut = D8 x D10 (small group id <80, 39>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-3, (Y2, Y3), (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, (Y2 * Y1^-1)^2, (Y3 * Y1^-1)^2, (Y3^-1 * Y1^-1)^2, (Y2^-1 * Y1^-1)^2, Y1^4, Y3 * Y2 * Y1^-1 * Y2^-2 * Y1^-1, Y2 * Y3 * Y2^2 * Y1^-2, Y2^-1 * Y1^2 * Y2 * Y1^-2, Y2^20 ] Map:: non-degenerate R = (1, 41, 2, 42, 8, 48, 5, 45)(3, 43, 13, 53, 23, 63, 11, 51)(4, 44, 17, 57, 24, 64, 12, 52)(6, 46, 19, 59, 25, 65, 9, 49)(7, 47, 20, 60, 26, 66, 10, 50)(14, 54, 31, 71, 22, 62, 28, 68)(15, 55, 32, 72, 21, 61, 27, 67)(16, 56, 30, 70, 37, 77, 33, 73)(18, 58, 29, 69, 38, 78, 35, 75)(34, 74, 39, 79, 36, 76, 40, 80)(81, 121, 83, 123, 94, 134, 106, 146, 117, 157, 116, 156, 98, 138, 84, 124, 95, 135, 105, 145, 88, 128, 103, 143, 102, 142, 87, 127, 96, 136, 114, 154, 118, 158, 104, 144, 101, 141, 86, 126)(82, 122, 89, 129, 107, 147, 97, 137, 115, 155, 120, 160, 110, 150, 90, 130, 108, 148, 93, 133, 85, 125, 99, 139, 112, 152, 92, 132, 109, 149, 119, 159, 113, 153, 100, 140, 111, 151, 91, 131) L = (1, 84)(2, 90)(3, 95)(4, 96)(5, 100)(6, 98)(7, 81)(8, 104)(9, 108)(10, 109)(11, 110)(12, 82)(13, 113)(14, 105)(15, 114)(16, 83)(17, 85)(18, 87)(19, 111)(20, 115)(21, 116)(22, 86)(23, 101)(24, 117)(25, 118)(26, 88)(27, 93)(28, 119)(29, 89)(30, 92)(31, 120)(32, 91)(33, 97)(34, 94)(35, 99)(36, 102)(37, 103)(38, 106)(39, 107)(40, 112)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 4, 20, 4, 20, 4, 20, 4, 20 ), ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) } Outer automorphisms :: reflexible Dual of E23.244 Graph:: bipartite v = 12 e = 80 f = 24 degree seq :: [ 8^10, 40^2 ] E23.249 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10, 20}) Quotient :: dipole Aut^+ = C20 x C2 (small group id <40, 9>) Aut = C2 x D40 (small group id <80, 37>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^4, (Y3, Y2), (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y3 * Y1 * Y3^-1 * Y1, Y2^-1 * Y1 * Y2 * Y1, Y3^-5 * 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 ] Map:: non-degenerate R = (1, 41, 2, 42)(3, 43, 7, 47)(4, 44, 8, 48)(5, 45, 9, 49)(6, 46, 10, 50)(11, 51, 18, 58)(12, 52, 19, 59)(13, 53, 20, 60)(14, 54, 21, 61)(15, 55, 22, 62)(16, 56, 23, 63)(17, 57, 24, 64)(25, 65, 31, 71)(26, 66, 32, 72)(27, 67, 33, 73)(28, 68, 34, 74)(29, 69, 35, 75)(30, 70, 36, 76)(37, 77, 39, 79)(38, 78, 40, 80)(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, 110, 150)(97, 137, 108, 148, 118, 158, 109, 149)(101, 141, 113, 153, 119, 159, 116, 156)(104, 144, 114, 154, 120, 160, 115, 155) L = (1, 84)(2, 88)(3, 92)(4, 94)(5, 95)(6, 81)(7, 99)(8, 101)(9, 102)(10, 82)(11, 105)(12, 107)(13, 83)(14, 109)(15, 110)(16, 85)(17, 86)(18, 111)(19, 113)(20, 87)(21, 115)(22, 116)(23, 89)(24, 90)(25, 117)(26, 91)(27, 97)(28, 93)(29, 96)(30, 118)(31, 119)(32, 98)(33, 104)(34, 100)(35, 103)(36, 120)(37, 108)(38, 106)(39, 114)(40, 112)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 20, 40, 20, 40 ), ( 20, 40, 20, 40, 20, 40, 20, 40 ) } Outer automorphisms :: reflexible Dual of E23.263 Graph:: simple bipartite v = 30 e = 80 f = 6 degree seq :: [ 4^20, 8^10 ] E23.250 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10, 20}) Quotient :: dipole Aut^+ = C20 x C2 (small group id <40, 9>) Aut = C2 x D40 (small group id <80, 37>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y1 * Y3^-1 * Y1 * Y3, (Y3, Y2), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y2^-1 * Y1 * Y2 * Y1, Y2^4, Y2^2 * Y1 * Y2 * Y1 * Y2, Y1 * Y3^5 * Y2^-1 ] Map:: non-degenerate R = (1, 41, 2, 42)(3, 43, 7, 47)(4, 44, 8, 48)(5, 45, 9, 49)(6, 46, 10, 50)(11, 51, 18, 58)(12, 52, 19, 59)(13, 53, 20, 60)(14, 54, 21, 61)(15, 55, 22, 62)(16, 56, 23, 63)(17, 57, 24, 64)(25, 65, 33, 73)(26, 66, 34, 74)(27, 67, 35, 75)(28, 68, 29, 69)(30, 70, 32, 72)(31, 71, 36, 76)(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, 113, 153, 102, 142)(90, 130, 100, 140, 114, 154, 103, 143)(94, 134, 107, 147, 117, 157, 110, 150)(97, 137, 108, 148, 118, 158, 111, 151)(101, 141, 115, 155, 120, 160, 112, 152)(104, 144, 109, 149, 119, 159, 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, 109)(15, 110)(16, 85)(17, 86)(18, 113)(19, 115)(20, 87)(21, 108)(22, 112)(23, 89)(24, 90)(25, 117)(26, 91)(27, 119)(28, 93)(29, 100)(30, 104)(31, 96)(32, 97)(33, 120)(34, 98)(35, 118)(36, 103)(37, 116)(38, 106)(39, 114)(40, 111)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 20, 40, 20, 40 ), ( 20, 40, 20, 40, 20, 40, 20, 40 ) } Outer automorphisms :: reflexible Dual of E23.262 Graph:: simple bipartite v = 30 e = 80 f = 6 degree seq :: [ 4^20, 8^10 ] E23.251 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10, 20}) Quotient :: dipole Aut^+ = C20 x C2 (small group id <40, 9>) Aut = C2 x D40 (small group id <80, 37>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2 * Y1 * Y2, Y3^-1 * Y1 * Y3 * Y1, (R * Y1)^2, (Y3, Y2^-1), (R * Y3)^2, (R * Y2)^2, Y3^10 * Y1, (Y2^-1 * Y3)^10 ] Map:: non-degenerate R = (1, 41, 2, 42)(3, 43, 5, 45)(4, 44, 7, 47)(6, 46, 8, 48)(9, 49, 12, 52)(10, 50, 13, 53)(11, 51, 15, 55)(14, 54, 16, 56)(17, 57, 20, 60)(18, 58, 21, 61)(19, 59, 23, 63)(22, 62, 24, 64)(25, 65, 28, 68)(26, 66, 29, 69)(27, 67, 31, 71)(30, 70, 32, 72)(33, 73, 36, 76)(34, 74, 37, 77)(35, 75, 38, 78)(39, 79, 40, 80)(81, 121, 83, 123, 82, 122, 85, 125)(84, 124, 89, 129, 87, 127, 92, 132)(86, 126, 90, 130, 88, 128, 93, 133)(91, 131, 97, 137, 95, 135, 100, 140)(94, 134, 98, 138, 96, 136, 101, 141)(99, 139, 105, 145, 103, 143, 108, 148)(102, 142, 106, 146, 104, 144, 109, 149)(107, 147, 113, 153, 111, 151, 116, 156)(110, 150, 114, 154, 112, 152, 117, 157)(115, 155, 119, 159, 118, 158, 120, 160) L = (1, 84)(2, 87)(3, 89)(4, 91)(5, 92)(6, 81)(7, 95)(8, 82)(9, 97)(10, 83)(11, 99)(12, 100)(13, 85)(14, 86)(15, 103)(16, 88)(17, 105)(18, 90)(19, 107)(20, 108)(21, 93)(22, 94)(23, 111)(24, 96)(25, 113)(26, 98)(27, 115)(28, 116)(29, 101)(30, 102)(31, 118)(32, 104)(33, 119)(34, 106)(35, 112)(36, 120)(37, 109)(38, 110)(39, 117)(40, 114)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 20, 40, 20, 40 ), ( 20, 40, 20, 40, 20, 40, 20, 40 ) } Outer automorphisms :: reflexible Dual of E23.261 Graph:: bipartite v = 30 e = 80 f = 6 degree seq :: [ 4^20, 8^10 ] E23.252 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10, 20}) Quotient :: dipole Aut^+ = C20 x C2 (small group id <40, 9>) Aut = C2 x D40 (small group id <80, 37>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2 * Y1 * Y2^-1 * Y1, (Y3, Y2), Y3 * Y1 * Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2^4, Y3^-5 * Y1 * Y2^-1 ] Map:: non-degenerate R = (1, 41, 2, 42)(3, 43, 7, 47)(4, 44, 8, 48)(5, 45, 9, 49)(6, 46, 10, 50)(11, 51, 18, 58)(12, 52, 19, 59)(13, 53, 20, 60)(14, 54, 21, 61)(15, 55, 22, 62)(16, 56, 23, 63)(17, 57, 24, 64)(25, 65, 33, 73)(26, 66, 34, 74)(27, 67, 32, 72)(28, 68, 35, 75)(29, 69, 31, 71)(30, 70, 36, 76)(37, 77, 39, 79)(38, 78, 40, 80)(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, 113, 153, 102, 142)(90, 130, 100, 140, 114, 154, 103, 143)(94, 134, 107, 147, 117, 157, 110, 150)(97, 137, 108, 148, 118, 158, 111, 151)(101, 141, 112, 152, 119, 159, 116, 156)(104, 144, 115, 155, 120, 160, 109, 149) L = (1, 84)(2, 88)(3, 92)(4, 94)(5, 95)(6, 81)(7, 99)(8, 101)(9, 102)(10, 82)(11, 105)(12, 107)(13, 83)(14, 109)(15, 110)(16, 85)(17, 86)(18, 113)(19, 112)(20, 87)(21, 111)(22, 116)(23, 89)(24, 90)(25, 117)(26, 91)(27, 104)(28, 93)(29, 103)(30, 120)(31, 96)(32, 97)(33, 119)(34, 98)(35, 100)(36, 118)(37, 115)(38, 106)(39, 108)(40, 114)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 20, 40, 20, 40 ), ( 20, 40, 20, 40, 20, 40, 20, 40 ) } Outer automorphisms :: reflexible Dual of E23.264 Graph:: simple bipartite v = 30 e = 80 f = 6 degree seq :: [ 4^20, 8^10 ] E23.253 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10, 20}) Quotient :: dipole Aut^+ = C20 x C2 (small group id <40, 9>) Aut = C2 x D40 (small group id <80, 37>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-1, (Y2, Y1^-1), (R * Y1)^2, (R * Y3)^2, Y1^4, (Y3^-1 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y2^10, (Y3 * Y2^-1)^20 ] Map:: non-degenerate R = (1, 41, 2, 42, 6, 46, 4, 44)(3, 43, 7, 47, 13, 53, 10, 50)(5, 45, 8, 48, 14, 54, 11, 51)(9, 49, 15, 55, 21, 61, 18, 58)(12, 52, 16, 56, 22, 62, 19, 59)(17, 57, 23, 63, 29, 69, 26, 66)(20, 60, 24, 64, 30, 70, 27, 67)(25, 65, 31, 71, 36, 76, 34, 74)(28, 68, 32, 72, 37, 77, 35, 75)(33, 73, 38, 78, 40, 80, 39, 79)(81, 121, 83, 123, 89, 129, 97, 137, 105, 145, 113, 153, 108, 148, 100, 140, 92, 132, 85, 125)(82, 122, 87, 127, 95, 135, 103, 143, 111, 151, 118, 158, 112, 152, 104, 144, 96, 136, 88, 128)(84, 124, 90, 130, 98, 138, 106, 146, 114, 154, 119, 159, 115, 155, 107, 147, 99, 139, 91, 131)(86, 126, 93, 133, 101, 141, 109, 149, 116, 156, 120, 160, 117, 157, 110, 150, 102, 142, 94, 134) L = (1, 82)(2, 86)(3, 87)(4, 81)(5, 88)(6, 84)(7, 93)(8, 94)(9, 95)(10, 83)(11, 85)(12, 96)(13, 90)(14, 91)(15, 101)(16, 102)(17, 103)(18, 89)(19, 92)(20, 104)(21, 98)(22, 99)(23, 109)(24, 110)(25, 111)(26, 97)(27, 100)(28, 112)(29, 106)(30, 107)(31, 116)(32, 117)(33, 118)(34, 105)(35, 108)(36, 114)(37, 115)(38, 120)(39, 113)(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) :: { ( 4, 40, 4, 40, 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 E23.260 Graph:: bipartite v = 14 e = 80 f = 22 degree seq :: [ 8^10, 20^4 ] E23.254 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10, 20}) Quotient :: dipole Aut^+ = C20 x C2 (small group id <40, 9>) Aut = C2 x D40 (small group id <80, 37>) |r| :: 2 Presentation :: [ R^2, Y3^-2 * Y1^2, (Y1^-1, Y3^-1), Y1^-1 * Y3^-2 * Y1^-1, (R * Y1)^2, (Y1^-1 * Y3)^2, (R * Y2)^2, (R * Y3)^2, (Y1^-1, Y2), (Y2^-1, Y3^-1), Y2 * Y3^-2 * Y1 * Y2^-1 * Y1, Y2^-1 * Y1 * Y3^-1 * Y2 * Y1^-1 * Y3, Y2^-1 * Y3 * Y1 * Y2 * Y3^-1 * Y1^-1, Y2 * Y1^-1 * Y3 * Y2^4, (Y2^-1 * Y3)^20 ] Map:: non-degenerate R = (1, 41, 2, 42, 8, 48, 5, 45)(3, 43, 9, 49, 21, 61, 15, 55)(4, 44, 10, 50, 7, 47, 12, 52)(6, 46, 11, 51, 22, 62, 18, 58)(13, 53, 23, 63, 37, 77, 31, 71)(14, 54, 24, 64, 16, 56, 25, 65)(17, 57, 26, 66, 20, 60, 28, 68)(19, 59, 27, 67, 38, 78, 34, 74)(29, 69, 33, 73, 40, 80, 36, 76)(30, 70, 39, 79, 32, 72, 35, 75)(81, 121, 83, 123, 93, 133, 109, 149, 108, 148, 92, 132, 105, 145, 115, 155, 99, 139, 86, 126)(82, 122, 89, 129, 103, 143, 113, 153, 97, 137, 84, 124, 94, 134, 110, 150, 107, 147, 91, 131)(85, 125, 95, 135, 111, 151, 116, 156, 100, 140, 87, 127, 96, 136, 112, 152, 114, 154, 98, 138)(88, 128, 101, 141, 117, 157, 120, 160, 106, 146, 90, 130, 104, 144, 119, 159, 118, 158, 102, 142) L = (1, 84)(2, 90)(3, 94)(4, 88)(5, 92)(6, 97)(7, 81)(8, 87)(9, 104)(10, 85)(11, 106)(12, 82)(13, 110)(14, 101)(15, 105)(16, 83)(17, 102)(18, 108)(19, 113)(20, 86)(21, 96)(22, 100)(23, 119)(24, 95)(25, 89)(26, 98)(27, 120)(28, 91)(29, 107)(30, 117)(31, 115)(32, 93)(33, 118)(34, 109)(35, 103)(36, 99)(37, 112)(38, 116)(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, 40, 4, 40, 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 E23.258 Graph:: bipartite v = 14 e = 80 f = 22 degree seq :: [ 8^10, 20^4 ] E23.255 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10, 20}) Quotient :: dipole Aut^+ = C20 x C2 (small group id <40, 9>) Aut = C2 x D40 (small group id <80, 37>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^2 * Y3, Y3^2 * Y1^-2, Y3^4, (Y1^-1, Y2^-1), (R * Y1)^2, (Y3, Y1^-1), (R * Y3)^2, (Y2, Y3^-1), (R * Y2)^2, Y2^-1 * Y3 * Y1 * Y2 * Y3^-1 * Y1^-1, Y3 * Y2 * Y1^2 * Y2^-1 * Y3, Y2^-1 * Y1 * Y2^-1 * Y3 * Y2^-3, Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y1^-1 * Y2^2 ] Map:: non-degenerate R = (1, 41, 2, 42, 8, 48, 5, 45)(3, 43, 9, 49, 21, 61, 15, 55)(4, 44, 10, 50, 7, 47, 12, 52)(6, 46, 11, 51, 22, 62, 18, 58)(13, 53, 23, 63, 37, 77, 31, 71)(14, 54, 24, 64, 16, 56, 25, 65)(17, 57, 26, 66, 20, 60, 28, 68)(19, 59, 27, 67, 38, 78, 34, 74)(29, 69, 36, 76, 40, 80, 33, 73)(30, 70, 35, 75, 32, 72, 39, 79)(81, 121, 83, 123, 93, 133, 109, 149, 106, 146, 90, 130, 104, 144, 115, 155, 99, 139, 86, 126)(82, 122, 89, 129, 103, 143, 116, 156, 100, 140, 87, 127, 96, 136, 112, 152, 107, 147, 91, 131)(84, 124, 94, 134, 110, 150, 114, 154, 98, 138, 85, 125, 95, 135, 111, 151, 113, 153, 97, 137)(88, 128, 101, 141, 117, 157, 120, 160, 108, 148, 92, 132, 105, 145, 119, 159, 118, 158, 102, 142) L = (1, 84)(2, 90)(3, 94)(4, 88)(5, 92)(6, 97)(7, 81)(8, 87)(9, 104)(10, 85)(11, 106)(12, 82)(13, 110)(14, 101)(15, 105)(16, 83)(17, 102)(18, 108)(19, 113)(20, 86)(21, 96)(22, 100)(23, 115)(24, 95)(25, 89)(26, 98)(27, 109)(28, 91)(29, 114)(30, 117)(31, 119)(32, 93)(33, 118)(34, 120)(35, 111)(36, 99)(37, 112)(38, 116)(39, 103)(40, 107)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 4, 40, 4, 40, 4, 40, 4, 40 ), ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ) } Outer automorphisms :: reflexible Dual of E23.259 Graph:: bipartite v = 14 e = 80 f = 22 degree seq :: [ 8^10, 20^4 ] E23.256 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10, 20}) Quotient :: dipole Aut^+ = C20 x C2 (small group id <40, 9>) Aut = C2 x D40 (small group id <80, 37>) |r| :: 2 Presentation :: [ R^2, Y3^4, Y1^-1 * Y3^-2 * Y1^-1, (Y3^-1 * Y1)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y3^-1 * Y1^-1)^2, Y3^2 * Y1^-2, (Y2, Y1^-1), (Y2, Y3^-1), Y1 * Y2^-1 * Y1 * Y3 * Y2 * Y3, Y2^-1 * Y3 * Y1 * Y2 * Y3^-1 * Y1^-1, Y2^5 * Y3^2 ] Map:: non-degenerate R = (1, 41, 2, 42, 8, 48, 5, 45)(3, 43, 9, 49, 21, 61, 15, 55)(4, 44, 10, 50, 7, 47, 12, 52)(6, 46, 11, 51, 22, 62, 18, 58)(13, 53, 23, 63, 35, 75, 31, 71)(14, 54, 24, 64, 16, 56, 25, 65)(17, 57, 26, 66, 20, 60, 28, 68)(19, 59, 27, 67, 29, 69, 34, 74)(30, 70, 37, 77, 32, 72, 38, 78)(33, 73, 39, 79, 36, 76, 40, 80)(81, 121, 83, 123, 93, 133, 109, 149, 102, 142, 88, 128, 101, 141, 115, 155, 99, 139, 86, 126)(82, 122, 89, 129, 103, 143, 114, 154, 98, 138, 85, 125, 95, 135, 111, 151, 107, 147, 91, 131)(84, 124, 94, 134, 110, 150, 116, 156, 100, 140, 87, 127, 96, 136, 112, 152, 113, 153, 97, 137)(90, 130, 104, 144, 117, 157, 120, 160, 108, 148, 92, 132, 105, 145, 118, 158, 119, 159, 106, 146) L = (1, 84)(2, 90)(3, 94)(4, 88)(5, 92)(6, 97)(7, 81)(8, 87)(9, 104)(10, 85)(11, 106)(12, 82)(13, 110)(14, 101)(15, 105)(16, 83)(17, 102)(18, 108)(19, 113)(20, 86)(21, 96)(22, 100)(23, 117)(24, 95)(25, 89)(26, 98)(27, 119)(28, 91)(29, 116)(30, 115)(31, 118)(32, 93)(33, 109)(34, 120)(35, 112)(36, 99)(37, 111)(38, 103)(39, 114)(40, 107)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 4, 40, 4, 40, 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 E23.257 Graph:: bipartite v = 14 e = 80 f = 22 degree seq :: [ 8^10, 20^4 ] E23.257 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10, 20}) Quotient :: dipole Aut^+ = C20 x C2 (small group id <40, 9>) Aut = C2 x D40 (small group id <80, 37>) |r| :: 2 Presentation :: [ R^2, Y2^2, (R * Y2)^2, (R * Y3)^2, (Y1, Y3^-1), (R * Y1)^2, Y3 * Y2 * Y3^-1 * Y2, Y2 * Y1 * Y2 * Y1^-1, Y3^4, Y1^-5 * Y3, Y3 * Y2 * Y1^-2 * Y2 * Y3^-1 * Y1^2, (Y1^-1 * Y3^2 * Y1^-1)^5 ] Map:: non-degenerate R = (1, 41, 2, 42, 7, 47, 18, 58, 15, 55, 4, 44, 9, 49, 20, 60, 32, 72, 29, 69, 14, 54, 24, 64, 35, 75, 30, 70, 17, 57, 6, 46, 10, 50, 21, 61, 16, 56, 5, 45)(3, 43, 8, 48, 19, 59, 31, 71, 26, 66, 11, 51, 22, 62, 33, 73, 39, 79, 37, 77, 25, 65, 36, 76, 40, 80, 38, 78, 28, 68, 13, 53, 23, 63, 34, 74, 27, 67, 12, 52)(81, 121, 83, 123)(82, 122, 88, 128)(84, 124, 91, 131)(85, 125, 92, 132)(86, 126, 93, 133)(87, 127, 99, 139)(89, 129, 102, 142)(90, 130, 103, 143)(94, 134, 105, 145)(95, 135, 106, 146)(96, 136, 107, 147)(97, 137, 108, 148)(98, 138, 111, 151)(100, 140, 113, 153)(101, 141, 114, 154)(104, 144, 116, 156)(109, 149, 117, 157)(110, 150, 118, 158)(112, 152, 119, 159)(115, 155, 120, 160) L = (1, 84)(2, 89)(3, 91)(4, 94)(5, 95)(6, 81)(7, 100)(8, 102)(9, 104)(10, 82)(11, 105)(12, 106)(13, 83)(14, 86)(15, 109)(16, 98)(17, 85)(18, 112)(19, 113)(20, 115)(21, 87)(22, 116)(23, 88)(24, 90)(25, 93)(26, 117)(27, 111)(28, 92)(29, 97)(30, 96)(31, 119)(32, 110)(33, 120)(34, 99)(35, 101)(36, 103)(37, 108)(38, 107)(39, 118)(40, 114)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 8, 20, 8, 20 ), ( 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20 ) } Outer automorphisms :: reflexible Dual of E23.256 Graph:: bipartite v = 22 e = 80 f = 14 degree seq :: [ 4^20, 40^2 ] E23.258 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10, 20}) Quotient :: dipole Aut^+ = C20 x C2 (small group id <40, 9>) Aut = C2 x D40 (small group id <80, 37>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y1 * Y2 * Y1^-1 * Y2, (Y1, Y3^-1), (R * Y3)^2, Y3^-1 * Y2 * Y3 * Y2, (R * Y1)^2, (R * Y2)^2, Y3^4, Y2 * Y1^2 * Y3^-1 * Y1^3, Y1^-7 * Y2 * Y1^2 * Y3 ] Map:: non-degenerate R = (1, 41, 2, 42, 7, 47, 18, 58, 26, 66, 11, 51, 22, 62, 34, 74, 39, 79, 29, 69, 14, 54, 24, 64, 35, 75, 38, 78, 28, 68, 13, 53, 23, 63, 31, 71, 16, 56, 5, 45)(3, 43, 8, 48, 19, 59, 30, 70, 15, 55, 4, 44, 9, 49, 20, 60, 33, 73, 37, 77, 25, 65, 36, 76, 40, 80, 32, 72, 17, 57, 6, 46, 10, 50, 21, 61, 27, 67, 12, 52)(81, 121, 83, 123)(82, 122, 88, 128)(84, 124, 91, 131)(85, 125, 92, 132)(86, 126, 93, 133)(87, 127, 99, 139)(89, 129, 102, 142)(90, 130, 103, 143)(94, 134, 105, 145)(95, 135, 106, 146)(96, 136, 107, 147)(97, 137, 108, 148)(98, 138, 110, 150)(100, 140, 114, 154)(101, 141, 111, 151)(104, 144, 116, 156)(109, 149, 117, 157)(112, 152, 118, 158)(113, 153, 119, 159)(115, 155, 120, 160) L = (1, 84)(2, 89)(3, 91)(4, 94)(5, 95)(6, 81)(7, 100)(8, 102)(9, 104)(10, 82)(11, 105)(12, 106)(13, 83)(14, 86)(15, 109)(16, 110)(17, 85)(18, 113)(19, 114)(20, 115)(21, 87)(22, 116)(23, 88)(24, 90)(25, 93)(26, 117)(27, 98)(28, 92)(29, 97)(30, 119)(31, 99)(32, 96)(33, 118)(34, 120)(35, 101)(36, 103)(37, 108)(38, 107)(39, 112)(40, 111)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 8, 20, 8, 20 ), ( 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20 ) } Outer automorphisms :: reflexible Dual of E23.254 Graph:: bipartite v = 22 e = 80 f = 14 degree seq :: [ 4^20, 40^2 ] E23.259 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10, 20}) Quotient :: dipole Aut^+ = C20 x C2 (small group id <40, 9>) Aut = C2 x D40 (small group id <80, 37>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y2 * Y3 * Y2 * Y3^-1, (Y3, Y1), Y3^4, (R * Y1)^2, (R * Y3)^2, Y2 * Y1 * Y2 * Y1^-1, (R * Y2)^2, Y1 * Y3 * Y2 * Y1^-1 * Y3^-1 * Y2, Y1 * Y3 * Y1 * Y2 * Y1^3, Y3^3 * Y1^2 * Y3 * Y1^-2 ] Map:: non-degenerate R = (1, 41, 2, 42, 7, 47, 18, 58, 28, 68, 13, 53, 23, 63, 34, 74, 39, 79, 29, 69, 14, 54, 24, 64, 35, 75, 38, 78, 26, 66, 11, 51, 22, 62, 31, 71, 16, 56, 5, 45)(3, 43, 8, 48, 19, 59, 32, 72, 17, 57, 6, 46, 10, 50, 21, 61, 33, 73, 37, 77, 25, 65, 36, 76, 40, 80, 30, 70, 15, 55, 4, 44, 9, 49, 20, 60, 27, 67, 12, 52)(81, 121, 83, 123)(82, 122, 88, 128)(84, 124, 91, 131)(85, 125, 92, 132)(86, 126, 93, 133)(87, 127, 99, 139)(89, 129, 102, 142)(90, 130, 103, 143)(94, 134, 105, 145)(95, 135, 106, 146)(96, 136, 107, 147)(97, 137, 108, 148)(98, 138, 112, 152)(100, 140, 111, 151)(101, 141, 114, 154)(104, 144, 116, 156)(109, 149, 117, 157)(110, 150, 118, 158)(113, 153, 119, 159)(115, 155, 120, 160) L = (1, 84)(2, 89)(3, 91)(4, 94)(5, 95)(6, 81)(7, 100)(8, 102)(9, 104)(10, 82)(11, 105)(12, 106)(13, 83)(14, 86)(15, 109)(16, 110)(17, 85)(18, 107)(19, 111)(20, 115)(21, 87)(22, 116)(23, 88)(24, 90)(25, 93)(26, 117)(27, 118)(28, 92)(29, 97)(30, 119)(31, 120)(32, 96)(33, 98)(34, 99)(35, 101)(36, 103)(37, 108)(38, 113)(39, 112)(40, 114)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 8, 20, 8, 20 ), ( 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20 ) } Outer automorphisms :: reflexible Dual of E23.255 Graph:: bipartite v = 22 e = 80 f = 14 degree seq :: [ 4^20, 40^2 ] E23.260 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10, 20}) Quotient :: dipole Aut^+ = C20 x C2 (small group id <40, 9>) Aut = C2 x D40 (small group id <80, 37>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y2 * Y3^2, (R * Y2)^2, (Y1, Y3), (R * Y1)^2, Y2 * Y1^-1 * Y2 * Y1, (R * Y3)^2, Y2 * Y1^10, 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, 41, 2, 42, 7, 47, 15, 55, 23, 63, 31, 71, 35, 75, 27, 67, 19, 59, 11, 51, 3, 43, 8, 48, 16, 56, 24, 64, 32, 72, 37, 77, 29, 69, 21, 61, 13, 53, 5, 45)(4, 44, 9, 49, 17, 57, 25, 65, 33, 73, 39, 79, 38, 78, 30, 70, 22, 62, 14, 54, 6, 46, 10, 50, 18, 58, 26, 66, 34, 74, 40, 80, 36, 76, 28, 68, 20, 60, 12, 52)(81, 121, 83, 123)(82, 122, 88, 128)(84, 124, 86, 126)(85, 125, 91, 131)(87, 127, 96, 136)(89, 129, 90, 130)(92, 132, 94, 134)(93, 133, 99, 139)(95, 135, 104, 144)(97, 137, 98, 138)(100, 140, 102, 142)(101, 141, 107, 147)(103, 143, 112, 152)(105, 145, 106, 146)(108, 148, 110, 150)(109, 149, 115, 155)(111, 151, 117, 157)(113, 153, 114, 154)(116, 156, 118, 158)(119, 159, 120, 160) L = (1, 84)(2, 89)(3, 86)(4, 83)(5, 92)(6, 81)(7, 97)(8, 90)(9, 88)(10, 82)(11, 94)(12, 91)(13, 100)(14, 85)(15, 105)(16, 98)(17, 96)(18, 87)(19, 102)(20, 99)(21, 108)(22, 93)(23, 113)(24, 106)(25, 104)(26, 95)(27, 110)(28, 107)(29, 116)(30, 101)(31, 119)(32, 114)(33, 112)(34, 103)(35, 118)(36, 115)(37, 120)(38, 109)(39, 117)(40, 111)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 8, 20, 8, 20 ), ( 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20, 8, 20 ) } Outer automorphisms :: reflexible Dual of E23.253 Graph:: bipartite v = 22 e = 80 f = 14 degree seq :: [ 4^20, 40^2 ] E23.261 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10, 20}) Quotient :: dipole Aut^+ = C20 x C2 (small group id <40, 9>) Aut = C2 x D40 (small group id <80, 37>) |r| :: 2 Presentation :: [ R^2, (Y3^-1, Y2), (Y2^-1 * Y3)^2, Y2^-1 * Y1^-1 * Y3^-1 * Y1^-1, Y1^-2 * Y3^-1 * Y2^-1, (R * Y2)^2, (Y3^-1, Y1^-1), (R * Y1)^2, (R * Y3)^2, Y2 * Y1^-3 * Y2^-2 * Y3^-1 * Y1, Y3^-1 * Y2^-1 * Y1^8, Y2^3 * Y3 * Y1^-1 * Y2 * Y1^-1 * Y3 * Y2^2, (Y3^-1 * Y1 * Y2^-1 * Y1 * Y3^-1)^4 ] Map:: non-degenerate R = (1, 41, 2, 42, 8, 48, 19, 59, 29, 69, 37, 77, 33, 73, 28, 68, 14, 54, 5, 45)(3, 43, 9, 49, 7, 47, 12, 52, 21, 61, 31, 71, 39, 79, 36, 76, 26, 66, 15, 55)(4, 44, 10, 50, 6, 46, 11, 51, 20, 60, 30, 70, 38, 78, 35, 75, 25, 65, 17, 57)(13, 53, 22, 62, 16, 56, 23, 63, 18, 58, 24, 64, 32, 72, 40, 80, 34, 74, 27, 67)(81, 121, 83, 123, 93, 133, 105, 145, 113, 153, 119, 159, 112, 152, 100, 140, 88, 128, 87, 127, 96, 136, 84, 124, 94, 134, 106, 146, 114, 154, 118, 158, 109, 149, 101, 141, 98, 138, 86, 126)(82, 122, 89, 129, 102, 142, 97, 137, 108, 148, 116, 156, 120, 160, 110, 150, 99, 139, 92, 132, 103, 143, 90, 130, 85, 125, 95, 135, 107, 147, 115, 155, 117, 157, 111, 151, 104, 144, 91, 131) L = (1, 84)(2, 90)(3, 94)(4, 93)(5, 97)(6, 96)(7, 81)(8, 86)(9, 85)(10, 102)(11, 103)(12, 82)(13, 106)(14, 105)(15, 108)(16, 83)(17, 107)(18, 87)(19, 91)(20, 98)(21, 88)(22, 95)(23, 89)(24, 92)(25, 114)(26, 113)(27, 116)(28, 115)(29, 100)(30, 104)(31, 99)(32, 101)(33, 118)(34, 119)(35, 120)(36, 117)(37, 110)(38, 112)(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, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 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 E23.251 Graph:: bipartite v = 6 e = 80 f = 30 degree seq :: [ 20^4, 40^2 ] E23.262 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10, 20}) Quotient :: dipole Aut^+ = C20 x C2 (small group id <40, 9>) Aut = C2 x D40 (small group id <80, 37>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-2 * Y2, (R * Y1)^2, (Y1^-1, Y2), (Y3^-1, Y2^-1), (R * Y3)^2, (R * Y2)^2, (Y3, Y1^-1), Y2 * Y1^-1 * Y3 * Y2^2, Y1 * Y3^-2 * Y1^-1 * Y2^2, Y3^-2 * Y1^-1 * Y3^-1 * Y1^2 * Y2^-1, Y1 * Y2 * Y1^4 * Y3^-1, Y1 * Y2^-1 * Y1^2 * Y3 * Y1^2 ] Map:: non-degenerate R = (1, 41, 2, 42, 8, 48, 23, 63, 32, 72, 16, 56, 30, 70, 34, 74, 18, 58, 5, 45)(3, 43, 9, 49, 24, 64, 33, 73, 17, 57, 4, 44, 10, 50, 25, 65, 31, 71, 15, 55)(6, 46, 11, 51, 26, 66, 36, 76, 20, 60, 7, 47, 12, 52, 27, 67, 35, 75, 19, 59)(13, 53, 28, 68, 39, 79, 37, 77, 21, 61, 14, 54, 29, 69, 40, 80, 38, 78, 22, 62)(81, 121, 83, 123, 93, 133, 92, 132, 110, 150, 90, 130, 109, 149, 106, 146, 88, 128, 104, 144, 119, 159, 115, 155, 98, 138, 111, 151, 118, 158, 100, 140, 112, 152, 97, 137, 101, 141, 86, 126)(82, 122, 89, 129, 108, 148, 107, 147, 114, 154, 105, 145, 120, 160, 116, 156, 103, 143, 113, 153, 117, 157, 99, 139, 85, 125, 95, 135, 102, 142, 87, 127, 96, 136, 84, 124, 94, 134, 91, 131) L = (1, 84)(2, 90)(3, 94)(4, 93)(5, 97)(6, 96)(7, 81)(8, 105)(9, 109)(10, 108)(11, 110)(12, 82)(13, 91)(14, 92)(15, 101)(16, 83)(17, 102)(18, 113)(19, 112)(20, 85)(21, 87)(22, 86)(23, 111)(24, 120)(25, 119)(26, 114)(27, 88)(28, 106)(29, 107)(30, 89)(31, 117)(32, 95)(33, 118)(34, 104)(35, 103)(36, 98)(37, 100)(38, 99)(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, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 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 E23.250 Graph:: bipartite v = 6 e = 80 f = 30 degree seq :: [ 20^4, 40^2 ] E23.263 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10, 20}) Quotient :: dipole Aut^+ = C20 x C2 (small group id <40, 9>) Aut = C2 x D40 (small group id <80, 37>) |r| :: 2 Presentation :: [ R^2, Y3^2 * Y2^-2, (Y2^-1, Y1^-1), (Y1^-1, Y3), (R * Y3)^2, (Y3^-1, Y2^-1), (R * Y1)^2, (R * Y2)^2, Y3^2 * Y1^-3, Y2 * Y1 * Y2^5, (Y1^-1 * Y3^-1)^4 ] Map:: non-degenerate R = (1, 41, 2, 42, 8, 48, 13, 53, 25, 65, 39, 79, 35, 75, 21, 61, 18, 58, 5, 45)(3, 43, 9, 49, 23, 63, 29, 69, 37, 77, 33, 73, 19, 59, 6, 46, 11, 51, 15, 55)(4, 44, 10, 50, 24, 64, 30, 70, 38, 78, 34, 74, 20, 60, 7, 47, 12, 52, 17, 57)(14, 54, 26, 66, 40, 80, 36, 76, 22, 62, 28, 68, 32, 72, 16, 56, 27, 67, 31, 71)(81, 121, 83, 123, 93, 133, 109, 149, 115, 155, 99, 139, 85, 125, 95, 135, 88, 128, 103, 143, 119, 159, 113, 153, 98, 138, 91, 131, 82, 122, 89, 129, 105, 145, 117, 157, 101, 141, 86, 126)(84, 124, 94, 134, 110, 150, 116, 156, 100, 140, 112, 152, 97, 137, 111, 151, 104, 144, 120, 160, 114, 154, 108, 148, 92, 132, 107, 147, 90, 130, 106, 146, 118, 158, 102, 142, 87, 127, 96, 136) L = (1, 84)(2, 90)(3, 94)(4, 93)(5, 97)(6, 96)(7, 81)(8, 104)(9, 106)(10, 105)(11, 107)(12, 82)(13, 110)(14, 109)(15, 111)(16, 83)(17, 88)(18, 92)(19, 112)(20, 85)(21, 87)(22, 86)(23, 120)(24, 119)(25, 118)(26, 117)(27, 89)(28, 91)(29, 116)(30, 115)(31, 103)(32, 95)(33, 108)(34, 98)(35, 100)(36, 99)(37, 102)(38, 101)(39, 114)(40, 113)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 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 E23.249 Graph:: bipartite v = 6 e = 80 f = 30 degree seq :: [ 20^4, 40^2 ] E23.264 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10, 20}) Quotient :: dipole Aut^+ = C20 x C2 (small group id <40, 9>) Aut = C2 x D40 (small group id <80, 37>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y3^2 * Y2^-1, (R * Y3)^2, (Y1^-1, Y3), (Y3^-1, Y2^-1), (Y2^-1, Y1^-1), (R * Y2)^2, (R * Y1)^2, Y1 * Y3^-1 * Y1 * Y2^-1 * Y1, Y3 * Y1 * Y2 * Y3 * Y2 * Y3 * Y2, Y2 * Y3 * Y1 * Y3^2 * Y2^2, Y1^-1 * Y2^-2 * Y1^-2 * Y3^-1 * Y1^-1 * Y3^-1, Y2^12 * Y1^2 ] Map:: non-degenerate R = (1, 41, 2, 42, 8, 48, 14, 54, 26, 66, 40, 80, 36, 76, 22, 62, 18, 58, 5, 45)(3, 43, 9, 49, 23, 63, 30, 70, 37, 77, 34, 74, 20, 60, 7, 47, 12, 52, 15, 55)(4, 44, 10, 50, 24, 64, 29, 69, 38, 78, 33, 73, 19, 59, 6, 46, 11, 51, 17, 57)(13, 53, 25, 65, 39, 79, 35, 75, 21, 61, 28, 68, 32, 72, 16, 56, 27, 67, 31, 71)(81, 121, 83, 123, 93, 133, 109, 149, 116, 156, 100, 140, 112, 152, 97, 137, 88, 128, 103, 143, 119, 159, 113, 153, 98, 138, 92, 132, 107, 147, 90, 130, 106, 146, 117, 157, 101, 141, 86, 126)(82, 122, 89, 129, 105, 145, 118, 158, 102, 142, 87, 127, 96, 136, 84, 124, 94, 134, 110, 150, 115, 155, 99, 139, 85, 125, 95, 135, 111, 151, 104, 144, 120, 160, 114, 154, 108, 148, 91, 131) L = (1, 84)(2, 90)(3, 94)(4, 93)(5, 97)(6, 96)(7, 81)(8, 104)(9, 106)(10, 105)(11, 107)(12, 82)(13, 110)(14, 109)(15, 88)(16, 83)(17, 111)(18, 91)(19, 112)(20, 85)(21, 87)(22, 86)(23, 120)(24, 119)(25, 117)(26, 118)(27, 89)(28, 92)(29, 115)(30, 116)(31, 103)(32, 95)(33, 108)(34, 98)(35, 100)(36, 99)(37, 102)(38, 101)(39, 114)(40, 113)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 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 E23.252 Graph:: bipartite v = 6 e = 80 f = 30 degree seq :: [ 20^4, 40^2 ] E23.265 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10, 20}) Quotient :: dipole Aut^+ = C20 x C2 (small group id <40, 9>) Aut = C2 x D40 (small group id <80, 37>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y3, Y2), (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y1 * Y2 * Y1, (R * Y2)^2, Y3 * Y1 * Y3^-1 * Y1, Y2^5 * Y1, Y2 * Y3^4 * Y1, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 41, 2, 42)(3, 43, 7, 47)(4, 44, 8, 48)(5, 45, 9, 49)(6, 46, 10, 50)(11, 51, 19, 59)(12, 52, 20, 60)(13, 53, 21, 61)(14, 54, 22, 62)(15, 55, 23, 63)(16, 56, 24, 64)(17, 57, 25, 65)(18, 58, 26, 66)(27, 67, 33, 73)(28, 68, 34, 74)(29, 69, 35, 75)(30, 70, 36, 76)(31, 71, 37, 77)(32, 72, 38, 78)(39, 79, 40, 80)(81, 121, 83, 123, 91, 131, 104, 144, 89, 129, 82, 122, 87, 127, 99, 139, 96, 136, 85, 125)(84, 124, 92, 132, 107, 147, 117, 157, 103, 143, 88, 128, 100, 140, 113, 153, 111, 151, 95, 135)(86, 126, 93, 133, 108, 148, 118, 158, 105, 145, 90, 130, 101, 141, 114, 154, 112, 152, 97, 137)(94, 134, 106, 146, 115, 155, 120, 160, 116, 156, 102, 142, 98, 138, 109, 149, 119, 159, 110, 150) L = (1, 84)(2, 88)(3, 92)(4, 94)(5, 95)(6, 81)(7, 100)(8, 102)(9, 103)(10, 82)(11, 107)(12, 106)(13, 83)(14, 105)(15, 110)(16, 111)(17, 85)(18, 86)(19, 113)(20, 98)(21, 87)(22, 97)(23, 116)(24, 117)(25, 89)(26, 90)(27, 115)(28, 91)(29, 93)(30, 118)(31, 119)(32, 96)(33, 109)(34, 99)(35, 101)(36, 112)(37, 120)(38, 104)(39, 108)(40, 114)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 8, 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 E23.271 Graph:: bipartite v = 24 e = 80 f = 12 degree seq :: [ 4^20, 20^4 ] E23.266 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10, 20}) Quotient :: dipole Aut^+ = C20 x C2 (small group id <40, 9>) Aut = C2 x D40 (small group id <80, 37>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y3^-1, Y2^-1), (R * Y3)^2, Y2 * Y1 * Y2^-1 * Y1, (R * Y1)^2, (R * Y2)^2, Y3 * Y1 * Y3^-1 * Y1, Y2^-1 * Y1 * Y3^2 * Y2^-1, Y2 * Y1 * Y3^-1 * Y2 * Y3^-1, Y3^-4 * Y2^-6, Y3^20 ] Map:: non-degenerate R = (1, 41, 2, 42)(3, 43, 7, 47)(4, 44, 8, 48)(5, 45, 9, 49)(6, 46, 10, 50)(11, 51, 14, 54)(12, 52, 19, 59)(13, 53, 15, 55)(16, 56, 18, 58)(17, 57, 20, 60)(21, 61, 23, 63)(22, 62, 24, 64)(25, 65, 27, 67)(26, 66, 28, 68)(29, 69, 31, 71)(30, 70, 32, 72)(33, 73, 35, 75)(34, 74, 36, 76)(37, 77, 39, 79)(38, 78, 40, 80)(81, 121, 83, 123, 91, 131, 101, 141, 109, 149, 117, 157, 113, 153, 105, 145, 96, 136, 85, 125)(82, 122, 87, 127, 94, 134, 103, 143, 111, 151, 119, 159, 115, 155, 107, 147, 98, 138, 89, 129)(84, 124, 92, 132, 102, 142, 110, 150, 118, 158, 116, 156, 108, 148, 100, 140, 90, 130, 95, 135)(86, 126, 93, 133, 88, 128, 99, 139, 104, 144, 112, 152, 120, 160, 114, 154, 106, 146, 97, 137) L = (1, 84)(2, 88)(3, 92)(4, 94)(5, 95)(6, 81)(7, 99)(8, 91)(9, 93)(10, 82)(11, 102)(12, 103)(13, 83)(14, 104)(15, 87)(16, 90)(17, 85)(18, 86)(19, 101)(20, 89)(21, 110)(22, 111)(23, 112)(24, 109)(25, 100)(26, 96)(27, 97)(28, 98)(29, 118)(30, 119)(31, 120)(32, 117)(33, 108)(34, 105)(35, 106)(36, 107)(37, 116)(38, 115)(39, 114)(40, 113)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 8, 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 E23.272 Graph:: simple bipartite v = 24 e = 80 f = 12 degree seq :: [ 4^20, 20^4 ] E23.267 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10, 20}) Quotient :: dipole Aut^+ = C20 x C2 (small group id <40, 9>) Aut = C2 x D40 (small group id <80, 37>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3 * Y1 * Y3^-1 * Y1, (Y3, Y2), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2^-1 * Y1 * Y2 * Y1, Y3^-2 * Y1 * Y2^-3, Y2^-1 * Y3^-1 * Y2^-2 * Y3^-1 * Y1, Y2^-1 * Y3^-1 * Y1 * Y2 * Y3 * Y1, Y3^4 * Y2^-4, Y2^10 ] Map:: non-degenerate R = (1, 41, 2, 42)(3, 43, 7, 47)(4, 44, 8, 48)(5, 45, 9, 49)(6, 46, 10, 50)(11, 51, 19, 59)(12, 52, 20, 60)(13, 53, 21, 61)(14, 54, 22, 62)(15, 55, 23, 63)(16, 56, 24, 64)(17, 57, 25, 65)(18, 58, 26, 66)(27, 67, 33, 73)(28, 68, 34, 74)(29, 69, 35, 75)(30, 70, 36, 76)(31, 71, 37, 77)(32, 72, 38, 78)(39, 79, 40, 80)(81, 121, 83, 123, 91, 131, 106, 146, 114, 154, 120, 160, 116, 156, 102, 142, 96, 136, 85, 125)(82, 122, 87, 127, 99, 139, 98, 138, 108, 148, 119, 159, 110, 150, 94, 134, 104, 144, 89, 129)(84, 124, 92, 132, 105, 145, 90, 130, 101, 141, 113, 153, 112, 152, 115, 155, 111, 151, 95, 135)(86, 126, 93, 133, 107, 147, 118, 158, 109, 149, 117, 157, 103, 143, 88, 128, 100, 140, 97, 137) L = (1, 84)(2, 88)(3, 92)(4, 94)(5, 95)(6, 81)(7, 100)(8, 102)(9, 103)(10, 82)(11, 105)(12, 104)(13, 83)(14, 109)(15, 110)(16, 111)(17, 85)(18, 86)(19, 97)(20, 96)(21, 87)(22, 115)(23, 116)(24, 117)(25, 89)(26, 90)(27, 91)(28, 93)(29, 114)(30, 118)(31, 119)(32, 98)(33, 99)(34, 101)(35, 108)(36, 112)(37, 120)(38, 106)(39, 107)(40, 113)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 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 E23.270 Graph:: simple bipartite v = 24 e = 80 f = 12 degree seq :: [ 4^20, 20^4 ] E23.268 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10, 20}) Quotient :: dipole Aut^+ = C20 x C2 (small group id <40, 9>) Aut = C2 x D40 (small group id <80, 37>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y3, Y2^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2^-1 * Y1 * Y2 * Y1, Y3 * Y1 * Y3^-1 * Y1, Y3^-1 * Y2^-1 * Y3^-1 * Y2^-2, Y3^-1 * Y2 * Y3^-5, (Y2^-1 * Y3)^4 ] Map:: non-degenerate R = (1, 41, 2, 42)(3, 43, 7, 47)(4, 44, 8, 48)(5, 45, 9, 49)(6, 46, 10, 50)(11, 51, 19, 59)(12, 52, 20, 60)(13, 53, 21, 61)(14, 54, 22, 62)(15, 55, 23, 63)(16, 56, 24, 64)(17, 57, 25, 65)(18, 58, 26, 66)(27, 67, 33, 73)(28, 68, 34, 74)(29, 69, 35, 75)(30, 70, 36, 76)(31, 71, 37, 77)(32, 72, 38, 78)(39, 79, 40, 80)(81, 121, 83, 123, 91, 131, 98, 138, 108, 148, 119, 159, 110, 150, 94, 134, 96, 136, 85, 125)(82, 122, 87, 127, 99, 139, 106, 146, 114, 154, 120, 160, 116, 156, 102, 142, 104, 144, 89, 129)(84, 124, 92, 132, 97, 137, 86, 126, 93, 133, 107, 147, 112, 152, 109, 149, 111, 151, 95, 135)(88, 128, 100, 140, 105, 145, 90, 130, 101, 141, 113, 153, 118, 158, 115, 155, 117, 157, 103, 143) L = (1, 84)(2, 88)(3, 92)(4, 94)(5, 95)(6, 81)(7, 100)(8, 102)(9, 103)(10, 82)(11, 97)(12, 96)(13, 83)(14, 109)(15, 110)(16, 111)(17, 85)(18, 86)(19, 105)(20, 104)(21, 87)(22, 115)(23, 116)(24, 117)(25, 89)(26, 90)(27, 91)(28, 93)(29, 108)(30, 112)(31, 119)(32, 98)(33, 99)(34, 101)(35, 114)(36, 118)(37, 120)(38, 106)(39, 107)(40, 113)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 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 E23.269 Graph:: simple bipartite v = 24 e = 80 f = 12 degree seq :: [ 4^20, 20^4 ] E23.269 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10, 20}) Quotient :: dipole Aut^+ = C20 x C2 (small group id <40, 9>) Aut = C2 x D40 (small group id <80, 37>) |r| :: 2 Presentation :: [ R^2, Y3^2 * Y1^-2, Y3^4, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, (Y2, Y1^-1), (Y3, Y1^-1), (Y2, Y3^-1), Y3^-1 * Y2^-5, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-2 ] Map:: non-degenerate R = (1, 41, 2, 42, 8, 48, 5, 45)(3, 43, 9, 49, 21, 61, 15, 55)(4, 44, 10, 50, 7, 47, 12, 52)(6, 46, 11, 51, 22, 62, 18, 58)(13, 53, 23, 63, 35, 75, 31, 71)(14, 54, 24, 64, 16, 56, 25, 65)(17, 57, 26, 66, 20, 60, 28, 68)(19, 59, 27, 67, 36, 76, 34, 74)(29, 69, 37, 77, 33, 73, 40, 80)(30, 70, 38, 78, 32, 72, 39, 79)(81, 121, 83, 123, 93, 133, 109, 149, 100, 140, 87, 127, 96, 136, 112, 152, 116, 156, 102, 142, 88, 128, 101, 141, 115, 155, 113, 153, 97, 137, 84, 124, 94, 134, 110, 150, 99, 139, 86, 126)(82, 122, 89, 129, 103, 143, 117, 157, 108, 148, 92, 132, 105, 145, 119, 159, 114, 154, 98, 138, 85, 125, 95, 135, 111, 151, 120, 160, 106, 146, 90, 130, 104, 144, 118, 158, 107, 147, 91, 131) L = (1, 84)(2, 90)(3, 94)(4, 88)(5, 92)(6, 97)(7, 81)(8, 87)(9, 104)(10, 85)(11, 106)(12, 82)(13, 110)(14, 101)(15, 105)(16, 83)(17, 102)(18, 108)(19, 113)(20, 86)(21, 96)(22, 100)(23, 118)(24, 95)(25, 89)(26, 98)(27, 120)(28, 91)(29, 99)(30, 115)(31, 119)(32, 93)(33, 116)(34, 117)(35, 112)(36, 109)(37, 107)(38, 111)(39, 103)(40, 114)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 4, 20, 4, 20, 4, 20, 4, 20 ), ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 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 E23.268 Graph:: bipartite v = 12 e = 80 f = 24 degree seq :: [ 8^10, 40^2 ] E23.270 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10, 20}) Quotient :: dipole Aut^+ = C20 x C2 (small group id <40, 9>) Aut = C2 x D40 (small group id <80, 37>) |r| :: 2 Presentation :: [ R^2, (Y3, Y1), Y3^2 * Y1^-2, Y3^2 * Y1^2, (R * Y3)^2, Y1^4, (R * Y1)^2, (Y2, Y3^-1), (R * Y2)^2, (Y2, Y1^-1), Y2^5 * Y1^-1, Y2^-1 * Y3 * Y1 * Y2 * Y3^-1 * 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 ] Map:: non-degenerate R = (1, 41, 2, 42, 8, 48, 5, 45)(3, 43, 9, 49, 21, 61, 15, 55)(4, 44, 10, 50, 7, 47, 12, 52)(6, 46, 11, 51, 22, 62, 18, 58)(13, 53, 23, 63, 35, 75, 30, 70)(14, 54, 24, 64, 16, 56, 25, 65)(17, 57, 26, 66, 20, 60, 28, 68)(19, 59, 27, 67, 36, 76, 33, 73)(29, 69, 37, 77, 31, 71, 38, 78)(32, 72, 39, 79, 34, 74, 40, 80)(81, 121, 83, 123, 93, 133, 107, 147, 91, 131, 82, 122, 89, 129, 103, 143, 116, 156, 102, 142, 88, 128, 101, 141, 115, 155, 113, 153, 98, 138, 85, 125, 95, 135, 110, 150, 99, 139, 86, 126)(84, 124, 94, 134, 109, 149, 119, 159, 106, 146, 90, 130, 104, 144, 117, 157, 114, 154, 100, 140, 87, 127, 96, 136, 111, 151, 120, 160, 108, 148, 92, 132, 105, 145, 118, 158, 112, 152, 97, 137) L = (1, 84)(2, 90)(3, 94)(4, 88)(5, 92)(6, 97)(7, 81)(8, 87)(9, 104)(10, 85)(11, 106)(12, 82)(13, 109)(14, 101)(15, 105)(16, 83)(17, 102)(18, 108)(19, 112)(20, 86)(21, 96)(22, 100)(23, 117)(24, 95)(25, 89)(26, 98)(27, 119)(28, 91)(29, 115)(30, 118)(31, 93)(32, 116)(33, 120)(34, 99)(35, 111)(36, 114)(37, 110)(38, 103)(39, 113)(40, 107)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 4, 20, 4, 20, 4, 20, 4, 20 ), ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 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 E23.267 Graph:: bipartite v = 12 e = 80 f = 24 degree seq :: [ 8^10, 40^2 ] E23.271 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10, 20}) Quotient :: dipole Aut^+ = C20 x C2 (small group id <40, 9>) Aut = C2 x D40 (small group id <80, 37>) |r| :: 2 Presentation :: [ R^2, Y3^2 * Y1^-2, (Y3^-1 * Y1^-1)^2, Y1^-2 * Y3^-2, Y1^4, (R * Y1)^2, (Y3^-1, Y2^-1), (R * Y3)^2, (Y2, Y1^-1), (Y3 * Y1^-1)^2, (R * Y2)^2, Y2^-5 * Y1^-1, Y2^-1 * Y3 * Y1 * Y2 * Y3^-1 * 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 ] Map:: non-degenerate R = (1, 41, 2, 42, 8, 48, 5, 45)(3, 43, 9, 49, 21, 61, 15, 55)(4, 44, 10, 50, 7, 47, 12, 52)(6, 46, 11, 51, 22, 62, 18, 58)(13, 53, 23, 63, 35, 75, 31, 71)(14, 54, 24, 64, 16, 56, 25, 65)(17, 57, 26, 66, 20, 60, 28, 68)(19, 59, 27, 67, 36, 76, 29, 69)(30, 70, 37, 77, 32, 72, 38, 78)(33, 73, 39, 79, 34, 74, 40, 80)(81, 121, 83, 123, 93, 133, 109, 149, 98, 138, 85, 125, 95, 135, 111, 151, 116, 156, 102, 142, 88, 128, 101, 141, 115, 155, 107, 147, 91, 131, 82, 122, 89, 129, 103, 143, 99, 139, 86, 126)(84, 124, 94, 134, 110, 150, 120, 160, 108, 148, 92, 132, 105, 145, 118, 158, 114, 154, 100, 140, 87, 127, 96, 136, 112, 152, 119, 159, 106, 146, 90, 130, 104, 144, 117, 157, 113, 153, 97, 137) L = (1, 84)(2, 90)(3, 94)(4, 88)(5, 92)(6, 97)(7, 81)(8, 87)(9, 104)(10, 85)(11, 106)(12, 82)(13, 110)(14, 101)(15, 105)(16, 83)(17, 102)(18, 108)(19, 113)(20, 86)(21, 96)(22, 100)(23, 117)(24, 95)(25, 89)(26, 98)(27, 119)(28, 91)(29, 120)(30, 115)(31, 118)(32, 93)(33, 116)(34, 99)(35, 112)(36, 114)(37, 111)(38, 103)(39, 109)(40, 107)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 4, 20, 4, 20, 4, 20, 4, 20 ), ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) } Outer automorphisms :: reflexible Dual of E23.265 Graph:: bipartite v = 12 e = 80 f = 24 degree seq :: [ 8^10, 40^2 ] E23.272 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 10, 20}) Quotient :: dipole Aut^+ = C20 x C2 (small group id <40, 9>) Aut = C2 x D40 (small group id <80, 37>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-1, Y1^4, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1), (Y3^-1 * Y1^-1)^2, Y1^4, (R * Y2 * Y3^-1)^2, Y2^10 * Y1^2, (Y3 * Y2^-1)^10 ] Map:: non-degenerate R = (1, 41, 2, 42, 6, 46, 4, 44)(3, 43, 7, 47, 13, 53, 10, 50)(5, 45, 8, 48, 14, 54, 11, 51)(9, 49, 15, 55, 21, 61, 18, 58)(12, 52, 16, 56, 22, 62, 19, 59)(17, 57, 23, 63, 29, 69, 26, 66)(20, 60, 24, 64, 30, 70, 27, 67)(25, 65, 31, 71, 37, 77, 34, 74)(28, 68, 32, 72, 38, 78, 35, 75)(33, 73, 39, 79, 36, 76, 40, 80)(81, 121, 83, 123, 89, 129, 97, 137, 105, 145, 113, 153, 118, 158, 110, 150, 102, 142, 94, 134, 86, 126, 93, 133, 101, 141, 109, 149, 117, 157, 116, 156, 108, 148, 100, 140, 92, 132, 85, 125)(82, 122, 87, 127, 95, 135, 103, 143, 111, 151, 119, 159, 115, 155, 107, 147, 99, 139, 91, 131, 84, 124, 90, 130, 98, 138, 106, 146, 114, 154, 120, 160, 112, 152, 104, 144, 96, 136, 88, 128) L = (1, 82)(2, 86)(3, 87)(4, 81)(5, 88)(6, 84)(7, 93)(8, 94)(9, 95)(10, 83)(11, 85)(12, 96)(13, 90)(14, 91)(15, 101)(16, 102)(17, 103)(18, 89)(19, 92)(20, 104)(21, 98)(22, 99)(23, 109)(24, 110)(25, 111)(26, 97)(27, 100)(28, 112)(29, 106)(30, 107)(31, 117)(32, 118)(33, 119)(34, 105)(35, 108)(36, 120)(37, 114)(38, 115)(39, 116)(40, 113)(41, 121)(42, 122)(43, 123)(44, 124)(45, 125)(46, 126)(47, 127)(48, 128)(49, 129)(50, 130)(51, 131)(52, 132)(53, 133)(54, 134)(55, 135)(56, 136)(57, 137)(58, 138)(59, 139)(60, 140)(61, 141)(62, 142)(63, 143)(64, 144)(65, 145)(66, 146)(67, 147)(68, 148)(69, 149)(70, 150)(71, 151)(72, 152)(73, 153)(74, 154)(75, 155)(76, 156)(77, 157)(78, 158)(79, 159)(80, 160) local type(s) :: { ( 4, 20, 4, 20, 4, 20, 4, 20 ), ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 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 E23.266 Graph:: bipartite v = 12 e = 80 f = 24 degree seq :: [ 8^10, 40^2 ] E23.273 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 14, 21}) Quotient :: dipole Aut^+ = C7 x S3 (small group id <42, 3>) Aut = S3 x D14 (small group id <84, 8>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^3, (Y2 * Y1)^2, (R * Y1)^2, R * Y2 * R * Y2^-1, (R * Y3)^2, Y2 * Y3^-1 * Y2 * Y3, Y1 * Y2^-1 * Y3 * Y1 * Y3^-1, Y2^-1 * Y1 * Y3^-7 ] Map:: non-degenerate R = (1, 43, 2, 44)(3, 45, 9, 51)(4, 46, 13, 55)(5, 47, 7, 49)(6, 48, 17, 59)(8, 50, 14, 56)(10, 52, 16, 58)(11, 53, 19, 61)(12, 54, 20, 62)(15, 57, 21, 63)(18, 60, 22, 64)(23, 65, 25, 67)(24, 66, 29, 71)(26, 68, 31, 73)(27, 69, 37, 79)(28, 70, 32, 74)(30, 72, 41, 83)(33, 75, 38, 80)(34, 76, 40, 82)(35, 77, 42, 84)(36, 78, 39, 81)(85, 127, 87, 129, 89, 131)(86, 128, 91, 133, 93, 135)(88, 130, 98, 140, 95, 137)(90, 132, 100, 142, 96, 138)(92, 134, 97, 139, 103, 145)(94, 136, 101, 143, 104, 146)(99, 141, 107, 149, 110, 152)(102, 144, 108, 150, 112, 154)(105, 147, 115, 157, 109, 151)(106, 148, 116, 158, 113, 155)(111, 153, 122, 164, 119, 161)(114, 156, 124, 166, 120, 162)(117, 159, 121, 163, 126, 168)(118, 160, 125, 167, 123, 165) L = (1, 88)(2, 92)(3, 95)(4, 99)(5, 98)(6, 85)(7, 103)(8, 105)(9, 97)(10, 86)(11, 107)(12, 87)(13, 109)(14, 110)(15, 111)(16, 89)(17, 93)(18, 90)(19, 115)(20, 91)(21, 117)(22, 94)(23, 119)(24, 96)(25, 121)(26, 122)(27, 123)(28, 100)(29, 101)(30, 102)(31, 126)(32, 104)(33, 120)(34, 106)(35, 118)(36, 108)(37, 124)(38, 125)(39, 116)(40, 112)(41, 113)(42, 114)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 28, 42, 28, 42 ), ( 28, 42, 28, 42, 28, 42 ) } Outer automorphisms :: reflexible Dual of E23.279 Graph:: simple bipartite v = 35 e = 84 f = 5 degree seq :: [ 4^21, 6^14 ] E23.274 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 14, 21}) Quotient :: dipole Aut^+ = C7 x S3 (small group id <42, 3>) Aut = S3 x D14 (small group id <84, 8>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^3, (Y1 * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y3 * Y2^-1 * Y3^-1, R * Y2 * R * Y2^-1, Y2^-1 * Y1 * Y3^-1 * Y1 * Y3, Y1 * Y3^2 * Y2^-1 * Y3^5, Y1 * Y2 * Y3^-3 * Y2 * Y3 * Y1 * Y3^-2 * Y2 * Y1 * Y3^-3 ] Map:: non-degenerate R = (1, 43, 2, 44)(3, 45, 9, 51)(4, 46, 13, 55)(5, 47, 7, 49)(6, 48, 17, 59)(8, 50, 11, 53)(10, 52, 12, 54)(14, 56, 19, 61)(15, 57, 20, 62)(16, 58, 21, 63)(18, 60, 22, 64)(23, 65, 31, 73)(24, 66, 33, 75)(25, 67, 26, 68)(27, 69, 37, 79)(28, 70, 29, 71)(30, 72, 41, 83)(32, 74, 35, 77)(34, 76, 36, 78)(38, 80, 42, 84)(39, 81, 40, 82)(85, 127, 87, 129, 89, 131)(86, 128, 91, 133, 93, 135)(88, 130, 98, 140, 95, 137)(90, 132, 100, 142, 96, 138)(92, 134, 103, 145, 97, 139)(94, 136, 105, 147, 101, 143)(99, 141, 107, 149, 110, 152)(102, 144, 108, 150, 112, 154)(104, 146, 109, 151, 115, 157)(106, 148, 113, 155, 117, 159)(111, 153, 122, 164, 119, 161)(114, 156, 124, 166, 120, 162)(116, 158, 126, 168, 121, 163)(118, 160, 123, 165, 125, 167) L = (1, 88)(2, 92)(3, 95)(4, 99)(5, 98)(6, 85)(7, 97)(8, 104)(9, 103)(10, 86)(11, 107)(12, 87)(13, 109)(14, 110)(15, 111)(16, 89)(17, 91)(18, 90)(19, 115)(20, 116)(21, 93)(22, 94)(23, 119)(24, 96)(25, 121)(26, 122)(27, 123)(28, 100)(29, 101)(30, 102)(31, 126)(32, 124)(33, 105)(34, 106)(35, 125)(36, 108)(37, 120)(38, 118)(39, 117)(40, 112)(41, 113)(42, 114)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 28, 42, 28, 42 ), ( 28, 42, 28, 42, 28, 42 ) } Outer automorphisms :: reflexible Dual of E23.280 Graph:: simple bipartite v = 35 e = 84 f = 5 degree seq :: [ 4^21, 6^14 ] E23.275 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 14, 21}) Quotient :: dipole Aut^+ = C7 x S3 (small group id <42, 3>) Aut = S3 x D14 (small group id <84, 8>) |r| :: 2 Presentation :: [ Y3^2, R^2, Y1^3, Y2 * Y1^-1 * Y2^-1 * Y1^-1, (R * Y3)^2, (Y3 * Y1)^2, (R * Y1)^2, Y2^-1 * Y3 * Y2 * Y1 * Y3, R * Y2 * Y1 * R * Y2, Y3 * Y2^-2 * Y3 * Y2^2, Y2 * Y3 * Y1 * Y2^-1 * Y3 * Y1, Y2^-1 * Y1^-1 * Y2^-2 * Y3 * Y2^-4, Y2^-1 * Y1 * Y2^-2 * Y1 * Y2^-2 * Y1 * Y2^-2 * Y1 * Y2^-2 * Y1 * Y2^-2 * Y1 * Y2^-2 * Y1 * Y2^-1 * Y1 ] Map:: non-degenerate R = (1, 43, 2, 44, 5, 47)(3, 45, 10, 52, 7, 49)(4, 46, 13, 55, 8, 50)(6, 48, 16, 58, 9, 51)(11, 53, 19, 61, 23, 65)(12, 54, 20, 62, 14, 56)(15, 57, 17, 59, 21, 63)(18, 60, 22, 64, 28, 70)(24, 66, 35, 77, 31, 73)(25, 67, 32, 74, 26, 68)(27, 69, 33, 75, 29, 71)(30, 72, 40, 82, 34, 76)(36, 78, 39, 81, 41, 83)(37, 79, 42, 84, 38, 80)(85, 127, 87, 129, 95, 137, 108, 150, 120, 162, 117, 159, 105, 147, 97, 139, 104, 146, 116, 158, 126, 168, 114, 156, 102, 144, 90, 132)(86, 128, 91, 133, 103, 145, 115, 157, 123, 165, 111, 153, 99, 141, 88, 130, 98, 140, 109, 151, 122, 164, 118, 160, 106, 148, 93, 135)(89, 131, 94, 136, 107, 149, 119, 161, 125, 167, 113, 155, 101, 143, 92, 134, 96, 138, 110, 152, 121, 163, 124, 166, 112, 154, 100, 142) L = (1, 88)(2, 92)(3, 96)(4, 85)(5, 97)(6, 101)(7, 104)(8, 86)(9, 105)(10, 98)(11, 109)(12, 87)(13, 89)(14, 94)(15, 100)(16, 99)(17, 90)(18, 111)(19, 110)(20, 91)(21, 93)(22, 113)(23, 116)(24, 121)(25, 95)(26, 103)(27, 102)(28, 117)(29, 106)(30, 125)(31, 126)(32, 107)(33, 112)(34, 120)(35, 122)(36, 118)(37, 108)(38, 119)(39, 124)(40, 123)(41, 114)(42, 115)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 4, 42, 4, 42, 4, 42 ), ( 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42 ) } Outer automorphisms :: reflexible Dual of E23.277 Graph:: bipartite v = 17 e = 84 f = 23 degree seq :: [ 6^14, 28^3 ] E23.276 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 14, 21}) Quotient :: dipole Aut^+ = C7 x S3 (small group id <42, 3>) Aut = S3 x D14 (small group id <84, 8>) |r| :: 2 Presentation :: [ Y3^2, R^2, Y1^3, Y2^-1 * Y1^-1 * Y2 * Y1^-1, (Y1 * Y3)^2, (R * Y3)^2, (R * Y1)^2, R * Y2 * Y1^-1 * R * Y2, Y2 * Y1^-1 * Y3 * Y2^-1 * Y3, Y3 * Y1^-1 * Y2^-1 * Y3 * Y1^-1 * Y2, Y1^-1 * Y2^3 * Y3 * Y2^4, Y1^-1 * Y3 * Y2^2 * Y1 * Y2 * Y3 * Y2^2 * Y1 * Y2 * Y3 * Y2^2 * Y1 * Y2 * Y3 * Y2^2 * Y1 * Y2^-2 * Y1^-1 * Y2^-1 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 43, 2, 44, 5, 47)(3, 45, 10, 52, 7, 49)(4, 46, 13, 55, 8, 50)(6, 48, 16, 58, 9, 51)(11, 53, 19, 61, 23, 65)(12, 54, 14, 56, 20, 62)(15, 57, 21, 63, 17, 59)(18, 60, 22, 64, 28, 70)(24, 66, 35, 77, 31, 73)(25, 67, 26, 68, 32, 74)(27, 69, 29, 71, 33, 75)(30, 72, 40, 82, 34, 76)(36, 78, 41, 83, 39, 81)(37, 79, 38, 80, 42, 84)(85, 127, 87, 129, 95, 137, 108, 150, 120, 162, 117, 159, 105, 147, 92, 134, 104, 146, 116, 158, 126, 168, 114, 156, 102, 144, 90, 132)(86, 128, 91, 133, 103, 145, 115, 157, 125, 167, 113, 155, 101, 143, 97, 139, 96, 138, 110, 152, 121, 163, 118, 160, 106, 148, 93, 135)(88, 130, 98, 140, 109, 151, 122, 164, 124, 166, 112, 154, 100, 142, 89, 131, 94, 136, 107, 149, 119, 161, 123, 165, 111, 153, 99, 141) L = (1, 88)(2, 92)(3, 96)(4, 85)(5, 97)(6, 101)(7, 98)(8, 86)(9, 99)(10, 104)(11, 109)(12, 87)(13, 89)(14, 91)(15, 93)(16, 105)(17, 90)(18, 111)(19, 116)(20, 94)(21, 100)(22, 117)(23, 110)(24, 121)(25, 95)(26, 107)(27, 102)(28, 113)(29, 112)(30, 125)(31, 122)(32, 103)(33, 106)(34, 123)(35, 126)(36, 124)(37, 108)(38, 115)(39, 118)(40, 120)(41, 114)(42, 119)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 4, 42, 4, 42, 4, 42 ), ( 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42 ) } Outer automorphisms :: reflexible Dual of E23.278 Graph:: bipartite v = 17 e = 84 f = 23 degree seq :: [ 6^14, 28^3 ] E23.277 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 14, 21}) Quotient :: dipole Aut^+ = C7 x S3 (small group id <42, 3>) Aut = S3 x D14 (small group id <84, 8>) |r| :: 2 Presentation :: [ Y3^2, Y2^2, R^2, Y1 * Y3 * Y1^-1 * Y2, (R * Y1)^2, (R * Y3)^2, Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y3, Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y2, (R * Y2 * Y3)^2, Y3 * Y2 * Y1^-1 * Y3 * Y1 * Y2, Y1^3 * Y2 * Y1^2 * Y2 * Y1^2, (Y1^-2 * Y2 * Y3)^7 ] Map:: non-degenerate R = (1, 43, 2, 44, 6, 48, 16, 58, 29, 71, 36, 78, 24, 66, 12, 54, 22, 64, 34, 76, 41, 83, 42, 84, 35, 77, 23, 65, 9, 51, 19, 61, 32, 74, 40, 82, 28, 70, 15, 57, 5, 47)(3, 45, 8, 50, 21, 63, 30, 72, 39, 81, 27, 69, 14, 56, 20, 62, 7, 49, 18, 60, 33, 75, 38, 80, 26, 68, 13, 55, 4, 46, 11, 53, 17, 59, 31, 73, 37, 79, 25, 67, 10, 52)(85, 127, 87, 129)(86, 128, 91, 133)(88, 130, 96, 138)(89, 131, 97, 139)(90, 132, 101, 143)(92, 134, 106, 148)(93, 135, 104, 146)(94, 136, 107, 149)(95, 137, 103, 145)(98, 140, 108, 150)(99, 141, 111, 153)(100, 142, 114, 156)(102, 144, 118, 160)(105, 147, 116, 158)(109, 151, 120, 162)(110, 152, 119, 161)(112, 154, 121, 163)(113, 155, 122, 164)(115, 157, 125, 167)(117, 159, 124, 166)(123, 165, 126, 168) L = (1, 88)(2, 92)(3, 93)(4, 85)(5, 98)(6, 102)(7, 103)(8, 86)(9, 87)(10, 108)(11, 106)(12, 104)(13, 107)(14, 89)(15, 109)(16, 115)(17, 116)(18, 90)(19, 91)(20, 96)(21, 118)(22, 95)(23, 97)(24, 94)(25, 99)(26, 120)(27, 119)(28, 122)(29, 123)(30, 124)(31, 100)(32, 101)(33, 125)(34, 105)(35, 111)(36, 110)(37, 126)(38, 112)(39, 113)(40, 114)(41, 117)(42, 121)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 6, 28, 6, 28 ), ( 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28 ) } Outer automorphisms :: reflexible Dual of E23.275 Graph:: bipartite v = 23 e = 84 f = 17 degree seq :: [ 4^21, 42^2 ] E23.278 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 14, 21}) Quotient :: dipole Aut^+ = C7 x S3 (small group id <42, 3>) Aut = S3 x D14 (small group id <84, 8>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y1 * Y2 * Y1^-1 * Y3, (R * Y3)^2, (R * Y1)^2, (Y2 * Y3)^3, (R * Y2 * Y3)^2, Y2 * Y1 * Y3 * Y2 * Y3 * Y1^-1, Y3 * Y2 * Y3 * Y1 * Y3 * Y1^-1, Y1^2 * Y3 * Y1^-2 * Y2, Y1^7 * Y3 * Y2, Y1^-1 * Y3 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-2 ] Map:: non-degenerate R = (1, 43, 2, 44, 6, 48, 16, 58, 29, 71, 35, 77, 23, 65, 10, 52, 20, 62, 33, 75, 41, 83, 42, 84, 36, 78, 24, 66, 12, 54, 21, 63, 34, 76, 40, 82, 28, 70, 15, 57, 5, 47)(3, 45, 9, 51, 18, 60, 30, 72, 38, 80, 26, 68, 13, 55, 4, 46, 7, 49, 19, 61, 31, 73, 39, 81, 27, 69, 14, 56, 22, 64, 8, 50, 17, 59, 32, 74, 37, 79, 25, 67, 11, 53)(85, 127, 87, 129)(86, 128, 91, 133)(88, 130, 96, 138)(89, 131, 98, 140)(90, 132, 101, 143)(92, 134, 105, 147)(93, 135, 104, 146)(94, 136, 106, 148)(95, 137, 108, 150)(97, 139, 107, 149)(99, 141, 110, 152)(100, 142, 114, 156)(102, 144, 118, 160)(103, 145, 117, 159)(109, 151, 119, 161)(111, 153, 120, 162)(112, 154, 121, 163)(113, 155, 123, 165)(115, 157, 124, 166)(116, 158, 125, 167)(122, 164, 126, 168) L = (1, 88)(2, 92)(3, 94)(4, 85)(5, 95)(6, 102)(7, 104)(8, 86)(9, 105)(10, 87)(11, 89)(12, 106)(13, 108)(14, 107)(15, 111)(16, 115)(17, 117)(18, 90)(19, 118)(20, 91)(21, 93)(22, 96)(23, 98)(24, 97)(25, 120)(26, 119)(27, 99)(28, 122)(29, 121)(30, 125)(31, 100)(32, 124)(33, 101)(34, 103)(35, 110)(36, 109)(37, 113)(38, 112)(39, 126)(40, 116)(41, 114)(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) :: { ( 6, 28, 6, 28 ), ( 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28 ) } Outer automorphisms :: reflexible Dual of E23.276 Graph:: bipartite v = 23 e = 84 f = 17 degree seq :: [ 4^21, 42^2 ] E23.279 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 14, 21}) Quotient :: dipole Aut^+ = C7 x S3 (small group id <42, 3>) Aut = S3 x D14 (small group id <84, 8>) |r| :: 2 Presentation :: [ R^2, (Y2 * Y3^-1)^2, (Y2^-1 * Y1^-1)^2, Y3^-1 * Y1^-2 * Y3^-1, (R * Y1)^2, Y2^-1 * Y3^-1 * Y2 * Y1^-1, (R * Y3)^2, (Y1^-1 * R * Y2^-1)^2, Y1^-1 * Y3^2 * Y2^-2 * Y3^-1, (R * Y2 * Y3^-1)^2, (Y1 * Y3)^3, Y1^-1 * Y3 * Y1 * Y2^-2 * Y1^-1, Y1^-1 * Y2^-1 * Y1 * Y2^-1 * Y1^-2, Y2^-2 * Y1^-1 * Y3 * Y1 * Y3, Y3^-1 * Y1 * Y2^-5, Y2^-1 * Y1 * Y2^-2 * Y3^-1 * Y2^-2 ] Map:: non-degenerate R = (1, 43, 2, 44, 8, 50, 25, 67, 37, 79, 15, 57, 30, 72, 17, 59, 32, 74, 24, 66, 36, 78, 41, 83, 19, 61, 5, 47)(3, 45, 13, 55, 26, 68, 11, 53, 34, 76, 38, 80, 21, 63, 29, 71, 10, 52, 33, 75, 12, 54, 35, 77, 40, 82, 16, 58)(4, 46, 18, 60, 7, 49, 23, 65, 28, 70, 42, 84, 20, 62, 31, 73, 9, 51, 6, 48, 22, 64, 27, 69, 39, 81, 14, 56)(85, 127, 87, 129, 98, 140, 121, 163, 118, 160, 107, 149, 116, 158, 94, 136, 115, 157, 103, 145, 124, 166, 111, 153, 92, 134, 110, 152, 102, 144, 114, 156, 105, 147, 126, 168, 120, 162, 96, 138, 90, 132)(86, 128, 93, 135, 113, 155, 99, 141, 123, 165, 119, 161, 108, 150, 91, 133, 97, 139, 89, 131, 104, 146, 122, 164, 109, 151, 106, 148, 117, 159, 101, 143, 88, 130, 100, 142, 125, 167, 112, 154, 95, 137) L = (1, 88)(2, 94)(3, 99)(4, 103)(5, 105)(6, 97)(7, 85)(8, 91)(9, 114)(10, 89)(11, 90)(12, 86)(13, 115)(14, 122)(15, 124)(16, 126)(17, 87)(18, 113)(19, 123)(20, 121)(21, 125)(22, 116)(23, 117)(24, 110)(25, 96)(26, 101)(27, 95)(28, 92)(29, 98)(30, 104)(31, 100)(32, 93)(33, 102)(34, 108)(35, 107)(36, 106)(37, 112)(38, 111)(39, 120)(40, 109)(41, 118)(42, 119)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E23.273 Graph:: bipartite v = 5 e = 84 f = 35 degree seq :: [ 28^3, 42^2 ] E23.280 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 14, 21}) Quotient :: dipole Aut^+ = C7 x S3 (small group id <42, 3>) Aut = S3 x D14 (small group id <84, 8>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^2 * Y1, (R * Y3)^2, Y2^-2 * Y1^-1 * Y3, (R * Y1)^2, (Y3 * Y2^-1)^2, (Y2^-1 * Y1^-1)^2, Y3^-1 * Y1 * Y2^-1 * Y3 * Y2 * Y1^-1, Y1^-1 * Y2^-1 * Y1 * Y2^-1 * Y1^-2, Y3 * Y1^-1 * Y2^-2 * Y3^-1 * Y1^-1, (Y3 * Y1)^3, Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1^-1, (R * Y2 * Y3^-1)^2, Y3^-1 * Y1 * Y2^-1 * Y1^4, Y3^-3 * Y1^3 * Y2^-1, Y1^-2 * Y3 * Y1^-1 * Y2^17 ] Map:: non-degenerate R = (1, 43, 2, 44, 8, 50, 25, 67, 37, 79, 18, 60, 31, 73, 22, 64, 34, 76, 24, 66, 36, 78, 38, 80, 19, 61, 5, 47)(3, 45, 13, 55, 26, 68, 11, 53, 33, 75, 40, 82, 20, 62, 4, 46, 17, 59, 7, 49, 23, 65, 28, 70, 41, 83, 16, 58)(6, 48, 21, 63, 27, 69, 39, 81, 14, 56, 32, 74, 10, 52, 30, 72, 12, 54, 35, 77, 42, 84, 15, 57, 29, 71, 9, 51)(85, 127, 87, 129, 98, 140, 121, 163, 117, 159, 96, 138, 118, 160, 101, 143, 113, 155, 103, 145, 125, 167, 111, 153, 92, 134, 110, 152, 94, 136, 115, 157, 104, 146, 126, 168, 120, 162, 107, 149, 90, 132)(86, 128, 93, 135, 88, 130, 102, 144, 123, 165, 112, 154, 108, 150, 114, 156, 97, 139, 89, 131, 99, 141, 124, 166, 109, 151, 105, 147, 91, 133, 106, 148, 116, 158, 100, 142, 122, 164, 119, 161, 95, 137) L = (1, 88)(2, 94)(3, 99)(4, 103)(5, 98)(6, 106)(7, 85)(8, 91)(9, 87)(10, 89)(11, 118)(12, 86)(13, 115)(14, 122)(15, 125)(16, 121)(17, 116)(18, 126)(19, 124)(20, 123)(21, 110)(22, 113)(23, 114)(24, 90)(25, 96)(26, 93)(27, 108)(28, 92)(29, 102)(30, 101)(31, 100)(32, 104)(33, 105)(34, 97)(35, 107)(36, 95)(37, 112)(38, 111)(39, 117)(40, 120)(41, 119)(42, 109)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E23.274 Graph:: bipartite v = 5 e = 84 f = 35 degree seq :: [ 28^3, 42^2 ] E23.281 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 14, 21}) Quotient :: dipole Aut^+ = C42 (small group id <42, 6>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^3, Y1 * Y2 * Y1 * Y2^-1, Y1 * Y2^-1 * Y1 * Y2, (R * Y3)^2, (R * Y1)^2, Y1 * Y3^-1 * Y1 * Y3, (R * Y2)^2, (Y3, Y2), Y3^3 * Y1 * Y2^-1 * Y3^4 ] Map:: non-degenerate R = (1, 43, 2, 44)(3, 45, 7, 49)(4, 46, 8, 50)(5, 47, 9, 51)(6, 48, 10, 52)(11, 53, 17, 59)(12, 54, 18, 60)(13, 55, 19, 61)(14, 56, 20, 62)(15, 57, 21, 63)(16, 58, 22, 64)(23, 65, 29, 71)(24, 66, 30, 72)(25, 67, 31, 73)(26, 68, 32, 74)(27, 69, 33, 75)(28, 70, 34, 76)(35, 77, 41, 83)(36, 78, 37, 79)(38, 80, 40, 82)(39, 81, 42, 84)(85, 127, 87, 129, 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, 122, 164)(112, 154, 120, 162, 123, 165)(115, 157, 125, 167, 124, 166)(118, 160, 121, 163, 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, 121)(26, 122)(27, 99)(28, 100)(29, 125)(30, 102)(31, 120)(32, 124)(33, 105)(34, 106)(35, 126)(36, 108)(37, 114)(38, 118)(39, 111)(40, 112)(41, 123)(42, 117)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 28, 42, 28, 42 ), ( 28, 42, 28, 42, 28, 42 ) } Outer automorphisms :: reflexible Dual of E23.284 Graph:: simple bipartite v = 35 e = 84 f = 5 degree seq :: [ 4^21, 6^14 ] E23.282 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 14, 21}) Quotient :: dipole Aut^+ = C42 (small group id <42, 6>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ R^2, Y1^3, Y1 * Y3^-2, (R * Y2)^2, (R * Y3)^2, (Y2^-1, Y1^-1), (R * Y1)^2, (Y2, Y3), (Y1^-1 * Y3^-1)^2, Y3 * Y2^2 * Y1^2 * Y3 * Y2^-2, Y1 * Y2^2 * Y3 * Y1 * Y3 * Y2^-2, Y2^-3 * Y1 * Y3 * Y2^-4, (Y2^-1 * Y3)^21 ] Map:: non-degenerate R = (1, 43, 2, 44, 5, 47)(3, 45, 8, 50, 13, 55)(4, 46, 9, 51, 7, 49)(6, 48, 10, 52, 16, 58)(11, 53, 19, 61, 25, 67)(12, 54, 20, 62, 14, 56)(15, 57, 21, 63, 18, 60)(17, 59, 22, 64, 28, 70)(23, 65, 31, 73, 37, 79)(24, 66, 32, 74, 26, 68)(27, 69, 33, 75, 30, 72)(29, 71, 34, 76, 40, 82)(35, 77, 42, 84, 39, 81)(36, 78, 41, 83, 38, 80)(85, 127, 87, 129, 95, 137, 107, 149, 119, 161, 117, 159, 105, 147, 93, 135, 104, 146, 116, 158, 125, 167, 113, 155, 101, 143, 90, 132)(86, 128, 92, 134, 103, 145, 115, 157, 126, 168, 114, 156, 102, 144, 91, 133, 98, 140, 110, 152, 122, 164, 118, 160, 106, 148, 94, 136)(88, 130, 96, 138, 108, 150, 120, 162, 124, 166, 112, 154, 100, 142, 89, 131, 97, 139, 109, 151, 121, 163, 123, 165, 111, 153, 99, 141) L = (1, 88)(2, 93)(3, 96)(4, 86)(5, 91)(6, 99)(7, 85)(8, 104)(9, 89)(10, 105)(11, 108)(12, 92)(13, 98)(14, 87)(15, 94)(16, 102)(17, 111)(18, 90)(19, 116)(20, 97)(21, 100)(22, 117)(23, 120)(24, 103)(25, 110)(26, 95)(27, 106)(28, 114)(29, 123)(30, 101)(31, 125)(32, 109)(33, 112)(34, 119)(35, 124)(36, 115)(37, 122)(38, 107)(39, 118)(40, 126)(41, 121)(42, 113)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 4, 42, 4, 42, 4, 42 ), ( 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42, 4, 42 ) } Outer automorphisms :: reflexible Dual of E23.283 Graph:: bipartite v = 17 e = 84 f = 23 degree seq :: [ 6^14, 28^3 ] E23.283 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 14, 21}) Quotient :: dipole Aut^+ = C42 (small group id <42, 6>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y1 * Y2 * Y1^-1 * Y2, Y3^-3 * Y2, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y3, Y1), Y1^2 * Y3^-1 * Y1^4 * Y3^-1 * Y1, Y1^2 * Y2 * Y1^2 * Y3 * Y1^3, (Y1^-1 * Y3^-1)^14 ] Map:: non-degenerate R = (1, 43, 2, 44, 7, 49, 17, 59, 29, 71, 37, 79, 25, 67, 13, 55, 22, 64, 34, 76, 41, 83, 42, 84, 35, 77, 23, 65, 11, 53, 21, 63, 33, 75, 39, 81, 27, 69, 15, 57, 5, 47)(3, 45, 8, 50, 18, 60, 30, 72, 40, 82, 28, 70, 16, 58, 6, 48, 10, 52, 20, 62, 32, 74, 38, 80, 26, 68, 14, 56, 4, 46, 9, 51, 19, 61, 31, 73, 36, 78, 24, 66, 12, 54)(85, 127, 87, 129)(86, 128, 92, 134)(88, 130, 95, 137)(89, 131, 96, 138)(90, 132, 97, 139)(91, 133, 102, 144)(93, 135, 105, 147)(94, 136, 106, 148)(98, 140, 107, 149)(99, 141, 108, 150)(100, 142, 109, 151)(101, 143, 114, 156)(103, 145, 117, 159)(104, 146, 118, 160)(110, 152, 119, 161)(111, 153, 120, 162)(112, 154, 121, 163)(113, 155, 124, 166)(115, 157, 123, 165)(116, 158, 125, 167)(122, 164, 126, 168) L = (1, 88)(2, 93)(3, 95)(4, 97)(5, 98)(6, 85)(7, 103)(8, 105)(9, 106)(10, 86)(11, 90)(12, 107)(13, 87)(14, 109)(15, 110)(16, 89)(17, 115)(18, 117)(19, 118)(20, 91)(21, 94)(22, 92)(23, 100)(24, 119)(25, 96)(26, 121)(27, 122)(28, 99)(29, 120)(30, 123)(31, 125)(32, 101)(33, 104)(34, 102)(35, 112)(36, 126)(37, 108)(38, 113)(39, 116)(40, 111)(41, 114)(42, 124)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 6, 28, 6, 28 ), ( 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28, 6, 28 ) } Outer automorphisms :: reflexible Dual of E23.282 Graph:: bipartite v = 23 e = 84 f = 17 degree seq :: [ 4^21, 42^2 ] E23.284 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 14, 21}) Quotient :: dipole Aut^+ = C42 (small group id <42, 6>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ R^2, (Y2, Y1), Y2^-2 * Y3^2, (Y3, Y2^-1), (Y3, Y1^-1), (R * Y2)^2, (Y3 * Y2^-1)^2, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y1^-3 * Y2^-1 * Y3^-1, Y1^-1 * Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1, Y1 * Y2^-1 * Y1^2 * Y2^-2 * Y1, Y2^-1 * Y1 * Y3^-1 * Y2^-4, Y2^-1 * Y1^2 * Y3^-1 * Y1^2 * Y3^-1, Y2^-1 * Y1^-2 * Y3 * Y1^9 ] Map:: non-degenerate R = (1, 43, 2, 44, 8, 50, 23, 65, 33, 75, 42, 84, 38, 80, 16, 58, 30, 72, 41, 83, 40, 82, 34, 76, 18, 60, 5, 47)(3, 45, 9, 51, 24, 66, 22, 64, 32, 74, 39, 81, 17, 59, 4, 46, 10, 52, 25, 67, 21, 63, 31, 73, 37, 79, 15, 57)(6, 48, 11, 53, 26, 68, 35, 77, 13, 55, 28, 70, 20, 62, 7, 49, 12, 54, 27, 69, 36, 78, 14, 56, 29, 71, 19, 61)(85, 127, 87, 129, 97, 139, 117, 159, 116, 158, 96, 138, 114, 156, 94, 136, 113, 155, 102, 144, 121, 163, 110, 152, 92, 134, 108, 150, 104, 146, 122, 164, 101, 143, 120, 162, 124, 166, 105, 147, 90, 132)(86, 128, 93, 135, 112, 154, 126, 168, 123, 165, 111, 153, 125, 167, 109, 151, 103, 145, 89, 131, 99, 141, 119, 161, 107, 149, 106, 148, 91, 133, 100, 142, 88, 130, 98, 140, 118, 160, 115, 157, 95, 137) L = (1, 88)(2, 94)(3, 98)(4, 97)(5, 101)(6, 100)(7, 85)(8, 109)(9, 113)(10, 112)(11, 114)(12, 86)(13, 118)(14, 117)(15, 120)(16, 87)(17, 119)(18, 123)(19, 122)(20, 89)(21, 91)(22, 90)(23, 105)(24, 103)(25, 104)(26, 125)(27, 92)(28, 102)(29, 126)(30, 93)(31, 96)(32, 95)(33, 115)(34, 116)(35, 124)(36, 107)(37, 111)(38, 99)(39, 110)(40, 106)(41, 108)(42, 121)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ), ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E23.281 Graph:: bipartite v = 5 e = 84 f = 35 degree seq :: [ 28^3, 42^2 ] E23.285 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 14, 21}) Quotient :: dipole Aut^+ = C42 (small group id <42, 6>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y3^-1, Y2^-1), Y2 * Y1 * Y2^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3 * Y1 * Y3^-1 * Y1, Y3 * Y2^-1 * Y1 * Y3^-1 * Y2 * Y1, Y3^-3 * Y2^3, Y2^2 * Y3 * Y2 * Y3^2 * Y2 * Y1, Y3^-12 * Y2^-2, Y2^14, Y3^-19 * Y1 * Y3^-2 ] Map:: non-degenerate R = (1, 43, 2, 44)(3, 45, 7, 49)(4, 46, 8, 50)(5, 47, 9, 51)(6, 48, 10, 52)(11, 53, 19, 61)(12, 54, 20, 62)(13, 55, 21, 63)(14, 56, 22, 64)(15, 57, 23, 65)(16, 58, 24, 66)(17, 59, 25, 67)(18, 60, 26, 68)(27, 69, 35, 77)(28, 70, 36, 78)(29, 71, 37, 79)(30, 72, 38, 80)(31, 73, 39, 81)(32, 74, 40, 82)(33, 75, 41, 83)(34, 76, 42, 84)(85, 127, 87, 129, 95, 137, 111, 153, 124, 166, 108, 150, 93, 135, 86, 128, 91, 133, 103, 145, 119, 161, 116, 158, 100, 142, 89, 131)(88, 130, 96, 138, 112, 154, 126, 168, 110, 152, 123, 165, 107, 149, 92, 134, 104, 146, 120, 162, 118, 160, 102, 144, 115, 157, 99, 141)(90, 132, 97, 139, 113, 155, 98, 140, 114, 156, 125, 167, 109, 151, 94, 136, 105, 147, 121, 163, 106, 148, 122, 164, 117, 159, 101, 143) L = (1, 88)(2, 92)(3, 96)(4, 98)(5, 99)(6, 85)(7, 104)(8, 106)(9, 107)(10, 86)(11, 112)(12, 114)(13, 87)(14, 111)(15, 113)(16, 115)(17, 89)(18, 90)(19, 120)(20, 122)(21, 91)(22, 119)(23, 121)(24, 123)(25, 93)(26, 94)(27, 126)(28, 125)(29, 95)(30, 124)(31, 97)(32, 102)(33, 100)(34, 101)(35, 118)(36, 117)(37, 103)(38, 116)(39, 105)(40, 110)(41, 108)(42, 109)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 6, 42, 6, 42 ), ( 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42, 6, 42 ) } Outer automorphisms :: reflexible Dual of E23.286 Graph:: bipartite v = 24 e = 84 f = 16 degree seq :: [ 4^21, 28^3 ] E23.286 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 14, 21}) Quotient :: dipole Aut^+ = C42 (small group id <42, 6>) Aut = D84 (small group id <84, 14>) |r| :: 2 Presentation :: [ R^2, Y1^3, Y1 * Y3^-2, (R * Y3)^2, (Y2, Y3), (Y2^-1, Y1^-1), (R * Y1)^2, (R * Y2)^2, (Y3^-1 * Y1^-1)^2, Y2^7 * Y1, (Y2^-1 * Y3)^14 ] Map:: non-degenerate R = (1, 43, 2, 44, 5, 47)(3, 45, 8, 50, 13, 55)(4, 46, 9, 51, 7, 49)(6, 48, 10, 52, 16, 58)(11, 53, 19, 61, 25, 67)(12, 54, 20, 62, 14, 56)(15, 57, 21, 63, 18, 60)(17, 59, 22, 64, 28, 70)(23, 65, 31, 73, 37, 79)(24, 66, 32, 74, 26, 68)(27, 69, 33, 75, 30, 72)(29, 71, 34, 76, 35, 77)(36, 78, 41, 83, 38, 80)(39, 81, 42, 84, 40, 82)(85, 127, 87, 129, 95, 137, 107, 149, 119, 161, 112, 154, 100, 142, 89, 131, 97, 139, 109, 151, 121, 163, 118, 160, 106, 148, 94, 136, 86, 128, 92, 134, 103, 145, 115, 157, 113, 155, 101, 143, 90, 132)(88, 130, 96, 138, 108, 150, 120, 162, 124, 166, 114, 156, 102, 144, 91, 133, 98, 140, 110, 152, 122, 164, 126, 168, 117, 159, 105, 147, 93, 135, 104, 146, 116, 158, 125, 167, 123, 165, 111, 153, 99, 141) L = (1, 88)(2, 93)(3, 96)(4, 86)(5, 91)(6, 99)(7, 85)(8, 104)(9, 89)(10, 105)(11, 108)(12, 92)(13, 98)(14, 87)(15, 94)(16, 102)(17, 111)(18, 90)(19, 116)(20, 97)(21, 100)(22, 117)(23, 120)(24, 103)(25, 110)(26, 95)(27, 106)(28, 114)(29, 123)(30, 101)(31, 125)(32, 109)(33, 112)(34, 126)(35, 124)(36, 115)(37, 122)(38, 107)(39, 118)(40, 113)(41, 121)(42, 119)(43, 127)(44, 128)(45, 129)(46, 130)(47, 131)(48, 132)(49, 133)(50, 134)(51, 135)(52, 136)(53, 137)(54, 138)(55, 139)(56, 140)(57, 141)(58, 142)(59, 143)(60, 144)(61, 145)(62, 146)(63, 147)(64, 148)(65, 149)(66, 150)(67, 151)(68, 152)(69, 153)(70, 154)(71, 155)(72, 156)(73, 157)(74, 158)(75, 159)(76, 160)(77, 161)(78, 162)(79, 163)(80, 164)(81, 165)(82, 166)(83, 167)(84, 168) local type(s) :: { ( 4, 28, 4, 28, 4, 28 ), ( 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28, 4, 28 ) } Outer automorphisms :: reflexible Dual of E23.285 Graph:: bipartite v = 16 e = 84 f = 24 degree seq :: [ 6^14, 42^2 ] E23.287 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 4, 4}) Quotient :: edge^2 Aut^+ = C11 : C4 (small group id <44, 1>) Aut = (C22 x C2) : C2 (small group id <88, 7>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1, Y1^2 * Y3^2, Y3^4, Y3^-1 * Y1^2 * Y3^-1, R * Y2 * R * Y1, (R * Y3)^2, Y2^4, Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1, Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 45, 3, 47, 6, 50, 5, 49)(2, 46, 7, 51, 4, 48, 8, 52)(9, 53, 13, 57, 10, 54, 14, 58)(11, 55, 15, 59, 12, 56, 16, 60)(17, 61, 21, 65, 18, 62, 22, 66)(19, 63, 23, 67, 20, 64, 24, 68)(25, 69, 29, 73, 26, 70, 30, 74)(27, 71, 31, 75, 28, 72, 32, 76)(33, 77, 37, 81, 34, 78, 38, 82)(35, 79, 39, 83, 36, 80, 40, 84)(41, 85, 43, 87, 42, 86, 44, 88)(89, 90, 94, 92)(91, 97, 93, 98)(95, 99, 96, 100)(101, 105, 102, 106)(103, 107, 104, 108)(109, 113, 110, 114)(111, 115, 112, 116)(117, 121, 118, 122)(119, 123, 120, 124)(125, 129, 126, 130)(127, 131, 128, 132)(133, 134, 138, 136)(135, 141, 137, 142)(139, 143, 140, 144)(145, 149, 146, 150)(147, 151, 148, 152)(153, 157, 154, 158)(155, 159, 156, 160)(161, 165, 162, 166)(163, 167, 164, 168)(169, 173, 170, 174)(171, 175, 172, 176) L = (1, 89)(2, 90)(3, 91)(4, 92)(5, 93)(6, 94)(7, 95)(8, 96)(9, 97)(10, 98)(11, 99)(12, 100)(13, 101)(14, 102)(15, 103)(16, 104)(17, 105)(18, 106)(19, 107)(20, 108)(21, 109)(22, 110)(23, 111)(24, 112)(25, 113)(26, 114)(27, 115)(28, 116)(29, 117)(30, 118)(31, 119)(32, 120)(33, 121)(34, 122)(35, 123)(36, 124)(37, 125)(38, 126)(39, 127)(40, 128)(41, 129)(42, 130)(43, 131)(44, 132)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176) local type(s) :: { ( 16^4 ), ( 16^8 ) } Outer automorphisms :: reflexible Dual of E23.289 Graph:: bipartite v = 33 e = 88 f = 11 degree seq :: [ 4^22, 8^11 ] E23.288 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {4, 4, 4, 4}) Quotient :: edge^2 Aut^+ = C11 : C4 (small group id <44, 1>) Aut = (C22 x C2) : C2 (small group id <88, 7>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1, Y3^4, Y1^-2 * Y3^2, Y3^-1 * Y1^-2 * Y3^-1, R * Y2 * R * Y1, (R * Y3)^2, Y2^4, Y3^-1 * Y1^-1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 45, 3, 47, 6, 50, 5, 49)(2, 46, 7, 51, 4, 48, 8, 52)(9, 53, 13, 57, 10, 54, 14, 58)(11, 55, 15, 59, 12, 56, 16, 60)(17, 61, 21, 65, 18, 62, 22, 66)(19, 63, 23, 67, 20, 64, 24, 68)(25, 69, 29, 73, 26, 70, 30, 74)(27, 71, 31, 75, 28, 72, 32, 76)(33, 77, 37, 81, 34, 78, 38, 82)(35, 79, 39, 83, 36, 80, 40, 84)(41, 85, 44, 88, 42, 86, 43, 87)(89, 90, 94, 92)(91, 97, 93, 98)(95, 99, 96, 100)(101, 105, 102, 106)(103, 107, 104, 108)(109, 113, 110, 114)(111, 115, 112, 116)(117, 121, 118, 122)(119, 123, 120, 124)(125, 129, 126, 130)(127, 131, 128, 132)(133, 134, 138, 136)(135, 141, 137, 142)(139, 143, 140, 144)(145, 149, 146, 150)(147, 151, 148, 152)(153, 157, 154, 158)(155, 159, 156, 160)(161, 165, 162, 166)(163, 167, 164, 168)(169, 173, 170, 174)(171, 175, 172, 176) L = (1, 89)(2, 90)(3, 91)(4, 92)(5, 93)(6, 94)(7, 95)(8, 96)(9, 97)(10, 98)(11, 99)(12, 100)(13, 101)(14, 102)(15, 103)(16, 104)(17, 105)(18, 106)(19, 107)(20, 108)(21, 109)(22, 110)(23, 111)(24, 112)(25, 113)(26, 114)(27, 115)(28, 116)(29, 117)(30, 118)(31, 119)(32, 120)(33, 121)(34, 122)(35, 123)(36, 124)(37, 125)(38, 126)(39, 127)(40, 128)(41, 129)(42, 130)(43, 131)(44, 132)(45, 133)(46, 134)(47, 135)(48, 136)(49, 137)(50, 138)(51, 139)(52, 140)(53, 141)(54, 142)(55, 143)(56, 144)(57, 145)(58, 146)(59, 147)(60, 148)(61, 149)(62, 150)(63, 151)(64, 152)(65, 153)(66, 154)(67, 155)(68, 156)(69, 157)(70, 158)(71, 159)(72, 160)(73, 161)(74, 162)(75, 163)(76, 164)(77, 165)(78, 166)(79, 167)(80, 168)(81, 169)(82, 170)(83, 171)(84, 172)(85, 173)(86, 174)(87, 175)(88, 176) local type(s) :: { ( 16^4 ), ( 16^8 ) } Outer automorphisms :: reflexible Dual of E23.290 Graph:: bipartite v = 33 e = 88 f = 11 degree seq :: [ 4^22, 8^11 ] E23.289 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 4, 4}) Quotient :: loop^2 Aut^+ = C11 : C4 (small group id <44, 1>) Aut = (C22 x C2) : C2 (small group id <88, 7>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1, Y1^2 * Y3^2, Y3^4, Y3^-1 * Y1^2 * Y3^-1, R * Y2 * R * Y1, (R * Y3)^2, Y2^4, Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1 * Y2^-1 * Y1^-1, Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 45, 89, 133, 3, 47, 91, 135, 6, 50, 94, 138, 5, 49, 93, 137)(2, 46, 90, 134, 7, 51, 95, 139, 4, 48, 92, 136, 8, 52, 96, 140)(9, 53, 97, 141, 13, 57, 101, 145, 10, 54, 98, 142, 14, 58, 102, 146)(11, 55, 99, 143, 15, 59, 103, 147, 12, 56, 100, 144, 16, 60, 104, 148)(17, 61, 105, 149, 21, 65, 109, 153, 18, 62, 106, 150, 22, 66, 110, 154)(19, 63, 107, 151, 23, 67, 111, 155, 20, 64, 108, 152, 24, 68, 112, 156)(25, 69, 113, 157, 29, 73, 117, 161, 26, 70, 114, 158, 30, 74, 118, 162)(27, 71, 115, 159, 31, 75, 119, 163, 28, 72, 116, 160, 32, 76, 120, 164)(33, 77, 121, 165, 37, 81, 125, 169, 34, 78, 122, 166, 38, 82, 126, 170)(35, 79, 123, 167, 39, 83, 127, 171, 36, 80, 124, 168, 40, 84, 128, 172)(41, 85, 129, 173, 43, 87, 131, 175, 42, 86, 130, 174, 44, 88, 132, 176) L = (1, 46)(2, 50)(3, 53)(4, 45)(5, 54)(6, 48)(7, 55)(8, 56)(9, 49)(10, 47)(11, 52)(12, 51)(13, 61)(14, 62)(15, 63)(16, 64)(17, 58)(18, 57)(19, 60)(20, 59)(21, 69)(22, 70)(23, 71)(24, 72)(25, 66)(26, 65)(27, 68)(28, 67)(29, 77)(30, 78)(31, 79)(32, 80)(33, 74)(34, 73)(35, 76)(36, 75)(37, 85)(38, 86)(39, 87)(40, 88)(41, 82)(42, 81)(43, 84)(44, 83)(89, 134)(90, 138)(91, 141)(92, 133)(93, 142)(94, 136)(95, 143)(96, 144)(97, 137)(98, 135)(99, 140)(100, 139)(101, 149)(102, 150)(103, 151)(104, 152)(105, 146)(106, 145)(107, 148)(108, 147)(109, 157)(110, 158)(111, 159)(112, 160)(113, 154)(114, 153)(115, 156)(116, 155)(117, 165)(118, 166)(119, 167)(120, 168)(121, 162)(122, 161)(123, 164)(124, 163)(125, 173)(126, 174)(127, 175)(128, 176)(129, 170)(130, 169)(131, 172)(132, 171) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E23.287 Transitivity :: VT+ Graph:: v = 11 e = 88 f = 33 degree seq :: [ 16^11 ] E23.290 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {4, 4, 4, 4}) Quotient :: loop^2 Aut^+ = C11 : C4 (small group id <44, 1>) Aut = (C22 x C2) : C2 (small group id <88, 7>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1, Y3^4, Y1^-2 * Y3^2, Y3^-1 * Y1^-2 * Y3^-1, R * Y2 * R * Y1, (R * Y3)^2, Y2^4, Y3^-1 * Y1^-1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 45, 89, 133, 3, 47, 91, 135, 6, 50, 94, 138, 5, 49, 93, 137)(2, 46, 90, 134, 7, 51, 95, 139, 4, 48, 92, 136, 8, 52, 96, 140)(9, 53, 97, 141, 13, 57, 101, 145, 10, 54, 98, 142, 14, 58, 102, 146)(11, 55, 99, 143, 15, 59, 103, 147, 12, 56, 100, 144, 16, 60, 104, 148)(17, 61, 105, 149, 21, 65, 109, 153, 18, 62, 106, 150, 22, 66, 110, 154)(19, 63, 107, 151, 23, 67, 111, 155, 20, 64, 108, 152, 24, 68, 112, 156)(25, 69, 113, 157, 29, 73, 117, 161, 26, 70, 114, 158, 30, 74, 118, 162)(27, 71, 115, 159, 31, 75, 119, 163, 28, 72, 116, 160, 32, 76, 120, 164)(33, 77, 121, 165, 37, 81, 125, 169, 34, 78, 122, 166, 38, 82, 126, 170)(35, 79, 123, 167, 39, 83, 127, 171, 36, 80, 124, 168, 40, 84, 128, 172)(41, 85, 129, 173, 44, 88, 132, 176, 42, 86, 130, 174, 43, 87, 131, 175) L = (1, 46)(2, 50)(3, 53)(4, 45)(5, 54)(6, 48)(7, 55)(8, 56)(9, 49)(10, 47)(11, 52)(12, 51)(13, 61)(14, 62)(15, 63)(16, 64)(17, 58)(18, 57)(19, 60)(20, 59)(21, 69)(22, 70)(23, 71)(24, 72)(25, 66)(26, 65)(27, 68)(28, 67)(29, 77)(30, 78)(31, 79)(32, 80)(33, 74)(34, 73)(35, 76)(36, 75)(37, 85)(38, 86)(39, 87)(40, 88)(41, 82)(42, 81)(43, 84)(44, 83)(89, 134)(90, 138)(91, 141)(92, 133)(93, 142)(94, 136)(95, 143)(96, 144)(97, 137)(98, 135)(99, 140)(100, 139)(101, 149)(102, 150)(103, 151)(104, 152)(105, 146)(106, 145)(107, 148)(108, 147)(109, 157)(110, 158)(111, 159)(112, 160)(113, 154)(114, 153)(115, 156)(116, 155)(117, 165)(118, 166)(119, 167)(120, 168)(121, 162)(122, 161)(123, 164)(124, 163)(125, 173)(126, 174)(127, 175)(128, 176)(129, 170)(130, 169)(131, 172)(132, 171) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E23.288 Transitivity :: VT+ Graph:: v = 11 e = 88 f = 33 degree seq :: [ 16^11 ] E23.291 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 46, 46}) Quotient :: dipole Aut^+ = C46 (small group id <46, 2>) Aut = D92 (small group id <92, 3>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y1^2, R^2, (R * Y1)^2, (Y3^-1 * Y1)^2, (R * Y3)^2, Y2^-1 * Y1 * Y2 * Y1, (R * Y2 * Y3^-1)^2, Y2^23 * Y1, (Y3 * Y2^-1)^46 ] Map:: R = (1, 47, 2, 48)(3, 49, 5, 51)(4, 50, 6, 52)(7, 53, 9, 55)(8, 54, 10, 56)(11, 57, 13, 59)(12, 58, 14, 60)(15, 61, 17, 63)(16, 62, 18, 64)(19, 65, 21, 67)(20, 66, 22, 68)(23, 69, 25, 71)(24, 70, 26, 72)(27, 73, 29, 75)(28, 74, 30, 76)(31, 77, 33, 79)(32, 78, 34, 80)(35, 81, 37, 83)(36, 82, 38, 84)(39, 85, 41, 87)(40, 86, 42, 88)(43, 89, 45, 91)(44, 90, 46, 92)(93, 139, 95, 141, 99, 145, 103, 149, 107, 153, 111, 157, 115, 161, 119, 165, 123, 169, 127, 173, 131, 177, 135, 181, 138, 184, 134, 180, 130, 176, 126, 172, 122, 168, 118, 164, 114, 160, 110, 156, 106, 152, 102, 148, 98, 144, 94, 140, 97, 143, 101, 147, 105, 151, 109, 155, 113, 159, 117, 163, 121, 167, 125, 171, 129, 175, 133, 179, 137, 183, 136, 182, 132, 178, 128, 174, 124, 170, 120, 166, 116, 162, 112, 158, 108, 154, 104, 150, 100, 146, 96, 142) L = (1, 93)(2, 94)(3, 95)(4, 96)(5, 97)(6, 98)(7, 99)(8, 100)(9, 101)(10, 102)(11, 103)(12, 104)(13, 105)(14, 106)(15, 107)(16, 108)(17, 109)(18, 110)(19, 111)(20, 112)(21, 113)(22, 114)(23, 115)(24, 116)(25, 117)(26, 118)(27, 119)(28, 120)(29, 121)(30, 122)(31, 123)(32, 124)(33, 125)(34, 126)(35, 127)(36, 128)(37, 129)(38, 130)(39, 131)(40, 132)(41, 133)(42, 134)(43, 135)(44, 136)(45, 137)(46, 138)(47, 139)(48, 140)(49, 141)(50, 142)(51, 143)(52, 144)(53, 145)(54, 146)(55, 147)(56, 148)(57, 149)(58, 150)(59, 151)(60, 152)(61, 153)(62, 154)(63, 155)(64, 156)(65, 157)(66, 158)(67, 159)(68, 160)(69, 161)(70, 162)(71, 163)(72, 164)(73, 165)(74, 166)(75, 167)(76, 168)(77, 169)(78, 170)(79, 171)(80, 172)(81, 173)(82, 174)(83, 175)(84, 176)(85, 177)(86, 178)(87, 179)(88, 180)(89, 181)(90, 182)(91, 183)(92, 184) local type(s) :: { ( 4, 92, 4, 92 ), ( 4, 92, 4, 92, 4, 92, 4, 92, 4, 92, 4, 92, 4, 92, 4, 92, 4, 92, 4, 92, 4, 92, 4, 92, 4, 92, 4, 92, 4, 92, 4, 92, 4, 92, 4, 92, 4, 92, 4, 92, 4, 92, 4, 92, 4, 92, 4, 92, 4, 92, 4, 92, 4, 92, 4, 92, 4, 92, 4, 92, 4, 92, 4, 92, 4, 92, 4, 92, 4, 92, 4, 92, 4, 92, 4, 92, 4, 92, 4, 92, 4, 92, 4, 92, 4, 92, 4, 92, 4, 92, 4, 92 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 24 e = 92 f = 24 degree seq :: [ 4^23, 92 ] E23.292 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {47, 47, 47}) Quotient :: edge Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ F^2, T2 * T1^-2, (F * T1)^2, (F * T2)^2, T1 * T2^23, (T2^-1 * T1^-1)^47 ] Map:: non-degenerate R = (1, 3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 43, 47, 44, 40, 36, 32, 28, 24, 20, 16, 12, 8, 4, 2, 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 45, 41, 37, 33, 29, 25, 21, 17, 13, 9, 5)(48, 49, 50, 53, 54, 57, 58, 61, 62, 65, 66, 69, 70, 73, 74, 77, 78, 81, 82, 85, 86, 89, 90, 93, 94, 92, 91, 88, 87, 84, 83, 80, 79, 76, 75, 72, 71, 68, 67, 64, 63, 60, 59, 56, 55, 52, 51) L = (1, 48)(2, 49)(3, 50)(4, 51)(5, 52)(6, 53)(7, 54)(8, 55)(9, 56)(10, 57)(11, 58)(12, 59)(13, 60)(14, 61)(15, 62)(16, 63)(17, 64)(18, 65)(19, 66)(20, 67)(21, 68)(22, 69)(23, 70)(24, 71)(25, 72)(26, 73)(27, 74)(28, 75)(29, 76)(30, 77)(31, 78)(32, 79)(33, 80)(34, 81)(35, 82)(36, 83)(37, 84)(38, 85)(39, 86)(40, 87)(41, 88)(42, 89)(43, 90)(44, 91)(45, 92)(46, 93)(47, 94) local type(s) :: { ( 94^47 ) } Outer automorphisms :: reflexible Dual of E23.317 Transitivity :: ET+ Graph:: bipartite v = 2 e = 47 f = 1 degree seq :: [ 47^2 ] E23.293 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {47, 47, 47}) Quotient :: edge Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ F^2, T2 * T1^2, (F * T1)^2, (F * T2)^2, T2^-23 * T1 ] Map:: non-degenerate R = (1, 3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 43, 46, 42, 38, 34, 30, 26, 22, 18, 14, 10, 6, 2, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 47, 45, 41, 37, 33, 29, 25, 21, 17, 13, 9, 5)(48, 49, 52, 53, 56, 57, 60, 61, 64, 65, 68, 69, 72, 73, 76, 77, 80, 81, 84, 85, 88, 89, 92, 93, 94, 90, 91, 86, 87, 82, 83, 78, 79, 74, 75, 70, 71, 66, 67, 62, 63, 58, 59, 54, 55, 50, 51) L = (1, 48)(2, 49)(3, 50)(4, 51)(5, 52)(6, 53)(7, 54)(8, 55)(9, 56)(10, 57)(11, 58)(12, 59)(13, 60)(14, 61)(15, 62)(16, 63)(17, 64)(18, 65)(19, 66)(20, 67)(21, 68)(22, 69)(23, 70)(24, 71)(25, 72)(26, 73)(27, 74)(28, 75)(29, 76)(30, 77)(31, 78)(32, 79)(33, 80)(34, 81)(35, 82)(36, 83)(37, 84)(38, 85)(39, 86)(40, 87)(41, 88)(42, 89)(43, 90)(44, 91)(45, 92)(46, 93)(47, 94) local type(s) :: { ( 94^47 ) } Outer automorphisms :: reflexible Dual of E23.314 Transitivity :: ET+ Graph:: bipartite v = 2 e = 47 f = 1 degree seq :: [ 47^2 ] E23.294 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {47, 47, 47}) Quotient :: edge Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ F^2, T2 * T1^-3, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2 * T1^-1 * T2^15, (T1^-1 * T2^-1)^47 ] Map:: non-degenerate R = (1, 3, 9, 15, 21, 27, 33, 39, 45, 44, 38, 32, 26, 20, 14, 8, 2, 7, 13, 19, 25, 31, 37, 43, 46, 40, 34, 28, 22, 16, 10, 4, 6, 12, 18, 24, 30, 36, 42, 47, 41, 35, 29, 23, 17, 11, 5)(48, 49, 53, 50, 54, 59, 56, 60, 65, 62, 66, 71, 68, 72, 77, 74, 78, 83, 80, 84, 89, 86, 90, 94, 92, 93, 88, 91, 87, 82, 85, 81, 76, 79, 75, 70, 73, 69, 64, 67, 63, 58, 61, 57, 52, 55, 51) L = (1, 48)(2, 49)(3, 50)(4, 51)(5, 52)(6, 53)(7, 54)(8, 55)(9, 56)(10, 57)(11, 58)(12, 59)(13, 60)(14, 61)(15, 62)(16, 63)(17, 64)(18, 65)(19, 66)(20, 67)(21, 68)(22, 69)(23, 70)(24, 71)(25, 72)(26, 73)(27, 74)(28, 75)(29, 76)(30, 77)(31, 78)(32, 79)(33, 80)(34, 81)(35, 82)(36, 83)(37, 84)(38, 85)(39, 86)(40, 87)(41, 88)(42, 89)(43, 90)(44, 91)(45, 92)(46, 93)(47, 94) local type(s) :: { ( 94^47 ) } Outer automorphisms :: reflexible Dual of E23.319 Transitivity :: ET+ Graph:: bipartite v = 2 e = 47 f = 1 degree seq :: [ 47^2 ] E23.295 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {47, 47, 47}) Quotient :: edge Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ F^2, T1^-3 * T2^-1, (F * T2)^2, (F * T1)^2, T2^-1 * T1^-1 * T2^-15 ] Map:: non-degenerate R = (1, 3, 9, 15, 21, 27, 33, 39, 45, 42, 36, 30, 24, 18, 12, 6, 4, 10, 16, 22, 28, 34, 40, 46, 44, 38, 32, 26, 20, 14, 8, 2, 7, 13, 19, 25, 31, 37, 43, 47, 41, 35, 29, 23, 17, 11, 5)(48, 49, 53, 52, 55, 59, 58, 61, 65, 64, 67, 71, 70, 73, 77, 76, 79, 83, 82, 85, 89, 88, 91, 92, 94, 93, 86, 90, 87, 80, 84, 81, 74, 78, 75, 68, 72, 69, 62, 66, 63, 56, 60, 57, 50, 54, 51) L = (1, 48)(2, 49)(3, 50)(4, 51)(5, 52)(6, 53)(7, 54)(8, 55)(9, 56)(10, 57)(11, 58)(12, 59)(13, 60)(14, 61)(15, 62)(16, 63)(17, 64)(18, 65)(19, 66)(20, 67)(21, 68)(22, 69)(23, 70)(24, 71)(25, 72)(26, 73)(27, 74)(28, 75)(29, 76)(30, 77)(31, 78)(32, 79)(33, 80)(34, 81)(35, 82)(36, 83)(37, 84)(38, 85)(39, 86)(40, 87)(41, 88)(42, 89)(43, 90)(44, 91)(45, 92)(46, 93)(47, 94) local type(s) :: { ( 94^47 ) } Outer automorphisms :: reflexible Dual of E23.315 Transitivity :: ET+ Graph:: bipartite v = 2 e = 47 f = 1 degree seq :: [ 47^2 ] E23.296 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {47, 47, 47}) Quotient :: edge Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ F^2, (T1^-1, T2), (F * T2)^2, (F * T1)^2, T1^2 * T2^-1 * T1^2, T2^11 * T1^-1 * T2, T2^-1 * T1^-1 * T2^-4 * T1^-1 * T2^-6 * T1^-1, (T1^-1 * T2^-1)^47 ] Map:: non-degenerate R = (1, 3, 9, 17, 25, 33, 41, 40, 32, 24, 16, 8, 2, 7, 15, 23, 31, 39, 47, 43, 35, 27, 19, 11, 6, 14, 22, 30, 38, 46, 44, 36, 28, 20, 12, 4, 10, 18, 26, 34, 42, 45, 37, 29, 21, 13, 5)(48, 49, 53, 57, 50, 54, 61, 65, 56, 62, 69, 73, 64, 70, 77, 81, 72, 78, 85, 89, 80, 86, 93, 92, 88, 94, 91, 84, 87, 90, 83, 76, 79, 82, 75, 68, 71, 74, 67, 60, 63, 66, 59, 52, 55, 58, 51) L = (1, 48)(2, 49)(3, 50)(4, 51)(5, 52)(6, 53)(7, 54)(8, 55)(9, 56)(10, 57)(11, 58)(12, 59)(13, 60)(14, 61)(15, 62)(16, 63)(17, 64)(18, 65)(19, 66)(20, 67)(21, 68)(22, 69)(23, 70)(24, 71)(25, 72)(26, 73)(27, 74)(28, 75)(29, 76)(30, 77)(31, 78)(32, 79)(33, 80)(34, 81)(35, 82)(36, 83)(37, 84)(38, 85)(39, 86)(40, 87)(41, 88)(42, 89)(43, 90)(44, 91)(45, 92)(46, 93)(47, 94) local type(s) :: { ( 94^47 ) } Outer automorphisms :: reflexible Dual of E23.321 Transitivity :: ET+ Graph:: bipartite v = 2 e = 47 f = 1 degree seq :: [ 47^2 ] E23.297 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {47, 47, 47}) Quotient :: edge Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T2, T1^-1), T1^-2 * T2^-1 * T1^-2, T2^-11 * T1^-1 * T2^-1, T2^4 * T1^-1 * T2^6 * T1^-2 * T2, T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1^2 * T2^-1 ] Map:: non-degenerate R = (1, 3, 9, 17, 25, 33, 41, 44, 36, 28, 20, 12, 4, 10, 18, 26, 34, 42, 46, 38, 30, 22, 14, 6, 11, 19, 27, 35, 43, 47, 40, 32, 24, 16, 8, 2, 7, 15, 23, 31, 39, 45, 37, 29, 21, 13, 5)(48, 49, 53, 59, 52, 55, 61, 67, 60, 63, 69, 75, 68, 71, 77, 83, 76, 79, 85, 91, 84, 87, 93, 88, 92, 94, 89, 80, 86, 90, 81, 72, 78, 82, 73, 64, 70, 74, 65, 56, 62, 66, 57, 50, 54, 58, 51) L = (1, 48)(2, 49)(3, 50)(4, 51)(5, 52)(6, 53)(7, 54)(8, 55)(9, 56)(10, 57)(11, 58)(12, 59)(13, 60)(14, 61)(15, 62)(16, 63)(17, 64)(18, 65)(19, 66)(20, 67)(21, 68)(22, 69)(23, 70)(24, 71)(25, 72)(26, 73)(27, 74)(28, 75)(29, 76)(30, 77)(31, 78)(32, 79)(33, 80)(34, 81)(35, 82)(36, 83)(37, 84)(38, 85)(39, 86)(40, 87)(41, 88)(42, 89)(43, 90)(44, 91)(45, 92)(46, 93)(47, 94) local type(s) :: { ( 94^47 ) } Outer automorphisms :: reflexible Dual of E23.316 Transitivity :: ET+ Graph:: bipartite v = 2 e = 47 f = 1 degree seq :: [ 47^2 ] E23.298 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {47, 47, 47}) Quotient :: edge Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T2 * T1^-2 * T2^-1 * T1^2, T1^-1 * T2 * T1^-4, T1 * T2 * T1 * T2^8, (T1^-1 * T2^-1)^47 ] Map:: non-degenerate R = (1, 3, 9, 19, 29, 39, 41, 31, 21, 11, 14, 24, 34, 44, 46, 38, 28, 18, 8, 2, 7, 17, 27, 37, 42, 32, 22, 12, 4, 10, 20, 30, 40, 47, 45, 36, 26, 16, 6, 15, 25, 35, 43, 33, 23, 13, 5)(48, 49, 53, 61, 57, 50, 54, 62, 71, 67, 56, 64, 72, 81, 77, 66, 74, 82, 91, 87, 76, 84, 90, 93, 94, 86, 89, 80, 85, 92, 88, 79, 70, 75, 83, 78, 69, 60, 65, 73, 68, 59, 52, 55, 63, 58, 51) L = (1, 48)(2, 49)(3, 50)(4, 51)(5, 52)(6, 53)(7, 54)(8, 55)(9, 56)(10, 57)(11, 58)(12, 59)(13, 60)(14, 61)(15, 62)(16, 63)(17, 64)(18, 65)(19, 66)(20, 67)(21, 68)(22, 69)(23, 70)(24, 71)(25, 72)(26, 73)(27, 74)(28, 75)(29, 76)(30, 77)(31, 78)(32, 79)(33, 80)(34, 81)(35, 82)(36, 83)(37, 84)(38, 85)(39, 86)(40, 87)(41, 88)(42, 89)(43, 90)(44, 91)(45, 92)(46, 93)(47, 94) local type(s) :: { ( 94^47 ) } Outer automorphisms :: reflexible Dual of E23.323 Transitivity :: ET+ Graph:: bipartite v = 2 e = 47 f = 1 degree seq :: [ 47^2 ] E23.299 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {47, 47, 47}) Quotient :: edge Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T2 * T1^2 * T2^-1 * T1^-2, T2^-1 * T1^-5, T2^-1 * T1 * T2^-8 * T1, T1^-2 * T2^-2 * T1 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^3 * 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^-4 ] Map:: non-degenerate R = (1, 3, 9, 19, 29, 39, 36, 26, 16, 6, 15, 25, 35, 45, 47, 42, 32, 22, 12, 4, 10, 20, 30, 40, 38, 28, 18, 8, 2, 7, 17, 27, 37, 46, 44, 34, 24, 14, 11, 21, 31, 41, 43, 33, 23, 13, 5)(48, 49, 53, 61, 59, 52, 55, 63, 71, 69, 60, 65, 73, 81, 79, 70, 75, 83, 91, 89, 80, 85, 86, 93, 94, 90, 87, 76, 84, 92, 88, 77, 66, 74, 82, 78, 67, 56, 64, 72, 68, 57, 50, 54, 62, 58, 51) L = (1, 48)(2, 49)(3, 50)(4, 51)(5, 52)(6, 53)(7, 54)(8, 55)(9, 56)(10, 57)(11, 58)(12, 59)(13, 60)(14, 61)(15, 62)(16, 63)(17, 64)(18, 65)(19, 66)(20, 67)(21, 68)(22, 69)(23, 70)(24, 71)(25, 72)(26, 73)(27, 74)(28, 75)(29, 76)(30, 77)(31, 78)(32, 79)(33, 80)(34, 81)(35, 82)(36, 83)(37, 84)(38, 85)(39, 86)(40, 87)(41, 88)(42, 89)(43, 90)(44, 91)(45, 92)(46, 93)(47, 94) local type(s) :: { ( 94^47 ) } Outer automorphisms :: reflexible Dual of E23.318 Transitivity :: ET+ Graph:: bipartite v = 2 e = 47 f = 1 degree seq :: [ 47^2 ] E23.300 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {47, 47, 47}) Quotient :: edge Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^4 * T2^-1 * T1^2, T2^-7 * T1 * T2^-1, (T1^-1 * T2^-1)^47 ] Map:: non-degenerate R = (1, 3, 9, 19, 31, 30, 18, 8, 2, 7, 17, 29, 41, 40, 28, 16, 6, 15, 27, 39, 47, 43, 34, 22, 14, 26, 38, 46, 44, 35, 23, 11, 21, 33, 42, 45, 36, 24, 12, 4, 10, 20, 32, 37, 25, 13, 5)(48, 49, 53, 61, 68, 57, 50, 54, 62, 73, 80, 67, 56, 64, 74, 85, 89, 79, 66, 76, 86, 93, 92, 84, 78, 88, 94, 91, 83, 72, 77, 87, 90, 82, 71, 60, 65, 75, 81, 70, 59, 52, 55, 63, 69, 58, 51) L = (1, 48)(2, 49)(3, 50)(4, 51)(5, 52)(6, 53)(7, 54)(8, 55)(9, 56)(10, 57)(11, 58)(12, 59)(13, 60)(14, 61)(15, 62)(16, 63)(17, 64)(18, 65)(19, 66)(20, 67)(21, 68)(22, 69)(23, 70)(24, 71)(25, 72)(26, 73)(27, 74)(28, 75)(29, 76)(30, 77)(31, 78)(32, 79)(33, 80)(34, 81)(35, 82)(36, 83)(37, 84)(38, 85)(39, 86)(40, 87)(41, 88)(42, 89)(43, 90)(44, 91)(45, 92)(46, 93)(47, 94) local type(s) :: { ( 94^47 ) } Outer automorphisms :: reflexible Dual of E23.324 Transitivity :: ET+ Graph:: bipartite v = 2 e = 47 f = 1 degree seq :: [ 47^2 ] E23.301 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {47, 47, 47}) Quotient :: edge Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^3 * T2 * T1^3, T2^-6 * T1^-1 * T2^-2, T2^2 * T1^-1 * T2 * T1^-1 * T2^4 * T1^-3, T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^3 ] Map:: non-degenerate R = (1, 3, 9, 19, 31, 36, 24, 12, 4, 10, 20, 32, 42, 45, 35, 23, 11, 21, 33, 43, 46, 38, 26, 14, 22, 34, 44, 47, 40, 28, 16, 6, 15, 27, 39, 41, 30, 18, 8, 2, 7, 17, 29, 37, 25, 13, 5)(48, 49, 53, 61, 70, 59, 52, 55, 63, 73, 82, 71, 60, 65, 75, 85, 92, 83, 72, 77, 87, 93, 89, 78, 84, 88, 94, 90, 79, 66, 76, 86, 91, 80, 67, 56, 64, 74, 81, 68, 57, 50, 54, 62, 69, 58, 51) L = (1, 48)(2, 49)(3, 50)(4, 51)(5, 52)(6, 53)(7, 54)(8, 55)(9, 56)(10, 57)(11, 58)(12, 59)(13, 60)(14, 61)(15, 62)(16, 63)(17, 64)(18, 65)(19, 66)(20, 67)(21, 68)(22, 69)(23, 70)(24, 71)(25, 72)(26, 73)(27, 74)(28, 75)(29, 76)(30, 77)(31, 78)(32, 79)(33, 80)(34, 81)(35, 82)(36, 83)(37, 84)(38, 85)(39, 86)(40, 87)(41, 88)(42, 89)(43, 90)(44, 91)(45, 92)(46, 93)(47, 94) local type(s) :: { ( 94^47 ) } Outer automorphisms :: reflexible Dual of E23.320 Transitivity :: ET+ Graph:: bipartite v = 2 e = 47 f = 1 degree seq :: [ 47^2 ] E23.302 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {47, 47, 47}) Quotient :: edge Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T2, T1^-1), T1^-3 * T2 * T1^-4, T2 * T1^-1 * T2 * T1^-1 * T2^5, T1 * T2 * T1 * T2 * T1 * T2^4 * T1^2, T1^-1 * T2^2 * T1^2 * T2^3 * T1^2 * T2^3 * T1^2 * T2^3 * T1^2 * T2^3 * T1^2 * T2^3 * T1^2 * T2^3 * T1^2 * T2^3 * T1^2 * T2^3 * T1^2 * T2^3 * T1^2 * T2^3 * T1^2 * T2^3 * T1^2 * T2^3 * T1^2 * T2^3 * T1^2 * T2^3 * T1^2 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 3, 9, 19, 33, 30, 16, 6, 15, 29, 43, 45, 36, 22, 26, 40, 47, 38, 24, 12, 4, 10, 20, 34, 32, 18, 8, 2, 7, 17, 31, 44, 42, 28, 14, 27, 41, 46, 37, 23, 11, 21, 35, 39, 25, 13, 5)(48, 49, 53, 61, 73, 68, 57, 50, 54, 62, 74, 87, 82, 67, 56, 64, 76, 88, 94, 86, 81, 66, 78, 90, 93, 85, 72, 79, 80, 91, 92, 84, 71, 60, 65, 77, 89, 83, 70, 59, 52, 55, 63, 75, 69, 58, 51) L = (1, 48)(2, 49)(3, 50)(4, 51)(5, 52)(6, 53)(7, 54)(8, 55)(9, 56)(10, 57)(11, 58)(12, 59)(13, 60)(14, 61)(15, 62)(16, 63)(17, 64)(18, 65)(19, 66)(20, 67)(21, 68)(22, 69)(23, 70)(24, 71)(25, 72)(26, 73)(27, 74)(28, 75)(29, 76)(30, 77)(31, 78)(32, 79)(33, 80)(34, 81)(35, 82)(36, 83)(37, 84)(38, 85)(39, 86)(40, 87)(41, 88)(42, 89)(43, 90)(44, 91)(45, 92)(46, 93)(47, 94) local type(s) :: { ( 94^47 ) } Outer automorphisms :: reflexible Dual of E23.326 Transitivity :: ET+ Graph:: bipartite v = 2 e = 47 f = 1 degree seq :: [ 47^2 ] E23.303 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {47, 47, 47}) Quotient :: edge Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^-1 * T2^-1 * T1^-6, T2 * T1 * T2^2 * T1 * T2^4, T1^2 * T2^-1 * T1 * T2^-1 * T1 * T2^-4 * T1, T2^2 * T1^-1 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-1, (T1^-1 * T2^-1)^47 ] Map:: non-degenerate R = (1, 3, 9, 19, 33, 37, 23, 11, 21, 35, 46, 42, 28, 14, 27, 41, 44, 32, 18, 8, 2, 7, 17, 31, 38, 24, 12, 4, 10, 20, 34, 45, 40, 26, 22, 36, 47, 43, 30, 16, 6, 15, 29, 39, 25, 13, 5)(48, 49, 53, 61, 73, 70, 59, 52, 55, 63, 75, 87, 84, 71, 60, 65, 77, 89, 92, 80, 85, 72, 79, 90, 93, 81, 66, 78, 86, 91, 94, 82, 67, 56, 64, 76, 88, 83, 68, 57, 50, 54, 62, 74, 69, 58, 51) L = (1, 48)(2, 49)(3, 50)(4, 51)(5, 52)(6, 53)(7, 54)(8, 55)(9, 56)(10, 57)(11, 58)(12, 59)(13, 60)(14, 61)(15, 62)(16, 63)(17, 64)(18, 65)(19, 66)(20, 67)(21, 68)(22, 69)(23, 70)(24, 71)(25, 72)(26, 73)(27, 74)(28, 75)(29, 76)(30, 77)(31, 78)(32, 79)(33, 80)(34, 81)(35, 82)(36, 83)(37, 84)(38, 85)(39, 86)(40, 87)(41, 88)(42, 89)(43, 90)(44, 91)(45, 92)(46, 93)(47, 94) local type(s) :: { ( 94^47 ) } Outer automorphisms :: reflexible Dual of E23.322 Transitivity :: ET+ Graph:: bipartite v = 2 e = 47 f = 1 degree seq :: [ 47^2 ] E23.304 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {47, 47, 47}) Quotient :: edge Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1 * T2 * T1 * T2^4, T1^-3 * T2 * T1^-6, T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 3, 9, 19, 23, 11, 21, 32, 41, 43, 34, 36, 44, 46, 39, 28, 14, 27, 30, 18, 8, 2, 7, 17, 24, 12, 4, 10, 20, 31, 35, 22, 33, 42, 47, 45, 38, 26, 37, 40, 29, 16, 6, 15, 25, 13, 5)(48, 49, 53, 61, 73, 83, 80, 68, 57, 50, 54, 62, 74, 84, 91, 89, 79, 67, 56, 64, 72, 77, 87, 93, 94, 88, 78, 66, 71, 60, 65, 76, 86, 92, 90, 82, 70, 59, 52, 55, 63, 75, 85, 81, 69, 58, 51) L = (1, 48)(2, 49)(3, 50)(4, 51)(5, 52)(6, 53)(7, 54)(8, 55)(9, 56)(10, 57)(11, 58)(12, 59)(13, 60)(14, 61)(15, 62)(16, 63)(17, 64)(18, 65)(19, 66)(20, 67)(21, 68)(22, 69)(23, 70)(24, 71)(25, 72)(26, 73)(27, 74)(28, 75)(29, 76)(30, 77)(31, 78)(32, 79)(33, 80)(34, 81)(35, 82)(36, 83)(37, 84)(38, 85)(39, 86)(40, 87)(41, 88)(42, 89)(43, 90)(44, 91)(45, 92)(46, 93)(47, 94) local type(s) :: { ( 94^47 ) } Outer automorphisms :: reflexible Dual of E23.329 Transitivity :: ET+ Graph:: bipartite v = 2 e = 47 f = 1 degree seq :: [ 47^2 ] E23.305 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {47, 47, 47}) Quotient :: edge Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T2 * T1^-1 * T2^4 * T1^-1, T1^-2 * T2^-1 * T1^-7, (T1^-1 * T2^-1)^47 ] Map:: non-degenerate R = (1, 3, 9, 19, 16, 6, 15, 29, 40, 38, 26, 37, 45, 47, 42, 33, 22, 31, 35, 24, 12, 4, 10, 20, 18, 8, 2, 7, 17, 30, 28, 14, 27, 39, 46, 44, 36, 32, 41, 43, 34, 23, 11, 21, 25, 13, 5)(48, 49, 53, 61, 73, 83, 80, 70, 59, 52, 55, 63, 75, 85, 91, 89, 81, 71, 60, 65, 66, 77, 87, 93, 94, 90, 82, 72, 67, 56, 64, 76, 86, 92, 88, 78, 68, 57, 50, 54, 62, 74, 84, 79, 69, 58, 51) L = (1, 48)(2, 49)(3, 50)(4, 51)(5, 52)(6, 53)(7, 54)(8, 55)(9, 56)(10, 57)(11, 58)(12, 59)(13, 60)(14, 61)(15, 62)(16, 63)(17, 64)(18, 65)(19, 66)(20, 67)(21, 68)(22, 69)(23, 70)(24, 71)(25, 72)(26, 73)(27, 74)(28, 75)(29, 76)(30, 77)(31, 78)(32, 79)(33, 80)(34, 81)(35, 82)(36, 83)(37, 84)(38, 85)(39, 86)(40, 87)(41, 88)(42, 89)(43, 90)(44, 91)(45, 92)(46, 93)(47, 94) local type(s) :: { ( 94^47 ) } Outer automorphisms :: reflexible Dual of E23.325 Transitivity :: ET+ Graph:: bipartite v = 2 e = 47 f = 1 degree seq :: [ 47^2 ] E23.306 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {47, 47, 47}) Quotient :: edge Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (T2^-1, T1), (F * T1)^2, T2^3 * T1^-1 * T2 * T1^-2 * T2, T1^7 * T2^4, T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 3, 9, 19, 28, 14, 27, 41, 45, 34, 43, 37, 24, 12, 4, 10, 20, 30, 16, 6, 15, 29, 42, 44, 38, 47, 36, 23, 11, 21, 32, 18, 8, 2, 7, 17, 31, 40, 26, 39, 46, 35, 22, 33, 25, 13, 5)(48, 49, 53, 61, 73, 85, 90, 80, 68, 57, 50, 54, 62, 74, 86, 94, 84, 72, 79, 67, 56, 64, 76, 88, 93, 83, 71, 60, 65, 77, 66, 78, 89, 92, 82, 70, 59, 52, 55, 63, 75, 87, 91, 81, 69, 58, 51) L = (1, 48)(2, 49)(3, 50)(4, 51)(5, 52)(6, 53)(7, 54)(8, 55)(9, 56)(10, 57)(11, 58)(12, 59)(13, 60)(14, 61)(15, 62)(16, 63)(17, 64)(18, 65)(19, 66)(20, 67)(21, 68)(22, 69)(23, 70)(24, 71)(25, 72)(26, 73)(27, 74)(28, 75)(29, 76)(30, 77)(31, 78)(32, 79)(33, 80)(34, 81)(35, 82)(36, 83)(37, 84)(38, 85)(39, 86)(40, 87)(41, 88)(42, 89)(43, 90)(44, 91)(45, 92)(46, 93)(47, 94) local type(s) :: { ( 94^47 ) } Outer automorphisms :: reflexible Dual of E23.330 Transitivity :: ET+ Graph:: bipartite v = 2 e = 47 f = 1 degree seq :: [ 47^2 ] E23.307 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {47, 47, 47}) Quotient :: edge Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T2^2 * T1^-1 * T2^-2 * T1, T1^-2 * T2^-1 * T1^-1 * T2^-4, T2^-3 * T1 * T2^-1 * T1^6, T2^3 * T1 * T2^3 * T1 * T2^3 * T1 * T2^3 * T1 * T2^3 * T1 * T2^3 * T1 * T2^3 * T1 * T2^3 * T1 * T2^3 * T1 * T2^3 * T1 * T2^3 * T1 * T2^3 * T1 * T2^3 * T1 * T2^3 * T1 * T2^3 * T1 * T2^3 * T1 * T2^3 * T1 * T2^3 * T1 * T2^3 * T1 * T2^3 * T1 * T2^3 * T1 * T2^3 * T1 * T2^2 ] Map:: non-degenerate R = (1, 3, 9, 19, 33, 22, 36, 45, 40, 26, 39, 32, 18, 8, 2, 7, 17, 31, 23, 11, 21, 35, 44, 38, 47, 42, 30, 16, 6, 15, 29, 24, 12, 4, 10, 20, 34, 43, 37, 46, 41, 28, 14, 27, 25, 13, 5)(48, 49, 53, 61, 73, 85, 90, 80, 70, 59, 52, 55, 63, 75, 87, 91, 81, 66, 78, 71, 60, 65, 77, 88, 92, 82, 67, 56, 64, 76, 72, 79, 89, 93, 83, 68, 57, 50, 54, 62, 74, 86, 94, 84, 69, 58, 51) L = (1, 48)(2, 49)(3, 50)(4, 51)(5, 52)(6, 53)(7, 54)(8, 55)(9, 56)(10, 57)(11, 58)(12, 59)(13, 60)(14, 61)(15, 62)(16, 63)(17, 64)(18, 65)(19, 66)(20, 67)(21, 68)(22, 69)(23, 70)(24, 71)(25, 72)(26, 73)(27, 74)(28, 75)(29, 76)(30, 77)(31, 78)(32, 79)(33, 80)(34, 81)(35, 82)(36, 83)(37, 84)(38, 85)(39, 86)(40, 87)(41, 88)(42, 89)(43, 90)(44, 91)(45, 92)(46, 93)(47, 94) local type(s) :: { ( 94^47 ) } Outer automorphisms :: reflexible Dual of E23.327 Transitivity :: ET+ Graph:: bipartite v = 2 e = 47 f = 1 degree seq :: [ 47^2 ] E23.308 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {47, 47, 47}) Quotient :: edge Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^-3 * T2^-4, T1^-11 * T2 ] Map:: non-degenerate R = (1, 3, 9, 19, 22, 32, 39, 46, 43, 34, 37, 28, 16, 6, 15, 24, 12, 4, 10, 20, 30, 33, 40, 47, 44, 35, 26, 29, 18, 8, 2, 7, 17, 23, 11, 21, 31, 38, 41, 42, 45, 36, 27, 14, 25, 13, 5)(48, 49, 53, 61, 73, 81, 89, 87, 79, 68, 57, 50, 54, 62, 72, 76, 84, 92, 94, 86, 78, 67, 56, 64, 71, 60, 65, 75, 83, 91, 93, 85, 77, 66, 70, 59, 52, 55, 63, 74, 82, 90, 88, 80, 69, 58, 51) L = (1, 48)(2, 49)(3, 50)(4, 51)(5, 52)(6, 53)(7, 54)(8, 55)(9, 56)(10, 57)(11, 58)(12, 59)(13, 60)(14, 61)(15, 62)(16, 63)(17, 64)(18, 65)(19, 66)(20, 67)(21, 68)(22, 69)(23, 70)(24, 71)(25, 72)(26, 73)(27, 74)(28, 75)(29, 76)(30, 77)(31, 78)(32, 79)(33, 80)(34, 81)(35, 82)(36, 83)(37, 84)(38, 85)(39, 86)(40, 87)(41, 88)(42, 89)(43, 90)(44, 91)(45, 92)(46, 93)(47, 94) local type(s) :: { ( 94^47 ) } Outer automorphisms :: reflexible Dual of E23.332 Transitivity :: ET+ Graph:: bipartite v = 2 e = 47 f = 1 degree seq :: [ 47^2 ] E23.309 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {47, 47, 47}) Quotient :: edge Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1 * T2^-1 * T1 * T2^-3 * T1, T1^7 * T2 * T1^4, (T1^-1 * T2^-1)^47 ] Map:: non-degenerate R = (1, 3, 9, 19, 14, 27, 36, 45, 42, 38, 41, 32, 23, 11, 21, 18, 8, 2, 7, 17, 29, 26, 35, 44, 46, 39, 30, 33, 24, 12, 4, 10, 20, 16, 6, 15, 28, 37, 34, 43, 47, 40, 31, 22, 25, 13, 5)(48, 49, 53, 61, 73, 81, 89, 86, 78, 70, 59, 52, 55, 63, 66, 76, 84, 92, 93, 87, 79, 71, 60, 65, 67, 56, 64, 75, 83, 91, 94, 88, 80, 72, 68, 57, 50, 54, 62, 74, 82, 90, 85, 77, 69, 58, 51) L = (1, 48)(2, 49)(3, 50)(4, 51)(5, 52)(6, 53)(7, 54)(8, 55)(9, 56)(10, 57)(11, 58)(12, 59)(13, 60)(14, 61)(15, 62)(16, 63)(17, 64)(18, 65)(19, 66)(20, 67)(21, 68)(22, 69)(23, 70)(24, 71)(25, 72)(26, 73)(27, 74)(28, 75)(29, 76)(30, 77)(31, 78)(32, 79)(33, 80)(34, 81)(35, 82)(36, 83)(37, 84)(38, 85)(39, 86)(40, 87)(41, 88)(42, 89)(43, 90)(44, 91)(45, 92)(46, 93)(47, 94) local type(s) :: { ( 94^47 ) } Outer automorphisms :: reflexible Dual of E23.328 Transitivity :: ET+ Graph:: bipartite v = 2 e = 47 f = 1 degree seq :: [ 47^2 ] E23.310 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {47, 47, 47}) Quotient :: edge Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1^-1, T2^-1), T1^4 * T2^-1 * T1 * T2^-3, T2^-2 * T1^-2 * T2^-5 * T1^-1, T1^-1 * T2^3 * T1^-1 * T2^3 * T1^-1 * T2^3 * T1^-1 * T2^3 * T1^-1 * T2^3 * T1^-1 * T2^3 * T1^-1 * T2^3 * T1^-1 * T2^3 * T1^-1 * T2^3 * T1^-1 * T2^3 * T1^-1 * T2^7 ] Map:: non-degenerate R = (1, 3, 9, 19, 33, 46, 38, 22, 36, 30, 16, 6, 15, 29, 44, 40, 24, 12, 4, 10, 20, 34, 26, 42, 47, 37, 32, 18, 8, 2, 7, 17, 31, 45, 39, 23, 11, 21, 35, 28, 14, 27, 43, 41, 25, 13, 5)(48, 49, 53, 61, 73, 80, 92, 87, 72, 79, 83, 68, 57, 50, 54, 62, 74, 89, 93, 86, 71, 60, 65, 77, 82, 67, 56, 64, 76, 90, 94, 85, 70, 59, 52, 55, 63, 75, 81, 66, 78, 91, 88, 84, 69, 58, 51) L = (1, 48)(2, 49)(3, 50)(4, 51)(5, 52)(6, 53)(7, 54)(8, 55)(9, 56)(10, 57)(11, 58)(12, 59)(13, 60)(14, 61)(15, 62)(16, 63)(17, 64)(18, 65)(19, 66)(20, 67)(21, 68)(22, 69)(23, 70)(24, 71)(25, 72)(26, 73)(27, 74)(28, 75)(29, 76)(30, 77)(31, 78)(32, 79)(33, 80)(34, 81)(35, 82)(36, 83)(37, 84)(38, 85)(39, 86)(40, 87)(41, 88)(42, 89)(43, 90)(44, 91)(45, 92)(46, 93)(47, 94) local type(s) :: { ( 94^47 ) } Outer automorphisms :: reflexible Dual of E23.334 Transitivity :: ET+ Graph:: bipartite v = 2 e = 47 f = 1 degree seq :: [ 47^2 ] E23.311 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {47, 47, 47}) Quotient :: edge Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (T2^-1, T1^-1), (F * T1)^2, T1^4 * T2^4 * T1, T2^2 * T1 * T2 * T1^4 * T2, T2^2 * T1^-1 * T2^5 * T1^-2, T1^-2 * T2^-11, T1^3 * T2^-2 * T1^3 * T2^-2 * T1^3 * T2^-2 * T1^3 * T2^-2 * T1^3 * T2^-2 * T1^3 * T2^-2 * T1^3 * T2^-2 * T1^3 * T2^-2 * T1^3, (T1^-1 * T2^-1)^47 ] Map:: non-degenerate R = (1, 3, 9, 19, 33, 43, 28, 14, 27, 39, 23, 11, 21, 35, 45, 32, 18, 8, 2, 7, 17, 31, 37, 47, 42, 26, 40, 24, 12, 4, 10, 20, 34, 44, 30, 16, 6, 15, 29, 38, 22, 36, 46, 41, 25, 13, 5)(48, 49, 53, 61, 73, 88, 92, 81, 66, 78, 85, 70, 59, 52, 55, 63, 75, 89, 93, 82, 67, 56, 64, 76, 86, 71, 60, 65, 77, 90, 94, 83, 68, 57, 50, 54, 62, 74, 87, 72, 79, 91, 80, 84, 69, 58, 51) L = (1, 48)(2, 49)(3, 50)(4, 51)(5, 52)(6, 53)(7, 54)(8, 55)(9, 56)(10, 57)(11, 58)(12, 59)(13, 60)(14, 61)(15, 62)(16, 63)(17, 64)(18, 65)(19, 66)(20, 67)(21, 68)(22, 69)(23, 70)(24, 71)(25, 72)(26, 73)(27, 74)(28, 75)(29, 76)(30, 77)(31, 78)(32, 79)(33, 80)(34, 81)(35, 82)(36, 83)(37, 84)(38, 85)(39, 86)(40, 87)(41, 88)(42, 89)(43, 90)(44, 91)(45, 92)(46, 93)(47, 94) local type(s) :: { ( 94^47 ) } Outer automorphisms :: reflexible Dual of E23.331 Transitivity :: ET+ Graph:: bipartite v = 2 e = 47 f = 1 degree seq :: [ 47^2 ] E23.312 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {47, 47, 47}) Quotient :: edge Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T2, T1^-1), T2 * T1 * T2^2 * T1, T1^-15 * T2, T1^-1 * T2^22 ] Map:: non-degenerate R = (1, 3, 9, 11, 18, 23, 25, 30, 35, 37, 42, 47, 45, 38, 40, 33, 26, 28, 21, 14, 16, 8, 2, 7, 12, 4, 10, 17, 19, 24, 29, 31, 36, 41, 43, 44, 46, 39, 32, 34, 27, 20, 22, 15, 6, 13, 5)(48, 49, 53, 61, 67, 73, 79, 85, 91, 89, 83, 77, 71, 65, 57, 50, 54, 60, 63, 69, 75, 81, 87, 93, 94, 88, 82, 76, 70, 64, 56, 59, 52, 55, 62, 68, 74, 80, 86, 92, 90, 84, 78, 72, 66, 58, 51) L = (1, 48)(2, 49)(3, 50)(4, 51)(5, 52)(6, 53)(7, 54)(8, 55)(9, 56)(10, 57)(11, 58)(12, 59)(13, 60)(14, 61)(15, 62)(16, 63)(17, 64)(18, 65)(19, 66)(20, 67)(21, 68)(22, 69)(23, 70)(24, 71)(25, 72)(26, 73)(27, 74)(28, 75)(29, 76)(30, 77)(31, 78)(32, 79)(33, 80)(34, 81)(35, 82)(36, 83)(37, 84)(38, 85)(39, 86)(40, 87)(41, 88)(42, 89)(43, 90)(44, 91)(45, 92)(46, 93)(47, 94) local type(s) :: { ( 94^47 ) } Outer automorphisms :: reflexible Dual of E23.335 Transitivity :: ET+ Graph:: bipartite v = 2 e = 47 f = 1 degree seq :: [ 47^2 ] E23.313 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {47, 47, 47}) Quotient :: edge Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T2^-1, T1^-1), T2^-1 * T1 * T2^-2 * T1, T1^-6 * T2^-1 * T1^-9, (T1^-1 * T2^-1)^47 ] Map:: non-degenerate R = (1, 3, 9, 6, 15, 22, 20, 27, 34, 32, 39, 46, 44, 41, 43, 36, 29, 31, 24, 17, 19, 12, 4, 10, 8, 2, 7, 16, 14, 21, 28, 26, 33, 40, 38, 45, 47, 42, 35, 37, 30, 23, 25, 18, 11, 13, 5)(48, 49, 53, 61, 67, 73, 79, 85, 91, 89, 83, 77, 71, 65, 59, 52, 55, 56, 63, 69, 75, 81, 87, 93, 94, 90, 84, 78, 72, 66, 60, 57, 50, 54, 62, 68, 74, 80, 86, 92, 88, 82, 76, 70, 64, 58, 51) L = (1, 48)(2, 49)(3, 50)(4, 51)(5, 52)(6, 53)(7, 54)(8, 55)(9, 56)(10, 57)(11, 58)(12, 59)(13, 60)(14, 61)(15, 62)(16, 63)(17, 64)(18, 65)(19, 66)(20, 67)(21, 68)(22, 69)(23, 70)(24, 71)(25, 72)(26, 73)(27, 74)(28, 75)(29, 76)(30, 77)(31, 78)(32, 79)(33, 80)(34, 81)(35, 82)(36, 83)(37, 84)(38, 85)(39, 86)(40, 87)(41, 88)(42, 89)(43, 90)(44, 91)(45, 92)(46, 93)(47, 94) local type(s) :: { ( 94^47 ) } Outer automorphisms :: reflexible Dual of E23.333 Transitivity :: ET+ Graph:: bipartite v = 2 e = 47 f = 1 degree seq :: [ 47^2 ] E23.314 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {47, 47, 47}) Quotient :: loop Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ F^2, T2^-1 * T1, (F * T1)^2, (F * T2)^2, T2^47, T1^47, (T2^-1 * T1^-1)^47 ] Map:: non-degenerate R = (1, 48, 2, 49, 6, 53, 14, 61, 26, 73, 34, 81, 42, 89, 40, 87, 32, 79, 21, 68, 10, 57, 3, 50, 7, 54, 15, 62, 25, 72, 29, 76, 37, 84, 45, 92, 47, 94, 39, 86, 31, 78, 20, 67, 9, 56, 17, 64, 24, 71, 13, 60, 18, 65, 28, 75, 36, 83, 44, 91, 46, 93, 38, 85, 30, 77, 19, 66, 23, 70, 12, 59, 5, 52, 8, 55, 16, 63, 27, 74, 35, 82, 43, 90, 41, 88, 33, 80, 22, 69, 11, 58, 4, 51) L = (1, 49)(2, 53)(3, 54)(4, 48)(5, 55)(6, 61)(7, 62)(8, 63)(9, 64)(10, 50)(11, 51)(12, 52)(13, 65)(14, 73)(15, 72)(16, 74)(17, 71)(18, 75)(19, 70)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 76)(26, 81)(27, 82)(28, 83)(29, 84)(30, 66)(31, 67)(32, 68)(33, 69)(34, 89)(35, 90)(36, 91)(37, 92)(38, 77)(39, 78)(40, 79)(41, 80)(42, 87)(43, 88)(44, 93)(45, 94)(46, 85)(47, 86) local type(s) :: { ( 47^94 ) } Outer automorphisms :: reflexible Dual of E23.293 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 47 f = 2 degree seq :: [ 94 ] E23.315 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {47, 47, 47}) Quotient :: loop Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ F^2, T2 * T1^-2, (F * T1)^2, (F * T2)^2, T1 * T2^23, (T2^-1 * T1^-1)^47 ] Map:: non-degenerate R = (1, 48, 3, 50, 7, 54, 11, 58, 15, 62, 19, 66, 23, 70, 27, 74, 31, 78, 35, 82, 39, 86, 43, 90, 47, 94, 44, 91, 40, 87, 36, 83, 32, 79, 28, 75, 24, 71, 20, 67, 16, 63, 12, 59, 8, 55, 4, 51, 2, 49, 6, 53, 10, 57, 14, 61, 18, 65, 22, 69, 26, 73, 30, 77, 34, 81, 38, 85, 42, 89, 46, 93, 45, 92, 41, 88, 37, 84, 33, 80, 29, 76, 25, 72, 21, 68, 17, 64, 13, 60, 9, 56, 5, 52) L = (1, 49)(2, 50)(3, 53)(4, 48)(5, 51)(6, 54)(7, 57)(8, 52)(9, 55)(10, 58)(11, 61)(12, 56)(13, 59)(14, 62)(15, 65)(16, 60)(17, 63)(18, 66)(19, 69)(20, 64)(21, 67)(22, 70)(23, 73)(24, 68)(25, 71)(26, 74)(27, 77)(28, 72)(29, 75)(30, 78)(31, 81)(32, 76)(33, 79)(34, 82)(35, 85)(36, 80)(37, 83)(38, 86)(39, 89)(40, 84)(41, 87)(42, 90)(43, 93)(44, 88)(45, 91)(46, 94)(47, 92) local type(s) :: { ( 47^94 ) } Outer automorphisms :: reflexible Dual of E23.295 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 47 f = 2 degree seq :: [ 94 ] E23.316 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {47, 47, 47}) Quotient :: loop Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ F^2, T2 * T1^-3, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2 * T1^-1 * T2^15, (T1^-1 * T2^-1)^47 ] Map:: non-degenerate R = (1, 48, 3, 50, 9, 56, 15, 62, 21, 68, 27, 74, 33, 80, 39, 86, 45, 92, 44, 91, 38, 85, 32, 79, 26, 73, 20, 67, 14, 61, 8, 55, 2, 49, 7, 54, 13, 60, 19, 66, 25, 72, 31, 78, 37, 84, 43, 90, 46, 93, 40, 87, 34, 81, 28, 75, 22, 69, 16, 63, 10, 57, 4, 51, 6, 53, 12, 59, 18, 65, 24, 71, 30, 77, 36, 83, 42, 89, 47, 94, 41, 88, 35, 82, 29, 76, 23, 70, 17, 64, 11, 58, 5, 52) L = (1, 49)(2, 53)(3, 54)(4, 48)(5, 55)(6, 50)(7, 59)(8, 51)(9, 60)(10, 52)(11, 61)(12, 56)(13, 65)(14, 57)(15, 66)(16, 58)(17, 67)(18, 62)(19, 71)(20, 63)(21, 72)(22, 64)(23, 73)(24, 68)(25, 77)(26, 69)(27, 78)(28, 70)(29, 79)(30, 74)(31, 83)(32, 75)(33, 84)(34, 76)(35, 85)(36, 80)(37, 89)(38, 81)(39, 90)(40, 82)(41, 91)(42, 86)(43, 94)(44, 87)(45, 93)(46, 88)(47, 92) local type(s) :: { ( 47^94 ) } Outer automorphisms :: reflexible Dual of E23.297 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 47 f = 2 degree seq :: [ 94 ] E23.317 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {47, 47, 47}) Quotient :: loop Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ F^2, T1^-3 * T2^-1, (F * T2)^2, (F * T1)^2, T2^-1 * T1^-1 * T2^-15 ] Map:: non-degenerate R = (1, 48, 3, 50, 9, 56, 15, 62, 21, 68, 27, 74, 33, 80, 39, 86, 45, 92, 42, 89, 36, 83, 30, 77, 24, 71, 18, 65, 12, 59, 6, 53, 4, 51, 10, 57, 16, 63, 22, 69, 28, 75, 34, 81, 40, 87, 46, 93, 44, 91, 38, 85, 32, 79, 26, 73, 20, 67, 14, 61, 8, 55, 2, 49, 7, 54, 13, 60, 19, 66, 25, 72, 31, 78, 37, 84, 43, 90, 47, 94, 41, 88, 35, 82, 29, 76, 23, 70, 17, 64, 11, 58, 5, 52) L = (1, 49)(2, 53)(3, 54)(4, 48)(5, 55)(6, 52)(7, 51)(8, 59)(9, 60)(10, 50)(11, 61)(12, 58)(13, 57)(14, 65)(15, 66)(16, 56)(17, 67)(18, 64)(19, 63)(20, 71)(21, 72)(22, 62)(23, 73)(24, 70)(25, 69)(26, 77)(27, 78)(28, 68)(29, 79)(30, 76)(31, 75)(32, 83)(33, 84)(34, 74)(35, 85)(36, 82)(37, 81)(38, 89)(39, 90)(40, 80)(41, 91)(42, 88)(43, 87)(44, 92)(45, 94)(46, 86)(47, 93) local type(s) :: { ( 47^94 ) } Outer automorphisms :: reflexible Dual of E23.292 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 47 f = 2 degree seq :: [ 94 ] E23.318 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {47, 47, 47}) Quotient :: loop Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ F^2, (T1^-1, T2), (F * T2)^2, (F * T1)^2, T1^2 * T2^-1 * T1^2, T2^11 * T1^-1 * T2, T2^-1 * T1^-1 * T2^-4 * T1^-1 * T2^-6 * T1^-1, (T1^-1 * T2^-1)^47 ] Map:: non-degenerate R = (1, 48, 3, 50, 9, 56, 17, 64, 25, 72, 33, 80, 41, 88, 40, 87, 32, 79, 24, 71, 16, 63, 8, 55, 2, 49, 7, 54, 15, 62, 23, 70, 31, 78, 39, 86, 47, 94, 43, 90, 35, 82, 27, 74, 19, 66, 11, 58, 6, 53, 14, 61, 22, 69, 30, 77, 38, 85, 46, 93, 44, 91, 36, 83, 28, 75, 20, 67, 12, 59, 4, 51, 10, 57, 18, 65, 26, 73, 34, 81, 42, 89, 45, 92, 37, 84, 29, 76, 21, 68, 13, 60, 5, 52) L = (1, 49)(2, 53)(3, 54)(4, 48)(5, 55)(6, 57)(7, 61)(8, 58)(9, 62)(10, 50)(11, 51)(12, 52)(13, 63)(14, 65)(15, 69)(16, 66)(17, 70)(18, 56)(19, 59)(20, 60)(21, 71)(22, 73)(23, 77)(24, 74)(25, 78)(26, 64)(27, 67)(28, 68)(29, 79)(30, 81)(31, 85)(32, 82)(33, 86)(34, 72)(35, 75)(36, 76)(37, 87)(38, 89)(39, 93)(40, 90)(41, 94)(42, 80)(43, 83)(44, 84)(45, 88)(46, 92)(47, 91) local type(s) :: { ( 47^94 ) } Outer automorphisms :: reflexible Dual of E23.299 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 47 f = 2 degree seq :: [ 94 ] E23.319 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {47, 47, 47}) Quotient :: loop Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T2, T1^-1), T1^-2 * T2^-1 * T1^-2, T2^-11 * T1^-1 * T2^-1, T2^4 * T1^-1 * T2^6 * T1^-2 * T2, T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1 * T2^-2 * T1^2 * T2^-1 ] Map:: non-degenerate R = (1, 48, 3, 50, 9, 56, 17, 64, 25, 72, 33, 80, 41, 88, 44, 91, 36, 83, 28, 75, 20, 67, 12, 59, 4, 51, 10, 57, 18, 65, 26, 73, 34, 81, 42, 89, 46, 93, 38, 85, 30, 77, 22, 69, 14, 61, 6, 53, 11, 58, 19, 66, 27, 74, 35, 82, 43, 90, 47, 94, 40, 87, 32, 79, 24, 71, 16, 63, 8, 55, 2, 49, 7, 54, 15, 62, 23, 70, 31, 78, 39, 86, 45, 92, 37, 84, 29, 76, 21, 68, 13, 60, 5, 52) L = (1, 49)(2, 53)(3, 54)(4, 48)(5, 55)(6, 59)(7, 58)(8, 61)(9, 62)(10, 50)(11, 51)(12, 52)(13, 63)(14, 67)(15, 66)(16, 69)(17, 70)(18, 56)(19, 57)(20, 60)(21, 71)(22, 75)(23, 74)(24, 77)(25, 78)(26, 64)(27, 65)(28, 68)(29, 79)(30, 83)(31, 82)(32, 85)(33, 86)(34, 72)(35, 73)(36, 76)(37, 87)(38, 91)(39, 90)(40, 93)(41, 92)(42, 80)(43, 81)(44, 84)(45, 94)(46, 88)(47, 89) local type(s) :: { ( 47^94 ) } Outer automorphisms :: reflexible Dual of E23.294 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 47 f = 2 degree seq :: [ 94 ] E23.320 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {47, 47, 47}) Quotient :: loop Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T2 * T1^-2 * T2^-1 * T1^2, T1^-1 * T2 * T1^-4, T1 * T2 * T1 * T2^8, (T1^-1 * T2^-1)^47 ] Map:: non-degenerate R = (1, 48, 3, 50, 9, 56, 19, 66, 29, 76, 39, 86, 41, 88, 31, 78, 21, 68, 11, 58, 14, 61, 24, 71, 34, 81, 44, 91, 46, 93, 38, 85, 28, 75, 18, 65, 8, 55, 2, 49, 7, 54, 17, 64, 27, 74, 37, 84, 42, 89, 32, 79, 22, 69, 12, 59, 4, 51, 10, 57, 20, 67, 30, 77, 40, 87, 47, 94, 45, 92, 36, 83, 26, 73, 16, 63, 6, 53, 15, 62, 25, 72, 35, 82, 43, 90, 33, 80, 23, 70, 13, 60, 5, 52) L = (1, 49)(2, 53)(3, 54)(4, 48)(5, 55)(6, 61)(7, 62)(8, 63)(9, 64)(10, 50)(11, 51)(12, 52)(13, 65)(14, 57)(15, 71)(16, 58)(17, 72)(18, 73)(19, 74)(20, 56)(21, 59)(22, 60)(23, 75)(24, 67)(25, 81)(26, 68)(27, 82)(28, 83)(29, 84)(30, 66)(31, 69)(32, 70)(33, 85)(34, 77)(35, 91)(36, 78)(37, 90)(38, 92)(39, 89)(40, 76)(41, 79)(42, 80)(43, 93)(44, 87)(45, 88)(46, 94)(47, 86) local type(s) :: { ( 47^94 ) } Outer automorphisms :: reflexible Dual of E23.301 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 47 f = 2 degree seq :: [ 94 ] E23.321 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {47, 47, 47}) Quotient :: loop Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T2 * T1^2 * T2^-1 * T1^-2, T2^-1 * T1^-5, T2^-1 * T1 * T2^-8 * T1, T1^-2 * T2^-2 * T1 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^3 * T2^-1 * T1^3 * 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^-4 ] Map:: non-degenerate R = (1, 48, 3, 50, 9, 56, 19, 66, 29, 76, 39, 86, 36, 83, 26, 73, 16, 63, 6, 53, 15, 62, 25, 72, 35, 82, 45, 92, 47, 94, 42, 89, 32, 79, 22, 69, 12, 59, 4, 51, 10, 57, 20, 67, 30, 77, 40, 87, 38, 85, 28, 75, 18, 65, 8, 55, 2, 49, 7, 54, 17, 64, 27, 74, 37, 84, 46, 93, 44, 91, 34, 81, 24, 71, 14, 61, 11, 58, 21, 68, 31, 78, 41, 88, 43, 90, 33, 80, 23, 70, 13, 60, 5, 52) L = (1, 49)(2, 53)(3, 54)(4, 48)(5, 55)(6, 61)(7, 62)(8, 63)(9, 64)(10, 50)(11, 51)(12, 52)(13, 65)(14, 59)(15, 58)(16, 71)(17, 72)(18, 73)(19, 74)(20, 56)(21, 57)(22, 60)(23, 75)(24, 69)(25, 68)(26, 81)(27, 82)(28, 83)(29, 84)(30, 66)(31, 67)(32, 70)(33, 85)(34, 79)(35, 78)(36, 91)(37, 92)(38, 86)(39, 93)(40, 76)(41, 77)(42, 80)(43, 87)(44, 89)(45, 88)(46, 94)(47, 90) local type(s) :: { ( 47^94 ) } Outer automorphisms :: reflexible Dual of E23.296 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 47 f = 2 degree seq :: [ 94 ] E23.322 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {47, 47, 47}) Quotient :: loop Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^4 * T2^-1 * T1^2, T2^-7 * T1 * T2^-1, (T1^-1 * T2^-1)^47 ] Map:: non-degenerate R = (1, 48, 3, 50, 9, 56, 19, 66, 31, 78, 30, 77, 18, 65, 8, 55, 2, 49, 7, 54, 17, 64, 29, 76, 41, 88, 40, 87, 28, 75, 16, 63, 6, 53, 15, 62, 27, 74, 39, 86, 47, 94, 43, 90, 34, 81, 22, 69, 14, 61, 26, 73, 38, 85, 46, 93, 44, 91, 35, 82, 23, 70, 11, 58, 21, 68, 33, 80, 42, 89, 45, 92, 36, 83, 24, 71, 12, 59, 4, 51, 10, 57, 20, 67, 32, 79, 37, 84, 25, 72, 13, 60, 5, 52) L = (1, 49)(2, 53)(3, 54)(4, 48)(5, 55)(6, 61)(7, 62)(8, 63)(9, 64)(10, 50)(11, 51)(12, 52)(13, 65)(14, 68)(15, 73)(16, 69)(17, 74)(18, 75)(19, 76)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 77)(26, 80)(27, 85)(28, 81)(29, 86)(30, 87)(31, 88)(32, 66)(33, 67)(34, 70)(35, 71)(36, 72)(37, 78)(38, 89)(39, 93)(40, 90)(41, 94)(42, 79)(43, 82)(44, 83)(45, 84)(46, 92)(47, 91) local type(s) :: { ( 47^94 ) } Outer automorphisms :: reflexible Dual of E23.303 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 47 f = 2 degree seq :: [ 94 ] E23.323 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {47, 47, 47}) Quotient :: loop Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^3 * T2 * T1^3, T2^-6 * T1^-1 * T2^-2, T2^2 * T1^-1 * T2 * T1^-1 * T2^4 * T1^-3, T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^3 ] Map:: non-degenerate R = (1, 48, 3, 50, 9, 56, 19, 66, 31, 78, 36, 83, 24, 71, 12, 59, 4, 51, 10, 57, 20, 67, 32, 79, 42, 89, 45, 92, 35, 82, 23, 70, 11, 58, 21, 68, 33, 80, 43, 90, 46, 93, 38, 85, 26, 73, 14, 61, 22, 69, 34, 81, 44, 91, 47, 94, 40, 87, 28, 75, 16, 63, 6, 53, 15, 62, 27, 74, 39, 86, 41, 88, 30, 77, 18, 65, 8, 55, 2, 49, 7, 54, 17, 64, 29, 76, 37, 84, 25, 72, 13, 60, 5, 52) L = (1, 49)(2, 53)(3, 54)(4, 48)(5, 55)(6, 61)(7, 62)(8, 63)(9, 64)(10, 50)(11, 51)(12, 52)(13, 65)(14, 70)(15, 69)(16, 73)(17, 74)(18, 75)(19, 76)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 77)(26, 82)(27, 81)(28, 85)(29, 86)(30, 87)(31, 84)(32, 66)(33, 67)(34, 68)(35, 71)(36, 72)(37, 88)(38, 92)(39, 91)(40, 93)(41, 94)(42, 78)(43, 79)(44, 80)(45, 83)(46, 89)(47, 90) local type(s) :: { ( 47^94 ) } Outer automorphisms :: reflexible Dual of E23.298 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 47 f = 2 degree seq :: [ 94 ] E23.324 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {47, 47, 47}) Quotient :: loop Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^-1 * T2^-1 * T1^-6, T2 * T1 * T2^2 * T1 * T2^4, T1^2 * T2^-1 * T1 * T2^-1 * T1 * T2^-4 * T1, T2^2 * T1^-1 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-1, (T1^-1 * T2^-1)^47 ] Map:: non-degenerate R = (1, 48, 3, 50, 9, 56, 19, 66, 33, 80, 37, 84, 23, 70, 11, 58, 21, 68, 35, 82, 46, 93, 42, 89, 28, 75, 14, 61, 27, 74, 41, 88, 44, 91, 32, 79, 18, 65, 8, 55, 2, 49, 7, 54, 17, 64, 31, 78, 38, 85, 24, 71, 12, 59, 4, 51, 10, 57, 20, 67, 34, 81, 45, 92, 40, 87, 26, 73, 22, 69, 36, 83, 47, 94, 43, 90, 30, 77, 16, 63, 6, 53, 15, 62, 29, 76, 39, 86, 25, 72, 13, 60, 5, 52) L = (1, 49)(2, 53)(3, 54)(4, 48)(5, 55)(6, 61)(7, 62)(8, 63)(9, 64)(10, 50)(11, 51)(12, 52)(13, 65)(14, 73)(15, 74)(16, 75)(17, 76)(18, 77)(19, 78)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 79)(26, 70)(27, 69)(28, 87)(29, 88)(30, 89)(31, 86)(32, 90)(33, 85)(34, 66)(35, 67)(36, 68)(37, 71)(38, 72)(39, 91)(40, 84)(41, 83)(42, 92)(43, 93)(44, 94)(45, 80)(46, 81)(47, 82) local type(s) :: { ( 47^94 ) } Outer automorphisms :: reflexible Dual of E23.300 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 47 f = 2 degree seq :: [ 94 ] E23.325 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {47, 47, 47}) Quotient :: loop Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T2^5 * T1^-1 * T2, T1^-3 * T2 * T1^-5, T1^-3 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-2 * T1^-2 * T2^-3 ] Map:: non-degenerate R = (1, 48, 3, 50, 9, 56, 19, 66, 18, 65, 8, 55, 2, 49, 7, 54, 17, 64, 31, 78, 30, 77, 16, 63, 6, 53, 15, 62, 29, 76, 41, 88, 40, 87, 28, 75, 14, 61, 27, 74, 39, 86, 47, 94, 43, 90, 34, 81, 26, 73, 38, 85, 46, 93, 44, 91, 35, 82, 22, 69, 33, 80, 42, 89, 45, 92, 36, 83, 23, 70, 11, 58, 21, 68, 32, 79, 37, 84, 24, 71, 12, 59, 4, 51, 10, 57, 20, 67, 25, 72, 13, 60, 5, 52) L = (1, 49)(2, 53)(3, 54)(4, 48)(5, 55)(6, 61)(7, 62)(8, 63)(9, 64)(10, 50)(11, 51)(12, 52)(13, 65)(14, 73)(15, 74)(16, 75)(17, 76)(18, 77)(19, 78)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 66)(26, 80)(27, 85)(28, 81)(29, 86)(30, 87)(31, 88)(32, 67)(33, 68)(34, 69)(35, 70)(36, 71)(37, 72)(38, 89)(39, 93)(40, 90)(41, 94)(42, 79)(43, 82)(44, 83)(45, 84)(46, 92)(47, 91) local type(s) :: { ( 47^94 ) } Outer automorphisms :: reflexible Dual of E23.305 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 47 f = 2 degree seq :: [ 94 ] E23.326 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {47, 47, 47}) Quotient :: loop Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T2^-4 * T1^-1 * T2^-2, T1^4 * T2 * T1^4, T2 * T1^-1 * T2 * T1^-2 * T2^3 * T1^-4, (T1^-1 * T2^-1)^47 ] Map:: non-degenerate R = (1, 48, 3, 50, 9, 56, 19, 66, 24, 71, 12, 59, 4, 51, 10, 57, 20, 67, 32, 79, 37, 84, 23, 70, 11, 58, 21, 68, 33, 80, 42, 89, 45, 92, 36, 83, 22, 69, 34, 81, 43, 90, 46, 93, 38, 85, 26, 73, 35, 82, 44, 91, 47, 94, 40, 87, 28, 75, 14, 61, 27, 74, 39, 86, 41, 88, 30, 77, 16, 63, 6, 53, 15, 62, 29, 76, 31, 78, 18, 65, 8, 55, 2, 49, 7, 54, 17, 64, 25, 72, 13, 60, 5, 52) L = (1, 49)(2, 53)(3, 54)(4, 48)(5, 55)(6, 61)(7, 62)(8, 63)(9, 64)(10, 50)(11, 51)(12, 52)(13, 65)(14, 73)(15, 74)(16, 75)(17, 76)(18, 77)(19, 72)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 78)(26, 83)(27, 82)(28, 85)(29, 86)(30, 87)(31, 88)(32, 66)(33, 67)(34, 68)(35, 69)(36, 70)(37, 71)(38, 92)(39, 91)(40, 93)(41, 94)(42, 79)(43, 80)(44, 81)(45, 84)(46, 89)(47, 90) local type(s) :: { ( 47^94 ) } Outer automorphisms :: reflexible Dual of E23.302 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 47 f = 2 degree seq :: [ 94 ] E23.327 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {47, 47, 47}) Quotient :: loop Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1 * T2 * T1 * T2^4, T1^-3 * T2 * T1^-6, T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-2 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 48, 3, 50, 9, 56, 19, 66, 23, 70, 11, 58, 21, 68, 32, 79, 41, 88, 43, 90, 34, 81, 36, 83, 44, 91, 46, 93, 39, 86, 28, 75, 14, 61, 27, 74, 30, 77, 18, 65, 8, 55, 2, 49, 7, 54, 17, 64, 24, 71, 12, 59, 4, 51, 10, 57, 20, 67, 31, 78, 35, 82, 22, 69, 33, 80, 42, 89, 47, 94, 45, 92, 38, 85, 26, 73, 37, 84, 40, 87, 29, 76, 16, 63, 6, 53, 15, 62, 25, 72, 13, 60, 5, 52) L = (1, 49)(2, 53)(3, 54)(4, 48)(5, 55)(6, 61)(7, 62)(8, 63)(9, 64)(10, 50)(11, 51)(12, 52)(13, 65)(14, 73)(15, 74)(16, 75)(17, 72)(18, 76)(19, 71)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 77)(26, 83)(27, 84)(28, 85)(29, 86)(30, 87)(31, 66)(32, 67)(33, 68)(34, 69)(35, 70)(36, 80)(37, 91)(38, 81)(39, 92)(40, 93)(41, 78)(42, 79)(43, 82)(44, 89)(45, 90)(46, 94)(47, 88) local type(s) :: { ( 47^94 ) } Outer automorphisms :: reflexible Dual of E23.307 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 47 f = 2 degree seq :: [ 94 ] E23.328 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {47, 47, 47}) Quotient :: loop Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (T2^-1, T1), (F * T1)^2, T2^3 * T1^-1 * T2 * T1^-2 * T2, T1^7 * T2^4, T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 48, 3, 50, 9, 56, 19, 66, 28, 75, 14, 61, 27, 74, 41, 88, 45, 92, 34, 81, 43, 90, 37, 84, 24, 71, 12, 59, 4, 51, 10, 57, 20, 67, 30, 77, 16, 63, 6, 53, 15, 62, 29, 76, 42, 89, 44, 91, 38, 85, 47, 94, 36, 83, 23, 70, 11, 58, 21, 68, 32, 79, 18, 65, 8, 55, 2, 49, 7, 54, 17, 64, 31, 78, 40, 87, 26, 73, 39, 86, 46, 93, 35, 82, 22, 69, 33, 80, 25, 72, 13, 60, 5, 52) L = (1, 49)(2, 53)(3, 54)(4, 48)(5, 55)(6, 61)(7, 62)(8, 63)(9, 64)(10, 50)(11, 51)(12, 52)(13, 65)(14, 73)(15, 74)(16, 75)(17, 76)(18, 77)(19, 78)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 79)(26, 85)(27, 86)(28, 87)(29, 88)(30, 66)(31, 89)(32, 67)(33, 68)(34, 69)(35, 70)(36, 71)(37, 72)(38, 90)(39, 94)(40, 91)(41, 93)(42, 92)(43, 80)(44, 81)(45, 82)(46, 83)(47, 84) local type(s) :: { ( 47^94 ) } Outer automorphisms :: reflexible Dual of E23.309 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 47 f = 2 degree seq :: [ 94 ] E23.329 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {47, 47, 47}) Quotient :: loop Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T2^2 * T1^-1 * T2^-2 * T1, T1^-2 * T2^-1 * T1^-1 * T2^-4, T2^-3 * T1 * T2^-1 * T1^6, T2^3 * T1 * T2^3 * T1 * T2^3 * T1 * T2^3 * T1 * T2^3 * T1 * T2^3 * T1 * T2^3 * T1 * T2^3 * T1 * T2^3 * T1 * T2^3 * T1 * T2^3 * T1 * T2^3 * T1 * T2^3 * T1 * T2^3 * T1 * T2^3 * T1 * T2^3 * T1 * T2^3 * T1 * T2^3 * T1 * T2^3 * T1 * T2^3 * T1 * T2^3 * T1 * T2^3 * T1 * T2^2 ] Map:: non-degenerate R = (1, 48, 3, 50, 9, 56, 19, 66, 33, 80, 22, 69, 36, 83, 45, 92, 40, 87, 26, 73, 39, 86, 32, 79, 18, 65, 8, 55, 2, 49, 7, 54, 17, 64, 31, 78, 23, 70, 11, 58, 21, 68, 35, 82, 44, 91, 38, 85, 47, 94, 42, 89, 30, 77, 16, 63, 6, 53, 15, 62, 29, 76, 24, 71, 12, 59, 4, 51, 10, 57, 20, 67, 34, 81, 43, 90, 37, 84, 46, 93, 41, 88, 28, 75, 14, 61, 27, 74, 25, 72, 13, 60, 5, 52) L = (1, 49)(2, 53)(3, 54)(4, 48)(5, 55)(6, 61)(7, 62)(8, 63)(9, 64)(10, 50)(11, 51)(12, 52)(13, 65)(14, 73)(15, 74)(16, 75)(17, 76)(18, 77)(19, 78)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 79)(26, 85)(27, 86)(28, 87)(29, 72)(30, 88)(31, 71)(32, 89)(33, 70)(34, 66)(35, 67)(36, 68)(37, 69)(38, 90)(39, 94)(40, 91)(41, 92)(42, 93)(43, 80)(44, 81)(45, 82)(46, 83)(47, 84) local type(s) :: { ( 47^94 ) } Outer automorphisms :: reflexible Dual of E23.304 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 47 f = 2 degree seq :: [ 94 ] E23.330 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {47, 47, 47}) Quotient :: loop Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1 * T2^-1 * T1 * T2^-3 * T1, T1^7 * T2 * T1^4, (T1^-1 * T2^-1)^47 ] Map:: non-degenerate R = (1, 48, 3, 50, 9, 56, 19, 66, 14, 61, 27, 74, 36, 83, 45, 92, 42, 89, 38, 85, 41, 88, 32, 79, 23, 70, 11, 58, 21, 68, 18, 65, 8, 55, 2, 49, 7, 54, 17, 64, 29, 76, 26, 73, 35, 82, 44, 91, 46, 93, 39, 86, 30, 77, 33, 80, 24, 71, 12, 59, 4, 51, 10, 57, 20, 67, 16, 63, 6, 53, 15, 62, 28, 75, 37, 84, 34, 81, 43, 90, 47, 94, 40, 87, 31, 78, 22, 69, 25, 72, 13, 60, 5, 52) L = (1, 49)(2, 53)(3, 54)(4, 48)(5, 55)(6, 61)(7, 62)(8, 63)(9, 64)(10, 50)(11, 51)(12, 52)(13, 65)(14, 73)(15, 74)(16, 66)(17, 75)(18, 67)(19, 76)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 68)(26, 81)(27, 82)(28, 83)(29, 84)(30, 69)(31, 70)(32, 71)(33, 72)(34, 89)(35, 90)(36, 91)(37, 92)(38, 77)(39, 78)(40, 79)(41, 80)(42, 86)(43, 85)(44, 94)(45, 93)(46, 87)(47, 88) local type(s) :: { ( 47^94 ) } Outer automorphisms :: reflexible Dual of E23.306 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 47 f = 2 degree seq :: [ 94 ] E23.331 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {47, 47, 47}) Quotient :: loop Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2^-1, T1^-1), T2^3 * T1^-1 * T2, T1^10 * T2^-1 * T1^2, (T1^-1 * T2^-1)^47 ] Map:: non-degenerate R = (1, 48, 3, 50, 9, 56, 8, 55, 2, 49, 7, 54, 17, 64, 16, 63, 6, 53, 15, 62, 25, 72, 24, 71, 14, 61, 23, 70, 33, 80, 32, 79, 22, 69, 31, 78, 41, 88, 40, 87, 30, 77, 39, 86, 47, 94, 43, 90, 38, 85, 46, 93, 44, 91, 35, 82, 42, 89, 45, 92, 36, 83, 27, 74, 34, 81, 37, 84, 28, 75, 19, 66, 26, 73, 29, 76, 20, 67, 11, 58, 18, 65, 21, 68, 12, 59, 4, 51, 10, 57, 13, 60, 5, 52) L = (1, 49)(2, 53)(3, 54)(4, 48)(5, 55)(6, 61)(7, 62)(8, 63)(9, 64)(10, 50)(11, 51)(12, 52)(13, 56)(14, 69)(15, 70)(16, 71)(17, 72)(18, 57)(19, 58)(20, 59)(21, 60)(22, 77)(23, 78)(24, 79)(25, 80)(26, 65)(27, 66)(28, 67)(29, 68)(30, 85)(31, 86)(32, 87)(33, 88)(34, 73)(35, 74)(36, 75)(37, 76)(38, 89)(39, 93)(40, 90)(41, 94)(42, 81)(43, 82)(44, 83)(45, 84)(46, 92)(47, 91) local type(s) :: { ( 47^94 ) } Outer automorphisms :: reflexible Dual of E23.311 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 47 f = 2 degree seq :: [ 94 ] E23.332 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {47, 47, 47}) Quotient :: loop Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T2, T1), T2^-2 * T1^-1 * T2^-2, T2 * T1^-4 * T2^2 * T1 * T2 * T1^4, T1^-11 * T2^-1 * T1^-1, T2^2 * T1^-1 * T2^2 * T1^-1 * T2^2 * T1^-1 * T2^2 * T1^-1 * T2^2 * T1^-1 * T2^2 * T1^-1 * T2^2 * T1^-1 * T2^2 * T1^-1 * T2^2 * T1^-1 * T2^2 * T1^-1 * T2^2 * T1^-1 * T2^2 * T1^-1 * T2^2 * T1^-1 * T2^2 * T1^-1 * T2^2 * T1^-1 * T2^2 * T1^-1 * T2^2 * T1^-1 * T2^2 * T1^-1 * T2^2 * T1^-1 * T2^2 * T1^-1 * T2^2 * T1^-1 * T2 * T1^-2 * T2^2 * T1^-1 ] Map:: non-degenerate R = (1, 48, 3, 50, 9, 56, 12, 59, 4, 51, 10, 57, 18, 65, 21, 68, 11, 58, 19, 66, 26, 73, 29, 76, 20, 67, 27, 74, 34, 81, 37, 84, 28, 75, 35, 82, 42, 89, 45, 92, 36, 83, 43, 90, 46, 93, 38, 85, 44, 91, 47, 94, 40, 87, 30, 77, 39, 86, 41, 88, 32, 79, 22, 69, 31, 78, 33, 80, 24, 71, 14, 61, 23, 70, 25, 72, 16, 63, 6, 53, 15, 62, 17, 64, 8, 55, 2, 49, 7, 54, 13, 60, 5, 52) L = (1, 49)(2, 53)(3, 54)(4, 48)(5, 55)(6, 61)(7, 62)(8, 63)(9, 60)(10, 50)(11, 51)(12, 52)(13, 64)(14, 69)(15, 70)(16, 71)(17, 72)(18, 56)(19, 57)(20, 58)(21, 59)(22, 77)(23, 78)(24, 79)(25, 80)(26, 65)(27, 66)(28, 67)(29, 68)(30, 85)(31, 86)(32, 87)(33, 88)(34, 73)(35, 74)(36, 75)(37, 76)(38, 92)(39, 91)(40, 93)(41, 94)(42, 81)(43, 82)(44, 83)(45, 84)(46, 89)(47, 90) local type(s) :: { ( 47^94 ) } Outer automorphisms :: reflexible Dual of E23.308 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 47 f = 2 degree seq :: [ 94 ] E23.333 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {47, 47, 47}) Quotient :: loop Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ F^2, (T2, T1), (F * T2)^2, (F * T1)^2, T1^2 * T2^-1 * T1^-2 * T2, T1^4 * T2 * T1 * T2^2, T1^-2 * T2 * T1^-1 * T2^6 * T1^-1, T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-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, 48, 3, 50, 9, 56, 19, 66, 33, 80, 43, 90, 38, 85, 26, 73, 24, 71, 12, 59, 4, 51, 10, 57, 20, 67, 34, 81, 44, 91, 39, 86, 28, 75, 14, 61, 27, 74, 23, 70, 11, 58, 21, 68, 35, 82, 45, 92, 40, 87, 30, 77, 16, 63, 6, 53, 15, 62, 29, 76, 22, 69, 36, 83, 46, 93, 42, 89, 32, 79, 18, 65, 8, 55, 2, 49, 7, 54, 17, 64, 31, 78, 41, 88, 47, 94, 37, 84, 25, 72, 13, 60, 5, 52) L = (1, 49)(2, 53)(3, 54)(4, 48)(5, 55)(6, 61)(7, 62)(8, 63)(9, 64)(10, 50)(11, 51)(12, 52)(13, 65)(14, 73)(15, 74)(16, 75)(17, 76)(18, 77)(19, 78)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 79)(26, 72)(27, 71)(28, 85)(29, 70)(30, 86)(31, 69)(32, 87)(33, 88)(34, 66)(35, 67)(36, 68)(37, 89)(38, 84)(39, 90)(40, 91)(41, 83)(42, 92)(43, 94)(44, 80)(45, 81)(46, 82)(47, 93) local type(s) :: { ( 47^94 ) } Outer automorphisms :: reflexible Dual of E23.313 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 47 f = 2 degree seq :: [ 94 ] E23.334 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {47, 47, 47}) Quotient :: loop Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^-2 * T2 * T1^-1 * T2^2 * T1^-2, T1^-3 * T2^-1 * T1^-1 * T2^-6, (T1^-1 * T2^-1)^47 ] Map:: non-degenerate R = (1, 48, 3, 50, 9, 56, 19, 66, 33, 80, 43, 90, 42, 89, 32, 79, 18, 65, 8, 55, 2, 49, 7, 54, 17, 64, 31, 78, 41, 88, 44, 91, 34, 81, 22, 69, 30, 77, 16, 63, 6, 53, 15, 62, 29, 76, 40, 87, 45, 92, 35, 82, 23, 70, 11, 58, 21, 68, 28, 75, 14, 61, 27, 74, 39, 86, 46, 93, 36, 83, 24, 71, 12, 59, 4, 51, 10, 57, 20, 67, 26, 73, 38, 85, 47, 94, 37, 84, 25, 72, 13, 60, 5, 52) L = (1, 49)(2, 53)(3, 54)(4, 48)(5, 55)(6, 61)(7, 62)(8, 63)(9, 64)(10, 50)(11, 51)(12, 52)(13, 65)(14, 73)(15, 74)(16, 75)(17, 76)(18, 77)(19, 78)(20, 56)(21, 57)(22, 58)(23, 59)(24, 60)(25, 79)(26, 66)(27, 85)(28, 67)(29, 86)(30, 68)(31, 87)(32, 69)(33, 88)(34, 70)(35, 71)(36, 72)(37, 89)(38, 80)(39, 94)(40, 93)(41, 92)(42, 81)(43, 91)(44, 82)(45, 83)(46, 84)(47, 90) local type(s) :: { ( 47^94 ) } Outer automorphisms :: reflexible Dual of E23.310 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 47 f = 2 degree seq :: [ 94 ] E23.335 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {47, 47, 47}) Quotient :: loop Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ F^2, T2^-3 * T1^-1, (F * T2)^2, (F * T1)^2, T1^-1 * T2^-1 * T1^-15 ] Map:: non-degenerate R = (1, 48, 3, 50, 9, 56, 4, 51, 10, 57, 15, 62, 11, 58, 16, 63, 21, 68, 17, 64, 22, 69, 27, 74, 23, 70, 28, 75, 33, 80, 29, 76, 34, 81, 39, 86, 35, 82, 40, 87, 45, 92, 41, 88, 46, 93, 42, 89, 47, 94, 44, 91, 36, 83, 43, 90, 38, 85, 30, 77, 37, 84, 32, 79, 24, 71, 31, 78, 26, 73, 18, 65, 25, 72, 20, 67, 12, 59, 19, 66, 14, 61, 6, 53, 13, 60, 8, 55, 2, 49, 7, 54, 5, 52) L = (1, 49)(2, 53)(3, 54)(4, 48)(5, 55)(6, 59)(7, 60)(8, 61)(9, 52)(10, 50)(11, 51)(12, 65)(13, 66)(14, 67)(15, 56)(16, 57)(17, 58)(18, 71)(19, 72)(20, 73)(21, 62)(22, 63)(23, 64)(24, 77)(25, 78)(26, 79)(27, 68)(28, 69)(29, 70)(30, 83)(31, 84)(32, 85)(33, 74)(34, 75)(35, 76)(36, 89)(37, 90)(38, 91)(39, 80)(40, 81)(41, 82)(42, 92)(43, 94)(44, 93)(45, 86)(46, 87)(47, 88) local type(s) :: { ( 47^94 ) } Outer automorphisms :: reflexible Dual of E23.312 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 47 f = 2 degree seq :: [ 94 ] E23.336 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {47, 47, 47}) Quotient :: dipole Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y1 * Y2^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y3^23 * Y2, Y2 * Y1^-23 ] Map:: R = (1, 48, 2, 49, 6, 53, 10, 57, 14, 61, 18, 65, 22, 69, 26, 73, 30, 77, 34, 81, 38, 85, 42, 89, 46, 93, 44, 91, 40, 87, 36, 83, 32, 79, 28, 75, 24, 71, 20, 67, 16, 63, 12, 59, 8, 55, 3, 50, 5, 52, 7, 54, 11, 58, 15, 62, 19, 66, 23, 70, 27, 74, 31, 78, 35, 82, 39, 86, 43, 90, 47, 94, 45, 92, 41, 88, 37, 84, 33, 80, 29, 76, 25, 72, 21, 68, 17, 64, 13, 60, 9, 56, 4, 51)(95, 142, 97, 144, 98, 145, 102, 149, 103, 150, 106, 153, 107, 154, 110, 157, 111, 158, 114, 161, 115, 162, 118, 165, 119, 166, 122, 169, 123, 170, 126, 173, 127, 174, 130, 177, 131, 178, 134, 181, 135, 182, 138, 185, 139, 186, 140, 187, 141, 188, 136, 183, 137, 184, 132, 179, 133, 180, 128, 175, 129, 176, 124, 171, 125, 172, 120, 167, 121, 168, 116, 163, 117, 164, 112, 159, 113, 160, 108, 155, 109, 156, 104, 151, 105, 152, 100, 147, 101, 148, 96, 143, 99, 146) L = (1, 98)(2, 95)(3, 102)(4, 103)(5, 97)(6, 96)(7, 99)(8, 106)(9, 107)(10, 100)(11, 101)(12, 110)(13, 111)(14, 104)(15, 105)(16, 114)(17, 115)(18, 108)(19, 109)(20, 118)(21, 119)(22, 112)(23, 113)(24, 122)(25, 123)(26, 116)(27, 117)(28, 126)(29, 127)(30, 120)(31, 121)(32, 130)(33, 131)(34, 124)(35, 125)(36, 134)(37, 135)(38, 128)(39, 129)(40, 138)(41, 139)(42, 132)(43, 133)(44, 140)(45, 141)(46, 136)(47, 137)(48, 142)(49, 143)(50, 144)(51, 145)(52, 146)(53, 147)(54, 148)(55, 149)(56, 150)(57, 151)(58, 152)(59, 153)(60, 154)(61, 155)(62, 156)(63, 157)(64, 158)(65, 159)(66, 160)(67, 161)(68, 162)(69, 163)(70, 164)(71, 165)(72, 166)(73, 167)(74, 168)(75, 169)(76, 170)(77, 171)(78, 172)(79, 173)(80, 174)(81, 175)(82, 176)(83, 177)(84, 178)(85, 179)(86, 180)(87, 181)(88, 182)(89, 183)(90, 184)(91, 185)(92, 186)(93, 187)(94, 188) local type(s) :: { ( 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94 ) } Outer automorphisms :: reflexible Dual of E23.358 Graph:: bipartite v = 2 e = 94 f = 48 degree seq :: [ 94^2 ] E23.337 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {47, 47, 47}) Quotient :: dipole Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, Y3 * Y2^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y2^-1, Y1^-1), Y2 * Y3^-23, Y3^-12 * Y1^35, (Y3 * Y2^-1)^47 ] Map:: R = (1, 48, 2, 49, 6, 53, 10, 57, 14, 61, 18, 65, 22, 69, 26, 73, 30, 77, 34, 81, 38, 85, 42, 89, 46, 93, 45, 92, 41, 88, 37, 84, 33, 80, 29, 76, 25, 72, 21, 68, 17, 64, 13, 60, 9, 56, 5, 52, 3, 50, 7, 54, 11, 58, 15, 62, 19, 66, 23, 70, 27, 74, 31, 78, 35, 82, 39, 86, 43, 90, 47, 94, 44, 91, 40, 87, 36, 83, 32, 79, 28, 75, 24, 71, 20, 67, 16, 63, 12, 59, 8, 55, 4, 51)(95, 142, 97, 144, 96, 143, 101, 148, 100, 147, 105, 152, 104, 151, 109, 156, 108, 155, 113, 160, 112, 159, 117, 164, 116, 163, 121, 168, 120, 167, 125, 172, 124, 171, 129, 176, 128, 175, 133, 180, 132, 179, 137, 184, 136, 183, 141, 188, 140, 187, 138, 185, 139, 186, 134, 181, 135, 182, 130, 177, 131, 178, 126, 173, 127, 174, 122, 169, 123, 170, 118, 165, 119, 166, 114, 161, 115, 162, 110, 157, 111, 158, 106, 153, 107, 154, 102, 149, 103, 150, 98, 145, 99, 146) L = (1, 98)(2, 95)(3, 99)(4, 102)(5, 103)(6, 96)(7, 97)(8, 106)(9, 107)(10, 100)(11, 101)(12, 110)(13, 111)(14, 104)(15, 105)(16, 114)(17, 115)(18, 108)(19, 109)(20, 118)(21, 119)(22, 112)(23, 113)(24, 122)(25, 123)(26, 116)(27, 117)(28, 126)(29, 127)(30, 120)(31, 121)(32, 130)(33, 131)(34, 124)(35, 125)(36, 134)(37, 135)(38, 128)(39, 129)(40, 138)(41, 139)(42, 132)(43, 133)(44, 141)(45, 140)(46, 136)(47, 137)(48, 142)(49, 143)(50, 144)(51, 145)(52, 146)(53, 147)(54, 148)(55, 149)(56, 150)(57, 151)(58, 152)(59, 153)(60, 154)(61, 155)(62, 156)(63, 157)(64, 158)(65, 159)(66, 160)(67, 161)(68, 162)(69, 163)(70, 164)(71, 165)(72, 166)(73, 167)(74, 168)(75, 169)(76, 170)(77, 171)(78, 172)(79, 173)(80, 174)(81, 175)(82, 176)(83, 177)(84, 178)(85, 179)(86, 180)(87, 181)(88, 182)(89, 183)(90, 184)(91, 185)(92, 186)(93, 187)(94, 188) local type(s) :: { ( 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94 ) } Outer automorphisms :: reflexible Dual of E23.372 Graph:: bipartite v = 2 e = 94 f = 48 degree seq :: [ 94^2 ] E23.338 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {47, 47, 47}) Quotient :: dipole Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, Y2^-2 * Y1^-1 * Y2^-1, (Y3^-1, Y2^-1), (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y3^-5 * Y2^-1 * Y1^-5 * Y2, Y1^-1 * Y2^-1 * Y1^-15, Y1^6 * Y2^-2 * Y1 * 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 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * 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, 48, 2, 49, 6, 53, 12, 59, 18, 65, 24, 71, 30, 77, 36, 83, 42, 89, 45, 92, 39, 86, 33, 80, 27, 74, 21, 68, 15, 62, 9, 56, 5, 52, 8, 55, 14, 61, 20, 67, 26, 73, 32, 79, 38, 85, 44, 91, 46, 93, 40, 87, 34, 81, 28, 75, 22, 69, 16, 63, 10, 57, 3, 50, 7, 54, 13, 60, 19, 66, 25, 72, 31, 78, 37, 84, 43, 90, 47, 94, 41, 88, 35, 82, 29, 76, 23, 70, 17, 64, 11, 58, 4, 51)(95, 142, 97, 144, 103, 150, 98, 145, 104, 151, 109, 156, 105, 152, 110, 157, 115, 162, 111, 158, 116, 163, 121, 168, 117, 164, 122, 169, 127, 174, 123, 170, 128, 175, 133, 180, 129, 176, 134, 181, 139, 186, 135, 182, 140, 187, 136, 183, 141, 188, 138, 185, 130, 177, 137, 184, 132, 179, 124, 171, 131, 178, 126, 173, 118, 165, 125, 172, 120, 167, 112, 159, 119, 166, 114, 161, 106, 153, 113, 160, 108, 155, 100, 147, 107, 154, 102, 149, 96, 143, 101, 148, 99, 146) L = (1, 98)(2, 95)(3, 104)(4, 105)(5, 103)(6, 96)(7, 97)(8, 99)(9, 109)(10, 110)(11, 111)(12, 100)(13, 101)(14, 102)(15, 115)(16, 116)(17, 117)(18, 106)(19, 107)(20, 108)(21, 121)(22, 122)(23, 123)(24, 112)(25, 113)(26, 114)(27, 127)(28, 128)(29, 129)(30, 118)(31, 119)(32, 120)(33, 133)(34, 134)(35, 135)(36, 124)(37, 125)(38, 126)(39, 139)(40, 140)(41, 141)(42, 130)(43, 131)(44, 132)(45, 136)(46, 138)(47, 137)(48, 142)(49, 143)(50, 144)(51, 145)(52, 146)(53, 147)(54, 148)(55, 149)(56, 150)(57, 151)(58, 152)(59, 153)(60, 154)(61, 155)(62, 156)(63, 157)(64, 158)(65, 159)(66, 160)(67, 161)(68, 162)(69, 163)(70, 164)(71, 165)(72, 166)(73, 167)(74, 168)(75, 169)(76, 170)(77, 171)(78, 172)(79, 173)(80, 174)(81, 175)(82, 176)(83, 177)(84, 178)(85, 179)(86, 180)(87, 181)(88, 182)(89, 183)(90, 184)(91, 185)(92, 186)(93, 187)(94, 188) local type(s) :: { ( 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94 ) } Outer automorphisms :: reflexible Dual of E23.379 Graph:: bipartite v = 2 e = 94 f = 48 degree seq :: [ 94^2 ] E23.339 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {47, 47, 47}) Quotient :: dipole Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, Y2^-2 * Y3^-1 * Y2^-1, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), Y3^-6 * Y2^-1 * Y1^2 * Y3^-8, Y2^-1 * Y3^-7 * Y1^9, Y2^-2 * Y1^-6 * Y2^-2 * Y3^6 * Y2^-2 * Y3^6 * Y2^-2 * Y3^6 * Y2^-2 * Y3^4, (Y3 * Y2^-1)^47 ] Map:: R = (1, 48, 2, 49, 6, 53, 12, 59, 18, 65, 24, 71, 30, 77, 36, 83, 42, 89, 45, 92, 39, 86, 33, 80, 27, 74, 21, 68, 15, 62, 9, 56, 3, 50, 7, 54, 13, 60, 19, 66, 25, 72, 31, 78, 37, 84, 43, 90, 47, 94, 41, 88, 35, 82, 29, 76, 23, 70, 17, 64, 11, 58, 5, 52, 8, 55, 14, 61, 20, 67, 26, 73, 32, 79, 38, 85, 44, 91, 46, 93, 40, 87, 34, 81, 28, 75, 22, 69, 16, 63, 10, 57, 4, 51)(95, 142, 97, 144, 102, 149, 96, 143, 101, 148, 108, 155, 100, 147, 107, 154, 114, 161, 106, 153, 113, 160, 120, 167, 112, 159, 119, 166, 126, 173, 118, 165, 125, 172, 132, 179, 124, 171, 131, 178, 138, 185, 130, 177, 137, 184, 140, 187, 136, 183, 141, 188, 134, 181, 139, 186, 135, 182, 128, 175, 133, 180, 129, 176, 122, 169, 127, 174, 123, 170, 116, 163, 121, 168, 117, 164, 110, 157, 115, 162, 111, 158, 104, 151, 109, 156, 105, 152, 98, 145, 103, 150, 99, 146) L = (1, 98)(2, 95)(3, 103)(4, 104)(5, 105)(6, 96)(7, 97)(8, 99)(9, 109)(10, 110)(11, 111)(12, 100)(13, 101)(14, 102)(15, 115)(16, 116)(17, 117)(18, 106)(19, 107)(20, 108)(21, 121)(22, 122)(23, 123)(24, 112)(25, 113)(26, 114)(27, 127)(28, 128)(29, 129)(30, 118)(31, 119)(32, 120)(33, 133)(34, 134)(35, 135)(36, 124)(37, 125)(38, 126)(39, 139)(40, 140)(41, 141)(42, 130)(43, 131)(44, 132)(45, 136)(46, 138)(47, 137)(48, 142)(49, 143)(50, 144)(51, 145)(52, 146)(53, 147)(54, 148)(55, 149)(56, 150)(57, 151)(58, 152)(59, 153)(60, 154)(61, 155)(62, 156)(63, 157)(64, 158)(65, 159)(66, 160)(67, 161)(68, 162)(69, 163)(70, 164)(71, 165)(72, 166)(73, 167)(74, 168)(75, 169)(76, 170)(77, 171)(78, 172)(79, 173)(80, 174)(81, 175)(82, 176)(83, 177)(84, 178)(85, 179)(86, 180)(87, 181)(88, 182)(89, 183)(90, 184)(91, 185)(92, 186)(93, 187)(94, 188) local type(s) :: { ( 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94 ) } Outer automorphisms :: reflexible Dual of E23.368 Graph:: bipartite v = 2 e = 94 f = 48 degree seq :: [ 94^2 ] E23.340 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {47, 47, 47}) Quotient :: dipole Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y1^-1, Y2^-1), (Y2, Y3^-1), Y2^-3 * Y1^-1 * Y2^-1, Y1^-10 * Y2^-1 * Y1^-2, Y3 * Y2 * Y3^4 * Y2^2 * Y1^-6, Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2 * Y3^2 * Y2^2 * Y3 ] Map:: R = (1, 48, 2, 49, 6, 53, 14, 61, 22, 69, 30, 77, 38, 85, 45, 92, 37, 84, 29, 76, 21, 68, 12, 59, 5, 52, 8, 55, 16, 63, 24, 71, 32, 79, 40, 87, 46, 93, 42, 89, 34, 81, 26, 73, 18, 65, 9, 56, 13, 60, 17, 64, 25, 72, 33, 80, 41, 88, 47, 94, 43, 90, 35, 82, 27, 74, 19, 66, 10, 57, 3, 50, 7, 54, 15, 62, 23, 70, 31, 78, 39, 86, 44, 91, 36, 83, 28, 75, 20, 67, 11, 58, 4, 51)(95, 142, 97, 144, 103, 150, 106, 153, 98, 145, 104, 151, 112, 159, 115, 162, 105, 152, 113, 160, 120, 167, 123, 170, 114, 161, 121, 168, 128, 175, 131, 178, 122, 169, 129, 176, 136, 183, 139, 186, 130, 177, 137, 184, 140, 187, 132, 179, 138, 185, 141, 188, 134, 181, 124, 171, 133, 180, 135, 182, 126, 173, 116, 163, 125, 172, 127, 174, 118, 165, 108, 155, 117, 164, 119, 166, 110, 157, 100, 147, 109, 156, 111, 158, 102, 149, 96, 143, 101, 148, 107, 154, 99, 146) L = (1, 98)(2, 95)(3, 104)(4, 105)(5, 106)(6, 96)(7, 97)(8, 99)(9, 112)(10, 113)(11, 114)(12, 115)(13, 103)(14, 100)(15, 101)(16, 102)(17, 107)(18, 120)(19, 121)(20, 122)(21, 123)(22, 108)(23, 109)(24, 110)(25, 111)(26, 128)(27, 129)(28, 130)(29, 131)(30, 116)(31, 117)(32, 118)(33, 119)(34, 136)(35, 137)(36, 138)(37, 139)(38, 124)(39, 125)(40, 126)(41, 127)(42, 140)(43, 141)(44, 133)(45, 132)(46, 134)(47, 135)(48, 142)(49, 143)(50, 144)(51, 145)(52, 146)(53, 147)(54, 148)(55, 149)(56, 150)(57, 151)(58, 152)(59, 153)(60, 154)(61, 155)(62, 156)(63, 157)(64, 158)(65, 159)(66, 160)(67, 161)(68, 162)(69, 163)(70, 164)(71, 165)(72, 166)(73, 167)(74, 168)(75, 169)(76, 170)(77, 171)(78, 172)(79, 173)(80, 174)(81, 175)(82, 176)(83, 177)(84, 178)(85, 179)(86, 180)(87, 181)(88, 182)(89, 183)(90, 184)(91, 185)(92, 186)(93, 187)(94, 188) local type(s) :: { ( 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94 ) } Outer automorphisms :: reflexible Dual of E23.373 Graph:: bipartite v = 2 e = 94 f = 48 degree seq :: [ 94^2 ] E23.341 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {47, 47, 47}) Quotient :: dipole Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, (Y1^-1, Y2), (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y2, Y3^-1), Y2^-4 * Y1, Y1^10 * Y2^-1 * Y1^2, Y3 * Y2 * Y3^4 * Y2 * Y3^5 * Y2 * Y3^5 * Y2 * Y3^5 * Y2 * Y3^5 * Y2, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 48, 2, 49, 6, 53, 14, 61, 22, 69, 30, 77, 38, 85, 42, 89, 34, 81, 26, 73, 18, 65, 10, 57, 3, 50, 7, 54, 15, 62, 23, 70, 31, 78, 39, 86, 46, 93, 45, 92, 37, 84, 29, 76, 21, 68, 13, 60, 9, 56, 17, 64, 25, 72, 33, 80, 41, 88, 47, 94, 44, 91, 36, 83, 28, 75, 20, 67, 12, 59, 5, 52, 8, 55, 16, 63, 24, 71, 32, 79, 40, 87, 43, 90, 35, 82, 27, 74, 19, 66, 11, 58, 4, 51)(95, 142, 97, 144, 103, 150, 102, 149, 96, 143, 101, 148, 111, 158, 110, 157, 100, 147, 109, 156, 119, 166, 118, 165, 108, 155, 117, 164, 127, 174, 126, 173, 116, 163, 125, 172, 135, 182, 134, 181, 124, 171, 133, 180, 141, 188, 137, 184, 132, 179, 140, 187, 138, 185, 129, 176, 136, 183, 139, 186, 130, 177, 121, 168, 128, 175, 131, 178, 122, 169, 113, 160, 120, 167, 123, 170, 114, 161, 105, 152, 112, 159, 115, 162, 106, 153, 98, 145, 104, 151, 107, 154, 99, 146) L = (1, 98)(2, 95)(3, 104)(4, 105)(5, 106)(6, 96)(7, 97)(8, 99)(9, 107)(10, 112)(11, 113)(12, 114)(13, 115)(14, 100)(15, 101)(16, 102)(17, 103)(18, 120)(19, 121)(20, 122)(21, 123)(22, 108)(23, 109)(24, 110)(25, 111)(26, 128)(27, 129)(28, 130)(29, 131)(30, 116)(31, 117)(32, 118)(33, 119)(34, 136)(35, 137)(36, 138)(37, 139)(38, 124)(39, 125)(40, 126)(41, 127)(42, 132)(43, 134)(44, 141)(45, 140)(46, 133)(47, 135)(48, 142)(49, 143)(50, 144)(51, 145)(52, 146)(53, 147)(54, 148)(55, 149)(56, 150)(57, 151)(58, 152)(59, 153)(60, 154)(61, 155)(62, 156)(63, 157)(64, 158)(65, 159)(66, 160)(67, 161)(68, 162)(69, 163)(70, 164)(71, 165)(72, 166)(73, 167)(74, 168)(75, 169)(76, 170)(77, 171)(78, 172)(79, 173)(80, 174)(81, 175)(82, 176)(83, 177)(84, 178)(85, 179)(86, 180)(87, 181)(88, 182)(89, 183)(90, 184)(91, 185)(92, 186)(93, 187)(94, 188) local type(s) :: { ( 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94 ) } Outer automorphisms :: reflexible Dual of E23.375 Graph:: bipartite v = 2 e = 94 f = 48 degree seq :: [ 94^2 ] E23.342 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {47, 47, 47}) Quotient :: dipole Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, (R * Y2)^2, (Y2, Y1^-1), (R * Y1)^2, (R * Y3)^2, (Y3^-1, Y2^-1), Y2^3 * Y3^-1 * Y2^2, Y1^-1 * Y2 * Y1^-8 * Y2, Y3^2 * Y2^2 * Y3^3 * Y2^2 * Y3^3 * Y2^2 * Y3^3 * Y2^2 * Y3^3 * Y2^2 * Y3^3 * Y2^-1, Y2^-1 * Y3^2 * Y2^2 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 48, 2, 49, 6, 53, 14, 61, 24, 71, 34, 81, 40, 87, 30, 77, 20, 67, 9, 56, 17, 64, 27, 74, 37, 84, 45, 92, 47, 94, 43, 90, 33, 80, 23, 70, 12, 59, 5, 52, 8, 55, 16, 63, 26, 73, 36, 83, 41, 88, 31, 78, 21, 68, 10, 57, 3, 50, 7, 54, 15, 62, 25, 72, 35, 82, 44, 91, 46, 93, 39, 86, 29, 76, 19, 66, 13, 60, 18, 65, 28, 75, 38, 85, 42, 89, 32, 79, 22, 69, 11, 58, 4, 51)(95, 142, 97, 144, 103, 150, 113, 160, 106, 153, 98, 145, 104, 151, 114, 161, 123, 170, 117, 164, 105, 152, 115, 162, 124, 171, 133, 180, 127, 174, 116, 163, 125, 172, 134, 181, 140, 187, 137, 184, 126, 173, 135, 182, 128, 175, 138, 185, 141, 188, 136, 183, 130, 177, 118, 165, 129, 176, 139, 186, 132, 179, 120, 167, 108, 155, 119, 166, 131, 178, 122, 169, 110, 157, 100, 147, 109, 156, 121, 168, 112, 159, 102, 149, 96, 143, 101, 148, 111, 158, 107, 154, 99, 146) L = (1, 98)(2, 95)(3, 104)(4, 105)(5, 106)(6, 96)(7, 97)(8, 99)(9, 114)(10, 115)(11, 116)(12, 117)(13, 113)(14, 100)(15, 101)(16, 102)(17, 103)(18, 107)(19, 123)(20, 124)(21, 125)(22, 126)(23, 127)(24, 108)(25, 109)(26, 110)(27, 111)(28, 112)(29, 133)(30, 134)(31, 135)(32, 136)(33, 137)(34, 118)(35, 119)(36, 120)(37, 121)(38, 122)(39, 140)(40, 128)(41, 130)(42, 132)(43, 141)(44, 129)(45, 131)(46, 138)(47, 139)(48, 142)(49, 143)(50, 144)(51, 145)(52, 146)(53, 147)(54, 148)(55, 149)(56, 150)(57, 151)(58, 152)(59, 153)(60, 154)(61, 155)(62, 156)(63, 157)(64, 158)(65, 159)(66, 160)(67, 161)(68, 162)(69, 163)(70, 164)(71, 165)(72, 166)(73, 167)(74, 168)(75, 169)(76, 170)(77, 171)(78, 172)(79, 173)(80, 174)(81, 175)(82, 176)(83, 177)(84, 178)(85, 179)(86, 180)(87, 181)(88, 182)(89, 183)(90, 184)(91, 185)(92, 186)(93, 187)(94, 188) local type(s) :: { ( 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94 ) } Outer automorphisms :: reflexible Dual of E23.369 Graph:: bipartite v = 2 e = 94 f = 48 degree seq :: [ 94^2 ] E23.343 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {47, 47, 47}) Quotient :: dipole Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, (R * Y1)^2, (R * Y2)^2, (Y2^-1, Y1^-1), (Y3^-1, Y2^-1), (R * Y3)^2, Y2^4 * Y1^-1 * Y2, Y2^5 * Y3, Y1 * Y2 * Y1^8 * Y2, Y3^-4 * Y1 * Y2^-1 * Y1 * Y3^-3 * Y2^3, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 48, 2, 49, 6, 53, 14, 61, 24, 71, 34, 81, 43, 90, 33, 80, 23, 70, 13, 60, 18, 65, 28, 75, 38, 85, 45, 92, 47, 94, 40, 87, 30, 77, 20, 67, 10, 57, 3, 50, 7, 54, 15, 62, 25, 72, 35, 82, 42, 89, 32, 79, 22, 69, 12, 59, 5, 52, 8, 55, 16, 63, 26, 73, 36, 83, 44, 91, 46, 93, 39, 86, 29, 76, 19, 66, 9, 56, 17, 64, 27, 74, 37, 84, 41, 88, 31, 78, 21, 68, 11, 58, 4, 51)(95, 142, 97, 144, 103, 150, 112, 159, 102, 149, 96, 143, 101, 148, 111, 158, 122, 169, 110, 157, 100, 147, 109, 156, 121, 168, 132, 179, 120, 167, 108, 155, 119, 166, 131, 178, 139, 186, 130, 177, 118, 165, 129, 176, 135, 182, 141, 188, 138, 185, 128, 175, 136, 183, 125, 172, 134, 181, 140, 187, 137, 184, 126, 173, 115, 162, 124, 171, 133, 180, 127, 174, 116, 163, 105, 152, 114, 161, 123, 170, 117, 164, 106, 153, 98, 145, 104, 151, 113, 160, 107, 154, 99, 146) L = (1, 98)(2, 95)(3, 104)(4, 105)(5, 106)(6, 96)(7, 97)(8, 99)(9, 113)(10, 114)(11, 115)(12, 116)(13, 117)(14, 100)(15, 101)(16, 102)(17, 103)(18, 107)(19, 123)(20, 124)(21, 125)(22, 126)(23, 127)(24, 108)(25, 109)(26, 110)(27, 111)(28, 112)(29, 133)(30, 134)(31, 135)(32, 136)(33, 137)(34, 118)(35, 119)(36, 120)(37, 121)(38, 122)(39, 140)(40, 141)(41, 131)(42, 129)(43, 128)(44, 130)(45, 132)(46, 138)(47, 139)(48, 142)(49, 143)(50, 144)(51, 145)(52, 146)(53, 147)(54, 148)(55, 149)(56, 150)(57, 151)(58, 152)(59, 153)(60, 154)(61, 155)(62, 156)(63, 157)(64, 158)(65, 159)(66, 160)(67, 161)(68, 162)(69, 163)(70, 164)(71, 165)(72, 166)(73, 167)(74, 168)(75, 169)(76, 170)(77, 171)(78, 172)(79, 173)(80, 174)(81, 175)(82, 176)(83, 177)(84, 178)(85, 179)(86, 180)(87, 181)(88, 182)(89, 183)(90, 184)(91, 185)(92, 186)(93, 187)(94, 188) local type(s) :: { ( 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94 ) } Outer automorphisms :: reflexible Dual of E23.364 Graph:: bipartite v = 2 e = 94 f = 48 degree seq :: [ 94^2 ] E23.344 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {47, 47, 47}) Quotient :: dipole Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y1)^2, (Y3^-1, Y2^-1), (Y1^-1, Y2^-1), (R * Y3)^2, (R * Y2)^2, Y2^4 * Y3^-1 * Y2^2, Y1^3 * Y2 * Y1^2 * Y3^-3, Y3^7 * Y2^-1 * Y3, Y2 * Y3 * Y2 * Y3^2 * Y2^3 * Y1^-4, Y1^2 * Y2^-1 * Y3^-3 * Y2^2 * Y1^-4 * Y3 * Y2^-1, Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^3 ] Map:: R = (1, 48, 2, 49, 6, 53, 14, 61, 26, 73, 36, 83, 23, 70, 12, 59, 5, 52, 8, 55, 16, 63, 28, 75, 38, 85, 45, 92, 37, 84, 24, 71, 13, 60, 18, 65, 30, 77, 40, 87, 46, 93, 42, 89, 32, 79, 19, 66, 25, 72, 31, 78, 41, 88, 47, 94, 43, 90, 33, 80, 20, 67, 9, 56, 17, 64, 29, 76, 39, 86, 44, 91, 34, 81, 21, 68, 10, 57, 3, 50, 7, 54, 15, 62, 27, 74, 35, 82, 22, 69, 11, 58, 4, 51)(95, 142, 97, 144, 103, 150, 113, 160, 118, 165, 106, 153, 98, 145, 104, 151, 114, 161, 126, 173, 131, 178, 117, 164, 105, 152, 115, 162, 127, 174, 136, 183, 139, 186, 130, 177, 116, 163, 128, 175, 137, 184, 140, 187, 132, 179, 120, 167, 129, 176, 138, 185, 141, 188, 134, 181, 122, 169, 108, 155, 121, 168, 133, 180, 135, 182, 124, 171, 110, 157, 100, 147, 109, 156, 123, 170, 125, 172, 112, 159, 102, 149, 96, 143, 101, 148, 111, 158, 119, 166, 107, 154, 99, 146) L = (1, 98)(2, 95)(3, 104)(4, 105)(5, 106)(6, 96)(7, 97)(8, 99)(9, 114)(10, 115)(11, 116)(12, 117)(13, 118)(14, 100)(15, 101)(16, 102)(17, 103)(18, 107)(19, 126)(20, 127)(21, 128)(22, 129)(23, 130)(24, 131)(25, 113)(26, 108)(27, 109)(28, 110)(29, 111)(30, 112)(31, 119)(32, 136)(33, 137)(34, 138)(35, 121)(36, 120)(37, 139)(38, 122)(39, 123)(40, 124)(41, 125)(42, 140)(43, 141)(44, 133)(45, 132)(46, 134)(47, 135)(48, 142)(49, 143)(50, 144)(51, 145)(52, 146)(53, 147)(54, 148)(55, 149)(56, 150)(57, 151)(58, 152)(59, 153)(60, 154)(61, 155)(62, 156)(63, 157)(64, 158)(65, 159)(66, 160)(67, 161)(68, 162)(69, 163)(70, 164)(71, 165)(72, 166)(73, 167)(74, 168)(75, 169)(76, 170)(77, 171)(78, 172)(79, 173)(80, 174)(81, 175)(82, 176)(83, 177)(84, 178)(85, 179)(86, 180)(87, 181)(88, 182)(89, 183)(90, 184)(91, 185)(92, 186)(93, 187)(94, 188) local type(s) :: { ( 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94 ) } Outer automorphisms :: reflexible Dual of E23.376 Graph:: bipartite v = 2 e = 94 f = 48 degree seq :: [ 94^2 ] E23.345 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {47, 47, 47}) Quotient :: dipole Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, (R * Y1)^2, (Y2, Y1^-1), (R * Y3)^2, (R * Y2)^2, (Y3^-1, Y2^-1), Y2^2 * Y3 * Y2^4, Y3 * Y2 * Y3^2 * Y1^2 * Y3^-1 * Y2^-1, Y1^5 * Y3^-1 * Y2^-1 * Y3^-2, Y3 * Y2 * Y3^2 * Y2 * Y3^3 * Y2 * Y3^3 * Y2 * Y3^3 * Y2 * Y3^3 * Y2 * Y3^3 * Y2 * Y3^3 * Y2 * Y3^3 * Y2 * Y3, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * 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, 48, 2, 49, 6, 53, 14, 61, 26, 73, 33, 80, 21, 68, 10, 57, 3, 50, 7, 54, 15, 62, 27, 74, 38, 85, 42, 89, 32, 79, 20, 67, 9, 56, 17, 64, 29, 76, 39, 86, 46, 93, 45, 92, 37, 84, 25, 72, 19, 66, 31, 78, 41, 88, 47, 94, 44, 91, 36, 83, 24, 71, 13, 60, 18, 65, 30, 77, 40, 87, 43, 90, 35, 82, 23, 70, 12, 59, 5, 52, 8, 55, 16, 63, 28, 75, 34, 81, 22, 69, 11, 58, 4, 51)(95, 142, 97, 144, 103, 150, 113, 160, 112, 159, 102, 149, 96, 143, 101, 148, 111, 158, 125, 172, 124, 171, 110, 157, 100, 147, 109, 156, 123, 170, 135, 182, 134, 181, 122, 169, 108, 155, 121, 168, 133, 180, 141, 188, 137, 184, 128, 175, 120, 167, 132, 179, 140, 187, 138, 185, 129, 176, 116, 163, 127, 174, 136, 183, 139, 186, 130, 177, 117, 164, 105, 152, 115, 162, 126, 173, 131, 178, 118, 165, 106, 153, 98, 145, 104, 151, 114, 161, 119, 166, 107, 154, 99, 146) L = (1, 98)(2, 95)(3, 104)(4, 105)(5, 106)(6, 96)(7, 97)(8, 99)(9, 114)(10, 115)(11, 116)(12, 117)(13, 118)(14, 100)(15, 101)(16, 102)(17, 103)(18, 107)(19, 119)(20, 126)(21, 127)(22, 128)(23, 129)(24, 130)(25, 131)(26, 108)(27, 109)(28, 110)(29, 111)(30, 112)(31, 113)(32, 136)(33, 120)(34, 122)(35, 137)(36, 138)(37, 139)(38, 121)(39, 123)(40, 124)(41, 125)(42, 132)(43, 134)(44, 141)(45, 140)(46, 133)(47, 135)(48, 142)(49, 143)(50, 144)(51, 145)(52, 146)(53, 147)(54, 148)(55, 149)(56, 150)(57, 151)(58, 152)(59, 153)(60, 154)(61, 155)(62, 156)(63, 157)(64, 158)(65, 159)(66, 160)(67, 161)(68, 162)(69, 163)(70, 164)(71, 165)(72, 166)(73, 167)(74, 168)(75, 169)(76, 170)(77, 171)(78, 172)(79, 173)(80, 174)(81, 175)(82, 176)(83, 177)(84, 178)(85, 179)(86, 180)(87, 181)(88, 182)(89, 183)(90, 184)(91, 185)(92, 186)(93, 187)(94, 188) local type(s) :: { ( 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94 ) } Outer automorphisms :: reflexible Dual of E23.377 Graph:: bipartite v = 2 e = 94 f = 48 degree seq :: [ 94^2 ] E23.346 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {47, 47, 47}) Quotient :: dipole Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y3^-1 * Y1^-1, (Y2^-1, Y1^-1), (R * Y3)^2, (R * Y2)^2, (Y3^-1, Y2^-1), (R * Y1)^2, Y2^-1 * Y3 * Y2^-6, Y1 * Y2 * Y3^-4 * Y1 * Y2 * Y3^-1, Y1^5 * Y2^2 * Y3^-2, Y1^2 * Y2^-1 * Y1^3 * Y3^-2 * Y2^3, Y1 * Y2^-1 * Y1 * Y2^-2 * Y1 * Y3^-3 * Y2^-2, Y1^2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^-2, Y2 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3^2 * Y2^2 ] Map:: R = (1, 48, 2, 49, 6, 53, 14, 61, 26, 73, 39, 86, 24, 71, 13, 60, 18, 65, 30, 77, 41, 88, 45, 92, 34, 81, 19, 66, 31, 78, 42, 89, 47, 94, 36, 83, 21, 68, 10, 57, 3, 50, 7, 54, 15, 62, 27, 74, 38, 85, 23, 70, 12, 59, 5, 52, 8, 55, 16, 63, 28, 75, 40, 87, 44, 91, 33, 80, 25, 72, 32, 79, 43, 90, 46, 93, 35, 82, 20, 67, 9, 56, 17, 64, 29, 76, 37, 84, 22, 69, 11, 58, 4, 51)(95, 142, 97, 144, 103, 150, 113, 160, 127, 174, 118, 165, 106, 153, 98, 145, 104, 151, 114, 161, 128, 175, 138, 185, 133, 180, 117, 164, 105, 152, 115, 162, 129, 176, 139, 186, 134, 181, 120, 167, 132, 179, 116, 163, 130, 177, 140, 187, 135, 182, 122, 169, 108, 155, 121, 168, 131, 178, 141, 188, 137, 184, 124, 171, 110, 157, 100, 147, 109, 156, 123, 170, 136, 183, 126, 173, 112, 159, 102, 149, 96, 143, 101, 148, 111, 158, 125, 172, 119, 166, 107, 154, 99, 146) L = (1, 98)(2, 95)(3, 104)(4, 105)(5, 106)(6, 96)(7, 97)(8, 99)(9, 114)(10, 115)(11, 116)(12, 117)(13, 118)(14, 100)(15, 101)(16, 102)(17, 103)(18, 107)(19, 128)(20, 129)(21, 130)(22, 131)(23, 132)(24, 133)(25, 127)(26, 108)(27, 109)(28, 110)(29, 111)(30, 112)(31, 113)(32, 119)(33, 138)(34, 139)(35, 140)(36, 141)(37, 123)(38, 121)(39, 120)(40, 122)(41, 124)(42, 125)(43, 126)(44, 134)(45, 135)(46, 137)(47, 136)(48, 142)(49, 143)(50, 144)(51, 145)(52, 146)(53, 147)(54, 148)(55, 149)(56, 150)(57, 151)(58, 152)(59, 153)(60, 154)(61, 155)(62, 156)(63, 157)(64, 158)(65, 159)(66, 160)(67, 161)(68, 162)(69, 163)(70, 164)(71, 165)(72, 166)(73, 167)(74, 168)(75, 169)(76, 170)(77, 171)(78, 172)(79, 173)(80, 174)(81, 175)(82, 176)(83, 177)(84, 178)(85, 179)(86, 180)(87, 181)(88, 182)(89, 183)(90, 184)(91, 185)(92, 186)(93, 187)(94, 188) local type(s) :: { ( 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94 ) } Outer automorphisms :: reflexible Dual of E23.365 Graph:: bipartite v = 2 e = 94 f = 48 degree seq :: [ 94^2 ] E23.347 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {47, 47, 47}) Quotient :: dipole Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, Y1^-1 * Y3^-1, Y1^-1 * Y3^-1, Y1 * Y3, Y1 * Y2 * Y3 * Y2^-1, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y2^-2 * Y3^-1 * Y2^2 * Y1^-1, Y2^7 * Y1^-1, Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y3^-4, Y1 * Y2 * Y3^-2 * Y2^-2 * Y3^3 * Y2, Y1 * Y2 * Y1 * Y2 * Y1 * Y2^3 * Y1 * Y3^-2, Y1^47, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 48, 2, 49, 6, 53, 14, 61, 26, 73, 34, 81, 20, 67, 9, 56, 17, 64, 29, 76, 41, 88, 47, 94, 39, 86, 25, 72, 32, 79, 43, 90, 45, 92, 37, 84, 23, 70, 12, 59, 5, 52, 8, 55, 16, 63, 28, 75, 35, 82, 21, 68, 10, 57, 3, 50, 7, 54, 15, 62, 27, 74, 40, 87, 44, 91, 33, 80, 19, 66, 31, 78, 42, 89, 46, 93, 38, 85, 24, 71, 13, 60, 18, 65, 30, 77, 36, 83, 22, 69, 11, 58, 4, 51)(95, 142, 97, 144, 103, 150, 113, 160, 126, 173, 112, 159, 102, 149, 96, 143, 101, 148, 111, 158, 125, 172, 137, 184, 124, 171, 110, 157, 100, 147, 109, 156, 123, 170, 136, 183, 139, 186, 130, 177, 122, 169, 108, 155, 121, 168, 135, 182, 140, 187, 131, 178, 116, 163, 129, 176, 120, 167, 134, 181, 141, 188, 132, 179, 117, 164, 105, 152, 115, 162, 128, 175, 138, 185, 133, 180, 118, 165, 106, 153, 98, 145, 104, 151, 114, 161, 127, 174, 119, 166, 107, 154, 99, 146) L = (1, 98)(2, 95)(3, 104)(4, 105)(5, 106)(6, 96)(7, 97)(8, 99)(9, 114)(10, 115)(11, 116)(12, 117)(13, 118)(14, 100)(15, 101)(16, 102)(17, 103)(18, 107)(19, 127)(20, 128)(21, 129)(22, 130)(23, 131)(24, 132)(25, 133)(26, 108)(27, 109)(28, 110)(29, 111)(30, 112)(31, 113)(32, 119)(33, 138)(34, 120)(35, 122)(36, 124)(37, 139)(38, 140)(39, 141)(40, 121)(41, 123)(42, 125)(43, 126)(44, 134)(45, 137)(46, 136)(47, 135)(48, 142)(49, 143)(50, 144)(51, 145)(52, 146)(53, 147)(54, 148)(55, 149)(56, 150)(57, 151)(58, 152)(59, 153)(60, 154)(61, 155)(62, 156)(63, 157)(64, 158)(65, 159)(66, 160)(67, 161)(68, 162)(69, 163)(70, 164)(71, 165)(72, 166)(73, 167)(74, 168)(75, 169)(76, 170)(77, 171)(78, 172)(79, 173)(80, 174)(81, 175)(82, 176)(83, 177)(84, 178)(85, 179)(86, 180)(87, 181)(88, 182)(89, 183)(90, 184)(91, 185)(92, 186)(93, 187)(94, 188) local type(s) :: { ( 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94 ) } Outer automorphisms :: reflexible Dual of E23.362 Graph:: bipartite v = 2 e = 94 f = 48 degree seq :: [ 94^2 ] E23.348 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {47, 47, 47}) Quotient :: dipole Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, (R * Y1)^2, (Y1^-1, Y2), (Y3^-1, Y2^-1), (R * Y3)^2, (R * Y2)^2, Y2 * Y3 * Y2^-1 * Y1^2 * Y3, Y2^-2 * Y1^2 * Y3^-3, Y1^4 * Y2^-2 * Y3^-1, Y2^-1 * Y3 * Y2^-8, Y1 * Y2 * Y1 * Y2 * Y3^-3 * Y2^2 * Y3^-3 * Y2^2 * Y3^-3 * Y2^2 * Y3^-3 * Y2^2 * Y3^-3 * Y2^2, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 48, 2, 49, 6, 53, 14, 61, 20, 67, 9, 56, 17, 64, 27, 74, 36, 83, 41, 88, 30, 77, 38, 85, 45, 92, 47, 94, 43, 90, 34, 81, 25, 72, 29, 76, 32, 79, 23, 70, 12, 59, 5, 52, 8, 55, 16, 63, 21, 68, 10, 57, 3, 50, 7, 54, 15, 62, 26, 73, 31, 78, 19, 66, 28, 75, 37, 84, 44, 91, 46, 93, 40, 87, 35, 82, 39, 86, 42, 89, 33, 80, 24, 71, 13, 60, 18, 65, 22, 69, 11, 58, 4, 51)(95, 142, 97, 144, 103, 150, 113, 160, 124, 171, 134, 181, 128, 175, 118, 165, 106, 153, 98, 145, 104, 151, 114, 161, 125, 172, 135, 182, 140, 187, 137, 184, 127, 174, 117, 164, 105, 152, 115, 162, 108, 155, 120, 167, 130, 177, 138, 185, 141, 188, 136, 183, 126, 173, 116, 163, 110, 157, 100, 147, 109, 156, 121, 168, 131, 178, 139, 186, 133, 180, 123, 170, 112, 159, 102, 149, 96, 143, 101, 148, 111, 158, 122, 169, 132, 179, 129, 176, 119, 166, 107, 154, 99, 146) L = (1, 98)(2, 95)(3, 104)(4, 105)(5, 106)(6, 96)(7, 97)(8, 99)(9, 114)(10, 115)(11, 116)(12, 117)(13, 118)(14, 100)(15, 101)(16, 102)(17, 103)(18, 107)(19, 125)(20, 108)(21, 110)(22, 112)(23, 126)(24, 127)(25, 128)(26, 109)(27, 111)(28, 113)(29, 119)(30, 135)(31, 120)(32, 123)(33, 136)(34, 137)(35, 134)(36, 121)(37, 122)(38, 124)(39, 129)(40, 140)(41, 130)(42, 133)(43, 141)(44, 131)(45, 132)(46, 138)(47, 139)(48, 142)(49, 143)(50, 144)(51, 145)(52, 146)(53, 147)(54, 148)(55, 149)(56, 150)(57, 151)(58, 152)(59, 153)(60, 154)(61, 155)(62, 156)(63, 157)(64, 158)(65, 159)(66, 160)(67, 161)(68, 162)(69, 163)(70, 164)(71, 165)(72, 166)(73, 167)(74, 168)(75, 169)(76, 170)(77, 171)(78, 172)(79, 173)(80, 174)(81, 175)(82, 176)(83, 177)(84, 178)(85, 179)(86, 180)(87, 181)(88, 182)(89, 183)(90, 184)(91, 185)(92, 186)(93, 187)(94, 188) local type(s) :: { ( 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94 ) } Outer automorphisms :: reflexible Dual of E23.363 Graph:: bipartite v = 2 e = 94 f = 48 degree seq :: [ 94^2 ] E23.349 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {47, 47, 47}) Quotient :: dipole Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, (R * Y3)^2, (R * Y1)^2, Y2 * Y1 * Y2^-1 * Y3, Y1 * Y2 * Y3 * Y2^-1, (R * Y2)^2, Y2 * Y1^-1 * Y3 * Y2^-1 * Y3^-2, Y1^2 * Y2 * Y3^-2 * Y2 * Y3^-1, Y2 * Y3^-1 * Y2 * Y3^-3 * Y1, Y2^-4 * Y1 * Y2^-5, Y3^-2 * Y2^-2 * Y1 * Y3^-2 * Y2^4, Y2^-1 * Y3^-1 * Y2^-3 * Y3^-3 * Y2^-2 * Y3^-3 * Y2^-2 * Y3^-3 * Y2^-2 * Y3^-3 * Y2^-2 * Y3 * Y2^-2, (Y2^-1 * Y1^-1)^47 ] Map:: R = (1, 48, 2, 49, 6, 53, 14, 61, 24, 71, 13, 60, 18, 65, 27, 74, 36, 83, 43, 90, 35, 82, 39, 86, 45, 92, 47, 94, 41, 88, 31, 78, 19, 66, 28, 75, 33, 80, 21, 68, 10, 57, 3, 50, 7, 54, 15, 62, 23, 70, 12, 59, 5, 52, 8, 55, 16, 63, 26, 73, 34, 81, 25, 72, 29, 76, 37, 84, 44, 91, 46, 93, 40, 87, 30, 77, 38, 85, 42, 89, 32, 79, 20, 67, 9, 56, 17, 64, 22, 69, 11, 58, 4, 51)(95, 142, 97, 144, 103, 150, 113, 160, 124, 171, 133, 180, 123, 170, 112, 159, 102, 149, 96, 143, 101, 148, 111, 158, 122, 169, 132, 179, 139, 186, 131, 178, 121, 168, 110, 157, 100, 147, 109, 156, 116, 163, 127, 174, 136, 183, 141, 188, 138, 185, 130, 177, 120, 167, 108, 155, 117, 164, 105, 152, 115, 162, 126, 173, 135, 182, 140, 187, 137, 184, 128, 175, 118, 165, 106, 153, 98, 145, 104, 151, 114, 161, 125, 172, 134, 181, 129, 176, 119, 166, 107, 154, 99, 146) L = (1, 98)(2, 95)(3, 104)(4, 105)(5, 106)(6, 96)(7, 97)(8, 99)(9, 114)(10, 115)(11, 116)(12, 117)(13, 118)(14, 100)(15, 101)(16, 102)(17, 103)(18, 107)(19, 125)(20, 126)(21, 127)(22, 111)(23, 109)(24, 108)(25, 128)(26, 110)(27, 112)(28, 113)(29, 119)(30, 134)(31, 135)(32, 136)(33, 122)(34, 120)(35, 137)(36, 121)(37, 123)(38, 124)(39, 129)(40, 140)(41, 141)(42, 132)(43, 130)(44, 131)(45, 133)(46, 138)(47, 139)(48, 142)(49, 143)(50, 144)(51, 145)(52, 146)(53, 147)(54, 148)(55, 149)(56, 150)(57, 151)(58, 152)(59, 153)(60, 154)(61, 155)(62, 156)(63, 157)(64, 158)(65, 159)(66, 160)(67, 161)(68, 162)(69, 163)(70, 164)(71, 165)(72, 166)(73, 167)(74, 168)(75, 169)(76, 170)(77, 171)(78, 172)(79, 173)(80, 174)(81, 175)(82, 176)(83, 177)(84, 178)(85, 179)(86, 180)(87, 181)(88, 182)(89, 183)(90, 184)(91, 185)(92, 186)(93, 187)(94, 188) local type(s) :: { ( 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94 ) } Outer automorphisms :: reflexible Dual of E23.371 Graph:: bipartite v = 2 e = 94 f = 48 degree seq :: [ 94^2 ] E23.350 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {47, 47, 47}) Quotient :: dipole Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y1^-1 * Y3^-1, Y3 * Y1, Y1 * Y2 * Y3 * Y2^-1, (R * Y2)^2, Y2^-1 * Y1^-1 * Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y2^-2 * Y1 * Y3^-1 * Y1^-1 * Y2^2 * Y1^-1, Y2^-2 * Y3 * Y2^-1 * Y1^-4, Y1^-1 * Y2^-1 * Y1^-1 * Y3 * Y2^-2 * Y3 * Y1^-1, Y1 * Y2^-1 * Y1 * Y2^-2 * Y1 * Y3^-1 * Y2^-4, Y2^4 * Y1 * Y2^6, Y2^-3 * Y1^42, (Y2^-1 * Y3)^47 ] Map:: R = (1, 48, 2, 49, 6, 53, 14, 61, 26, 73, 25, 72, 32, 79, 40, 87, 44, 91, 33, 80, 41, 88, 36, 83, 21, 68, 10, 57, 3, 50, 7, 54, 15, 62, 27, 74, 24, 71, 13, 60, 18, 65, 30, 77, 39, 86, 43, 90, 47, 94, 46, 93, 35, 82, 20, 67, 9, 56, 17, 64, 29, 76, 23, 70, 12, 59, 5, 52, 8, 55, 16, 63, 28, 75, 38, 85, 37, 84, 42, 89, 45, 92, 34, 81, 19, 66, 31, 78, 22, 69, 11, 58, 4, 51)(95, 142, 97, 144, 103, 150, 113, 160, 127, 174, 137, 184, 132, 179, 120, 167, 118, 165, 106, 153, 98, 145, 104, 151, 114, 161, 128, 175, 138, 185, 133, 180, 122, 169, 108, 155, 121, 168, 117, 164, 105, 152, 115, 162, 129, 176, 139, 186, 134, 181, 124, 171, 110, 157, 100, 147, 109, 156, 123, 170, 116, 163, 130, 177, 140, 187, 136, 183, 126, 173, 112, 159, 102, 149, 96, 143, 101, 148, 111, 158, 125, 172, 135, 182, 141, 188, 131, 178, 119, 166, 107, 154, 99, 146) L = (1, 98)(2, 95)(3, 104)(4, 105)(5, 106)(6, 96)(7, 97)(8, 99)(9, 114)(10, 115)(11, 116)(12, 117)(13, 118)(14, 100)(15, 101)(16, 102)(17, 103)(18, 107)(19, 128)(20, 129)(21, 130)(22, 125)(23, 123)(24, 121)(25, 120)(26, 108)(27, 109)(28, 110)(29, 111)(30, 112)(31, 113)(32, 119)(33, 138)(34, 139)(35, 140)(36, 135)(37, 132)(38, 122)(39, 124)(40, 126)(41, 127)(42, 131)(43, 133)(44, 134)(45, 136)(46, 141)(47, 137)(48, 142)(49, 143)(50, 144)(51, 145)(52, 146)(53, 147)(54, 148)(55, 149)(56, 150)(57, 151)(58, 152)(59, 153)(60, 154)(61, 155)(62, 156)(63, 157)(64, 158)(65, 159)(66, 160)(67, 161)(68, 162)(69, 163)(70, 164)(71, 165)(72, 166)(73, 167)(74, 168)(75, 169)(76, 170)(77, 171)(78, 172)(79, 173)(80, 174)(81, 175)(82, 176)(83, 177)(84, 178)(85, 179)(86, 180)(87, 181)(88, 182)(89, 183)(90, 184)(91, 185)(92, 186)(93, 187)(94, 188) local type(s) :: { ( 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94 ) } Outer automorphisms :: reflexible Dual of E23.378 Graph:: bipartite v = 2 e = 94 f = 48 degree seq :: [ 94^2 ] E23.351 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {47, 47, 47}) Quotient :: dipole Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, (Y3^-1, Y2^-1), (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y2, Y1^-1), Y2^-1 * Y3^-1 * Y1 * Y2 * Y3 * Y1^-1, Y2^3 * Y1 * Y2^-3 * Y1^-1, Y1 * Y2^-1 * Y1 * Y2^-1 * Y3^-1 * Y1 * Y2^-1 * Y3^-1, Y2^2 * Y3 * Y2 * Y1^-4, Y2 * Y3 * Y2 * Y3^2 * Y2 * Y3 * Y1^-1, Y2^4 * Y1 * Y2^3 * Y3^-3, Y3^3 * Y1^-1 * Y3^3 * Y1^-1 * Y3^3 * Y1^-1 * Y3 * Y2^-1 * Y3, Y2^2 * Y3 * Y2 * Y1^43, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 48, 2, 49, 6, 53, 14, 61, 26, 73, 19, 66, 31, 78, 40, 87, 46, 93, 37, 84, 42, 89, 34, 81, 23, 70, 12, 59, 5, 52, 8, 55, 16, 63, 28, 75, 20, 67, 9, 56, 17, 64, 29, 76, 39, 86, 47, 94, 43, 90, 44, 91, 35, 82, 24, 71, 13, 60, 18, 65, 30, 77, 21, 68, 10, 57, 3, 50, 7, 54, 15, 62, 27, 74, 38, 85, 33, 80, 41, 88, 45, 92, 36, 83, 25, 72, 32, 79, 22, 69, 11, 58, 4, 51)(95, 142, 97, 144, 103, 150, 113, 160, 127, 174, 137, 184, 136, 183, 126, 173, 112, 159, 102, 149, 96, 143, 101, 148, 111, 158, 125, 172, 135, 182, 138, 185, 128, 175, 116, 163, 124, 171, 110, 157, 100, 147, 109, 156, 123, 170, 134, 181, 139, 186, 129, 176, 117, 164, 105, 152, 115, 162, 122, 169, 108, 155, 121, 168, 133, 180, 140, 187, 130, 177, 118, 165, 106, 153, 98, 145, 104, 151, 114, 161, 120, 167, 132, 179, 141, 188, 131, 178, 119, 166, 107, 154, 99, 146) L = (1, 98)(2, 95)(3, 104)(4, 105)(5, 106)(6, 96)(7, 97)(8, 99)(9, 114)(10, 115)(11, 116)(12, 117)(13, 118)(14, 100)(15, 101)(16, 102)(17, 103)(18, 107)(19, 120)(20, 122)(21, 124)(22, 126)(23, 128)(24, 129)(25, 130)(26, 108)(27, 109)(28, 110)(29, 111)(30, 112)(31, 113)(32, 119)(33, 132)(34, 136)(35, 138)(36, 139)(37, 140)(38, 121)(39, 123)(40, 125)(41, 127)(42, 131)(43, 141)(44, 137)(45, 135)(46, 134)(47, 133)(48, 142)(49, 143)(50, 144)(51, 145)(52, 146)(53, 147)(54, 148)(55, 149)(56, 150)(57, 151)(58, 152)(59, 153)(60, 154)(61, 155)(62, 156)(63, 157)(64, 158)(65, 159)(66, 160)(67, 161)(68, 162)(69, 163)(70, 164)(71, 165)(72, 166)(73, 167)(74, 168)(75, 169)(76, 170)(77, 171)(78, 172)(79, 173)(80, 174)(81, 175)(82, 176)(83, 177)(84, 178)(85, 179)(86, 180)(87, 181)(88, 182)(89, 183)(90, 184)(91, 185)(92, 186)(93, 187)(94, 188) local type(s) :: { ( 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94 ) } Outer automorphisms :: reflexible Dual of E23.374 Graph:: bipartite v = 2 e = 94 f = 48 degree seq :: [ 94^2 ] E23.352 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {47, 47, 47}) Quotient :: dipole Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, Y3^-1 * Y1^-1, (Y3^-1, Y2^-1), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2, Y1^-1), Y2^-1 * Y3^-2 * Y1^-1 * Y2 * Y1^-1, Y2^-1 * Y1 * Y2^-1 * Y1 * Y3^-2 * Y2^-1, Y2^3 * Y1 * Y2^8, 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 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * 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, 48, 2, 49, 6, 53, 14, 61, 19, 66, 28, 75, 35, 82, 42, 89, 45, 92, 41, 88, 38, 85, 31, 78, 24, 71, 13, 60, 18, 65, 21, 68, 10, 57, 3, 50, 7, 54, 15, 62, 26, 73, 29, 76, 36, 83, 43, 90, 47, 94, 40, 87, 33, 80, 30, 77, 23, 70, 12, 59, 5, 52, 8, 55, 16, 63, 20, 67, 9, 56, 17, 64, 27, 74, 34, 81, 37, 84, 44, 91, 46, 93, 39, 86, 32, 79, 25, 72, 22, 69, 11, 58, 4, 51)(95, 142, 97, 144, 103, 150, 113, 160, 123, 170, 131, 178, 139, 186, 134, 181, 126, 173, 118, 165, 106, 153, 98, 145, 104, 151, 114, 161, 108, 155, 120, 167, 128, 175, 136, 183, 141, 188, 133, 180, 125, 172, 117, 164, 105, 152, 115, 162, 110, 157, 100, 147, 109, 156, 121, 168, 129, 176, 137, 184, 140, 187, 132, 179, 124, 171, 116, 163, 112, 159, 102, 149, 96, 143, 101, 148, 111, 158, 122, 169, 130, 177, 138, 185, 135, 182, 127, 174, 119, 166, 107, 154, 99, 146) L = (1, 98)(2, 95)(3, 104)(4, 105)(5, 106)(6, 96)(7, 97)(8, 99)(9, 114)(10, 115)(11, 116)(12, 117)(13, 118)(14, 100)(15, 101)(16, 102)(17, 103)(18, 107)(19, 108)(20, 110)(21, 112)(22, 119)(23, 124)(24, 125)(25, 126)(26, 109)(27, 111)(28, 113)(29, 120)(30, 127)(31, 132)(32, 133)(33, 134)(34, 121)(35, 122)(36, 123)(37, 128)(38, 135)(39, 140)(40, 141)(41, 139)(42, 129)(43, 130)(44, 131)(45, 136)(46, 138)(47, 137)(48, 142)(49, 143)(50, 144)(51, 145)(52, 146)(53, 147)(54, 148)(55, 149)(56, 150)(57, 151)(58, 152)(59, 153)(60, 154)(61, 155)(62, 156)(63, 157)(64, 158)(65, 159)(66, 160)(67, 161)(68, 162)(69, 163)(70, 164)(71, 165)(72, 166)(73, 167)(74, 168)(75, 169)(76, 170)(77, 171)(78, 172)(79, 173)(80, 174)(81, 175)(82, 176)(83, 177)(84, 178)(85, 179)(86, 180)(87, 181)(88, 182)(89, 183)(90, 184)(91, 185)(92, 186)(93, 187)(94, 188) local type(s) :: { ( 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94 ) } Outer automorphisms :: reflexible Dual of E23.370 Graph:: bipartite v = 2 e = 94 f = 48 degree seq :: [ 94^2 ] E23.353 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {47, 47, 47}) Quotient :: dipole Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, (Y3^-1, Y2^-1), (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, (Y2, Y1^-1), Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y1^-2, Y2^9 * Y1^-1 * Y2^2, Y3^-2 * Y1 * Y2^-4 * Y3^-2 * Y2^-4, Y2^-1 * Y3^2 * Y2^-10 * Y1^3 ] Map:: R = (1, 48, 2, 49, 6, 53, 14, 61, 25, 72, 28, 75, 35, 82, 42, 89, 45, 92, 37, 84, 40, 87, 31, 78, 20, 67, 9, 56, 17, 64, 23, 70, 12, 59, 5, 52, 8, 55, 16, 63, 26, 73, 33, 80, 36, 83, 43, 90, 46, 93, 38, 85, 29, 76, 32, 79, 21, 68, 10, 57, 3, 50, 7, 54, 15, 62, 24, 71, 13, 60, 18, 65, 27, 74, 34, 81, 41, 88, 44, 91, 47, 94, 39, 86, 30, 77, 19, 66, 22, 69, 11, 58, 4, 51)(95, 142, 97, 144, 103, 150, 113, 160, 123, 170, 131, 178, 138, 185, 130, 177, 122, 169, 112, 159, 102, 149, 96, 143, 101, 148, 111, 158, 116, 163, 126, 173, 134, 181, 141, 188, 137, 184, 129, 176, 121, 168, 110, 157, 100, 147, 109, 156, 117, 164, 105, 152, 115, 162, 125, 172, 133, 180, 140, 187, 136, 183, 128, 175, 120, 167, 108, 155, 118, 165, 106, 153, 98, 145, 104, 151, 114, 161, 124, 171, 132, 179, 139, 186, 135, 182, 127, 174, 119, 166, 107, 154, 99, 146) L = (1, 98)(2, 95)(3, 104)(4, 105)(5, 106)(6, 96)(7, 97)(8, 99)(9, 114)(10, 115)(11, 116)(12, 117)(13, 118)(14, 100)(15, 101)(16, 102)(17, 103)(18, 107)(19, 124)(20, 125)(21, 126)(22, 113)(23, 111)(24, 109)(25, 108)(26, 110)(27, 112)(28, 119)(29, 132)(30, 133)(31, 134)(32, 123)(33, 120)(34, 121)(35, 122)(36, 127)(37, 139)(38, 140)(39, 141)(40, 131)(41, 128)(42, 129)(43, 130)(44, 135)(45, 136)(46, 137)(47, 138)(48, 142)(49, 143)(50, 144)(51, 145)(52, 146)(53, 147)(54, 148)(55, 149)(56, 150)(57, 151)(58, 152)(59, 153)(60, 154)(61, 155)(62, 156)(63, 157)(64, 158)(65, 159)(66, 160)(67, 161)(68, 162)(69, 163)(70, 164)(71, 165)(72, 166)(73, 167)(74, 168)(75, 169)(76, 170)(77, 171)(78, 172)(79, 173)(80, 174)(81, 175)(82, 176)(83, 177)(84, 178)(85, 179)(86, 180)(87, 181)(88, 182)(89, 183)(90, 184)(91, 185)(92, 186)(93, 187)(94, 188) local type(s) :: { ( 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94 ) } Outer automorphisms :: reflexible Dual of E23.360 Graph:: bipartite v = 2 e = 94 f = 48 degree seq :: [ 94^2 ] E23.354 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {47, 47, 47}) Quotient :: dipole Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, Y1 * Y3^2 * Y1, (R * Y2)^2, (Y1^-1, Y2), (R * Y1)^2, (R * Y3)^2, Y3^2 * Y2 * Y3^-2 * Y2^-1, Y1^4 * Y2^5, Y2^3 * Y3^-2 * Y2 * Y3^-2 * Y2, Y2^2 * Y1^-1 * Y3^2 * Y1^-3 * Y2 * Y1^-1, Y3^2 * Y2 * Y3^2 * Y2 * Y1^-1 * Y2 * Y1^-2, Y3^25 * Y2^4, Y1^-47, Y1^47, (Y3 * Y2^-1)^47 ] Map:: R = (1, 48, 2, 49, 6, 53, 14, 61, 26, 73, 42, 89, 34, 81, 19, 66, 31, 78, 39, 86, 24, 71, 13, 60, 18, 65, 30, 77, 44, 91, 36, 83, 21, 68, 10, 57, 3, 50, 7, 54, 15, 62, 27, 74, 41, 88, 46, 93, 47, 94, 33, 80, 38, 85, 23, 70, 12, 59, 5, 52, 8, 55, 16, 63, 28, 75, 43, 90, 35, 82, 20, 67, 9, 56, 17, 64, 29, 76, 40, 87, 25, 72, 32, 79, 45, 92, 37, 84, 22, 69, 11, 58, 4, 51)(95, 142, 97, 144, 103, 150, 113, 160, 127, 174, 131, 178, 138, 185, 122, 169, 108, 155, 121, 168, 134, 181, 118, 165, 106, 153, 98, 145, 104, 151, 114, 161, 128, 175, 141, 188, 139, 186, 124, 171, 110, 157, 100, 147, 109, 156, 123, 170, 133, 180, 117, 164, 105, 152, 115, 162, 129, 176, 136, 183, 140, 187, 126, 173, 112, 159, 102, 149, 96, 143, 101, 148, 111, 158, 125, 172, 132, 179, 116, 163, 130, 177, 137, 184, 120, 167, 135, 182, 119, 166, 107, 154, 99, 146) L = (1, 98)(2, 95)(3, 104)(4, 105)(5, 106)(6, 96)(7, 97)(8, 99)(9, 114)(10, 115)(11, 116)(12, 117)(13, 118)(14, 100)(15, 101)(16, 102)(17, 103)(18, 107)(19, 128)(20, 129)(21, 130)(22, 131)(23, 132)(24, 133)(25, 134)(26, 108)(27, 109)(28, 110)(29, 111)(30, 112)(31, 113)(32, 119)(33, 141)(34, 136)(35, 137)(36, 138)(37, 139)(38, 127)(39, 125)(40, 123)(41, 121)(42, 120)(43, 122)(44, 124)(45, 126)(46, 135)(47, 140)(48, 142)(49, 143)(50, 144)(51, 145)(52, 146)(53, 147)(54, 148)(55, 149)(56, 150)(57, 151)(58, 152)(59, 153)(60, 154)(61, 155)(62, 156)(63, 157)(64, 158)(65, 159)(66, 160)(67, 161)(68, 162)(69, 163)(70, 164)(71, 165)(72, 166)(73, 167)(74, 168)(75, 169)(76, 170)(77, 171)(78, 172)(79, 173)(80, 174)(81, 175)(82, 176)(83, 177)(84, 178)(85, 179)(86, 180)(87, 181)(88, 182)(89, 183)(90, 184)(91, 185)(92, 186)(93, 187)(94, 188) local type(s) :: { ( 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94 ) } Outer automorphisms :: reflexible Dual of E23.361 Graph:: bipartite v = 2 e = 94 f = 48 degree seq :: [ 94^2 ] E23.355 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {47, 47, 47}) Quotient :: dipole Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, Y1 * Y2 * Y3 * Y2^-1, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y1^2 * Y2^-1 * Y3^2 * Y2, Y2^-2 * Y3 * Y1^-1 * Y2 * Y1 * Y2 * Y1, Y2^-1 * Y1 * Y2^-2 * Y1 * Y3^-2 * Y2^-2, Y3 * Y2 * Y3^3 * Y2^4, Y2^-3 * Y1^-7, Y3^2 * Y1^-1 * Y2^-1 * Y1^-1 * Y3 * Y2^-2 * Y1^-2, Y1^5 * Y3 * Y2^-5, Y1^5 * Y2^-18, Y3^-24 * Y2^4 * Y3^-1, Y2^-1 * Y3^-2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * 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, 48, 2, 49, 6, 53, 14, 61, 26, 73, 42, 89, 40, 87, 25, 72, 32, 79, 35, 82, 20, 67, 9, 56, 17, 64, 29, 76, 44, 91, 38, 85, 23, 70, 12, 59, 5, 52, 8, 55, 16, 63, 28, 75, 33, 80, 46, 93, 47, 94, 41, 88, 36, 83, 21, 68, 10, 57, 3, 50, 7, 54, 15, 62, 27, 74, 43, 90, 39, 86, 24, 71, 13, 60, 18, 65, 30, 77, 34, 81, 19, 66, 31, 78, 45, 92, 37, 84, 22, 69, 11, 58, 4, 51)(95, 142, 97, 144, 103, 150, 113, 160, 127, 174, 120, 167, 137, 184, 132, 179, 116, 163, 130, 177, 126, 173, 112, 159, 102, 149, 96, 143, 101, 148, 111, 158, 125, 172, 140, 187, 136, 183, 133, 180, 117, 164, 105, 152, 115, 162, 129, 176, 124, 171, 110, 157, 100, 147, 109, 156, 123, 170, 139, 186, 141, 188, 134, 181, 118, 165, 106, 153, 98, 145, 104, 151, 114, 161, 128, 175, 122, 169, 108, 155, 121, 168, 138, 185, 131, 178, 135, 182, 119, 166, 107, 154, 99, 146) L = (1, 98)(2, 95)(3, 104)(4, 105)(5, 106)(6, 96)(7, 97)(8, 99)(9, 114)(10, 115)(11, 116)(12, 117)(13, 118)(14, 100)(15, 101)(16, 102)(17, 103)(18, 107)(19, 128)(20, 129)(21, 130)(22, 131)(23, 132)(24, 133)(25, 134)(26, 108)(27, 109)(28, 110)(29, 111)(30, 112)(31, 113)(32, 119)(33, 122)(34, 124)(35, 126)(36, 135)(37, 139)(38, 138)(39, 137)(40, 136)(41, 141)(42, 120)(43, 121)(44, 123)(45, 125)(46, 127)(47, 140)(48, 142)(49, 143)(50, 144)(51, 145)(52, 146)(53, 147)(54, 148)(55, 149)(56, 150)(57, 151)(58, 152)(59, 153)(60, 154)(61, 155)(62, 156)(63, 157)(64, 158)(65, 159)(66, 160)(67, 161)(68, 162)(69, 163)(70, 164)(71, 165)(72, 166)(73, 167)(74, 168)(75, 169)(76, 170)(77, 171)(78, 172)(79, 173)(80, 174)(81, 175)(82, 176)(83, 177)(84, 178)(85, 179)(86, 180)(87, 181)(88, 182)(89, 183)(90, 184)(91, 185)(92, 186)(93, 187)(94, 188) local type(s) :: { ( 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94 ) } Outer automorphisms :: reflexible Dual of E23.367 Graph:: bipartite v = 2 e = 94 f = 48 degree seq :: [ 94^2 ] E23.356 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {47, 47, 47}) Quotient :: dipole Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, (Y2, Y3^-1), (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), Y3 * Y2 * Y3 * Y2 * Y3, Y2 * Y1^-1 * Y2 * Y1^-2, Y2^-13 * Y1^-1 * Y2^-2, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 48, 2, 49, 6, 53, 9, 56, 15, 62, 20, 67, 22, 69, 27, 74, 32, 79, 34, 81, 39, 86, 44, 91, 46, 93, 43, 90, 41, 88, 36, 83, 31, 78, 29, 76, 24, 71, 19, 66, 17, 64, 12, 59, 5, 52, 8, 55, 10, 57, 3, 50, 7, 54, 14, 61, 16, 63, 21, 68, 26, 73, 28, 75, 33, 80, 38, 85, 40, 87, 45, 92, 47, 94, 42, 89, 37, 84, 35, 82, 30, 77, 25, 72, 23, 70, 18, 65, 13, 60, 11, 58, 4, 51)(95, 142, 97, 144, 103, 150, 110, 157, 116, 163, 122, 169, 128, 175, 134, 181, 140, 187, 136, 183, 130, 177, 124, 171, 118, 165, 112, 159, 106, 153, 98, 145, 104, 151, 100, 147, 108, 155, 114, 161, 120, 167, 126, 173, 132, 179, 138, 185, 141, 188, 135, 182, 129, 176, 123, 170, 117, 164, 111, 158, 105, 152, 102, 149, 96, 143, 101, 148, 109, 156, 115, 162, 121, 168, 127, 174, 133, 180, 139, 186, 137, 184, 131, 178, 125, 172, 119, 166, 113, 160, 107, 154, 99, 146) L = (1, 98)(2, 95)(3, 104)(4, 105)(5, 106)(6, 96)(7, 97)(8, 99)(9, 100)(10, 102)(11, 107)(12, 111)(13, 112)(14, 101)(15, 103)(16, 108)(17, 113)(18, 117)(19, 118)(20, 109)(21, 110)(22, 114)(23, 119)(24, 123)(25, 124)(26, 115)(27, 116)(28, 120)(29, 125)(30, 129)(31, 130)(32, 121)(33, 122)(34, 126)(35, 131)(36, 135)(37, 136)(38, 127)(39, 128)(40, 132)(41, 137)(42, 141)(43, 140)(44, 133)(45, 134)(46, 138)(47, 139)(48, 142)(49, 143)(50, 144)(51, 145)(52, 146)(53, 147)(54, 148)(55, 149)(56, 150)(57, 151)(58, 152)(59, 153)(60, 154)(61, 155)(62, 156)(63, 157)(64, 158)(65, 159)(66, 160)(67, 161)(68, 162)(69, 163)(70, 164)(71, 165)(72, 166)(73, 167)(74, 168)(75, 169)(76, 170)(77, 171)(78, 172)(79, 173)(80, 174)(81, 175)(82, 176)(83, 177)(84, 178)(85, 179)(86, 180)(87, 181)(88, 182)(89, 183)(90, 184)(91, 185)(92, 186)(93, 187)(94, 188) local type(s) :: { ( 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94 ) } Outer automorphisms :: reflexible Dual of E23.366 Graph:: bipartite v = 2 e = 94 f = 48 degree seq :: [ 94^2 ] E23.357 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {47, 47, 47}) Quotient :: dipole Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y3^-1 * Y1^-1, (Y3^-1, Y2^-1), (R * Y1)^2, (R * Y3)^2, (Y2, Y1^-1), (R * Y2)^2, Y2 * Y1 * Y2 * Y1^2, Y2^13 * Y1^-1 * Y2^2, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 48, 2, 49, 6, 53, 13, 60, 15, 62, 20, 67, 25, 72, 27, 74, 32, 79, 37, 84, 39, 86, 44, 91, 46, 93, 40, 87, 42, 89, 35, 82, 28, 75, 30, 77, 23, 70, 16, 63, 18, 65, 10, 57, 3, 50, 7, 54, 12, 59, 5, 52, 8, 55, 14, 61, 19, 66, 21, 68, 26, 73, 31, 78, 33, 80, 38, 85, 43, 90, 45, 92, 47, 94, 41, 88, 34, 81, 36, 83, 29, 76, 22, 69, 24, 71, 17, 64, 9, 56, 11, 58, 4, 51)(95, 142, 97, 144, 103, 150, 110, 157, 116, 163, 122, 169, 128, 175, 134, 181, 139, 186, 133, 180, 127, 174, 121, 168, 115, 162, 109, 156, 102, 149, 96, 143, 101, 148, 105, 152, 112, 159, 118, 165, 124, 171, 130, 177, 136, 183, 141, 188, 138, 185, 132, 179, 126, 173, 120, 167, 114, 161, 108, 155, 100, 147, 106, 153, 98, 145, 104, 151, 111, 158, 117, 164, 123, 170, 129, 176, 135, 182, 140, 187, 137, 184, 131, 178, 125, 172, 119, 166, 113, 160, 107, 154, 99, 146) L = (1, 98)(2, 95)(3, 104)(4, 105)(5, 106)(6, 96)(7, 97)(8, 99)(9, 111)(10, 112)(11, 103)(12, 101)(13, 100)(14, 102)(15, 107)(16, 117)(17, 118)(18, 110)(19, 108)(20, 109)(21, 113)(22, 123)(23, 124)(24, 116)(25, 114)(26, 115)(27, 119)(28, 129)(29, 130)(30, 122)(31, 120)(32, 121)(33, 125)(34, 135)(35, 136)(36, 128)(37, 126)(38, 127)(39, 131)(40, 140)(41, 141)(42, 134)(43, 132)(44, 133)(45, 137)(46, 138)(47, 139)(48, 142)(49, 143)(50, 144)(51, 145)(52, 146)(53, 147)(54, 148)(55, 149)(56, 150)(57, 151)(58, 152)(59, 153)(60, 154)(61, 155)(62, 156)(63, 157)(64, 158)(65, 159)(66, 160)(67, 161)(68, 162)(69, 163)(70, 164)(71, 165)(72, 166)(73, 167)(74, 168)(75, 169)(76, 170)(77, 171)(78, 172)(79, 173)(80, 174)(81, 175)(82, 176)(83, 177)(84, 178)(85, 179)(86, 180)(87, 181)(88, 182)(89, 183)(90, 184)(91, 185)(92, 186)(93, 187)(94, 188) local type(s) :: { ( 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94 ) } Outer automorphisms :: reflexible Dual of E23.359 Graph:: bipartite v = 2 e = 94 f = 48 degree seq :: [ 94^2 ] E23.358 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {47, 47, 47}) Quotient :: dipole Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ Y1, R^2, Y3 * Y2, (R * Y1)^2, R * Y2 * R * Y3^-1, Y2^47, (Y3 * Y2^-1)^47, (Y3^-1 * Y1^-1)^47 ] Map:: R = (1, 48)(2, 49)(3, 50)(4, 51)(5, 52)(6, 53)(7, 54)(8, 55)(9, 56)(10, 57)(11, 58)(12, 59)(13, 60)(14, 61)(15, 62)(16, 63)(17, 64)(18, 65)(19, 66)(20, 67)(21, 68)(22, 69)(23, 70)(24, 71)(25, 72)(26, 73)(27, 74)(28, 75)(29, 76)(30, 77)(31, 78)(32, 79)(33, 80)(34, 81)(35, 82)(36, 83)(37, 84)(38, 85)(39, 86)(40, 87)(41, 88)(42, 89)(43, 90)(44, 91)(45, 92)(46, 93)(47, 94)(95, 142, 96, 143, 98, 145, 100, 147, 102, 149, 104, 151, 106, 153, 108, 155, 117, 164, 126, 173, 136, 183, 141, 188, 140, 187, 139, 186, 138, 185, 137, 184, 127, 174, 135, 182, 134, 181, 133, 180, 132, 179, 131, 178, 130, 177, 129, 176, 128, 175, 125, 172, 124, 171, 123, 170, 122, 169, 121, 168, 120, 167, 119, 166, 118, 165, 116, 163, 115, 162, 114, 161, 113, 160, 112, 159, 111, 158, 110, 157, 109, 156, 107, 154, 105, 152, 103, 150, 101, 148, 99, 146, 97, 144) L = (1, 97)(2, 95)(3, 99)(4, 96)(5, 101)(6, 98)(7, 103)(8, 100)(9, 105)(10, 102)(11, 107)(12, 104)(13, 109)(14, 106)(15, 110)(16, 111)(17, 112)(18, 113)(19, 114)(20, 115)(21, 116)(22, 118)(23, 108)(24, 119)(25, 120)(26, 121)(27, 122)(28, 123)(29, 124)(30, 125)(31, 128)(32, 117)(33, 137)(34, 129)(35, 130)(36, 131)(37, 132)(38, 133)(39, 134)(40, 135)(41, 127)(42, 126)(43, 138)(44, 139)(45, 140)(46, 141)(47, 136)(48, 142)(49, 143)(50, 144)(51, 145)(52, 146)(53, 147)(54, 148)(55, 149)(56, 150)(57, 151)(58, 152)(59, 153)(60, 154)(61, 155)(62, 156)(63, 157)(64, 158)(65, 159)(66, 160)(67, 161)(68, 162)(69, 163)(70, 164)(71, 165)(72, 166)(73, 167)(74, 168)(75, 169)(76, 170)(77, 171)(78, 172)(79, 173)(80, 174)(81, 175)(82, 176)(83, 177)(84, 178)(85, 179)(86, 180)(87, 181)(88, 182)(89, 183)(90, 184)(91, 185)(92, 186)(93, 187)(94, 188) local type(s) :: { ( 94, 94 ), ( 94^94 ) } Outer automorphisms :: reflexible Dual of E23.336 Graph:: bipartite v = 48 e = 94 f = 2 degree seq :: [ 2^47, 94 ] E23.359 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {47, 47, 47}) Quotient :: dipole Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ Y1, R^2, Y3 * Y2^2, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y2 * Y3^-23, (Y3^-1 * Y1^-1)^47, (Y3 * Y2^-1)^47 ] Map:: R = (1, 48)(2, 49)(3, 50)(4, 51)(5, 52)(6, 53)(7, 54)(8, 55)(9, 56)(10, 57)(11, 58)(12, 59)(13, 60)(14, 61)(15, 62)(16, 63)(17, 64)(18, 65)(19, 66)(20, 67)(21, 68)(22, 69)(23, 70)(24, 71)(25, 72)(26, 73)(27, 74)(28, 75)(29, 76)(30, 77)(31, 78)(32, 79)(33, 80)(34, 81)(35, 82)(36, 83)(37, 84)(38, 85)(39, 86)(40, 87)(41, 88)(42, 89)(43, 90)(44, 91)(45, 92)(46, 93)(47, 94)(95, 142, 96, 143, 99, 146, 100, 147, 103, 150, 104, 151, 107, 154, 108, 155, 111, 158, 112, 159, 115, 162, 116, 163, 119, 166, 120, 167, 123, 170, 124, 171, 127, 174, 128, 175, 131, 178, 132, 179, 135, 182, 136, 183, 139, 186, 140, 187, 141, 188, 137, 184, 138, 185, 133, 180, 134, 181, 129, 176, 130, 177, 125, 172, 126, 173, 121, 168, 122, 169, 117, 164, 118, 165, 113, 160, 114, 161, 109, 156, 110, 157, 105, 152, 106, 153, 101, 148, 102, 149, 97, 144, 98, 145) L = (1, 97)(2, 98)(3, 101)(4, 102)(5, 95)(6, 96)(7, 105)(8, 106)(9, 99)(10, 100)(11, 109)(12, 110)(13, 103)(14, 104)(15, 113)(16, 114)(17, 107)(18, 108)(19, 117)(20, 118)(21, 111)(22, 112)(23, 121)(24, 122)(25, 115)(26, 116)(27, 125)(28, 126)(29, 119)(30, 120)(31, 129)(32, 130)(33, 123)(34, 124)(35, 133)(36, 134)(37, 127)(38, 128)(39, 137)(40, 138)(41, 131)(42, 132)(43, 140)(44, 141)(45, 135)(46, 136)(47, 139)(48, 142)(49, 143)(50, 144)(51, 145)(52, 146)(53, 147)(54, 148)(55, 149)(56, 150)(57, 151)(58, 152)(59, 153)(60, 154)(61, 155)(62, 156)(63, 157)(64, 158)(65, 159)(66, 160)(67, 161)(68, 162)(69, 163)(70, 164)(71, 165)(72, 166)(73, 167)(74, 168)(75, 169)(76, 170)(77, 171)(78, 172)(79, 173)(80, 174)(81, 175)(82, 176)(83, 177)(84, 178)(85, 179)(86, 180)(87, 181)(88, 182)(89, 183)(90, 184)(91, 185)(92, 186)(93, 187)(94, 188) local type(s) :: { ( 94, 94 ), ( 94^94 ) } Outer automorphisms :: reflexible Dual of E23.357 Graph:: bipartite v = 48 e = 94 f = 2 degree seq :: [ 2^47, 94 ] E23.360 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {47, 47, 47}) Quotient :: dipole Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ Y1, R^2, Y3^-1 * Y2^-3, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3^-1 * Y2^-1 * Y3^-15, (Y3^-1 * Y1^-1)^47, (Y3 * Y2^-1)^47 ] Map:: R = (1, 48)(2, 49)(3, 50)(4, 51)(5, 52)(6, 53)(7, 54)(8, 55)(9, 56)(10, 57)(11, 58)(12, 59)(13, 60)(14, 61)(15, 62)(16, 63)(17, 64)(18, 65)(19, 66)(20, 67)(21, 68)(22, 69)(23, 70)(24, 71)(25, 72)(26, 73)(27, 74)(28, 75)(29, 76)(30, 77)(31, 78)(32, 79)(33, 80)(34, 81)(35, 82)(36, 83)(37, 84)(38, 85)(39, 86)(40, 87)(41, 88)(42, 89)(43, 90)(44, 91)(45, 92)(46, 93)(47, 94)(95, 142, 96, 143, 100, 147, 99, 146, 102, 149, 106, 153, 105, 152, 108, 155, 112, 159, 111, 158, 114, 161, 118, 165, 117, 164, 120, 167, 124, 171, 123, 170, 126, 173, 130, 177, 129, 176, 132, 179, 136, 183, 135, 182, 138, 185, 139, 186, 141, 188, 140, 187, 133, 180, 137, 184, 134, 181, 127, 174, 131, 178, 128, 175, 121, 168, 125, 172, 122, 169, 115, 162, 119, 166, 116, 163, 109, 156, 113, 160, 110, 157, 103, 150, 107, 154, 104, 151, 97, 144, 101, 148, 98, 145) L = (1, 97)(2, 101)(3, 103)(4, 104)(5, 95)(6, 98)(7, 107)(8, 96)(9, 109)(10, 110)(11, 99)(12, 100)(13, 113)(14, 102)(15, 115)(16, 116)(17, 105)(18, 106)(19, 119)(20, 108)(21, 121)(22, 122)(23, 111)(24, 112)(25, 125)(26, 114)(27, 127)(28, 128)(29, 117)(30, 118)(31, 131)(32, 120)(33, 133)(34, 134)(35, 123)(36, 124)(37, 137)(38, 126)(39, 139)(40, 140)(41, 129)(42, 130)(43, 141)(44, 132)(45, 136)(46, 138)(47, 135)(48, 142)(49, 143)(50, 144)(51, 145)(52, 146)(53, 147)(54, 148)(55, 149)(56, 150)(57, 151)(58, 152)(59, 153)(60, 154)(61, 155)(62, 156)(63, 157)(64, 158)(65, 159)(66, 160)(67, 161)(68, 162)(69, 163)(70, 164)(71, 165)(72, 166)(73, 167)(74, 168)(75, 169)(76, 170)(77, 171)(78, 172)(79, 173)(80, 174)(81, 175)(82, 176)(83, 177)(84, 178)(85, 179)(86, 180)(87, 181)(88, 182)(89, 183)(90, 184)(91, 185)(92, 186)(93, 187)(94, 188) local type(s) :: { ( 94, 94 ), ( 94^94 ) } Outer automorphisms :: reflexible Dual of E23.353 Graph:: bipartite v = 48 e = 94 f = 2 degree seq :: [ 2^47, 94 ] E23.361 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {47, 47, 47}) Quotient :: dipole Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y3, Y2^-1), Y3 * Y2^4, Y3^-11 * Y2^-1 * Y3^-1, Y3^3 * Y2^-1 * Y3 * Y2^-1 * Y3^6 * Y2^-1 * Y3, (Y2^-1 * Y3)^47, (Y3^-1 * Y1^-1)^47 ] Map:: R = (1, 48)(2, 49)(3, 50)(4, 51)(5, 52)(6, 53)(7, 54)(8, 55)(9, 56)(10, 57)(11, 58)(12, 59)(13, 60)(14, 61)(15, 62)(16, 63)(17, 64)(18, 65)(19, 66)(20, 67)(21, 68)(22, 69)(23, 70)(24, 71)(25, 72)(26, 73)(27, 74)(28, 75)(29, 76)(30, 77)(31, 78)(32, 79)(33, 80)(34, 81)(35, 82)(36, 83)(37, 84)(38, 85)(39, 86)(40, 87)(41, 88)(42, 89)(43, 90)(44, 91)(45, 92)(46, 93)(47, 94)(95, 142, 96, 143, 100, 147, 106, 153, 99, 146, 102, 149, 108, 155, 114, 161, 107, 154, 110, 157, 116, 163, 122, 169, 115, 162, 118, 165, 124, 171, 130, 177, 123, 170, 126, 173, 132, 179, 138, 185, 131, 178, 134, 181, 140, 187, 135, 182, 139, 186, 141, 188, 136, 183, 127, 174, 133, 180, 137, 184, 128, 175, 119, 166, 125, 172, 129, 176, 120, 167, 111, 158, 117, 164, 121, 168, 112, 159, 103, 150, 109, 156, 113, 160, 104, 151, 97, 144, 101, 148, 105, 152, 98, 145) L = (1, 97)(2, 101)(3, 103)(4, 104)(5, 95)(6, 105)(7, 109)(8, 96)(9, 111)(10, 112)(11, 113)(12, 98)(13, 99)(14, 100)(15, 117)(16, 102)(17, 119)(18, 120)(19, 121)(20, 106)(21, 107)(22, 108)(23, 125)(24, 110)(25, 127)(26, 128)(27, 129)(28, 114)(29, 115)(30, 116)(31, 133)(32, 118)(33, 135)(34, 136)(35, 137)(36, 122)(37, 123)(38, 124)(39, 139)(40, 126)(41, 138)(42, 140)(43, 141)(44, 130)(45, 131)(46, 132)(47, 134)(48, 142)(49, 143)(50, 144)(51, 145)(52, 146)(53, 147)(54, 148)(55, 149)(56, 150)(57, 151)(58, 152)(59, 153)(60, 154)(61, 155)(62, 156)(63, 157)(64, 158)(65, 159)(66, 160)(67, 161)(68, 162)(69, 163)(70, 164)(71, 165)(72, 166)(73, 167)(74, 168)(75, 169)(76, 170)(77, 171)(78, 172)(79, 173)(80, 174)(81, 175)(82, 176)(83, 177)(84, 178)(85, 179)(86, 180)(87, 181)(88, 182)(89, 183)(90, 184)(91, 185)(92, 186)(93, 187)(94, 188) local type(s) :: { ( 94, 94 ), ( 94^94 ) } Outer automorphisms :: reflexible Dual of E23.354 Graph:: bipartite v = 48 e = 94 f = 2 degree seq :: [ 2^47, 94 ] E23.362 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {47, 47, 47}) Quotient :: dipole Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2, Y3^-1), Y3 * Y2^2 * Y3^-1 * Y2^-2, Y3^-1 * Y2^-5, Y3^-1 * Y2 * Y3^-8 * Y2, Y2 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3^4, (Y3^-1 * Y1^-1)^47 ] Map:: R = (1, 48)(2, 49)(3, 50)(4, 51)(5, 52)(6, 53)(7, 54)(8, 55)(9, 56)(10, 57)(11, 58)(12, 59)(13, 60)(14, 61)(15, 62)(16, 63)(17, 64)(18, 65)(19, 66)(20, 67)(21, 68)(22, 69)(23, 70)(24, 71)(25, 72)(26, 73)(27, 74)(28, 75)(29, 76)(30, 77)(31, 78)(32, 79)(33, 80)(34, 81)(35, 82)(36, 83)(37, 84)(38, 85)(39, 86)(40, 87)(41, 88)(42, 89)(43, 90)(44, 91)(45, 92)(46, 93)(47, 94)(95, 142, 96, 143, 100, 147, 108, 155, 106, 153, 99, 146, 102, 149, 110, 157, 118, 165, 116, 163, 107, 154, 112, 159, 120, 167, 128, 175, 126, 173, 117, 164, 122, 169, 130, 177, 138, 185, 136, 183, 127, 174, 132, 179, 133, 180, 140, 187, 141, 188, 137, 184, 134, 181, 123, 170, 131, 178, 139, 186, 135, 182, 124, 171, 113, 160, 121, 168, 129, 176, 125, 172, 114, 161, 103, 150, 111, 158, 119, 166, 115, 162, 104, 151, 97, 144, 101, 148, 109, 156, 105, 152, 98, 145) L = (1, 97)(2, 101)(3, 103)(4, 104)(5, 95)(6, 109)(7, 111)(8, 96)(9, 113)(10, 114)(11, 115)(12, 98)(13, 99)(14, 105)(15, 119)(16, 100)(17, 121)(18, 102)(19, 123)(20, 124)(21, 125)(22, 106)(23, 107)(24, 108)(25, 129)(26, 110)(27, 131)(28, 112)(29, 133)(30, 134)(31, 135)(32, 116)(33, 117)(34, 118)(35, 139)(36, 120)(37, 140)(38, 122)(39, 130)(40, 132)(41, 137)(42, 126)(43, 127)(44, 128)(45, 141)(46, 138)(47, 136)(48, 142)(49, 143)(50, 144)(51, 145)(52, 146)(53, 147)(54, 148)(55, 149)(56, 150)(57, 151)(58, 152)(59, 153)(60, 154)(61, 155)(62, 156)(63, 157)(64, 158)(65, 159)(66, 160)(67, 161)(68, 162)(69, 163)(70, 164)(71, 165)(72, 166)(73, 167)(74, 168)(75, 169)(76, 170)(77, 171)(78, 172)(79, 173)(80, 174)(81, 175)(82, 176)(83, 177)(84, 178)(85, 179)(86, 180)(87, 181)(88, 182)(89, 183)(90, 184)(91, 185)(92, 186)(93, 187)(94, 188) local type(s) :: { ( 94, 94 ), ( 94^94 ) } Outer automorphisms :: reflexible Dual of E23.347 Graph:: bipartite v = 48 e = 94 f = 2 degree seq :: [ 2^47, 94 ] E23.363 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {47, 47, 47}) Quotient :: dipole Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y2, Y3^-1), Y2^3 * Y3 * Y2^3, Y3^-6 * Y2^-1 * Y3^-2, Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3^4 * Y2^-3, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-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)^47 ] Map:: R = (1, 48)(2, 49)(3, 50)(4, 51)(5, 52)(6, 53)(7, 54)(8, 55)(9, 56)(10, 57)(11, 58)(12, 59)(13, 60)(14, 61)(15, 62)(16, 63)(17, 64)(18, 65)(19, 66)(20, 67)(21, 68)(22, 69)(23, 70)(24, 71)(25, 72)(26, 73)(27, 74)(28, 75)(29, 76)(30, 77)(31, 78)(32, 79)(33, 80)(34, 81)(35, 82)(36, 83)(37, 84)(38, 85)(39, 86)(40, 87)(41, 88)(42, 89)(43, 90)(44, 91)(45, 92)(46, 93)(47, 94)(95, 142, 96, 143, 100, 147, 108, 155, 117, 164, 106, 153, 99, 146, 102, 149, 110, 157, 120, 167, 129, 176, 118, 165, 107, 154, 112, 159, 122, 169, 132, 179, 139, 186, 130, 177, 119, 166, 124, 171, 134, 181, 140, 187, 136, 183, 125, 172, 131, 178, 135, 182, 141, 188, 137, 184, 126, 173, 113, 160, 123, 170, 133, 180, 138, 185, 127, 174, 114, 161, 103, 150, 111, 158, 121, 168, 128, 175, 115, 162, 104, 151, 97, 144, 101, 148, 109, 156, 116, 163, 105, 152, 98, 145) L = (1, 97)(2, 101)(3, 103)(4, 104)(5, 95)(6, 109)(7, 111)(8, 96)(9, 113)(10, 114)(11, 115)(12, 98)(13, 99)(14, 116)(15, 121)(16, 100)(17, 123)(18, 102)(19, 125)(20, 126)(21, 127)(22, 128)(23, 105)(24, 106)(25, 107)(26, 108)(27, 133)(28, 110)(29, 131)(30, 112)(31, 130)(32, 136)(33, 137)(34, 138)(35, 117)(36, 118)(37, 119)(38, 120)(39, 135)(40, 122)(41, 124)(42, 139)(43, 140)(44, 141)(45, 129)(46, 132)(47, 134)(48, 142)(49, 143)(50, 144)(51, 145)(52, 146)(53, 147)(54, 148)(55, 149)(56, 150)(57, 151)(58, 152)(59, 153)(60, 154)(61, 155)(62, 156)(63, 157)(64, 158)(65, 159)(66, 160)(67, 161)(68, 162)(69, 163)(70, 164)(71, 165)(72, 166)(73, 167)(74, 168)(75, 169)(76, 170)(77, 171)(78, 172)(79, 173)(80, 174)(81, 175)(82, 176)(83, 177)(84, 178)(85, 179)(86, 180)(87, 181)(88, 182)(89, 183)(90, 184)(91, 185)(92, 186)(93, 187)(94, 188) local type(s) :: { ( 94, 94 ), ( 94^94 ) } Outer automorphisms :: reflexible Dual of E23.348 Graph:: bipartite v = 48 e = 94 f = 2 degree seq :: [ 2^47, 94 ] E23.364 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {47, 47, 47}) Quotient :: dipole Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2, Y3^-1), Y2^-1 * Y3^-1 * Y2^-6, Y3^2 * Y2 * Y3^4 * Y2 * Y3, Y2^2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-4 * Y2, Y2^-1 * Y3^-2 * Y2^2 * Y3^-3 * Y2^2 * Y3^-3 * Y2^2 * Y3^-3 * Y2^2 * Y3^-3 * Y2^2 * Y3^-3 * Y2^2 * Y3^-3 * Y2^2 * Y3^-3 * Y2^2 * Y3^-3 * Y2^2 * Y3^-3 * Y2^2 * Y3^-3 * Y2^2 * Y3^-3 * Y2^2 * Y3^-3 * Y2^2 * Y3^-3 * Y2^2 * Y3^-3 * Y2^2 * Y3 * Y2^-1, (Y3^-1 * Y1^-1)^47 ] Map:: R = (1, 48)(2, 49)(3, 50)(4, 51)(5, 52)(6, 53)(7, 54)(8, 55)(9, 56)(10, 57)(11, 58)(12, 59)(13, 60)(14, 61)(15, 62)(16, 63)(17, 64)(18, 65)(19, 66)(20, 67)(21, 68)(22, 69)(23, 70)(24, 71)(25, 72)(26, 73)(27, 74)(28, 75)(29, 76)(30, 77)(31, 78)(32, 79)(33, 80)(34, 81)(35, 82)(36, 83)(37, 84)(38, 85)(39, 86)(40, 87)(41, 88)(42, 89)(43, 90)(44, 91)(45, 92)(46, 93)(47, 94)(95, 142, 96, 143, 100, 147, 108, 155, 120, 167, 117, 164, 106, 153, 99, 146, 102, 149, 110, 157, 122, 169, 134, 181, 131, 178, 118, 165, 107, 154, 112, 159, 124, 171, 136, 183, 139, 186, 127, 174, 132, 179, 119, 166, 126, 173, 137, 184, 140, 187, 128, 175, 113, 160, 125, 172, 133, 180, 138, 185, 141, 188, 129, 176, 114, 161, 103, 150, 111, 158, 123, 170, 135, 182, 130, 177, 115, 162, 104, 151, 97, 144, 101, 148, 109, 156, 121, 168, 116, 163, 105, 152, 98, 145) L = (1, 97)(2, 101)(3, 103)(4, 104)(5, 95)(6, 109)(7, 111)(8, 96)(9, 113)(10, 114)(11, 115)(12, 98)(13, 99)(14, 121)(15, 123)(16, 100)(17, 125)(18, 102)(19, 127)(20, 128)(21, 129)(22, 130)(23, 105)(24, 106)(25, 107)(26, 116)(27, 135)(28, 108)(29, 133)(30, 110)(31, 132)(32, 112)(33, 131)(34, 139)(35, 140)(36, 141)(37, 117)(38, 118)(39, 119)(40, 120)(41, 138)(42, 122)(43, 124)(44, 126)(45, 134)(46, 136)(47, 137)(48, 142)(49, 143)(50, 144)(51, 145)(52, 146)(53, 147)(54, 148)(55, 149)(56, 150)(57, 151)(58, 152)(59, 153)(60, 154)(61, 155)(62, 156)(63, 157)(64, 158)(65, 159)(66, 160)(67, 161)(68, 162)(69, 163)(70, 164)(71, 165)(72, 166)(73, 167)(74, 168)(75, 169)(76, 170)(77, 171)(78, 172)(79, 173)(80, 174)(81, 175)(82, 176)(83, 177)(84, 178)(85, 179)(86, 180)(87, 181)(88, 182)(89, 183)(90, 184)(91, 185)(92, 186)(93, 187)(94, 188) local type(s) :: { ( 94, 94 ), ( 94^94 ) } Outer automorphisms :: reflexible Dual of E23.343 Graph:: bipartite v = 48 e = 94 f = 2 degree seq :: [ 2^47, 94 ] E23.365 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {47, 47, 47}) Quotient :: dipole Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y2, Y3^-1), Y3^-4 * Y2^-1 * Y3^-2, Y2^4 * Y3 * Y2^4, Y3 * Y2^-1 * Y3 * Y2^-2 * Y3^3 * Y2^-4, Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * 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)^47 ] Map:: R = (1, 48)(2, 49)(3, 50)(4, 51)(5, 52)(6, 53)(7, 54)(8, 55)(9, 56)(10, 57)(11, 58)(12, 59)(13, 60)(14, 61)(15, 62)(16, 63)(17, 64)(18, 65)(19, 66)(20, 67)(21, 68)(22, 69)(23, 70)(24, 71)(25, 72)(26, 73)(27, 74)(28, 75)(29, 76)(30, 77)(31, 78)(32, 79)(33, 80)(34, 81)(35, 82)(36, 83)(37, 84)(38, 85)(39, 86)(40, 87)(41, 88)(42, 89)(43, 90)(44, 91)(45, 92)(46, 93)(47, 94)(95, 142, 96, 143, 100, 147, 108, 155, 120, 167, 130, 177, 117, 164, 106, 153, 99, 146, 102, 149, 110, 157, 122, 169, 132, 179, 139, 186, 131, 178, 118, 165, 107, 154, 112, 159, 124, 171, 134, 181, 140, 187, 136, 183, 126, 173, 113, 160, 119, 166, 125, 172, 135, 182, 141, 188, 137, 184, 127, 174, 114, 161, 103, 150, 111, 158, 123, 170, 133, 180, 138, 185, 128, 175, 115, 162, 104, 151, 97, 144, 101, 148, 109, 156, 121, 168, 129, 176, 116, 163, 105, 152, 98, 145) L = (1, 97)(2, 101)(3, 103)(4, 104)(5, 95)(6, 109)(7, 111)(8, 96)(9, 113)(10, 114)(11, 115)(12, 98)(13, 99)(14, 121)(15, 123)(16, 100)(17, 119)(18, 102)(19, 118)(20, 126)(21, 127)(22, 128)(23, 105)(24, 106)(25, 107)(26, 129)(27, 133)(28, 108)(29, 125)(30, 110)(31, 112)(32, 131)(33, 136)(34, 137)(35, 138)(36, 116)(37, 117)(38, 120)(39, 135)(40, 122)(41, 124)(42, 139)(43, 140)(44, 141)(45, 130)(46, 132)(47, 134)(48, 142)(49, 143)(50, 144)(51, 145)(52, 146)(53, 147)(54, 148)(55, 149)(56, 150)(57, 151)(58, 152)(59, 153)(60, 154)(61, 155)(62, 156)(63, 157)(64, 158)(65, 159)(66, 160)(67, 161)(68, 162)(69, 163)(70, 164)(71, 165)(72, 166)(73, 167)(74, 168)(75, 169)(76, 170)(77, 171)(78, 172)(79, 173)(80, 174)(81, 175)(82, 176)(83, 177)(84, 178)(85, 179)(86, 180)(87, 181)(88, 182)(89, 183)(90, 184)(91, 185)(92, 186)(93, 187)(94, 188) local type(s) :: { ( 94, 94 ), ( 94^94 ) } Outer automorphisms :: reflexible Dual of E23.346 Graph:: bipartite v = 48 e = 94 f = 2 degree seq :: [ 2^47, 94 ] E23.366 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {47, 47, 47}) Quotient :: dipole Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2, Y3^-1), Y3 * Y2^-1 * Y3^4 * Y2^-1, Y2^-2 * Y3^-1 * Y2^-7, Y2^-2 * Y3 * Y2^-2 * Y3 * Y2^-2 * Y3 * Y2^-2 * Y3 * Y2^-2 * Y3 * Y2^-2 * Y3 * Y2^-2 * Y3 * Y2^-2 * Y3 * Y2^-2 * Y3 * Y2^-2 * Y3 * Y2^-2 * Y3 * Y2^-2 * Y3 * Y2^-2 * Y3 * Y2^-2 * Y3 * Y2^-2 * Y3 * Y2^-2 * Y3 * Y2^-2 * Y3 * Y2^-1, (Y3^-1 * Y1^-1)^47 ] Map:: R = (1, 48)(2, 49)(3, 50)(4, 51)(5, 52)(6, 53)(7, 54)(8, 55)(9, 56)(10, 57)(11, 58)(12, 59)(13, 60)(14, 61)(15, 62)(16, 63)(17, 64)(18, 65)(19, 66)(20, 67)(21, 68)(22, 69)(23, 70)(24, 71)(25, 72)(26, 73)(27, 74)(28, 75)(29, 76)(30, 77)(31, 78)(32, 79)(33, 80)(34, 81)(35, 82)(36, 83)(37, 84)(38, 85)(39, 86)(40, 87)(41, 88)(42, 89)(43, 90)(44, 91)(45, 92)(46, 93)(47, 94)(95, 142, 96, 143, 100, 147, 108, 155, 120, 167, 130, 177, 127, 174, 117, 164, 106, 153, 99, 146, 102, 149, 110, 157, 122, 169, 132, 179, 138, 185, 136, 183, 128, 175, 118, 165, 107, 154, 112, 159, 113, 160, 124, 171, 134, 181, 140, 187, 141, 188, 137, 184, 129, 176, 119, 166, 114, 161, 103, 150, 111, 158, 123, 170, 133, 180, 139, 186, 135, 182, 125, 172, 115, 162, 104, 151, 97, 144, 101, 148, 109, 156, 121, 168, 131, 178, 126, 173, 116, 163, 105, 152, 98, 145) L = (1, 97)(2, 101)(3, 103)(4, 104)(5, 95)(6, 109)(7, 111)(8, 96)(9, 113)(10, 114)(11, 115)(12, 98)(13, 99)(14, 121)(15, 123)(16, 100)(17, 124)(18, 102)(19, 110)(20, 112)(21, 119)(22, 125)(23, 105)(24, 106)(25, 107)(26, 131)(27, 133)(28, 108)(29, 134)(30, 122)(31, 129)(32, 135)(33, 116)(34, 117)(35, 118)(36, 126)(37, 139)(38, 120)(39, 140)(40, 132)(41, 137)(42, 127)(43, 128)(44, 130)(45, 141)(46, 138)(47, 136)(48, 142)(49, 143)(50, 144)(51, 145)(52, 146)(53, 147)(54, 148)(55, 149)(56, 150)(57, 151)(58, 152)(59, 153)(60, 154)(61, 155)(62, 156)(63, 157)(64, 158)(65, 159)(66, 160)(67, 161)(68, 162)(69, 163)(70, 164)(71, 165)(72, 166)(73, 167)(74, 168)(75, 169)(76, 170)(77, 171)(78, 172)(79, 173)(80, 174)(81, 175)(82, 176)(83, 177)(84, 178)(85, 179)(86, 180)(87, 181)(88, 182)(89, 183)(90, 184)(91, 185)(92, 186)(93, 187)(94, 188) local type(s) :: { ( 94, 94 ), ( 94^94 ) } Outer automorphisms :: reflexible Dual of E23.356 Graph:: bipartite v = 48 e = 94 f = 2 degree seq :: [ 2^47, 94 ] E23.367 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {47, 47, 47}) Quotient :: dipole Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2, Y3^-1), Y2^-2 * Y3^-1 * Y2^-1 * Y3^-4, Y3^3 * Y2^-1 * 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 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * 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)^47 ] Map:: R = (1, 48)(2, 49)(3, 50)(4, 51)(5, 52)(6, 53)(7, 54)(8, 55)(9, 56)(10, 57)(11, 58)(12, 59)(13, 60)(14, 61)(15, 62)(16, 63)(17, 64)(18, 65)(19, 66)(20, 67)(21, 68)(22, 69)(23, 70)(24, 71)(25, 72)(26, 73)(27, 74)(28, 75)(29, 76)(30, 77)(31, 78)(32, 79)(33, 80)(34, 81)(35, 82)(36, 83)(37, 84)(38, 85)(39, 86)(40, 87)(41, 88)(42, 89)(43, 90)(44, 91)(45, 92)(46, 93)(47, 94)(95, 142, 96, 143, 100, 147, 108, 155, 120, 167, 132, 179, 137, 184, 127, 174, 117, 164, 106, 153, 99, 146, 102, 149, 110, 157, 122, 169, 134, 181, 138, 185, 128, 175, 113, 160, 125, 172, 118, 165, 107, 154, 112, 159, 124, 171, 135, 182, 139, 186, 129, 176, 114, 161, 103, 150, 111, 158, 123, 170, 119, 166, 126, 173, 136, 183, 140, 187, 130, 177, 115, 162, 104, 151, 97, 144, 101, 148, 109, 156, 121, 168, 133, 180, 141, 188, 131, 178, 116, 163, 105, 152, 98, 145) L = (1, 97)(2, 101)(3, 103)(4, 104)(5, 95)(6, 109)(7, 111)(8, 96)(9, 113)(10, 114)(11, 115)(12, 98)(13, 99)(14, 121)(15, 123)(16, 100)(17, 125)(18, 102)(19, 127)(20, 128)(21, 129)(22, 130)(23, 105)(24, 106)(25, 107)(26, 133)(27, 119)(28, 108)(29, 118)(30, 110)(31, 117)(32, 112)(33, 116)(34, 137)(35, 138)(36, 139)(37, 140)(38, 141)(39, 126)(40, 120)(41, 122)(42, 124)(43, 131)(44, 132)(45, 134)(46, 135)(47, 136)(48, 142)(49, 143)(50, 144)(51, 145)(52, 146)(53, 147)(54, 148)(55, 149)(56, 150)(57, 151)(58, 152)(59, 153)(60, 154)(61, 155)(62, 156)(63, 157)(64, 158)(65, 159)(66, 160)(67, 161)(68, 162)(69, 163)(70, 164)(71, 165)(72, 166)(73, 167)(74, 168)(75, 169)(76, 170)(77, 171)(78, 172)(79, 173)(80, 174)(81, 175)(82, 176)(83, 177)(84, 178)(85, 179)(86, 180)(87, 181)(88, 182)(89, 183)(90, 184)(91, 185)(92, 186)(93, 187)(94, 188) local type(s) :: { ( 94, 94 ), ( 94^94 ) } Outer automorphisms :: reflexible Dual of E23.355 Graph:: bipartite v = 48 e = 94 f = 2 degree seq :: [ 2^47, 94 ] E23.368 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {47, 47, 47}) Quotient :: dipole Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2, Y3^-1), Y2 * Y3^-1 * Y2^2 * Y3^-3, Y3 * Y2^4 * Y3^-1 * Y2^-4, Y2^-11 * Y3^-1, (Y3^-1 * Y1^-1)^47 ] Map:: R = (1, 48)(2, 49)(3, 50)(4, 51)(5, 52)(6, 53)(7, 54)(8, 55)(9, 56)(10, 57)(11, 58)(12, 59)(13, 60)(14, 61)(15, 62)(16, 63)(17, 64)(18, 65)(19, 66)(20, 67)(21, 68)(22, 69)(23, 70)(24, 71)(25, 72)(26, 73)(27, 74)(28, 75)(29, 76)(30, 77)(31, 78)(32, 79)(33, 80)(34, 81)(35, 82)(36, 83)(37, 84)(38, 85)(39, 86)(40, 87)(41, 88)(42, 89)(43, 90)(44, 91)(45, 92)(46, 93)(47, 94)(95, 142, 96, 143, 100, 147, 108, 155, 120, 167, 128, 175, 136, 183, 133, 180, 125, 172, 117, 164, 106, 153, 99, 146, 102, 149, 110, 157, 113, 160, 123, 170, 131, 178, 139, 186, 140, 187, 134, 181, 126, 173, 118, 165, 107, 154, 112, 159, 114, 161, 103, 150, 111, 158, 122, 169, 130, 177, 138, 185, 141, 188, 135, 182, 127, 174, 119, 166, 115, 162, 104, 151, 97, 144, 101, 148, 109, 156, 121, 168, 129, 176, 137, 184, 132, 179, 124, 171, 116, 163, 105, 152, 98, 145) L = (1, 97)(2, 101)(3, 103)(4, 104)(5, 95)(6, 109)(7, 111)(8, 96)(9, 113)(10, 114)(11, 115)(12, 98)(13, 99)(14, 121)(15, 122)(16, 100)(17, 123)(18, 102)(19, 108)(20, 110)(21, 112)(22, 119)(23, 105)(24, 106)(25, 107)(26, 129)(27, 130)(28, 131)(29, 120)(30, 127)(31, 116)(32, 117)(33, 118)(34, 137)(35, 138)(36, 139)(37, 128)(38, 135)(39, 124)(40, 125)(41, 126)(42, 132)(43, 141)(44, 140)(45, 136)(46, 133)(47, 134)(48, 142)(49, 143)(50, 144)(51, 145)(52, 146)(53, 147)(54, 148)(55, 149)(56, 150)(57, 151)(58, 152)(59, 153)(60, 154)(61, 155)(62, 156)(63, 157)(64, 158)(65, 159)(66, 160)(67, 161)(68, 162)(69, 163)(70, 164)(71, 165)(72, 166)(73, 167)(74, 168)(75, 169)(76, 170)(77, 171)(78, 172)(79, 173)(80, 174)(81, 175)(82, 176)(83, 177)(84, 178)(85, 179)(86, 180)(87, 181)(88, 182)(89, 183)(90, 184)(91, 185)(92, 186)(93, 187)(94, 188) local type(s) :: { ( 94, 94 ), ( 94^94 ) } Outer automorphisms :: reflexible Dual of E23.339 Graph:: bipartite v = 48 e = 94 f = 2 degree seq :: [ 2^47, 94 ] E23.369 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {47, 47, 47}) Quotient :: dipole Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3, Y2^-1), Y3^4 * Y2, Y2^5 * Y3 * Y2^7, Y2^-5 * Y3^2 * Y2^-6 * Y3, (Y2^-1 * Y3)^47, (Y3^-1 * Y1^-1)^47 ] Map:: R = (1, 48)(2, 49)(3, 50)(4, 51)(5, 52)(6, 53)(7, 54)(8, 55)(9, 56)(10, 57)(11, 58)(12, 59)(13, 60)(14, 61)(15, 62)(16, 63)(17, 64)(18, 65)(19, 66)(20, 67)(21, 68)(22, 69)(23, 70)(24, 71)(25, 72)(26, 73)(27, 74)(28, 75)(29, 76)(30, 77)(31, 78)(32, 79)(33, 80)(34, 81)(35, 82)(36, 83)(37, 84)(38, 85)(39, 86)(40, 87)(41, 88)(42, 89)(43, 90)(44, 91)(45, 92)(46, 93)(47, 94)(95, 142, 96, 143, 100, 147, 108, 155, 116, 163, 124, 171, 132, 179, 139, 186, 131, 178, 123, 170, 115, 162, 106, 153, 99, 146, 102, 149, 110, 157, 118, 165, 126, 173, 134, 181, 140, 187, 136, 183, 128, 175, 120, 167, 112, 159, 103, 150, 107, 154, 111, 158, 119, 166, 127, 174, 135, 182, 141, 188, 137, 184, 129, 176, 121, 168, 113, 160, 104, 151, 97, 144, 101, 148, 109, 156, 117, 164, 125, 172, 133, 180, 138, 185, 130, 177, 122, 169, 114, 161, 105, 152, 98, 145) L = (1, 97)(2, 101)(3, 103)(4, 104)(5, 95)(6, 109)(7, 107)(8, 96)(9, 106)(10, 112)(11, 113)(12, 98)(13, 99)(14, 117)(15, 111)(16, 100)(17, 102)(18, 115)(19, 120)(20, 121)(21, 105)(22, 125)(23, 119)(24, 108)(25, 110)(26, 123)(27, 128)(28, 129)(29, 114)(30, 133)(31, 127)(32, 116)(33, 118)(34, 131)(35, 136)(36, 137)(37, 122)(38, 138)(39, 135)(40, 124)(41, 126)(42, 139)(43, 140)(44, 141)(45, 130)(46, 132)(47, 134)(48, 142)(49, 143)(50, 144)(51, 145)(52, 146)(53, 147)(54, 148)(55, 149)(56, 150)(57, 151)(58, 152)(59, 153)(60, 154)(61, 155)(62, 156)(63, 157)(64, 158)(65, 159)(66, 160)(67, 161)(68, 162)(69, 163)(70, 164)(71, 165)(72, 166)(73, 167)(74, 168)(75, 169)(76, 170)(77, 171)(78, 172)(79, 173)(80, 174)(81, 175)(82, 176)(83, 177)(84, 178)(85, 179)(86, 180)(87, 181)(88, 182)(89, 183)(90, 184)(91, 185)(92, 186)(93, 187)(94, 188) local type(s) :: { ( 94, 94 ), ( 94^94 ) } Outer automorphisms :: reflexible Dual of E23.342 Graph:: bipartite v = 48 e = 94 f = 2 degree seq :: [ 2^47, 94 ] E23.370 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {47, 47, 47}) Quotient :: dipole Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ Y1, R^2, (Y3^-1, Y2), (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y3 * Y2 * Y3^3 * Y2^4, Y2^-1 * Y3 * Y2^-1 * Y3^6 * Y2^-1, Y2^2 * Y3^-1 * Y2^5 * Y3^-2 * Y2, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1, (Y3^-1 * Y1^-1)^47 ] Map:: R = (1, 48)(2, 49)(3, 50)(4, 51)(5, 52)(6, 53)(7, 54)(8, 55)(9, 56)(10, 57)(11, 58)(12, 59)(13, 60)(14, 61)(15, 62)(16, 63)(17, 64)(18, 65)(19, 66)(20, 67)(21, 68)(22, 69)(23, 70)(24, 71)(25, 72)(26, 73)(27, 74)(28, 75)(29, 76)(30, 77)(31, 78)(32, 79)(33, 80)(34, 81)(35, 82)(36, 83)(37, 84)(38, 85)(39, 86)(40, 87)(41, 88)(42, 89)(43, 90)(44, 91)(45, 92)(46, 93)(47, 94)(95, 142, 96, 143, 100, 147, 108, 155, 120, 167, 135, 182, 139, 186, 128, 175, 113, 160, 125, 172, 132, 179, 117, 164, 106, 153, 99, 146, 102, 149, 110, 157, 122, 169, 136, 183, 140, 187, 129, 176, 114, 161, 103, 150, 111, 158, 123, 170, 133, 180, 118, 165, 107, 154, 112, 159, 124, 171, 137, 184, 141, 188, 130, 177, 115, 162, 104, 151, 97, 144, 101, 148, 109, 156, 121, 168, 134, 181, 119, 166, 126, 173, 138, 185, 127, 174, 131, 178, 116, 163, 105, 152, 98, 145) L = (1, 97)(2, 101)(3, 103)(4, 104)(5, 95)(6, 109)(7, 111)(8, 96)(9, 113)(10, 114)(11, 115)(12, 98)(13, 99)(14, 121)(15, 123)(16, 100)(17, 125)(18, 102)(19, 127)(20, 128)(21, 129)(22, 130)(23, 105)(24, 106)(25, 107)(26, 134)(27, 133)(28, 108)(29, 132)(30, 110)(31, 131)(32, 112)(33, 137)(34, 138)(35, 139)(36, 140)(37, 141)(38, 116)(39, 117)(40, 118)(41, 119)(42, 120)(43, 122)(44, 124)(45, 126)(46, 135)(47, 136)(48, 142)(49, 143)(50, 144)(51, 145)(52, 146)(53, 147)(54, 148)(55, 149)(56, 150)(57, 151)(58, 152)(59, 153)(60, 154)(61, 155)(62, 156)(63, 157)(64, 158)(65, 159)(66, 160)(67, 161)(68, 162)(69, 163)(70, 164)(71, 165)(72, 166)(73, 167)(74, 168)(75, 169)(76, 170)(77, 171)(78, 172)(79, 173)(80, 174)(81, 175)(82, 176)(83, 177)(84, 178)(85, 179)(86, 180)(87, 181)(88, 182)(89, 183)(90, 184)(91, 185)(92, 186)(93, 187)(94, 188) local type(s) :: { ( 94, 94 ), ( 94^94 ) } Outer automorphisms :: reflexible Dual of E23.352 Graph:: bipartite v = 48 e = 94 f = 2 degree seq :: [ 2^47, 94 ] E23.371 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {47, 47, 47}) Quotient :: dipole Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y3^-1, Y2^-1), Y2^2 * Y3 * Y2^-2 * Y3^-1, Y2^-2 * Y3 * Y2^-1 * Y3^2 * Y2^-2, Y2^-3 * Y3^-1 * Y2^-1 * Y3^-6, Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3, (Y3^-1 * Y1^-1)^47 ] Map:: R = (1, 48)(2, 49)(3, 50)(4, 51)(5, 52)(6, 53)(7, 54)(8, 55)(9, 56)(10, 57)(11, 58)(12, 59)(13, 60)(14, 61)(15, 62)(16, 63)(17, 64)(18, 65)(19, 66)(20, 67)(21, 68)(22, 69)(23, 70)(24, 71)(25, 72)(26, 73)(27, 74)(28, 75)(29, 76)(30, 77)(31, 78)(32, 79)(33, 80)(34, 81)(35, 82)(36, 83)(37, 84)(38, 85)(39, 86)(40, 87)(41, 88)(42, 89)(43, 90)(44, 91)(45, 92)(46, 93)(47, 94)(95, 142, 96, 143, 100, 147, 108, 155, 120, 167, 113, 160, 125, 172, 134, 181, 140, 187, 131, 178, 136, 183, 128, 175, 117, 164, 106, 153, 99, 146, 102, 149, 110, 157, 122, 169, 114, 161, 103, 150, 111, 158, 123, 170, 133, 180, 141, 188, 137, 184, 138, 185, 129, 176, 118, 165, 107, 154, 112, 159, 124, 171, 115, 162, 104, 151, 97, 144, 101, 148, 109, 156, 121, 168, 132, 179, 127, 174, 135, 182, 139, 186, 130, 177, 119, 166, 126, 173, 116, 163, 105, 152, 98, 145) L = (1, 97)(2, 101)(3, 103)(4, 104)(5, 95)(6, 109)(7, 111)(8, 96)(9, 113)(10, 114)(11, 115)(12, 98)(13, 99)(14, 121)(15, 123)(16, 100)(17, 125)(18, 102)(19, 127)(20, 120)(21, 122)(22, 124)(23, 105)(24, 106)(25, 107)(26, 132)(27, 133)(28, 108)(29, 134)(30, 110)(31, 135)(32, 112)(33, 137)(34, 116)(35, 117)(36, 118)(37, 119)(38, 141)(39, 140)(40, 139)(41, 138)(42, 126)(43, 136)(44, 128)(45, 129)(46, 130)(47, 131)(48, 142)(49, 143)(50, 144)(51, 145)(52, 146)(53, 147)(54, 148)(55, 149)(56, 150)(57, 151)(58, 152)(59, 153)(60, 154)(61, 155)(62, 156)(63, 157)(64, 158)(65, 159)(66, 160)(67, 161)(68, 162)(69, 163)(70, 164)(71, 165)(72, 166)(73, 167)(74, 168)(75, 169)(76, 170)(77, 171)(78, 172)(79, 173)(80, 174)(81, 175)(82, 176)(83, 177)(84, 178)(85, 179)(86, 180)(87, 181)(88, 182)(89, 183)(90, 184)(91, 185)(92, 186)(93, 187)(94, 188) local type(s) :: { ( 94, 94 ), ( 94^94 ) } Outer automorphisms :: reflexible Dual of E23.349 Graph:: bipartite v = 48 e = 94 f = 2 degree seq :: [ 2^47, 94 ] E23.372 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {47, 47, 47}) Quotient :: dipole Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y2^-1), Y3^-1 * Y2 * Y3^-2 * Y2, Y2^-7 * Y3^-1 * Y2^-8, Y2^-1 * Y3^-22, (Y3^-1 * Y1^-1)^47 ] Map:: R = (1, 48)(2, 49)(3, 50)(4, 51)(5, 52)(6, 53)(7, 54)(8, 55)(9, 56)(10, 57)(11, 58)(12, 59)(13, 60)(14, 61)(15, 62)(16, 63)(17, 64)(18, 65)(19, 66)(20, 67)(21, 68)(22, 69)(23, 70)(24, 71)(25, 72)(26, 73)(27, 74)(28, 75)(29, 76)(30, 77)(31, 78)(32, 79)(33, 80)(34, 81)(35, 82)(36, 83)(37, 84)(38, 85)(39, 86)(40, 87)(41, 88)(42, 89)(43, 90)(44, 91)(45, 92)(46, 93)(47, 94)(95, 142, 96, 143, 100, 147, 108, 155, 114, 161, 120, 167, 126, 173, 132, 179, 138, 185, 136, 183, 130, 177, 124, 171, 118, 165, 112, 159, 106, 153, 99, 146, 102, 149, 103, 150, 110, 157, 116, 163, 122, 169, 128, 175, 134, 181, 140, 187, 141, 188, 137, 184, 131, 178, 125, 172, 119, 166, 113, 160, 107, 154, 104, 151, 97, 144, 101, 148, 109, 156, 115, 162, 121, 168, 127, 174, 133, 180, 139, 186, 135, 182, 129, 176, 123, 170, 117, 164, 111, 158, 105, 152, 98, 145) L = (1, 97)(2, 101)(3, 103)(4, 104)(5, 95)(6, 109)(7, 110)(8, 96)(9, 100)(10, 102)(11, 107)(12, 98)(13, 99)(14, 115)(15, 116)(16, 108)(17, 113)(18, 105)(19, 106)(20, 121)(21, 122)(22, 114)(23, 119)(24, 111)(25, 112)(26, 127)(27, 128)(28, 120)(29, 125)(30, 117)(31, 118)(32, 133)(33, 134)(34, 126)(35, 131)(36, 123)(37, 124)(38, 139)(39, 140)(40, 132)(41, 137)(42, 129)(43, 130)(44, 135)(45, 141)(46, 138)(47, 136)(48, 142)(49, 143)(50, 144)(51, 145)(52, 146)(53, 147)(54, 148)(55, 149)(56, 150)(57, 151)(58, 152)(59, 153)(60, 154)(61, 155)(62, 156)(63, 157)(64, 158)(65, 159)(66, 160)(67, 161)(68, 162)(69, 163)(70, 164)(71, 165)(72, 166)(73, 167)(74, 168)(75, 169)(76, 170)(77, 171)(78, 172)(79, 173)(80, 174)(81, 175)(82, 176)(83, 177)(84, 178)(85, 179)(86, 180)(87, 181)(88, 182)(89, 183)(90, 184)(91, 185)(92, 186)(93, 187)(94, 188) local type(s) :: { ( 94, 94 ), ( 94^94 ) } Outer automorphisms :: reflexible Dual of E23.337 Graph:: bipartite v = 48 e = 94 f = 2 degree seq :: [ 2^47, 94 ] E23.373 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {47, 47, 47}) Quotient :: dipole Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ Y1, R^2, Y3^-3 * Y2^-1, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y2^16 * Y3, (Y3^-1 * Y1^-1)^47, (Y3 * Y2^-1)^47 ] Map:: R = (1, 48)(2, 49)(3, 50)(4, 51)(5, 52)(6, 53)(7, 54)(8, 55)(9, 56)(10, 57)(11, 58)(12, 59)(13, 60)(14, 61)(15, 62)(16, 63)(17, 64)(18, 65)(19, 66)(20, 67)(21, 68)(22, 69)(23, 70)(24, 71)(25, 72)(26, 73)(27, 74)(28, 75)(29, 76)(30, 77)(31, 78)(32, 79)(33, 80)(34, 81)(35, 82)(36, 83)(37, 84)(38, 85)(39, 86)(40, 87)(41, 88)(42, 89)(43, 90)(44, 91)(45, 92)(46, 93)(47, 94)(95, 142, 96, 143, 100, 147, 106, 153, 112, 159, 118, 165, 124, 171, 130, 177, 136, 183, 139, 186, 133, 180, 127, 174, 121, 168, 115, 162, 109, 156, 103, 150, 99, 146, 102, 149, 108, 155, 114, 161, 120, 167, 126, 173, 132, 179, 138, 185, 140, 187, 134, 181, 128, 175, 122, 169, 116, 163, 110, 157, 104, 151, 97, 144, 101, 148, 107, 154, 113, 160, 119, 166, 125, 172, 131, 178, 137, 184, 141, 188, 135, 182, 129, 176, 123, 170, 117, 164, 111, 158, 105, 152, 98, 145) L = (1, 97)(2, 101)(3, 103)(4, 104)(5, 95)(6, 107)(7, 99)(8, 96)(9, 98)(10, 109)(11, 110)(12, 113)(13, 102)(14, 100)(15, 105)(16, 115)(17, 116)(18, 119)(19, 108)(20, 106)(21, 111)(22, 121)(23, 122)(24, 125)(25, 114)(26, 112)(27, 117)(28, 127)(29, 128)(30, 131)(31, 120)(32, 118)(33, 123)(34, 133)(35, 134)(36, 137)(37, 126)(38, 124)(39, 129)(40, 139)(41, 140)(42, 141)(43, 132)(44, 130)(45, 135)(46, 136)(47, 138)(48, 142)(49, 143)(50, 144)(51, 145)(52, 146)(53, 147)(54, 148)(55, 149)(56, 150)(57, 151)(58, 152)(59, 153)(60, 154)(61, 155)(62, 156)(63, 157)(64, 158)(65, 159)(66, 160)(67, 161)(68, 162)(69, 163)(70, 164)(71, 165)(72, 166)(73, 167)(74, 168)(75, 169)(76, 170)(77, 171)(78, 172)(79, 173)(80, 174)(81, 175)(82, 176)(83, 177)(84, 178)(85, 179)(86, 180)(87, 181)(88, 182)(89, 183)(90, 184)(91, 185)(92, 186)(93, 187)(94, 188) local type(s) :: { ( 94, 94 ), ( 94^94 ) } Outer automorphisms :: reflexible Dual of E23.340 Graph:: bipartite v = 48 e = 94 f = 2 degree seq :: [ 2^47, 94 ] E23.374 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {47, 47, 47}) Quotient :: dipole Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y2)^2, (Y3^-1, Y2^-1), (R * Y3)^2, Y2^3 * Y3^3 * Y2, Y3^-1 * Y2^-1 * Y3^-1 * Y2^-3 * Y3^-1, Y3^10 * Y2^-1 * Y3, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * 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)^47 ] Map:: R = (1, 48)(2, 49)(3, 50)(4, 51)(5, 52)(6, 53)(7, 54)(8, 55)(9, 56)(10, 57)(11, 58)(12, 59)(13, 60)(14, 61)(15, 62)(16, 63)(17, 64)(18, 65)(19, 66)(20, 67)(21, 68)(22, 69)(23, 70)(24, 71)(25, 72)(26, 73)(27, 74)(28, 75)(29, 76)(30, 77)(31, 78)(32, 79)(33, 80)(34, 81)(35, 82)(36, 83)(37, 84)(38, 85)(39, 86)(40, 87)(41, 88)(42, 89)(43, 90)(44, 91)(45, 92)(46, 93)(47, 94)(95, 142, 96, 143, 100, 147, 108, 155, 119, 166, 122, 169, 129, 176, 136, 183, 139, 186, 131, 178, 134, 181, 125, 172, 114, 161, 103, 150, 111, 158, 117, 164, 106, 153, 99, 146, 102, 149, 110, 157, 120, 167, 127, 174, 130, 177, 137, 184, 140, 187, 132, 179, 123, 170, 126, 173, 115, 162, 104, 151, 97, 144, 101, 148, 109, 156, 118, 165, 107, 154, 112, 159, 121, 168, 128, 175, 135, 182, 138, 185, 141, 188, 133, 180, 124, 171, 113, 160, 116, 163, 105, 152, 98, 145) L = (1, 97)(2, 101)(3, 103)(4, 104)(5, 95)(6, 109)(7, 111)(8, 96)(9, 113)(10, 114)(11, 115)(12, 98)(13, 99)(14, 118)(15, 117)(16, 100)(17, 116)(18, 102)(19, 123)(20, 124)(21, 125)(22, 126)(23, 105)(24, 106)(25, 107)(26, 108)(27, 110)(28, 112)(29, 131)(30, 132)(31, 133)(32, 134)(33, 119)(34, 120)(35, 121)(36, 122)(37, 138)(38, 139)(39, 140)(40, 141)(41, 127)(42, 128)(43, 129)(44, 130)(45, 135)(46, 136)(47, 137)(48, 142)(49, 143)(50, 144)(51, 145)(52, 146)(53, 147)(54, 148)(55, 149)(56, 150)(57, 151)(58, 152)(59, 153)(60, 154)(61, 155)(62, 156)(63, 157)(64, 158)(65, 159)(66, 160)(67, 161)(68, 162)(69, 163)(70, 164)(71, 165)(72, 166)(73, 167)(74, 168)(75, 169)(76, 170)(77, 171)(78, 172)(79, 173)(80, 174)(81, 175)(82, 176)(83, 177)(84, 178)(85, 179)(86, 180)(87, 181)(88, 182)(89, 183)(90, 184)(91, 185)(92, 186)(93, 187)(94, 188) local type(s) :: { ( 94, 94 ), ( 94^94 ) } Outer automorphisms :: reflexible Dual of E23.351 Graph:: bipartite v = 48 e = 94 f = 2 degree seq :: [ 2^47, 94 ] E23.375 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {47, 47, 47}) Quotient :: dipole Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (Y2, Y3), (R * Y3)^2, (R * Y2)^2, Y3^-2 * Y2^-1 * Y3^2 * Y2, Y3^-1 * Y2 * Y3^-3 * Y2^3 * Y3^-1, Y2^-3 * Y3^-1 * Y2^-1 * Y3^-2 * Y2^-3, (Y2^-1 * Y3)^47, (Y3^-1 * Y1^-1)^47 ] Map:: R = (1, 48)(2, 49)(3, 50)(4, 51)(5, 52)(6, 53)(7, 54)(8, 55)(9, 56)(10, 57)(11, 58)(12, 59)(13, 60)(14, 61)(15, 62)(16, 63)(17, 64)(18, 65)(19, 66)(20, 67)(21, 68)(22, 69)(23, 70)(24, 71)(25, 72)(26, 73)(27, 74)(28, 75)(29, 76)(30, 77)(31, 78)(32, 79)(33, 80)(34, 81)(35, 82)(36, 83)(37, 84)(38, 85)(39, 86)(40, 87)(41, 88)(42, 89)(43, 90)(44, 91)(45, 92)(46, 93)(47, 94)(95, 142, 96, 143, 100, 147, 108, 155, 120, 167, 136, 183, 134, 181, 119, 166, 126, 173, 129, 176, 114, 161, 103, 150, 111, 158, 123, 170, 138, 185, 132, 179, 117, 164, 106, 153, 99, 146, 102, 149, 110, 157, 122, 169, 127, 174, 140, 187, 141, 188, 135, 182, 130, 177, 115, 162, 104, 151, 97, 144, 101, 148, 109, 156, 121, 168, 137, 184, 133, 180, 118, 165, 107, 154, 112, 159, 124, 171, 128, 175, 113, 160, 125, 172, 139, 186, 131, 178, 116, 163, 105, 152, 98, 145) L = (1, 97)(2, 101)(3, 103)(4, 104)(5, 95)(6, 109)(7, 111)(8, 96)(9, 113)(10, 114)(11, 115)(12, 98)(13, 99)(14, 121)(15, 123)(16, 100)(17, 125)(18, 102)(19, 127)(20, 128)(21, 129)(22, 130)(23, 105)(24, 106)(25, 107)(26, 137)(27, 138)(28, 108)(29, 139)(30, 110)(31, 140)(32, 112)(33, 120)(34, 122)(35, 124)(36, 126)(37, 135)(38, 116)(39, 117)(40, 118)(41, 119)(42, 133)(43, 132)(44, 131)(45, 141)(46, 136)(47, 134)(48, 142)(49, 143)(50, 144)(51, 145)(52, 146)(53, 147)(54, 148)(55, 149)(56, 150)(57, 151)(58, 152)(59, 153)(60, 154)(61, 155)(62, 156)(63, 157)(64, 158)(65, 159)(66, 160)(67, 161)(68, 162)(69, 163)(70, 164)(71, 165)(72, 166)(73, 167)(74, 168)(75, 169)(76, 170)(77, 171)(78, 172)(79, 173)(80, 174)(81, 175)(82, 176)(83, 177)(84, 178)(85, 179)(86, 180)(87, 181)(88, 182)(89, 183)(90, 184)(91, 185)(92, 186)(93, 187)(94, 188) local type(s) :: { ( 94, 94 ), ( 94^94 ) } Outer automorphisms :: reflexible Dual of E23.341 Graph:: bipartite v = 48 e = 94 f = 2 degree seq :: [ 2^47, 94 ] E23.376 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {47, 47, 47}) Quotient :: dipole Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y2, Y3^-1), Y2^-1 * Y3^-2 * Y2 * Y3^2, Y3^-3 * Y2^-1 * Y3^-2, Y2^7 * Y3^-1 * Y2 * Y3^-1 * Y2, Y2^-3 * 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^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * 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)^47 ] Map:: R = (1, 48)(2, 49)(3, 50)(4, 51)(5, 52)(6, 53)(7, 54)(8, 55)(9, 56)(10, 57)(11, 58)(12, 59)(13, 60)(14, 61)(15, 62)(16, 63)(17, 64)(18, 65)(19, 66)(20, 67)(21, 68)(22, 69)(23, 70)(24, 71)(25, 72)(26, 73)(27, 74)(28, 75)(29, 76)(30, 77)(31, 78)(32, 79)(33, 80)(34, 81)(35, 82)(36, 83)(37, 84)(38, 85)(39, 86)(40, 87)(41, 88)(42, 89)(43, 90)(44, 91)(45, 92)(46, 93)(47, 94)(95, 142, 96, 143, 100, 147, 108, 155, 118, 165, 128, 175, 134, 181, 124, 171, 114, 161, 103, 150, 111, 158, 121, 168, 131, 178, 139, 186, 141, 188, 137, 184, 127, 174, 117, 164, 106, 153, 99, 146, 102, 149, 110, 157, 120, 167, 130, 177, 135, 182, 125, 172, 115, 162, 104, 151, 97, 144, 101, 148, 109, 156, 119, 166, 129, 176, 138, 185, 140, 187, 133, 180, 123, 170, 113, 160, 107, 154, 112, 159, 122, 169, 132, 179, 136, 183, 126, 173, 116, 163, 105, 152, 98, 145) L = (1, 97)(2, 101)(3, 103)(4, 104)(5, 95)(6, 109)(7, 111)(8, 96)(9, 113)(10, 114)(11, 115)(12, 98)(13, 99)(14, 119)(15, 121)(16, 100)(17, 107)(18, 102)(19, 106)(20, 123)(21, 124)(22, 125)(23, 105)(24, 129)(25, 131)(26, 108)(27, 112)(28, 110)(29, 117)(30, 133)(31, 134)(32, 135)(33, 116)(34, 138)(35, 139)(36, 118)(37, 122)(38, 120)(39, 127)(40, 140)(41, 128)(42, 130)(43, 126)(44, 141)(45, 132)(46, 137)(47, 136)(48, 142)(49, 143)(50, 144)(51, 145)(52, 146)(53, 147)(54, 148)(55, 149)(56, 150)(57, 151)(58, 152)(59, 153)(60, 154)(61, 155)(62, 156)(63, 157)(64, 158)(65, 159)(66, 160)(67, 161)(68, 162)(69, 163)(70, 164)(71, 165)(72, 166)(73, 167)(74, 168)(75, 169)(76, 170)(77, 171)(78, 172)(79, 173)(80, 174)(81, 175)(82, 176)(83, 177)(84, 178)(85, 179)(86, 180)(87, 181)(88, 182)(89, 183)(90, 184)(91, 185)(92, 186)(93, 187)(94, 188) local type(s) :: { ( 94, 94 ), ( 94^94 ) } Outer automorphisms :: reflexible Dual of E23.344 Graph:: bipartite v = 48 e = 94 f = 2 degree seq :: [ 2^47, 94 ] E23.377 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {47, 47, 47}) Quotient :: dipole Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2, Y3^-1), Y3^6 * Y2^-1 * Y3, Y2^2 * Y3^-2 * Y2^5, Y2^-1 * Y3^-3 * Y2^-2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * 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)^47 ] Map:: R = (1, 48)(2, 49)(3, 50)(4, 51)(5, 52)(6, 53)(7, 54)(8, 55)(9, 56)(10, 57)(11, 58)(12, 59)(13, 60)(14, 61)(15, 62)(16, 63)(17, 64)(18, 65)(19, 66)(20, 67)(21, 68)(22, 69)(23, 70)(24, 71)(25, 72)(26, 73)(27, 74)(28, 75)(29, 76)(30, 77)(31, 78)(32, 79)(33, 80)(34, 81)(35, 82)(36, 83)(37, 84)(38, 85)(39, 86)(40, 87)(41, 88)(42, 89)(43, 90)(44, 91)(45, 92)(46, 93)(47, 94)(95, 142, 96, 143, 100, 147, 108, 155, 120, 167, 128, 175, 114, 161, 103, 150, 111, 158, 123, 170, 135, 182, 141, 188, 133, 180, 119, 166, 126, 173, 137, 184, 139, 186, 131, 178, 117, 164, 106, 153, 99, 146, 102, 149, 110, 157, 122, 169, 129, 176, 115, 162, 104, 151, 97, 144, 101, 148, 109, 156, 121, 168, 134, 181, 138, 185, 127, 174, 113, 160, 125, 172, 136, 183, 140, 187, 132, 179, 118, 165, 107, 154, 112, 159, 124, 171, 130, 177, 116, 163, 105, 152, 98, 145) L = (1, 97)(2, 101)(3, 103)(4, 104)(5, 95)(6, 109)(7, 111)(8, 96)(9, 113)(10, 114)(11, 115)(12, 98)(13, 99)(14, 121)(15, 123)(16, 100)(17, 125)(18, 102)(19, 126)(20, 127)(21, 128)(22, 129)(23, 105)(24, 106)(25, 107)(26, 134)(27, 135)(28, 108)(29, 136)(30, 110)(31, 137)(32, 112)(33, 119)(34, 138)(35, 120)(36, 122)(37, 116)(38, 117)(39, 118)(40, 141)(41, 140)(42, 139)(43, 124)(44, 133)(45, 130)(46, 131)(47, 132)(48, 142)(49, 143)(50, 144)(51, 145)(52, 146)(53, 147)(54, 148)(55, 149)(56, 150)(57, 151)(58, 152)(59, 153)(60, 154)(61, 155)(62, 156)(63, 157)(64, 158)(65, 159)(66, 160)(67, 161)(68, 162)(69, 163)(70, 164)(71, 165)(72, 166)(73, 167)(74, 168)(75, 169)(76, 170)(77, 171)(78, 172)(79, 173)(80, 174)(81, 175)(82, 176)(83, 177)(84, 178)(85, 179)(86, 180)(87, 181)(88, 182)(89, 183)(90, 184)(91, 185)(92, 186)(93, 187)(94, 188) local type(s) :: { ( 94, 94 ), ( 94^94 ) } Outer automorphisms :: reflexible Dual of E23.345 Graph:: bipartite v = 48 e = 94 f = 2 degree seq :: [ 2^47, 94 ] E23.378 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {47, 47, 47}) Quotient :: dipole Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2, Y3^-1), Y3^-2 * Y2^5, Y3^-1 * Y2^-1 * Y3^-8, Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-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)^47 ] Map:: R = (1, 48)(2, 49)(3, 50)(4, 51)(5, 52)(6, 53)(7, 54)(8, 55)(9, 56)(10, 57)(11, 58)(12, 59)(13, 60)(14, 61)(15, 62)(16, 63)(17, 64)(18, 65)(19, 66)(20, 67)(21, 68)(22, 69)(23, 70)(24, 71)(25, 72)(26, 73)(27, 74)(28, 75)(29, 76)(30, 77)(31, 78)(32, 79)(33, 80)(34, 81)(35, 82)(36, 83)(37, 84)(38, 85)(39, 86)(40, 87)(41, 88)(42, 89)(43, 90)(44, 91)(45, 92)(46, 93)(47, 94)(95, 142, 96, 143, 100, 147, 108, 155, 114, 161, 103, 150, 111, 158, 121, 168, 130, 177, 135, 182, 124, 171, 132, 179, 139, 186, 141, 188, 137, 184, 128, 175, 119, 166, 123, 170, 126, 173, 117, 164, 106, 153, 99, 146, 102, 149, 110, 157, 115, 162, 104, 151, 97, 144, 101, 148, 109, 156, 120, 167, 125, 172, 113, 160, 122, 169, 131, 178, 138, 185, 140, 187, 134, 181, 129, 176, 133, 180, 136, 183, 127, 174, 118, 165, 107, 154, 112, 159, 116, 163, 105, 152, 98, 145) L = (1, 97)(2, 101)(3, 103)(4, 104)(5, 95)(6, 109)(7, 111)(8, 96)(9, 113)(10, 114)(11, 115)(12, 98)(13, 99)(14, 120)(15, 121)(16, 100)(17, 122)(18, 102)(19, 124)(20, 125)(21, 108)(22, 110)(23, 105)(24, 106)(25, 107)(26, 130)(27, 131)(28, 132)(29, 112)(30, 134)(31, 135)(32, 116)(33, 117)(34, 118)(35, 119)(36, 138)(37, 139)(38, 129)(39, 123)(40, 128)(41, 140)(42, 126)(43, 127)(44, 141)(45, 133)(46, 137)(47, 136)(48, 142)(49, 143)(50, 144)(51, 145)(52, 146)(53, 147)(54, 148)(55, 149)(56, 150)(57, 151)(58, 152)(59, 153)(60, 154)(61, 155)(62, 156)(63, 157)(64, 158)(65, 159)(66, 160)(67, 161)(68, 162)(69, 163)(70, 164)(71, 165)(72, 166)(73, 167)(74, 168)(75, 169)(76, 170)(77, 171)(78, 172)(79, 173)(80, 174)(81, 175)(82, 176)(83, 177)(84, 178)(85, 179)(86, 180)(87, 181)(88, 182)(89, 183)(90, 184)(91, 185)(92, 186)(93, 187)(94, 188) local type(s) :: { ( 94, 94 ), ( 94^94 ) } Outer automorphisms :: reflexible Dual of E23.350 Graph:: bipartite v = 48 e = 94 f = 2 degree seq :: [ 2^47, 94 ] E23.379 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {47, 47, 47}) Quotient :: dipole Aut^+ = C47 (small group id <47, 1>) Aut = D94 (small group id <94, 1>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1, Y2^-1), Y2 * Y3^-1 * Y2 * Y3^-1 * Y2, Y3^13 * Y2 * Y3^2, (Y3^-1 * Y1^-1)^47 ] Map:: R = (1, 48)(2, 49)(3, 50)(4, 51)(5, 52)(6, 53)(7, 54)(8, 55)(9, 56)(10, 57)(11, 58)(12, 59)(13, 60)(14, 61)(15, 62)(16, 63)(17, 64)(18, 65)(19, 66)(20, 67)(21, 68)(22, 69)(23, 70)(24, 71)(25, 72)(26, 73)(27, 74)(28, 75)(29, 76)(30, 77)(31, 78)(32, 79)(33, 80)(34, 81)(35, 82)(36, 83)(37, 84)(38, 85)(39, 86)(40, 87)(41, 88)(42, 89)(43, 90)(44, 91)(45, 92)(46, 93)(47, 94)(95, 142, 96, 143, 100, 147, 103, 150, 109, 156, 114, 161, 116, 163, 121, 168, 126, 173, 128, 175, 133, 180, 138, 185, 140, 187, 137, 184, 135, 182, 130, 177, 125, 172, 123, 170, 118, 165, 113, 160, 111, 158, 106, 153, 99, 146, 102, 149, 104, 151, 97, 144, 101, 148, 108, 155, 110, 157, 115, 162, 120, 167, 122, 169, 127, 174, 132, 179, 134, 181, 139, 186, 141, 188, 136, 183, 131, 178, 129, 176, 124, 171, 119, 166, 117, 164, 112, 159, 107, 154, 105, 152, 98, 145) L = (1, 97)(2, 101)(3, 103)(4, 104)(5, 95)(6, 108)(7, 109)(8, 96)(9, 110)(10, 100)(11, 102)(12, 98)(13, 99)(14, 114)(15, 115)(16, 116)(17, 105)(18, 106)(19, 107)(20, 120)(21, 121)(22, 122)(23, 111)(24, 112)(25, 113)(26, 126)(27, 127)(28, 128)(29, 117)(30, 118)(31, 119)(32, 132)(33, 133)(34, 134)(35, 123)(36, 124)(37, 125)(38, 138)(39, 139)(40, 140)(41, 129)(42, 130)(43, 131)(44, 141)(45, 137)(46, 136)(47, 135)(48, 142)(49, 143)(50, 144)(51, 145)(52, 146)(53, 147)(54, 148)(55, 149)(56, 150)(57, 151)(58, 152)(59, 153)(60, 154)(61, 155)(62, 156)(63, 157)(64, 158)(65, 159)(66, 160)(67, 161)(68, 162)(69, 163)(70, 164)(71, 165)(72, 166)(73, 167)(74, 168)(75, 169)(76, 170)(77, 171)(78, 172)(79, 173)(80, 174)(81, 175)(82, 176)(83, 177)(84, 178)(85, 179)(86, 180)(87, 181)(88, 182)(89, 183)(90, 184)(91, 185)(92, 186)(93, 187)(94, 188) local type(s) :: { ( 94, 94 ), ( 94^94 ) } Outer automorphisms :: reflexible Dual of E23.338 Graph:: bipartite v = 48 e = 94 f = 2 degree seq :: [ 2^47, 94 ] E23.380 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 4, 4}) Quotient :: dipole Aut^+ = C4 x (C3 : C4) (small group id <48, 11>) Aut = (C6 x D8) : C2 (small group id <96, 147>) |r| :: 2 Presentation :: [ R^2, Y1^3, (R * Y2)^2, (R * Y3)^2, Y2 * Y1^-1 * Y2^-1 * Y1^-1, (R * Y1)^2, (Y3, Y2), Y3^4, Y3^-1 * Y1 * Y3 * Y1, Y2^4 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50, 5, 53)(3, 51, 12, 60, 8, 56)(4, 52, 16, 64, 9, 57)(6, 54, 19, 67, 10, 58)(7, 55, 20, 68, 11, 59)(13, 61, 22, 70, 28, 76)(14, 62, 23, 71, 29, 77)(15, 63, 24, 72, 30, 78)(17, 65, 25, 73, 34, 82)(18, 66, 26, 74, 35, 83)(21, 69, 27, 75, 37, 85)(31, 79, 42, 90, 38, 86)(32, 80, 43, 91, 39, 87)(33, 81, 44, 92, 40, 88)(36, 84, 46, 94, 41, 89)(45, 93, 47, 95, 48, 96)(97, 145, 99, 147, 109, 157, 102, 150)(98, 146, 104, 152, 118, 166, 106, 154)(100, 148, 110, 158, 127, 175, 114, 162)(101, 149, 108, 156, 124, 172, 115, 163)(103, 151, 111, 159, 128, 176, 117, 165)(105, 153, 119, 167, 134, 182, 122, 170)(107, 155, 120, 168, 135, 183, 123, 171)(112, 160, 125, 173, 138, 186, 131, 179)(113, 161, 129, 177, 141, 189, 132, 180)(116, 164, 126, 174, 139, 187, 133, 181)(121, 169, 136, 184, 143, 191, 137, 185)(130, 178, 140, 188, 144, 192, 142, 190) L = (1, 100)(2, 105)(3, 110)(4, 113)(5, 112)(6, 114)(7, 97)(8, 119)(9, 121)(10, 122)(11, 98)(12, 125)(13, 127)(14, 129)(15, 99)(16, 130)(17, 103)(18, 132)(19, 131)(20, 101)(21, 102)(22, 134)(23, 136)(24, 104)(25, 107)(26, 137)(27, 106)(28, 138)(29, 140)(30, 108)(31, 141)(32, 109)(33, 111)(34, 116)(35, 142)(36, 117)(37, 115)(38, 143)(39, 118)(40, 120)(41, 123)(42, 144)(43, 124)(44, 126)(45, 128)(46, 133)(47, 135)(48, 139)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8^6 ), ( 8^8 ) } Outer automorphisms :: reflexible Dual of E23.381 Graph:: simple bipartite v = 28 e = 96 f = 24 degree seq :: [ 6^16, 8^12 ] E23.381 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 4, 4}) Quotient :: dipole Aut^+ = C4 x (C3 : C4) (small group id <48, 11>) Aut = (C6 x D8) : C2 (small group id <96, 147>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^2 * Y3^-1, Y3^2 * Y1^2, (R * Y2)^2, (R * Y3)^2, (Y2^-1, Y1^-1), (Y2, Y3^-1), Y1^4, (R * Y1)^2, Y2^4, Y3 * Y1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1, Y2^-1 * Y3 * Y2^-1 * Y1^-2 * Y2^-1 * Y3 * Y2^-1 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 9, 57, 22, 70, 15, 63)(4, 52, 17, 65, 7, 55, 18, 66)(6, 54, 11, 59, 23, 71, 20, 68)(10, 58, 27, 75, 12, 60, 28, 76)(13, 61, 24, 72, 38, 86, 32, 80)(14, 62, 34, 82, 16, 64, 35, 83)(19, 67, 36, 84, 21, 69, 37, 85)(25, 73, 41, 89, 26, 74, 42, 90)(29, 77, 43, 91, 30, 78, 44, 92)(31, 79, 45, 93, 33, 81, 46, 94)(39, 87, 47, 95, 40, 88, 48, 96)(97, 145, 99, 147, 109, 157, 102, 150)(98, 146, 105, 153, 120, 168, 107, 155)(100, 148, 110, 158, 127, 175, 115, 163)(101, 149, 111, 159, 128, 176, 116, 164)(103, 151, 112, 160, 129, 177, 117, 165)(104, 152, 118, 166, 134, 182, 119, 167)(106, 154, 121, 169, 135, 183, 125, 173)(108, 156, 122, 170, 136, 184, 126, 174)(113, 161, 130, 178, 141, 189, 132, 180)(114, 162, 131, 179, 142, 190, 133, 181)(123, 171, 137, 185, 143, 191, 139, 187)(124, 172, 138, 186, 144, 192, 140, 188) L = (1, 100)(2, 106)(3, 110)(4, 104)(5, 108)(6, 115)(7, 97)(8, 103)(9, 121)(10, 101)(11, 125)(12, 98)(13, 127)(14, 118)(15, 122)(16, 99)(17, 124)(18, 123)(19, 119)(20, 126)(21, 102)(22, 112)(23, 117)(24, 135)(25, 111)(26, 105)(27, 113)(28, 114)(29, 116)(30, 107)(31, 134)(32, 136)(33, 109)(34, 138)(35, 137)(36, 140)(37, 139)(38, 129)(39, 128)(40, 120)(41, 130)(42, 131)(43, 132)(44, 133)(45, 144)(46, 143)(47, 141)(48, 142)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E23.380 Graph:: simple bipartite v = 24 e = 96 f = 28 degree seq :: [ 8^24 ] E23.382 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 4, 4}) Quotient :: dipole Aut^+ = (C3 : C4) : C4 (small group id <48, 12>) Aut = (C2 x C4 x S3) : C2 (small group id <96, 91>) |r| :: 2 Presentation :: [ R^2, Y1^3, R * Y2 * R * Y2^-1, (R * Y3)^2, Y2^-1 * Y1^-1 * Y2 * Y1^-1, (R * Y1)^2, Y3^-1 * Y2^-1 * Y3 * Y2^-1, Y3^4, Y3^-1 * Y1 * Y3 * Y1, Y2^4 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50, 5, 53)(3, 51, 12, 60, 8, 56)(4, 52, 16, 64, 9, 57)(6, 54, 19, 67, 10, 58)(7, 55, 20, 68, 11, 59)(13, 61, 22, 70, 28, 76)(14, 62, 23, 71, 29, 77)(15, 63, 24, 72, 30, 78)(17, 65, 25, 73, 34, 82)(18, 66, 26, 74, 35, 83)(21, 69, 27, 75, 37, 85)(31, 79, 42, 90, 38, 86)(32, 80, 43, 91, 39, 87)(33, 81, 44, 92, 40, 88)(36, 84, 46, 94, 41, 89)(45, 93, 47, 95, 48, 96)(97, 145, 99, 147, 109, 157, 102, 150)(98, 146, 104, 152, 118, 166, 106, 154)(100, 148, 113, 161, 127, 175, 110, 158)(101, 149, 108, 156, 124, 172, 115, 163)(103, 151, 117, 165, 128, 176, 111, 159)(105, 153, 121, 169, 134, 182, 119, 167)(107, 155, 123, 171, 135, 183, 120, 168)(112, 160, 130, 178, 138, 186, 125, 173)(114, 162, 129, 177, 141, 189, 132, 180)(116, 164, 133, 181, 139, 187, 126, 174)(122, 170, 136, 184, 143, 191, 137, 185)(131, 179, 140, 188, 144, 192, 142, 190) L = (1, 100)(2, 105)(3, 110)(4, 114)(5, 112)(6, 113)(7, 97)(8, 119)(9, 122)(10, 121)(11, 98)(12, 125)(13, 127)(14, 129)(15, 99)(16, 131)(17, 132)(18, 103)(19, 130)(20, 101)(21, 102)(22, 134)(23, 136)(24, 104)(25, 137)(26, 107)(27, 106)(28, 138)(29, 140)(30, 108)(31, 141)(32, 109)(33, 111)(34, 142)(35, 116)(36, 117)(37, 115)(38, 143)(39, 118)(40, 120)(41, 123)(42, 144)(43, 124)(44, 126)(45, 128)(46, 133)(47, 135)(48, 139)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8^6 ), ( 8^8 ) } Outer automorphisms :: reflexible Dual of E23.386 Graph:: simple bipartite v = 28 e = 96 f = 24 degree seq :: [ 6^16, 8^12 ] E23.383 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 4, 4}) Quotient :: dipole Aut^+ = (C3 : C4) : C4 (small group id <48, 12>) Aut = (C2 x C4 x S3) : C2 (small group id <96, 91>) |r| :: 2 Presentation :: [ R^2, Y1^3, Y3^-1 * Y2 * Y3^-1 * Y2^-1, (R * Y3)^2, (R * Y1)^2, Y2 * Y1^-1 * Y2^-1 * Y1^-1, Y3^-1 * Y1 * Y3 * Y1, Y2^4, Y3^4, (R * Y2 * Y3^-1)^2 ] Map:: non-degenerate R = (1, 49, 2, 50, 5, 53)(3, 51, 12, 60, 8, 56)(4, 52, 16, 64, 9, 57)(6, 54, 19, 67, 10, 58)(7, 55, 20, 68, 11, 59)(13, 61, 22, 70, 28, 76)(14, 62, 23, 71, 29, 77)(15, 63, 24, 72, 30, 78)(17, 65, 25, 73, 34, 82)(18, 66, 26, 74, 35, 83)(21, 69, 27, 75, 37, 85)(31, 79, 42, 90, 38, 86)(32, 80, 43, 91, 39, 87)(33, 81, 44, 92, 40, 88)(36, 84, 46, 94, 41, 89)(45, 93, 47, 95, 48, 96)(97, 145, 99, 147, 109, 157, 102, 150)(98, 146, 104, 152, 118, 166, 106, 154)(100, 148, 111, 159, 127, 175, 114, 162)(101, 149, 108, 156, 124, 172, 115, 163)(103, 151, 110, 158, 128, 176, 117, 165)(105, 153, 120, 168, 134, 182, 122, 170)(107, 155, 119, 167, 135, 183, 123, 171)(112, 160, 126, 174, 138, 186, 131, 179)(113, 161, 129, 177, 141, 189, 132, 180)(116, 164, 125, 173, 139, 187, 133, 181)(121, 169, 136, 184, 143, 191, 137, 185)(130, 178, 140, 188, 144, 192, 142, 190) L = (1, 100)(2, 105)(3, 110)(4, 113)(5, 112)(6, 117)(7, 97)(8, 119)(9, 121)(10, 123)(11, 98)(12, 125)(13, 127)(14, 129)(15, 99)(16, 130)(17, 103)(18, 102)(19, 133)(20, 101)(21, 132)(22, 134)(23, 136)(24, 104)(25, 107)(26, 106)(27, 137)(28, 138)(29, 140)(30, 108)(31, 141)(32, 109)(33, 111)(34, 116)(35, 115)(36, 114)(37, 142)(38, 143)(39, 118)(40, 120)(41, 122)(42, 144)(43, 124)(44, 126)(45, 128)(46, 131)(47, 135)(48, 139)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8^6 ), ( 8^8 ) } Outer automorphisms :: reflexible Dual of E23.385 Graph:: simple bipartite v = 28 e = 96 f = 24 degree seq :: [ 6^16, 8^12 ] E23.384 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 4, 4}) Quotient :: dipole Aut^+ = (C3 : C4) : C4 (small group id <48, 12>) Aut = (C2 x C2 x (C3 : C4)) : C2 (small group id <96, 146>) |r| :: 2 Presentation :: [ R^2, Y1^3, (Y2^-1, Y1^-1), (R * Y3)^2, (R * Y1)^2, Y2^4, Y3^-1 * Y1 * Y3 * Y1, Y2^-1 * Y3^-1 * Y2 * Y3^-1, Y3^4, Y1^-1 * Y3 * Y2 * Y1^-1 * Y3 * Y2^-1, (R * Y2 * Y3^-1)^2 ] Map:: non-degenerate R = (1, 49, 2, 50, 5, 53)(3, 51, 8, 56, 14, 62)(4, 52, 16, 64, 9, 57)(6, 54, 10, 58, 19, 67)(7, 55, 20, 68, 11, 59)(12, 60, 22, 70, 29, 77)(13, 61, 31, 79, 23, 71)(15, 63, 33, 81, 24, 72)(17, 65, 25, 73, 34, 82)(18, 66, 35, 83, 26, 74)(21, 69, 37, 85, 27, 75)(28, 76, 42, 90, 38, 86)(30, 78, 44, 92, 39, 87)(32, 80, 40, 88, 45, 93)(36, 84, 41, 89, 46, 94)(43, 91, 47, 95, 48, 96)(97, 145, 99, 147, 108, 156, 102, 150)(98, 146, 104, 152, 118, 166, 106, 154)(100, 148, 111, 159, 124, 172, 114, 162)(101, 149, 110, 158, 125, 173, 115, 163)(103, 151, 109, 157, 126, 174, 117, 165)(105, 153, 120, 168, 134, 182, 122, 170)(107, 155, 119, 167, 135, 183, 123, 171)(112, 160, 129, 177, 138, 186, 131, 179)(113, 161, 128, 176, 139, 187, 132, 180)(116, 164, 127, 175, 140, 188, 133, 181)(121, 169, 136, 184, 143, 191, 137, 185)(130, 178, 141, 189, 144, 192, 142, 190) L = (1, 100)(2, 105)(3, 109)(4, 113)(5, 112)(6, 117)(7, 97)(8, 119)(9, 121)(10, 123)(11, 98)(12, 124)(13, 128)(14, 127)(15, 99)(16, 130)(17, 103)(18, 102)(19, 133)(20, 101)(21, 132)(22, 134)(23, 136)(24, 104)(25, 107)(26, 106)(27, 137)(28, 139)(29, 138)(30, 108)(31, 141)(32, 111)(33, 110)(34, 116)(35, 115)(36, 114)(37, 142)(38, 143)(39, 118)(40, 120)(41, 122)(42, 144)(43, 126)(44, 125)(45, 129)(46, 131)(47, 135)(48, 140)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8^6 ), ( 8^8 ) } Outer automorphisms :: reflexible Dual of E23.387 Graph:: simple bipartite v = 28 e = 96 f = 24 degree seq :: [ 6^16, 8^12 ] E23.385 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 4, 4}) Quotient :: dipole Aut^+ = (C3 : C4) : C4 (small group id <48, 12>) Aut = (C2 x C4 x S3) : C2 (small group id <96, 91>) |r| :: 2 Presentation :: [ R^2, Y1^2 * Y3^-2, Y1^4, Y3^2 * Y1^2, Y2^-1 * Y3^-1 * Y2 * Y3^-1, (R * Y3)^2, Y2^4, (R * Y1)^2, Y2^-1 * Y1^-1 * Y2 * Y1^-1, Y3 * Y1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1, (R * Y2 * Y3^-1)^2 ] Map:: non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 22, 70, 9, 57)(4, 52, 17, 65, 7, 55, 18, 66)(6, 54, 20, 68, 23, 71, 11, 59)(10, 58, 27, 75, 12, 60, 28, 76)(14, 62, 24, 72, 38, 86, 31, 79)(15, 63, 34, 82, 16, 64, 35, 83)(19, 67, 37, 85, 21, 69, 36, 84)(25, 73, 41, 89, 26, 74, 42, 90)(29, 77, 44, 92, 30, 78, 43, 91)(32, 80, 45, 93, 33, 81, 46, 94)(39, 87, 47, 95, 40, 88, 48, 96)(97, 145, 99, 147, 110, 158, 102, 150)(98, 146, 105, 153, 120, 168, 107, 155)(100, 148, 112, 160, 128, 176, 115, 163)(101, 149, 109, 157, 127, 175, 116, 164)(103, 151, 111, 159, 129, 177, 117, 165)(104, 152, 118, 166, 134, 182, 119, 167)(106, 154, 122, 170, 135, 183, 125, 173)(108, 156, 121, 169, 136, 184, 126, 174)(113, 161, 130, 178, 141, 189, 132, 180)(114, 162, 131, 179, 142, 190, 133, 181)(123, 171, 137, 185, 143, 191, 139, 187)(124, 172, 138, 186, 144, 192, 140, 188) L = (1, 100)(2, 106)(3, 111)(4, 104)(5, 108)(6, 117)(7, 97)(8, 103)(9, 121)(10, 101)(11, 126)(12, 98)(13, 122)(14, 128)(15, 118)(16, 99)(17, 124)(18, 123)(19, 102)(20, 125)(21, 119)(22, 112)(23, 115)(24, 135)(25, 109)(26, 105)(27, 113)(28, 114)(29, 107)(30, 116)(31, 136)(32, 134)(33, 110)(34, 137)(35, 138)(36, 139)(37, 140)(38, 129)(39, 127)(40, 120)(41, 131)(42, 130)(43, 133)(44, 132)(45, 144)(46, 143)(47, 141)(48, 142)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E23.383 Graph:: simple bipartite v = 24 e = 96 f = 28 degree seq :: [ 8^24 ] E23.386 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 4, 4}) Quotient :: dipole Aut^+ = (C3 : C4) : C4 (small group id <48, 12>) Aut = (C2 x C4 x S3) : C2 (small group id <96, 91>) |r| :: 2 Presentation :: [ R^2, Y3^4, Y3^2 * Y1^2, Y2^-1 * Y3^-2 * Y2^-1, Y3 * Y2^-2 * Y3, Y2^2 * Y1^-2, Y3^2 * Y1^-2, (R * Y3)^2, Y2 * Y1^2 * Y2, (R * Y1)^2, Y2 * Y1 * R * Y2^-1 * R * Y1, (R * Y2 * Y3^-1)^2, Y3 * Y1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1, Y2 * Y1^-1 * R * Y2^-1 * R * Y1^-1, Y3^-1 * Y2^-1 * Y3^-1 * Y1 * Y2^-1 * Y1^-1, (Y3^-1 * Y2)^4, Y3^-1 * Y2^-1 * R * Y2^-1 * R * Y2^-1 * Y3^-1 * Y2^-1 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 6, 54, 15, 63)(4, 52, 17, 65, 7, 55, 19, 67)(9, 57, 21, 69, 11, 59, 23, 71)(10, 58, 25, 73, 12, 60, 27, 75)(14, 62, 31, 79, 16, 64, 33, 81)(18, 66, 35, 83, 20, 68, 36, 84)(22, 70, 39, 87, 24, 72, 41, 89)(26, 74, 43, 91, 28, 76, 44, 92)(29, 77, 37, 85, 30, 78, 38, 86)(32, 80, 45, 93, 34, 82, 46, 94)(40, 88, 47, 95, 42, 90, 48, 96)(97, 145, 99, 147, 104, 152, 102, 150)(98, 146, 105, 153, 101, 149, 107, 155)(100, 148, 114, 162, 103, 151, 116, 164)(106, 154, 122, 170, 108, 156, 124, 172)(109, 157, 125, 173, 111, 159, 126, 174)(110, 158, 128, 176, 112, 160, 130, 178)(113, 161, 127, 175, 115, 163, 129, 177)(117, 165, 133, 181, 119, 167, 134, 182)(118, 166, 136, 184, 120, 168, 138, 186)(121, 169, 135, 183, 123, 171, 137, 185)(131, 179, 141, 189, 132, 180, 142, 190)(139, 187, 143, 191, 140, 188, 144, 192) L = (1, 100)(2, 106)(3, 110)(4, 104)(5, 108)(6, 112)(7, 97)(8, 103)(9, 118)(10, 101)(11, 120)(12, 98)(13, 122)(14, 102)(15, 124)(16, 99)(17, 123)(18, 117)(19, 121)(20, 119)(21, 116)(22, 107)(23, 114)(24, 105)(25, 113)(26, 111)(27, 115)(28, 109)(29, 136)(30, 138)(31, 140)(32, 133)(33, 139)(34, 134)(35, 137)(36, 135)(37, 130)(38, 128)(39, 131)(40, 126)(41, 132)(42, 125)(43, 127)(44, 129)(45, 144)(46, 143)(47, 141)(48, 142)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E23.382 Graph:: bipartite v = 24 e = 96 f = 28 degree seq :: [ 8^24 ] E23.387 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 4, 4}) Quotient :: dipole Aut^+ = (C3 : C4) : C4 (small group id <48, 12>) Aut = (C2 x C2 x (C3 : C4)) : C2 (small group id <96, 146>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^2 * Y1^-1, Y3^-1 * Y1^-2 * Y3^-1, (R * Y1)^2, Y2^4, Y3^-1 * Y2^-1 * Y3 * Y2^-1, (R * Y3)^2, Y1^4, R * Y2 * R * Y2^-1, Y2^-1 * Y3 * Y1 * Y3^-1 * Y2^-1 * Y1^-1, Y3 * Y1 * Y3^-1 * Y1 * Y3 * Y1^-1, Y2 * Y1 * Y3^-1 * Y1^-1 * Y2 * Y1^-1, Y2 * Y3^2 * Y2^-1 * Y1^-2, Y3^-1 * Y2^-1 * Y1 * Y3 * Y2 * Y1^-1, Y2 * Y1 * Y2 * Y1^-1 * Y3^-1 * Y1^-1, Y1^-1 * Y2^-1 * Y1 * Y2^2 * Y1 * Y2^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 26, 74, 16, 64)(4, 52, 18, 66, 7, 55, 20, 68)(6, 54, 23, 71, 27, 75, 24, 72)(9, 57, 28, 76, 21, 69, 31, 79)(10, 58, 33, 81, 12, 60, 35, 83)(11, 59, 36, 84, 22, 70, 37, 85)(14, 62, 29, 77, 44, 92, 41, 89)(15, 63, 34, 82, 17, 65, 38, 86)(19, 67, 30, 78, 25, 73, 32, 80)(39, 87, 47, 95, 43, 91, 46, 94)(40, 88, 48, 96, 42, 90, 45, 93)(97, 145, 99, 147, 110, 158, 102, 150)(98, 146, 105, 153, 125, 173, 107, 155)(100, 148, 115, 163, 136, 184, 111, 159)(101, 149, 117, 165, 137, 185, 118, 166)(103, 151, 121, 169, 138, 186, 113, 161)(104, 152, 122, 170, 140, 188, 123, 171)(106, 154, 130, 178, 142, 190, 126, 174)(108, 156, 134, 182, 143, 191, 128, 176)(109, 157, 129, 177, 119, 167, 135, 183)(112, 160, 131, 179, 120, 168, 139, 187)(114, 162, 133, 181, 144, 192, 127, 175)(116, 164, 132, 180, 141, 189, 124, 172) L = (1, 100)(2, 106)(3, 111)(4, 104)(5, 108)(6, 115)(7, 97)(8, 103)(9, 126)(10, 101)(11, 130)(12, 98)(13, 133)(14, 136)(15, 122)(16, 132)(17, 99)(18, 131)(19, 123)(20, 129)(21, 128)(22, 134)(23, 127)(24, 124)(25, 102)(26, 113)(27, 121)(28, 119)(29, 142)(30, 117)(31, 120)(32, 105)(33, 114)(34, 118)(35, 116)(36, 109)(37, 112)(38, 107)(39, 144)(40, 140)(41, 143)(42, 110)(43, 141)(44, 138)(45, 135)(46, 137)(47, 125)(48, 139)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E23.384 Graph:: simple bipartite v = 24 e = 96 f = 28 degree seq :: [ 8^24 ] E23.388 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 4, 4}) Quotient :: dipole Aut^+ = C12 : C4 (small group id <48, 13>) Aut = (C12 x C2 x C2) : C2 (small group id <96, 137>) |r| :: 2 Presentation :: [ R^2, Y1^3, Y2^-1 * Y3^2 * Y2^-1, Y3^2 * Y2^2, Y2 * Y1^-1 * Y2^-1 * Y1^-1, (R * Y3)^2, (R * Y1)^2, Y3^4, Y3^-1 * Y1^-1 * Y3 * Y1^-1, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y2)^4 ] Map:: non-degenerate R = (1, 49, 2, 50, 5, 53)(3, 51, 12, 60, 8, 56)(4, 52, 16, 64, 9, 57)(6, 54, 19, 67, 10, 58)(7, 55, 20, 68, 11, 59)(13, 61, 21, 69, 26, 74)(14, 62, 22, 70, 27, 75)(15, 63, 23, 71, 28, 76)(17, 65, 24, 72, 31, 79)(18, 66, 25, 73, 32, 80)(29, 77, 39, 87, 35, 83)(30, 78, 40, 88, 36, 84)(33, 81, 43, 91, 37, 85)(34, 82, 44, 92, 38, 86)(41, 89, 45, 93, 47, 95)(42, 90, 46, 94, 48, 96)(97, 145, 99, 147, 109, 157, 102, 150)(98, 146, 104, 152, 117, 165, 106, 154)(100, 148, 113, 161, 103, 151, 114, 162)(101, 149, 108, 156, 122, 170, 115, 163)(105, 153, 120, 168, 107, 155, 121, 169)(110, 158, 125, 173, 111, 159, 126, 174)(112, 160, 127, 175, 116, 164, 128, 176)(118, 166, 131, 179, 119, 167, 132, 180)(123, 171, 135, 183, 124, 172, 136, 184)(129, 177, 137, 185, 130, 178, 138, 186)(133, 181, 141, 189, 134, 182, 142, 190)(139, 187, 143, 191, 140, 188, 144, 192) L = (1, 100)(2, 105)(3, 110)(4, 109)(5, 112)(6, 111)(7, 97)(8, 118)(9, 117)(10, 119)(11, 98)(12, 123)(13, 103)(14, 102)(15, 99)(16, 122)(17, 129)(18, 130)(19, 124)(20, 101)(21, 107)(22, 106)(23, 104)(24, 133)(25, 134)(26, 116)(27, 115)(28, 108)(29, 137)(30, 138)(31, 139)(32, 140)(33, 114)(34, 113)(35, 141)(36, 142)(37, 121)(38, 120)(39, 143)(40, 144)(41, 126)(42, 125)(43, 128)(44, 127)(45, 132)(46, 131)(47, 136)(48, 135)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8^6 ), ( 8^8 ) } Outer automorphisms :: reflexible Dual of E23.389 Graph:: simple bipartite v = 28 e = 96 f = 24 degree seq :: [ 6^16, 8^12 ] E23.389 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 4, 4}) Quotient :: dipole Aut^+ = C12 : C4 (small group id <48, 13>) Aut = (C12 x C2 x C2) : C2 (small group id <96, 137>) |r| :: 2 Presentation :: [ R^2, Y3^-2 * Y1^-2, Y3^4, R * Y2 * R * Y2^-1, (R * Y3)^2, Y2^-1 * Y1 * Y2^-1 * Y1^-1, Y1^4, Y2^4, (R * Y1)^2, Y2^-1 * Y3 * Y2^-1 * Y3^-1, (Y3 * Y1)^3 ] Map:: non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 11, 59, 22, 70, 15, 63)(4, 52, 17, 65, 7, 55, 19, 67)(6, 54, 9, 57, 23, 71, 20, 68)(10, 58, 27, 75, 12, 60, 29, 77)(13, 61, 24, 72, 38, 86, 32, 80)(14, 62, 34, 82, 16, 64, 35, 83)(18, 66, 36, 84, 21, 69, 37, 85)(25, 73, 41, 89, 26, 74, 42, 90)(28, 76, 43, 91, 30, 78, 44, 92)(31, 79, 45, 93, 33, 81, 46, 94)(39, 87, 47, 95, 40, 88, 48, 96)(97, 145, 99, 147, 109, 157, 102, 150)(98, 146, 105, 153, 120, 168, 107, 155)(100, 148, 114, 162, 127, 175, 110, 158)(101, 149, 116, 164, 128, 176, 111, 159)(103, 151, 117, 165, 129, 177, 112, 160)(104, 152, 118, 166, 134, 182, 119, 167)(106, 154, 124, 172, 135, 183, 121, 169)(108, 156, 126, 174, 136, 184, 122, 170)(113, 161, 130, 178, 141, 189, 132, 180)(115, 163, 131, 179, 142, 190, 133, 181)(123, 171, 137, 185, 143, 191, 139, 187)(125, 173, 138, 186, 144, 192, 140, 188) L = (1, 100)(2, 106)(3, 110)(4, 104)(5, 108)(6, 114)(7, 97)(8, 103)(9, 121)(10, 101)(11, 124)(12, 98)(13, 127)(14, 118)(15, 126)(16, 99)(17, 125)(18, 119)(19, 123)(20, 122)(21, 102)(22, 112)(23, 117)(24, 135)(25, 116)(26, 105)(27, 113)(28, 111)(29, 115)(30, 107)(31, 134)(32, 136)(33, 109)(34, 140)(35, 139)(36, 138)(37, 137)(38, 129)(39, 128)(40, 120)(41, 132)(42, 133)(43, 130)(44, 131)(45, 144)(46, 143)(47, 141)(48, 142)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E23.388 Graph:: simple bipartite v = 24 e = 96 f = 28 degree seq :: [ 8^24 ] E23.390 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 4, 4}) Quotient :: dipole Aut^+ = C2 . S4 = SL(2,3) . C2 (small group id <48, 28>) Aut = (C2 x SL(2,3)) : C2 (small group id <96, 190>) |r| :: 2 Presentation :: [ R^2, Y1^3, Y3^3, Y2 * Y3^-1 * Y2^-1 * Y3^-1, Y2^4, Y3 * Y2 * Y3 * Y2^-1, (R * Y1)^2, (R * Y3)^2, Y3^-1 * Y2 * Y1^-1 * Y2 * Y1, Y1 * Y3 * Y1 * Y2^-2 * Y3, Y1 * Y2^-1 * Y3^-1 * Y1 * Y3 * Y2, (R * Y2 * Y3^-1)^2, Y2^-2 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1, Y1^-1 * Y2^-2 * Y1 * Y2^2, Y3 * Y1 * Y2 * Y1^-1 * Y2^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 49, 2, 50, 5, 53)(3, 51, 12, 60, 15, 63)(4, 52, 17, 65, 18, 66)(6, 54, 24, 72, 26, 74)(7, 55, 27, 75, 28, 76)(8, 56, 29, 77, 31, 79)(9, 57, 33, 81, 34, 82)(10, 58, 36, 84, 37, 85)(11, 59, 38, 86, 39, 87)(13, 61, 30, 78, 42, 90)(14, 62, 43, 91, 22, 70)(16, 64, 46, 94, 32, 80)(19, 67, 48, 96, 35, 83)(20, 68, 25, 73, 45, 93)(21, 69, 40, 88, 47, 95)(23, 71, 44, 92, 41, 89)(97, 145, 99, 147, 109, 157, 102, 150)(98, 146, 104, 152, 126, 174, 106, 154)(100, 148, 112, 160, 137, 185, 115, 163)(101, 149, 116, 164, 138, 186, 118, 166)(103, 151, 110, 158, 129, 177, 121, 169)(105, 153, 128, 176, 124, 172, 131, 179)(107, 155, 120, 168, 136, 184, 108, 156)(111, 159, 114, 162, 122, 170, 140, 188)(113, 161, 125, 173, 119, 167, 132, 180)(117, 165, 142, 190, 135, 183, 144, 192)(123, 171, 127, 175, 130, 178, 133, 181)(134, 182, 141, 189, 143, 191, 139, 187) L = (1, 100)(2, 105)(3, 110)(4, 103)(5, 117)(6, 121)(7, 97)(8, 120)(9, 107)(10, 108)(11, 98)(12, 131)(13, 137)(14, 112)(15, 127)(16, 99)(17, 138)(18, 143)(19, 102)(20, 132)(21, 119)(22, 125)(23, 101)(24, 128)(25, 115)(26, 133)(27, 140)(28, 136)(29, 144)(30, 124)(31, 141)(32, 104)(33, 109)(34, 114)(35, 106)(36, 142)(37, 139)(38, 123)(39, 113)(40, 126)(41, 129)(42, 135)(43, 122)(44, 134)(45, 111)(46, 116)(47, 130)(48, 118)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8^6 ), ( 8^8 ) } Outer automorphisms :: reflexible Dual of E23.392 Graph:: simple bipartite v = 28 e = 96 f = 24 degree seq :: [ 6^16, 8^12 ] E23.391 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 4, 4}) Quotient :: dipole Aut^+ = C2 . S4 = SL(2,3) . C2 (small group id <48, 28>) Aut = (C2 x SL(2,3)) : C2 (small group id <96, 190>) |r| :: 2 Presentation :: [ R^2, Y1^3, Y2^2 * Y3^-2, Y2 * Y3^-1 * Y2 * Y3, Y3 * Y2^2 * Y3, Y2^4, Y1^-1 * Y3 * Y1^-1 * Y3^-1, (R * Y3)^2, (R * Y1)^2, R * Y2 * R * Y2^-1, Y2^-1 * Y3 * Y2 * Y3, Y2^-1 * Y1^-1 * Y2^2 * Y1 * Y2^-1, Y2^-1 * Y3^-1 * Y1 * Y2^-1 * Y1^-1 * Y2 * Y1, Y2 * Y1^-1 * Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2 * Y1^-1 ] Map:: non-degenerate R = (1, 49, 2, 50, 5, 53)(3, 51, 12, 60, 15, 63)(4, 52, 17, 65, 9, 57)(6, 54, 21, 69, 22, 70)(7, 55, 20, 68, 11, 59)(8, 56, 23, 71, 26, 74)(10, 58, 28, 76, 29, 77)(13, 61, 24, 72, 34, 82)(14, 62, 35, 83, 31, 79)(16, 64, 38, 86, 33, 81)(18, 66, 41, 89, 42, 90)(19, 67, 43, 91, 44, 92)(25, 73, 32, 80, 46, 94)(27, 75, 30, 78, 48, 96)(36, 84, 40, 88, 47, 95)(37, 85, 39, 87, 45, 93)(97, 145, 99, 147, 109, 157, 102, 150)(98, 146, 104, 152, 120, 168, 106, 154)(100, 148, 112, 160, 103, 151, 110, 158)(101, 149, 114, 162, 130, 178, 115, 163)(105, 153, 123, 171, 107, 155, 121, 169)(108, 156, 126, 174, 117, 165, 128, 176)(111, 159, 132, 180, 118, 166, 133, 181)(113, 161, 135, 183, 116, 164, 136, 184)(119, 167, 141, 189, 124, 172, 143, 191)(122, 170, 127, 175, 125, 173, 129, 177)(131, 179, 137, 185, 134, 182, 139, 187)(138, 186, 142, 190, 140, 188, 144, 192) L = (1, 100)(2, 105)(3, 110)(4, 109)(5, 113)(6, 112)(7, 97)(8, 121)(9, 120)(10, 123)(11, 98)(12, 127)(13, 103)(14, 102)(15, 131)(16, 99)(17, 130)(18, 136)(19, 135)(20, 101)(21, 129)(22, 134)(23, 142)(24, 107)(25, 106)(26, 128)(27, 104)(28, 144)(29, 126)(30, 122)(31, 117)(32, 125)(33, 108)(34, 116)(35, 118)(36, 139)(37, 137)(38, 111)(39, 114)(40, 115)(41, 132)(42, 143)(43, 133)(44, 141)(45, 138)(46, 124)(47, 140)(48, 119)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8^6 ), ( 8^8 ) } Outer automorphisms :: reflexible Dual of E23.393 Graph:: simple bipartite v = 28 e = 96 f = 24 degree seq :: [ 6^16, 8^12 ] E23.392 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 4, 4}) Quotient :: dipole Aut^+ = C2 . S4 = SL(2,3) . C2 (small group id <48, 28>) Aut = (C2 x SL(2,3)) : C2 (small group id <96, 190>) |r| :: 2 Presentation :: [ R^2, Y3^2 * Y2^-2, Y3^-1 * Y2 * Y3^-1 * Y2^-1, Y3^4, Y3^-2 * Y1^2, Y3^2 * Y2^2, Y3^-1 * Y1^-2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, R * Y2 * R * Y2^-1, (Y3^-1 * Y1^-1)^3, Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2^-1 * Y1^-1, Y1 * Y2 * Y1 * Y3^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y3^-1, Y1 * Y2 * Y1^-1 * Y3^-1 * Y1 * Y2 * Y1^-1 * Y3^-1 * Y2^-1, Y1 * Y3^-1 * Y2 * Y1 * Y2^-1 * Y1 * Y3^-1 * Y1^-1 * Y2^-1 ] Map:: non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 6, 54, 15, 63)(4, 52, 17, 65, 7, 55, 18, 66)(9, 57, 19, 67, 11, 59, 21, 69)(10, 58, 23, 71, 12, 60, 24, 72)(14, 62, 29, 77, 16, 64, 30, 78)(20, 68, 37, 85, 22, 70, 38, 86)(25, 73, 35, 83, 27, 75, 33, 81)(26, 74, 43, 91, 28, 76, 44, 92)(31, 79, 47, 95, 32, 80, 48, 96)(34, 82, 46, 94, 36, 84, 45, 93)(39, 87, 42, 90, 40, 88, 41, 89)(97, 145, 99, 147, 104, 152, 102, 150)(98, 146, 105, 153, 101, 149, 107, 155)(100, 148, 112, 160, 103, 151, 110, 158)(106, 154, 118, 166, 108, 156, 116, 164)(109, 157, 121, 169, 111, 159, 123, 171)(113, 161, 127, 175, 114, 162, 128, 176)(115, 163, 129, 177, 117, 165, 131, 179)(119, 167, 135, 183, 120, 168, 136, 184)(122, 170, 138, 186, 124, 172, 137, 185)(125, 173, 141, 189, 126, 174, 142, 190)(130, 178, 144, 192, 132, 180, 143, 191)(133, 181, 139, 187, 134, 182, 140, 188) L = (1, 100)(2, 106)(3, 110)(4, 104)(5, 108)(6, 112)(7, 97)(8, 103)(9, 116)(10, 101)(11, 118)(12, 98)(13, 122)(14, 102)(15, 124)(16, 99)(17, 120)(18, 119)(19, 130)(20, 107)(21, 132)(22, 105)(23, 113)(24, 114)(25, 137)(26, 111)(27, 138)(28, 109)(29, 140)(30, 139)(31, 135)(32, 136)(33, 143)(34, 117)(35, 144)(36, 115)(37, 141)(38, 142)(39, 128)(40, 127)(41, 123)(42, 121)(43, 125)(44, 126)(45, 134)(46, 133)(47, 131)(48, 129)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E23.390 Graph:: bipartite v = 24 e = 96 f = 28 degree seq :: [ 8^24 ] E23.393 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 4, 4, 4}) Quotient :: dipole Aut^+ = C2 . S4 = SL(2,3) . C2 (small group id <48, 28>) Aut = (C2 x SL(2,3)) : C2 (small group id <96, 190>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y3^2 * Y2^-1, Y3 * Y2 * Y3 * Y2^-1, Y1^4, Y3^2 * Y2^2, Y3^-1 * Y1^-2 * Y3^-1, (R * Y1)^2, Y3^-2 * Y1^2, R * Y2 * R * Y2^-1, Y3 * Y2^-1 * Y3^-1 * Y2^-1, (R * Y3)^2, (Y3^-1 * Y1^-1)^3, Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2^-1 * Y1^-1, Y1 * Y2 * Y3 * Y1 * Y3 * Y2 * Y1^-1 * Y3^-1 * Y2^-1, Y1 * Y2 * Y1 * Y3 * Y2^-1 * Y1 * Y2^-1 * Y1^-1 * Y3^-1, Y1 * Y3 * Y1 * Y2 * Y1 * Y2 * Y3^-1 * Y1^-1 * Y2^-1 ] Map:: non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 6, 54, 15, 63)(4, 52, 17, 65, 7, 55, 18, 66)(9, 57, 19, 67, 11, 59, 21, 69)(10, 58, 23, 71, 12, 60, 24, 72)(14, 62, 29, 77, 16, 64, 30, 78)(20, 68, 37, 85, 22, 70, 38, 86)(25, 73, 35, 83, 27, 75, 33, 81)(26, 74, 43, 91, 28, 76, 44, 92)(31, 79, 47, 95, 32, 80, 48, 96)(34, 82, 45, 93, 36, 84, 46, 94)(39, 87, 41, 89, 40, 88, 42, 90)(97, 145, 99, 147, 104, 152, 102, 150)(98, 146, 105, 153, 101, 149, 107, 155)(100, 148, 112, 160, 103, 151, 110, 158)(106, 154, 118, 166, 108, 156, 116, 164)(109, 157, 121, 169, 111, 159, 123, 171)(113, 161, 127, 175, 114, 162, 128, 176)(115, 163, 129, 177, 117, 165, 131, 179)(119, 167, 135, 183, 120, 168, 136, 184)(122, 170, 138, 186, 124, 172, 137, 185)(125, 173, 141, 189, 126, 174, 142, 190)(130, 178, 143, 191, 132, 180, 144, 192)(133, 181, 140, 188, 134, 182, 139, 187) L = (1, 100)(2, 106)(3, 110)(4, 104)(5, 108)(6, 112)(7, 97)(8, 103)(9, 116)(10, 101)(11, 118)(12, 98)(13, 122)(14, 102)(15, 124)(16, 99)(17, 120)(18, 119)(19, 130)(20, 107)(21, 132)(22, 105)(23, 113)(24, 114)(25, 137)(26, 111)(27, 138)(28, 109)(29, 140)(30, 139)(31, 135)(32, 136)(33, 144)(34, 117)(35, 143)(36, 115)(37, 142)(38, 141)(39, 128)(40, 127)(41, 123)(42, 121)(43, 125)(44, 126)(45, 133)(46, 134)(47, 129)(48, 131)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E23.391 Graph:: bipartite v = 24 e = 96 f = 28 degree seq :: [ 8^24 ] E23.394 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {3, 3, 4, 6}) Quotient :: edge^2 Aut^+ = C2 x SL(2,3) (small group id <48, 32>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1, Y1 * Y2 * Y1, Y1^3, Y2^3, Y3^4, R * Y1 * R * Y2, Y3^4, (R * Y3)^2, Y3^-2 * Y1 * Y3^-2 * Y1^-1, Y1 * Y3^2 * Y1 * Y3^-2 * Y2, Y3^-1 * Y1 * Y3^-1 * Y1^-1 * Y3 * Y1 * Y3^-1 * Y1^-1, (Y1^-1 * Y3^-1 * Y2^-1)^6 ] Map:: polytopal non-degenerate R = (1, 49, 3, 51, 9, 57, 5, 53)(2, 50, 6, 54, 16, 64, 7, 55)(4, 52, 11, 59, 22, 70, 12, 60)(8, 56, 20, 68, 13, 61, 21, 69)(10, 58, 23, 71, 14, 62, 24, 72)(15, 63, 29, 77, 18, 66, 30, 78)(17, 65, 31, 79, 19, 67, 32, 80)(25, 73, 37, 85, 27, 75, 35, 83)(26, 74, 39, 87, 28, 76, 40, 88)(33, 81, 43, 91, 34, 82, 44, 92)(36, 84, 45, 93, 38, 86, 46, 94)(41, 89, 47, 95, 42, 90, 48, 96)(97, 98, 100)(99, 104, 106)(101, 109, 110)(102, 111, 113)(103, 114, 115)(105, 112, 118)(107, 121, 122)(108, 123, 124)(116, 129, 128)(117, 130, 127)(119, 131, 132)(120, 133, 134)(125, 137, 136)(126, 138, 135)(139, 143, 142)(140, 144, 141)(145, 146, 148)(147, 152, 154)(149, 157, 158)(150, 159, 161)(151, 162, 163)(153, 160, 166)(155, 169, 170)(156, 171, 172)(164, 177, 176)(165, 178, 175)(167, 179, 180)(168, 181, 182)(173, 185, 184)(174, 186, 183)(187, 191, 190)(188, 192, 189) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 24^3 ), ( 24^8 ) } Outer automorphisms :: reflexible Dual of E23.397 Graph:: simple bipartite v = 44 e = 96 f = 8 degree seq :: [ 3^32, 8^12 ] E23.395 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {3, 3, 4, 6}) Quotient :: edge^2 Aut^+ = C2 x SL(2,3) (small group id <48, 32>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ R^2, Y2^3, Y1^3, Y1 * Y3^-1 * Y2^-1 * Y3, R * Y2 * R * Y1, (R * Y3)^2, Y3^-2 * Y1 * Y2^-1 * Y1^-1, Y2 * Y3^2 * Y2^-1 * Y1, Y1^-1 * Y2^-1 * Y3 * Y2 * Y1 * Y3^-1, Y2 * Y1 * Y2 * Y1 * Y3^2, Y3^6, Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: polytopal non-degenerate R = (1, 49, 4, 52, 17, 65, 44, 92, 29, 77, 7, 55)(2, 50, 9, 57, 33, 81, 40, 88, 38, 86, 11, 59)(3, 51, 13, 61, 20, 68, 31, 79, 8, 56, 15, 63)(5, 53, 21, 69, 25, 73, 43, 91, 14, 62, 23, 71)(6, 54, 18, 66, 41, 89, 46, 94, 30, 78, 26, 74)(10, 58, 34, 82, 47, 95, 27, 75, 39, 87, 16, 64)(12, 60, 32, 80, 22, 70, 45, 93, 48, 96, 36, 84)(19, 67, 35, 83, 37, 85, 24, 72, 28, 76, 42, 90)(97, 98, 101)(99, 108, 110)(100, 109, 114)(102, 120, 121)(103, 123, 124)(104, 126, 125)(105, 111, 130)(106, 131, 113)(107, 132, 133)(112, 128, 122)(115, 119, 142)(116, 135, 134)(117, 127, 141)(118, 138, 129)(136, 139, 140)(137, 143, 144)(145, 147, 150)(146, 152, 154)(148, 160, 163)(149, 164, 166)(151, 155, 167)(153, 176, 172)(156, 174, 183)(157, 171, 184)(158, 185, 186)(159, 180, 187)(161, 177, 169)(162, 178, 189)(165, 170, 181)(168, 173, 191)(175, 190, 188)(179, 182, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 16^3 ), ( 16^12 ) } Outer automorphisms :: reflexible Dual of E23.396 Graph:: simple bipartite v = 40 e = 96 f = 12 degree seq :: [ 3^32, 12^8 ] E23.396 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {3, 3, 4, 6}) Quotient :: loop^2 Aut^+ = C2 x SL(2,3) (small group id <48, 32>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1, Y1 * Y2 * Y1, Y1^3, Y2^3, Y3^4, R * Y1 * R * Y2, Y3^4, (R * Y3)^2, Y3^-2 * Y1 * Y3^-2 * Y1^-1, Y1 * Y3^2 * Y1 * Y3^-2 * Y2, Y3^-1 * Y1 * Y3^-1 * Y1^-1 * Y3 * Y1 * Y3^-1 * Y1^-1, (Y1^-1 * Y3^-1 * Y2^-1)^6 ] Map:: polytopal non-degenerate R = (1, 49, 97, 145, 3, 51, 99, 147, 9, 57, 105, 153, 5, 53, 101, 149)(2, 50, 98, 146, 6, 54, 102, 150, 16, 64, 112, 160, 7, 55, 103, 151)(4, 52, 100, 148, 11, 59, 107, 155, 22, 70, 118, 166, 12, 60, 108, 156)(8, 56, 104, 152, 20, 68, 116, 164, 13, 61, 109, 157, 21, 69, 117, 165)(10, 58, 106, 154, 23, 71, 119, 167, 14, 62, 110, 158, 24, 72, 120, 168)(15, 63, 111, 159, 29, 77, 125, 173, 18, 66, 114, 162, 30, 78, 126, 174)(17, 65, 113, 161, 31, 79, 127, 175, 19, 67, 115, 163, 32, 80, 128, 176)(25, 73, 121, 169, 37, 85, 133, 181, 27, 75, 123, 171, 35, 83, 131, 179)(26, 74, 122, 170, 39, 87, 135, 183, 28, 76, 124, 172, 40, 88, 136, 184)(33, 81, 129, 177, 43, 91, 139, 187, 34, 82, 130, 178, 44, 92, 140, 188)(36, 84, 132, 180, 45, 93, 141, 189, 38, 86, 134, 182, 46, 94, 142, 190)(41, 89, 137, 185, 47, 95, 143, 191, 42, 90, 138, 186, 48, 96, 144, 192) L = (1, 50)(2, 52)(3, 56)(4, 49)(5, 61)(6, 63)(7, 66)(8, 58)(9, 64)(10, 51)(11, 73)(12, 75)(13, 62)(14, 53)(15, 65)(16, 70)(17, 54)(18, 67)(19, 55)(20, 81)(21, 82)(22, 57)(23, 83)(24, 85)(25, 74)(26, 59)(27, 76)(28, 60)(29, 89)(30, 90)(31, 69)(32, 68)(33, 80)(34, 79)(35, 84)(36, 71)(37, 86)(38, 72)(39, 78)(40, 77)(41, 88)(42, 87)(43, 95)(44, 96)(45, 92)(46, 91)(47, 94)(48, 93)(97, 146)(98, 148)(99, 152)(100, 145)(101, 157)(102, 159)(103, 162)(104, 154)(105, 160)(106, 147)(107, 169)(108, 171)(109, 158)(110, 149)(111, 161)(112, 166)(113, 150)(114, 163)(115, 151)(116, 177)(117, 178)(118, 153)(119, 179)(120, 181)(121, 170)(122, 155)(123, 172)(124, 156)(125, 185)(126, 186)(127, 165)(128, 164)(129, 176)(130, 175)(131, 180)(132, 167)(133, 182)(134, 168)(135, 174)(136, 173)(137, 184)(138, 183)(139, 191)(140, 192)(141, 188)(142, 187)(143, 190)(144, 189) local type(s) :: { ( 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12, 3, 12 ) } Outer automorphisms :: reflexible Dual of E23.395 Transitivity :: VT+ Graph:: v = 12 e = 96 f = 40 degree seq :: [ 16^12 ] E23.397 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {3, 3, 4, 6}) Quotient :: loop^2 Aut^+ = C2 x SL(2,3) (small group id <48, 32>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ R^2, Y2^3, Y1^3, Y1 * Y3^-1 * Y2^-1 * Y3, R * Y2 * R * Y1, (R * Y3)^2, Y3^-2 * Y1 * Y2^-1 * Y1^-1, Y2 * Y3^2 * Y2^-1 * Y1, Y1^-1 * Y2^-1 * Y3 * Y2 * Y1 * Y3^-1, Y2 * Y1 * Y2 * Y1 * Y3^2, Y3^6, Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: polytopal non-degenerate R = (1, 49, 97, 145, 4, 52, 100, 148, 17, 65, 113, 161, 44, 92, 140, 188, 29, 77, 125, 173, 7, 55, 103, 151)(2, 50, 98, 146, 9, 57, 105, 153, 33, 81, 129, 177, 40, 88, 136, 184, 38, 86, 134, 182, 11, 59, 107, 155)(3, 51, 99, 147, 13, 61, 109, 157, 20, 68, 116, 164, 31, 79, 127, 175, 8, 56, 104, 152, 15, 63, 111, 159)(5, 53, 101, 149, 21, 69, 117, 165, 25, 73, 121, 169, 43, 91, 139, 187, 14, 62, 110, 158, 23, 71, 119, 167)(6, 54, 102, 150, 18, 66, 114, 162, 41, 89, 137, 185, 46, 94, 142, 190, 30, 78, 126, 174, 26, 74, 122, 170)(10, 58, 106, 154, 34, 82, 130, 178, 47, 95, 143, 191, 27, 75, 123, 171, 39, 87, 135, 183, 16, 64, 112, 160)(12, 60, 108, 156, 32, 80, 128, 176, 22, 70, 118, 166, 45, 93, 141, 189, 48, 96, 144, 192, 36, 84, 132, 180)(19, 67, 115, 163, 35, 83, 131, 179, 37, 85, 133, 181, 24, 72, 120, 168, 28, 76, 124, 172, 42, 90, 138, 186) L = (1, 50)(2, 53)(3, 60)(4, 61)(5, 49)(6, 72)(7, 75)(8, 78)(9, 63)(10, 83)(11, 84)(12, 62)(13, 66)(14, 51)(15, 82)(16, 80)(17, 58)(18, 52)(19, 71)(20, 87)(21, 79)(22, 90)(23, 94)(24, 73)(25, 54)(26, 64)(27, 76)(28, 55)(29, 56)(30, 77)(31, 93)(32, 74)(33, 70)(34, 57)(35, 65)(36, 85)(37, 59)(38, 68)(39, 86)(40, 91)(41, 95)(42, 81)(43, 92)(44, 88)(45, 69)(46, 67)(47, 96)(48, 89)(97, 147)(98, 152)(99, 150)(100, 160)(101, 164)(102, 145)(103, 155)(104, 154)(105, 176)(106, 146)(107, 167)(108, 174)(109, 171)(110, 185)(111, 180)(112, 163)(113, 177)(114, 178)(115, 148)(116, 166)(117, 170)(118, 149)(119, 151)(120, 173)(121, 161)(122, 181)(123, 184)(124, 153)(125, 191)(126, 183)(127, 190)(128, 172)(129, 169)(130, 189)(131, 182)(132, 187)(133, 165)(134, 192)(135, 156)(136, 157)(137, 186)(138, 158)(139, 159)(140, 175)(141, 162)(142, 188)(143, 168)(144, 179) 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 E23.394 Transitivity :: VT+ Graph:: v = 8 e = 96 f = 44 degree seq :: [ 24^8 ] E23.398 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 4, 6}) Quotient :: dipole Aut^+ = C2 x SL(2,3) (small group id <48, 32>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^2, Y2^3, Y1^3, (R * Y3)^2, (R * Y1)^2, (Y3 * Y1^-1)^2, Y3 * Y2 * Y1^-1 * Y3 * Y2^-1 * Y1^-1, Y2^-1 * R * Y2^-1 * Y1^-1 * Y2 * R, (R * Y2 * Y3^-1)^2, Y2^-1 * Y3^-1 * Y2 * Y1 * Y2 * Y3^-1, Y2 * Y3 * Y1^-1 * Y2^-1 * Y3 * Y1^-1, (Y2 * Y1^-1)^4, (Y2 * Y3^-1 * Y2 * Y1^-1)^2, (Y3 * Y2^-1)^4 ] Map:: non-degenerate R = (1, 49, 2, 50, 5, 53)(3, 51, 11, 59, 13, 61)(4, 52, 7, 55, 10, 58)(6, 54, 19, 67, 21, 69)(8, 56, 25, 73, 27, 75)(9, 57, 29, 77, 31, 79)(12, 60, 14, 62, 33, 81)(15, 63, 26, 74, 28, 76)(16, 64, 30, 78, 32, 80)(17, 65, 35, 83, 41, 89)(18, 66, 38, 86, 43, 91)(20, 68, 22, 70, 34, 82)(23, 71, 36, 84, 42, 90)(24, 72, 40, 88, 44, 92)(37, 85, 45, 93, 47, 95)(39, 87, 46, 94, 48, 96)(97, 145, 99, 147, 102, 150)(98, 146, 104, 152, 105, 153)(100, 148, 111, 159, 112, 160)(101, 149, 113, 161, 114, 162)(103, 151, 119, 167, 120, 168)(106, 154, 129, 177, 130, 178)(107, 155, 121, 169, 131, 179)(108, 156, 122, 170, 132, 180)(109, 157, 133, 181, 134, 182)(110, 158, 135, 183, 136, 184)(115, 163, 123, 171, 141, 189)(116, 164, 124, 172, 142, 190)(117, 165, 127, 175, 139, 187)(118, 166, 128, 176, 140, 188)(125, 173, 137, 185, 143, 191)(126, 174, 138, 186, 144, 192) L = (1, 100)(2, 103)(3, 108)(4, 101)(5, 106)(6, 116)(7, 97)(8, 122)(9, 126)(10, 98)(11, 110)(12, 109)(13, 129)(14, 99)(15, 121)(16, 125)(17, 132)(18, 136)(19, 118)(20, 117)(21, 130)(22, 102)(23, 131)(24, 134)(25, 124)(26, 123)(27, 111)(28, 104)(29, 128)(30, 127)(31, 112)(32, 105)(33, 107)(34, 115)(35, 138)(36, 137)(37, 142)(38, 140)(39, 141)(40, 139)(41, 119)(42, 113)(43, 120)(44, 114)(45, 144)(46, 143)(47, 135)(48, 133)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E23.403 Graph:: simple bipartite v = 32 e = 96 f = 20 degree seq :: [ 6^32 ] E23.399 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 4, 6}) Quotient :: dipole Aut^+ = C2 x SL(2,3) (small group id <48, 32>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-1, Y1^3, Y2^4, Y2^4, (R * Y3)^2, (R * Y1)^2, Y2^-2 * Y1 * Y2^-2 * Y1^-1, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^3, Y2^-1 * Y1 * Y2^-1 * Y1^-1 * Y2 * Y1 * Y2^-1 * Y1^-1, (Y3 * Y2^-1)^6 ] Map:: non-degenerate R = (1, 49, 2, 50, 4, 52)(3, 51, 8, 56, 10, 58)(5, 53, 13, 61, 14, 62)(6, 54, 15, 63, 17, 65)(7, 55, 18, 66, 19, 67)(9, 57, 16, 64, 22, 70)(11, 59, 25, 73, 26, 74)(12, 60, 27, 75, 28, 76)(20, 68, 33, 81, 32, 80)(21, 69, 34, 82, 31, 79)(23, 71, 35, 83, 36, 84)(24, 72, 37, 85, 38, 86)(29, 77, 41, 89, 40, 88)(30, 78, 42, 90, 39, 87)(43, 91, 47, 95, 46, 94)(44, 92, 48, 96, 45, 93)(97, 145, 99, 147, 105, 153, 101, 149)(98, 146, 102, 150, 112, 160, 103, 151)(100, 148, 107, 155, 118, 166, 108, 156)(104, 152, 116, 164, 109, 157, 117, 165)(106, 154, 119, 167, 110, 158, 120, 168)(111, 159, 125, 173, 114, 162, 126, 174)(113, 161, 127, 175, 115, 163, 128, 176)(121, 169, 133, 181, 123, 171, 131, 179)(122, 170, 135, 183, 124, 172, 136, 184)(129, 177, 139, 187, 130, 178, 140, 188)(132, 180, 141, 189, 134, 182, 142, 190)(137, 185, 143, 191, 138, 186, 144, 192) L = (1, 98)(2, 100)(3, 104)(4, 97)(5, 109)(6, 111)(7, 114)(8, 106)(9, 112)(10, 99)(11, 121)(12, 123)(13, 110)(14, 101)(15, 113)(16, 118)(17, 102)(18, 115)(19, 103)(20, 129)(21, 130)(22, 105)(23, 131)(24, 133)(25, 122)(26, 107)(27, 124)(28, 108)(29, 137)(30, 138)(31, 117)(32, 116)(33, 128)(34, 127)(35, 132)(36, 119)(37, 134)(38, 120)(39, 126)(40, 125)(41, 136)(42, 135)(43, 143)(44, 144)(45, 140)(46, 139)(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) :: { ( 6, 12, 6, 12, 6, 12 ), ( 6, 12, 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E23.401 Graph:: bipartite v = 28 e = 96 f = 24 degree seq :: [ 6^16, 8^12 ] E23.400 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 4, 6}) Quotient :: dipole Aut^+ = C2 x SL(2,3) (small group id <48, 32>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ R^2, Y1^3, (R * Y3)^2, (R * Y1)^2, Y2^4, Y3^2 * Y2^-2 * Y3, Y2^-1 * Y3 * Y1 * Y2 * Y1, Y3^-1 * Y1 * Y3^2 * Y1, Y1 * Y3 * Y2^-1 * Y3 * Y2^-1, Y1 * Y3 * Y2 * Y3 * Y2, Y1 * Y2 * Y3 * Y1 * Y2^-1, (R * Y2 * Y3^-1)^2, Y3 * Y2 * Y3^-1 * Y1 * Y2^-1 * Y1^-1, (Y3^-1 * Y1^-1)^3, Y2 * Y3 * Y1^-1 * Y2^-1 * Y3 * Y1^-1 ] Map:: non-degenerate R = (1, 49, 2, 50, 5, 53)(3, 51, 12, 60, 15, 63)(4, 52, 17, 65, 20, 68)(6, 54, 26, 74, 28, 76)(7, 55, 30, 78, 32, 80)(8, 56, 31, 79, 36, 84)(9, 57, 38, 86, 39, 87)(10, 58, 33, 81, 40, 88)(11, 59, 34, 82, 43, 91)(13, 61, 35, 83, 46, 94)(14, 62, 22, 70, 42, 90)(16, 64, 37, 85, 21, 69)(18, 66, 29, 77, 41, 89)(19, 67, 23, 71, 47, 95)(24, 72, 44, 92, 27, 75)(25, 73, 45, 93, 48, 96)(97, 145, 99, 147, 109, 157, 102, 150)(98, 146, 104, 152, 131, 179, 106, 154)(100, 148, 114, 162, 130, 178, 117, 165)(101, 149, 118, 166, 142, 190, 120, 168)(103, 151, 127, 175, 115, 163, 129, 177)(105, 153, 125, 173, 141, 189, 112, 160)(107, 155, 138, 186, 116, 164, 140, 188)(108, 156, 135, 183, 122, 170, 121, 169)(110, 158, 128, 176, 123, 171, 143, 191)(111, 159, 139, 187, 124, 172, 113, 161)(119, 167, 137, 185, 126, 174, 133, 181)(132, 180, 144, 192, 136, 184, 134, 182) L = (1, 100)(2, 105)(3, 110)(4, 115)(5, 119)(6, 123)(7, 97)(8, 111)(9, 116)(10, 124)(11, 98)(12, 129)(13, 130)(14, 125)(15, 137)(16, 99)(17, 144)(18, 120)(19, 109)(20, 131)(21, 118)(22, 132)(23, 135)(24, 136)(25, 101)(26, 127)(27, 112)(28, 133)(29, 102)(30, 121)(31, 140)(32, 113)(33, 138)(34, 103)(35, 141)(36, 114)(37, 104)(38, 128)(39, 142)(40, 117)(41, 106)(42, 122)(43, 134)(44, 108)(45, 107)(46, 126)(47, 139)(48, 143)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 6, 12, 6, 12, 6, 12 ), ( 6, 12, 6, 12, 6, 12, 6, 12 ) } Outer automorphisms :: reflexible Dual of E23.402 Graph:: simple bipartite v = 28 e = 96 f = 24 degree seq :: [ 6^16, 8^12 ] E23.401 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 4, 6}) Quotient :: dipole Aut^+ = C2 x SL(2,3) (small group id <48, 32>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2, Y2^3, R * Y2 * R * Y3^-1, (R * Y1)^2, Y1^6, (Y3 * Y2^-1)^3, Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y2^-1 * Y1, Y1 * Y2 * Y1^2 * Y2^-1 * Y1^-1 * Y3^-1, Y1^2 * Y3 * Y1^-1 * Y3^-1 * Y1 * Y3^-1, Y1 * Y2 * Y1 * Y3 * Y1^2 * Y2^-1, Y1 * Y3 * Y1^-1 * Y3 * Y1^-2 * Y3^-1, Y1 * Y2 * Y1 * Y3^-1 * Y1^-1 * Y2^-1 * Y1, (Y3^-1 * Y1^-1)^4 ] Map:: non-degenerate R = (1, 49, 2, 50, 6, 54, 16, 64, 15, 63, 5, 53)(3, 51, 9, 57, 23, 71, 41, 89, 28, 76, 10, 58)(4, 52, 11, 59, 29, 77, 42, 90, 34, 82, 12, 60)(7, 55, 19, 67, 30, 78, 39, 87, 24, 72, 20, 68)(8, 56, 21, 69, 32, 80, 40, 88, 46, 94, 22, 70)(13, 61, 35, 83, 43, 91, 17, 65, 25, 73, 36, 84)(14, 62, 37, 85, 33, 81, 18, 66, 27, 75, 38, 86)(26, 74, 44, 92, 48, 96, 47, 95, 31, 79, 45, 93)(97, 145, 99, 147, 100, 148)(98, 146, 103, 151, 104, 152)(101, 149, 109, 157, 110, 158)(102, 150, 113, 161, 114, 162)(105, 153, 120, 168, 121, 169)(106, 154, 122, 170, 123, 171)(107, 155, 126, 174, 127, 175)(108, 156, 128, 176, 129, 177)(111, 159, 135, 183, 136, 184)(112, 160, 137, 185, 138, 186)(115, 163, 131, 179, 124, 172)(116, 164, 140, 188, 130, 178)(117, 165, 132, 180, 141, 189)(118, 166, 134, 182, 125, 173)(119, 167, 143, 191, 133, 181)(139, 187, 144, 192, 142, 190) L = (1, 100)(2, 104)(3, 97)(4, 99)(5, 110)(6, 114)(7, 98)(8, 103)(9, 121)(10, 123)(11, 127)(12, 129)(13, 101)(14, 109)(15, 136)(16, 138)(17, 102)(18, 113)(19, 124)(20, 130)(21, 141)(22, 125)(23, 133)(24, 105)(25, 120)(26, 106)(27, 122)(28, 131)(29, 134)(30, 107)(31, 126)(32, 108)(33, 128)(34, 140)(35, 115)(36, 117)(37, 143)(38, 118)(39, 111)(40, 135)(41, 112)(42, 137)(43, 142)(44, 116)(45, 132)(46, 144)(47, 119)(48, 139)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 6, 8, 6, 8, 6, 8 ), ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E23.399 Graph:: bipartite v = 24 e = 96 f = 28 degree seq :: [ 6^16, 12^8 ] E23.402 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 4, 6}) Quotient :: dipole Aut^+ = C2 x SL(2,3) (small group id <48, 32>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ R^2, Y2^3, (R * Y3)^2, Y1^2 * Y3 * Y2^-1, (R * Y1)^2, Y1 * Y3^-1 * Y2^-1 * Y1 * Y2, Y2 * Y3^-2 * Y2 * Y3, Y1 * Y2^-1 * Y3^-1 * Y1 * Y3^-1, Y1 * Y2 * Y1^-1 * Y3^-1 * Y2, (R * Y2 * Y3^-1)^2, (Y2 * Y3^-1)^3, Y3^6 ] Map:: non-degenerate R = (1, 49, 2, 50, 8, 56, 32, 80, 20, 68, 5, 53)(3, 51, 13, 61, 27, 75, 21, 69, 41, 89, 15, 63)(4, 52, 16, 64, 25, 73, 9, 57, 14, 62, 19, 67)(6, 54, 24, 72, 7, 55, 28, 76, 46, 94, 26, 74)(10, 58, 18, 66, 38, 86, 33, 81, 35, 83, 36, 84)(11, 59, 37, 85, 12, 60, 17, 65, 44, 92, 29, 77)(22, 70, 31, 79, 23, 71, 34, 82, 42, 90, 30, 78)(39, 87, 40, 88, 48, 96, 47, 95, 43, 91, 45, 93)(97, 145, 99, 147, 102, 150)(98, 146, 105, 153, 107, 155)(100, 148, 113, 161, 116, 164)(101, 149, 106, 154, 118, 166)(103, 151, 125, 173, 126, 174)(104, 152, 129, 177, 130, 178)(108, 156, 119, 167, 122, 170)(109, 157, 112, 160, 131, 179)(110, 158, 114, 162, 137, 185)(111, 159, 135, 183, 138, 186)(115, 163, 139, 187, 120, 168)(117, 165, 124, 172, 128, 176)(121, 169, 136, 184, 142, 190)(123, 171, 143, 191, 127, 175)(132, 180, 141, 189, 133, 181)(134, 182, 144, 192, 140, 188) L = (1, 100)(2, 106)(3, 110)(4, 114)(5, 117)(6, 121)(7, 97)(8, 99)(9, 131)(10, 109)(11, 134)(12, 98)(13, 135)(14, 136)(15, 124)(16, 139)(17, 132)(18, 141)(19, 107)(20, 129)(21, 112)(22, 111)(23, 101)(24, 108)(25, 113)(26, 128)(27, 102)(28, 115)(29, 116)(30, 104)(31, 103)(32, 105)(33, 137)(34, 123)(35, 144)(36, 130)(37, 126)(38, 118)(39, 120)(40, 133)(41, 143)(42, 122)(43, 140)(44, 119)(45, 127)(46, 125)(47, 142)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 6, 8, 6, 8, 6, 8 ), ( 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E23.400 Graph:: bipartite v = 24 e = 96 f = 28 degree seq :: [ 6^16, 12^8 ] E23.403 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 3, 4, 6}) Quotient :: dipole Aut^+ = C2 x SL(2,3) (small group id <48, 32>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3, R * Y2 * R * Y3^-1, (R * Y1)^2, Y1^4, Y1^-1 * Y2 * Y1^-2 * Y3 * Y1^-1, Y2 * Y1^-1 * Y2 * Y1^-1 * Y3^-1 * Y1^-1, Y1 * Y3 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1, (Y3 * Y2^-1)^3, Y2^6, Y3 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y3^-1 * Y1^-1, Y2^2 * Y1^-2 * Y2^-2 * Y1^-2, Y1 * Y3^3 * Y1^-1 * Y2^-3, Y2^2 * Y1 * Y2 * Y3^-1 * Y1 * Y2^-1 * Y1 ] Map:: non-degenerate R = (1, 49, 2, 50, 6, 54, 5, 53)(3, 51, 9, 57, 17, 65, 11, 59)(4, 52, 12, 60, 18, 66, 14, 62)(7, 55, 19, 67, 15, 63, 21, 69)(8, 56, 22, 70, 16, 64, 24, 72)(10, 58, 26, 74, 36, 84, 28, 76)(13, 61, 31, 79, 37, 85, 32, 80)(20, 68, 39, 87, 34, 82, 41, 89)(23, 71, 44, 92, 35, 83, 45, 93)(25, 73, 42, 90, 29, 77, 38, 86)(27, 75, 40, 88, 48, 96, 47, 95)(30, 78, 46, 94, 33, 81, 43, 91)(97, 145, 99, 147, 106, 154, 123, 171, 109, 157, 100, 148)(98, 146, 103, 151, 116, 164, 136, 184, 119, 167, 104, 152)(101, 149, 111, 159, 130, 178, 143, 191, 131, 179, 112, 160)(102, 150, 113, 161, 132, 180, 144, 192, 133, 181, 114, 162)(105, 153, 120, 168, 142, 190, 127, 175, 137, 185, 121, 169)(107, 155, 118, 166, 139, 187, 128, 176, 135, 183, 125, 173)(108, 156, 126, 174, 140, 188, 122, 170, 134, 182, 115, 163)(110, 158, 129, 177, 141, 189, 124, 172, 138, 186, 117, 165) L = (1, 100)(2, 104)(3, 97)(4, 109)(5, 112)(6, 114)(7, 98)(8, 119)(9, 121)(10, 99)(11, 125)(12, 115)(13, 123)(14, 117)(15, 101)(16, 131)(17, 102)(18, 133)(19, 134)(20, 103)(21, 138)(22, 107)(23, 136)(24, 105)(25, 137)(26, 140)(27, 106)(28, 141)(29, 135)(30, 108)(31, 142)(32, 139)(33, 110)(34, 111)(35, 143)(36, 113)(37, 144)(38, 122)(39, 128)(40, 116)(41, 127)(42, 124)(43, 118)(44, 126)(45, 129)(46, 120)(47, 130)(48, 132)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 6^8 ), ( 6^12 ) } Outer automorphisms :: reflexible Dual of E23.398 Graph:: bipartite v = 20 e = 96 f = 32 degree seq :: [ 8^12, 12^8 ] E23.404 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C2 x SL(2,3) (small group id <48, 32>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^3, Y2^4, (R * Y1)^2, Y3^-1 * Y1 * Y3 * Y1, (R * Y3)^2, Y2 * Y1 * Y2^-1 * Y1, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y2^-1)^3, (Y2^-1 * R * Y2^-1)^2, Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 8, 56)(5, 53, 9, 57)(6, 54, 10, 58)(11, 59, 20, 68)(12, 60, 21, 69)(13, 61, 22, 70)(14, 62, 23, 71)(15, 63, 24, 72)(16, 64, 25, 73)(17, 65, 26, 74)(18, 66, 27, 75)(19, 67, 28, 76)(29, 77, 39, 87)(30, 78, 40, 88)(31, 79, 41, 89)(32, 80, 42, 90)(33, 81, 43, 91)(34, 82, 44, 92)(35, 83, 45, 93)(36, 84, 46, 94)(37, 85, 47, 95)(38, 86, 48, 96)(97, 145, 99, 147, 107, 155, 101, 149)(98, 146, 103, 151, 116, 164, 105, 153)(100, 148, 110, 158, 125, 173, 111, 159)(102, 150, 114, 162, 126, 174, 115, 163)(104, 152, 119, 167, 135, 183, 120, 168)(106, 154, 123, 171, 136, 184, 124, 172)(108, 156, 127, 175, 112, 160, 128, 176)(109, 157, 129, 177, 113, 161, 130, 178)(117, 165, 137, 185, 121, 169, 138, 186)(118, 166, 139, 187, 122, 170, 140, 188)(131, 179, 133, 181, 132, 180, 134, 182)(141, 189, 143, 191, 142, 190, 144, 192) L = (1, 100)(2, 104)(3, 108)(4, 102)(5, 112)(6, 97)(7, 117)(8, 106)(9, 121)(10, 98)(11, 125)(12, 109)(13, 99)(14, 129)(15, 130)(16, 113)(17, 101)(18, 133)(19, 134)(20, 135)(21, 118)(22, 103)(23, 139)(24, 140)(25, 122)(26, 105)(27, 143)(28, 144)(29, 126)(30, 107)(31, 115)(32, 114)(33, 131)(34, 132)(35, 110)(36, 111)(37, 128)(38, 127)(39, 136)(40, 116)(41, 124)(42, 123)(43, 141)(44, 142)(45, 119)(46, 120)(47, 138)(48, 137)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 12^4 ), ( 12^8 ) } Outer automorphisms :: reflexible Dual of E23.434 Graph:: simple bipartite v = 36 e = 96 f = 16 degree seq :: [ 4^24, 8^12 ] E23.405 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C2 x SL(2,3) (small group id <48, 32>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1 * Y3 * Y1, Y2^4, (R * Y1)^2, Y1 * Y2^-1 * Y1 * Y2, (R * Y3)^2, Y1 * Y2^2 * Y3^-3, Y1 * Y3 * Y2^-2 * Y3^2, Y2 * Y3^3 * Y1 * Y2, (R * Y2 * Y3^-1)^2, (Y2^-1 * R * Y2^-1)^2, Y2 * Y3^-1 * Y2^-1 * Y1 * Y3^-1 * Y2 * Y3^-1, Y2 * Y3^-2 * Y2^-1 * Y3 * Y2 * Y3 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 8, 56)(5, 53, 9, 57)(6, 54, 10, 58)(11, 59, 22, 70)(12, 60, 23, 71)(13, 61, 24, 72)(14, 62, 25, 73)(15, 63, 26, 74)(16, 64, 27, 75)(17, 65, 28, 76)(18, 66, 29, 77)(19, 67, 30, 78)(20, 68, 31, 79)(21, 69, 32, 80)(33, 81, 44, 92)(34, 82, 42, 90)(35, 83, 37, 85)(36, 84, 39, 87)(38, 86, 45, 93)(40, 88, 46, 94)(41, 89, 47, 95)(43, 91, 48, 96)(97, 145, 99, 147, 107, 155, 101, 149)(98, 146, 103, 151, 118, 166, 105, 153)(100, 148, 110, 158, 128, 176, 112, 160)(102, 150, 115, 163, 122, 170, 116, 164)(104, 152, 121, 169, 117, 165, 123, 171)(106, 154, 126, 174, 111, 159, 127, 175)(108, 156, 129, 177, 113, 161, 130, 178)(109, 157, 131, 179, 114, 162, 132, 180)(119, 167, 140, 188, 124, 172, 138, 186)(120, 168, 133, 181, 125, 173, 135, 183)(134, 182, 139, 187, 136, 184, 137, 185)(141, 189, 144, 192, 142, 190, 143, 191) L = (1, 100)(2, 104)(3, 108)(4, 111)(5, 113)(6, 97)(7, 119)(8, 122)(9, 124)(10, 98)(11, 128)(12, 125)(13, 99)(14, 133)(15, 118)(16, 135)(17, 120)(18, 101)(19, 137)(20, 139)(21, 102)(22, 117)(23, 114)(24, 103)(25, 131)(26, 107)(27, 132)(28, 109)(29, 105)(30, 143)(31, 144)(32, 106)(33, 127)(34, 126)(35, 136)(36, 134)(37, 142)(38, 110)(39, 141)(40, 112)(41, 129)(42, 115)(43, 130)(44, 116)(45, 121)(46, 123)(47, 140)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 12^4 ), ( 12^8 ) } Outer automorphisms :: reflexible Dual of E23.436 Graph:: simple bipartite v = 36 e = 96 f = 16 degree seq :: [ 4^24, 8^12 ] E23.406 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C2 x SL(2,3) (small group id <48, 32>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^3, Y1 * Y3 * Y1 * Y3^-1, Y2 * Y1 * Y2^-1 * Y1, Y2^4, (R * Y3)^2, (R * Y1)^2, Y3^-1 * Y2^-2 * Y3 * Y2^-2, (Y2^-1 * R * Y2^-1)^2, (R * Y2 * Y3^-1)^2, Y2 * Y3^-1 * Y2^-1 * Y3^-1 * Y2 * Y1 * Y3^-1, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2 * Y1 * Y3 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 8, 56)(5, 53, 9, 57)(6, 54, 10, 58)(11, 59, 20, 68)(12, 60, 21, 69)(13, 61, 22, 70)(14, 62, 23, 71)(15, 63, 24, 72)(16, 64, 25, 73)(17, 65, 26, 74)(18, 66, 27, 75)(19, 67, 28, 76)(29, 77, 43, 91)(30, 78, 44, 92)(31, 79, 42, 90)(32, 80, 40, 88)(33, 81, 35, 83)(34, 82, 37, 85)(36, 84, 45, 93)(38, 86, 46, 94)(39, 87, 47, 95)(41, 89, 48, 96)(97, 145, 99, 147, 107, 155, 101, 149)(98, 146, 103, 151, 116, 164, 105, 153)(100, 148, 110, 158, 125, 173, 111, 159)(102, 150, 114, 162, 126, 174, 115, 163)(104, 152, 119, 167, 139, 187, 120, 168)(106, 154, 123, 171, 140, 188, 124, 172)(108, 156, 127, 175, 112, 160, 128, 176)(109, 157, 129, 177, 113, 161, 130, 178)(117, 165, 138, 186, 121, 169, 136, 184)(118, 166, 131, 179, 122, 170, 133, 181)(132, 180, 143, 191, 134, 182, 144, 192)(135, 183, 142, 190, 137, 185, 141, 189) L = (1, 100)(2, 104)(3, 108)(4, 102)(5, 112)(6, 97)(7, 117)(8, 106)(9, 121)(10, 98)(11, 125)(12, 109)(13, 99)(14, 131)(15, 133)(16, 113)(17, 101)(18, 135)(19, 137)(20, 139)(21, 118)(22, 103)(23, 129)(24, 130)(25, 122)(26, 105)(27, 143)(28, 144)(29, 126)(30, 107)(31, 124)(32, 123)(33, 141)(34, 142)(35, 132)(36, 110)(37, 134)(38, 111)(39, 136)(40, 114)(41, 138)(42, 115)(43, 140)(44, 116)(45, 119)(46, 120)(47, 128)(48, 127)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 12^4 ), ( 12^8 ) } Outer automorphisms :: reflexible Dual of E23.435 Graph:: simple bipartite v = 36 e = 96 f = 16 degree seq :: [ 4^24, 8^12 ] E23.407 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C2 x SL(2,3) (small group id <48, 32>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^3, Y2 * Y1 * Y2, Y3^-1 * Y1 * Y3 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2 * Y3^-1 * Y2^-1 * Y3 * Y2^-1 * Y3^-1 * Y2^-1 * Y3, (Y3 * Y2^-1)^6 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 5, 53)(4, 52, 7, 55)(6, 54, 8, 56)(9, 57, 13, 61)(10, 58, 14, 62)(11, 59, 12, 60)(15, 63, 16, 64)(17, 65, 18, 66)(19, 67, 20, 68)(21, 69, 23, 71)(22, 70, 24, 72)(25, 73, 27, 75)(26, 74, 28, 76)(29, 77, 31, 79)(30, 78, 32, 80)(33, 81, 35, 83)(34, 82, 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, 99, 147, 98, 146, 101, 149)(100, 148, 107, 155, 103, 151, 108, 156)(102, 150, 111, 159, 104, 152, 112, 160)(105, 153, 113, 161, 109, 157, 114, 162)(106, 154, 115, 163, 110, 158, 116, 164)(117, 165, 133, 181, 119, 167, 134, 182)(118, 166, 128, 176, 120, 168, 126, 174)(121, 169, 131, 179, 123, 171, 129, 177)(122, 170, 135, 183, 124, 172, 136, 184)(125, 173, 137, 185, 127, 175, 138, 186)(130, 178, 139, 187, 132, 180, 140, 188)(141, 189, 143, 191, 142, 190, 144, 192) L = (1, 100)(2, 103)(3, 105)(4, 102)(5, 109)(6, 97)(7, 104)(8, 98)(9, 106)(10, 99)(11, 117)(12, 119)(13, 110)(14, 101)(15, 121)(16, 123)(17, 125)(18, 127)(19, 129)(20, 131)(21, 118)(22, 107)(23, 120)(24, 108)(25, 122)(26, 111)(27, 124)(28, 112)(29, 126)(30, 113)(31, 128)(32, 114)(33, 130)(34, 115)(35, 132)(36, 116)(37, 141)(38, 142)(39, 134)(40, 133)(41, 143)(42, 144)(43, 138)(44, 137)(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) :: { ( 12^4 ), ( 12^8 ) } Outer automorphisms :: reflexible Dual of E23.437 Graph:: bipartite v = 36 e = 96 f = 16 degree seq :: [ 4^24, 8^12 ] E23.408 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C2 x SL(2,3) (small group id <48, 32>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-1, Y1^4, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, (R * Y1)^2, Y1^4, (R * Y2 * Y3^-1)^2, Y2 * Y1^-2 * Y2^-1 * Y1^-2, Y2^6, Y1 * Y2^-2 * Y1^-1 * Y2 * Y1^-1 * Y2, Y1 * Y2^-1 * R * Y2^-2 * R * Y2^-1, (Y3 * Y2^-1)^6 ] Map:: non-degenerate R = (1, 49, 2, 50, 6, 54, 4, 52)(3, 51, 9, 57, 17, 65, 11, 59)(5, 53, 14, 62, 18, 66, 15, 63)(7, 55, 19, 67, 12, 60, 21, 69)(8, 56, 22, 70, 13, 61, 23, 71)(10, 58, 27, 75, 40, 88, 29, 77)(16, 64, 38, 86, 41, 89, 39, 87)(20, 68, 25, 73, 32, 80, 30, 78)(24, 72, 37, 85, 33, 81, 35, 83)(26, 74, 34, 82, 31, 79, 36, 84)(28, 76, 42, 90, 48, 96, 45, 93)(43, 91, 44, 92, 47, 95, 46, 94)(97, 145, 99, 147, 106, 154, 124, 172, 112, 160, 101, 149)(98, 146, 103, 151, 116, 164, 138, 186, 120, 168, 104, 152)(100, 148, 108, 156, 128, 176, 141, 189, 129, 177, 109, 157)(102, 150, 113, 161, 136, 184, 144, 192, 137, 185, 114, 162)(105, 153, 121, 169, 139, 187, 134, 182, 118, 166, 122, 170)(107, 155, 126, 174, 143, 191, 135, 183, 119, 167, 127, 175)(110, 158, 130, 178, 117, 165, 123, 171, 140, 188, 131, 179)(111, 159, 132, 180, 115, 163, 125, 173, 142, 190, 133, 181) L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 110)(6, 100)(7, 115)(8, 118)(9, 113)(10, 123)(11, 99)(12, 117)(13, 119)(14, 114)(15, 101)(16, 134)(17, 107)(18, 111)(19, 108)(20, 121)(21, 103)(22, 109)(23, 104)(24, 133)(25, 128)(26, 130)(27, 136)(28, 138)(29, 106)(30, 116)(31, 132)(32, 126)(33, 131)(34, 127)(35, 120)(36, 122)(37, 129)(38, 137)(39, 112)(40, 125)(41, 135)(42, 144)(43, 140)(44, 143)(45, 124)(46, 139)(47, 142)(48, 141)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 12, 4, 12, 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E23.431 Graph:: bipartite v = 20 e = 96 f = 32 degree seq :: [ 8^12, 12^8 ] E23.409 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C2 x SL(2,3) (small group id <48, 32>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ R^2, Y3^2 * Y1^-2, (R * Y1)^2, Y3^4, Y1^2 * Y3^2, (R * Y3)^2, (Y3^-1, Y1^-1), Y2^2 * Y1^-1 * Y3 * Y2, (R * Y2 * Y3^-1)^2, Y2 * Y3^-2 * Y2^-1 * Y1^-2, Y1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1 * Y2^-1, Y2 * Y3 * Y2 * Y3^-1 * Y2 * Y1^-1, Y1^-1 * Y2 * Y3^-1 * Y2 * Y3 * Y2 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 29, 77, 16, 64)(4, 52, 10, 58, 7, 55, 12, 60)(6, 54, 22, 70, 30, 78, 24, 72)(9, 57, 31, 79, 20, 68, 33, 81)(11, 59, 37, 85, 21, 69, 39, 87)(14, 62, 23, 71, 36, 84, 26, 74)(15, 63, 35, 83, 17, 65, 25, 73)(18, 66, 32, 80, 27, 75, 34, 82)(19, 67, 38, 86, 28, 76, 40, 88)(41, 89, 46, 94, 43, 91, 48, 96)(42, 90, 45, 93, 44, 92, 47, 95)(97, 145, 99, 147, 110, 158, 108, 156, 121, 169, 102, 150)(98, 146, 105, 153, 115, 163, 100, 148, 114, 162, 107, 155)(101, 149, 116, 164, 124, 172, 103, 151, 123, 171, 117, 165)(104, 152, 125, 173, 132, 180, 106, 154, 131, 179, 126, 174)(109, 157, 133, 181, 138, 186, 111, 159, 134, 182, 137, 185)(112, 160, 135, 183, 140, 188, 113, 161, 136, 184, 139, 187)(118, 166, 141, 189, 130, 178, 119, 167, 142, 190, 129, 177)(120, 168, 143, 191, 128, 176, 122, 170, 144, 192, 127, 175) L = (1, 100)(2, 106)(3, 111)(4, 104)(5, 108)(6, 119)(7, 97)(8, 103)(9, 128)(10, 101)(11, 134)(12, 98)(13, 131)(14, 118)(15, 125)(16, 121)(17, 99)(18, 127)(19, 133)(20, 130)(21, 136)(22, 132)(23, 126)(24, 110)(25, 109)(26, 102)(27, 129)(28, 135)(29, 113)(30, 122)(31, 123)(32, 116)(33, 114)(34, 105)(35, 112)(36, 120)(37, 124)(38, 117)(39, 115)(40, 107)(41, 141)(42, 142)(43, 143)(44, 144)(45, 139)(46, 140)(47, 137)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 12, 4, 12, 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E23.422 Graph:: bipartite v = 20 e = 96 f = 32 degree seq :: [ 8^12, 12^8 ] E23.410 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C2 x SL(2,3) (small group id <48, 32>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ R^2, Y3^2 * Y1^-2, (R * Y1)^2, Y3^4, Y3^2 * Y1^2, (Y3^-1, Y1^-1), (R * Y3)^2, Y2 * Y3^-1 * Y1^-1 * Y2^2, Y2^-1 * Y3^-2 * Y2 * Y3^-2, Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y1^-1, (R * Y2 * Y3^-1)^2, R * Y2 * Y1 * Y2 * R * Y2^-1, Y2 * Y3 * Y1^-1 * Y2^-1 * Y3 * Y1^-1, R * Y2^-2 * R * Y2^-1 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 29, 77, 16, 64)(4, 52, 10, 58, 7, 55, 12, 60)(6, 54, 22, 70, 30, 78, 24, 72)(9, 57, 31, 79, 20, 68, 33, 81)(11, 59, 35, 83, 21, 69, 37, 85)(14, 62, 26, 74, 40, 88, 23, 71)(15, 63, 25, 73, 17, 65, 39, 87)(18, 66, 32, 80, 27, 75, 34, 82)(19, 67, 36, 84, 28, 76, 38, 86)(41, 89, 46, 94, 43, 91, 48, 96)(42, 90, 45, 93, 44, 92, 47, 95)(97, 145, 99, 147, 110, 158, 106, 154, 121, 169, 102, 150)(98, 146, 105, 153, 124, 172, 103, 151, 123, 171, 107, 155)(100, 148, 114, 162, 117, 165, 101, 149, 116, 164, 115, 163)(104, 152, 125, 173, 136, 184, 108, 156, 135, 183, 126, 174)(109, 157, 133, 181, 140, 188, 113, 161, 132, 180, 137, 185)(111, 159, 134, 182, 139, 187, 112, 160, 131, 179, 138, 186)(118, 166, 141, 189, 130, 178, 122, 170, 144, 192, 127, 175)(119, 167, 142, 190, 129, 177, 120, 168, 143, 191, 128, 176) L = (1, 100)(2, 106)(3, 111)(4, 104)(5, 108)(6, 119)(7, 97)(8, 103)(9, 128)(10, 101)(11, 132)(12, 98)(13, 121)(14, 120)(15, 125)(16, 135)(17, 99)(18, 127)(19, 131)(20, 130)(21, 134)(22, 110)(23, 126)(24, 136)(25, 112)(26, 102)(27, 129)(28, 133)(29, 113)(30, 122)(31, 123)(32, 116)(33, 114)(34, 105)(35, 124)(36, 117)(37, 115)(38, 107)(39, 109)(40, 118)(41, 141)(42, 142)(43, 143)(44, 144)(45, 139)(46, 140)(47, 137)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 12, 4, 12, 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E23.425 Graph:: bipartite v = 20 e = 96 f = 32 degree seq :: [ 8^12, 12^8 ] E23.411 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C2 x SL(2,3) (small group id <48, 32>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^-1, (R * Y3)^2, (R * Y1)^2, Y3^-1 * Y1^-3, Y2 * Y3^-1 * Y1^-1 * Y2^-1 * Y1^-2, (R * Y2 * Y3^-1)^2, Y2^6, Y1 * Y2 * R * Y2^2 * R * Y2, Y1 * Y2^-2 * Y1 * Y2 * Y1^-1 * Y2, Y1 * Y2^2 * Y1 * Y2^-1 * Y1 * Y2^-1, (Y3 * Y2^-1)^6 ] Map:: non-degenerate R = (1, 49, 2, 50, 6, 54, 4, 52)(3, 51, 9, 57, 17, 65, 11, 59)(5, 53, 14, 62, 18, 66, 15, 63)(7, 55, 19, 67, 12, 60, 21, 69)(8, 56, 22, 70, 13, 61, 23, 71)(10, 58, 27, 75, 40, 88, 29, 77)(16, 64, 38, 86, 41, 89, 39, 87)(20, 68, 30, 78, 32, 80, 25, 73)(24, 72, 35, 83, 33, 81, 37, 85)(26, 74, 36, 84, 31, 79, 34, 82)(28, 76, 42, 90, 48, 96, 45, 93)(43, 91, 46, 94, 47, 95, 44, 92)(97, 145, 99, 147, 106, 154, 124, 172, 112, 160, 101, 149)(98, 146, 103, 151, 116, 164, 138, 186, 120, 168, 104, 152)(100, 148, 108, 156, 128, 176, 141, 189, 129, 177, 109, 157)(102, 150, 113, 161, 136, 184, 144, 192, 137, 185, 114, 162)(105, 153, 121, 169, 139, 187, 134, 182, 119, 167, 122, 170)(107, 155, 126, 174, 143, 191, 135, 183, 118, 166, 127, 175)(110, 158, 130, 178, 115, 163, 123, 171, 140, 188, 131, 179)(111, 159, 132, 180, 117, 165, 125, 173, 142, 190, 133, 181) L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 110)(6, 100)(7, 115)(8, 118)(9, 113)(10, 123)(11, 99)(12, 117)(13, 119)(14, 114)(15, 101)(16, 134)(17, 107)(18, 111)(19, 108)(20, 126)(21, 103)(22, 109)(23, 104)(24, 131)(25, 116)(26, 132)(27, 136)(28, 138)(29, 106)(30, 128)(31, 130)(32, 121)(33, 133)(34, 122)(35, 129)(36, 127)(37, 120)(38, 137)(39, 112)(40, 125)(41, 135)(42, 144)(43, 142)(44, 139)(45, 124)(46, 143)(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, 12, 4, 12, 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E23.430 Graph:: bipartite v = 20 e = 96 f = 32 degree seq :: [ 8^12, 12^8 ] E23.412 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C2 x SL(2,3) (small group id <48, 32>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ R^2, Y3^-2 * Y1^2, Y3^2 * Y1^2, (Y3^-1, Y1^-1), (R * Y3)^2, (R * Y1)^2, Y1^4, Y3 * Y2^3 * Y1^-1, (R * Y2 * Y3^-1)^2, Y3^-2 * Y2 * Y3^-2 * Y2^-1, Y1 * Y3^-1 * Y2^-1 * Y1 * Y3^-1 * Y2, Y2 * Y3 * Y2 * Y3 * Y2 * Y1^-1, Y1 * Y3 * Y2 * Y3 * Y1 * Y2^-1, R * Y2 * Y1 * Y2 * R * Y2^-1, Y2^2 * R * Y2^-2 * R * Y2^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 29, 77, 16, 64)(4, 52, 10, 58, 7, 55, 12, 60)(6, 54, 22, 70, 30, 78, 24, 72)(9, 57, 31, 79, 20, 68, 33, 81)(11, 59, 37, 85, 21, 69, 39, 87)(14, 62, 23, 71, 36, 84, 26, 74)(15, 63, 35, 83, 17, 65, 25, 73)(18, 66, 32, 80, 27, 75, 34, 82)(19, 67, 38, 86, 28, 76, 40, 88)(41, 89, 48, 96, 43, 91, 46, 94)(42, 90, 47, 95, 44, 92, 45, 93)(97, 145, 99, 147, 110, 158, 108, 156, 121, 169, 102, 150)(98, 146, 105, 153, 115, 163, 100, 148, 114, 162, 107, 155)(101, 149, 116, 164, 124, 172, 103, 151, 123, 171, 117, 165)(104, 152, 125, 173, 132, 180, 106, 154, 131, 179, 126, 174)(109, 157, 135, 183, 138, 186, 111, 159, 136, 184, 137, 185)(112, 160, 133, 181, 140, 188, 113, 161, 134, 182, 139, 187)(118, 166, 141, 189, 128, 176, 119, 167, 142, 190, 127, 175)(120, 168, 143, 191, 130, 178, 122, 170, 144, 192, 129, 177) L = (1, 100)(2, 106)(3, 111)(4, 104)(5, 108)(6, 119)(7, 97)(8, 103)(9, 128)(10, 101)(11, 134)(12, 98)(13, 131)(14, 118)(15, 125)(16, 121)(17, 99)(18, 127)(19, 133)(20, 130)(21, 136)(22, 132)(23, 126)(24, 110)(25, 109)(26, 102)(27, 129)(28, 135)(29, 113)(30, 122)(31, 123)(32, 116)(33, 114)(34, 105)(35, 112)(36, 120)(37, 124)(38, 117)(39, 115)(40, 107)(41, 143)(42, 144)(43, 141)(44, 142)(45, 137)(46, 138)(47, 139)(48, 140)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 12, 4, 12, 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E23.424 Graph:: bipartite v = 20 e = 96 f = 32 degree seq :: [ 8^12, 12^8 ] E23.413 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C2 x SL(2,3) (small group id <48, 32>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ R^2, Y3^2 * Y1^2, Y3^4, (R * Y3)^2, (R * Y1)^2, Y1^4, (Y3^-1, Y1^-1), Y2^2 * Y1 * Y3 * Y2, Y2 * Y1^-1 * Y2 * Y1 * Y2 * Y1^-1, Y3^-1 * Y2 * Y1^2 * Y2^-1 * Y3^-1, Y3 * Y2^-1 * Y3 * Y2^-1 * Y1^-1 * Y2^-1, Y2 * Y3 * Y1^-1 * Y2^-1 * Y3 * Y1^-1, (R * Y2 * Y3^-1)^2 ] Map:: non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 29, 77, 16, 64)(4, 52, 10, 58, 7, 55, 12, 60)(6, 54, 22, 70, 30, 78, 24, 72)(9, 57, 31, 79, 20, 68, 33, 81)(11, 59, 35, 83, 21, 69, 37, 85)(14, 62, 26, 74, 40, 88, 23, 71)(15, 63, 25, 73, 17, 65, 39, 87)(18, 66, 32, 80, 27, 75, 34, 82)(19, 67, 36, 84, 28, 76, 38, 86)(41, 89, 48, 96, 43, 91, 46, 94)(42, 90, 47, 95, 44, 92, 45, 93)(97, 145, 99, 147, 110, 158, 106, 154, 121, 169, 102, 150)(98, 146, 105, 153, 124, 172, 103, 151, 123, 171, 107, 155)(100, 148, 114, 162, 117, 165, 101, 149, 116, 164, 115, 163)(104, 152, 125, 173, 136, 184, 108, 156, 135, 183, 126, 174)(109, 157, 131, 179, 140, 188, 113, 161, 134, 182, 137, 185)(111, 159, 132, 180, 139, 187, 112, 160, 133, 181, 138, 186)(118, 166, 141, 189, 128, 176, 122, 170, 144, 192, 129, 177)(119, 167, 142, 190, 127, 175, 120, 168, 143, 191, 130, 178) L = (1, 100)(2, 106)(3, 111)(4, 104)(5, 108)(6, 119)(7, 97)(8, 103)(9, 128)(10, 101)(11, 132)(12, 98)(13, 121)(14, 120)(15, 125)(16, 135)(17, 99)(18, 127)(19, 131)(20, 130)(21, 134)(22, 110)(23, 126)(24, 136)(25, 112)(26, 102)(27, 129)(28, 133)(29, 113)(30, 122)(31, 123)(32, 116)(33, 114)(34, 105)(35, 124)(36, 117)(37, 115)(38, 107)(39, 109)(40, 118)(41, 143)(42, 144)(43, 141)(44, 142)(45, 137)(46, 138)(47, 139)(48, 140)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 12, 4, 12, 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E23.421 Graph:: bipartite v = 20 e = 96 f = 32 degree seq :: [ 8^12, 12^8 ] E23.414 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C2 x SL(2,3) (small group id <48, 32>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ R^2, Y3^2 * Y1^2, Y3^-2 * Y1^2, (R * Y1)^2, (Y3^-1, Y1^-1), Y1^4, (R * Y3)^2, Y2^2 * Y1^-1 * Y3 * Y2, Y1^2 * Y2^-1 * Y1^2 * Y2, (R * Y2 * Y3^-1)^2, Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2^-1, Y2 * Y3 * Y2 * Y1^-1 * Y2 * Y1^-1, Y2 * Y3 * R * Y2^-2 * R * Y1^-1, (Y3 * Y2^-1)^6 ] Map:: non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 29, 77, 16, 64)(4, 52, 10, 58, 7, 55, 12, 60)(6, 54, 22, 70, 30, 78, 24, 72)(9, 57, 31, 79, 20, 68, 33, 81)(11, 59, 37, 85, 21, 69, 39, 87)(14, 62, 23, 71, 36, 84, 26, 74)(15, 63, 35, 83, 17, 65, 25, 73)(18, 66, 32, 80, 27, 75, 34, 82)(19, 67, 38, 86, 28, 76, 40, 88)(41, 89, 45, 93, 43, 91, 47, 95)(42, 90, 46, 94, 44, 92, 48, 96)(97, 145, 99, 147, 110, 158, 108, 156, 121, 169, 102, 150)(98, 146, 105, 153, 115, 163, 100, 148, 114, 162, 107, 155)(101, 149, 116, 164, 124, 172, 103, 151, 123, 171, 117, 165)(104, 152, 125, 173, 132, 180, 106, 154, 131, 179, 126, 174)(109, 157, 134, 182, 138, 186, 111, 159, 133, 181, 137, 185)(112, 160, 136, 184, 140, 188, 113, 161, 135, 183, 139, 187)(118, 166, 141, 189, 129, 177, 119, 167, 142, 190, 130, 178)(120, 168, 143, 191, 127, 175, 122, 170, 144, 192, 128, 176) L = (1, 100)(2, 106)(3, 111)(4, 104)(5, 108)(6, 119)(7, 97)(8, 103)(9, 128)(10, 101)(11, 134)(12, 98)(13, 131)(14, 118)(15, 125)(16, 121)(17, 99)(18, 127)(19, 133)(20, 130)(21, 136)(22, 132)(23, 126)(24, 110)(25, 109)(26, 102)(27, 129)(28, 135)(29, 113)(30, 122)(31, 123)(32, 116)(33, 114)(34, 105)(35, 112)(36, 120)(37, 124)(38, 117)(39, 115)(40, 107)(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) :: { ( 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 E23.427 Graph:: bipartite v = 20 e = 96 f = 32 degree seq :: [ 8^12, 12^8 ] E23.415 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C2 x SL(2,3) (small group id <48, 32>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ R^2, Y1^2 * Y3^2, (Y1^-1, Y3), (R * Y1)^2, (R * Y3)^2, Y1^2 * Y3^-2, Y1^4, Y3^4, Y1^-1 * Y2^-3 * Y3^-1, Y1 * Y2 * Y1 * Y3^-1 * Y2^-1 * Y3^-1, Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y3^-1, (R * Y2 * Y3^-1)^2, Y1 * Y2^-1 * Y3^2 * Y2 * Y1, Y2^-1 * Y1^-1 * R * Y2^2 * R * Y3^-1, (Y3 * Y2^-1)^6 ] Map:: non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 29, 77, 16, 64)(4, 52, 10, 58, 7, 55, 12, 60)(6, 54, 22, 70, 30, 78, 24, 72)(9, 57, 31, 79, 20, 68, 33, 81)(11, 59, 35, 83, 21, 69, 37, 85)(14, 62, 26, 74, 40, 88, 23, 71)(15, 63, 25, 73, 17, 65, 39, 87)(18, 66, 32, 80, 27, 75, 34, 82)(19, 67, 36, 84, 28, 76, 38, 86)(41, 89, 47, 95, 43, 91, 45, 93)(42, 90, 48, 96, 44, 92, 46, 94)(97, 145, 99, 147, 110, 158, 106, 154, 121, 169, 102, 150)(98, 146, 105, 153, 124, 172, 103, 151, 123, 171, 107, 155)(100, 148, 114, 162, 117, 165, 101, 149, 116, 164, 115, 163)(104, 152, 125, 173, 136, 184, 108, 156, 135, 183, 126, 174)(109, 157, 132, 180, 140, 188, 113, 161, 133, 181, 137, 185)(111, 159, 131, 179, 139, 187, 112, 160, 134, 182, 138, 186)(118, 166, 141, 189, 127, 175, 122, 170, 144, 192, 130, 178)(119, 167, 142, 190, 128, 176, 120, 168, 143, 191, 129, 177) L = (1, 100)(2, 106)(3, 111)(4, 104)(5, 108)(6, 119)(7, 97)(8, 103)(9, 128)(10, 101)(11, 132)(12, 98)(13, 121)(14, 120)(15, 125)(16, 135)(17, 99)(18, 127)(19, 131)(20, 130)(21, 134)(22, 110)(23, 126)(24, 136)(25, 112)(26, 102)(27, 129)(28, 133)(29, 113)(30, 122)(31, 123)(32, 116)(33, 114)(34, 105)(35, 124)(36, 117)(37, 115)(38, 107)(39, 109)(40, 118)(41, 144)(42, 143)(43, 142)(44, 141)(45, 138)(46, 137)(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) :: { ( 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 E23.428 Graph:: bipartite v = 20 e = 96 f = 32 degree seq :: [ 8^12, 12^8 ] E23.416 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C2 x SL(2,3) (small group id <48, 32>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-1, Y1^-1 * Y3^-1 * Y1^-2, Y1^4, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, (Y2^-1 * Y1^-1)^3, Y1^-2 * Y2 * Y1^-2 * Y2^-1, (R * Y2 * Y3^-1)^2, Y2^6, R * Y2^2 * Y1 * Y2^-1 * R * Y2^-2, Y2^-3 * Y1 * Y2^-3 * Y1^-1, Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2 * Y1 * Y2^-1 * Y1^-1, (Y3 * Y2^-1)^6 ] Map:: non-degenerate R = (1, 49, 2, 50, 6, 54, 4, 52)(3, 51, 9, 57, 17, 65, 11, 59)(5, 53, 14, 62, 18, 66, 15, 63)(7, 55, 19, 67, 12, 60, 21, 69)(8, 56, 22, 70, 13, 61, 23, 71)(10, 58, 26, 74, 36, 84, 28, 76)(16, 64, 34, 82, 37, 85, 35, 83)(20, 68, 39, 87, 30, 78, 41, 89)(24, 72, 45, 93, 31, 79, 46, 94)(25, 73, 42, 90, 29, 77, 38, 86)(27, 75, 40, 88, 48, 96, 47, 95)(32, 80, 44, 92, 33, 81, 43, 91)(97, 145, 99, 147, 106, 154, 123, 171, 112, 160, 101, 149)(98, 146, 103, 151, 116, 164, 136, 184, 120, 168, 104, 152)(100, 148, 108, 156, 126, 174, 143, 191, 127, 175, 109, 157)(102, 150, 113, 161, 132, 180, 144, 192, 133, 181, 114, 162)(105, 153, 118, 166, 139, 187, 130, 178, 135, 183, 121, 169)(107, 155, 119, 167, 140, 188, 131, 179, 137, 185, 125, 173)(110, 158, 128, 176, 142, 190, 122, 170, 138, 186, 117, 165)(111, 159, 129, 177, 141, 189, 124, 172, 134, 182, 115, 163) L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 110)(6, 100)(7, 115)(8, 118)(9, 113)(10, 122)(11, 99)(12, 117)(13, 119)(14, 114)(15, 101)(16, 130)(17, 107)(18, 111)(19, 108)(20, 135)(21, 103)(22, 109)(23, 104)(24, 141)(25, 138)(26, 132)(27, 136)(28, 106)(29, 134)(30, 137)(31, 142)(32, 140)(33, 139)(34, 133)(35, 112)(36, 124)(37, 131)(38, 121)(39, 126)(40, 144)(41, 116)(42, 125)(43, 128)(44, 129)(45, 127)(46, 120)(47, 123)(48, 143)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 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 E23.433 Graph:: bipartite v = 20 e = 96 f = 32 degree seq :: [ 8^12, 12^8 ] E23.417 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C2 x SL(2,3) (small group id <48, 32>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ R^2, Y3^2 * Y1^2, Y1^4, Y1^2 * Y3^-2, (R * Y3)^2, (Y3, Y1), Y3^4, (R * Y1)^2, Y2^2 * Y1^2 * Y2, Y1^-1 * Y2 * Y3 * Y2 * Y1^-1 * Y2, Y3^-1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1, (R * Y2 * Y3^-1)^2, Y3 * Y1 * Y2 * Y1^-1 * Y3^-1 * Y2^-1, Y1 * Y2^-1 * Y1^-1 * Y2^-1 * Y3 * Y2^-1, Y3 * Y2 * Y1 * Y3^-1 * Y2^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 25, 73, 16, 64)(4, 52, 10, 58, 7, 55, 12, 60)(6, 54, 22, 70, 14, 62, 24, 72)(9, 57, 29, 77, 20, 68, 31, 79)(11, 59, 35, 83, 21, 69, 37, 85)(15, 63, 33, 81, 17, 65, 39, 87)(18, 66, 30, 78, 27, 75, 32, 80)(19, 67, 36, 84, 28, 76, 38, 86)(23, 71, 34, 82, 26, 74, 40, 88)(41, 89, 48, 96, 43, 91, 46, 94)(42, 90, 47, 95, 44, 92, 45, 93)(97, 145, 99, 147, 110, 158, 104, 152, 121, 169, 102, 150)(98, 146, 105, 153, 117, 165, 101, 149, 116, 164, 107, 155)(100, 148, 114, 162, 124, 172, 103, 151, 123, 171, 115, 163)(106, 154, 129, 177, 136, 184, 108, 156, 135, 183, 130, 178)(109, 157, 132, 180, 139, 187, 112, 160, 134, 182, 137, 185)(111, 159, 131, 179, 140, 188, 113, 161, 133, 181, 138, 186)(118, 166, 141, 189, 126, 174, 120, 168, 143, 191, 128, 176)(119, 167, 142, 190, 125, 173, 122, 170, 144, 192, 127, 175) L = (1, 100)(2, 106)(3, 111)(4, 104)(5, 108)(6, 119)(7, 97)(8, 103)(9, 126)(10, 101)(11, 132)(12, 98)(13, 129)(14, 122)(15, 121)(16, 135)(17, 99)(18, 125)(19, 131)(20, 128)(21, 134)(22, 130)(23, 110)(24, 136)(25, 113)(26, 102)(27, 127)(28, 133)(29, 123)(30, 116)(31, 114)(32, 105)(33, 112)(34, 120)(35, 124)(36, 117)(37, 115)(38, 107)(39, 109)(40, 118)(41, 143)(42, 144)(43, 141)(44, 142)(45, 137)(46, 138)(47, 139)(48, 140)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 12, 4, 12, 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E23.423 Graph:: bipartite v = 20 e = 96 f = 32 degree seq :: [ 8^12, 12^8 ] E23.418 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C2 x SL(2,3) (small group id <48, 32>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ R^2, Y3^2 * Y1^2, (Y3^-1, Y1^-1), (R * Y1)^2, Y3^2 * Y1^-2, Y1^4, Y3^4, (R * Y3)^2, Y1^-1 * Y2^3 * Y1^-1, Y3 * Y2^-1 * Y3^-1 * Y1^-1 * Y2 * Y1, (R * Y2 * Y3^-1)^2, Y1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3 * Y2^-1, Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y1^-1, Y2 * Y3 * Y1^-1 * Y2^-1 * Y3 * Y1^-1, Y3^-1 * Y2^-1 * Y3 * Y1 * Y2 * Y1^-1, (Y2^-1 * Y1^-1)^3, Y2^-1 * Y1^-1 * R * Y2^2 * R * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 25, 73, 16, 64)(4, 52, 10, 58, 7, 55, 12, 60)(6, 54, 22, 70, 14, 62, 24, 72)(9, 57, 29, 77, 20, 68, 31, 79)(11, 59, 35, 83, 21, 69, 37, 85)(15, 63, 33, 81, 17, 65, 39, 87)(18, 66, 30, 78, 27, 75, 32, 80)(19, 67, 36, 84, 28, 76, 38, 86)(23, 71, 34, 82, 26, 74, 40, 88)(41, 89, 47, 95, 43, 91, 45, 93)(42, 90, 48, 96, 44, 92, 46, 94)(97, 145, 99, 147, 110, 158, 104, 152, 121, 169, 102, 150)(98, 146, 105, 153, 117, 165, 101, 149, 116, 164, 107, 155)(100, 148, 114, 162, 124, 172, 103, 151, 123, 171, 115, 163)(106, 154, 129, 177, 136, 184, 108, 156, 135, 183, 130, 178)(109, 157, 131, 179, 139, 187, 112, 160, 133, 181, 137, 185)(111, 159, 132, 180, 140, 188, 113, 161, 134, 182, 138, 186)(118, 166, 141, 189, 125, 173, 120, 168, 143, 191, 127, 175)(119, 167, 142, 190, 126, 174, 122, 170, 144, 192, 128, 176) L = (1, 100)(2, 106)(3, 111)(4, 104)(5, 108)(6, 119)(7, 97)(8, 103)(9, 126)(10, 101)(11, 132)(12, 98)(13, 129)(14, 122)(15, 121)(16, 135)(17, 99)(18, 125)(19, 131)(20, 128)(21, 134)(22, 130)(23, 110)(24, 136)(25, 113)(26, 102)(27, 127)(28, 133)(29, 123)(30, 116)(31, 114)(32, 105)(33, 112)(34, 120)(35, 124)(36, 117)(37, 115)(38, 107)(39, 109)(40, 118)(41, 144)(42, 143)(43, 142)(44, 141)(45, 138)(46, 137)(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) :: { ( 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 E23.426 Graph:: bipartite v = 20 e = 96 f = 32 degree seq :: [ 8^12, 12^8 ] E23.419 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C2 x SL(2,3) (small group id <48, 32>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ R^2, Y3^-2 * Y1^2, (Y3^-1, Y1), Y1^4, Y3^2 * Y1^2, (R * Y1)^2, (R * Y3)^2, Y2^2 * Y3^2 * Y2, Y1^2 * Y2 * Y1^2 * Y2^-1, Y2^-1 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1, (R * Y2 * Y3^-1)^2, (Y2 * Y1^-1)^3, Y1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1, R * Y2 * Y1 * Y2 * R * Y2^-1, Y1 * Y2 * Y3^-1 * Y1 * Y2^-1 * Y3^-1, Y2^2 * R * Y2^-2 * R * Y2^-1 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 25, 73, 16, 64)(4, 52, 10, 58, 7, 55, 12, 60)(6, 54, 22, 70, 14, 62, 24, 72)(9, 57, 29, 77, 20, 68, 31, 79)(11, 59, 35, 83, 21, 69, 37, 85)(15, 63, 33, 81, 17, 65, 39, 87)(18, 66, 30, 78, 27, 75, 32, 80)(19, 67, 36, 84, 28, 76, 38, 86)(23, 71, 34, 82, 26, 74, 40, 88)(41, 89, 45, 93, 43, 91, 47, 95)(42, 90, 46, 94, 44, 92, 48, 96)(97, 145, 99, 147, 110, 158, 104, 152, 121, 169, 102, 150)(98, 146, 105, 153, 117, 165, 101, 149, 116, 164, 107, 155)(100, 148, 114, 162, 124, 172, 103, 151, 123, 171, 115, 163)(106, 154, 129, 177, 136, 184, 108, 156, 135, 183, 130, 178)(109, 157, 133, 181, 139, 187, 112, 160, 131, 179, 137, 185)(111, 159, 134, 182, 140, 188, 113, 161, 132, 180, 138, 186)(118, 166, 141, 189, 127, 175, 120, 168, 143, 191, 125, 173)(119, 167, 142, 190, 128, 176, 122, 170, 144, 192, 126, 174) L = (1, 100)(2, 106)(3, 111)(4, 104)(5, 108)(6, 119)(7, 97)(8, 103)(9, 126)(10, 101)(11, 132)(12, 98)(13, 129)(14, 122)(15, 121)(16, 135)(17, 99)(18, 125)(19, 131)(20, 128)(21, 134)(22, 130)(23, 110)(24, 136)(25, 113)(26, 102)(27, 127)(28, 133)(29, 123)(30, 116)(31, 114)(32, 105)(33, 112)(34, 120)(35, 124)(36, 117)(37, 115)(38, 107)(39, 109)(40, 118)(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) :: { ( 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 E23.429 Graph:: bipartite v = 20 e = 96 f = 32 degree seq :: [ 8^12, 12^8 ] E23.420 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C2 x SL(2,3) (small group id <48, 32>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-1, Y1^4, (Y3^-1 * Y1^-1)^2, (R * Y3)^2, (R * Y1)^2, Y1 * Y2^-3 * Y1, Y1^-1 * Y2^3 * Y1^-1, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2 * Y3 * Y1 * Y2^-1 * Y1^-1, Y2^-1 * Y1 * Y2 * Y3^-1 * Y2^-1 * Y1^-1 * Y2 * Y1^-1, Y2 * R * Y2 * Y1 * Y2^-1 * R * Y2^-1 * Y1^-1, Y2 * Y1 * Y2^2 * Y1 * Y2^-1 * Y1 * Y3 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, (Y3 * Y2^-1)^6 ] Map:: non-degenerate 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, 37, 85, 23, 71, 38, 86)(22, 70, 32, 80, 24, 72, 30, 78)(25, 73, 35, 83, 27, 75, 33, 81)(26, 74, 39, 87, 28, 76, 40, 88)(29, 77, 41, 89, 31, 79, 42, 90)(34, 82, 43, 91, 36, 84, 44, 92)(45, 93, 47, 95, 46, 94, 48, 96)(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, 98)(2, 102)(3, 105)(4, 97)(5, 110)(6, 100)(7, 113)(8, 115)(9, 112)(10, 111)(11, 99)(12, 114)(13, 116)(14, 106)(15, 101)(16, 107)(17, 108)(18, 103)(19, 109)(20, 104)(21, 133)(22, 128)(23, 134)(24, 126)(25, 131)(26, 135)(27, 129)(28, 136)(29, 137)(30, 118)(31, 138)(32, 120)(33, 121)(34, 139)(35, 123)(36, 140)(37, 119)(38, 117)(39, 124)(40, 122)(41, 127)(42, 125)(43, 132)(44, 130)(45, 143)(46, 144)(47, 142)(48, 141)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 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 E23.432 Graph:: bipartite v = 20 e = 96 f = 32 degree seq :: [ 8^12, 12^8 ] E23.421 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C2 x SL(2,3) (small group id <48, 32>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y1^-1 * Y2 * Y1 * Y2, Y1^-3 * Y2, Y3^4, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3^-1 * Y2 * Y3 * Y2, Y3^-2 * Y1^-1 * Y3^-2 * Y1, Y2 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3^-1, Y1^-2 * Y3 * Y1 * Y3 * Y1 * Y3 ] Map:: non-degenerate R = (1, 49, 2, 50, 7, 55, 3, 51, 8, 56, 5, 53)(4, 52, 13, 61, 31, 79, 11, 59, 29, 77, 15, 63)(6, 54, 18, 66, 33, 81, 12, 60, 32, 80, 19, 67)(9, 57, 24, 72, 47, 95, 22, 70, 37, 85, 26, 74)(10, 58, 27, 75, 48, 96, 23, 71, 38, 86, 28, 76)(14, 62, 25, 73, 44, 92, 30, 78, 46, 94, 36, 84)(16, 64, 39, 87, 35, 83, 20, 68, 43, 91, 40, 88)(17, 65, 41, 89, 34, 82, 21, 69, 45, 93, 42, 90)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 107, 155)(101, 149, 103, 151)(102, 150, 108, 156)(105, 153, 118, 166)(106, 154, 119, 167)(109, 157, 125, 173)(110, 158, 126, 174)(111, 159, 127, 175)(112, 160, 116, 164)(113, 161, 117, 165)(114, 162, 128, 176)(115, 163, 129, 177)(120, 168, 133, 181)(121, 169, 142, 190)(122, 170, 143, 191)(123, 171, 134, 182)(124, 172, 144, 192)(130, 178, 138, 186)(131, 179, 136, 184)(132, 180, 140, 188)(135, 183, 139, 187)(137, 185, 141, 189) L = (1, 100)(2, 105)(3, 107)(4, 110)(5, 112)(6, 97)(7, 116)(8, 118)(9, 121)(10, 98)(11, 126)(12, 99)(13, 130)(14, 102)(15, 133)(16, 132)(17, 101)(18, 131)(19, 134)(20, 140)(21, 103)(22, 142)(23, 104)(24, 129)(25, 106)(26, 135)(27, 127)(28, 137)(29, 138)(30, 108)(31, 120)(32, 136)(33, 123)(34, 114)(35, 109)(36, 113)(37, 115)(38, 111)(39, 124)(40, 125)(41, 122)(42, 128)(43, 144)(44, 117)(45, 143)(46, 119)(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) :: { ( 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E23.413 Graph:: bipartite v = 32 e = 96 f = 20 degree seq :: [ 4^24, 12^8 ] E23.422 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C2 x SL(2,3) (small group id <48, 32>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^4, Y1^-2 * Y2 * Y1^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3^-1 * Y2 * Y3 * Y2, Y3^-2 * Y1^-1 * Y3^-2 * Y1, Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3 * Y2 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50, 7, 55, 3, 51, 8, 56, 5, 53)(4, 52, 13, 61, 31, 79, 11, 59, 29, 77, 15, 63)(6, 54, 18, 66, 33, 81, 12, 60, 32, 80, 19, 67)(9, 57, 24, 72, 47, 95, 22, 70, 38, 86, 26, 74)(10, 58, 27, 75, 48, 96, 23, 71, 37, 85, 28, 76)(14, 62, 25, 73, 44, 92, 30, 78, 46, 94, 36, 84)(16, 64, 39, 87, 34, 82, 20, 68, 43, 91, 40, 88)(17, 65, 41, 89, 35, 83, 21, 69, 45, 93, 42, 90)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 107, 155)(101, 149, 103, 151)(102, 150, 108, 156)(105, 153, 118, 166)(106, 154, 119, 167)(109, 157, 125, 173)(110, 158, 126, 174)(111, 159, 127, 175)(112, 160, 116, 164)(113, 161, 117, 165)(114, 162, 128, 176)(115, 163, 129, 177)(120, 168, 134, 182)(121, 169, 142, 190)(122, 170, 143, 191)(123, 171, 133, 181)(124, 172, 144, 192)(130, 178, 136, 184)(131, 179, 138, 186)(132, 180, 140, 188)(135, 183, 139, 187)(137, 185, 141, 189) L = (1, 100)(2, 105)(3, 107)(4, 110)(5, 112)(6, 97)(7, 116)(8, 118)(9, 121)(10, 98)(11, 126)(12, 99)(13, 130)(14, 102)(15, 133)(16, 132)(17, 101)(18, 131)(19, 134)(20, 140)(21, 103)(22, 142)(23, 104)(24, 127)(25, 106)(26, 137)(27, 129)(28, 135)(29, 136)(30, 108)(31, 123)(32, 138)(33, 120)(34, 114)(35, 109)(36, 113)(37, 115)(38, 111)(39, 122)(40, 128)(41, 124)(42, 125)(43, 143)(44, 117)(45, 144)(46, 119)(47, 141)(48, 139)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E23.409 Graph:: bipartite v = 32 e = 96 f = 20 degree seq :: [ 4^24, 12^8 ] E23.423 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C2 x SL(2,3) (small group id <48, 32>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ R^2, Y2^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y3^4, Y3^-1 * Y2 * Y3 * Y2, Y2 * Y1 * Y2 * Y1^-1, Y3^-1 * Y1^-3 * Y3^-1, Y3 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 49, 2, 50, 7, 55, 15, 63, 18, 66, 5, 53)(3, 51, 8, 56, 22, 70, 30, 78, 33, 81, 12, 60)(4, 52, 14, 62, 21, 69, 6, 54, 20, 68, 16, 64)(9, 57, 25, 73, 28, 76, 10, 58, 27, 75, 26, 74)(11, 59, 29, 77, 36, 84, 13, 61, 35, 83, 31, 79)(17, 65, 39, 87, 38, 86, 19, 67, 40, 88, 37, 85)(23, 71, 41, 89, 44, 92, 24, 72, 43, 91, 42, 90)(32, 80, 47, 95, 46, 94, 34, 82, 48, 96, 45, 93)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 107, 155)(101, 149, 108, 156)(102, 150, 109, 157)(103, 151, 118, 166)(105, 153, 119, 167)(106, 154, 120, 168)(110, 158, 125, 173)(111, 159, 126, 174)(112, 160, 127, 175)(113, 161, 128, 176)(114, 162, 129, 177)(115, 163, 130, 178)(116, 164, 131, 179)(117, 165, 132, 180)(121, 169, 137, 185)(122, 170, 138, 186)(123, 171, 139, 187)(124, 172, 140, 188)(133, 181, 141, 189)(134, 182, 142, 190)(135, 183, 143, 191)(136, 184, 144, 192) L = (1, 100)(2, 105)(3, 107)(4, 111)(5, 113)(6, 97)(7, 115)(8, 119)(9, 114)(10, 98)(11, 126)(12, 128)(13, 99)(14, 133)(15, 102)(16, 123)(17, 103)(18, 106)(19, 101)(20, 134)(21, 121)(22, 130)(23, 129)(24, 104)(25, 112)(26, 135)(27, 117)(28, 136)(29, 141)(30, 109)(31, 139)(32, 118)(33, 120)(34, 108)(35, 142)(36, 137)(37, 116)(38, 110)(39, 124)(40, 122)(41, 127)(42, 143)(43, 132)(44, 144)(45, 131)(46, 125)(47, 140)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E23.417 Graph:: simple bipartite v = 32 e = 96 f = 20 degree seq :: [ 4^24, 12^8 ] E23.424 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C2 x SL(2,3) (small group id <48, 32>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^4, (R * Y3)^2, Y2 * Y3 * Y2 * Y3^-1, (R * Y1)^2, Y1^-1 * Y2 * Y1 * Y2, (R * Y2)^2, Y1^-2 * Y2 * Y3^-2 * Y1^-1, Y2 * Y3^-2 * Y1^3, Y2 * Y1^-2 * Y3^-2 * Y1^-1, Y2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3, Y2 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 ] Map:: non-degenerate R = (1, 49, 2, 50, 7, 55, 22, 70, 18, 66, 5, 53)(3, 51, 8, 56, 23, 71, 15, 63, 29, 77, 12, 60)(4, 52, 14, 62, 36, 84, 13, 61, 35, 83, 16, 64)(6, 54, 20, 68, 34, 82, 11, 59, 33, 81, 21, 69)(9, 57, 28, 76, 48, 96, 27, 75, 39, 87, 30, 78)(10, 58, 31, 79, 47, 95, 26, 74, 40, 88, 32, 80)(17, 65, 41, 89, 38, 86, 24, 72, 45, 93, 42, 90)(19, 67, 43, 91, 37, 85, 25, 73, 46, 94, 44, 92)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 107, 155)(101, 149, 108, 156)(102, 150, 109, 157)(103, 151, 119, 167)(105, 153, 122, 170)(106, 154, 123, 171)(110, 158, 129, 177)(111, 159, 118, 166)(112, 160, 130, 178)(113, 161, 121, 169)(114, 162, 125, 173)(115, 163, 120, 168)(116, 164, 131, 179)(117, 165, 132, 180)(124, 172, 136, 184)(126, 174, 143, 191)(127, 175, 135, 183)(128, 176, 144, 192)(133, 181, 138, 186)(134, 182, 140, 188)(137, 185, 142, 190)(139, 187, 141, 189) L = (1, 100)(2, 105)(3, 107)(4, 111)(5, 113)(6, 97)(7, 120)(8, 122)(9, 125)(10, 98)(11, 118)(12, 121)(13, 99)(14, 133)(15, 102)(16, 135)(17, 119)(18, 123)(19, 101)(20, 134)(21, 136)(22, 109)(23, 115)(24, 108)(25, 103)(26, 114)(27, 104)(28, 130)(29, 106)(30, 137)(31, 132)(32, 139)(33, 138)(34, 127)(35, 140)(36, 124)(37, 116)(38, 110)(39, 117)(40, 112)(41, 128)(42, 131)(43, 126)(44, 129)(45, 143)(46, 144)(47, 142)(48, 141)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E23.412 Graph:: simple bipartite v = 32 e = 96 f = 20 degree seq :: [ 4^24, 12^8 ] E23.425 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C2 x SL(2,3) (small group id <48, 32>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^4, Y1 * Y2 * Y1^-1 * Y2, Y2 * Y3 * Y2 * Y3^-1, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y1^-1 * Y2 * Y3^2 * Y1^-2, Y2 * Y3^2 * Y1^3, Y3^-2 * Y1^-2 * Y2 * Y1^-1, Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y2 * Y3^-1, Y1 * Y3 * Y2 * Y1 * Y3^-1 * Y1 * Y3^-1, (Y3^-1 * Y1^-1)^6 ] Map:: non-degenerate R = (1, 49, 2, 50, 7, 55, 22, 70, 18, 66, 5, 53)(3, 51, 8, 56, 23, 71, 15, 63, 29, 77, 12, 60)(4, 52, 14, 62, 36, 84, 13, 61, 35, 83, 16, 64)(6, 54, 20, 68, 34, 82, 11, 59, 33, 81, 21, 69)(9, 57, 28, 76, 48, 96, 27, 75, 40, 88, 30, 78)(10, 58, 31, 79, 47, 95, 26, 74, 39, 87, 32, 80)(17, 65, 41, 89, 37, 85, 24, 72, 45, 93, 42, 90)(19, 67, 43, 91, 38, 86, 25, 73, 46, 94, 44, 92)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 107, 155)(101, 149, 108, 156)(102, 150, 109, 157)(103, 151, 119, 167)(105, 153, 122, 170)(106, 154, 123, 171)(110, 158, 129, 177)(111, 159, 118, 166)(112, 160, 130, 178)(113, 161, 121, 169)(114, 162, 125, 173)(115, 163, 120, 168)(116, 164, 131, 179)(117, 165, 132, 180)(124, 172, 135, 183)(126, 174, 143, 191)(127, 175, 136, 184)(128, 176, 144, 192)(133, 181, 140, 188)(134, 182, 138, 186)(137, 185, 142, 190)(139, 187, 141, 189) L = (1, 100)(2, 105)(3, 107)(4, 111)(5, 113)(6, 97)(7, 120)(8, 122)(9, 125)(10, 98)(11, 118)(12, 121)(13, 99)(14, 133)(15, 102)(16, 135)(17, 119)(18, 123)(19, 101)(20, 134)(21, 136)(22, 109)(23, 115)(24, 108)(25, 103)(26, 114)(27, 104)(28, 132)(29, 106)(30, 139)(31, 130)(32, 137)(33, 140)(34, 124)(35, 138)(36, 127)(37, 116)(38, 110)(39, 117)(40, 112)(41, 126)(42, 129)(43, 128)(44, 131)(45, 144)(46, 143)(47, 141)(48, 142)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E23.410 Graph:: simple bipartite v = 32 e = 96 f = 20 degree seq :: [ 4^24, 12^8 ] E23.426 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C2 x SL(2,3) (small group id <48, 32>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y2 * Y1^-3, (R * Y3)^2, (R * Y1)^2, Y2 * Y1 * Y2 * Y1^-1, Y3^4, (R * Y2)^2, Y3^-1 * Y2 * Y3 * Y2, (Y1 * Y3^-1)^3, Y3 * Y1 * Y3^-1 * Y1 * Y3 * Y1 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50, 7, 55, 3, 51, 8, 56, 5, 53)(4, 52, 13, 61, 31, 79, 11, 59, 29, 77, 15, 63)(6, 54, 18, 66, 33, 81, 12, 60, 32, 80, 19, 67)(9, 57, 24, 72, 46, 94, 22, 70, 44, 92, 26, 74)(10, 58, 27, 75, 48, 96, 23, 71, 47, 95, 28, 76)(14, 62, 25, 73, 40, 88, 30, 78, 45, 93, 36, 84)(16, 64, 37, 85, 41, 89, 20, 68, 39, 87, 34, 82)(17, 65, 38, 86, 43, 91, 21, 69, 42, 90, 35, 83)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 107, 155)(101, 149, 103, 151)(102, 150, 108, 156)(105, 153, 118, 166)(106, 154, 119, 167)(109, 157, 125, 173)(110, 158, 126, 174)(111, 159, 127, 175)(112, 160, 116, 164)(113, 161, 117, 165)(114, 162, 128, 176)(115, 163, 129, 177)(120, 168, 140, 188)(121, 169, 141, 189)(122, 170, 142, 190)(123, 171, 143, 191)(124, 172, 144, 192)(130, 178, 137, 185)(131, 179, 139, 187)(132, 180, 136, 184)(133, 181, 135, 183)(134, 182, 138, 186) L = (1, 100)(2, 105)(3, 107)(4, 110)(5, 112)(6, 97)(7, 116)(8, 118)(9, 121)(10, 98)(11, 126)(12, 99)(13, 130)(14, 102)(15, 123)(16, 132)(17, 101)(18, 131)(19, 120)(20, 136)(21, 103)(22, 141)(23, 104)(24, 111)(25, 106)(26, 138)(27, 115)(28, 135)(29, 137)(30, 108)(31, 143)(32, 139)(33, 140)(34, 114)(35, 109)(36, 113)(37, 142)(38, 144)(39, 122)(40, 117)(41, 128)(42, 124)(43, 125)(44, 127)(45, 119)(46, 134)(47, 129)(48, 133)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E23.418 Graph:: bipartite v = 32 e = 96 f = 20 degree seq :: [ 4^24, 12^8 ] E23.427 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C2 x SL(2,3) (small group id <48, 32>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ R^2, Y2^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y2 * Y1 * Y2 * Y1^-1, Y3 * Y2 * Y3^-1 * Y2, Y3^4, Y3^-1 * Y1^3 * Y3^-1, Y3 * Y1 * Y2 * Y3 * Y1 * Y3^-1 * Y1, Y2 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1, Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1 * Y3^-1 * Y1^-1, (Y1 * Y2 * Y3^-1)^3 ] Map:: non-degenerate R = (1, 49, 2, 50, 7, 55, 15, 63, 18, 66, 5, 53)(3, 51, 8, 56, 22, 70, 30, 78, 33, 81, 12, 60)(4, 52, 14, 62, 21, 69, 6, 54, 20, 68, 16, 64)(9, 57, 25, 73, 28, 76, 10, 58, 27, 75, 26, 74)(11, 59, 29, 77, 36, 84, 13, 61, 35, 83, 31, 79)(17, 65, 41, 89, 44, 92, 19, 67, 43, 91, 42, 90)(23, 71, 40, 88, 46, 94, 24, 72, 39, 87, 45, 93)(32, 80, 47, 95, 38, 86, 34, 82, 48, 96, 37, 85)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 107, 155)(101, 149, 108, 156)(102, 150, 109, 157)(103, 151, 118, 166)(105, 153, 119, 167)(106, 154, 120, 168)(110, 158, 125, 173)(111, 159, 126, 174)(112, 160, 127, 175)(113, 161, 128, 176)(114, 162, 129, 177)(115, 163, 130, 178)(116, 164, 131, 179)(117, 165, 132, 180)(121, 169, 136, 184)(122, 170, 141, 189)(123, 171, 135, 183)(124, 172, 142, 190)(133, 181, 138, 186)(134, 182, 140, 188)(137, 185, 143, 191)(139, 187, 144, 192) L = (1, 100)(2, 105)(3, 107)(4, 111)(5, 113)(6, 97)(7, 115)(8, 119)(9, 114)(10, 98)(11, 126)(12, 128)(13, 99)(14, 133)(15, 102)(16, 135)(17, 103)(18, 106)(19, 101)(20, 134)(21, 136)(22, 130)(23, 129)(24, 104)(25, 127)(26, 143)(27, 132)(28, 144)(29, 138)(30, 109)(31, 123)(32, 118)(33, 120)(34, 108)(35, 140)(36, 121)(37, 116)(38, 110)(39, 117)(40, 112)(41, 142)(42, 131)(43, 141)(44, 125)(45, 137)(46, 139)(47, 124)(48, 122)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E23.414 Graph:: simple bipartite v = 32 e = 96 f = 20 degree seq :: [ 4^24, 12^8 ] E23.428 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C2 x SL(2,3) (small group id <48, 32>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ R^2, Y2^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y2 * Y1^-1 * Y2 * Y1, Y3^4, Y3^-1 * Y2 * Y3 * Y2, Y3^-1 * Y1^3 * Y3^-1, Y3 * Y1 * Y2 * Y3 * Y1 * Y3 * Y1, Y2 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1, Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 49, 2, 50, 7, 55, 15, 63, 18, 66, 5, 53)(3, 51, 8, 56, 22, 70, 30, 78, 33, 81, 12, 60)(4, 52, 14, 62, 21, 69, 6, 54, 20, 68, 16, 64)(9, 57, 25, 73, 28, 76, 10, 58, 27, 75, 26, 74)(11, 59, 29, 77, 36, 84, 13, 61, 35, 83, 31, 79)(17, 65, 41, 89, 44, 92, 19, 67, 43, 91, 42, 90)(23, 71, 39, 87, 46, 94, 24, 72, 40, 88, 45, 93)(32, 80, 48, 96, 37, 85, 34, 82, 47, 95, 38, 86)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 107, 155)(101, 149, 108, 156)(102, 150, 109, 157)(103, 151, 118, 166)(105, 153, 119, 167)(106, 154, 120, 168)(110, 158, 125, 173)(111, 159, 126, 174)(112, 160, 127, 175)(113, 161, 128, 176)(114, 162, 129, 177)(115, 163, 130, 178)(116, 164, 131, 179)(117, 165, 132, 180)(121, 169, 135, 183)(122, 170, 141, 189)(123, 171, 136, 184)(124, 172, 142, 190)(133, 181, 140, 188)(134, 182, 138, 186)(137, 185, 144, 192)(139, 187, 143, 191) L = (1, 100)(2, 105)(3, 107)(4, 111)(5, 113)(6, 97)(7, 115)(8, 119)(9, 114)(10, 98)(11, 126)(12, 128)(13, 99)(14, 133)(15, 102)(16, 135)(17, 103)(18, 106)(19, 101)(20, 134)(21, 136)(22, 130)(23, 129)(24, 104)(25, 132)(26, 143)(27, 127)(28, 144)(29, 140)(30, 109)(31, 121)(32, 118)(33, 120)(34, 108)(35, 138)(36, 123)(37, 116)(38, 110)(39, 117)(40, 112)(41, 141)(42, 125)(43, 142)(44, 131)(45, 139)(46, 137)(47, 124)(48, 122)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E23.415 Graph:: simple bipartite v = 32 e = 96 f = 20 degree seq :: [ 4^24, 12^8 ] E23.429 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C2 x SL(2,3) (small group id <48, 32>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y2 * Y3 * Y2 * Y3^-1, (R * Y3)^2, (R * Y1)^2, Y3^4, (R * Y2)^2, Y2 * Y1 * Y2 * Y1^-1, Y3 * Y1 * Y3^2 * Y1^-1 * Y3, Y1^-2 * Y3^2 * Y1^-1 * Y2, Y1^6, Y1^-1 * Y2 * Y1^-1 * Y3^-2 * Y1^-1, (Y3 * Y1^-1)^3, Y3^-1 * Y1^-2 * Y3 * Y1 * Y3 * Y1^-2 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50, 7, 55, 22, 70, 18, 66, 5, 53)(3, 51, 8, 56, 23, 71, 15, 63, 29, 77, 12, 60)(4, 52, 14, 62, 36, 84, 13, 61, 35, 83, 16, 64)(6, 54, 20, 68, 34, 82, 11, 59, 33, 81, 21, 69)(9, 57, 28, 76, 48, 96, 27, 75, 47, 95, 30, 78)(10, 58, 31, 79, 46, 94, 26, 74, 45, 93, 32, 80)(17, 65, 39, 87, 42, 90, 24, 72, 41, 89, 37, 85)(19, 67, 40, 88, 44, 92, 25, 73, 43, 91, 38, 86)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 107, 155)(101, 149, 108, 156)(102, 150, 109, 157)(103, 151, 119, 167)(105, 153, 122, 170)(106, 154, 123, 171)(110, 158, 129, 177)(111, 159, 118, 166)(112, 160, 130, 178)(113, 161, 121, 169)(114, 162, 125, 173)(115, 163, 120, 168)(116, 164, 131, 179)(117, 165, 132, 180)(124, 172, 141, 189)(126, 174, 142, 190)(127, 175, 143, 191)(128, 176, 144, 192)(133, 181, 140, 188)(134, 182, 138, 186)(135, 183, 139, 187)(136, 184, 137, 185) L = (1, 100)(2, 105)(3, 107)(4, 111)(5, 113)(6, 97)(7, 120)(8, 122)(9, 125)(10, 98)(11, 118)(12, 121)(13, 99)(14, 133)(15, 102)(16, 127)(17, 119)(18, 123)(19, 101)(20, 134)(21, 124)(22, 109)(23, 115)(24, 108)(25, 103)(26, 114)(27, 104)(28, 112)(29, 106)(30, 139)(31, 117)(32, 137)(33, 140)(34, 143)(35, 138)(36, 141)(37, 116)(38, 110)(39, 144)(40, 142)(41, 126)(42, 129)(43, 128)(44, 131)(45, 130)(46, 135)(47, 132)(48, 136)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E23.419 Graph:: simple bipartite v = 32 e = 96 f = 20 degree seq :: [ 4^24, 12^8 ] E23.430 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C2 x SL(2,3) (small group id <48, 32>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y2 * Y3^-2, Y1 * Y2 * Y1^-1 * Y2, (R * Y2)^2, (Y3 * R)^2, (R * Y1)^2, Y1^6, Y1 * Y3^-1 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1, Y1^2 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3^-1, (Y3^-1 * Y1^-1)^6 ] Map:: non-degenerate R = (1, 49, 2, 50, 7, 55, 19, 67, 15, 63, 5, 53)(3, 51, 8, 56, 20, 68, 42, 90, 27, 75, 11, 59)(4, 52, 12, 60, 28, 76, 43, 91, 32, 80, 13, 61)(6, 54, 17, 65, 40, 88, 44, 92, 41, 89, 18, 66)(9, 57, 23, 71, 47, 95, 36, 84, 31, 79, 24, 72)(10, 58, 25, 73, 48, 96, 37, 85, 33, 81, 26, 74)(14, 62, 34, 82, 30, 78, 21, 69, 45, 93, 35, 83)(16, 64, 38, 86, 29, 77, 22, 70, 46, 94, 39, 87)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 102, 150)(101, 149, 107, 155)(103, 151, 116, 164)(105, 153, 106, 154)(108, 156, 113, 161)(109, 157, 114, 162)(110, 158, 112, 160)(111, 159, 123, 171)(115, 163, 138, 186)(117, 165, 118, 166)(119, 167, 121, 169)(120, 168, 122, 170)(124, 172, 136, 184)(125, 173, 126, 174)(127, 175, 129, 177)(128, 176, 137, 185)(130, 178, 134, 182)(131, 179, 135, 183)(132, 180, 133, 181)(139, 187, 140, 188)(141, 189, 142, 190)(143, 191, 144, 192) L = (1, 100)(2, 105)(3, 102)(4, 99)(5, 110)(6, 97)(7, 117)(8, 106)(9, 104)(10, 98)(11, 112)(12, 125)(13, 127)(14, 107)(15, 132)(16, 101)(17, 126)(18, 129)(19, 139)(20, 118)(21, 116)(22, 103)(23, 136)(24, 130)(25, 124)(26, 134)(27, 133)(28, 119)(29, 113)(30, 108)(31, 114)(32, 135)(33, 109)(34, 122)(35, 128)(36, 123)(37, 111)(38, 120)(39, 137)(40, 121)(41, 131)(42, 140)(43, 138)(44, 115)(45, 144)(46, 143)(47, 141)(48, 142)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E23.411 Graph:: simple bipartite v = 32 e = 96 f = 20 degree seq :: [ 4^24, 12^8 ] E23.431 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C2 x SL(2,3) (small group id <48, 32>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y2 * Y3^-2, Y1 * Y2 * Y1^-1 * Y2, (Y3 * R)^2, (R * Y1)^2, (R * Y2)^2, Y1^6, Y1^2 * Y3 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1, Y1 * Y3 * Y1 * Y3 * Y1^-2 * Y3^-1, (Y1^-2 * Y3^-1)^3 ] Map:: non-degenerate R = (1, 49, 2, 50, 7, 55, 19, 67, 15, 63, 5, 53)(3, 51, 8, 56, 20, 68, 42, 90, 27, 75, 11, 59)(4, 52, 12, 60, 28, 76, 43, 91, 32, 80, 13, 61)(6, 54, 17, 65, 40, 88, 44, 92, 41, 89, 18, 66)(9, 57, 23, 71, 47, 95, 36, 84, 33, 81, 24, 72)(10, 58, 25, 73, 48, 96, 37, 85, 31, 79, 26, 74)(14, 62, 34, 82, 29, 77, 21, 69, 45, 93, 35, 83)(16, 64, 38, 86, 30, 78, 22, 70, 46, 94, 39, 87)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 102, 150)(101, 149, 107, 155)(103, 151, 116, 164)(105, 153, 106, 154)(108, 156, 113, 161)(109, 157, 114, 162)(110, 158, 112, 160)(111, 159, 123, 171)(115, 163, 138, 186)(117, 165, 118, 166)(119, 167, 121, 169)(120, 168, 122, 170)(124, 172, 136, 184)(125, 173, 126, 174)(127, 175, 129, 177)(128, 176, 137, 185)(130, 178, 134, 182)(131, 179, 135, 183)(132, 180, 133, 181)(139, 187, 140, 188)(141, 189, 142, 190)(143, 191, 144, 192) L = (1, 100)(2, 105)(3, 102)(4, 99)(5, 110)(6, 97)(7, 117)(8, 106)(9, 104)(10, 98)(11, 112)(12, 125)(13, 127)(14, 107)(15, 132)(16, 101)(17, 126)(18, 129)(19, 139)(20, 118)(21, 116)(22, 103)(23, 124)(24, 134)(25, 136)(26, 130)(27, 133)(28, 121)(29, 113)(30, 108)(31, 114)(32, 131)(33, 109)(34, 120)(35, 137)(36, 123)(37, 111)(38, 122)(39, 128)(40, 119)(41, 135)(42, 140)(43, 138)(44, 115)(45, 143)(46, 144)(47, 142)(48, 141)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E23.408 Graph:: simple bipartite v = 32 e = 96 f = 20 degree seq :: [ 4^24, 12^8 ] E23.432 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C2 x SL(2,3) (small group id <48, 32>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y2 * Y3^-2, Y1 * Y2 * Y1^-1 * Y2, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y1^-1)^3, Y1^6, Y3 * Y1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1 * Y3^-1 * Y1^-1, Y1^-2 * Y3^-1 * Y1^-3 * Y3 * Y1^-1 ] Map:: non-degenerate R = (1, 49, 2, 50, 7, 55, 19, 67, 15, 63, 5, 53)(3, 51, 8, 56, 20, 68, 38, 86, 27, 75, 11, 59)(4, 52, 12, 60, 28, 76, 39, 87, 31, 79, 13, 61)(6, 54, 17, 65, 36, 84, 40, 88, 37, 85, 18, 66)(9, 57, 23, 71, 45, 93, 33, 81, 46, 94, 24, 72)(10, 58, 25, 73, 47, 95, 34, 82, 48, 96, 26, 74)(14, 62, 32, 80, 42, 90, 21, 69, 41, 89, 29, 77)(16, 64, 35, 83, 44, 92, 22, 70, 43, 91, 30, 78)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 102, 150)(101, 149, 107, 155)(103, 151, 116, 164)(105, 153, 106, 154)(108, 156, 113, 161)(109, 157, 114, 162)(110, 158, 112, 160)(111, 159, 123, 171)(115, 163, 134, 182)(117, 165, 118, 166)(119, 167, 121, 169)(120, 168, 122, 170)(124, 172, 132, 180)(125, 173, 126, 174)(127, 175, 133, 181)(128, 176, 131, 179)(129, 177, 130, 178)(135, 183, 136, 184)(137, 185, 139, 187)(138, 186, 140, 188)(141, 189, 143, 191)(142, 190, 144, 192) L = (1, 100)(2, 105)(3, 102)(4, 99)(5, 110)(6, 97)(7, 117)(8, 106)(9, 104)(10, 98)(11, 112)(12, 125)(13, 121)(14, 107)(15, 129)(16, 101)(17, 126)(18, 119)(19, 135)(20, 118)(21, 116)(22, 103)(23, 109)(24, 139)(25, 114)(26, 137)(27, 130)(28, 144)(29, 113)(30, 108)(31, 138)(32, 141)(33, 123)(34, 111)(35, 143)(36, 142)(37, 140)(38, 136)(39, 134)(40, 115)(41, 120)(42, 133)(43, 122)(44, 127)(45, 131)(46, 124)(47, 128)(48, 132)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E23.420 Graph:: simple bipartite v = 32 e = 96 f = 20 degree seq :: [ 4^24, 12^8 ] E23.433 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C2 x SL(2,3) (small group id <48, 32>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3 * Y2 * Y3, Y1^-3 * Y2, (Y3 * R)^2, (R * Y1)^2, (R * Y2)^2, Y1^-2 * Y3 * Y1 * Y2 * Y1^-1 * Y3^-1 * Y1^-1, Y3 * Y1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1 * Y3^-1 * Y1^-1, (Y3^-1 * Y1^-1)^6 ] Map:: non-degenerate R = (1, 49, 2, 50, 7, 55, 3, 51, 8, 56, 5, 53)(4, 52, 11, 59, 16, 64, 6, 54, 15, 63, 12, 60)(9, 57, 17, 65, 20, 68, 10, 58, 19, 67, 18, 66)(13, 61, 25, 73, 28, 76, 14, 62, 27, 75, 26, 74)(21, 69, 33, 81, 31, 79, 22, 70, 34, 82, 32, 80)(23, 71, 35, 83, 38, 86, 24, 72, 37, 85, 36, 84)(29, 77, 41, 89, 40, 88, 30, 78, 42, 90, 39, 87)(43, 91, 47, 95, 46, 94, 44, 92, 48, 96, 45, 93)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 102, 150)(101, 149, 103, 151)(105, 153, 106, 154)(107, 155, 111, 159)(108, 156, 112, 160)(109, 157, 110, 158)(113, 161, 115, 163)(114, 162, 116, 164)(117, 165, 118, 166)(119, 167, 120, 168)(121, 169, 123, 171)(122, 170, 124, 172)(125, 173, 126, 174)(127, 175, 128, 176)(129, 177, 130, 178)(131, 179, 133, 181)(132, 180, 134, 182)(135, 183, 136, 184)(137, 185, 138, 186)(139, 187, 140, 188)(141, 189, 142, 190)(143, 191, 144, 192) L = (1, 100)(2, 105)(3, 102)(4, 99)(5, 109)(6, 97)(7, 110)(8, 106)(9, 104)(10, 98)(11, 117)(12, 119)(13, 103)(14, 101)(15, 118)(16, 120)(17, 125)(18, 127)(19, 126)(20, 128)(21, 111)(22, 107)(23, 112)(24, 108)(25, 133)(26, 135)(27, 131)(28, 136)(29, 115)(30, 113)(31, 116)(32, 114)(33, 139)(34, 140)(35, 121)(36, 141)(37, 123)(38, 142)(39, 124)(40, 122)(41, 143)(42, 144)(43, 130)(44, 129)(45, 134)(46, 132)(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 ) } Outer automorphisms :: reflexible Dual of E23.416 Graph:: bipartite v = 32 e = 96 f = 20 degree seq :: [ 4^24, 12^8 ] E23.434 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C2 x SL(2,3) (small group id <48, 32>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ R^2, Y3^3, Y2 * Y3 * Y2, (Y2 * R)^2, (R * Y1)^2, (R * Y3)^2, (Y2^-1 * Y3)^2, Y1^2 * Y3^-1 * Y1^-1 * Y3^-1, Y1^-2 * Y2 * Y1 * Y2, Y3 * Y1 * Y3 * Y1^-2, Y1 * Y3 * Y2^-1 * Y1^-1 * Y3 * Y2^-1, Y1 * Y2^-1 * Y1 * Y3^-1 * Y1 * Y2^-1, Y1^6, Y3 * Y1^-1 * Y3^-1 * Y2 * Y1 * Y2^-1 ] Map:: non-degenerate R = (1, 49, 2, 50, 8, 56, 27, 75, 20, 68, 5, 53)(3, 51, 13, 61, 35, 83, 45, 93, 21, 69, 14, 62)(4, 52, 16, 64, 40, 88, 46, 94, 22, 70, 17, 65)(6, 54, 23, 71, 9, 57, 30, 78, 38, 86, 24, 72)(7, 55, 25, 73, 10, 58, 32, 80, 37, 85, 26, 74)(11, 59, 33, 81, 28, 76, 43, 91, 41, 89, 18, 66)(12, 60, 34, 82, 29, 77, 44, 92, 42, 90, 19, 67)(15, 63, 31, 79, 36, 84, 48, 96, 47, 95, 39, 87)(97, 145, 99, 147, 103, 151, 111, 159, 100, 148, 102, 150)(98, 146, 105, 153, 108, 156, 127, 175, 106, 154, 107, 155)(101, 149, 114, 162, 118, 166, 135, 183, 115, 163, 117, 165)(104, 152, 124, 172, 112, 160, 132, 180, 125, 173, 109, 157)(110, 158, 130, 178, 134, 182, 113, 161, 129, 177, 133, 181)(116, 164, 120, 168, 140, 188, 143, 191, 122, 170, 139, 187)(119, 167, 136, 184, 137, 185, 121, 169, 131, 179, 138, 186)(123, 171, 141, 189, 128, 176, 144, 192, 142, 190, 126, 174) L = (1, 100)(2, 106)(3, 102)(4, 103)(5, 115)(6, 111)(7, 97)(8, 125)(9, 107)(10, 108)(11, 127)(12, 98)(13, 132)(14, 129)(15, 99)(16, 104)(17, 130)(18, 117)(19, 118)(20, 122)(21, 135)(22, 101)(23, 131)(24, 139)(25, 136)(26, 140)(27, 142)(28, 109)(29, 112)(30, 144)(31, 105)(32, 123)(33, 134)(34, 133)(35, 137)(36, 124)(37, 113)(38, 110)(39, 114)(40, 138)(41, 119)(42, 121)(43, 143)(44, 116)(45, 126)(46, 128)(47, 120)(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, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E23.404 Graph:: bipartite v = 16 e = 96 f = 36 degree seq :: [ 12^16 ] E23.435 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C2 x SL(2,3) (small group id <48, 32>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ R^2, Y3^3, Y2 * Y3 * Y2, (Y2 * R)^2, (Y2^-1 * Y3)^2, (R * Y1)^2, (R * Y3)^2, Y1^-2 * Y3 * Y1 * Y2, Y1 * Y3 * Y1^-2 * Y2, Y1 * Y2^-1 * Y3 * Y1^-1 * Y3 * Y2^-1, (Y1 * Y2^-1)^3, Y1^6, Y2 * Y1^2 * Y2 * Y1 * Y3^-1 * Y1, (Y3^-1 * Y1^-1)^4 ] Map:: non-degenerate R = (1, 49, 2, 50, 8, 56, 27, 75, 20, 68, 5, 53)(3, 51, 13, 61, 35, 83, 46, 94, 22, 70, 14, 62)(4, 52, 16, 64, 40, 88, 45, 93, 21, 69, 17, 65)(6, 54, 23, 71, 10, 58, 32, 80, 37, 85, 24, 72)(7, 55, 25, 73, 9, 57, 30, 78, 38, 86, 26, 74)(11, 59, 33, 81, 29, 77, 43, 91, 42, 90, 19, 67)(12, 60, 34, 82, 28, 76, 44, 92, 41, 89, 18, 66)(15, 63, 31, 79, 36, 84, 48, 96, 47, 95, 39, 87)(97, 145, 99, 147, 103, 151, 111, 159, 100, 148, 102, 150)(98, 146, 105, 153, 108, 156, 127, 175, 106, 154, 107, 155)(101, 149, 114, 162, 118, 166, 135, 183, 115, 163, 117, 165)(104, 152, 124, 172, 109, 157, 132, 180, 125, 173, 112, 160)(110, 158, 129, 177, 134, 182, 113, 161, 130, 178, 133, 181)(116, 164, 122, 170, 140, 188, 143, 191, 120, 168, 139, 187)(119, 167, 131, 179, 138, 186, 121, 169, 136, 184, 137, 185)(123, 171, 142, 190, 126, 174, 144, 192, 141, 189, 128, 176) L = (1, 100)(2, 106)(3, 102)(4, 103)(5, 115)(6, 111)(7, 97)(8, 125)(9, 107)(10, 108)(11, 127)(12, 98)(13, 104)(14, 130)(15, 99)(16, 132)(17, 129)(18, 117)(19, 118)(20, 120)(21, 135)(22, 101)(23, 136)(24, 140)(25, 131)(26, 139)(27, 141)(28, 112)(29, 109)(30, 123)(31, 105)(32, 144)(33, 133)(34, 134)(35, 137)(36, 124)(37, 113)(38, 110)(39, 114)(40, 138)(41, 121)(42, 119)(43, 143)(44, 116)(45, 126)(46, 128)(47, 122)(48, 142)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E23.406 Graph:: bipartite v = 16 e = 96 f = 36 degree seq :: [ 12^16 ] E23.436 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C2 x SL(2,3) (small group id <48, 32>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ R^2, Y2^-2 * Y3^2, (R * Y2)^2, (Y2, Y3), (R * Y1)^2, (R * Y3)^2, Y1 * Y2 * Y1^-2 * Y2, Y1 * Y3 * Y1 * Y2^-2, Y1^2 * Y3^-1 * Y1^-1 * Y3^-1, Y1 * Y2 * Y1 * Y2^-1 * Y3^-1, Y2^6, Y1^6 ] Map:: non-degenerate R = (1, 49, 2, 50, 8, 56, 31, 79, 22, 70, 5, 53)(3, 51, 13, 61, 39, 87, 28, 76, 23, 71, 16, 64)(4, 52, 18, 66, 47, 95, 27, 75, 24, 72, 19, 67)(6, 54, 25, 73, 9, 57, 15, 63, 43, 91, 26, 74)(7, 55, 29, 77, 10, 58, 14, 62, 41, 89, 30, 78)(11, 59, 37, 85, 32, 80, 35, 83, 45, 93, 20, 68)(12, 60, 38, 86, 33, 81, 34, 82, 44, 92, 21, 69)(17, 65, 36, 84, 40, 88, 42, 90, 48, 96, 46, 94)(97, 145, 99, 147, 110, 158, 138, 186, 123, 171, 102, 150)(98, 146, 105, 153, 130, 178, 144, 192, 126, 174, 107, 155)(100, 148, 111, 159, 127, 175, 124, 172, 103, 151, 113, 161)(101, 149, 116, 164, 114, 162, 136, 184, 129, 177, 119, 167)(104, 152, 128, 176, 120, 168, 142, 190, 117, 165, 109, 157)(106, 154, 131, 179, 118, 166, 122, 170, 108, 156, 132, 180)(112, 160, 140, 188, 139, 187, 143, 191, 133, 181, 125, 173)(115, 163, 141, 189, 137, 185, 135, 183, 134, 182, 121, 169) L = (1, 100)(2, 106)(3, 111)(4, 110)(5, 117)(6, 113)(7, 97)(8, 129)(9, 131)(10, 130)(11, 132)(12, 98)(13, 136)(14, 127)(15, 138)(16, 141)(17, 99)(18, 104)(19, 140)(20, 109)(21, 114)(22, 126)(23, 142)(24, 101)(25, 112)(26, 107)(27, 103)(28, 102)(29, 115)(30, 108)(31, 123)(32, 119)(33, 120)(34, 118)(35, 144)(36, 105)(37, 121)(38, 125)(39, 133)(40, 128)(41, 143)(42, 124)(43, 135)(44, 137)(45, 139)(46, 116)(47, 134)(48, 122)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E23.405 Graph:: bipartite v = 16 e = 96 f = 36 degree seq :: [ 12^16 ] E23.437 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C2 x SL(2,3) (small group id <48, 32>) Aut = C2 x GL(2,3) (small group id <96, 189>) |r| :: 2 Presentation :: [ R^2, Y2^2 * Y3^-2, (R * Y3)^2, (R * Y1)^2, (Y2, Y3), Y1 * Y3 * Y1 * Y2, (R * Y2)^2, Y2^-1 * Y1^-3 * Y3, Y1 * Y2^-2 * Y1 * Y2^-1 * Y3^-1, Y2^6 ] Map:: non-degenerate R = (1, 49, 2, 50, 8, 56, 17, 65, 22, 70, 5, 53)(3, 51, 13, 61, 19, 67, 4, 52, 18, 66, 16, 64)(6, 54, 23, 71, 9, 57, 7, 55, 26, 74, 10, 58)(11, 59, 29, 77, 21, 69, 12, 60, 32, 80, 20, 68)(14, 62, 35, 83, 30, 78, 15, 63, 38, 86, 31, 79)(24, 72, 42, 90, 43, 91, 25, 73, 41, 89, 44, 92)(27, 75, 39, 87, 33, 81, 28, 76, 40, 88, 34, 82)(36, 84, 45, 93, 47, 95, 37, 85, 46, 94, 48, 96)(97, 145, 99, 147, 110, 158, 132, 180, 120, 168, 102, 150)(98, 146, 105, 153, 123, 171, 141, 189, 126, 174, 107, 155)(100, 148, 111, 159, 133, 181, 121, 169, 103, 151, 113, 161)(101, 149, 116, 164, 137, 185, 144, 192, 130, 178, 114, 162)(104, 152, 117, 165, 138, 186, 143, 191, 129, 177, 109, 157)(106, 154, 124, 172, 142, 190, 127, 175, 108, 156, 118, 166)(112, 160, 135, 183, 122, 170, 140, 188, 125, 173, 134, 182)(115, 163, 136, 184, 119, 167, 139, 187, 128, 176, 131, 179) L = (1, 100)(2, 106)(3, 111)(4, 110)(5, 117)(6, 113)(7, 97)(8, 116)(9, 124)(10, 123)(11, 118)(12, 98)(13, 101)(14, 133)(15, 132)(16, 136)(17, 99)(18, 104)(19, 135)(20, 138)(21, 137)(22, 105)(23, 140)(24, 103)(25, 102)(26, 139)(27, 142)(28, 141)(29, 131)(30, 108)(31, 107)(32, 134)(33, 114)(34, 109)(35, 112)(36, 121)(37, 120)(38, 115)(39, 119)(40, 122)(41, 143)(42, 144)(43, 125)(44, 128)(45, 127)(46, 126)(47, 130)(48, 129)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E23.407 Graph:: bipartite v = 16 e = 96 f = 36 degree seq :: [ 12^16 ] E23.438 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = SL(2,3) : C2 (small group id <48, 33>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ R^2, Y3^2 * Y1^-2, (Y3^-1 * Y1)^2, Y3^-2 * Y1^-2, (Y3 * Y1)^2, (R * Y1)^2, (Y2^-1, Y1^-1), Y3^4, (R * Y3)^2, Y2^-1 * Y1 * Y2^-2 * Y1, Y2^2 * Y3^-2 * Y2, (R * Y2 * Y3^-1)^2, (Y2^-1 * Y3^-1)^3 ] Map:: non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 9, 57, 21, 69, 15, 63)(4, 52, 10, 58, 7, 55, 12, 60)(6, 54, 11, 59, 13, 61, 19, 67)(14, 62, 25, 73, 16, 64, 26, 74)(17, 65, 27, 75, 23, 71, 31, 79)(18, 66, 28, 76, 24, 72, 32, 80)(20, 68, 29, 77, 22, 70, 30, 78)(33, 81, 41, 89, 35, 83, 43, 91)(34, 82, 42, 90, 36, 84, 44, 92)(37, 85, 45, 93, 38, 86, 46, 94)(39, 87, 47, 95, 40, 88, 48, 96)(97, 145, 99, 147, 109, 157, 104, 152, 117, 165, 102, 150)(98, 146, 105, 153, 115, 163, 101, 149, 111, 159, 107, 155)(100, 148, 113, 161, 120, 168, 103, 151, 119, 167, 114, 162)(106, 154, 123, 171, 128, 176, 108, 156, 127, 175, 124, 172)(110, 158, 129, 177, 132, 180, 112, 160, 131, 179, 130, 178)(116, 164, 135, 183, 133, 181, 118, 166, 136, 184, 134, 182)(121, 169, 137, 185, 140, 188, 122, 170, 139, 187, 138, 186)(125, 173, 143, 191, 141, 189, 126, 174, 144, 192, 142, 190) L = (1, 100)(2, 106)(3, 110)(4, 104)(5, 108)(6, 116)(7, 97)(8, 103)(9, 121)(10, 101)(11, 125)(12, 98)(13, 118)(14, 117)(15, 122)(16, 99)(17, 133)(18, 129)(19, 126)(20, 109)(21, 112)(22, 102)(23, 134)(24, 131)(25, 111)(26, 105)(27, 141)(28, 137)(29, 115)(30, 107)(31, 142)(32, 139)(33, 120)(34, 136)(35, 114)(36, 135)(37, 119)(38, 113)(39, 130)(40, 132)(41, 128)(42, 144)(43, 124)(44, 143)(45, 127)(46, 123)(47, 138)(48, 140)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 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 E23.439 Graph:: bipartite v = 20 e = 96 f = 32 degree seq :: [ 8^12, 12^8 ] E23.439 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = SL(2,3) : C2 (small group id <48, 33>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y2 * Y3^-1 * Y2 * Y3, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3^4, Y3^-2 * Y1^-3, Y1 * Y3^-1 * Y2 * Y1^-1 * Y3 * Y2, Y1 * Y2 * Y1 * Y3 * Y1 * Y2, (Y1^-1 * Y3)^3 ] Map:: non-degenerate R = (1, 49, 2, 50, 7, 55, 16, 64, 20, 68, 5, 53)(3, 51, 11, 59, 33, 81, 37, 85, 40, 88, 13, 61)(4, 52, 15, 63, 23, 71, 6, 54, 22, 70, 17, 65)(8, 56, 25, 73, 48, 96, 45, 93, 39, 87, 27, 75)(9, 57, 29, 77, 32, 80, 10, 58, 31, 79, 30, 78)(12, 60, 26, 74, 41, 89, 14, 62, 28, 76, 38, 86)(18, 66, 43, 91, 36, 84, 24, 72, 47, 95, 35, 83)(19, 67, 44, 92, 34, 82, 21, 69, 46, 94, 42, 90)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 108, 156)(101, 149, 114, 162)(102, 150, 110, 158)(103, 151, 120, 168)(105, 153, 122, 170)(106, 154, 124, 172)(107, 155, 130, 178)(109, 157, 125, 173)(111, 159, 131, 179)(112, 160, 133, 181)(113, 161, 135, 183)(115, 163, 134, 182)(116, 164, 141, 189)(117, 165, 137, 185)(118, 166, 132, 180)(119, 167, 121, 169)(123, 171, 142, 190)(126, 174, 139, 187)(127, 175, 129, 177)(128, 176, 143, 191)(136, 184, 138, 186)(140, 188, 144, 192) L = (1, 100)(2, 105)(3, 108)(4, 112)(5, 115)(6, 97)(7, 117)(8, 122)(9, 116)(10, 98)(11, 131)(12, 133)(13, 135)(14, 99)(15, 138)(16, 102)(17, 127)(18, 134)(19, 103)(20, 106)(21, 101)(22, 130)(23, 125)(24, 137)(25, 109)(26, 141)(27, 139)(28, 104)(29, 113)(30, 140)(31, 119)(32, 142)(33, 121)(34, 111)(35, 136)(36, 107)(37, 110)(38, 120)(39, 129)(40, 132)(41, 114)(42, 118)(43, 144)(44, 128)(45, 124)(46, 126)(47, 123)(48, 143)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E23.438 Graph:: simple bipartite v = 32 e = 96 f = 20 degree seq :: [ 4^24, 12^8 ] E23.440 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 4, 6, 6}) Quotient :: edge^2 Aut^+ = D8 x S3 (small group id <48, 38>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2 * Y1^2 * Y2, R * Y2 * R * Y1, (R * Y3)^2, (Y2^-1 * Y3)^2, (Y3 * Y1^-1)^2, Y3 * Y2^2 * Y3 * Y1^-2, Y2^-2 * Y1^4, Y2^6, (Y1 * Y2)^4 ] Map:: polytopal non-degenerate R = (1, 49, 4, 52)(2, 50, 9, 57)(3, 51, 13, 61)(5, 53, 15, 63)(6, 54, 16, 64)(7, 55, 20, 68)(8, 56, 23, 71)(10, 58, 25, 73)(11, 59, 28, 76)(12, 60, 30, 78)(14, 62, 31, 79)(17, 65, 33, 81)(18, 66, 34, 82)(19, 67, 35, 83)(21, 69, 36, 84)(22, 70, 38, 86)(24, 72, 40, 88)(26, 74, 42, 90)(27, 75, 43, 91)(29, 77, 44, 92)(32, 80, 45, 93)(37, 85, 46, 94)(39, 87, 47, 95)(41, 89, 48, 96)(97, 98, 103, 115, 108, 101)(99, 107, 102, 114, 117, 110)(100, 111, 126, 131, 116, 105)(104, 118, 106, 122, 113, 120)(109, 127, 132, 130, 112, 124)(119, 136, 129, 138, 121, 134)(123, 133, 125, 135, 128, 137)(139, 144, 141, 143, 140, 142)(145, 147, 156, 165, 151, 150)(146, 152, 149, 161, 163, 154)(148, 160, 164, 180, 174, 157)(153, 169, 179, 177, 159, 167)(155, 171, 158, 176, 162, 173)(166, 181, 168, 185, 170, 183)(172, 188, 178, 189, 175, 187)(182, 191, 186, 192, 184, 190) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 16^4 ), ( 16^6 ) } Outer automorphisms :: reflexible Dual of E23.446 Graph:: simple bipartite v = 40 e = 96 f = 12 degree seq :: [ 4^24, 6^16 ] E23.441 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 4, 6, 6}) Quotient :: edge^2 Aut^+ = (C2 x (C3 : C4)) : C2 (small group id <48, 39>) Aut = (D8 x S3) : C2 (small group id <96, 118>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^2 * Y1^2, (R * Y3)^2, R * Y1 * R * Y2, (Y3 * Y2^-2)^2, Y2^-1 * Y1^-1 * Y3 * Y2 * Y3 * Y1^-1, (Y1^-1 * Y3 * Y1^-1)^2, Y2^-2 * Y1^4, Y2^6, Y2^-1 * Y3 * Y1 * Y3 * Y2^-1 * Y1^-1, Y3 * Y1 * Y2 * Y3 * Y2 * Y1 ] Map:: polytopal non-degenerate R = (1, 49, 4, 52)(2, 50, 9, 57)(3, 51, 13, 61)(5, 53, 20, 68)(6, 54, 22, 70)(7, 55, 24, 72)(8, 56, 27, 75)(10, 58, 34, 82)(11, 59, 32, 80)(12, 60, 37, 85)(14, 62, 41, 89)(15, 63, 35, 83)(16, 64, 26, 74)(17, 65, 36, 84)(18, 66, 28, 76)(19, 67, 38, 86)(21, 69, 30, 78)(23, 71, 42, 90)(25, 73, 45, 93)(29, 77, 46, 94)(31, 79, 47, 95)(33, 81, 43, 91)(39, 87, 48, 96)(40, 88, 44, 92)(97, 98, 103, 119, 108, 101)(99, 107, 102, 117, 121, 110)(100, 111, 133, 140, 120, 113)(104, 122, 106, 129, 115, 124)(105, 125, 116, 135, 138, 127)(109, 134, 141, 130, 118, 123)(112, 128, 114, 137, 139, 126)(131, 142, 132, 143, 136, 144)(145, 147, 156, 169, 151, 150)(146, 152, 149, 163, 167, 154)(148, 160, 168, 187, 181, 162)(153, 174, 186, 185, 164, 176)(155, 179, 158, 184, 165, 180)(157, 173, 166, 175, 189, 183)(159, 171, 161, 178, 188, 182)(170, 190, 172, 192, 177, 191) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 16^4 ), ( 16^6 ) } Outer automorphisms :: reflexible Dual of E23.447 Graph:: simple bipartite v = 40 e = 96 f = 12 degree seq :: [ 4^24, 6^16 ] E23.442 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 4, 6, 6}) Quotient :: edge^2 Aut^+ = D8 x S3 (small group id <48, 38>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ R^2, Y2^2 * Y1^2, (Y3^-1 * Y1^-1)^2, (R * Y3)^2, (Y2 * Y3)^2, (Y3 * Y2^-1)^2, (Y3^-1 * Y1)^2, Y3^4, R * Y1 * R * Y2, Y2^-1 * Y3^-1 * Y1 * Y3 * Y2^-1 * Y1^-1, (Y2^-1 * Y3^-1 * Y1^-1)^2, Y3^-1 * Y1 * Y2 * Y3 * Y2^-1 * Y1^-1, Y2^-2 * Y1^4, Y1^-1 * Y3^-1 * Y2 * Y1 * Y2 * Y3, Y2^6, (Y3 * Y2^-1 * Y1^-1)^2 ] Map:: polytopal non-degenerate R = (1, 49, 4, 52, 20, 68, 7, 55)(2, 50, 10, 58, 34, 82, 12, 60)(3, 51, 15, 63, 31, 79, 17, 65)(5, 53, 22, 70, 37, 85, 18, 66)(6, 54, 24, 72, 29, 77, 19, 67)(8, 56, 26, 74, 46, 94, 28, 76)(9, 57, 30, 78, 13, 61, 32, 80)(11, 59, 36, 84, 23, 71, 33, 81)(14, 62, 38, 86, 48, 96, 39, 87)(16, 64, 42, 90, 21, 69, 40, 88)(25, 73, 43, 91, 41, 89, 44, 92)(27, 75, 47, 95, 35, 83, 45, 93)(97, 98, 104, 121, 110, 101)(99, 109, 102, 119, 123, 112)(100, 114, 134, 140, 122, 108)(103, 118, 135, 139, 124, 106)(105, 125, 107, 131, 117, 127)(111, 136, 143, 132, 120, 126)(113, 138, 141, 129, 115, 128)(116, 130, 142, 137, 144, 133)(145, 147, 158, 171, 152, 150)(146, 153, 149, 165, 169, 155)(148, 163, 170, 189, 182, 161)(151, 168, 172, 191, 183, 159)(154, 177, 187, 186, 166, 176)(156, 180, 188, 184, 162, 174)(157, 181, 160, 185, 167, 178)(164, 175, 192, 179, 190, 173) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8^6 ), ( 8^8 ) } Outer automorphisms :: reflexible Dual of E23.444 Graph:: simple bipartite v = 28 e = 96 f = 24 degree seq :: [ 6^16, 8^12 ] E23.443 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 4, 6, 6}) Quotient :: edge^2 Aut^+ = (C2 x (C3 : C4)) : C2 (small group id <48, 39>) Aut = (D8 x S3) : C2 (small group id <96, 118>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1^2 * Y2, Y1 * Y3 * Y1 * Y3^-1, (R * Y3)^2, Y3^4, R * Y2 * R * Y1, Y2^-1 * Y3 * Y2^-1 * Y3^-1, Y1^-2 * Y2^4, (Y1^-1 * Y3 * Y2^-1)^2, Y3^-2 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 49, 4, 52, 20, 68, 7, 55)(2, 50, 10, 58, 34, 82, 12, 60)(3, 51, 15, 63, 31, 79, 17, 65)(5, 53, 18, 66, 37, 85, 22, 70)(6, 54, 19, 67, 29, 77, 24, 72)(8, 56, 26, 74, 46, 94, 28, 76)(9, 57, 30, 78, 13, 61, 32, 80)(11, 59, 33, 81, 23, 71, 36, 84)(14, 62, 38, 86, 48, 96, 39, 87)(16, 64, 40, 88, 21, 69, 42, 90)(25, 73, 43, 91, 41, 89, 44, 92)(27, 75, 45, 93, 35, 83, 47, 95)(97, 98, 104, 121, 110, 101)(99, 109, 102, 119, 123, 112)(100, 114, 134, 139, 122, 106)(103, 118, 135, 140, 124, 108)(105, 125, 107, 131, 117, 127)(111, 136, 141, 132, 115, 128)(113, 138, 143, 129, 120, 126)(116, 130, 142, 137, 144, 133)(145, 147, 158, 171, 152, 150)(146, 153, 149, 165, 169, 155)(148, 163, 170, 189, 182, 159)(151, 168, 172, 191, 183, 161)(154, 177, 187, 186, 162, 174)(156, 180, 188, 184, 166, 176)(157, 181, 160, 185, 167, 178)(164, 175, 192, 179, 190, 173) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8^6 ), ( 8^8 ) } Outer automorphisms :: reflexible Dual of E23.445 Graph:: simple bipartite v = 28 e = 96 f = 24 degree seq :: [ 6^16, 8^12 ] E23.444 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 4, 6, 6}) Quotient :: loop^2 Aut^+ = D8 x S3 (small group id <48, 38>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2 * Y1^2 * Y2, R * Y2 * R * Y1, (R * Y3)^2, (Y2^-1 * Y3)^2, (Y3 * Y1^-1)^2, Y3 * Y2^2 * Y3 * Y1^-2, Y2^-2 * Y1^4, Y2^6, (Y1 * Y2)^4 ] Map:: polytopal non-degenerate R = (1, 49, 97, 145, 4, 52, 100, 148)(2, 50, 98, 146, 9, 57, 105, 153)(3, 51, 99, 147, 13, 61, 109, 157)(5, 53, 101, 149, 15, 63, 111, 159)(6, 54, 102, 150, 16, 64, 112, 160)(7, 55, 103, 151, 20, 68, 116, 164)(8, 56, 104, 152, 23, 71, 119, 167)(10, 58, 106, 154, 25, 73, 121, 169)(11, 59, 107, 155, 28, 76, 124, 172)(12, 60, 108, 156, 30, 78, 126, 174)(14, 62, 110, 158, 31, 79, 127, 175)(17, 65, 113, 161, 33, 81, 129, 177)(18, 66, 114, 162, 34, 82, 130, 178)(19, 67, 115, 163, 35, 83, 131, 179)(21, 69, 117, 165, 36, 84, 132, 180)(22, 70, 118, 166, 38, 86, 134, 182)(24, 72, 120, 168, 40, 88, 136, 184)(26, 74, 122, 170, 42, 90, 138, 186)(27, 75, 123, 171, 43, 91, 139, 187)(29, 77, 125, 173, 44, 92, 140, 188)(32, 80, 128, 176, 45, 93, 141, 189)(37, 85, 133, 181, 46, 94, 142, 190)(39, 87, 135, 183, 47, 95, 143, 191)(41, 89, 137, 185, 48, 96, 144, 192) L = (1, 50)(2, 55)(3, 59)(4, 63)(5, 49)(6, 66)(7, 67)(8, 70)(9, 52)(10, 74)(11, 54)(12, 53)(13, 79)(14, 51)(15, 78)(16, 76)(17, 72)(18, 69)(19, 60)(20, 57)(21, 62)(22, 58)(23, 88)(24, 56)(25, 86)(26, 65)(27, 85)(28, 61)(29, 87)(30, 83)(31, 84)(32, 89)(33, 90)(34, 64)(35, 68)(36, 82)(37, 77)(38, 71)(39, 80)(40, 81)(41, 75)(42, 73)(43, 96)(44, 94)(45, 95)(46, 91)(47, 92)(48, 93)(97, 147)(98, 152)(99, 156)(100, 160)(101, 161)(102, 145)(103, 150)(104, 149)(105, 169)(106, 146)(107, 171)(108, 165)(109, 148)(110, 176)(111, 167)(112, 164)(113, 163)(114, 173)(115, 154)(116, 180)(117, 151)(118, 181)(119, 153)(120, 185)(121, 179)(122, 183)(123, 158)(124, 188)(125, 155)(126, 157)(127, 187)(128, 162)(129, 159)(130, 189)(131, 177)(132, 174)(133, 168)(134, 191)(135, 166)(136, 190)(137, 170)(138, 192)(139, 172)(140, 178)(141, 175)(142, 182)(143, 186)(144, 184) local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E23.442 Transitivity :: VT+ Graph:: bipartite v = 24 e = 96 f = 28 degree seq :: [ 8^24 ] E23.445 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 4, 6, 6}) Quotient :: loop^2 Aut^+ = (C2 x (C3 : C4)) : C2 (small group id <48, 39>) Aut = (D8 x S3) : C2 (small group id <96, 118>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^2 * Y1^2, (R * Y3)^2, R * Y1 * R * Y2, (Y3 * Y2^-2)^2, Y2^-1 * Y1^-1 * Y3 * Y2 * Y3 * Y1^-1, (Y1^-1 * Y3 * Y1^-1)^2, Y2^-2 * Y1^4, Y2^6, Y2^-1 * Y3 * Y1 * Y3 * Y2^-1 * Y1^-1, Y3 * Y1 * Y2 * Y3 * Y2 * Y1 ] Map:: polytopal non-degenerate R = (1, 49, 97, 145, 4, 52, 100, 148)(2, 50, 98, 146, 9, 57, 105, 153)(3, 51, 99, 147, 13, 61, 109, 157)(5, 53, 101, 149, 20, 68, 116, 164)(6, 54, 102, 150, 22, 70, 118, 166)(7, 55, 103, 151, 24, 72, 120, 168)(8, 56, 104, 152, 27, 75, 123, 171)(10, 58, 106, 154, 34, 82, 130, 178)(11, 59, 107, 155, 32, 80, 128, 176)(12, 60, 108, 156, 37, 85, 133, 181)(14, 62, 110, 158, 41, 89, 137, 185)(15, 63, 111, 159, 35, 83, 131, 179)(16, 64, 112, 160, 26, 74, 122, 170)(17, 65, 113, 161, 36, 84, 132, 180)(18, 66, 114, 162, 28, 76, 124, 172)(19, 67, 115, 163, 38, 86, 134, 182)(21, 69, 117, 165, 30, 78, 126, 174)(23, 71, 119, 167, 42, 90, 138, 186)(25, 73, 121, 169, 45, 93, 141, 189)(29, 77, 125, 173, 46, 94, 142, 190)(31, 79, 127, 175, 47, 95, 143, 191)(33, 81, 129, 177, 43, 91, 139, 187)(39, 87, 135, 183, 48, 96, 144, 192)(40, 88, 136, 184, 44, 92, 140, 188) L = (1, 50)(2, 55)(3, 59)(4, 63)(5, 49)(6, 69)(7, 71)(8, 74)(9, 77)(10, 81)(11, 54)(12, 53)(13, 86)(14, 51)(15, 85)(16, 80)(17, 52)(18, 89)(19, 76)(20, 87)(21, 73)(22, 75)(23, 60)(24, 65)(25, 62)(26, 58)(27, 61)(28, 56)(29, 68)(30, 64)(31, 57)(32, 66)(33, 67)(34, 70)(35, 94)(36, 95)(37, 92)(38, 93)(39, 90)(40, 96)(41, 91)(42, 79)(43, 78)(44, 72)(45, 82)(46, 84)(47, 88)(48, 83)(97, 147)(98, 152)(99, 156)(100, 160)(101, 163)(102, 145)(103, 150)(104, 149)(105, 174)(106, 146)(107, 179)(108, 169)(109, 173)(110, 184)(111, 171)(112, 168)(113, 178)(114, 148)(115, 167)(116, 176)(117, 180)(118, 175)(119, 154)(120, 187)(121, 151)(122, 190)(123, 161)(124, 192)(125, 166)(126, 186)(127, 189)(128, 153)(129, 191)(130, 188)(131, 158)(132, 155)(133, 162)(134, 159)(135, 157)(136, 165)(137, 164)(138, 185)(139, 181)(140, 182)(141, 183)(142, 172)(143, 170)(144, 177) local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E23.443 Transitivity :: VT+ Graph:: simple bipartite v = 24 e = 96 f = 28 degree seq :: [ 8^24 ] E23.446 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 4, 6, 6}) Quotient :: loop^2 Aut^+ = D8 x S3 (small group id <48, 38>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ R^2, Y2^2 * Y1^2, (Y3^-1 * Y1^-1)^2, (R * Y3)^2, (Y2 * Y3)^2, (Y3 * Y2^-1)^2, (Y3^-1 * Y1)^2, Y3^4, R * Y1 * R * Y2, Y2^-1 * Y3^-1 * Y1 * Y3 * Y2^-1 * Y1^-1, (Y2^-1 * Y3^-1 * Y1^-1)^2, Y3^-1 * Y1 * Y2 * Y3 * Y2^-1 * Y1^-1, Y2^-2 * Y1^4, Y1^-1 * Y3^-1 * Y2 * Y1 * Y2 * Y3, Y2^6, (Y3 * Y2^-1 * Y1^-1)^2 ] Map:: polytopal non-degenerate R = (1, 49, 97, 145, 4, 52, 100, 148, 20, 68, 116, 164, 7, 55, 103, 151)(2, 50, 98, 146, 10, 58, 106, 154, 34, 82, 130, 178, 12, 60, 108, 156)(3, 51, 99, 147, 15, 63, 111, 159, 31, 79, 127, 175, 17, 65, 113, 161)(5, 53, 101, 149, 22, 70, 118, 166, 37, 85, 133, 181, 18, 66, 114, 162)(6, 54, 102, 150, 24, 72, 120, 168, 29, 77, 125, 173, 19, 67, 115, 163)(8, 56, 104, 152, 26, 74, 122, 170, 46, 94, 142, 190, 28, 76, 124, 172)(9, 57, 105, 153, 30, 78, 126, 174, 13, 61, 109, 157, 32, 80, 128, 176)(11, 59, 107, 155, 36, 84, 132, 180, 23, 71, 119, 167, 33, 81, 129, 177)(14, 62, 110, 158, 38, 86, 134, 182, 48, 96, 144, 192, 39, 87, 135, 183)(16, 64, 112, 160, 42, 90, 138, 186, 21, 69, 117, 165, 40, 88, 136, 184)(25, 73, 121, 169, 43, 91, 139, 187, 41, 89, 137, 185, 44, 92, 140, 188)(27, 75, 123, 171, 47, 95, 143, 191, 35, 83, 131, 179, 45, 93, 141, 189) L = (1, 50)(2, 56)(3, 61)(4, 66)(5, 49)(6, 71)(7, 70)(8, 73)(9, 77)(10, 55)(11, 83)(12, 52)(13, 54)(14, 53)(15, 88)(16, 51)(17, 90)(18, 86)(19, 80)(20, 82)(21, 79)(22, 87)(23, 75)(24, 78)(25, 62)(26, 60)(27, 64)(28, 58)(29, 59)(30, 63)(31, 57)(32, 65)(33, 67)(34, 94)(35, 69)(36, 72)(37, 68)(38, 92)(39, 91)(40, 95)(41, 96)(42, 93)(43, 76)(44, 74)(45, 81)(46, 89)(47, 84)(48, 85)(97, 147)(98, 153)(99, 158)(100, 163)(101, 165)(102, 145)(103, 168)(104, 150)(105, 149)(106, 177)(107, 146)(108, 180)(109, 181)(110, 171)(111, 151)(112, 185)(113, 148)(114, 174)(115, 170)(116, 175)(117, 169)(118, 176)(119, 178)(120, 172)(121, 155)(122, 189)(123, 152)(124, 191)(125, 164)(126, 156)(127, 192)(128, 154)(129, 187)(130, 157)(131, 190)(132, 188)(133, 160)(134, 161)(135, 159)(136, 162)(137, 167)(138, 166)(139, 186)(140, 184)(141, 182)(142, 173)(143, 183)(144, 179) local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E23.440 Transitivity :: VT+ Graph:: bipartite v = 12 e = 96 f = 40 degree seq :: [ 16^12 ] E23.447 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 4, 6, 6}) Quotient :: loop^2 Aut^+ = (C2 x (C3 : C4)) : C2 (small group id <48, 39>) Aut = (D8 x S3) : C2 (small group id <96, 118>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1^2 * Y2, Y1 * Y3 * Y1 * Y3^-1, (R * Y3)^2, Y3^4, R * Y2 * R * Y1, Y2^-1 * Y3 * Y2^-1 * Y3^-1, Y1^-2 * Y2^4, (Y1^-1 * Y3 * Y2^-1)^2, Y3^-2 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 49, 97, 145, 4, 52, 100, 148, 20, 68, 116, 164, 7, 55, 103, 151)(2, 50, 98, 146, 10, 58, 106, 154, 34, 82, 130, 178, 12, 60, 108, 156)(3, 51, 99, 147, 15, 63, 111, 159, 31, 79, 127, 175, 17, 65, 113, 161)(5, 53, 101, 149, 18, 66, 114, 162, 37, 85, 133, 181, 22, 70, 118, 166)(6, 54, 102, 150, 19, 67, 115, 163, 29, 77, 125, 173, 24, 72, 120, 168)(8, 56, 104, 152, 26, 74, 122, 170, 46, 94, 142, 190, 28, 76, 124, 172)(9, 57, 105, 153, 30, 78, 126, 174, 13, 61, 109, 157, 32, 80, 128, 176)(11, 59, 107, 155, 33, 81, 129, 177, 23, 71, 119, 167, 36, 84, 132, 180)(14, 62, 110, 158, 38, 86, 134, 182, 48, 96, 144, 192, 39, 87, 135, 183)(16, 64, 112, 160, 40, 88, 136, 184, 21, 69, 117, 165, 42, 90, 138, 186)(25, 73, 121, 169, 43, 91, 139, 187, 41, 89, 137, 185, 44, 92, 140, 188)(27, 75, 123, 171, 45, 93, 141, 189, 35, 83, 131, 179, 47, 95, 143, 191) L = (1, 50)(2, 56)(3, 61)(4, 66)(5, 49)(6, 71)(7, 70)(8, 73)(9, 77)(10, 52)(11, 83)(12, 55)(13, 54)(14, 53)(15, 88)(16, 51)(17, 90)(18, 86)(19, 80)(20, 82)(21, 79)(22, 87)(23, 75)(24, 78)(25, 62)(26, 58)(27, 64)(28, 60)(29, 59)(30, 65)(31, 57)(32, 63)(33, 72)(34, 94)(35, 69)(36, 67)(37, 68)(38, 91)(39, 92)(40, 93)(41, 96)(42, 95)(43, 74)(44, 76)(45, 84)(46, 89)(47, 81)(48, 85)(97, 147)(98, 153)(99, 158)(100, 163)(101, 165)(102, 145)(103, 168)(104, 150)(105, 149)(106, 177)(107, 146)(108, 180)(109, 181)(110, 171)(111, 148)(112, 185)(113, 151)(114, 174)(115, 170)(116, 175)(117, 169)(118, 176)(119, 178)(120, 172)(121, 155)(122, 189)(123, 152)(124, 191)(125, 164)(126, 154)(127, 192)(128, 156)(129, 187)(130, 157)(131, 190)(132, 188)(133, 160)(134, 159)(135, 161)(136, 166)(137, 167)(138, 162)(139, 186)(140, 184)(141, 182)(142, 173)(143, 183)(144, 179) local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E23.441 Transitivity :: VT+ Graph:: bipartite v = 12 e = 96 f = 40 degree seq :: [ 16^12 ] E23.448 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C6 x D8 (small group id <48, 45>) Aut = C2 x D8 x S3 (small group id <96, 209>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3 * Y2^-1 * Y3^-1 * Y2^-1, Y3 * Y1 * Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (Y2 * Y1)^2, R * Y2 * R * Y2^-1, Y2^4, Y3^6 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50)(3, 51, 9, 57)(4, 52, 8, 56)(5, 53, 7, 55)(6, 54, 10, 58)(11, 59, 18, 66)(12, 60, 21, 69)(13, 61, 23, 71)(14, 62, 19, 67)(15, 63, 22, 70)(16, 64, 20, 68)(17, 65, 24, 72)(25, 73, 32, 80)(26, 74, 33, 81)(27, 75, 36, 84)(28, 76, 38, 86)(29, 77, 34, 82)(30, 78, 37, 85)(31, 79, 35, 83)(39, 87, 43, 91)(40, 88, 44, 92)(41, 89, 46, 94)(42, 90, 45, 93)(47, 95, 48, 96)(97, 145, 99, 147, 107, 155, 101, 149)(98, 146, 103, 151, 114, 162, 105, 153)(100, 148, 110, 158, 121, 169, 108, 156)(102, 150, 112, 160, 122, 170, 109, 157)(104, 152, 117, 165, 128, 176, 115, 163)(106, 154, 119, 167, 129, 177, 116, 164)(111, 159, 123, 171, 135, 183, 125, 173)(113, 161, 124, 172, 136, 184, 127, 175)(118, 166, 130, 178, 139, 187, 132, 180)(120, 168, 131, 179, 140, 188, 134, 182)(126, 174, 138, 186, 143, 191, 137, 185)(133, 181, 142, 190, 144, 192, 141, 189) L = (1, 100)(2, 104)(3, 108)(4, 111)(5, 110)(6, 97)(7, 115)(8, 118)(9, 117)(10, 98)(11, 121)(12, 123)(13, 99)(14, 125)(15, 126)(16, 101)(17, 102)(18, 128)(19, 130)(20, 103)(21, 132)(22, 133)(23, 105)(24, 106)(25, 135)(26, 107)(27, 137)(28, 109)(29, 138)(30, 113)(31, 112)(32, 139)(33, 114)(34, 141)(35, 116)(36, 142)(37, 120)(38, 119)(39, 143)(40, 122)(41, 124)(42, 127)(43, 144)(44, 129)(45, 131)(46, 134)(47, 136)(48, 140)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 12^4 ), ( 12^8 ) } Outer automorphisms :: reflexible Dual of E23.473 Graph:: simple bipartite v = 36 e = 96 f = 16 degree seq :: [ 4^24, 8^12 ] E23.449 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C6 x D8 (small group id <48, 45>) Aut = C2 x D8 x S3 (small group id <96, 209>) |r| :: 2 Presentation :: [ Y3^2, R^2, (R * Y1)^2, (Y2^-1, Y1^-1), (R * Y2)^2, (R * Y3)^2, Y3 * Y2 * Y3 * Y2^-1, (Y3 * Y1^-1)^2, Y1^4, Y2^6 ] Map:: non-degenerate R = (1, 49, 2, 50, 7, 55, 5, 53)(3, 51, 8, 56, 18, 66, 13, 61)(4, 52, 14, 62, 19, 67, 9, 57)(6, 54, 10, 58, 20, 68, 16, 64)(11, 59, 21, 69, 32, 80, 27, 75)(12, 60, 28, 76, 33, 81, 22, 70)(15, 63, 29, 77, 34, 82, 23, 71)(17, 65, 24, 72, 35, 83, 31, 79)(25, 73, 36, 84, 43, 91, 40, 88)(26, 74, 41, 89, 44, 92, 37, 85)(30, 78, 42, 90, 45, 93, 38, 86)(39, 87, 47, 95, 48, 96, 46, 94)(97, 145, 99, 147, 107, 155, 121, 169, 113, 161, 102, 150)(98, 146, 104, 152, 117, 165, 132, 180, 120, 168, 106, 154)(100, 148, 108, 156, 122, 170, 135, 183, 126, 174, 111, 159)(101, 149, 109, 157, 123, 171, 136, 184, 127, 175, 112, 160)(103, 151, 114, 162, 128, 176, 139, 187, 131, 179, 116, 164)(105, 153, 118, 166, 133, 181, 142, 190, 134, 182, 119, 167)(110, 158, 124, 172, 137, 185, 143, 191, 138, 186, 125, 173)(115, 163, 129, 177, 140, 188, 144, 192, 141, 189, 130, 178) L = (1, 100)(2, 105)(3, 108)(4, 97)(5, 110)(6, 111)(7, 115)(8, 118)(9, 98)(10, 119)(11, 122)(12, 99)(13, 124)(14, 101)(15, 102)(16, 125)(17, 126)(18, 129)(19, 103)(20, 130)(21, 133)(22, 104)(23, 106)(24, 134)(25, 135)(26, 107)(27, 137)(28, 109)(29, 112)(30, 113)(31, 138)(32, 140)(33, 114)(34, 116)(35, 141)(36, 142)(37, 117)(38, 120)(39, 121)(40, 143)(41, 123)(42, 127)(43, 144)(44, 128)(45, 131)(46, 132)(47, 136)(48, 139)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 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 E23.463 Graph:: simple bipartite v = 20 e = 96 f = 32 degree seq :: [ 8^12, 12^8 ] E23.450 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C2 x ((C6 x C2) : C2) (small group id <48, 43>) Aut = C2 x D8 x S3 (small group id <96, 209>) |r| :: 2 Presentation :: [ Y3^2, R^2, Y2 * Y1 * Y2 * Y1^-1, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y3 * Y2 * Y3 * Y2^-1, (Y3 * Y1^-1)^2, Y1^4, Y2^6 ] Map:: non-degenerate R = (1, 49, 2, 50, 7, 55, 5, 53)(3, 51, 10, 58, 18, 66, 13, 61)(4, 52, 14, 62, 19, 67, 9, 57)(6, 54, 8, 56, 20, 68, 16, 64)(11, 59, 24, 72, 32, 80, 27, 75)(12, 60, 28, 76, 33, 81, 23, 71)(15, 63, 29, 77, 34, 82, 22, 70)(17, 65, 21, 69, 35, 83, 31, 79)(25, 73, 36, 84, 43, 91, 40, 88)(26, 74, 41, 89, 44, 92, 38, 86)(30, 78, 42, 90, 45, 93, 37, 85)(39, 87, 47, 95, 48, 96, 46, 94)(97, 145, 99, 147, 107, 155, 121, 169, 113, 161, 102, 150)(98, 146, 104, 152, 117, 165, 132, 180, 120, 168, 106, 154)(100, 148, 108, 156, 122, 170, 135, 183, 126, 174, 111, 159)(101, 149, 112, 160, 127, 175, 136, 184, 123, 171, 109, 157)(103, 151, 114, 162, 128, 176, 139, 187, 131, 179, 116, 164)(105, 153, 118, 166, 133, 181, 142, 190, 134, 182, 119, 167)(110, 158, 125, 173, 138, 186, 143, 191, 137, 185, 124, 172)(115, 163, 129, 177, 140, 188, 144, 192, 141, 189, 130, 178) L = (1, 100)(2, 105)(3, 108)(4, 97)(5, 110)(6, 111)(7, 115)(8, 118)(9, 98)(10, 119)(11, 122)(12, 99)(13, 124)(14, 101)(15, 102)(16, 125)(17, 126)(18, 129)(19, 103)(20, 130)(21, 133)(22, 104)(23, 106)(24, 134)(25, 135)(26, 107)(27, 137)(28, 109)(29, 112)(30, 113)(31, 138)(32, 140)(33, 114)(34, 116)(35, 141)(36, 142)(37, 117)(38, 120)(39, 121)(40, 143)(41, 123)(42, 127)(43, 144)(44, 128)(45, 131)(46, 132)(47, 136)(48, 139)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 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 E23.467 Graph:: simple bipartite v = 20 e = 96 f = 32 degree seq :: [ 8^12, 12^8 ] E23.451 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C2 x ((C6 x C2) : C2) (small group id <48, 43>) Aut = C2 x D8 x S3 (small group id <96, 209>) |r| :: 2 Presentation :: [ R^2, (Y2^-1, Y3^-1), (R * Y2)^2, (Y3^-1 * Y1^-1)^2, (R * Y3)^2, (Y3 * Y2)^2, Y1^4, Y2 * Y1 * Y2 * Y1^-1, Y2^-2 * Y3^-2, (Y3 * Y1^-1)^2, (R * Y1)^2, Y3^-2 * Y2^4, (Y3 * Y2^-1)^6 ] Map:: non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 11, 59, 22, 70, 15, 63)(4, 52, 17, 65, 23, 71, 12, 60)(6, 54, 9, 57, 24, 72, 20, 68)(7, 55, 21, 69, 25, 73, 10, 58)(13, 61, 29, 77, 38, 86, 32, 80)(14, 62, 34, 82, 39, 87, 27, 75)(16, 64, 35, 83, 40, 88, 30, 78)(18, 66, 26, 74, 41, 89, 37, 85)(19, 67, 36, 84, 42, 90, 28, 76)(31, 79, 43, 91, 47, 95, 45, 93)(33, 81, 46, 94, 48, 96, 44, 92)(97, 145, 99, 147, 109, 157, 127, 175, 114, 162, 102, 150)(98, 146, 105, 153, 122, 170, 139, 187, 125, 173, 107, 155)(100, 148, 110, 158, 103, 151, 112, 160, 129, 177, 115, 163)(101, 149, 116, 164, 133, 181, 141, 189, 128, 176, 111, 159)(104, 152, 118, 166, 134, 182, 143, 191, 137, 185, 120, 168)(106, 154, 123, 171, 108, 156, 124, 172, 140, 188, 126, 174)(113, 161, 132, 180, 142, 190, 131, 179, 117, 165, 130, 178)(119, 167, 135, 183, 121, 169, 136, 184, 144, 192, 138, 186) L = (1, 100)(2, 106)(3, 110)(4, 114)(5, 117)(6, 115)(7, 97)(8, 119)(9, 123)(10, 125)(11, 126)(12, 98)(13, 103)(14, 102)(15, 131)(16, 99)(17, 101)(18, 129)(19, 127)(20, 130)(21, 128)(22, 135)(23, 137)(24, 138)(25, 104)(26, 108)(27, 107)(28, 105)(29, 140)(30, 139)(31, 112)(32, 142)(33, 109)(34, 111)(35, 141)(36, 116)(37, 113)(38, 121)(39, 120)(40, 118)(41, 144)(42, 143)(43, 124)(44, 122)(45, 132)(46, 133)(47, 136)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 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 E23.469 Graph:: simple bipartite v = 20 e = 96 f = 32 degree seq :: [ 8^12, 12^8 ] E23.452 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C6 x D8 (small group id <48, 45>) Aut = C2 x D8 x S3 (small group id <96, 209>) |r| :: 2 Presentation :: [ R^2, Y3^2, (R * Y2)^2, Y2^-1 * Y3 * Y2 * Y3, (R * Y1)^2, (R * Y3)^2, (Y3 * Y1^-1)^2, Y1^4, Y2 * Y1^-1 * Y2^-1 * Y1^-1, Y2^6 ] Map:: non-degenerate R = (1, 49, 2, 50, 7, 55, 5, 53)(3, 51, 11, 59, 18, 66, 8, 56)(4, 52, 14, 62, 19, 67, 9, 57)(6, 54, 16, 64, 20, 68, 10, 58)(12, 60, 21, 69, 32, 80, 25, 73)(13, 61, 22, 70, 33, 81, 26, 74)(15, 63, 23, 71, 34, 82, 29, 77)(17, 65, 24, 72, 35, 83, 31, 79)(27, 75, 39, 87, 43, 91, 36, 84)(28, 76, 40, 88, 44, 92, 37, 85)(30, 78, 42, 90, 45, 93, 38, 86)(41, 89, 46, 94, 48, 96, 47, 95)(97, 145, 99, 147, 108, 156, 123, 171, 113, 161, 102, 150)(98, 146, 104, 152, 117, 165, 132, 180, 120, 168, 106, 154)(100, 148, 109, 157, 124, 172, 137, 185, 126, 174, 111, 159)(101, 149, 107, 155, 121, 169, 135, 183, 127, 175, 112, 160)(103, 151, 114, 162, 128, 176, 139, 187, 131, 179, 116, 164)(105, 153, 118, 166, 133, 181, 142, 190, 134, 182, 119, 167)(110, 158, 122, 170, 136, 184, 143, 191, 138, 186, 125, 173)(115, 163, 129, 177, 140, 188, 144, 192, 141, 189, 130, 178) L = (1, 100)(2, 105)(3, 109)(4, 97)(5, 110)(6, 111)(7, 115)(8, 118)(9, 98)(10, 119)(11, 122)(12, 124)(13, 99)(14, 101)(15, 102)(16, 125)(17, 126)(18, 129)(19, 103)(20, 130)(21, 133)(22, 104)(23, 106)(24, 134)(25, 136)(26, 107)(27, 137)(28, 108)(29, 112)(30, 113)(31, 138)(32, 140)(33, 114)(34, 116)(35, 141)(36, 142)(37, 117)(38, 120)(39, 143)(40, 121)(41, 123)(42, 127)(43, 144)(44, 128)(45, 131)(46, 132)(47, 135)(48, 139)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 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 E23.462 Graph:: simple bipartite v = 20 e = 96 f = 32 degree seq :: [ 8^12, 12^8 ] E23.453 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C2 x ((C6 x C2) : C2) (small group id <48, 43>) Aut = C2 x D8 x S3 (small group id <96, 209>) |r| :: 2 Presentation :: [ R^2, Y3^2, (R * Y2)^2, Y2^-1 * Y3 * Y2 * Y3, (R * Y1)^2, (R * Y3)^2, (Y3 * Y1^-1)^2, (Y2 * Y1^-1)^2, (Y1^-1 * Y2^-1)^2, Y1^4, Y2^6 ] Map:: non-degenerate R = (1, 49, 2, 50, 7, 55, 5, 53)(3, 51, 11, 59, 18, 66, 10, 58)(4, 52, 14, 62, 19, 67, 9, 57)(6, 54, 16, 64, 20, 68, 8, 56)(12, 60, 24, 72, 32, 80, 26, 74)(13, 61, 23, 71, 33, 81, 25, 73)(15, 63, 22, 70, 34, 82, 29, 77)(17, 65, 21, 69, 35, 83, 31, 79)(27, 75, 40, 88, 43, 91, 36, 84)(28, 76, 39, 87, 44, 92, 38, 86)(30, 78, 42, 90, 45, 93, 37, 85)(41, 89, 46, 94, 48, 96, 47, 95)(97, 145, 99, 147, 108, 156, 123, 171, 113, 161, 102, 150)(98, 146, 104, 152, 117, 165, 132, 180, 120, 168, 106, 154)(100, 148, 109, 157, 124, 172, 137, 185, 126, 174, 111, 159)(101, 149, 112, 160, 127, 175, 136, 184, 122, 170, 107, 155)(103, 151, 114, 162, 128, 176, 139, 187, 131, 179, 116, 164)(105, 153, 118, 166, 133, 181, 142, 190, 134, 182, 119, 167)(110, 158, 125, 173, 138, 186, 143, 191, 135, 183, 121, 169)(115, 163, 129, 177, 140, 188, 144, 192, 141, 189, 130, 178) L = (1, 100)(2, 105)(3, 109)(4, 97)(5, 110)(6, 111)(7, 115)(8, 118)(9, 98)(10, 119)(11, 121)(12, 124)(13, 99)(14, 101)(15, 102)(16, 125)(17, 126)(18, 129)(19, 103)(20, 130)(21, 133)(22, 104)(23, 106)(24, 134)(25, 107)(26, 135)(27, 137)(28, 108)(29, 112)(30, 113)(31, 138)(32, 140)(33, 114)(34, 116)(35, 141)(36, 142)(37, 117)(38, 120)(39, 122)(40, 143)(41, 123)(42, 127)(43, 144)(44, 128)(45, 131)(46, 132)(47, 136)(48, 139)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 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 E23.466 Graph:: simple bipartite v = 20 e = 96 f = 32 degree seq :: [ 8^12, 12^8 ] E23.454 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C6 x D8 (small group id <48, 45>) Aut = C2 x D8 x S3 (small group id <96, 209>) |r| :: 2 Presentation :: [ R^2, (Y3^-1 * Y1)^2, Y1^-1 * Y3^2 * Y1^-1, Y1^-2 * Y3^-2, (Y3 * Y1)^2, Y3 * Y2 * Y3 * Y2^-1, Y1^4, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y1 * Y2 * Y1, (R * Y2 * Y3^-1)^2, Y2^6 ] Map:: non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 21, 69, 9, 57)(4, 52, 10, 58, 7, 55, 12, 60)(6, 54, 18, 66, 22, 70, 11, 59)(14, 62, 23, 71, 36, 84, 29, 77)(15, 63, 25, 73, 16, 64, 24, 72)(17, 65, 27, 75, 19, 67, 26, 74)(20, 68, 28, 76, 37, 85, 34, 82)(30, 78, 43, 91, 46, 94, 38, 86)(31, 79, 39, 87, 32, 80, 40, 88)(33, 81, 41, 89, 35, 83, 42, 90)(44, 92, 48, 96, 45, 93, 47, 95)(97, 145, 99, 147, 110, 158, 126, 174, 116, 164, 102, 150)(98, 146, 105, 153, 119, 167, 134, 182, 124, 172, 107, 155)(100, 148, 112, 160, 127, 175, 141, 189, 129, 177, 113, 161)(101, 149, 109, 157, 125, 173, 139, 187, 130, 178, 114, 162)(103, 151, 111, 159, 128, 176, 140, 188, 131, 179, 115, 163)(104, 152, 117, 165, 132, 180, 142, 190, 133, 181, 118, 166)(106, 154, 121, 169, 135, 183, 144, 192, 137, 185, 122, 170)(108, 156, 120, 168, 136, 184, 143, 191, 138, 186, 123, 171) L = (1, 100)(2, 106)(3, 111)(4, 104)(5, 108)(6, 115)(7, 97)(8, 103)(9, 120)(10, 101)(11, 123)(12, 98)(13, 121)(14, 127)(15, 117)(16, 99)(17, 102)(18, 122)(19, 118)(20, 129)(21, 112)(22, 113)(23, 135)(24, 109)(25, 105)(26, 107)(27, 114)(28, 137)(29, 136)(30, 140)(31, 132)(32, 110)(33, 133)(34, 138)(35, 116)(36, 128)(37, 131)(38, 143)(39, 125)(40, 119)(41, 130)(42, 124)(43, 144)(44, 142)(45, 126)(46, 141)(47, 139)(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, 12, 4, 12, 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E23.461 Graph:: simple bipartite v = 20 e = 96 f = 32 degree seq :: [ 8^12, 12^8 ] E23.455 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = D8 x S3 (small group id <48, 38>) Aut = C2 x D8 x S3 (small group id <96, 209>) |r| :: 2 Presentation :: [ R^2, (Y3 * Y1^-1)^2, Y3^4, Y1^-1 * Y3^-2 * Y1^-1, Y1 * Y3^-2 * Y1, (R * Y3)^2, (R * Y1)^2, (Y2^-1 * Y1^-1)^2, (Y3^-1 * Y1^-1)^2, (Y2^-1 * Y1)^2, Y3 * Y2 * Y3 * Y2^-1, (Y2^-1 * Y3^-1 * Y1^-1)^2, Y2^6, (R * Y2 * Y3^-1)^2 ] Map:: non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 21, 69, 11, 59)(4, 52, 10, 58, 7, 55, 12, 60)(6, 54, 18, 66, 22, 70, 9, 57)(14, 62, 28, 76, 36, 84, 29, 77)(15, 63, 26, 74, 16, 64, 27, 75)(17, 65, 24, 72, 19, 67, 25, 73)(20, 68, 23, 71, 37, 85, 34, 82)(30, 78, 43, 91, 46, 94, 38, 86)(31, 79, 41, 89, 32, 80, 42, 90)(33, 81, 39, 87, 35, 83, 40, 88)(44, 92, 48, 96, 45, 93, 47, 95)(97, 145, 99, 147, 110, 158, 126, 174, 116, 164, 102, 150)(98, 146, 105, 153, 119, 167, 134, 182, 124, 172, 107, 155)(100, 148, 112, 160, 127, 175, 141, 189, 129, 177, 113, 161)(101, 149, 114, 162, 130, 178, 139, 187, 125, 173, 109, 157)(103, 151, 111, 159, 128, 176, 140, 188, 131, 179, 115, 163)(104, 152, 117, 165, 132, 180, 142, 190, 133, 181, 118, 166)(106, 154, 121, 169, 135, 183, 144, 192, 137, 185, 122, 170)(108, 156, 120, 168, 136, 184, 143, 191, 138, 186, 123, 171) L = (1, 100)(2, 106)(3, 111)(4, 104)(5, 108)(6, 115)(7, 97)(8, 103)(9, 120)(10, 101)(11, 123)(12, 98)(13, 122)(14, 127)(15, 117)(16, 99)(17, 102)(18, 121)(19, 118)(20, 129)(21, 112)(22, 113)(23, 135)(24, 114)(25, 105)(26, 107)(27, 109)(28, 137)(29, 138)(30, 140)(31, 132)(32, 110)(33, 133)(34, 136)(35, 116)(36, 128)(37, 131)(38, 143)(39, 130)(40, 119)(41, 125)(42, 124)(43, 144)(44, 142)(45, 126)(46, 141)(47, 139)(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, 12, 4, 12, 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E23.464 Graph:: simple bipartite v = 20 e = 96 f = 32 degree seq :: [ 8^12, 12^8 ] E23.456 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C2 x ((C6 x C2) : C2) (small group id <48, 43>) Aut = C2 x D8 x S3 (small group id <96, 209>) |r| :: 2 Presentation :: [ R^2, (Y3, Y2), (Y2^-1 * Y1^-1)^2, (Y3^-1 * Y2^-1)^2, (Y2 * Y1^-1)^2, (R * Y1)^2, Y2^-2 * Y3^-2, (R * Y2)^2, (R * Y3)^2, Y1^4, (Y3^-1 * Y1^-1)^2, (Y3 * Y1^-1)^2, Y3^-2 * Y2^4, (Y3 * Y2^-1)^6 ] Map:: non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 22, 70, 11, 59)(4, 52, 17, 65, 23, 71, 12, 60)(6, 54, 20, 68, 24, 72, 9, 57)(7, 55, 21, 69, 25, 73, 10, 58)(14, 62, 29, 77, 38, 86, 32, 80)(15, 63, 27, 75, 39, 87, 33, 81)(16, 64, 30, 78, 40, 88, 31, 79)(18, 66, 26, 74, 41, 89, 37, 85)(19, 67, 28, 76, 42, 90, 36, 84)(34, 82, 45, 93, 47, 95, 43, 91)(35, 83, 46, 94, 48, 96, 44, 92)(97, 145, 99, 147, 110, 158, 130, 178, 114, 162, 102, 150)(98, 146, 105, 153, 122, 170, 139, 187, 125, 173, 107, 155)(100, 148, 111, 159, 103, 151, 112, 160, 131, 179, 115, 163)(101, 149, 116, 164, 133, 181, 141, 189, 128, 176, 109, 157)(104, 152, 118, 166, 134, 182, 143, 191, 137, 185, 120, 168)(106, 154, 123, 171, 108, 156, 124, 172, 140, 188, 126, 174)(113, 161, 132, 180, 142, 190, 127, 175, 117, 165, 129, 177)(119, 167, 135, 183, 121, 169, 136, 184, 144, 192, 138, 186) L = (1, 100)(2, 106)(3, 111)(4, 114)(5, 117)(6, 115)(7, 97)(8, 119)(9, 123)(10, 125)(11, 126)(12, 98)(13, 127)(14, 103)(15, 102)(16, 99)(17, 101)(18, 131)(19, 130)(20, 129)(21, 128)(22, 135)(23, 137)(24, 138)(25, 104)(26, 108)(27, 107)(28, 105)(29, 140)(30, 139)(31, 141)(32, 142)(33, 109)(34, 112)(35, 110)(36, 116)(37, 113)(38, 121)(39, 120)(40, 118)(41, 144)(42, 143)(43, 124)(44, 122)(45, 132)(46, 133)(47, 136)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 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 E23.468 Graph:: simple bipartite v = 20 e = 96 f = 32 degree seq :: [ 8^12, 12^8 ] E23.457 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = D8 x S3 (small group id <48, 38>) Aut = C2 x D8 x S3 (small group id <96, 209>) |r| :: 2 Presentation :: [ R^2, Y1^4, (Y2^-1 * Y3^-1)^2, (R * Y3)^2, (Y1^-1 * Y3)^2, (Y2^-1 * Y1^-1)^2, (Y2 * Y1^-1)^2, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, Y3 * Y2^-1 * Y1^-2 * Y3^-1 * Y2, Y3^-1 * Y2^-1 * Y3 * Y2 * Y1^-2, Y3^-1 * Y2 * Y3^-1 * Y2^3, (R * Y2 * Y3^-1)^2, Y1^-1 * Y2^-1 * Y3^-2 * Y2^-1 * Y1^-1, Y3^-1 * Y2 * Y3^-1 * Y2^-3, (Y2^-1 * Y3^-1 * Y1^-1)^2, Y3 * R * Y2 * R * Y3^-1 * Y2, Y1^-1 * Y3 * Y1^2 * Y3^-1 * Y1^-1, Y3^2 * Y2 * Y3^-2 * Y2^-1, (Y3^2 * Y2^-1)^2 ] Map:: non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 27, 75, 11, 59)(4, 52, 17, 65, 28, 76, 12, 60)(6, 54, 21, 69, 29, 77, 9, 57)(7, 55, 22, 70, 30, 78, 10, 58)(14, 62, 38, 86, 26, 74, 35, 83)(15, 63, 34, 82, 18, 66, 32, 80)(16, 64, 37, 85, 25, 73, 36, 84)(19, 67, 40, 88, 24, 72, 31, 79)(20, 68, 39, 87, 23, 71, 33, 81)(41, 89, 48, 96, 44, 92, 45, 93)(42, 90, 46, 94, 43, 91, 47, 95)(97, 145, 99, 147, 110, 158, 137, 185, 120, 168, 102, 150)(98, 146, 105, 153, 127, 175, 141, 189, 134, 182, 107, 155)(100, 148, 114, 162, 126, 174, 112, 160, 139, 187, 116, 164)(101, 149, 117, 165, 136, 184, 144, 192, 131, 179, 109, 157)(103, 151, 121, 169, 138, 186, 119, 167, 124, 172, 111, 159)(104, 152, 123, 171, 122, 170, 140, 188, 115, 163, 125, 173)(106, 154, 130, 178, 113, 161, 129, 177, 143, 191, 132, 180)(108, 156, 135, 183, 142, 190, 133, 181, 118, 166, 128, 176) L = (1, 100)(2, 106)(3, 111)(4, 115)(5, 118)(6, 119)(7, 97)(8, 124)(9, 128)(10, 131)(11, 133)(12, 98)(13, 132)(14, 126)(15, 125)(16, 99)(17, 101)(18, 102)(19, 138)(20, 137)(21, 130)(22, 134)(23, 140)(24, 139)(25, 123)(26, 103)(27, 114)(28, 120)(29, 116)(30, 104)(31, 113)(32, 109)(33, 105)(34, 107)(35, 142)(36, 141)(37, 144)(38, 143)(39, 117)(40, 108)(41, 121)(42, 110)(43, 122)(44, 112)(45, 135)(46, 127)(47, 136)(48, 129)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 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 E23.465 Graph:: simple bipartite v = 20 e = 96 f = 32 degree seq :: [ 8^12, 12^8 ] E23.458 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = (C2 x (C3 : C4)) : C2 (small group id <48, 39>) Aut = (C6 x D8) : C2 (small group id <96, 211>) |r| :: 2 Presentation :: [ R^2, (Y3^-1 * Y1)^2, Y3^4, Y1^-1 * Y3^-2 * Y1^-1, (R * Y3)^2, Y3 * Y2 * Y3 * Y2^-1, Y2^-1 * Y1 * Y2^-1 * Y1^-1, (Y3^-1 * Y1^-1)^2, (R * Y1)^2, Y3^2 * Y1^-2, Y2^6, (R * Y2 * Y3^-1)^2 ] Map:: non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 11, 59, 21, 69, 15, 63)(4, 52, 10, 58, 7, 55, 12, 60)(6, 54, 9, 57, 22, 70, 18, 66)(13, 61, 28, 76, 36, 84, 31, 79)(14, 62, 27, 75, 16, 64, 26, 74)(17, 65, 25, 73, 19, 67, 24, 72)(20, 68, 23, 71, 37, 85, 34, 82)(29, 77, 38, 86, 46, 94, 44, 92)(30, 78, 41, 89, 32, 80, 42, 90)(33, 81, 39, 87, 35, 83, 40, 88)(43, 91, 47, 95, 45, 93, 48, 96)(97, 145, 99, 147, 109, 157, 125, 173, 116, 164, 102, 150)(98, 146, 105, 153, 119, 167, 134, 182, 124, 172, 107, 155)(100, 148, 112, 160, 126, 174, 141, 189, 129, 177, 113, 161)(101, 149, 114, 162, 130, 178, 140, 188, 127, 175, 111, 159)(103, 151, 110, 158, 128, 176, 139, 187, 131, 179, 115, 163)(104, 152, 117, 165, 132, 180, 142, 190, 133, 181, 118, 166)(106, 154, 121, 169, 135, 183, 144, 192, 137, 185, 122, 170)(108, 156, 120, 168, 136, 184, 143, 191, 138, 186, 123, 171) L = (1, 100)(2, 106)(3, 110)(4, 104)(5, 108)(6, 115)(7, 97)(8, 103)(9, 120)(10, 101)(11, 123)(12, 98)(13, 126)(14, 117)(15, 122)(16, 99)(17, 102)(18, 121)(19, 118)(20, 129)(21, 112)(22, 113)(23, 135)(24, 114)(25, 105)(26, 107)(27, 111)(28, 137)(29, 139)(30, 132)(31, 138)(32, 109)(33, 133)(34, 136)(35, 116)(36, 128)(37, 131)(38, 143)(39, 130)(40, 119)(41, 127)(42, 124)(43, 142)(44, 144)(45, 125)(46, 141)(47, 140)(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, 12, 4, 12, 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E23.470 Graph:: simple bipartite v = 20 e = 96 f = 32 degree seq :: [ 8^12, 12^8 ] E23.459 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = (C2 x (C3 : C4)) : C2 (small group id <48, 39>) Aut = (C6 x D8) : C2 (small group id <96, 211>) |r| :: 2 Presentation :: [ R^2, (Y3^-1 * Y1^-1)^2, (Y1^-1 * Y3)^2, (Y3^-1 * Y2^-1)^2, Y1 * Y2 * Y1^-1 * Y2, (R * Y1)^2, Y1^4, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2^-1 * Y1 * Y3^-1 * Y2^-1 * Y1^-1, Y2^6, Y1^-1 * Y2 * Y3 * Y2^-1 * Y3^-1 * Y1^-1, Y1 * Y3 * Y2^-1 * Y3^-1 * Y2 * Y1, Y2 * Y1^-1 * R * Y2^-1 * R * Y1^-1, Y2 * Y3 * Y1^-1 * Y2^-1 * Y3^-1 * Y1^-1, Y3^-1 * Y2 * Y3^-1 * Y2^3, (Y3^-2 * Y2)^2, Y2^-2 * Y3^-1 * Y2 * Y3^-1 * Y2^-1, Y3^4 * Y2^-2 ] Map:: non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 11, 59, 27, 75, 15, 63)(4, 52, 17, 65, 28, 76, 12, 60)(6, 54, 9, 57, 29, 77, 21, 69)(7, 55, 22, 70, 30, 78, 10, 58)(13, 61, 38, 86, 26, 74, 35, 83)(14, 62, 32, 80, 18, 66, 34, 82)(16, 64, 36, 84, 25, 73, 37, 85)(19, 67, 40, 88, 24, 72, 31, 79)(20, 68, 33, 81, 23, 71, 39, 87)(41, 89, 45, 93, 44, 92, 48, 96)(42, 90, 46, 94, 43, 91, 47, 95)(97, 145, 99, 147, 109, 157, 137, 185, 120, 168, 102, 150)(98, 146, 105, 153, 127, 175, 141, 189, 134, 182, 107, 155)(100, 148, 114, 162, 126, 174, 112, 160, 139, 187, 116, 164)(101, 149, 117, 165, 136, 184, 144, 192, 131, 179, 111, 159)(103, 151, 121, 169, 138, 186, 119, 167, 124, 172, 110, 158)(104, 152, 123, 171, 122, 170, 140, 188, 115, 163, 125, 173)(106, 154, 130, 178, 113, 161, 129, 177, 143, 191, 132, 180)(108, 156, 135, 183, 142, 190, 133, 181, 118, 166, 128, 176) L = (1, 100)(2, 106)(3, 110)(4, 115)(5, 118)(6, 119)(7, 97)(8, 124)(9, 128)(10, 131)(11, 133)(12, 98)(13, 126)(14, 125)(15, 132)(16, 99)(17, 101)(18, 102)(19, 138)(20, 137)(21, 130)(22, 134)(23, 140)(24, 139)(25, 123)(26, 103)(27, 114)(28, 120)(29, 116)(30, 104)(31, 113)(32, 111)(33, 105)(34, 107)(35, 142)(36, 141)(37, 144)(38, 143)(39, 117)(40, 108)(41, 121)(42, 109)(43, 122)(44, 112)(45, 135)(46, 127)(47, 136)(48, 129)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 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 E23.471 Graph:: simple bipartite v = 20 e = 96 f = 32 degree seq :: [ 8^12, 12^8 ] E23.460 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C3 x ((C4 x C2) : C2) (small group id <48, 47>) Aut = (D8 x S3) : C2 (small group id <96, 216>) |r| :: 2 Presentation :: [ R^2, Y3^2 * Y1^2, Y1^4, Y3^-2 * Y1^2, Y3 * Y2 * Y3 * Y2^-1, (Y3, Y1^-1), (R * Y3)^2, (R * Y1)^2, (Y2, Y1^-1), (R * Y2 * Y3^-1)^2, Y2 * Y1 * Y3 * Y2^-1 * Y1^-1 * Y3, Y2^6 ] Map:: non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 9, 57, 21, 69, 15, 63)(4, 52, 10, 58, 7, 55, 12, 60)(6, 54, 11, 59, 22, 70, 18, 66)(13, 61, 23, 71, 36, 84, 31, 79)(14, 62, 24, 72, 16, 64, 25, 73)(17, 65, 26, 74, 19, 67, 27, 75)(20, 68, 28, 76, 37, 85, 34, 82)(29, 77, 38, 86, 46, 94, 44, 92)(30, 78, 39, 87, 32, 80, 40, 88)(33, 81, 41, 89, 35, 83, 42, 90)(43, 91, 47, 95, 45, 93, 48, 96)(97, 145, 99, 147, 109, 157, 125, 173, 116, 164, 102, 150)(98, 146, 105, 153, 119, 167, 134, 182, 124, 172, 107, 155)(100, 148, 112, 160, 126, 174, 141, 189, 129, 177, 113, 161)(101, 149, 111, 159, 127, 175, 140, 188, 130, 178, 114, 162)(103, 151, 110, 158, 128, 176, 139, 187, 131, 179, 115, 163)(104, 152, 117, 165, 132, 180, 142, 190, 133, 181, 118, 166)(106, 154, 121, 169, 135, 183, 144, 192, 137, 185, 122, 170)(108, 156, 120, 168, 136, 184, 143, 191, 138, 186, 123, 171) L = (1, 100)(2, 106)(3, 110)(4, 104)(5, 108)(6, 115)(7, 97)(8, 103)(9, 120)(10, 101)(11, 123)(12, 98)(13, 126)(14, 117)(15, 121)(16, 99)(17, 102)(18, 122)(19, 118)(20, 129)(21, 112)(22, 113)(23, 135)(24, 111)(25, 105)(26, 107)(27, 114)(28, 137)(29, 139)(30, 132)(31, 136)(32, 109)(33, 133)(34, 138)(35, 116)(36, 128)(37, 131)(38, 143)(39, 127)(40, 119)(41, 130)(42, 124)(43, 142)(44, 144)(45, 125)(46, 141)(47, 140)(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, 12, 4, 12, 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E23.472 Graph:: simple bipartite v = 20 e = 96 f = 32 degree seq :: [ 8^12, 12^8 ] E23.461 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C6 x D8 (small group id <48, 45>) Aut = C2 x D8 x S3 (small group id <96, 209>) |r| :: 2 Presentation :: [ R^2, Y2^2, (R * Y2)^2, (R * Y3)^2, Y3^-1 * Y1^-1 * Y3^-1 * Y1, (R * Y1)^2, Y2 * Y1 * Y2 * Y1^-1, Y3 * Y2 * Y3^-1 * Y2, Y3^4, Y1^6 ] Map:: non-degenerate R = (1, 49, 2, 50, 7, 55, 18, 66, 17, 65, 5, 53)(3, 51, 8, 56, 19, 67, 32, 80, 28, 76, 12, 60)(4, 52, 10, 58, 20, 68, 34, 82, 30, 78, 15, 63)(6, 54, 9, 57, 21, 69, 33, 81, 31, 79, 16, 64)(11, 59, 23, 71, 35, 83, 44, 92, 40, 88, 26, 74)(13, 61, 22, 70, 36, 84, 43, 91, 41, 89, 27, 75)(14, 62, 24, 72, 37, 85, 45, 93, 42, 90, 29, 77)(25, 73, 38, 86, 46, 94, 48, 96, 47, 95, 39, 87)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 107, 155)(101, 149, 108, 156)(102, 150, 109, 157)(103, 151, 115, 163)(105, 153, 118, 166)(106, 154, 119, 167)(110, 158, 121, 169)(111, 159, 122, 170)(112, 160, 123, 171)(113, 161, 124, 172)(114, 162, 128, 176)(116, 164, 131, 179)(117, 165, 132, 180)(120, 168, 134, 182)(125, 173, 135, 183)(126, 174, 136, 184)(127, 175, 137, 185)(129, 177, 139, 187)(130, 178, 140, 188)(133, 181, 142, 190)(138, 186, 143, 191)(141, 189, 144, 192) L = (1, 100)(2, 105)(3, 107)(4, 110)(5, 112)(6, 97)(7, 116)(8, 118)(9, 120)(10, 98)(11, 121)(12, 123)(13, 99)(14, 102)(15, 101)(16, 125)(17, 126)(18, 129)(19, 131)(20, 133)(21, 103)(22, 134)(23, 104)(24, 106)(25, 109)(26, 108)(27, 135)(28, 136)(29, 111)(30, 138)(31, 113)(32, 139)(33, 141)(34, 114)(35, 142)(36, 115)(37, 117)(38, 119)(39, 122)(40, 143)(41, 124)(42, 127)(43, 144)(44, 128)(45, 130)(46, 132)(47, 137)(48, 140)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E23.454 Graph:: simple bipartite v = 32 e = 96 f = 20 degree seq :: [ 4^24, 12^8 ] E23.462 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C6 x D8 (small group id <48, 45>) Aut = C2 x D8 x S3 (small group id <96, 209>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (R * Y3)^2, Y1^-1 * Y2 * Y1 * Y2, Y1^-1 * Y3 * Y1 * Y3, (R * Y1)^2, (R * Y2 * Y3)^2, Y1^6, (Y3 * Y2)^4 ] Map:: non-degenerate R = (1, 49, 2, 50, 6, 54, 14, 62, 13, 61, 5, 53)(3, 51, 7, 55, 15, 63, 25, 73, 21, 69, 10, 58)(4, 52, 8, 56, 16, 64, 26, 74, 24, 72, 12, 60)(9, 57, 17, 65, 27, 75, 36, 84, 33, 81, 20, 68)(11, 59, 18, 66, 28, 76, 37, 85, 35, 83, 23, 71)(19, 67, 29, 77, 38, 86, 44, 92, 42, 90, 32, 80)(22, 70, 30, 78, 39, 87, 45, 93, 43, 91, 34, 82)(31, 79, 40, 88, 46, 94, 48, 96, 47, 95, 41, 89)(97, 145, 99, 147)(98, 146, 103, 151)(100, 148, 107, 155)(101, 149, 106, 154)(102, 150, 111, 159)(104, 152, 114, 162)(105, 153, 115, 163)(108, 156, 119, 167)(109, 157, 117, 165)(110, 158, 121, 169)(112, 160, 124, 172)(113, 161, 125, 173)(116, 164, 128, 176)(118, 166, 127, 175)(120, 168, 131, 179)(122, 170, 133, 181)(123, 171, 134, 182)(126, 174, 136, 184)(129, 177, 138, 186)(130, 178, 137, 185)(132, 180, 140, 188)(135, 183, 142, 190)(139, 187, 143, 191)(141, 189, 144, 192) L = (1, 100)(2, 104)(3, 105)(4, 97)(5, 108)(6, 112)(7, 113)(8, 98)(9, 99)(10, 116)(11, 118)(12, 101)(13, 120)(14, 122)(15, 123)(16, 102)(17, 103)(18, 126)(19, 127)(20, 106)(21, 129)(22, 107)(23, 130)(24, 109)(25, 132)(26, 110)(27, 111)(28, 135)(29, 136)(30, 114)(31, 115)(32, 137)(33, 117)(34, 119)(35, 139)(36, 121)(37, 141)(38, 142)(39, 124)(40, 125)(41, 128)(42, 143)(43, 131)(44, 144)(45, 133)(46, 134)(47, 138)(48, 140)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E23.452 Graph:: simple bipartite v = 32 e = 96 f = 20 degree seq :: [ 4^24, 12^8 ] E23.463 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C6 x D8 (small group id <48, 45>) Aut = C2 x D8 x S3 (small group id <96, 209>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (R * Y3)^2, Y1^-1 * Y3 * Y1 * Y3, (R * Y1)^2, Y3 * Y2 * Y3 * Y1 * Y2 * Y1^-1, Y3 * Y2 * Y3 * Y1^-1 * Y2 * Y1, (R * Y2 * Y3)^2, Y1^6, (Y1 * Y2 * Y1^-1 * Y2)^2, Y2 * Y3 * Y2 * Y1 * Y2 * Y3 * Y2 * Y1^-1 ] Map:: non-degenerate R = (1, 49, 2, 50, 6, 54, 16, 64, 15, 63, 5, 53)(3, 51, 9, 57, 17, 65, 33, 81, 27, 75, 11, 59)(4, 52, 8, 56, 18, 66, 32, 80, 29, 77, 13, 61)(7, 55, 19, 67, 31, 79, 30, 78, 14, 62, 21, 69)(10, 58, 22, 70, 34, 82, 44, 92, 40, 88, 25, 73)(12, 60, 20, 68, 35, 83, 43, 91, 42, 90, 28, 76)(23, 71, 36, 84, 45, 93, 41, 89, 26, 74, 38, 86)(24, 72, 37, 85, 46, 94, 48, 96, 47, 95, 39, 87)(97, 145, 99, 147)(98, 146, 103, 151)(100, 148, 108, 156)(101, 149, 110, 158)(102, 150, 113, 161)(104, 152, 118, 166)(105, 153, 119, 167)(106, 154, 120, 168)(107, 155, 122, 170)(109, 157, 121, 169)(111, 159, 123, 171)(112, 160, 127, 175)(114, 162, 131, 179)(115, 163, 132, 180)(116, 164, 133, 181)(117, 165, 134, 182)(124, 172, 135, 183)(125, 173, 138, 186)(126, 174, 137, 185)(128, 176, 140, 188)(129, 177, 141, 189)(130, 178, 142, 190)(136, 184, 143, 191)(139, 187, 144, 192) L = (1, 100)(2, 104)(3, 106)(4, 97)(5, 109)(6, 114)(7, 116)(8, 98)(9, 118)(10, 99)(11, 121)(12, 117)(13, 101)(14, 124)(15, 125)(16, 128)(17, 130)(18, 102)(19, 131)(20, 103)(21, 108)(22, 105)(23, 133)(24, 134)(25, 107)(26, 135)(27, 136)(28, 110)(29, 111)(30, 138)(31, 139)(32, 112)(33, 140)(34, 113)(35, 115)(36, 142)(37, 119)(38, 120)(39, 122)(40, 123)(41, 143)(42, 126)(43, 127)(44, 129)(45, 144)(46, 132)(47, 137)(48, 141)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E23.449 Graph:: simple bipartite v = 32 e = 96 f = 20 degree seq :: [ 4^24, 12^8 ] E23.464 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = D8 x S3 (small group id <48, 38>) Aut = C2 x D8 x S3 (small group id <96, 209>) |r| :: 2 Presentation :: [ R^2, Y2^2, (R * Y2)^2, Y3^-1 * Y1 * Y3^-1 * Y1^-1, (R * Y1)^2, Y3 * Y2 * Y3^-1 * Y2, (R * Y3)^2, (Y2 * Y1^-1)^2, Y3^4, Y1^6 ] Map:: non-degenerate R = (1, 49, 2, 50, 7, 55, 18, 66, 17, 65, 5, 53)(3, 51, 11, 59, 25, 73, 32, 80, 19, 67, 8, 56)(4, 52, 10, 58, 20, 68, 34, 82, 30, 78, 15, 63)(6, 54, 9, 57, 21, 69, 33, 81, 31, 79, 16, 64)(12, 60, 27, 75, 39, 87, 44, 92, 35, 83, 23, 71)(13, 61, 26, 74, 40, 88, 43, 91, 36, 84, 22, 70)(14, 62, 24, 72, 37, 85, 45, 93, 42, 90, 29, 77)(28, 76, 41, 89, 47, 95, 48, 96, 46, 94, 38, 86)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 108, 156)(101, 149, 107, 155)(102, 150, 109, 157)(103, 151, 115, 163)(105, 153, 118, 166)(106, 154, 119, 167)(110, 158, 124, 172)(111, 159, 123, 171)(112, 160, 122, 170)(113, 161, 121, 169)(114, 162, 128, 176)(116, 164, 131, 179)(117, 165, 132, 180)(120, 168, 134, 182)(125, 173, 137, 185)(126, 174, 135, 183)(127, 175, 136, 184)(129, 177, 139, 187)(130, 178, 140, 188)(133, 181, 142, 190)(138, 186, 143, 191)(141, 189, 144, 192) L = (1, 100)(2, 105)(3, 108)(4, 110)(5, 112)(6, 97)(7, 116)(8, 118)(9, 120)(10, 98)(11, 122)(12, 124)(13, 99)(14, 102)(15, 101)(16, 125)(17, 126)(18, 129)(19, 131)(20, 133)(21, 103)(22, 134)(23, 104)(24, 106)(25, 135)(26, 137)(27, 107)(28, 109)(29, 111)(30, 138)(31, 113)(32, 139)(33, 141)(34, 114)(35, 142)(36, 115)(37, 117)(38, 119)(39, 143)(40, 121)(41, 123)(42, 127)(43, 144)(44, 128)(45, 130)(46, 132)(47, 136)(48, 140)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E23.455 Graph:: simple bipartite v = 32 e = 96 f = 20 degree seq :: [ 4^24, 12^8 ] E23.465 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = D8 x S3 (small group id <48, 38>) Aut = C2 x D8 x S3 (small group id <96, 209>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3 * Y1^-1)^2, (Y2 * Y1^-1)^2, (R * Y3)^2, (R * Y1^-1)^2, Y1^-1 * R * Y1 * Y2 * R * Y2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y1^-2 * Y3 * Y1^2, (Y3^-1 * Y2 * Y3^-1)^2, Y2 * Y3^-1 * Y2 * Y1^-1 * Y3^-1 * Y1, Y1 * Y3^-1 * Y1^-1 * Y2 * Y3^-1 * Y2, Y3 * Y1 * Y3^-3 * Y1, (Y3^2 * Y1)^2, Y3^-1 * Y1^-3 * Y3^-1 * Y1^-1, Y1^6, Y3^-1 * Y2 * Y3^-1 * Y2 * Y3 * Y2 * Y3 * Y2 ] Map:: non-degenerate R = (1, 49, 2, 50, 7, 55, 23, 71, 18, 66, 5, 53)(3, 51, 11, 59, 35, 83, 42, 90, 24, 72, 8, 56)(4, 52, 14, 62, 25, 73, 19, 67, 33, 81, 10, 58)(6, 54, 17, 65, 26, 74, 9, 57, 29, 77, 21, 69)(12, 60, 37, 85, 44, 92, 28, 76, 15, 63, 32, 80)(13, 61, 27, 75, 20, 68, 36, 84, 43, 91, 30, 78)(16, 64, 31, 79, 22, 70, 34, 82, 45, 93, 40, 88)(38, 86, 47, 95, 39, 87, 48, 96, 41, 89, 46, 94)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 111, 159)(101, 149, 107, 155)(102, 150, 116, 164)(103, 151, 120, 168)(105, 153, 126, 174)(106, 154, 128, 176)(108, 156, 129, 177)(109, 157, 122, 170)(110, 158, 124, 172)(112, 160, 135, 183)(113, 161, 123, 171)(114, 162, 131, 179)(115, 163, 133, 181)(117, 165, 132, 180)(118, 166, 134, 182)(119, 167, 138, 186)(121, 169, 140, 188)(125, 173, 139, 187)(127, 175, 143, 191)(130, 178, 142, 190)(136, 184, 144, 192)(137, 185, 141, 189) L = (1, 100)(2, 105)(3, 108)(4, 112)(5, 113)(6, 97)(7, 121)(8, 123)(9, 127)(10, 98)(11, 132)(12, 134)(13, 99)(14, 119)(15, 137)(16, 125)(17, 136)(18, 129)(19, 101)(20, 131)(21, 130)(22, 102)(23, 117)(24, 111)(25, 118)(26, 103)(27, 142)(28, 104)(29, 114)(30, 144)(31, 115)(32, 107)(33, 141)(34, 106)(35, 140)(36, 143)(37, 138)(38, 139)(39, 109)(40, 110)(41, 116)(42, 126)(43, 120)(44, 135)(45, 122)(46, 133)(47, 124)(48, 128)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E23.457 Graph:: simple bipartite v = 32 e = 96 f = 20 degree seq :: [ 4^24, 12^8 ] E23.466 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C2 x ((C6 x C2) : C2) (small group id <48, 43>) Aut = C2 x D8 x S3 (small group id <96, 209>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (R * Y3)^2, Y3 * Y1 * Y3 * Y1^-1, (Y2 * Y1^-1)^2, (R * Y1)^2, (R * Y2 * Y3)^2, Y1^6, (Y3 * Y2)^4 ] Map:: non-degenerate R = (1, 49, 2, 50, 6, 54, 14, 62, 13, 61, 5, 53)(3, 51, 9, 57, 19, 67, 25, 73, 15, 63, 7, 55)(4, 52, 8, 56, 16, 64, 26, 74, 24, 72, 12, 60)(10, 58, 20, 68, 31, 79, 36, 84, 27, 75, 17, 65)(11, 59, 22, 70, 34, 82, 37, 85, 28, 76, 18, 66)(21, 69, 29, 77, 38, 86, 44, 92, 41, 89, 32, 80)(23, 71, 35, 83, 43, 91, 45, 93, 39, 87, 30, 78)(33, 81, 40, 88, 46, 94, 48, 96, 47, 95, 42, 90)(97, 145, 99, 147)(98, 146, 103, 151)(100, 148, 107, 155)(101, 149, 105, 153)(102, 150, 111, 159)(104, 152, 114, 162)(106, 154, 117, 165)(108, 156, 118, 166)(109, 157, 115, 163)(110, 158, 121, 169)(112, 160, 124, 172)(113, 161, 125, 173)(116, 164, 128, 176)(119, 167, 129, 177)(120, 168, 130, 178)(122, 170, 133, 181)(123, 171, 134, 182)(126, 174, 136, 184)(127, 175, 137, 185)(131, 179, 138, 186)(132, 180, 140, 188)(135, 183, 142, 190)(139, 187, 143, 191)(141, 189, 144, 192) L = (1, 100)(2, 104)(3, 106)(4, 97)(5, 108)(6, 112)(7, 113)(8, 98)(9, 116)(10, 99)(11, 119)(12, 101)(13, 120)(14, 122)(15, 123)(16, 102)(17, 103)(18, 126)(19, 127)(20, 105)(21, 129)(22, 131)(23, 107)(24, 109)(25, 132)(26, 110)(27, 111)(28, 135)(29, 136)(30, 114)(31, 115)(32, 138)(33, 117)(34, 139)(35, 118)(36, 121)(37, 141)(38, 142)(39, 124)(40, 125)(41, 143)(42, 128)(43, 130)(44, 144)(45, 133)(46, 134)(47, 137)(48, 140)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E23.453 Graph:: simple bipartite v = 32 e = 96 f = 20 degree seq :: [ 4^24, 12^8 ] E23.467 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C2 x ((C6 x C2) : C2) (small group id <48, 43>) Aut = C2 x D8 x S3 (small group id <96, 209>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (R * Y3)^2, (R * Y1)^2, Y3 * Y1 * Y3 * Y1^-1, Y1^-1 * Y2 * Y1^-1 * R * Y2 * R, (Y2 * Y1^-1 * Y3)^2, Y3 * Y2 * Y3 * R * Y2 * R, Y1^6, Y2 * R * Y2 * R * Y2 * Y1^-1 * Y2 * Y1^-1 ] Map:: non-degenerate R = (1, 49, 2, 50, 6, 54, 16, 64, 15, 63, 5, 53)(3, 51, 9, 57, 23, 71, 34, 82, 17, 65, 11, 59)(4, 52, 8, 56, 18, 66, 32, 80, 29, 77, 13, 61)(7, 55, 19, 67, 14, 62, 30, 78, 31, 79, 21, 69)(10, 58, 25, 73, 39, 87, 44, 92, 33, 81, 22, 70)(12, 60, 28, 76, 42, 90, 43, 91, 35, 83, 20, 68)(24, 72, 36, 84, 27, 75, 38, 86, 46, 94, 41, 89)(26, 74, 37, 85, 45, 93, 48, 96, 47, 95, 40, 88)(97, 145, 99, 147)(98, 146, 103, 151)(100, 148, 108, 156)(101, 149, 110, 158)(102, 150, 113, 161)(104, 152, 118, 166)(105, 153, 120, 168)(106, 154, 122, 170)(107, 155, 123, 171)(109, 157, 121, 169)(111, 159, 119, 167)(112, 160, 127, 175)(114, 162, 131, 179)(115, 163, 132, 180)(116, 164, 133, 181)(117, 165, 134, 182)(124, 172, 136, 184)(125, 173, 138, 186)(126, 174, 137, 185)(128, 176, 140, 188)(129, 177, 141, 189)(130, 178, 142, 190)(135, 183, 143, 191)(139, 187, 144, 192) L = (1, 100)(2, 104)(3, 106)(4, 97)(5, 109)(6, 114)(7, 116)(8, 98)(9, 121)(10, 99)(11, 118)(12, 115)(13, 101)(14, 124)(15, 125)(16, 128)(17, 129)(18, 102)(19, 108)(20, 103)(21, 131)(22, 107)(23, 135)(24, 136)(25, 105)(26, 132)(27, 133)(28, 110)(29, 111)(30, 138)(31, 139)(32, 112)(33, 113)(34, 140)(35, 117)(36, 122)(37, 123)(38, 141)(39, 119)(40, 120)(41, 143)(42, 126)(43, 127)(44, 130)(45, 134)(46, 144)(47, 137)(48, 142)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E23.450 Graph:: simple bipartite v = 32 e = 96 f = 20 degree seq :: [ 4^24, 12^8 ] E23.468 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C2 x ((C6 x C2) : C2) (small group id <48, 43>) Aut = C2 x D8 x S3 (small group id <96, 209>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3 * Y1^-1)^2, (Y2 * Y1)^2, (R * Y3)^2, (R * Y1)^2, Y1^-2 * Y3^2, Y3^6, Y3^2 * Y1^4, Y2 * Y1^-2 * Y2 * Y3^-2, (R * Y2 * Y3^-1)^2, (Y3 * Y2)^4, (Y3^-1 * Y1^-1)^6 ] Map:: non-degenerate R = (1, 49, 2, 50, 7, 55, 18, 66, 15, 63, 5, 53)(3, 51, 11, 59, 25, 73, 33, 81, 19, 67, 8, 56)(4, 52, 9, 57, 20, 68, 16, 64, 6, 54, 10, 58)(12, 60, 26, 74, 34, 82, 22, 70, 13, 61, 21, 69)(14, 62, 24, 72, 17, 65, 31, 79, 35, 83, 23, 71)(27, 75, 36, 84, 28, 76, 37, 85, 45, 93, 41, 89)(29, 77, 40, 88, 32, 80, 39, 87, 30, 78, 38, 86)(42, 90, 46, 94, 44, 92, 48, 96, 43, 91, 47, 95)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 110, 158)(101, 149, 107, 155)(102, 150, 113, 161)(103, 151, 115, 163)(105, 153, 119, 167)(106, 154, 120, 168)(108, 156, 123, 171)(109, 157, 124, 172)(111, 159, 121, 169)(112, 160, 127, 175)(114, 162, 129, 177)(116, 164, 131, 179)(117, 165, 132, 180)(118, 166, 133, 181)(122, 170, 137, 185)(125, 173, 138, 186)(126, 174, 140, 188)(128, 176, 139, 187)(130, 178, 141, 189)(134, 182, 142, 190)(135, 183, 144, 192)(136, 184, 143, 191) L = (1, 100)(2, 105)(3, 108)(4, 103)(5, 106)(6, 97)(7, 116)(8, 117)(9, 114)(10, 98)(11, 122)(12, 121)(13, 99)(14, 125)(15, 102)(16, 101)(17, 128)(18, 112)(19, 109)(20, 111)(21, 107)(22, 104)(23, 134)(24, 136)(25, 130)(26, 129)(27, 138)(28, 140)(29, 113)(30, 110)(31, 135)(32, 131)(33, 118)(34, 115)(35, 126)(36, 142)(37, 144)(38, 120)(39, 119)(40, 127)(41, 143)(42, 124)(43, 123)(44, 141)(45, 139)(46, 133)(47, 132)(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 ) } Outer automorphisms :: reflexible Dual of E23.456 Graph:: simple bipartite v = 32 e = 96 f = 20 degree seq :: [ 4^24, 12^8 ] E23.469 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C2 x ((C6 x C2) : C2) (small group id <48, 43>) Aut = C2 x D8 x S3 (small group id <96, 209>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2 * Y1^-2, (Y3, Y1^-1), (R * Y3)^2, (R * Y1)^2, Y1^-6, Y1^-1 * Y2 * Y3^-2 * Y2 * Y1^-1, Y3 * Y2 * Y3 * Y1^-1 * Y2 * Y1^-1, (R * Y2 * Y3^-1)^2, Y3^6, Y3 * Y2 * Y3 * Y1 * Y2 * Y1, (Y1^-1 * Y2 * R * Y2)^2, (Y1 * Y2)^4, (Y2 * Y3^-1 * Y2 * Y1^-1)^2 ] Map:: non-degenerate R = (1, 49, 2, 50, 7, 55, 20, 68, 17, 65, 5, 53)(3, 51, 11, 59, 29, 77, 38, 86, 21, 69, 13, 61)(4, 52, 9, 57, 22, 70, 18, 66, 6, 54, 10, 58)(8, 56, 23, 71, 16, 64, 35, 83, 37, 85, 25, 73)(12, 60, 31, 79, 39, 87, 27, 75, 14, 62, 28, 76)(15, 63, 24, 72, 19, 67, 36, 84, 40, 88, 26, 74)(30, 78, 41, 89, 33, 81, 43, 91, 47, 95, 45, 93)(32, 80, 42, 90, 34, 82, 44, 92, 48, 96, 46, 94)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 111, 159)(101, 149, 112, 160)(102, 150, 115, 163)(103, 151, 117, 165)(105, 153, 123, 171)(106, 154, 124, 172)(107, 155, 126, 174)(108, 156, 128, 176)(109, 157, 129, 177)(110, 158, 130, 178)(113, 161, 125, 173)(114, 162, 127, 175)(116, 164, 133, 181)(118, 166, 136, 184)(119, 167, 137, 185)(120, 168, 138, 186)(121, 169, 139, 187)(122, 170, 140, 188)(131, 179, 141, 189)(132, 180, 142, 190)(134, 182, 143, 191)(135, 183, 144, 192) L = (1, 100)(2, 105)(3, 108)(4, 103)(5, 106)(6, 97)(7, 118)(8, 120)(9, 116)(10, 98)(11, 127)(12, 125)(13, 124)(14, 99)(15, 119)(16, 132)(17, 102)(18, 101)(19, 131)(20, 114)(21, 110)(22, 113)(23, 115)(24, 112)(25, 111)(26, 104)(27, 109)(28, 107)(29, 135)(30, 138)(31, 134)(32, 137)(33, 140)(34, 139)(35, 136)(36, 133)(37, 122)(38, 123)(39, 117)(40, 121)(41, 130)(42, 129)(43, 144)(44, 143)(45, 128)(46, 126)(47, 142)(48, 141)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E23.451 Graph:: simple bipartite v = 32 e = 96 f = 20 degree seq :: [ 4^24, 12^8 ] E23.470 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = (C2 x (C3 : C4)) : C2 (small group id <48, 39>) Aut = (C6 x D8) : C2 (small group id <96, 211>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y2 * Y3^-1 * Y2 * Y3, Y3 * Y1^-1 * Y3 * Y1, (Y2 * R)^2, (R * Y1)^2, Y3^4, (R * Y3)^2, Y3^2 * Y1^-1 * Y2 * Y1^-1 * Y2, Y1^-1 * Y2 * Y1^-1 * Y3^-2 * Y2, (Y2 * Y1^-2)^2, Y1^6 ] Map:: non-degenerate R = (1, 49, 2, 50, 7, 55, 20, 68, 19, 67, 5, 53)(3, 51, 11, 59, 29, 77, 40, 88, 21, 69, 13, 61)(4, 52, 10, 58, 22, 70, 38, 86, 33, 81, 16, 64)(6, 54, 9, 57, 23, 71, 37, 85, 35, 83, 18, 66)(8, 56, 24, 72, 17, 65, 34, 82, 36, 84, 26, 74)(12, 60, 32, 80, 43, 91, 46, 94, 39, 87, 25, 73)(14, 62, 31, 79, 44, 92, 47, 95, 41, 89, 27, 75)(15, 63, 28, 76, 42, 90, 48, 96, 45, 93, 30, 78)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 108, 156)(101, 149, 113, 161)(102, 150, 110, 158)(103, 151, 117, 165)(105, 153, 121, 169)(106, 154, 123, 171)(107, 155, 126, 174)(109, 157, 124, 172)(111, 159, 120, 168)(112, 160, 127, 175)(114, 162, 128, 176)(115, 163, 125, 173)(116, 164, 132, 180)(118, 166, 135, 183)(119, 167, 137, 185)(122, 170, 138, 186)(129, 177, 139, 187)(130, 178, 141, 189)(131, 179, 140, 188)(133, 181, 142, 190)(134, 182, 143, 191)(136, 184, 144, 192) L = (1, 100)(2, 105)(3, 108)(4, 111)(5, 114)(6, 97)(7, 118)(8, 121)(9, 124)(10, 98)(11, 127)(12, 120)(13, 123)(14, 99)(15, 102)(16, 101)(17, 128)(18, 126)(19, 129)(20, 133)(21, 135)(22, 138)(23, 103)(24, 110)(25, 109)(26, 137)(27, 104)(28, 106)(29, 139)(30, 112)(31, 113)(32, 107)(33, 141)(34, 140)(35, 115)(36, 142)(37, 144)(38, 116)(39, 122)(40, 143)(41, 117)(42, 119)(43, 130)(44, 125)(45, 131)(46, 136)(47, 132)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E23.458 Graph:: simple bipartite v = 32 e = 96 f = 20 degree seq :: [ 4^24, 12^8 ] E23.471 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = (C2 x (C3 : C4)) : C2 (small group id <48, 39>) Aut = (C6 x D8) : C2 (small group id <96, 211>) |r| :: 2 Presentation :: [ R^2, Y2^2, (R * Y3^-1)^2, (Y1^-1 * Y3)^2, (R * Y1)^2, Y2 * Y3^-1 * Y1 * Y3 * Y2 * Y1, Y1^3 * Y3^-1 * Y1^-1 * Y3^-1, (R * Y2 * Y3^-1)^2, Y1^-2 * R * Y2 * R * Y2, Y2 * Y1 * Y3^-2 * Y2 * Y1^-1, Y3^2 * Y1 * Y3^-2 * Y1^-1, Y2 * Y3 * Y2 * Y1^2 * Y3^-1, (Y3 * Y1 * Y3)^2, Y1^6, Y2 * Y1^-1 * Y3^-1 * Y2 * Y3^-1 * Y1^-1, Y3 * Y2 * Y1 * Y3^-1 * Y2 * Y1^-1, Y3^-1 * Y2 * Y3^2 * Y2 * Y3^-1 * Y1^-2 ] Map:: non-degenerate R = (1, 49, 2, 50, 7, 55, 25, 73, 20, 68, 5, 53)(3, 51, 11, 59, 39, 87, 45, 93, 26, 74, 13, 61)(4, 52, 15, 63, 27, 75, 21, 69, 37, 85, 10, 58)(6, 54, 19, 67, 28, 76, 9, 57, 33, 81, 23, 71)(8, 56, 29, 77, 18, 66, 42, 90, 44, 92, 31, 79)(12, 60, 41, 89, 47, 95, 34, 82, 16, 64, 30, 78)(14, 62, 36, 84, 22, 70, 40, 88, 46, 94, 32, 80)(17, 65, 35, 83, 24, 72, 38, 86, 48, 96, 43, 91)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 112, 160)(101, 149, 114, 162)(102, 150, 118, 166)(103, 151, 122, 170)(105, 153, 130, 178)(106, 154, 132, 180)(107, 155, 134, 182)(108, 156, 133, 181)(109, 157, 139, 187)(110, 158, 124, 172)(111, 159, 128, 176)(113, 161, 127, 175)(115, 163, 126, 174)(116, 164, 135, 183)(117, 165, 136, 184)(119, 167, 137, 185)(120, 168, 138, 186)(121, 169, 140, 188)(123, 171, 143, 191)(125, 173, 144, 192)(129, 177, 142, 190)(131, 179, 141, 189) L = (1, 100)(2, 105)(3, 108)(4, 113)(5, 115)(6, 97)(7, 123)(8, 126)(9, 131)(10, 98)(11, 136)(12, 138)(13, 132)(14, 99)(15, 121)(16, 125)(17, 129)(18, 137)(19, 139)(20, 133)(21, 101)(22, 135)(23, 134)(24, 102)(25, 119)(26, 112)(27, 120)(28, 103)(29, 118)(30, 107)(31, 110)(32, 104)(33, 116)(34, 109)(35, 117)(36, 114)(37, 144)(38, 106)(39, 143)(40, 140)(41, 141)(42, 142)(43, 111)(44, 130)(45, 128)(46, 122)(47, 127)(48, 124)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E23.459 Graph:: simple bipartite v = 32 e = 96 f = 20 degree seq :: [ 4^24, 12^8 ] E23.472 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C3 x ((C4 x C2) : C2) (small group id <48, 47>) Aut = (D8 x S3) : C2 (small group id <96, 216>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y2 * Y3^-1 * Y2 * Y3, Y3 * Y1^-1 * Y3 * Y1, (Y2 * R)^2, (R * Y1)^2, Y3^4, (R * Y3)^2, Y1 * Y3^-2 * Y2 * Y1^-1 * Y2, Y3^-2 * Y2 * Y1 * Y2 * Y1^-1, Y1^-2 * Y2 * Y1^2 * Y2, Y1^6 ] Map:: non-degenerate R = (1, 49, 2, 50, 7, 55, 20, 68, 19, 67, 5, 53)(3, 51, 11, 59, 21, 69, 39, 87, 32, 80, 13, 61)(4, 52, 10, 58, 22, 70, 38, 86, 33, 81, 16, 64)(6, 54, 9, 57, 23, 71, 37, 85, 35, 83, 18, 66)(8, 56, 24, 72, 36, 84, 34, 82, 17, 65, 26, 74)(12, 60, 25, 73, 40, 88, 46, 94, 43, 91, 29, 77)(14, 62, 27, 75, 41, 89, 47, 95, 45, 93, 31, 79)(15, 63, 28, 76, 42, 90, 48, 96, 44, 92, 30, 78)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 108, 156)(101, 149, 113, 161)(102, 150, 110, 158)(103, 151, 117, 165)(105, 153, 121, 169)(106, 154, 123, 171)(107, 155, 124, 172)(109, 157, 126, 174)(111, 159, 122, 170)(112, 160, 127, 175)(114, 162, 125, 173)(115, 163, 128, 176)(116, 164, 132, 180)(118, 166, 136, 184)(119, 167, 137, 185)(120, 168, 138, 186)(129, 177, 139, 187)(130, 178, 140, 188)(131, 179, 141, 189)(133, 181, 142, 190)(134, 182, 143, 191)(135, 183, 144, 192) L = (1, 100)(2, 105)(3, 108)(4, 111)(5, 114)(6, 97)(7, 118)(8, 121)(9, 124)(10, 98)(11, 123)(12, 122)(13, 127)(14, 99)(15, 102)(16, 101)(17, 125)(18, 126)(19, 129)(20, 133)(21, 136)(22, 138)(23, 103)(24, 137)(25, 107)(26, 110)(27, 104)(28, 106)(29, 109)(30, 112)(31, 113)(32, 139)(33, 140)(34, 141)(35, 115)(36, 142)(37, 144)(38, 116)(39, 143)(40, 120)(41, 117)(42, 119)(43, 130)(44, 131)(45, 128)(46, 135)(47, 132)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E23.460 Graph:: simple bipartite v = 32 e = 96 f = 20 degree seq :: [ 4^24, 12^8 ] E23.473 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C6 x D8 (small group id <48, 45>) Aut = C2 x D8 x S3 (small group id <96, 209>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y2^-2 * Y1^-1, Y3^-1 * Y1^-2 * Y3^-1, (Y3^-1, Y2^-1), Y2^-1 * Y3^2 * Y2^-1, (Y2^-1, Y1^-1), (R * Y2)^2, (Y2^-1 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2^2)^2, Y1^-2 * Y2^4, (Y3^-1 * Y1^-1)^4 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50, 8, 56, 22, 70, 13, 61, 5, 53)(3, 51, 9, 57, 6, 54, 11, 59, 23, 71, 15, 63)(4, 52, 17, 65, 7, 55, 21, 69, 24, 72, 18, 66)(10, 58, 27, 75, 12, 60, 30, 78, 19, 67, 28, 76)(14, 62, 31, 79, 16, 64, 33, 81, 20, 68, 32, 80)(25, 73, 37, 85, 26, 74, 39, 87, 29, 77, 38, 86)(34, 82, 40, 88, 35, 83, 41, 89, 36, 84, 42, 90)(43, 91, 46, 94, 44, 92, 47, 95, 45, 93, 48, 96)(97, 145, 99, 147, 109, 157, 119, 167, 104, 152, 102, 150)(98, 146, 105, 153, 101, 149, 111, 159, 118, 166, 107, 155)(100, 148, 110, 158, 120, 168, 116, 164, 103, 151, 112, 160)(106, 154, 121, 169, 115, 163, 125, 173, 108, 156, 122, 170)(113, 161, 127, 175, 114, 162, 128, 176, 117, 165, 129, 177)(123, 171, 133, 181, 124, 172, 134, 182, 126, 174, 135, 183)(130, 178, 139, 187, 132, 180, 141, 189, 131, 179, 140, 188)(136, 184, 142, 190, 138, 186, 144, 192, 137, 185, 143, 191) L = (1, 100)(2, 106)(3, 110)(4, 109)(5, 115)(6, 112)(7, 97)(8, 103)(9, 121)(10, 101)(11, 122)(12, 98)(13, 120)(14, 119)(15, 125)(16, 99)(17, 130)(18, 132)(19, 118)(20, 102)(21, 131)(22, 108)(23, 116)(24, 104)(25, 111)(26, 105)(27, 136)(28, 138)(29, 107)(30, 137)(31, 139)(32, 141)(33, 140)(34, 114)(35, 113)(36, 117)(37, 142)(38, 144)(39, 143)(40, 124)(41, 123)(42, 126)(43, 128)(44, 127)(45, 129)(46, 134)(47, 133)(48, 135)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E23.448 Graph:: bipartite v = 16 e = 96 f = 36 degree seq :: [ 12^16 ] E23.474 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 4, 6, 6}) Quotient :: edge^2 Aut^+ = C2 x S4 (small group id <48, 48>) Aut = C2 x C2 x S4 (small group id <96, 226>) |r| :: 2 Presentation :: [ R^2, Y3^2, (Y1 * Y2)^2, (R * Y3)^2, (Y3 * Y2^-1)^2, R * Y2 * R * Y1, (Y3 * Y1^-1)^2, (Y2 * Y1^-1)^3, Y2 * Y1^-2 * Y2^-2 * Y1, Y1^6, Y2^-1 * Y1^2 * Y2^2 * Y1^-1, Y1 * Y2^-3 * Y1^2 ] Map:: polytopal non-degenerate R = (1, 49, 4, 52)(2, 50, 9, 57)(3, 51, 13, 61)(5, 53, 15, 63)(6, 54, 16, 64)(7, 55, 23, 71)(8, 56, 26, 74)(10, 58, 28, 76)(11, 59, 32, 80)(12, 60, 33, 81)(14, 62, 34, 82)(17, 65, 36, 84)(18, 66, 35, 83)(19, 67, 38, 86)(20, 68, 37, 85)(21, 69, 39, 87)(22, 70, 40, 88)(24, 72, 42, 90)(25, 73, 43, 91)(27, 75, 44, 92)(29, 77, 46, 94)(30, 78, 45, 93)(31, 79, 47, 95)(41, 89, 48, 96)(97, 98, 103, 117, 114, 101)(99, 107, 127, 116, 120, 110)(100, 111, 131, 135, 119, 105)(102, 115, 126, 108, 123, 104)(106, 125, 113, 121, 137, 118)(109, 130, 138, 133, 143, 128)(112, 122, 140, 129, 141, 134)(124, 136, 144, 139, 132, 142)(145, 147, 156, 165, 164, 150)(146, 152, 169, 162, 174, 154)(148, 160, 181, 183, 177, 157)(149, 161, 168, 151, 166, 155)(153, 172, 189, 179, 187, 170)(158, 173, 163, 175, 185, 171)(159, 176, 184, 167, 186, 180)(178, 188, 192, 191, 182, 190) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 16^4 ), ( 16^6 ) } Outer automorphisms :: reflexible Dual of E23.480 Graph:: simple bipartite v = 40 e = 96 f = 12 degree seq :: [ 4^24, 6^16 ] E23.475 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 4, 6, 6}) Quotient :: edge^2 Aut^+ = C2 x S4 (small group id <48, 48>) Aut = C2 x C2 x S4 (small group id <96, 226>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y3 * Y2 * Y3 * Y1^-1, (Y1 * Y2)^2, (R * Y3)^2, R * Y2 * R * Y1, Y2^-3 * Y1^3, Y2^-1 * Y1 * Y2^-1 * Y1^-1 * Y2 * Y1^-1, Y1^-1 * Y2^-3 * Y1^-2, Y1^6, (Y1^-1 * Y2 * Y1^-1)^2, (Y2 * Y1^-1)^3, (Y2^2 * Y1^-1)^2, (Y1 * Y3 * Y1 * Y2^-1)^2 ] Map:: polytopal non-degenerate R = (1, 49, 4, 52)(2, 50, 9, 57)(3, 51, 13, 61)(5, 53, 16, 64)(6, 54, 15, 63)(7, 55, 23, 71)(8, 56, 26, 74)(10, 58, 28, 76)(11, 59, 32, 80)(12, 60, 33, 81)(14, 62, 34, 82)(17, 65, 37, 85)(18, 66, 38, 86)(19, 67, 35, 83)(20, 68, 36, 84)(21, 69, 39, 87)(22, 70, 40, 88)(24, 72, 42, 90)(25, 73, 43, 91)(27, 75, 44, 92)(29, 77, 45, 93)(30, 78, 46, 94)(31, 79, 47, 95)(41, 89, 48, 96)(97, 98, 103, 117, 114, 101)(99, 107, 127, 116, 120, 110)(100, 109, 129, 135, 132, 111)(102, 115, 126, 108, 123, 104)(105, 122, 139, 134, 142, 124)(106, 125, 113, 121, 137, 118)(112, 133, 138, 119, 136, 128)(130, 141, 131, 143, 144, 140)(145, 147, 156, 165, 164, 150)(146, 152, 169, 162, 174, 154)(148, 153, 167, 183, 182, 160)(149, 161, 168, 151, 166, 155)(157, 176, 191, 180, 186, 178)(158, 173, 163, 175, 185, 171)(159, 179, 190, 177, 188, 170)(172, 189, 181, 187, 192, 184) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 16^4 ), ( 16^6 ) } Outer automorphisms :: reflexible Dual of E23.481 Graph:: simple bipartite v = 40 e = 96 f = 12 degree seq :: [ 4^24, 6^16 ] E23.476 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 4, 6, 6}) Quotient :: edge^2 Aut^+ = C2 x S4 (small group id <48, 48>) Aut = C2 x C2 x S4 (small group id <96, 226>) |r| :: 2 Presentation :: [ R^2, (Y2^-1 * Y1^-1)^2, Y1^-1 * Y2^-1 * Y3^-2, (Y3^-1 * Y1^-1)^2, Y2 * Y1 * Y3^-2, Y2 * Y3^-1 * Y1^-1 * Y3, R * Y1 * R * Y2, (R * Y3)^2, (Y2 * Y1^-1)^3, Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1^-1, Y1^-1 * Y3^-1 * Y1 * Y2 * Y3^-1 * Y2^-1, Y1^6, Y2^-3 * Y1^-3, Y2^6, Y3^-1 * Y2 * Y3 * Y1 * Y2 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 49, 4, 52, 13, 61, 7, 55)(2, 50, 10, 58, 6, 54, 12, 60)(3, 51, 15, 63, 32, 80, 17, 65)(5, 53, 20, 68, 30, 78, 18, 66)(8, 56, 27, 75, 11, 59, 29, 77)(9, 57, 31, 79, 46, 94, 33, 81)(14, 62, 38, 86, 22, 70, 39, 87)(16, 64, 41, 89, 21, 69, 40, 88)(19, 67, 26, 74, 45, 93, 37, 85)(23, 71, 34, 82, 24, 72, 42, 90)(25, 73, 43, 91, 28, 76, 44, 92)(35, 83, 47, 95, 36, 84, 48, 96)(97, 98, 104, 121, 118, 101)(99, 109, 133, 120, 124, 112)(100, 114, 137, 139, 125, 115)(102, 119, 132, 110, 128, 105)(103, 113, 135, 140, 130, 106)(107, 131, 117, 126, 142, 122)(108, 129, 116, 134, 143, 123)(111, 136, 144, 138, 141, 127)(145, 147, 158, 169, 168, 150)(146, 153, 174, 166, 180, 155)(148, 154, 171, 187, 183, 164)(149, 165, 172, 152, 170, 157)(151, 163, 186, 188, 185, 159)(156, 178, 192, 182, 161, 175)(160, 179, 167, 181, 190, 176)(162, 177, 189, 173, 191, 184) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8^6 ), ( 8^8 ) } Outer automorphisms :: reflexible Dual of E23.478 Graph:: simple bipartite v = 28 e = 96 f = 24 degree seq :: [ 6^16, 8^12 ] E23.477 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 4, 6, 6}) Quotient :: edge^2 Aut^+ = C2 x S4 (small group id <48, 48>) Aut = C2 x C2 x S4 (small group id <96, 226>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y3^-2 * Y1^-1, Y2 * Y3 * Y1^-1 * Y3^-1, Y3^4, (R * Y3)^2, (Y3^-1 * Y1)^2, Y3^2 * Y2 * Y1, (Y3^-1 * Y2)^2, (Y2 * Y1)^2, R * Y1 * R * Y2, Y3^2 * Y1^-1 * Y2^-1, Y1^-1 * Y3^2 * Y2^-2 * Y1^-1, (Y3^-1 * Y1 * Y2^-1)^2, Y1^-1 * Y3^-1 * Y1 * Y2 * Y3^-1 * Y2^-1, Y2^-1 * Y1 * Y2^-1 * Y1^-1 * Y2 * Y1^-1, (Y2 * Y1^-2)^2, Y1^6, (Y2^2 * Y1^-1)^2, Y2^6 ] Map:: polytopal non-degenerate R = (1, 49, 4, 52, 13, 61, 7, 55)(2, 50, 10, 58, 6, 54, 12, 60)(3, 51, 15, 63, 32, 80, 17, 65)(5, 53, 20, 68, 30, 78, 22, 70)(8, 56, 27, 75, 11, 59, 29, 77)(9, 57, 31, 79, 45, 93, 33, 81)(14, 62, 38, 86, 21, 69, 39, 87)(16, 64, 40, 88, 19, 67, 41, 89)(18, 66, 37, 85, 46, 94, 26, 74)(23, 71, 42, 90, 24, 72, 34, 82)(25, 73, 43, 91, 28, 76, 44, 92)(35, 83, 48, 96, 36, 84, 47, 95)(97, 98, 104, 121, 117, 101)(99, 109, 133, 120, 124, 112)(100, 111, 134, 139, 130, 108)(102, 119, 132, 110, 128, 105)(103, 116, 137, 140, 123, 114)(106, 127, 118, 135, 143, 125)(107, 131, 115, 126, 141, 122)(113, 136, 144, 138, 142, 129)(145, 147, 158, 169, 168, 150)(146, 153, 174, 165, 180, 155)(148, 162, 186, 187, 185, 161)(149, 163, 172, 152, 170, 157)(151, 156, 173, 188, 182, 166)(154, 178, 192, 183, 159, 177)(160, 179, 167, 181, 189, 176)(164, 175, 190, 171, 191, 184) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8^6 ), ( 8^8 ) } Outer automorphisms :: reflexible Dual of E23.479 Graph:: simple bipartite v = 28 e = 96 f = 24 degree seq :: [ 6^16, 8^12 ] E23.478 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 4, 6, 6}) Quotient :: loop^2 Aut^+ = C2 x S4 (small group id <48, 48>) Aut = C2 x C2 x S4 (small group id <96, 226>) |r| :: 2 Presentation :: [ R^2, Y3^2, (Y1 * Y2)^2, (R * Y3)^2, (Y3 * Y2^-1)^2, R * Y2 * R * Y1, (Y3 * Y1^-1)^2, (Y2 * Y1^-1)^3, Y2 * Y1^-2 * Y2^-2 * Y1, Y1^6, Y2^-1 * Y1^2 * Y2^2 * Y1^-1, Y1 * Y2^-3 * Y1^2 ] Map:: polytopal non-degenerate R = (1, 49, 97, 145, 4, 52, 100, 148)(2, 50, 98, 146, 9, 57, 105, 153)(3, 51, 99, 147, 13, 61, 109, 157)(5, 53, 101, 149, 15, 63, 111, 159)(6, 54, 102, 150, 16, 64, 112, 160)(7, 55, 103, 151, 23, 71, 119, 167)(8, 56, 104, 152, 26, 74, 122, 170)(10, 58, 106, 154, 28, 76, 124, 172)(11, 59, 107, 155, 32, 80, 128, 176)(12, 60, 108, 156, 33, 81, 129, 177)(14, 62, 110, 158, 34, 82, 130, 178)(17, 65, 113, 161, 36, 84, 132, 180)(18, 66, 114, 162, 35, 83, 131, 179)(19, 67, 115, 163, 38, 86, 134, 182)(20, 68, 116, 164, 37, 85, 133, 181)(21, 69, 117, 165, 39, 87, 135, 183)(22, 70, 118, 166, 40, 88, 136, 184)(24, 72, 120, 168, 42, 90, 138, 186)(25, 73, 121, 169, 43, 91, 139, 187)(27, 75, 123, 171, 44, 92, 140, 188)(29, 77, 125, 173, 46, 94, 142, 190)(30, 78, 126, 174, 45, 93, 141, 189)(31, 79, 127, 175, 47, 95, 143, 191)(41, 89, 137, 185, 48, 96, 144, 192) L = (1, 50)(2, 55)(3, 59)(4, 63)(5, 49)(6, 67)(7, 69)(8, 54)(9, 52)(10, 77)(11, 79)(12, 75)(13, 82)(14, 51)(15, 83)(16, 74)(17, 73)(18, 53)(19, 78)(20, 72)(21, 66)(22, 58)(23, 57)(24, 62)(25, 89)(26, 92)(27, 56)(28, 88)(29, 65)(30, 60)(31, 68)(32, 61)(33, 93)(34, 90)(35, 87)(36, 94)(37, 95)(38, 64)(39, 71)(40, 96)(41, 70)(42, 85)(43, 84)(44, 81)(45, 86)(46, 76)(47, 80)(48, 91)(97, 147)(98, 152)(99, 156)(100, 160)(101, 161)(102, 145)(103, 166)(104, 169)(105, 172)(106, 146)(107, 149)(108, 165)(109, 148)(110, 173)(111, 176)(112, 181)(113, 168)(114, 174)(115, 175)(116, 150)(117, 164)(118, 155)(119, 186)(120, 151)(121, 162)(122, 153)(123, 158)(124, 189)(125, 163)(126, 154)(127, 185)(128, 184)(129, 157)(130, 188)(131, 187)(132, 159)(133, 183)(134, 190)(135, 177)(136, 167)(137, 171)(138, 180)(139, 170)(140, 192)(141, 179)(142, 178)(143, 182)(144, 191) local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E23.476 Transitivity :: VT+ Graph:: bipartite v = 24 e = 96 f = 28 degree seq :: [ 8^24 ] E23.479 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 4, 6, 6}) Quotient :: loop^2 Aut^+ = C2 x S4 (small group id <48, 48>) Aut = C2 x C2 x S4 (small group id <96, 226>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y3 * Y2 * Y3 * Y1^-1, (Y1 * Y2)^2, (R * Y3)^2, R * Y2 * R * Y1, Y2^-3 * Y1^3, Y2^-1 * Y1 * Y2^-1 * Y1^-1 * Y2 * Y1^-1, Y1^-1 * Y2^-3 * Y1^-2, Y1^6, (Y1^-1 * Y2 * Y1^-1)^2, (Y2 * Y1^-1)^3, (Y2^2 * Y1^-1)^2, (Y1 * Y3 * Y1 * Y2^-1)^2 ] Map:: polytopal non-degenerate R = (1, 49, 97, 145, 4, 52, 100, 148)(2, 50, 98, 146, 9, 57, 105, 153)(3, 51, 99, 147, 13, 61, 109, 157)(5, 53, 101, 149, 16, 64, 112, 160)(6, 54, 102, 150, 15, 63, 111, 159)(7, 55, 103, 151, 23, 71, 119, 167)(8, 56, 104, 152, 26, 74, 122, 170)(10, 58, 106, 154, 28, 76, 124, 172)(11, 59, 107, 155, 32, 80, 128, 176)(12, 60, 108, 156, 33, 81, 129, 177)(14, 62, 110, 158, 34, 82, 130, 178)(17, 65, 113, 161, 37, 85, 133, 181)(18, 66, 114, 162, 38, 86, 134, 182)(19, 67, 115, 163, 35, 83, 131, 179)(20, 68, 116, 164, 36, 84, 132, 180)(21, 69, 117, 165, 39, 87, 135, 183)(22, 70, 118, 166, 40, 88, 136, 184)(24, 72, 120, 168, 42, 90, 138, 186)(25, 73, 121, 169, 43, 91, 139, 187)(27, 75, 123, 171, 44, 92, 140, 188)(29, 77, 125, 173, 45, 93, 141, 189)(30, 78, 126, 174, 46, 94, 142, 190)(31, 79, 127, 175, 47, 95, 143, 191)(41, 89, 137, 185, 48, 96, 144, 192) L = (1, 50)(2, 55)(3, 59)(4, 61)(5, 49)(6, 67)(7, 69)(8, 54)(9, 74)(10, 77)(11, 79)(12, 75)(13, 81)(14, 51)(15, 52)(16, 85)(17, 73)(18, 53)(19, 78)(20, 72)(21, 66)(22, 58)(23, 88)(24, 62)(25, 89)(26, 91)(27, 56)(28, 57)(29, 65)(30, 60)(31, 68)(32, 64)(33, 87)(34, 93)(35, 95)(36, 63)(37, 90)(38, 94)(39, 84)(40, 80)(41, 70)(42, 71)(43, 86)(44, 82)(45, 83)(46, 76)(47, 96)(48, 92)(97, 147)(98, 152)(99, 156)(100, 153)(101, 161)(102, 145)(103, 166)(104, 169)(105, 167)(106, 146)(107, 149)(108, 165)(109, 176)(110, 173)(111, 179)(112, 148)(113, 168)(114, 174)(115, 175)(116, 150)(117, 164)(118, 155)(119, 183)(120, 151)(121, 162)(122, 159)(123, 158)(124, 189)(125, 163)(126, 154)(127, 185)(128, 191)(129, 188)(130, 157)(131, 190)(132, 186)(133, 187)(134, 160)(135, 182)(136, 172)(137, 171)(138, 178)(139, 192)(140, 170)(141, 181)(142, 177)(143, 180)(144, 184) local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E23.477 Transitivity :: VT+ Graph:: bipartite v = 24 e = 96 f = 28 degree seq :: [ 8^24 ] E23.480 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 4, 6, 6}) Quotient :: loop^2 Aut^+ = C2 x S4 (small group id <48, 48>) Aut = C2 x C2 x S4 (small group id <96, 226>) |r| :: 2 Presentation :: [ R^2, (Y2^-1 * Y1^-1)^2, Y1^-1 * Y2^-1 * Y3^-2, (Y3^-1 * Y1^-1)^2, Y2 * Y1 * Y3^-2, Y2 * Y3^-1 * Y1^-1 * Y3, R * Y1 * R * Y2, (R * Y3)^2, (Y2 * Y1^-1)^3, Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1^-1, Y1^-1 * Y3^-1 * Y1 * Y2 * Y3^-1 * Y2^-1, Y1^6, Y2^-3 * Y1^-3, Y2^6, Y3^-1 * Y2 * Y3 * Y1 * Y2 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 49, 97, 145, 4, 52, 100, 148, 13, 61, 109, 157, 7, 55, 103, 151)(2, 50, 98, 146, 10, 58, 106, 154, 6, 54, 102, 150, 12, 60, 108, 156)(3, 51, 99, 147, 15, 63, 111, 159, 32, 80, 128, 176, 17, 65, 113, 161)(5, 53, 101, 149, 20, 68, 116, 164, 30, 78, 126, 174, 18, 66, 114, 162)(8, 56, 104, 152, 27, 75, 123, 171, 11, 59, 107, 155, 29, 77, 125, 173)(9, 57, 105, 153, 31, 79, 127, 175, 46, 94, 142, 190, 33, 81, 129, 177)(14, 62, 110, 158, 38, 86, 134, 182, 22, 70, 118, 166, 39, 87, 135, 183)(16, 64, 112, 160, 41, 89, 137, 185, 21, 69, 117, 165, 40, 88, 136, 184)(19, 67, 115, 163, 26, 74, 122, 170, 45, 93, 141, 189, 37, 85, 133, 181)(23, 71, 119, 167, 34, 82, 130, 178, 24, 72, 120, 168, 42, 90, 138, 186)(25, 73, 121, 169, 43, 91, 139, 187, 28, 76, 124, 172, 44, 92, 140, 188)(35, 83, 131, 179, 47, 95, 143, 191, 36, 84, 132, 180, 48, 96, 144, 192) L = (1, 50)(2, 56)(3, 61)(4, 66)(5, 49)(6, 71)(7, 65)(8, 73)(9, 54)(10, 55)(11, 83)(12, 81)(13, 85)(14, 80)(15, 88)(16, 51)(17, 87)(18, 89)(19, 52)(20, 86)(21, 78)(22, 53)(23, 84)(24, 76)(25, 70)(26, 59)(27, 60)(28, 64)(29, 67)(30, 94)(31, 63)(32, 57)(33, 68)(34, 58)(35, 69)(36, 62)(37, 72)(38, 95)(39, 92)(40, 96)(41, 91)(42, 93)(43, 77)(44, 82)(45, 79)(46, 74)(47, 75)(48, 90)(97, 147)(98, 153)(99, 158)(100, 154)(101, 165)(102, 145)(103, 163)(104, 170)(105, 174)(106, 171)(107, 146)(108, 178)(109, 149)(110, 169)(111, 151)(112, 179)(113, 175)(114, 177)(115, 186)(116, 148)(117, 172)(118, 180)(119, 181)(120, 150)(121, 168)(122, 157)(123, 187)(124, 152)(125, 191)(126, 166)(127, 156)(128, 160)(129, 189)(130, 192)(131, 167)(132, 155)(133, 190)(134, 161)(135, 164)(136, 162)(137, 159)(138, 188)(139, 183)(140, 185)(141, 173)(142, 176)(143, 184)(144, 182) local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E23.474 Transitivity :: VT+ Graph:: bipartite v = 12 e = 96 f = 40 degree seq :: [ 16^12 ] E23.481 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 4, 6, 6}) Quotient :: loop^2 Aut^+ = C2 x S4 (small group id <48, 48>) Aut = C2 x C2 x S4 (small group id <96, 226>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y3^-2 * Y1^-1, Y2 * Y3 * Y1^-1 * Y3^-1, Y3^4, (R * Y3)^2, (Y3^-1 * Y1)^2, Y3^2 * Y2 * Y1, (Y3^-1 * Y2)^2, (Y2 * Y1)^2, R * Y1 * R * Y2, Y3^2 * Y1^-1 * Y2^-1, Y1^-1 * Y3^2 * Y2^-2 * Y1^-1, (Y3^-1 * Y1 * Y2^-1)^2, Y1^-1 * Y3^-1 * Y1 * Y2 * Y3^-1 * Y2^-1, Y2^-1 * Y1 * Y2^-1 * Y1^-1 * Y2 * Y1^-1, (Y2 * Y1^-2)^2, Y1^6, (Y2^2 * Y1^-1)^2, Y2^6 ] Map:: polytopal non-degenerate R = (1, 49, 97, 145, 4, 52, 100, 148, 13, 61, 109, 157, 7, 55, 103, 151)(2, 50, 98, 146, 10, 58, 106, 154, 6, 54, 102, 150, 12, 60, 108, 156)(3, 51, 99, 147, 15, 63, 111, 159, 32, 80, 128, 176, 17, 65, 113, 161)(5, 53, 101, 149, 20, 68, 116, 164, 30, 78, 126, 174, 22, 70, 118, 166)(8, 56, 104, 152, 27, 75, 123, 171, 11, 59, 107, 155, 29, 77, 125, 173)(9, 57, 105, 153, 31, 79, 127, 175, 45, 93, 141, 189, 33, 81, 129, 177)(14, 62, 110, 158, 38, 86, 134, 182, 21, 69, 117, 165, 39, 87, 135, 183)(16, 64, 112, 160, 40, 88, 136, 184, 19, 67, 115, 163, 41, 89, 137, 185)(18, 66, 114, 162, 37, 85, 133, 181, 46, 94, 142, 190, 26, 74, 122, 170)(23, 71, 119, 167, 42, 90, 138, 186, 24, 72, 120, 168, 34, 82, 130, 178)(25, 73, 121, 169, 43, 91, 139, 187, 28, 76, 124, 172, 44, 92, 140, 188)(35, 83, 131, 179, 48, 96, 144, 192, 36, 84, 132, 180, 47, 95, 143, 191) L = (1, 50)(2, 56)(3, 61)(4, 63)(5, 49)(6, 71)(7, 68)(8, 73)(9, 54)(10, 79)(11, 83)(12, 52)(13, 85)(14, 80)(15, 86)(16, 51)(17, 88)(18, 55)(19, 78)(20, 89)(21, 53)(22, 87)(23, 84)(24, 76)(25, 69)(26, 59)(27, 66)(28, 64)(29, 58)(30, 93)(31, 70)(32, 57)(33, 65)(34, 60)(35, 67)(36, 62)(37, 72)(38, 91)(39, 95)(40, 96)(41, 92)(42, 94)(43, 82)(44, 75)(45, 74)(46, 81)(47, 77)(48, 90)(97, 147)(98, 153)(99, 158)(100, 162)(101, 163)(102, 145)(103, 156)(104, 170)(105, 174)(106, 178)(107, 146)(108, 173)(109, 149)(110, 169)(111, 177)(112, 179)(113, 148)(114, 186)(115, 172)(116, 175)(117, 180)(118, 151)(119, 181)(120, 150)(121, 168)(122, 157)(123, 191)(124, 152)(125, 188)(126, 165)(127, 190)(128, 160)(129, 154)(130, 192)(131, 167)(132, 155)(133, 189)(134, 166)(135, 159)(136, 164)(137, 161)(138, 187)(139, 185)(140, 182)(141, 176)(142, 171)(143, 184)(144, 183) local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E23.475 Transitivity :: VT+ Graph:: bipartite v = 12 e = 96 f = 40 degree seq :: [ 16^12 ] E23.482 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C2 x S4 (small group id <48, 48>) Aut = C2 x C2 x S4 (small group id <96, 226>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y3 * Y2^-1, Y2^2 * Y3^-1, Y3^3, (Y1^-1 * Y2)^2, (Y3 * Y1)^2, (R * Y1)^2, (R * Y2)^2, Y1^4, (R * Y3)^2, Y1^2 * Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y3^-1, (Y1^-1 * Y3 * Y1^-1 * Y2^-1)^2 ] Map:: non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 29, 77, 11, 59)(4, 52, 15, 63, 34, 82, 16, 64)(6, 54, 17, 65, 35, 83, 20, 68)(7, 55, 21, 69, 28, 76, 10, 58)(9, 57, 26, 74, 41, 89, 24, 72)(12, 60, 30, 78, 40, 88, 23, 71)(14, 62, 27, 75, 39, 87, 33, 81)(18, 66, 25, 73, 42, 90, 36, 84)(19, 67, 22, 70, 38, 86, 37, 85)(31, 79, 45, 93, 47, 95, 43, 91)(32, 80, 46, 94, 48, 96, 44, 92)(97, 145, 99, 147, 100, 148, 110, 158, 103, 151, 102, 150)(98, 146, 105, 153, 106, 154, 123, 171, 108, 156, 107, 155)(101, 149, 113, 161, 114, 162, 129, 177, 111, 159, 115, 163)(104, 152, 118, 166, 119, 167, 135, 183, 121, 169, 120, 168)(109, 157, 127, 175, 116, 164, 117, 165, 128, 176, 112, 160)(122, 170, 139, 187, 125, 173, 126, 174, 140, 188, 124, 172)(130, 178, 142, 190, 132, 180, 131, 179, 141, 189, 133, 181)(134, 182, 143, 191, 137, 185, 138, 186, 144, 192, 136, 184) L = (1, 100)(2, 106)(3, 110)(4, 103)(5, 114)(6, 99)(7, 97)(8, 119)(9, 123)(10, 108)(11, 105)(12, 98)(13, 116)(14, 102)(15, 101)(16, 127)(17, 129)(18, 111)(19, 113)(20, 128)(21, 112)(22, 135)(23, 121)(24, 118)(25, 104)(26, 125)(27, 107)(28, 139)(29, 140)(30, 124)(31, 117)(32, 109)(33, 115)(34, 132)(35, 133)(36, 141)(37, 142)(38, 137)(39, 120)(40, 143)(41, 144)(42, 136)(43, 126)(44, 122)(45, 130)(46, 131)(47, 138)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 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 E23.485 Graph:: bipartite v = 20 e = 96 f = 32 degree seq :: [ 8^12, 12^8 ] E23.483 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C2 x S4 (small group id <48, 48>) Aut = C2 x C2 x S4 (small group id <96, 226>) |r| :: 2 Presentation :: [ R^2, Y3^3, Y3^3, (R * Y3)^2, (Y3 * Y1)^2, (Y2 * Y3)^2, (Y2^-1 * Y1^-1)^2, (R * Y1)^2, Y1^4, Y1 * Y3 * Y1^-1 * Y2^2, Y2^2 * Y1 * Y3 * Y1^-1, Y2^-1 * Y1^-2 * Y3 * Y2^-1, (R * Y2 * Y3^-1)^2, Y1^-1 * Y2 * Y1^-1 * R * Y2^-1 * R, Y2^6, (Y3 * Y2^-1)^6 ] Map:: non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 37, 85, 16, 64)(4, 52, 18, 66, 41, 89, 20, 68)(6, 54, 24, 72, 17, 65, 9, 57)(7, 55, 27, 75, 26, 74, 10, 58)(11, 59, 25, 73, 32, 80, 21, 69)(12, 60, 36, 84, 35, 83, 14, 62)(15, 63, 40, 88, 46, 94, 31, 79)(19, 67, 33, 81, 39, 87, 38, 86)(22, 70, 29, 77, 34, 82, 28, 76)(23, 71, 30, 78, 48, 96, 44, 92)(42, 90, 47, 95, 45, 93, 43, 91)(97, 145, 99, 147, 110, 158, 135, 183, 122, 170, 102, 150)(98, 146, 105, 153, 119, 167, 134, 182, 131, 179, 107, 155)(100, 148, 115, 163, 140, 188, 125, 173, 104, 152, 117, 165)(101, 149, 118, 166, 106, 154, 129, 177, 116, 164, 109, 157)(103, 151, 124, 172, 143, 191, 133, 181, 137, 185, 111, 159)(108, 156, 112, 160, 138, 186, 120, 168, 123, 171, 127, 175)(113, 161, 139, 187, 121, 169, 132, 180, 142, 190, 126, 174)(114, 162, 128, 176, 141, 189, 130, 178, 144, 192, 136, 184) L = (1, 100)(2, 106)(3, 111)(4, 103)(5, 119)(6, 121)(7, 97)(8, 110)(9, 127)(10, 108)(11, 130)(12, 98)(13, 120)(14, 126)(15, 113)(16, 118)(17, 99)(18, 101)(19, 102)(20, 141)(21, 142)(22, 136)(23, 114)(24, 134)(25, 115)(26, 143)(27, 116)(28, 117)(29, 133)(30, 104)(31, 128)(32, 105)(33, 107)(34, 129)(35, 138)(36, 122)(37, 135)(38, 109)(39, 125)(40, 112)(41, 140)(42, 144)(43, 137)(44, 139)(45, 123)(46, 124)(47, 132)(48, 131)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 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 E23.484 Graph:: bipartite v = 20 e = 96 f = 32 degree seq :: [ 8^12, 12^8 ] E23.484 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C2 x S4 (small group id <48, 48>) Aut = C2 x C2 x S4 (small group id <96, 226>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^3, (Y1^-1 * Y2)^2, (Y1 * Y3^-1)^2, (R * Y3^-1)^2, (R * Y1)^2, (Y1^-1 * Y3^-1 * Y1^-1)^2, Y2 * Y1^-2 * Y3 * Y2 * Y3^-1, Y2 * Y3^-1 * R * Y2 * R * Y3, Y1^6, Y3 * Y1^-2 * Y3^-1 * Y2 * Y3 * Y2, Y2 * Y1 * Y3 * Y1 * Y3 * Y2 * Y3 ] Map:: non-degenerate R = (1, 49, 2, 50, 7, 55, 21, 69, 17, 65, 5, 53)(3, 51, 11, 59, 31, 79, 44, 92, 22, 70, 8, 56)(4, 52, 14, 62, 38, 86, 45, 93, 30, 78, 10, 58)(6, 54, 16, 64, 36, 84, 46, 94, 23, 71, 20, 68)(9, 57, 27, 75, 18, 66, 35, 83, 39, 87, 24, 72)(12, 60, 34, 82, 40, 88, 28, 76, 42, 90, 33, 81)(13, 61, 25, 73, 19, 67, 41, 89, 47, 95, 37, 85)(15, 63, 29, 77, 48, 96, 32, 80, 43, 91, 26, 74)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 111, 159)(101, 149, 107, 155)(102, 150, 115, 163)(103, 151, 118, 166)(105, 153, 124, 172)(106, 154, 125, 173)(108, 156, 131, 179)(109, 157, 132, 180)(110, 158, 122, 170)(112, 160, 121, 169)(113, 161, 127, 175)(114, 162, 130, 178)(116, 164, 137, 185)(117, 165, 140, 188)(119, 167, 143, 191)(120, 168, 138, 186)(123, 171, 136, 184)(126, 174, 144, 192)(128, 176, 141, 189)(129, 177, 135, 183)(133, 181, 142, 190)(134, 182, 139, 187) L = (1, 100)(2, 105)(3, 108)(4, 102)(5, 112)(6, 97)(7, 119)(8, 121)(9, 106)(10, 98)(11, 128)(12, 109)(13, 99)(14, 135)(15, 136)(16, 114)(17, 131)(18, 101)(19, 138)(20, 110)(21, 141)(22, 111)(23, 120)(24, 103)(25, 122)(26, 104)(27, 132)(28, 137)(29, 133)(30, 123)(31, 143)(32, 129)(33, 107)(34, 125)(35, 134)(36, 126)(37, 130)(38, 113)(39, 116)(40, 118)(41, 140)(42, 139)(43, 115)(44, 124)(45, 142)(46, 117)(47, 144)(48, 127)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E23.483 Graph:: simple bipartite v = 32 e = 96 f = 20 degree seq :: [ 4^24, 12^8 ] E23.485 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 6, 6}) Quotient :: dipole Aut^+ = C2 x S4 (small group id <48, 48>) Aut = C2 x C2 x S4 (small group id <96, 226>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3 * Y1^2, Y3^3, (R * Y1^-1)^2, (R * Y3)^2, (R * Y1)^2, (Y1 * Y3^-1)^2, Y3 * Y1^-1 * Y2 * Y3^-1 * Y1 * Y2, (R * Y2 * Y3^-1)^2, (Y2 * Y3^-1 * Y2 * Y1^-1)^2, (Y2 * Y1 * Y2 * Y1^-1)^3 ] Map:: non-degenerate R = (1, 49, 2, 50, 6, 54, 8, 56, 4, 52, 5, 53)(3, 51, 9, 57, 12, 60, 20, 68, 10, 58, 11, 59)(7, 55, 16, 64, 19, 67, 13, 61, 17, 65, 18, 66)(14, 62, 25, 73, 28, 76, 15, 63, 26, 74, 27, 75)(21, 69, 33, 81, 36, 84, 22, 70, 34, 82, 35, 83)(23, 71, 37, 85, 30, 78, 24, 72, 38, 86, 29, 77)(31, 79, 41, 89, 39, 87, 32, 80, 42, 90, 40, 88)(43, 91, 47, 95, 45, 93, 44, 92, 48, 96, 46, 94)(97, 145, 99, 147)(98, 146, 103, 151)(100, 148, 109, 157)(101, 149, 110, 158)(102, 150, 111, 159)(104, 152, 116, 164)(105, 153, 117, 165)(106, 154, 118, 166)(107, 155, 119, 167)(108, 156, 120, 168)(112, 160, 125, 173)(113, 161, 126, 174)(114, 162, 127, 175)(115, 163, 128, 176)(121, 169, 135, 183)(122, 170, 136, 184)(123, 171, 129, 177)(124, 172, 130, 178)(131, 179, 139, 187)(132, 180, 140, 188)(133, 181, 141, 189)(134, 182, 142, 190)(137, 185, 143, 191)(138, 186, 144, 192) L = (1, 100)(2, 101)(3, 106)(4, 102)(5, 104)(6, 97)(7, 113)(8, 98)(9, 107)(10, 108)(11, 116)(12, 99)(13, 112)(14, 122)(15, 121)(16, 114)(17, 115)(18, 109)(19, 103)(20, 105)(21, 130)(22, 129)(23, 134)(24, 133)(25, 123)(26, 124)(27, 111)(28, 110)(29, 120)(30, 119)(31, 138)(32, 137)(33, 131)(34, 132)(35, 118)(36, 117)(37, 125)(38, 126)(39, 127)(40, 128)(41, 136)(42, 135)(43, 144)(44, 143)(45, 139)(46, 140)(47, 142)(48, 141)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 12, 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E23.482 Graph:: bipartite v = 32 e = 96 f = 20 degree seq :: [ 4^24, 12^8 ] E23.486 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 8, 8}) Quotient :: dipole Aut^+ = C8 x S3 (small group id <48, 4>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^3, R * Y2 * R * Y2^-1, (R * Y3)^2, (R * Y1)^2, Y3^-1 * Y2^-1 * Y3 * Y2^-1, Y3 * Y1 * Y3^-1 * Y1, (Y2 * Y1)^2, Y3^8 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50)(3, 51, 9, 57)(4, 52, 8, 56)(5, 53, 7, 55)(6, 54, 10, 58)(11, 59, 19, 67)(12, 60, 21, 69)(13, 61, 17, 65)(14, 62, 20, 68)(15, 63, 18, 66)(16, 64, 22, 70)(23, 71, 31, 79)(24, 72, 33, 81)(25, 73, 29, 77)(26, 74, 32, 80)(27, 75, 30, 78)(28, 76, 34, 82)(35, 83, 42, 90)(36, 84, 44, 92)(37, 85, 40, 88)(38, 86, 43, 91)(39, 87, 41, 89)(45, 93, 48, 96)(46, 94, 47, 95)(97, 145, 99, 147, 101, 149)(98, 146, 103, 151, 105, 153)(100, 148, 109, 157, 107, 155)(102, 150, 111, 159, 108, 156)(104, 152, 115, 163, 113, 161)(106, 154, 117, 165, 114, 162)(110, 158, 119, 167, 121, 169)(112, 160, 120, 168, 123, 171)(116, 164, 125, 173, 127, 175)(118, 166, 126, 174, 129, 177)(122, 170, 133, 181, 131, 179)(124, 172, 135, 183, 132, 180)(128, 176, 138, 186, 136, 184)(130, 178, 140, 188, 137, 185)(134, 182, 141, 189, 142, 190)(139, 187, 143, 191, 144, 192) L = (1, 100)(2, 104)(3, 107)(4, 110)(5, 109)(6, 97)(7, 113)(8, 116)(9, 115)(10, 98)(11, 119)(12, 99)(13, 121)(14, 122)(15, 101)(16, 102)(17, 125)(18, 103)(19, 127)(20, 128)(21, 105)(22, 106)(23, 131)(24, 108)(25, 133)(26, 134)(27, 111)(28, 112)(29, 136)(30, 114)(31, 138)(32, 139)(33, 117)(34, 118)(35, 141)(36, 120)(37, 142)(38, 124)(39, 123)(40, 143)(41, 126)(42, 144)(43, 130)(44, 129)(45, 132)(46, 135)(47, 137)(48, 140)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 16^4 ), ( 16^6 ) } Outer automorphisms :: reflexible Dual of E23.491 Graph:: simple bipartite v = 40 e = 96 f = 12 degree seq :: [ 4^24, 6^16 ] E23.487 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 8, 8}) Quotient :: dipole Aut^+ = C8 x S3 (small group id <48, 4>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1^3, Y2^-1 * Y3 * Y2 * Y3, (R * Y2)^2, (Y3 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, (Y2, Y1^-1), Y2^8 ] Map:: non-degenerate R = (1, 49, 2, 50, 5, 53)(3, 51, 7, 55, 12, 60)(4, 52, 13, 61, 8, 56)(6, 54, 9, 57, 15, 63)(10, 58, 17, 65, 23, 71)(11, 59, 24, 72, 18, 66)(14, 62, 25, 73, 19, 67)(16, 64, 20, 68, 27, 75)(21, 69, 29, 77, 35, 83)(22, 70, 36, 84, 30, 78)(26, 74, 37, 85, 31, 79)(28, 76, 32, 80, 39, 87)(33, 81, 40, 88, 44, 92)(34, 82, 45, 93, 41, 89)(38, 86, 46, 94, 42, 90)(43, 91, 48, 96, 47, 95)(97, 145, 99, 147, 106, 154, 117, 165, 129, 177, 124, 172, 112, 160, 102, 150)(98, 146, 103, 151, 113, 161, 125, 173, 136, 184, 128, 176, 116, 164, 105, 153)(100, 148, 107, 155, 118, 166, 130, 178, 139, 187, 134, 182, 122, 170, 110, 158)(101, 149, 108, 156, 119, 167, 131, 179, 140, 188, 135, 183, 123, 171, 111, 159)(104, 152, 114, 162, 126, 174, 137, 185, 143, 191, 138, 186, 127, 175, 115, 163)(109, 157, 120, 168, 132, 180, 141, 189, 144, 192, 142, 190, 133, 181, 121, 169) L = (1, 100)(2, 104)(3, 107)(4, 97)(5, 109)(6, 110)(7, 114)(8, 98)(9, 115)(10, 118)(11, 99)(12, 120)(13, 101)(14, 102)(15, 121)(16, 122)(17, 126)(18, 103)(19, 105)(20, 127)(21, 130)(22, 106)(23, 132)(24, 108)(25, 111)(26, 112)(27, 133)(28, 134)(29, 137)(30, 113)(31, 116)(32, 138)(33, 139)(34, 117)(35, 141)(36, 119)(37, 123)(38, 124)(39, 142)(40, 143)(41, 125)(42, 128)(43, 129)(44, 144)(45, 131)(46, 135)(47, 136)(48, 140)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 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 E23.490 Graph:: simple bipartite v = 22 e = 96 f = 30 degree seq :: [ 6^16, 16^6 ] E23.488 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 8, 8}) Quotient :: dipole Aut^+ = C8 x S3 (small group id <48, 4>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ Y3^2, R^2, Y1^3, Y2^-1 * Y3 * Y2 * Y3, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y3 * Y1^-1)^2, Y2 * Y1^-1 * Y2^-1 * Y1^-1, Y2^8 ] Map:: non-degenerate R = (1, 49, 2, 50, 5, 53)(3, 51, 10, 58, 7, 55)(4, 52, 13, 61, 8, 56)(6, 54, 15, 63, 9, 57)(11, 59, 17, 65, 21, 69)(12, 60, 18, 66, 22, 70)(14, 62, 19, 67, 25, 73)(16, 64, 20, 68, 27, 75)(23, 71, 33, 81, 29, 77)(24, 72, 34, 82, 30, 78)(26, 74, 37, 85, 31, 79)(28, 76, 39, 87, 32, 80)(35, 83, 40, 88, 43, 91)(36, 84, 41, 89, 44, 92)(38, 86, 42, 90, 46, 94)(45, 93, 48, 96, 47, 95)(97, 145, 99, 147, 107, 155, 119, 167, 131, 179, 124, 172, 112, 160, 102, 150)(98, 146, 103, 151, 113, 161, 125, 173, 136, 184, 128, 176, 116, 164, 105, 153)(100, 148, 108, 156, 120, 168, 132, 180, 141, 189, 134, 182, 122, 170, 110, 158)(101, 149, 106, 154, 117, 165, 129, 177, 139, 187, 135, 183, 123, 171, 111, 159)(104, 152, 114, 162, 126, 174, 137, 185, 143, 191, 138, 186, 127, 175, 115, 163)(109, 157, 118, 166, 130, 178, 140, 188, 144, 192, 142, 190, 133, 181, 121, 169) L = (1, 100)(2, 104)(3, 108)(4, 97)(5, 109)(6, 110)(7, 114)(8, 98)(9, 115)(10, 118)(11, 120)(12, 99)(13, 101)(14, 102)(15, 121)(16, 122)(17, 126)(18, 103)(19, 105)(20, 127)(21, 130)(22, 106)(23, 132)(24, 107)(25, 111)(26, 112)(27, 133)(28, 134)(29, 137)(30, 113)(31, 116)(32, 138)(33, 140)(34, 117)(35, 141)(36, 119)(37, 123)(38, 124)(39, 142)(40, 143)(41, 125)(42, 128)(43, 144)(44, 129)(45, 131)(46, 135)(47, 136)(48, 139)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 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 E23.489 Graph:: simple bipartite v = 22 e = 96 f = 30 degree seq :: [ 6^16, 16^6 ] E23.489 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 8, 8}) Quotient :: dipole Aut^+ = C8 x S3 (small group id <48, 4>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y1^-1 * Y3 * Y1 * Y3, (R * Y3)^2, Y2 * Y1 * Y2 * Y1^-1, (R * Y1)^2, (R * Y2 * Y3)^2, (Y3 * Y2)^3, Y1^8 ] Map:: non-degenerate R = (1, 49, 2, 50, 6, 54, 14, 62, 25, 73, 24, 72, 13, 61, 5, 53)(3, 51, 7, 55, 15, 63, 26, 74, 36, 84, 33, 81, 21, 69, 10, 58)(4, 52, 8, 56, 16, 64, 27, 75, 37, 85, 35, 83, 23, 71, 12, 60)(9, 57, 17, 65, 28, 76, 38, 86, 44, 92, 42, 90, 32, 80, 20, 68)(11, 59, 18, 66, 29, 77, 39, 87, 45, 93, 43, 91, 34, 82, 22, 70)(19, 67, 30, 78, 40, 88, 46, 94, 48, 96, 47, 95, 41, 89, 31, 79)(97, 145, 99, 147)(98, 146, 103, 151)(100, 148, 107, 155)(101, 149, 106, 154)(102, 150, 111, 159)(104, 152, 114, 162)(105, 153, 115, 163)(108, 156, 118, 166)(109, 157, 117, 165)(110, 158, 122, 170)(112, 160, 125, 173)(113, 161, 126, 174)(116, 164, 127, 175)(119, 167, 130, 178)(120, 168, 129, 177)(121, 169, 132, 180)(123, 171, 135, 183)(124, 172, 136, 184)(128, 176, 137, 185)(131, 179, 139, 187)(133, 181, 141, 189)(134, 182, 142, 190)(138, 186, 143, 191)(140, 188, 144, 192) L = (1, 100)(2, 104)(3, 105)(4, 97)(5, 108)(6, 112)(7, 113)(8, 98)(9, 99)(10, 116)(11, 115)(12, 101)(13, 119)(14, 123)(15, 124)(16, 102)(17, 103)(18, 126)(19, 107)(20, 106)(21, 128)(22, 127)(23, 109)(24, 131)(25, 133)(26, 134)(27, 110)(28, 111)(29, 136)(30, 114)(31, 118)(32, 117)(33, 138)(34, 137)(35, 120)(36, 140)(37, 121)(38, 122)(39, 142)(40, 125)(41, 130)(42, 129)(43, 143)(44, 132)(45, 144)(46, 135)(47, 139)(48, 141)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 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 E23.488 Graph:: simple bipartite v = 30 e = 96 f = 22 degree seq :: [ 4^24, 16^6 ] E23.490 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 8, 8}) Quotient :: dipole Aut^+ = C8 x S3 (small group id <48, 4>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y3 * Y1 * Y3 * Y1^-1, (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y3 * Y2 * Y1 * Y3 * Y2, (R * Y2 * Y3)^2, Y1^-1 * Y2 * Y3 * Y2 * Y1 * Y2, (Y3 * Y2)^3, Y1^8 ] Map:: non-degenerate R = (1, 49, 2, 50, 6, 54, 16, 64, 29, 77, 28, 76, 15, 63, 5, 53)(3, 51, 9, 57, 17, 65, 32, 80, 40, 88, 37, 85, 25, 73, 11, 59)(4, 52, 8, 56, 18, 66, 31, 79, 41, 89, 38, 86, 26, 74, 13, 61)(7, 55, 19, 67, 30, 78, 42, 90, 39, 87, 27, 75, 14, 62, 21, 69)(10, 58, 22, 70, 33, 81, 44, 92, 47, 95, 45, 93, 35, 83, 23, 71)(12, 60, 20, 68, 34, 82, 43, 91, 48, 96, 46, 94, 36, 84, 24, 72)(97, 145, 99, 147)(98, 146, 103, 151)(100, 148, 108, 156)(101, 149, 110, 158)(102, 150, 113, 161)(104, 152, 118, 166)(105, 153, 116, 164)(106, 154, 117, 165)(107, 155, 120, 168)(109, 157, 119, 167)(111, 159, 121, 169)(112, 160, 126, 174)(114, 162, 130, 178)(115, 163, 129, 177)(122, 170, 132, 180)(123, 171, 131, 179)(124, 172, 135, 183)(125, 173, 136, 184)(127, 175, 140, 188)(128, 176, 139, 187)(133, 181, 142, 190)(134, 182, 141, 189)(137, 185, 144, 192)(138, 186, 143, 191) L = (1, 100)(2, 104)(3, 106)(4, 97)(5, 109)(6, 114)(7, 116)(8, 98)(9, 118)(10, 99)(11, 119)(12, 117)(13, 101)(14, 120)(15, 122)(16, 127)(17, 129)(18, 102)(19, 130)(20, 103)(21, 108)(22, 105)(23, 107)(24, 110)(25, 131)(26, 111)(27, 132)(28, 134)(29, 137)(30, 139)(31, 112)(32, 140)(33, 113)(34, 115)(35, 121)(36, 123)(37, 141)(38, 124)(39, 142)(40, 143)(41, 125)(42, 144)(43, 126)(44, 128)(45, 133)(46, 135)(47, 136)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 6, 16, 6, 16 ), ( 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16 ) } Outer automorphisms :: reflexible Dual of E23.487 Graph:: simple bipartite v = 30 e = 96 f = 22 degree seq :: [ 4^24, 16^6 ] E23.491 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 8, 8}) Quotient :: dipole Aut^+ = C8 x S3 (small group id <48, 4>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ R^2, (Y3, Y2^-1), Y1^-1 * Y2^-2 * Y1^-1, Y3^2 * Y2^-2, Y3^-1 * Y1^-2 * Y3^-1, (R * Y2)^2, (R * Y1)^2, (Y2, Y1^-1), (R * Y3)^2, (Y3 * Y2^-1)^2, (Y3 * Y1)^3, Y3 * Y2 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y2 * Y1^-1, Y1^-3 * Y3^2 * Y1^-3, Y1^-2 * Y2^6, Y3 * Y2 * Y1^-1 * Y3^-1 * Y1 * Y2^-1 * Y3^-1 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50, 8, 56, 22, 70, 40, 88, 33, 81, 13, 61, 5, 53)(3, 51, 9, 57, 6, 54, 11, 59, 23, 71, 41, 89, 31, 79, 15, 63)(4, 52, 17, 65, 7, 55, 21, 69, 24, 72, 44, 92, 32, 80, 18, 66)(10, 58, 27, 75, 12, 60, 30, 78, 42, 90, 38, 86, 19, 67, 28, 76)(14, 62, 34, 82, 16, 64, 37, 85, 20, 68, 39, 87, 43, 91, 35, 83)(25, 73, 45, 93, 26, 74, 47, 95, 29, 77, 48, 96, 36, 84, 46, 94)(97, 145, 99, 147, 109, 157, 127, 175, 136, 184, 119, 167, 104, 152, 102, 150)(98, 146, 105, 153, 101, 149, 111, 159, 129, 177, 137, 185, 118, 166, 107, 155)(100, 148, 110, 158, 128, 176, 139, 187, 120, 168, 116, 164, 103, 151, 112, 160)(106, 154, 121, 169, 115, 163, 132, 180, 138, 186, 125, 173, 108, 156, 122, 170)(113, 161, 130, 178, 114, 162, 131, 179, 140, 188, 135, 183, 117, 165, 133, 181)(123, 171, 141, 189, 124, 172, 142, 190, 134, 182, 144, 192, 126, 174, 143, 191) L = (1, 100)(2, 106)(3, 110)(4, 109)(5, 115)(6, 112)(7, 97)(8, 103)(9, 121)(10, 101)(11, 122)(12, 98)(13, 128)(14, 127)(15, 132)(16, 99)(17, 124)(18, 134)(19, 129)(20, 102)(21, 123)(22, 108)(23, 116)(24, 104)(25, 111)(26, 105)(27, 113)(28, 114)(29, 107)(30, 117)(31, 139)(32, 136)(33, 138)(34, 142)(35, 144)(36, 137)(37, 141)(38, 140)(39, 143)(40, 120)(41, 125)(42, 118)(43, 119)(44, 126)(45, 130)(46, 131)(47, 133)(48, 135)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E23.486 Graph:: bipartite v = 12 e = 96 f = 40 degree seq :: [ 16^12 ] E23.492 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 8, 8}) Quotient :: dipole Aut^+ = C24 : C2 (small group id <48, 5>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^3, Y3 * Y2^-1 * Y3^-1 * Y2^-1, (R * Y3)^2, (R * Y1)^2, (Y2 * Y1)^2, R * Y2 * R * Y2^-1, Y3 * Y1 * Y3^3 * Y1, (Y1 * Y3^-1 * Y1 * Y3)^2 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50)(3, 51, 9, 57)(4, 52, 13, 61)(5, 53, 7, 55)(6, 54, 17, 65)(8, 56, 21, 69)(10, 58, 25, 73)(11, 59, 27, 75)(12, 60, 29, 77)(14, 62, 31, 79)(15, 63, 23, 71)(16, 64, 34, 82)(18, 66, 26, 74)(19, 67, 36, 84)(20, 68, 38, 86)(22, 70, 40, 88)(24, 72, 43, 91)(28, 76, 42, 90)(30, 78, 44, 92)(32, 80, 41, 89)(33, 81, 37, 85)(35, 83, 39, 87)(45, 93, 48, 96)(46, 94, 47, 95)(97, 145, 99, 147, 101, 149)(98, 146, 103, 151, 105, 153)(100, 148, 110, 158, 107, 155)(102, 150, 112, 160, 108, 156)(104, 152, 118, 166, 115, 163)(106, 154, 120, 168, 116, 164)(109, 157, 123, 171, 127, 175)(111, 159, 124, 172, 129, 177)(113, 161, 125, 173, 130, 178)(114, 162, 126, 174, 131, 179)(117, 165, 132, 180, 136, 184)(119, 167, 133, 181, 138, 186)(121, 169, 134, 182, 139, 187)(122, 170, 135, 183, 140, 188)(128, 176, 142, 190, 141, 189)(137, 185, 144, 192, 143, 191) L = (1, 100)(2, 104)(3, 107)(4, 111)(5, 110)(6, 97)(7, 115)(8, 119)(9, 118)(10, 98)(11, 124)(12, 99)(13, 122)(14, 129)(15, 121)(16, 101)(17, 128)(18, 102)(19, 133)(20, 103)(21, 114)(22, 138)(23, 113)(24, 105)(25, 137)(26, 106)(27, 140)(28, 139)(29, 141)(30, 108)(31, 135)(32, 109)(33, 134)(34, 142)(35, 112)(36, 131)(37, 130)(38, 143)(39, 116)(40, 126)(41, 117)(42, 125)(43, 144)(44, 120)(45, 123)(46, 127)(47, 132)(48, 136)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 16^4 ), ( 16^6 ) } Outer automorphisms :: reflexible Dual of E23.497 Graph:: simple bipartite v = 40 e = 96 f = 12 degree seq :: [ 4^24, 6^16 ] E23.493 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 8, 8}) Quotient :: dipole Aut^+ = C24 : C2 (small group id <48, 5>) Aut = (D8 x S3) : C2 (small group id <96, 118>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1^3, (Y2^-1, Y1^-1), (Y3 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, Y3 * Y2^-2 * Y3 * Y2^2, (R * Y2 * Y3)^2, Y2^-2 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 49, 2, 50, 5, 53)(3, 51, 7, 55, 12, 60)(4, 52, 13, 61, 8, 56)(6, 54, 9, 57, 16, 64)(10, 58, 19, 67, 27, 75)(11, 59, 28, 76, 20, 68)(14, 62, 31, 79, 21, 69)(15, 63, 32, 80, 22, 70)(17, 65, 34, 82, 23, 71)(18, 66, 24, 72, 35, 83)(25, 73, 36, 84, 42, 90)(26, 74, 43, 91, 37, 85)(29, 77, 44, 92, 38, 86)(30, 78, 45, 93, 39, 87)(33, 81, 40, 88, 46, 94)(41, 89, 47, 95, 48, 96)(97, 145, 99, 147, 106, 154, 121, 169, 137, 185, 129, 177, 114, 162, 102, 150)(98, 146, 103, 151, 115, 163, 132, 180, 143, 191, 136, 184, 120, 168, 105, 153)(100, 148, 110, 158, 122, 170, 113, 161, 126, 174, 107, 155, 125, 173, 111, 159)(101, 149, 108, 156, 123, 171, 138, 186, 144, 192, 142, 190, 131, 179, 112, 160)(104, 152, 117, 165, 133, 181, 119, 167, 135, 183, 116, 164, 134, 182, 118, 166)(109, 157, 127, 175, 139, 187, 130, 178, 141, 189, 124, 172, 140, 188, 128, 176) L = (1, 100)(2, 104)(3, 107)(4, 97)(5, 109)(6, 113)(7, 116)(8, 98)(9, 119)(10, 122)(11, 99)(12, 124)(13, 101)(14, 129)(15, 121)(16, 130)(17, 102)(18, 125)(19, 133)(20, 103)(21, 136)(22, 132)(23, 105)(24, 134)(25, 111)(26, 106)(27, 139)(28, 108)(29, 114)(30, 137)(31, 142)(32, 138)(33, 110)(34, 112)(35, 140)(36, 118)(37, 115)(38, 120)(39, 143)(40, 117)(41, 126)(42, 128)(43, 123)(44, 131)(45, 144)(46, 127)(47, 135)(48, 141)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 16, 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E23.495 Graph:: simple bipartite v = 22 e = 96 f = 30 degree seq :: [ 6^16, 16^6 ] E23.494 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 8, 8}) Quotient :: dipole Aut^+ = C24 : C2 (small group id <48, 5>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1^3, (R * Y3)^2, (Y3 * Y1^-1)^2, (R * Y1)^2, Y2 * Y1^-1 * Y2^-1 * Y1^-1, Y3 * Y2^-2 * Y3 * Y2^2, (R * Y2 * Y3)^2, Y2^-2 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 49, 2, 50, 5, 53)(3, 51, 10, 58, 7, 55)(4, 52, 13, 61, 8, 56)(6, 54, 16, 64, 9, 57)(11, 59, 19, 67, 25, 73)(12, 60, 20, 68, 26, 74)(14, 62, 21, 69, 31, 79)(15, 63, 22, 70, 32, 80)(17, 65, 23, 71, 34, 82)(18, 66, 24, 72, 35, 83)(27, 75, 41, 89, 36, 84)(28, 76, 42, 90, 37, 85)(29, 77, 43, 91, 38, 86)(30, 78, 44, 92, 39, 87)(33, 81, 46, 94, 40, 88)(45, 93, 47, 95, 48, 96)(97, 145, 99, 147, 107, 155, 123, 171, 141, 189, 129, 177, 114, 162, 102, 150)(98, 146, 103, 151, 115, 163, 132, 180, 143, 191, 136, 184, 120, 168, 105, 153)(100, 148, 110, 158, 124, 172, 113, 161, 126, 174, 108, 156, 125, 173, 111, 159)(101, 149, 106, 154, 121, 169, 137, 185, 144, 192, 142, 190, 131, 179, 112, 160)(104, 152, 117, 165, 133, 181, 119, 167, 135, 183, 116, 164, 134, 182, 118, 166)(109, 157, 127, 175, 138, 186, 130, 178, 140, 188, 122, 170, 139, 187, 128, 176) L = (1, 100)(2, 104)(3, 108)(4, 97)(5, 109)(6, 113)(7, 116)(8, 98)(9, 119)(10, 122)(11, 124)(12, 99)(13, 101)(14, 129)(15, 123)(16, 130)(17, 102)(18, 125)(19, 133)(20, 103)(21, 136)(22, 132)(23, 105)(24, 134)(25, 138)(26, 106)(27, 111)(28, 107)(29, 114)(30, 141)(31, 142)(32, 137)(33, 110)(34, 112)(35, 139)(36, 118)(37, 115)(38, 120)(39, 143)(40, 117)(41, 128)(42, 121)(43, 131)(44, 144)(45, 126)(46, 127)(47, 135)(48, 140)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 16, 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E23.496 Graph:: simple bipartite v = 22 e = 96 f = 30 degree seq :: [ 6^16, 16^6 ] E23.495 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 8, 8}) Quotient :: dipole Aut^+ = C24 : C2 (small group id <48, 5>) Aut = (D8 x S3) : C2 (small group id <96, 118>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (Y3 * R)^2, (R * Y1)^2, (Y3 * Y2)^3, Y1^3 * Y3 * Y1 * Y3, Y1^-1 * Y3 * Y1^2 * Y3 * Y1^-1, Y1 * Y2 * Y1^-2 * Y2 * Y1, (R * Y2 * Y3)^2, Y3 * Y2 * Y1 * Y3 * Y2 * Y1^-1, Y1^-1 * Y3 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1, (Y3 * Y1^-1 * Y3 * Y1)^2 ] Map:: non-degenerate R = (1, 49, 2, 50, 6, 54, 18, 66, 37, 85, 34, 82, 17, 65, 5, 53)(3, 51, 9, 57, 19, 67, 39, 87, 48, 96, 44, 92, 33, 81, 11, 59)(4, 52, 12, 60, 20, 68, 16, 64, 26, 74, 8, 56, 24, 72, 14, 62)(7, 55, 21, 69, 38, 86, 29, 77, 47, 95, 36, 84, 15, 63, 23, 71)(10, 58, 25, 73, 40, 88, 32, 80, 45, 93, 28, 76, 42, 90, 30, 78)(13, 61, 22, 70, 41, 89, 31, 79, 46, 94, 27, 75, 43, 91, 35, 83)(97, 145, 99, 147)(98, 146, 103, 151)(100, 148, 109, 157)(101, 149, 111, 159)(102, 150, 115, 163)(104, 152, 121, 169)(105, 153, 123, 171)(106, 154, 125, 173)(107, 155, 127, 175)(108, 156, 124, 172)(110, 158, 128, 176)(112, 160, 126, 174)(113, 161, 129, 177)(114, 162, 134, 182)(116, 164, 137, 185)(117, 165, 138, 186)(118, 166, 140, 188)(119, 167, 141, 189)(120, 168, 139, 187)(122, 170, 142, 190)(130, 178, 143, 191)(131, 179, 135, 183)(132, 180, 136, 184)(133, 181, 144, 192) L = (1, 100)(2, 104)(3, 106)(4, 97)(5, 112)(6, 116)(7, 118)(8, 98)(9, 124)(10, 99)(11, 128)(12, 130)(13, 125)(14, 114)(15, 131)(16, 101)(17, 120)(18, 110)(19, 136)(20, 102)(21, 139)(22, 103)(23, 142)(24, 113)(25, 140)(26, 133)(27, 143)(28, 105)(29, 109)(30, 135)(31, 134)(32, 107)(33, 138)(34, 108)(35, 111)(36, 137)(37, 122)(38, 127)(39, 126)(40, 115)(41, 132)(42, 129)(43, 117)(44, 121)(45, 144)(46, 119)(47, 123)(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) :: { ( 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 E23.493 Graph:: simple bipartite v = 30 e = 96 f = 22 degree seq :: [ 4^24, 16^6 ] E23.496 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 8, 8}) Quotient :: dipole Aut^+ = C24 : C2 (small group id <48, 5>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (R * Y3)^2, (R * Y1)^2, Y3 * Y1^-2 * Y3 * Y1^2, Y2 * Y3 * Y1 * Y3 * Y2 * Y1^-1, Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-2, (R * Y2 * Y3)^2, (Y3 * Y2)^3, Y1^2 * Y2 * Y1^-2 * Y2 ] Map:: non-degenerate R = (1, 49, 2, 50, 6, 54, 18, 66, 35, 83, 27, 75, 17, 65, 5, 53)(3, 51, 9, 57, 19, 67, 15, 63, 23, 71, 7, 55, 21, 69, 11, 59)(4, 52, 12, 60, 20, 68, 16, 64, 26, 74, 8, 56, 24, 72, 14, 62)(10, 58, 22, 70, 36, 84, 31, 79, 40, 88, 28, 76, 38, 86, 30, 78)(13, 61, 25, 73, 37, 85, 34, 82, 42, 90, 32, 80, 41, 89, 33, 81)(29, 77, 43, 91, 46, 94, 45, 93, 48, 96, 39, 87, 47, 95, 44, 92)(97, 145, 99, 147)(98, 146, 103, 151)(100, 148, 109, 157)(101, 149, 111, 159)(102, 150, 115, 163)(104, 152, 121, 169)(105, 153, 123, 171)(106, 154, 125, 173)(107, 155, 114, 162)(108, 156, 128, 176)(110, 158, 130, 178)(112, 160, 129, 177)(113, 161, 117, 165)(116, 164, 133, 181)(118, 166, 135, 183)(119, 167, 131, 179)(120, 168, 137, 185)(122, 170, 138, 186)(124, 172, 139, 187)(126, 174, 141, 189)(127, 175, 140, 188)(132, 180, 142, 190)(134, 182, 143, 191)(136, 184, 144, 192) L = (1, 100)(2, 104)(3, 106)(4, 97)(5, 112)(6, 116)(7, 118)(8, 98)(9, 124)(10, 99)(11, 127)(12, 123)(13, 125)(14, 114)(15, 126)(16, 101)(17, 120)(18, 110)(19, 132)(20, 102)(21, 134)(22, 103)(23, 136)(24, 113)(25, 135)(26, 131)(27, 108)(28, 105)(29, 109)(30, 111)(31, 107)(32, 139)(33, 141)(34, 140)(35, 122)(36, 115)(37, 142)(38, 117)(39, 121)(40, 119)(41, 143)(42, 144)(43, 128)(44, 130)(45, 129)(46, 133)(47, 137)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 6, 16, 6, 16 ), ( 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16 ) } Outer automorphisms :: reflexible Dual of E23.494 Graph:: simple bipartite v = 30 e = 96 f = 22 degree seq :: [ 4^24, 16^6 ] E23.497 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 8, 8}) Quotient :: dipole Aut^+ = C24 : C2 (small group id <48, 5>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-2 * Y3^-1, (Y3 * Y2^-1)^2, (R * Y3)^2, Y2^2 * Y1^-2, Y3^-2 * Y2^-2, (R * Y1)^2, (Y2^-1 * Y1^-1)^2, Y2^-1 * Y3^-1 * Y2^3 * Y3^-1, Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1^-1, Y2 * Y3 * R * Y2^-1 * R * Y3, Y3^-1 * Y1^-1 * Y2 * Y1^-1 * Y3^-1 * Y2^-1, Y3^3 * Y2^-1 * Y3^-1 * Y2^-1, (R * Y2 * Y3^-1)^2 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50, 8, 56, 24, 72, 42, 90, 35, 83, 19, 67, 5, 53)(3, 51, 13, 61, 25, 73, 11, 59, 28, 76, 9, 57, 6, 54, 15, 63)(4, 52, 17, 65, 7, 55, 23, 71, 26, 74, 44, 92, 37, 85, 20, 68)(10, 58, 30, 78, 12, 60, 34, 82, 43, 91, 41, 89, 21, 69, 32, 80)(14, 62, 36, 84, 16, 64, 39, 87, 18, 66, 40, 88, 22, 70, 38, 86)(27, 75, 45, 93, 29, 77, 47, 95, 31, 79, 48, 96, 33, 81, 46, 94)(97, 145, 99, 147, 104, 152, 121, 169, 138, 186, 124, 172, 115, 163, 102, 150)(98, 146, 105, 153, 120, 168, 111, 159, 131, 179, 109, 157, 101, 149, 107, 155)(100, 148, 114, 162, 103, 151, 118, 166, 122, 170, 110, 158, 133, 181, 112, 160)(106, 154, 127, 175, 108, 156, 129, 177, 139, 187, 123, 171, 117, 165, 125, 173)(113, 161, 132, 180, 119, 167, 135, 183, 140, 188, 136, 184, 116, 164, 134, 182)(126, 174, 141, 189, 130, 178, 143, 191, 137, 185, 144, 192, 128, 176, 142, 190) L = (1, 100)(2, 106)(3, 110)(4, 115)(5, 117)(6, 118)(7, 97)(8, 103)(9, 123)(10, 101)(11, 129)(12, 98)(13, 127)(14, 102)(15, 125)(16, 99)(17, 128)(18, 121)(19, 133)(20, 137)(21, 131)(22, 124)(23, 126)(24, 108)(25, 112)(26, 104)(27, 107)(28, 114)(29, 105)(30, 113)(31, 111)(32, 116)(33, 109)(34, 119)(35, 139)(36, 143)(37, 138)(38, 141)(39, 144)(40, 142)(41, 140)(42, 122)(43, 120)(44, 130)(45, 136)(46, 135)(47, 134)(48, 132)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E23.492 Graph:: bipartite v = 12 e = 96 f = 40 degree seq :: [ 16^12 ] E23.498 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 8, 8}) Quotient :: dipole Aut^+ = C2 x (C3 : C8) (small group id <48, 9>) Aut = C2 x ((C3 x D8) : C2) (small group id <96, 138>) |r| :: 2 Presentation :: [ R^2, Y1^3, Y1 * Y3^-2, (R * Y3)^2, Y2^-1 * Y3 * Y2 * Y3, Y2 * Y1^-1 * Y2^-1 * Y1^-1, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y2^8 ] Map:: non-degenerate R = (1, 49, 2, 50, 5, 53)(3, 51, 11, 59, 8, 56)(4, 52, 9, 57, 7, 55)(6, 54, 16, 64, 10, 58)(12, 60, 19, 67, 23, 71)(13, 61, 20, 68, 14, 62)(15, 63, 17, 65, 21, 69)(18, 66, 22, 70, 28, 76)(24, 72, 35, 83, 31, 79)(25, 73, 32, 80, 26, 74)(27, 75, 33, 81, 29, 77)(30, 78, 40, 88, 34, 82)(36, 84, 42, 90, 45, 93)(37, 85, 43, 91, 38, 86)(39, 87, 41, 89, 44, 92)(46, 94, 48, 96, 47, 95)(97, 145, 99, 147, 108, 156, 120, 168, 132, 180, 126, 174, 114, 162, 102, 150)(98, 146, 104, 152, 115, 163, 127, 175, 138, 186, 130, 178, 118, 166, 106, 154)(100, 148, 110, 158, 121, 169, 134, 182, 142, 190, 135, 183, 123, 171, 111, 159)(101, 149, 107, 155, 119, 167, 131, 179, 141, 189, 136, 184, 124, 172, 112, 160)(103, 151, 109, 157, 122, 170, 133, 181, 143, 191, 137, 185, 125, 173, 113, 161)(105, 153, 116, 164, 128, 176, 139, 187, 144, 192, 140, 188, 129, 177, 117, 165) L = (1, 100)(2, 105)(3, 109)(4, 98)(5, 103)(6, 113)(7, 97)(8, 110)(9, 101)(10, 111)(11, 116)(12, 121)(13, 107)(14, 99)(15, 102)(16, 117)(17, 112)(18, 123)(19, 128)(20, 104)(21, 106)(22, 129)(23, 122)(24, 133)(25, 115)(26, 108)(27, 118)(28, 125)(29, 114)(30, 137)(31, 134)(32, 119)(33, 124)(34, 135)(35, 139)(36, 142)(37, 131)(38, 120)(39, 126)(40, 140)(41, 136)(42, 144)(43, 127)(44, 130)(45, 143)(46, 138)(47, 132)(48, 141)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 16, 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E23.499 Graph:: simple bipartite v = 22 e = 96 f = 30 degree seq :: [ 6^16, 16^6 ] E23.499 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 8, 8}) Quotient :: dipole Aut^+ = C2 x (C3 : C8) (small group id <48, 9>) Aut = C2 x ((C3 x D8) : C2) (small group id <96, 138>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^3 * Y2, Y3^-1 * Y1^-1 * Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, Y3 * Y2 * Y3^-1 * Y2, (R * Y2)^2, Y2 * Y1 * Y2 * Y1^-1, Y1^8 ] Map:: non-degenerate R = (1, 49, 2, 50, 7, 55, 17, 65, 29, 77, 28, 76, 16, 64, 5, 53)(3, 51, 8, 56, 18, 66, 30, 78, 40, 88, 37, 85, 25, 73, 12, 60)(4, 52, 10, 58, 19, 67, 32, 80, 41, 89, 38, 86, 26, 74, 14, 62)(6, 54, 9, 57, 20, 68, 31, 79, 42, 90, 39, 87, 27, 75, 15, 63)(11, 59, 22, 70, 33, 81, 44, 92, 47, 95, 45, 93, 35, 83, 23, 71)(13, 61, 21, 69, 34, 82, 43, 91, 48, 96, 46, 94, 36, 84, 24, 72)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 107, 155)(101, 149, 108, 156)(102, 150, 109, 157)(103, 151, 114, 162)(105, 153, 117, 165)(106, 154, 118, 166)(110, 158, 119, 167)(111, 159, 120, 168)(112, 160, 121, 169)(113, 161, 126, 174)(115, 163, 129, 177)(116, 164, 130, 178)(122, 170, 131, 179)(123, 171, 132, 180)(124, 172, 133, 181)(125, 173, 136, 184)(127, 175, 139, 187)(128, 176, 140, 188)(134, 182, 141, 189)(135, 183, 142, 190)(137, 185, 143, 191)(138, 186, 144, 192) L = (1, 100)(2, 105)(3, 107)(4, 109)(5, 111)(6, 97)(7, 115)(8, 117)(9, 118)(10, 98)(11, 102)(12, 120)(13, 99)(14, 101)(15, 119)(16, 122)(17, 127)(18, 129)(19, 130)(20, 103)(21, 106)(22, 104)(23, 108)(24, 110)(25, 131)(26, 132)(27, 112)(28, 135)(29, 137)(30, 139)(31, 140)(32, 113)(33, 116)(34, 114)(35, 123)(36, 121)(37, 142)(38, 124)(39, 141)(40, 143)(41, 144)(42, 125)(43, 128)(44, 126)(45, 133)(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) :: { ( 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 E23.498 Graph:: simple bipartite v = 30 e = 96 f = 22 degree seq :: [ 4^24, 16^6 ] E23.500 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 8, 8}) Quotient :: dipole Aut^+ = (C3 : C8) : C2 (small group id <48, 10>) Aut = (C2 x D24) : C2 (small group id <96, 156>) |r| :: 2 Presentation :: [ R^2, Y1^3, Y1 * Y3^-2, Y2 * Y1 * Y2^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-2, Y3^-1 * Y2^-1 * Y3^-1 * Y2^5 ] Map:: non-degenerate R = (1, 49, 2, 50, 5, 53)(3, 51, 11, 59, 8, 56)(4, 52, 9, 57, 7, 55)(6, 54, 17, 65, 10, 58)(12, 60, 23, 71, 29, 77)(13, 61, 24, 72, 14, 62)(15, 63, 21, 69, 25, 73)(16, 64, 22, 70, 26, 74)(18, 66, 28, 76, 20, 68)(19, 67, 27, 75, 40, 88)(30, 78, 42, 90, 39, 87)(31, 79, 43, 91, 32, 80)(33, 81, 35, 83, 44, 92)(34, 82, 36, 84, 45, 93)(37, 85, 41, 89, 38, 86)(46, 94, 48, 96, 47, 95)(97, 145, 99, 147, 108, 156, 126, 174, 142, 190, 133, 181, 115, 163, 102, 150)(98, 146, 104, 152, 119, 167, 135, 183, 144, 192, 134, 182, 123, 171, 106, 154)(100, 148, 111, 159, 127, 175, 116, 164, 132, 180, 110, 158, 131, 179, 112, 160)(101, 149, 107, 155, 125, 173, 138, 186, 143, 191, 137, 185, 136, 184, 113, 161)(103, 151, 117, 165, 128, 176, 114, 162, 130, 178, 109, 157, 129, 177, 118, 166)(105, 153, 121, 169, 139, 187, 124, 172, 141, 189, 120, 168, 140, 188, 122, 170) L = (1, 100)(2, 105)(3, 109)(4, 98)(5, 103)(6, 114)(7, 97)(8, 110)(9, 101)(10, 116)(11, 120)(12, 127)(13, 107)(14, 99)(15, 133)(16, 126)(17, 124)(18, 113)(19, 131)(20, 102)(21, 137)(22, 138)(23, 139)(24, 104)(25, 134)(26, 135)(27, 140)(28, 106)(29, 128)(30, 118)(31, 119)(32, 108)(33, 115)(34, 142)(35, 123)(36, 144)(37, 117)(38, 111)(39, 112)(40, 129)(41, 121)(42, 122)(43, 125)(44, 136)(45, 143)(46, 132)(47, 130)(48, 141)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 16, 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E23.501 Graph:: simple bipartite v = 22 e = 96 f = 30 degree seq :: [ 6^16, 16^6 ] E23.501 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 8, 8}) Quotient :: dipole Aut^+ = (C3 : C8) : C2 (small group id <48, 10>) Aut = (C2 x D24) : C2 (small group id <96, 156>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^3 * Y2, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y2 * Y1^-2 * Y2 * Y1^2, Y3 * Y1^-3 * Y3 * Y1^-1, Y2 * Y3 * Y1 * Y3 * Y2 * Y1^-1, Y3 * Y1^-1 * Y3 * Y2 * Y1 * Y2, Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-2, Y1^-1 * Y3 * Y1^2 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 49, 2, 50, 7, 55, 23, 71, 42, 90, 35, 83, 19, 67, 5, 53)(3, 51, 11, 59, 24, 72, 17, 65, 29, 77, 8, 56, 27, 75, 13, 61)(4, 52, 15, 63, 25, 73, 20, 68, 34, 82, 10, 58, 33, 81, 16, 64)(6, 54, 21, 69, 26, 74, 18, 66, 32, 80, 9, 57, 31, 79, 22, 70)(12, 60, 30, 78, 43, 91, 40, 88, 47, 95, 37, 85, 45, 93, 38, 86)(14, 62, 28, 76, 44, 92, 39, 87, 48, 96, 36, 84, 46, 94, 41, 89)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 108, 156)(101, 149, 113, 161)(102, 150, 110, 158)(103, 151, 120, 168)(105, 153, 124, 172)(106, 154, 126, 174)(107, 155, 131, 179)(109, 157, 119, 167)(111, 159, 133, 181)(112, 160, 136, 184)(114, 162, 137, 185)(115, 163, 123, 171)(116, 164, 134, 182)(117, 165, 132, 180)(118, 166, 135, 183)(121, 169, 139, 187)(122, 170, 140, 188)(125, 173, 138, 186)(127, 175, 142, 190)(128, 176, 144, 192)(129, 177, 141, 189)(130, 178, 143, 191) L = (1, 100)(2, 105)(3, 108)(4, 110)(5, 114)(6, 97)(7, 121)(8, 124)(9, 126)(10, 98)(11, 132)(12, 102)(13, 135)(14, 99)(15, 131)(16, 119)(17, 137)(18, 134)(19, 129)(20, 101)(21, 133)(22, 136)(23, 118)(24, 139)(25, 140)(26, 103)(27, 141)(28, 106)(29, 143)(30, 104)(31, 115)(32, 138)(33, 142)(34, 144)(35, 117)(36, 111)(37, 107)(38, 113)(39, 112)(40, 109)(41, 116)(42, 130)(43, 122)(44, 120)(45, 127)(46, 123)(47, 128)(48, 125)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 6, 16, 6, 16 ), ( 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16, 6, 16 ) } Outer automorphisms :: reflexible Dual of E23.500 Graph:: simple bipartite v = 30 e = 96 f = 22 degree seq :: [ 4^24, 16^6 ] E23.502 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 8, 8}) Quotient :: dipole Aut^+ = C2 . S4 = SL(2,3) . C2 (small group id <48, 28>) Aut = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>) |r| :: 2 Presentation :: [ R^2, Y3^2 * Y1^-1, Y1^3, (Y1 * Y3)^2, Y2^-1 * Y3^-1 * Y2^-1 * Y1, (R * Y1)^2, (R * Y3^-1)^2, Y2 * R * Y2^-1 * R * Y3^-1, Y1^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2^-4 * Y1^-1, Y2 * Y1 * Y2 * Y1^-1 * Y2^2 * Y1^-1, Y2^2 * Y3^-1 * Y2^-2 * Y1 * Y2^2 * Y1, (Y3 * Y2^-1)^8 ] Map:: non-degenerate R = (1, 49, 2, 50, 5, 53)(3, 51, 11, 59, 13, 61)(4, 52, 9, 57, 7, 55)(6, 54, 15, 63, 20, 68)(8, 56, 23, 71, 16, 64)(10, 58, 26, 74, 14, 62)(12, 60, 31, 79, 32, 80)(17, 65, 19, 67, 27, 75)(18, 66, 22, 70, 25, 73)(21, 69, 33, 81, 30, 78)(24, 72, 34, 82, 41, 89)(28, 76, 29, 77, 40, 88)(35, 83, 39, 87, 37, 85)(36, 84, 42, 90, 38, 86)(43, 91, 46, 94, 47, 95)(44, 92, 45, 93, 48, 96)(97, 145, 99, 147, 108, 156, 123, 171, 105, 153, 122, 170, 117, 165, 102, 150)(98, 146, 104, 152, 120, 168, 109, 157, 103, 151, 118, 166, 124, 172, 106, 154)(100, 148, 111, 159, 131, 179, 114, 162, 101, 149, 113, 161, 132, 180, 112, 160)(107, 155, 125, 173, 139, 187, 128, 176, 110, 158, 130, 178, 140, 188, 126, 174)(115, 163, 129, 177, 142, 190, 134, 182, 116, 164, 127, 175, 141, 189, 133, 181)(119, 167, 135, 183, 143, 191, 137, 185, 121, 169, 138, 186, 144, 192, 136, 184) L = (1, 100)(2, 105)(3, 106)(4, 98)(5, 103)(6, 115)(7, 97)(8, 114)(9, 101)(10, 107)(11, 122)(12, 126)(13, 110)(14, 99)(15, 123)(16, 121)(17, 102)(18, 119)(19, 111)(20, 113)(21, 128)(22, 112)(23, 118)(24, 136)(25, 104)(26, 109)(27, 116)(28, 137)(29, 120)(30, 127)(31, 117)(32, 129)(33, 108)(34, 124)(35, 134)(36, 133)(37, 138)(38, 135)(39, 132)(40, 130)(41, 125)(42, 131)(43, 144)(44, 143)(45, 139)(46, 140)(47, 141)(48, 142)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 16, 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E23.503 Graph:: bipartite v = 22 e = 96 f = 30 degree seq :: [ 6^16, 16^6 ] E23.503 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 8, 8}) Quotient :: dipole Aut^+ = C2 . S4 = SL(2,3) . C2 (small group id <48, 28>) Aut = (C2 . S4 = SL(2,3) . C2) : C2 (small group id <96, 192>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^-3 * Y2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y2 * Y1 * Y2 * Y1^-1, Y3^-1 * Y1 * Y3^-1 * Y1 * Y2, Y2 * Y1^4, Y3 * Y1 * Y3 * Y1^2 * Y3 * Y1 * Y3 * Y1^-2 ] Map:: non-degenerate R = (1, 49, 2, 50, 7, 55, 12, 60, 3, 51, 8, 56, 17, 65, 5, 53)(4, 52, 14, 62, 26, 74, 10, 58, 11, 59, 27, 75, 31, 79, 15, 63)(6, 54, 19, 67, 35, 83, 29, 77, 13, 61, 16, 64, 32, 80, 20, 68)(9, 57, 24, 72, 38, 86, 22, 70, 23, 71, 39, 87, 41, 89, 25, 73)(18, 66, 21, 69, 37, 85, 43, 91, 28, 76, 33, 81, 45, 93, 34, 82)(30, 78, 44, 92, 48, 96, 42, 90, 36, 84, 46, 94, 47, 95, 40, 88)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 107, 155)(101, 149, 108, 156)(102, 150, 109, 157)(103, 151, 113, 161)(105, 153, 119, 167)(106, 154, 111, 159)(110, 158, 123, 171)(112, 160, 115, 163)(114, 162, 124, 172)(116, 164, 125, 173)(117, 165, 129, 177)(118, 166, 121, 169)(120, 168, 135, 183)(122, 170, 127, 175)(126, 174, 132, 180)(128, 176, 131, 179)(130, 178, 139, 187)(133, 181, 141, 189)(134, 182, 137, 185)(136, 184, 138, 186)(140, 188, 142, 190)(143, 191, 144, 192) L = (1, 100)(2, 105)(3, 107)(4, 109)(5, 112)(6, 97)(7, 117)(8, 119)(9, 111)(10, 98)(11, 102)(12, 115)(13, 99)(14, 126)(15, 104)(16, 124)(17, 129)(18, 101)(19, 114)(20, 110)(21, 121)(22, 103)(23, 106)(24, 136)(25, 113)(26, 120)(27, 132)(28, 108)(29, 123)(30, 125)(31, 135)(32, 140)(33, 118)(34, 128)(35, 142)(36, 116)(37, 143)(38, 133)(39, 138)(40, 127)(41, 141)(42, 122)(43, 131)(44, 139)(45, 144)(46, 130)(47, 137)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 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 E23.502 Graph:: bipartite v = 30 e = 96 f = 22 degree seq :: [ 4^24, 16^6 ] E23.504 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 8, 8}) Quotient :: dipole Aut^+ = GL(2,3) (small group id <48, 29>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^2, Y1^3, (Y3^-1 * Y1^-1)^2, (Y1 * Y2^-1)^2, (R * Y3)^2, (R * Y1)^2, (Y2^-1 * Y3^-1)^2, Y2 * R * Y2^-1 * R * Y1, Y2^-2 * Y3^-1 * Y1^-1 * Y2^-2, (R * Y2 * Y3^-1)^2, Y2^-1 * Y3^-1 * Y2^2 * Y1 * Y2^-1 * Y1^-1, Y2 * Y1 * Y2 * Y3 * Y2^-2 * Y1^-1, (Y3 * Y2^-1)^8 ] Map:: non-degenerate R = (1, 49, 2, 50, 5, 53)(3, 51, 11, 59, 10, 58)(4, 52, 9, 57, 7, 55)(6, 54, 17, 65, 20, 68)(8, 56, 23, 71, 18, 66)(12, 60, 31, 79, 30, 78)(13, 61, 26, 74, 14, 62)(15, 63, 19, 67, 27, 75)(16, 64, 22, 70, 25, 73)(21, 69, 33, 81, 32, 80)(24, 72, 34, 82, 40, 88)(28, 76, 29, 77, 41, 89)(35, 83, 39, 87, 37, 85)(36, 84, 42, 90, 38, 86)(43, 91, 46, 94, 47, 95)(44, 92, 45, 93, 48, 96)(97, 145, 99, 147, 108, 156, 123, 171, 105, 153, 122, 170, 117, 165, 102, 150)(98, 146, 104, 152, 120, 168, 109, 157, 103, 151, 118, 166, 124, 172, 106, 154)(100, 148, 111, 159, 131, 179, 114, 162, 101, 149, 113, 161, 132, 180, 112, 160)(107, 155, 125, 173, 139, 187, 128, 176, 110, 158, 130, 178, 140, 188, 126, 174)(115, 163, 127, 175, 141, 189, 134, 182, 116, 164, 129, 177, 142, 190, 133, 181)(119, 167, 135, 183, 143, 191, 137, 185, 121, 169, 138, 186, 144, 192, 136, 184) L = (1, 100)(2, 105)(3, 109)(4, 98)(5, 103)(6, 115)(7, 97)(8, 112)(9, 101)(10, 110)(11, 122)(12, 128)(13, 107)(14, 99)(15, 102)(16, 119)(17, 123)(18, 121)(19, 113)(20, 111)(21, 126)(22, 114)(23, 118)(24, 137)(25, 104)(26, 106)(27, 116)(28, 136)(29, 120)(30, 129)(31, 117)(32, 127)(33, 108)(34, 124)(35, 134)(36, 133)(37, 138)(38, 135)(39, 132)(40, 125)(41, 130)(42, 131)(43, 144)(44, 143)(45, 139)(46, 140)(47, 141)(48, 142)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 16, 4, 16, 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E23.505 Graph:: bipartite v = 22 e = 96 f = 30 degree seq :: [ 6^16, 16^6 ] E23.505 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 8, 8}) Quotient :: dipole Aut^+ = GL(2,3) (small group id <48, 29>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y2 * Y3 * Y2 * Y3^-1, Y3^-3 * Y2, (R * Y3)^2, (R * Y2)^2, (Y3^-1 * Y1)^2, Y2 * Y1 * Y2 * Y1^-1, (R * Y1)^2, Y2 * Y1^4, Y3^2 * Y1 * Y3^-1 * Y2 * Y1, (Y3^-1 * Y1^-1)^8 ] Map:: non-degenerate R = (1, 49, 2, 50, 7, 55, 12, 60, 3, 51, 8, 56, 16, 64, 5, 53)(4, 52, 14, 62, 29, 77, 22, 70, 11, 59, 25, 73, 24, 72, 10, 58)(6, 54, 15, 63, 31, 79, 28, 76, 13, 61, 26, 74, 35, 83, 18, 66)(9, 57, 23, 71, 39, 87, 33, 81, 21, 69, 38, 86, 37, 85, 20, 68)(17, 65, 32, 80, 46, 94, 42, 90, 27, 75, 19, 67, 36, 84, 34, 82)(30, 78, 44, 92, 48, 96, 40, 88, 41, 89, 45, 93, 47, 95, 43, 91)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 107, 155)(101, 149, 108, 156)(102, 150, 109, 157)(103, 151, 112, 160)(105, 153, 117, 165)(106, 154, 118, 166)(110, 158, 121, 169)(111, 159, 122, 170)(113, 161, 123, 171)(114, 162, 124, 172)(115, 163, 128, 176)(116, 164, 129, 177)(119, 167, 134, 182)(120, 168, 125, 173)(126, 174, 137, 185)(127, 175, 131, 179)(130, 178, 138, 186)(132, 180, 142, 190)(133, 181, 135, 183)(136, 184, 139, 187)(140, 188, 141, 189)(143, 191, 144, 192) L = (1, 100)(2, 105)(3, 107)(4, 109)(5, 111)(6, 97)(7, 115)(8, 117)(9, 118)(10, 98)(11, 102)(12, 122)(13, 99)(14, 126)(15, 123)(16, 128)(17, 101)(18, 121)(19, 129)(20, 103)(21, 106)(22, 104)(23, 136)(24, 134)(25, 137)(26, 113)(27, 108)(28, 110)(29, 119)(30, 114)(31, 141)(32, 116)(33, 112)(34, 131)(35, 140)(36, 143)(37, 142)(38, 139)(39, 132)(40, 120)(41, 124)(42, 127)(43, 125)(44, 138)(45, 130)(46, 144)(47, 133)(48, 135)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 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 E23.504 Graph:: bipartite v = 30 e = 96 f = 22 degree seq :: [ 4^24, 16^6 ] E23.506 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = C4 x (C3 : C4) (small group id <48, 11>) Aut = (C6 x D8) : C2 (small group id <96, 147>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y1)^2, Y2^-1 * Y1 * Y2 * Y1, (R * Y3)^2, Y2^4, Y3^-1 * Y1 * Y3 * Y1, Y3 * Y1 * Y2^-1 * Y3 * Y2, (R * Y2 * Y3^-1)^2, Y3^-6 * Y1, Y2^-1 * Y3^3 * Y2 * Y3^-3 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 8, 56)(5, 53, 9, 57)(6, 54, 10, 58)(11, 59, 22, 70)(12, 60, 19, 67)(13, 61, 14, 62)(15, 63, 23, 71)(16, 64, 18, 66)(17, 65, 20, 68)(21, 69, 24, 72)(25, 73, 29, 77)(26, 74, 27, 75)(28, 76, 36, 84)(30, 78, 31, 79)(32, 80, 38, 86)(33, 81, 34, 82)(35, 83, 37, 85)(39, 87, 43, 91)(40, 88, 41, 89)(42, 90, 44, 92)(45, 93, 46, 94)(47, 95, 48, 96)(97, 145, 99, 147, 107, 155, 101, 149)(98, 146, 103, 151, 118, 166, 105, 153)(100, 148, 110, 158, 121, 169, 112, 160)(102, 150, 115, 163, 122, 170, 116, 164)(104, 152, 109, 157, 125, 173, 114, 162)(106, 154, 108, 156, 123, 171, 113, 161)(111, 159, 126, 174, 135, 183, 129, 177)(117, 165, 124, 172, 136, 184, 131, 179)(119, 167, 127, 175, 139, 187, 130, 178)(120, 168, 132, 180, 137, 185, 133, 181)(128, 176, 138, 186, 143, 191, 141, 189)(134, 182, 140, 188, 144, 192, 142, 190) L = (1, 100)(2, 104)(3, 108)(4, 111)(5, 113)(6, 97)(7, 115)(8, 119)(9, 116)(10, 98)(11, 121)(12, 124)(13, 99)(14, 103)(15, 128)(16, 105)(17, 131)(18, 101)(19, 132)(20, 133)(21, 102)(22, 125)(23, 134)(24, 106)(25, 135)(26, 107)(27, 118)(28, 138)(29, 139)(30, 109)(31, 110)(32, 120)(33, 114)(34, 112)(35, 141)(36, 140)(37, 142)(38, 117)(39, 143)(40, 122)(41, 123)(42, 127)(43, 144)(44, 126)(45, 130)(46, 129)(47, 137)(48, 136)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24 ) } Outer automorphisms :: reflexible Dual of E23.511 Graph:: simple bipartite v = 36 e = 96 f = 16 degree seq :: [ 4^24, 8^12 ] E23.507 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = C4 x (C3 : C4) (small group id <48, 11>) Aut = (C6 x D8) : C2 (small group id <96, 147>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2 * Y1 * Y2, Y3 * Y1 * Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^-2 * Y2 * Y3^-2 * Y2^-1, (Y3 * Y2 * Y3 * Y2^-1)^2, Y3^3 * Y2 * Y3^-3 * Y2^-1, Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50)(3, 51, 5, 53)(4, 52, 7, 55)(6, 54, 8, 56)(9, 57, 14, 62)(10, 58, 15, 63)(11, 59, 13, 61)(12, 60, 19, 67)(16, 64, 17, 65)(18, 66, 20, 68)(21, 69, 23, 71)(22, 70, 33, 81)(24, 72, 25, 73)(26, 74, 30, 78)(27, 75, 31, 79)(28, 76, 32, 80)(29, 77, 37, 85)(34, 82, 35, 83)(36, 84, 38, 86)(39, 87, 42, 90)(40, 88, 43, 91)(41, 89, 47, 95)(44, 92, 45, 93)(46, 94, 48, 96)(97, 145, 99, 147, 98, 146, 101, 149)(100, 148, 107, 155, 103, 151, 109, 157)(102, 150, 112, 160, 104, 152, 113, 161)(105, 153, 117, 165, 110, 158, 119, 167)(106, 154, 120, 168, 111, 159, 121, 169)(108, 156, 122, 170, 115, 163, 126, 174)(114, 162, 118, 166, 116, 164, 129, 177)(123, 171, 135, 183, 127, 175, 138, 186)(124, 172, 140, 188, 128, 176, 141, 189)(125, 173, 137, 185, 133, 181, 143, 191)(130, 178, 136, 184, 131, 179, 139, 187)(132, 180, 142, 190, 134, 182, 144, 192) L = (1, 100)(2, 103)(3, 105)(4, 108)(5, 110)(6, 97)(7, 115)(8, 98)(9, 118)(10, 99)(11, 123)(12, 125)(13, 127)(14, 129)(15, 101)(16, 130)(17, 131)(18, 102)(19, 133)(20, 104)(21, 135)(22, 137)(23, 138)(24, 140)(25, 141)(26, 106)(27, 112)(28, 107)(29, 139)(30, 111)(31, 113)(32, 109)(33, 143)(34, 142)(35, 144)(36, 114)(37, 136)(38, 116)(39, 120)(40, 117)(41, 124)(42, 121)(43, 119)(44, 134)(45, 132)(46, 122)(47, 128)(48, 126)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24 ) } Outer automorphisms :: reflexible Dual of E23.513 Graph:: bipartite v = 36 e = 96 f = 16 degree seq :: [ 4^24, 8^12 ] E23.508 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = C4 x (C3 : C4) (small group id <48, 11>) Aut = (C6 x D8) : C2 (small group id <96, 147>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y3)^2, (R * Y1)^2, Y3^-1 * Y1 * Y3 * Y1, Y2^4, Y2^-1 * Y1 * Y2 * Y1, Y2 * Y1 * Y3 * Y2 * Y3, Y2^-1 * Y1 * Y3 * Y2^-1 * Y3, (R * Y2 * Y3^-1)^2, Y3 * Y2 * Y3^-5 * Y2^-1 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 8, 56)(5, 53, 9, 57)(6, 54, 10, 58)(11, 59, 22, 70)(12, 60, 20, 68)(13, 61, 16, 64)(14, 62, 18, 66)(15, 63, 23, 71)(17, 65, 19, 67)(21, 69, 24, 72)(25, 73, 29, 77)(26, 74, 28, 76)(27, 75, 37, 85)(30, 78, 34, 82)(31, 79, 33, 81)(32, 80, 39, 87)(35, 83, 36, 84)(38, 86, 40, 88)(41, 89, 45, 93)(42, 90, 44, 92)(43, 91, 48, 96)(46, 94, 47, 95)(97, 145, 99, 147, 107, 155, 101, 149)(98, 146, 103, 151, 118, 166, 105, 153)(100, 148, 110, 158, 121, 169, 112, 160)(102, 150, 115, 163, 122, 170, 116, 164)(104, 152, 114, 162, 125, 173, 109, 157)(106, 154, 113, 161, 124, 172, 108, 156)(111, 159, 126, 174, 137, 185, 129, 177)(117, 165, 123, 171, 138, 186, 131, 179)(119, 167, 130, 178, 141, 189, 127, 175)(120, 168, 133, 181, 140, 188, 132, 180)(128, 176, 139, 187, 136, 184, 143, 191)(134, 182, 142, 190, 135, 183, 144, 192) L = (1, 100)(2, 104)(3, 108)(4, 111)(5, 113)(6, 97)(7, 116)(8, 119)(9, 115)(10, 98)(11, 121)(12, 123)(13, 99)(14, 105)(15, 128)(16, 103)(17, 131)(18, 101)(19, 132)(20, 133)(21, 102)(22, 125)(23, 135)(24, 106)(25, 137)(26, 107)(27, 139)(28, 118)(29, 141)(30, 109)(31, 110)(32, 140)(33, 114)(34, 112)(35, 143)(36, 142)(37, 144)(38, 117)(39, 138)(40, 120)(41, 136)(42, 122)(43, 127)(44, 124)(45, 134)(46, 126)(47, 130)(48, 129)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24 ) } Outer automorphisms :: reflexible Dual of E23.512 Graph:: simple bipartite v = 36 e = 96 f = 16 degree seq :: [ 4^24, 8^12 ] E23.509 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = C4 x (C3 : C4) (small group id <48, 11>) Aut = (C6 x D8) : C2 (small group id <96, 147>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-1, (R * Y1)^2, (R * Y3)^2, Y2^4, (Y3^-1 * Y1^-1)^2, Y1^4, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2^-1 * Y1^-2 * Y2 * Y1^-1, Y2^-1 * Y1 * Y2^-2 * Y1^-1 * Y2^-1, (Y2^-1 * R * Y2^-1)^2, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, (Y3 * Y2^-1)^12 ] Map:: non-degenerate R = (1, 49, 2, 50, 6, 54, 4, 52)(3, 51, 9, 57, 16, 64, 11, 59)(5, 53, 14, 62, 17, 65, 15, 63)(7, 55, 18, 66, 12, 60, 20, 68)(8, 56, 21, 69, 13, 61, 22, 70)(10, 58, 19, 67, 28, 76, 25, 73)(23, 71, 33, 81, 26, 74, 34, 82)(24, 72, 35, 83, 27, 75, 36, 84)(29, 77, 37, 85, 31, 79, 38, 86)(30, 78, 39, 87, 32, 80, 40, 88)(41, 89, 45, 93, 43, 91, 47, 95)(42, 90, 46, 94, 44, 92, 48, 96)(97, 145, 99, 147, 106, 154, 101, 149)(98, 146, 103, 151, 115, 163, 104, 152)(100, 148, 108, 156, 121, 169, 109, 157)(102, 150, 112, 160, 124, 172, 113, 161)(105, 153, 119, 167, 110, 158, 120, 168)(107, 155, 122, 170, 111, 159, 123, 171)(114, 162, 125, 173, 117, 165, 126, 174)(116, 164, 127, 175, 118, 166, 128, 176)(129, 177, 137, 185, 131, 179, 138, 186)(130, 178, 139, 187, 132, 180, 140, 188)(133, 181, 141, 189, 135, 183, 142, 190)(134, 182, 143, 191, 136, 184, 144, 192) L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 110)(6, 100)(7, 114)(8, 117)(9, 112)(10, 115)(11, 99)(12, 116)(13, 118)(14, 113)(15, 101)(16, 107)(17, 111)(18, 108)(19, 124)(20, 103)(21, 109)(22, 104)(23, 129)(24, 131)(25, 106)(26, 130)(27, 132)(28, 121)(29, 133)(30, 135)(31, 134)(32, 136)(33, 122)(34, 119)(35, 123)(36, 120)(37, 127)(38, 125)(39, 128)(40, 126)(41, 141)(42, 142)(43, 143)(44, 144)(45, 139)(46, 140)(47, 137)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E23.510 Graph:: bipartite v = 24 e = 96 f = 28 degree seq :: [ 8^24 ] E23.510 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = C4 x (C3 : C4) (small group id <48, 11>) Aut = (C6 x D8) : C2 (small group id <96, 147>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y2 * Y3^2, Y1 * Y2 * Y1^-1 * Y2, (Y3 * R)^2, (R * Y1)^2, (R * Y2)^2, Y1^2 * Y3 * Y1^2 * Y3^-1, Y1^-2 * Y3 * Y1 * Y3^-1 * Y1^-3, Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 49, 2, 50, 7, 55, 19, 67, 37, 85, 30, 78, 44, 92, 32, 80, 46, 94, 34, 82, 15, 63, 5, 53)(3, 51, 8, 56, 20, 68, 38, 86, 48, 96, 29, 77, 43, 91, 31, 79, 45, 93, 47, 95, 27, 75, 11, 59)(4, 52, 12, 60, 28, 76, 39, 87, 24, 72, 9, 57, 23, 71, 14, 62, 33, 81, 41, 89, 21, 69, 13, 61)(6, 54, 17, 65, 35, 83, 40, 88, 26, 74, 10, 58, 25, 73, 16, 64, 36, 84, 42, 90, 22, 70, 18, 66)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 102, 150)(101, 149, 107, 155)(103, 151, 116, 164)(105, 153, 106, 154)(108, 156, 113, 161)(109, 157, 114, 162)(110, 158, 112, 160)(111, 159, 123, 171)(115, 163, 134, 182)(117, 165, 118, 166)(119, 167, 121, 169)(120, 168, 122, 170)(124, 172, 131, 179)(125, 173, 126, 174)(127, 175, 128, 176)(129, 177, 132, 180)(130, 178, 143, 191)(133, 181, 144, 192)(135, 183, 136, 184)(137, 185, 138, 186)(139, 187, 140, 188)(141, 189, 142, 190) L = (1, 100)(2, 105)(3, 102)(4, 99)(5, 110)(6, 97)(7, 117)(8, 106)(9, 104)(10, 98)(11, 112)(12, 125)(13, 127)(14, 107)(15, 124)(16, 101)(17, 126)(18, 128)(19, 135)(20, 118)(21, 116)(22, 103)(23, 139)(24, 141)(25, 140)(26, 142)(27, 131)(28, 123)(29, 113)(30, 108)(31, 114)(32, 109)(33, 144)(34, 137)(35, 111)(36, 133)(37, 129)(38, 136)(39, 134)(40, 115)(41, 143)(42, 130)(43, 121)(44, 119)(45, 122)(46, 120)(47, 138)(48, 132)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8^4 ), ( 8^24 ) } Outer automorphisms :: reflexible Dual of E23.509 Graph:: simple bipartite v = 28 e = 96 f = 24 degree seq :: [ 4^24, 24^4 ] E23.511 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = C4 x (C3 : C4) (small group id <48, 11>) Aut = (C6 x D8) : C2 (small group id <96, 147>) |r| :: 2 Presentation :: [ R^2, (Y3, Y2^-1), (Y3^-1 * Y2)^2, Y2^2 * Y3^-2, (R * Y2)^2, (R * Y1)^2, Y3 * Y1 * Y2 * Y1^-1, (R * Y3)^2, Y1^4, Y2 * Y1 * Y3 * Y1^-1, Y3^-2 * Y2^-1 * Y3^-1 * Y2^-2, Y3^2 * Y1 * Y3^-1 * Y2^-3 * Y1^-1, Y1^-1 * Y2 * Y1^-1 * Y3^-1 * Y2 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 12, 60, 22, 70, 15, 63)(4, 52, 11, 59, 23, 71, 17, 65)(6, 54, 10, 58, 24, 72, 19, 67)(7, 55, 9, 57, 25, 73, 18, 66)(13, 61, 29, 77, 38, 86, 33, 81)(14, 62, 30, 78, 39, 87, 34, 82)(16, 64, 28, 76, 40, 88, 35, 83)(20, 68, 26, 74, 41, 89, 36, 84)(21, 69, 27, 75, 42, 90, 37, 85)(31, 79, 43, 91, 47, 95, 45, 93)(32, 80, 44, 92, 48, 96, 46, 94)(97, 145, 99, 147, 109, 157, 127, 175, 117, 165, 103, 151, 112, 160, 100, 148, 110, 158, 128, 176, 116, 164, 102, 150)(98, 146, 105, 153, 122, 170, 139, 187, 126, 174, 108, 156, 124, 172, 106, 154, 123, 171, 140, 188, 125, 173, 107, 155)(101, 149, 114, 162, 132, 180, 141, 189, 130, 178, 111, 159, 131, 179, 115, 163, 133, 181, 142, 190, 129, 177, 113, 161)(104, 152, 118, 166, 134, 182, 143, 191, 138, 186, 121, 169, 136, 184, 119, 167, 135, 183, 144, 192, 137, 185, 120, 168) L = (1, 100)(2, 106)(3, 110)(4, 109)(5, 115)(6, 112)(7, 97)(8, 119)(9, 123)(10, 122)(11, 124)(12, 98)(13, 128)(14, 127)(15, 101)(16, 99)(17, 131)(18, 133)(19, 132)(20, 103)(21, 102)(22, 135)(23, 134)(24, 136)(25, 104)(26, 140)(27, 139)(28, 105)(29, 108)(30, 107)(31, 116)(32, 117)(33, 111)(34, 113)(35, 114)(36, 142)(37, 141)(38, 144)(39, 143)(40, 118)(41, 121)(42, 120)(43, 125)(44, 126)(45, 129)(46, 130)(47, 137)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ), ( 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 E23.506 Graph:: bipartite v = 16 e = 96 f = 36 degree seq :: [ 8^12, 24^4 ] E23.512 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = C4 x (C3 : C4) (small group id <48, 11>) Aut = (C6 x D8) : C2 (small group id <96, 147>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y1^2 * Y3, Y3^2 * Y2^-2, (Y3, Y2^-1), Y3^-1 * Y2 * Y1^2, Y3^-1 * Y1^-2 * Y2, (R * Y3)^2, Y2 * Y1^-2 * Y3^-1, (R * Y2)^2, (R * Y1)^2, Y1 * Y3^2 * Y1 * Y3 * Y2, Y3^-2 * Y2^-1 * Y1 * Y2^3 * Y1^-1, (Y2^-1 * Y1)^4, Y3 * Y1^-1 * Y2^-1 * Y3^-2 * Y2^-2 * Y1^-1, Y3^-1 * Y1^-1 * Y3 * Y1^-1 * Y2 * Y1^-1 * Y2^-1 * Y1^-1, Y2 * Y1^-1 * Y2^-1 * Y1 * Y2 * Y3^2 * Y2, Y3^12 ] Map:: non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 4, 52, 16, 64)(6, 54, 17, 65, 7, 55, 18, 66)(9, 57, 21, 69, 10, 58, 24, 72)(11, 59, 25, 73, 12, 60, 26, 74)(14, 62, 27, 75, 15, 63, 28, 76)(19, 67, 22, 70, 20, 68, 23, 71)(29, 77, 39, 87, 30, 78, 40, 88)(31, 79, 45, 93, 32, 80, 46, 94)(33, 81, 43, 91, 34, 82, 44, 92)(35, 83, 41, 89, 36, 84, 42, 90)(37, 85, 47, 95, 38, 86, 48, 96)(97, 145, 99, 147, 110, 158, 129, 177, 138, 186, 120, 168, 136, 184, 122, 170, 142, 190, 133, 181, 115, 163, 102, 150)(98, 146, 105, 153, 118, 166, 139, 187, 127, 175, 109, 157, 125, 173, 113, 161, 131, 179, 143, 191, 123, 171, 107, 155)(100, 148, 111, 159, 130, 178, 137, 185, 117, 165, 135, 183, 121, 169, 141, 189, 134, 182, 116, 164, 103, 151, 104, 152)(101, 149, 106, 154, 119, 167, 140, 188, 128, 176, 112, 160, 126, 174, 114, 162, 132, 180, 144, 192, 124, 172, 108, 156) L = (1, 100)(2, 106)(3, 111)(4, 110)(5, 105)(6, 104)(7, 97)(8, 99)(9, 119)(10, 118)(11, 101)(12, 98)(13, 126)(14, 130)(15, 129)(16, 125)(17, 132)(18, 131)(19, 103)(20, 102)(21, 136)(22, 140)(23, 139)(24, 135)(25, 142)(26, 141)(27, 108)(28, 107)(29, 114)(30, 113)(31, 112)(32, 109)(33, 137)(34, 138)(35, 144)(36, 143)(37, 116)(38, 115)(39, 122)(40, 121)(41, 120)(42, 117)(43, 128)(44, 127)(45, 133)(46, 134)(47, 124)(48, 123)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ), ( 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 E23.508 Graph:: bipartite v = 16 e = 96 f = 36 degree seq :: [ 8^12, 24^4 ] E23.513 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = C4 x (C3 : C4) (small group id <48, 11>) Aut = (C6 x D8) : C2 (small group id <96, 147>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y3^2 * Y2^-1, Y3 * Y1^-1 * Y2 * Y1^-1, (R * Y1)^2, (Y3, Y2), (R * Y3)^2, (R * Y2)^2, Y1^4, Y1^-1 * Y2^-1 * Y1^-1 * Y3^-1, Y1^-1 * Y3 * Y1 * Y2^-1 * Y1^-2 * Y3^2, Y2 * Y1^-1 * Y2^-1 * Y3^-3 * Y1^-1 * Y2, Y3^-2 * Y2^-1 * Y3^-2 * Y1 * Y2 * Y1^-1, Y2^-1 * Y1^-1 * Y2^2 * Y3 * Y2 * Y1^-1 * Y2^-1, Y3^2 * Y2^10 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 22, 70, 12, 60)(4, 52, 17, 65, 23, 71, 11, 59)(6, 54, 19, 67, 24, 72, 10, 58)(7, 55, 18, 66, 25, 73, 9, 57)(14, 62, 29, 77, 40, 88, 33, 81)(15, 63, 30, 78, 41, 89, 32, 80)(16, 64, 28, 76, 42, 90, 31, 79)(20, 68, 26, 74, 43, 91, 36, 84)(21, 69, 27, 75, 44, 92, 37, 85)(34, 82, 45, 93, 39, 87, 48, 96)(35, 83, 46, 94, 38, 86, 47, 95)(97, 145, 99, 147, 110, 158, 130, 178, 140, 188, 121, 169, 138, 186, 119, 167, 137, 185, 134, 182, 116, 164, 102, 150)(98, 146, 105, 153, 122, 170, 141, 189, 128, 176, 109, 157, 127, 175, 115, 163, 133, 181, 143, 191, 125, 173, 107, 155)(100, 148, 111, 159, 131, 179, 139, 187, 120, 168, 104, 152, 118, 166, 136, 184, 135, 183, 117, 165, 103, 151, 112, 160)(101, 149, 114, 162, 132, 180, 144, 192, 126, 174, 108, 156, 124, 172, 106, 154, 123, 171, 142, 190, 129, 177, 113, 161) L = (1, 100)(2, 106)(3, 111)(4, 110)(5, 115)(6, 112)(7, 97)(8, 119)(9, 123)(10, 122)(11, 124)(12, 98)(13, 101)(14, 131)(15, 130)(16, 99)(17, 127)(18, 133)(19, 132)(20, 103)(21, 102)(22, 137)(23, 136)(24, 138)(25, 104)(26, 142)(27, 141)(28, 105)(29, 108)(30, 107)(31, 114)(32, 113)(33, 109)(34, 139)(35, 140)(36, 143)(37, 144)(38, 117)(39, 116)(40, 134)(41, 135)(42, 118)(43, 121)(44, 120)(45, 129)(46, 128)(47, 126)(48, 125)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ), ( 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 E23.507 Graph:: bipartite v = 16 e = 96 f = 36 degree seq :: [ 8^12, 24^4 ] E23.514 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = (C3 : C4) : C4 (small group id <48, 12>) Aut = (C2 x C4 x S3) : C2 (small group id <96, 91>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^-2 * Y1, Y3 * Y1 * Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y3^2 * Y2^-1 * Y3^2 * Y2, (Y3 * Y2 * Y3 * Y2^-1)^2, (Y3^-1 * Y2^-1)^4, Y3^-4 * Y2^-1 * Y3 * Y2^-1 * Y3^-1 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50)(3, 51, 5, 53)(4, 52, 7, 55)(6, 54, 8, 56)(9, 57, 14, 62)(10, 58, 15, 63)(11, 59, 13, 61)(12, 60, 19, 67)(16, 64, 17, 65)(18, 66, 20, 68)(21, 69, 23, 71)(22, 70, 33, 81)(24, 72, 25, 73)(26, 74, 30, 78)(27, 75, 31, 79)(28, 76, 32, 80)(29, 77, 37, 85)(34, 82, 35, 83)(36, 84, 38, 86)(39, 87, 42, 90)(40, 88, 43, 91)(41, 89, 47, 95)(44, 92, 45, 93)(46, 94, 48, 96)(97, 145, 99, 147, 98, 146, 101, 149)(100, 148, 107, 155, 103, 151, 109, 157)(102, 150, 112, 160, 104, 152, 113, 161)(105, 153, 117, 165, 110, 158, 119, 167)(106, 154, 120, 168, 111, 159, 121, 169)(108, 156, 122, 170, 115, 163, 126, 174)(114, 162, 118, 166, 116, 164, 129, 177)(123, 171, 135, 183, 127, 175, 138, 186)(124, 172, 140, 188, 128, 176, 141, 189)(125, 173, 143, 191, 133, 181, 137, 185)(130, 178, 136, 184, 131, 179, 139, 187)(132, 180, 144, 192, 134, 182, 142, 190) L = (1, 100)(2, 103)(3, 105)(4, 108)(5, 110)(6, 97)(7, 115)(8, 98)(9, 118)(10, 99)(11, 123)(12, 125)(13, 127)(14, 129)(15, 101)(16, 130)(17, 131)(18, 102)(19, 133)(20, 104)(21, 135)(22, 137)(23, 138)(24, 140)(25, 141)(26, 106)(27, 112)(28, 107)(29, 136)(30, 111)(31, 113)(32, 109)(33, 143)(34, 144)(35, 142)(36, 114)(37, 139)(38, 116)(39, 120)(40, 117)(41, 128)(42, 121)(43, 119)(44, 132)(45, 134)(46, 122)(47, 124)(48, 126)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24 ) } Outer automorphisms :: reflexible Dual of E23.530 Graph:: bipartite v = 36 e = 96 f = 16 degree seq :: [ 4^24, 8^12 ] E23.515 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = (C3 : C4) : C4 (small group id <48, 12>) Aut = (C2 x C4 x S3) : C2 (small group id <96, 91>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y1)^2, (R * Y3)^2, Y3^-1 * Y1 * Y3 * Y1, Y2^-1 * Y1 * Y2 * Y1, Y2^4, Y2 * Y3^-1 * Y2^-1 * Y1 * Y3^-1, Y3 * Y1 * Y2^-1 * Y3 * Y2, (R * Y2 * Y3^-1)^2, Y3^5 * Y2^-1 * Y3^-1 * Y2^-1 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 8, 56)(5, 53, 9, 57)(6, 54, 10, 58)(11, 59, 22, 70)(12, 60, 19, 67)(13, 61, 14, 62)(15, 63, 23, 71)(16, 64, 18, 66)(17, 65, 20, 68)(21, 69, 24, 72)(25, 73, 29, 77)(26, 74, 27, 75)(28, 76, 36, 84)(30, 78, 31, 79)(32, 80, 39, 87)(33, 81, 34, 82)(35, 83, 37, 85)(38, 86, 40, 88)(41, 89, 45, 93)(42, 90, 43, 91)(44, 92, 48, 96)(46, 94, 47, 95)(97, 145, 99, 147, 107, 155, 101, 149)(98, 146, 103, 151, 118, 166, 105, 153)(100, 148, 110, 158, 121, 169, 112, 160)(102, 150, 115, 163, 122, 170, 116, 164)(104, 152, 109, 157, 125, 173, 114, 162)(106, 154, 108, 156, 123, 171, 113, 161)(111, 159, 126, 174, 137, 185, 129, 177)(117, 165, 124, 172, 138, 186, 131, 179)(119, 167, 127, 175, 141, 189, 130, 178)(120, 168, 132, 180, 139, 187, 133, 181)(128, 176, 143, 191, 136, 184, 140, 188)(134, 182, 144, 192, 135, 183, 142, 190) L = (1, 100)(2, 104)(3, 108)(4, 111)(5, 113)(6, 97)(7, 115)(8, 119)(9, 116)(10, 98)(11, 121)(12, 124)(13, 99)(14, 103)(15, 128)(16, 105)(17, 131)(18, 101)(19, 132)(20, 133)(21, 102)(22, 125)(23, 135)(24, 106)(25, 137)(26, 107)(27, 118)(28, 140)(29, 141)(30, 109)(31, 110)(32, 139)(33, 114)(34, 112)(35, 143)(36, 144)(37, 142)(38, 117)(39, 138)(40, 120)(41, 136)(42, 122)(43, 123)(44, 130)(45, 134)(46, 126)(47, 127)(48, 129)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24 ) } Outer automorphisms :: reflexible Dual of E23.526 Graph:: simple bipartite v = 36 e = 96 f = 16 degree seq :: [ 4^24, 8^12 ] E23.516 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = (C3 : C4) : C4 (small group id <48, 12>) Aut = (C2 x C4 x S3) : C2 (small group id <96, 91>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1 * Y3 * Y1, (R * Y3)^2, (R * Y1)^2, Y2^4, Y2^-1 * Y1 * Y2 * Y1, Y2 * Y1 * Y3 * Y2 * Y3, Y2^-1 * Y1 * Y3 * Y2^-1 * Y3, (R * Y2 * Y3^-1)^2, Y3^-6 * Y1, Y3^3 * Y2^-1 * Y3^-3 * Y2^-1 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 8, 56)(5, 53, 9, 57)(6, 54, 10, 58)(11, 59, 22, 70)(12, 60, 20, 68)(13, 61, 16, 64)(14, 62, 18, 66)(15, 63, 23, 71)(17, 65, 19, 67)(21, 69, 24, 72)(25, 73, 29, 77)(26, 74, 28, 76)(27, 75, 37, 85)(30, 78, 34, 82)(31, 79, 33, 81)(32, 80, 38, 86)(35, 83, 36, 84)(39, 87, 43, 91)(40, 88, 42, 90)(41, 89, 44, 92)(45, 93, 46, 94)(47, 95, 48, 96)(97, 145, 99, 147, 107, 155, 101, 149)(98, 146, 103, 151, 118, 166, 105, 153)(100, 148, 110, 158, 121, 169, 112, 160)(102, 150, 115, 163, 122, 170, 116, 164)(104, 152, 114, 162, 125, 173, 109, 157)(106, 154, 113, 161, 124, 172, 108, 156)(111, 159, 126, 174, 135, 183, 129, 177)(117, 165, 123, 171, 136, 184, 131, 179)(119, 167, 130, 178, 139, 187, 127, 175)(120, 168, 133, 181, 138, 186, 132, 180)(128, 176, 141, 189, 143, 191, 137, 185)(134, 182, 142, 190, 144, 192, 140, 188) L = (1, 100)(2, 104)(3, 108)(4, 111)(5, 113)(6, 97)(7, 116)(8, 119)(9, 115)(10, 98)(11, 121)(12, 123)(13, 99)(14, 105)(15, 128)(16, 103)(17, 131)(18, 101)(19, 132)(20, 133)(21, 102)(22, 125)(23, 134)(24, 106)(25, 135)(26, 107)(27, 137)(28, 118)(29, 139)(30, 109)(31, 110)(32, 120)(33, 114)(34, 112)(35, 141)(36, 142)(37, 140)(38, 117)(39, 143)(40, 122)(41, 130)(42, 124)(43, 144)(44, 126)(45, 127)(46, 129)(47, 138)(48, 136)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24 ) } Outer automorphisms :: reflexible Dual of E23.528 Graph:: simple bipartite v = 36 e = 96 f = 16 degree seq :: [ 4^24, 8^12 ] E23.517 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = (C3 : C4) : C4 (small group id <48, 12>) Aut = (C2 x C4 x S3) : C2 (small group id <96, 91>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^4, (R * Y3)^2, (R * Y1)^2, Y3^-1 * Y1 * Y3 * Y1, Y2^-1 * Y1 * Y2 * Y1, Y3^-1 * Y1 * Y2^-1 * Y3^-1 * Y2^-1, Y2^-1 * Y1 * Y3 * Y2^-1 * Y3, (R * Y2 * Y3^-1)^2, Y3^2 * Y2^-1 * Y3^-4 * Y2^-1 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 8, 56)(5, 53, 9, 57)(6, 54, 10, 58)(11, 59, 22, 70)(12, 60, 20, 68)(13, 61, 16, 64)(14, 62, 18, 66)(15, 63, 23, 71)(17, 65, 19, 67)(21, 69, 24, 72)(25, 73, 29, 77)(26, 74, 28, 76)(27, 75, 37, 85)(30, 78, 34, 82)(31, 79, 33, 81)(32, 80, 39, 87)(35, 83, 36, 84)(38, 86, 40, 88)(41, 89, 45, 93)(42, 90, 44, 92)(43, 91, 47, 95)(46, 94, 48, 96)(97, 145, 99, 147, 107, 155, 101, 149)(98, 146, 103, 151, 118, 166, 105, 153)(100, 148, 110, 158, 121, 169, 112, 160)(102, 150, 115, 163, 122, 170, 116, 164)(104, 152, 114, 162, 125, 173, 109, 157)(106, 154, 113, 161, 124, 172, 108, 156)(111, 159, 126, 174, 137, 185, 129, 177)(117, 165, 123, 171, 138, 186, 131, 179)(119, 167, 130, 178, 141, 189, 127, 175)(120, 168, 133, 181, 140, 188, 132, 180)(128, 176, 143, 191, 134, 182, 144, 192)(135, 183, 139, 187, 136, 184, 142, 190) L = (1, 100)(2, 104)(3, 108)(4, 111)(5, 113)(6, 97)(7, 116)(8, 119)(9, 115)(10, 98)(11, 121)(12, 123)(13, 99)(14, 105)(15, 128)(16, 103)(17, 131)(18, 101)(19, 132)(20, 133)(21, 102)(22, 125)(23, 135)(24, 106)(25, 137)(26, 107)(27, 139)(28, 118)(29, 141)(30, 109)(31, 110)(32, 138)(33, 114)(34, 112)(35, 142)(36, 144)(37, 143)(38, 117)(39, 140)(40, 120)(41, 134)(42, 122)(43, 129)(44, 124)(45, 136)(46, 126)(47, 127)(48, 130)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24 ) } Outer automorphisms :: reflexible Dual of E23.531 Graph:: simple bipartite v = 36 e = 96 f = 16 degree seq :: [ 4^24, 8^12 ] E23.518 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = (C3 : C4) : C4 (small group id <48, 12>) Aut = (C2 x C4 x S3) : C2 (small group id <96, 91>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^4, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y1 * Y2 * Y1, Y3^-1 * Y1 * Y3 * Y1, Y2 * Y1 * Y3^-1 * Y2^-1 * Y3^-1, (R * Y2 * Y3^-1)^2, Y3^2 * Y2^-1 * Y3^-4 * Y2^-1 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 8, 56)(5, 53, 9, 57)(6, 54, 10, 58)(11, 59, 22, 70)(12, 60, 19, 67)(13, 61, 14, 62)(15, 63, 23, 71)(16, 64, 18, 66)(17, 65, 20, 68)(21, 69, 24, 72)(25, 73, 29, 77)(26, 74, 27, 75)(28, 76, 36, 84)(30, 78, 31, 79)(32, 80, 39, 87)(33, 81, 34, 82)(35, 83, 37, 85)(38, 86, 40, 88)(41, 89, 45, 93)(42, 90, 43, 91)(44, 92, 48, 96)(46, 94, 47, 95)(97, 145, 99, 147, 107, 155, 101, 149)(98, 146, 103, 151, 118, 166, 105, 153)(100, 148, 110, 158, 121, 169, 112, 160)(102, 150, 115, 163, 122, 170, 116, 164)(104, 152, 109, 157, 125, 173, 114, 162)(106, 154, 108, 156, 123, 171, 113, 161)(111, 159, 126, 174, 137, 185, 129, 177)(117, 165, 124, 172, 138, 186, 131, 179)(119, 167, 127, 175, 141, 189, 130, 178)(120, 168, 132, 180, 139, 187, 133, 181)(128, 176, 143, 191, 134, 182, 144, 192)(135, 183, 142, 190, 136, 184, 140, 188) L = (1, 100)(2, 104)(3, 108)(4, 111)(5, 113)(6, 97)(7, 115)(8, 119)(9, 116)(10, 98)(11, 121)(12, 124)(13, 99)(14, 103)(15, 128)(16, 105)(17, 131)(18, 101)(19, 132)(20, 133)(21, 102)(22, 125)(23, 135)(24, 106)(25, 137)(26, 107)(27, 118)(28, 140)(29, 141)(30, 109)(31, 110)(32, 138)(33, 114)(34, 112)(35, 142)(36, 144)(37, 143)(38, 117)(39, 139)(40, 120)(41, 134)(42, 122)(43, 123)(44, 129)(45, 136)(46, 126)(47, 127)(48, 130)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24 ) } Outer automorphisms :: reflexible Dual of E23.527 Graph:: simple bipartite v = 36 e = 96 f = 16 degree seq :: [ 4^24, 8^12 ] E23.519 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = (C3 : C4) : C4 (small group id <48, 12>) Aut = (C2 x C4 x S3) : C2 (small group id <96, 91>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2 * Y1 * Y2, Y3 * Y1 * Y3^-1 * Y1, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y3^-1 * Y1 * Y3 * Y2^-1, (R * Y2 * Y3^-1)^2, Y2 * Y3^-2 * Y2^-1 * Y3^-2, Y3^-6 * Y1, Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 5, 53)(4, 52, 7, 55)(6, 54, 8, 56)(9, 57, 14, 62)(10, 58, 15, 63)(11, 59, 13, 61)(12, 60, 19, 67)(16, 64, 17, 65)(18, 66, 20, 68)(21, 69, 23, 71)(22, 70, 33, 81)(24, 72, 25, 73)(26, 74, 30, 78)(27, 75, 31, 79)(28, 76, 32, 80)(29, 77, 36, 84)(34, 82, 35, 83)(37, 85, 40, 88)(38, 86, 41, 89)(39, 87, 44, 92)(42, 90, 43, 91)(45, 93, 46, 94)(47, 95, 48, 96)(97, 145, 99, 147, 98, 146, 101, 149)(100, 148, 107, 155, 103, 151, 109, 157)(102, 150, 112, 160, 104, 152, 113, 161)(105, 153, 117, 165, 110, 158, 119, 167)(106, 154, 120, 168, 111, 159, 121, 169)(108, 156, 122, 170, 115, 163, 126, 174)(114, 162, 118, 166, 116, 164, 129, 177)(123, 171, 133, 181, 127, 175, 136, 184)(124, 172, 138, 186, 128, 176, 139, 187)(125, 173, 141, 189, 132, 180, 142, 190)(130, 178, 134, 182, 131, 179, 137, 185)(135, 183, 143, 191, 140, 188, 144, 192) L = (1, 100)(2, 103)(3, 105)(4, 108)(5, 110)(6, 97)(7, 115)(8, 98)(9, 118)(10, 99)(11, 123)(12, 125)(13, 127)(14, 129)(15, 101)(16, 130)(17, 131)(18, 102)(19, 132)(20, 104)(21, 133)(22, 135)(23, 136)(24, 138)(25, 139)(26, 106)(27, 112)(28, 107)(29, 116)(30, 111)(31, 113)(32, 109)(33, 140)(34, 142)(35, 141)(36, 114)(37, 120)(38, 117)(39, 126)(40, 121)(41, 119)(42, 144)(43, 143)(44, 122)(45, 124)(46, 128)(47, 134)(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, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24 ) } Outer automorphisms :: reflexible Dual of E23.529 Graph:: bipartite v = 36 e = 96 f = 16 degree seq :: [ 4^24, 8^12 ] E23.520 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = (C3 : C4) : C4 (small group id <48, 12>) Aut = (C2 x C4 x S3) : C2 (small group id <96, 91>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3, Y2^4, (R * Y1)^2, Y2^4, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, Y1^4, Y2^-1 * Y1^2 * Y2 * Y1 * Y3, Y2^-1 * Y1 * Y2^-2 * Y1^-1 * Y2^-1, (Y2^-1 * R * Y2^-1)^2, (R * Y2 * Y3^-1)^2, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, (Y3 * Y2^-1)^12 ] Map:: non-degenerate R = (1, 49, 2, 50, 6, 54, 4, 52)(3, 51, 9, 57, 16, 64, 11, 59)(5, 53, 14, 62, 17, 65, 15, 63)(7, 55, 18, 66, 12, 60, 20, 68)(8, 56, 21, 69, 13, 61, 22, 70)(10, 58, 19, 67, 28, 76, 25, 73)(23, 71, 33, 81, 26, 74, 34, 82)(24, 72, 35, 83, 27, 75, 36, 84)(29, 77, 37, 85, 31, 79, 38, 86)(30, 78, 39, 87, 32, 80, 40, 88)(41, 89, 46, 94, 43, 91, 48, 96)(42, 90, 45, 93, 44, 92, 47, 95)(97, 145, 99, 147, 106, 154, 101, 149)(98, 146, 103, 151, 115, 163, 104, 152)(100, 148, 108, 156, 121, 169, 109, 157)(102, 150, 112, 160, 124, 172, 113, 161)(105, 153, 119, 167, 110, 158, 120, 168)(107, 155, 122, 170, 111, 159, 123, 171)(114, 162, 125, 173, 117, 165, 126, 174)(116, 164, 127, 175, 118, 166, 128, 176)(129, 177, 137, 185, 131, 179, 138, 186)(130, 178, 139, 187, 132, 180, 140, 188)(133, 181, 141, 189, 135, 183, 142, 190)(134, 182, 143, 191, 136, 184, 144, 192) L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 110)(6, 100)(7, 114)(8, 117)(9, 112)(10, 115)(11, 99)(12, 116)(13, 118)(14, 113)(15, 101)(16, 107)(17, 111)(18, 108)(19, 124)(20, 103)(21, 109)(22, 104)(23, 129)(24, 131)(25, 106)(26, 130)(27, 132)(28, 121)(29, 133)(30, 135)(31, 134)(32, 136)(33, 122)(34, 119)(35, 123)(36, 120)(37, 127)(38, 125)(39, 128)(40, 126)(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) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E23.525 Graph:: bipartite v = 24 e = 96 f = 28 degree seq :: [ 8^24 ] E23.521 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = (C3 : C4) : C4 (small group id <48, 12>) Aut = (C2 x C4 x S3) : C2 (small group id <96, 91>) |r| :: 2 Presentation :: [ R^2, Y1^4, Y1^2 * Y3^2, Y2^-1 * Y3 * Y1 * Y2^-1, (R * Y3)^2, Y3^4, (Y1, Y3), (R * Y1)^2, Y1^-2 * Y3^2, Y3 * Y1 * Y2^2, (R * Y2 * Y3^-1)^2, Y3^-1 * R * Y2 * Y1 * R * Y2^-1, Y3 * Y2^-1 * Y1 * Y3^-1 * Y2 * Y1^-1, Y2 * Y1^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y3^-1, Y3 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2^-1 ] Map:: non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 19, 67, 15, 63)(4, 52, 10, 58, 7, 55, 12, 60)(6, 54, 16, 64, 20, 68, 14, 62)(9, 57, 21, 69, 18, 66, 23, 71)(11, 59, 24, 72, 17, 65, 22, 70)(25, 73, 33, 81, 28, 76, 35, 83)(26, 74, 36, 84, 27, 75, 34, 82)(29, 77, 37, 85, 32, 80, 39, 87)(30, 78, 40, 88, 31, 79, 38, 86)(41, 89, 46, 94, 44, 92, 47, 95)(42, 90, 45, 93, 43, 91, 48, 96)(97, 145, 99, 147, 106, 154, 102, 150)(98, 146, 105, 153, 103, 151, 107, 155)(100, 148, 113, 161, 101, 149, 114, 162)(104, 152, 115, 163, 108, 156, 116, 164)(109, 157, 121, 169, 112, 160, 122, 170)(110, 158, 123, 171, 111, 159, 124, 172)(117, 165, 125, 173, 120, 168, 126, 174)(118, 166, 127, 175, 119, 167, 128, 176)(129, 177, 137, 185, 132, 180, 138, 186)(130, 178, 139, 187, 131, 179, 140, 188)(133, 181, 141, 189, 136, 184, 142, 190)(134, 182, 143, 191, 135, 183, 144, 192) L = (1, 100)(2, 106)(3, 110)(4, 104)(5, 108)(6, 111)(7, 97)(8, 103)(9, 118)(10, 101)(11, 119)(12, 98)(13, 102)(14, 115)(15, 116)(16, 99)(17, 117)(18, 120)(19, 112)(20, 109)(21, 107)(22, 114)(23, 113)(24, 105)(25, 130)(26, 131)(27, 129)(28, 132)(29, 134)(30, 135)(31, 133)(32, 136)(33, 122)(34, 124)(35, 123)(36, 121)(37, 126)(38, 128)(39, 127)(40, 125)(41, 144)(42, 143)(43, 142)(44, 141)(45, 137)(46, 138)(47, 139)(48, 140)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E23.523 Graph:: bipartite v = 24 e = 96 f = 28 degree seq :: [ 8^24 ] E23.522 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = (C3 : C4) : C4 (small group id <48, 12>) Aut = (C2 x C4 x S3) : C2 (small group id <96, 91>) |r| :: 2 Presentation :: [ R^2, Y1 * Y2^-2 * Y3^-1, Y2^4, Y1^-1 * Y2^2 * Y3, Y3 * Y2^-2 * Y1^-1, Y3^2 * Y1^-2, (Y1 * Y3^-1)^2, Y1^4, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, Y2^-1 * R * Y1 * Y3^-1 * R * Y2^-1, (R * Y2 * Y3^-1)^2, Y1^-1 * Y2 * Y1^2 * Y2^-1 * Y1^-1, Y2 * Y3 * Y2^-1 * Y1 * Y2 * Y1^-1 * Y2 * Y1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, (Y1 * Y2)^12 ] Map:: non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 19, 67, 15, 63)(4, 52, 10, 58, 7, 55, 12, 60)(6, 54, 14, 62, 20, 68, 16, 64)(9, 57, 21, 69, 17, 65, 23, 71)(11, 59, 22, 70, 18, 66, 24, 72)(25, 73, 33, 81, 27, 75, 35, 83)(26, 74, 34, 82, 28, 76, 36, 84)(29, 77, 37, 85, 31, 79, 39, 87)(30, 78, 38, 86, 32, 80, 40, 88)(41, 89, 46, 94, 43, 91, 48, 96)(42, 90, 45, 93, 44, 92, 47, 95)(97, 145, 99, 147, 108, 156, 102, 150)(98, 146, 105, 153, 100, 148, 107, 155)(101, 149, 113, 161, 103, 151, 114, 162)(104, 152, 115, 163, 106, 154, 116, 164)(109, 157, 121, 169, 110, 158, 122, 170)(111, 159, 123, 171, 112, 160, 124, 172)(117, 165, 125, 173, 118, 166, 126, 174)(119, 167, 127, 175, 120, 168, 128, 176)(129, 177, 137, 185, 130, 178, 138, 186)(131, 179, 139, 187, 132, 180, 140, 188)(133, 181, 141, 189, 134, 182, 142, 190)(135, 183, 143, 191, 136, 184, 144, 192) L = (1, 100)(2, 106)(3, 110)(4, 104)(5, 108)(6, 109)(7, 97)(8, 103)(9, 118)(10, 101)(11, 117)(12, 98)(13, 116)(14, 115)(15, 102)(16, 99)(17, 120)(18, 119)(19, 112)(20, 111)(21, 114)(22, 113)(23, 107)(24, 105)(25, 130)(26, 129)(27, 132)(28, 131)(29, 134)(30, 133)(31, 136)(32, 135)(33, 124)(34, 123)(35, 122)(36, 121)(37, 128)(38, 127)(39, 126)(40, 125)(41, 141)(42, 142)(43, 143)(44, 144)(45, 139)(46, 140)(47, 137)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E23.524 Graph:: bipartite v = 24 e = 96 f = 28 degree seq :: [ 8^24 ] E23.523 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = (C3 : C4) : C4 (small group id <48, 12>) Aut = (C2 x C4 x S3) : C2 (small group id <96, 91>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y2 * Y3^2, Y1 * Y2 * Y1^-1 * Y2, (Y3 * R)^2, (R * Y2)^2, (R * Y1)^2, Y3^-1 * Y1 * Y3^-2 * Y1^-1 * Y3^-1, Y1^2 * Y3 * Y1^2 * Y3^-1, Y1^2 * Y3 * Y1 * Y2 * Y1 * Y3, Y1^-3 * Y3 * Y1 * Y3 * Y1^-2, (Y1^-1 * Y3 * Y1^-1 * Y3^-1)^2 ] Map:: non-degenerate R = (1, 49, 2, 50, 7, 55, 19, 67, 37, 85, 29, 77, 43, 91, 31, 79, 45, 93, 34, 82, 15, 63, 5, 53)(3, 51, 8, 56, 20, 68, 38, 86, 48, 96, 30, 78, 44, 92, 32, 80, 46, 94, 47, 95, 27, 75, 11, 59)(4, 52, 12, 60, 28, 76, 40, 88, 26, 74, 10, 58, 25, 73, 16, 64, 36, 84, 41, 89, 21, 69, 13, 61)(6, 54, 17, 65, 35, 83, 39, 87, 24, 72, 9, 57, 23, 71, 14, 62, 33, 81, 42, 90, 22, 70, 18, 66)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 102, 150)(101, 149, 107, 155)(103, 151, 116, 164)(105, 153, 106, 154)(108, 156, 113, 161)(109, 157, 114, 162)(110, 158, 112, 160)(111, 159, 123, 171)(115, 163, 134, 182)(117, 165, 118, 166)(119, 167, 121, 169)(120, 168, 122, 170)(124, 172, 131, 179)(125, 173, 126, 174)(127, 175, 128, 176)(129, 177, 132, 180)(130, 178, 143, 191)(133, 181, 144, 192)(135, 183, 136, 184)(137, 185, 138, 186)(139, 187, 140, 188)(141, 189, 142, 190) L = (1, 100)(2, 105)(3, 102)(4, 99)(5, 110)(6, 97)(7, 117)(8, 106)(9, 104)(10, 98)(11, 112)(12, 125)(13, 127)(14, 107)(15, 124)(16, 101)(17, 126)(18, 128)(19, 135)(20, 118)(21, 116)(22, 103)(23, 139)(24, 141)(25, 140)(26, 142)(27, 131)(28, 123)(29, 113)(30, 108)(31, 114)(32, 109)(33, 133)(34, 138)(35, 111)(36, 144)(37, 132)(38, 136)(39, 134)(40, 115)(41, 130)(42, 143)(43, 121)(44, 119)(45, 122)(46, 120)(47, 137)(48, 129)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8^4 ), ( 8^24 ) } Outer automorphisms :: reflexible Dual of E23.521 Graph:: simple bipartite v = 28 e = 96 f = 24 degree seq :: [ 4^24, 24^4 ] E23.524 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = (C3 : C4) : C4 (small group id <48, 12>) Aut = (C2 x C4 x S3) : C2 (small group id <96, 91>) |r| :: 2 Presentation :: [ R^2, Y2^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y2 * Y1 * Y2, Y3^4, Y3^-1 * Y2 * Y3 * Y2, Y1 * Y2 * Y3^-1 * Y1 * Y3, Y1^-1 * Y3^2 * Y1 * Y3^2, Y1^-1 * Y3 * Y1^3 * Y3 * Y1^-2, Y1^12 ] Map:: non-degenerate R = (1, 49, 2, 50, 7, 55, 22, 70, 39, 87, 32, 80, 29, 77, 34, 82, 46, 94, 36, 84, 18, 66, 5, 53)(3, 51, 8, 56, 23, 71, 40, 88, 48, 96, 33, 81, 15, 63, 26, 74, 43, 91, 47, 95, 30, 78, 12, 60)(4, 52, 14, 62, 31, 79, 42, 90, 28, 76, 10, 58, 13, 61, 19, 67, 38, 86, 44, 92, 24, 72, 16, 64)(6, 54, 20, 68, 37, 85, 41, 89, 27, 75, 9, 57, 11, 59, 17, 65, 35, 83, 45, 93, 25, 73, 21, 69)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 107, 155)(101, 149, 108, 156)(102, 150, 109, 157)(103, 151, 119, 167)(105, 153, 112, 160)(106, 154, 117, 165)(110, 158, 113, 161)(111, 159, 125, 173)(114, 162, 126, 174)(115, 163, 116, 164)(118, 166, 136, 184)(120, 168, 123, 171)(121, 169, 124, 172)(122, 170, 130, 178)(127, 175, 131, 179)(128, 176, 129, 177)(132, 180, 143, 191)(133, 181, 134, 182)(135, 183, 144, 192)(137, 185, 140, 188)(138, 186, 141, 189)(139, 187, 142, 190) L = (1, 100)(2, 105)(3, 107)(4, 111)(5, 113)(6, 97)(7, 120)(8, 112)(9, 122)(10, 98)(11, 125)(12, 110)(13, 99)(14, 128)(15, 102)(16, 130)(17, 129)(18, 127)(19, 101)(20, 108)(21, 104)(22, 137)(23, 123)(24, 139)(25, 103)(26, 106)(27, 142)(28, 119)(29, 109)(30, 131)(31, 144)(32, 116)(33, 115)(34, 117)(35, 135)(36, 141)(37, 114)(38, 126)(39, 134)(40, 140)(41, 143)(42, 118)(43, 121)(44, 132)(45, 136)(46, 124)(47, 138)(48, 133)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8^4 ), ( 8^24 ) } Outer automorphisms :: reflexible Dual of E23.522 Graph:: simple bipartite v = 28 e = 96 f = 24 degree seq :: [ 4^24, 24^4 ] E23.525 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = (C3 : C4) : C4 (small group id <48, 12>) Aut = (C2 x C4 x S3) : C2 (small group id <96, 91>) |r| :: 2 Presentation :: [ R^2, Y2^2, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y3^4, Y2 * Y1 * Y2 * Y1^-1, Y3^-1 * Y2 * Y3 * Y2, Y2 * Y1 * Y3^-1 * Y1 * Y3^-1, Y1 * Y2 * Y3 * Y1 * Y3, Y2 * Y1^-6 ] Map:: non-degenerate R = (1, 49, 2, 50, 7, 55, 22, 70, 30, 78, 12, 60, 3, 51, 8, 56, 23, 71, 36, 84, 18, 66, 5, 53)(4, 52, 14, 62, 31, 79, 40, 88, 28, 76, 10, 58, 11, 59, 19, 67, 38, 86, 42, 90, 24, 72, 16, 64)(6, 54, 20, 68, 37, 85, 39, 87, 27, 75, 9, 57, 13, 61, 17, 65, 35, 83, 43, 91, 25, 73, 21, 69)(15, 63, 26, 74, 41, 89, 47, 95, 46, 94, 32, 80, 29, 77, 34, 82, 44, 92, 48, 96, 45, 93, 33, 81)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 107, 155)(101, 149, 108, 156)(102, 150, 109, 157)(103, 151, 119, 167)(105, 153, 117, 165)(106, 154, 112, 160)(110, 158, 115, 163)(111, 159, 125, 173)(113, 161, 116, 164)(114, 162, 126, 174)(118, 166, 132, 180)(120, 168, 124, 172)(121, 169, 123, 171)(122, 170, 130, 178)(127, 175, 134, 182)(128, 176, 129, 177)(131, 179, 133, 181)(135, 183, 139, 187)(136, 184, 138, 186)(137, 185, 140, 188)(141, 189, 142, 190)(143, 191, 144, 192) L = (1, 100)(2, 105)(3, 107)(4, 111)(5, 113)(6, 97)(7, 120)(8, 117)(9, 122)(10, 98)(11, 125)(12, 116)(13, 99)(14, 108)(15, 102)(16, 104)(17, 129)(18, 127)(19, 101)(20, 128)(21, 130)(22, 135)(23, 124)(24, 137)(25, 103)(26, 106)(27, 119)(28, 140)(29, 109)(30, 134)(31, 141)(32, 110)(33, 115)(34, 112)(35, 126)(36, 139)(37, 114)(38, 142)(39, 143)(40, 118)(41, 121)(42, 132)(43, 144)(44, 123)(45, 133)(46, 131)(47, 136)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8^4 ), ( 8^24 ) } Outer automorphisms :: reflexible Dual of E23.520 Graph:: bipartite v = 28 e = 96 f = 24 degree seq :: [ 4^24, 24^4 ] E23.526 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = (C3 : C4) : C4 (small group id <48, 12>) Aut = (C2 x C4 x S3) : C2 (small group id <96, 91>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y3^2 * Y2^-1, (Y3 * Y2^-1)^2, (R * Y3)^2, Y1^-1 * Y3^-1 * Y1 * Y2^-1, Y1^4, (Y3, Y2), (R * Y2)^2, Y2 * Y1 * Y3 * Y1^-1, (R * Y1)^2, Y3^-1 * Y2 * Y1^-2 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1, Y3 * Y1^-1 * Y2^-1 * Y3^-2 * Y2^-2 * Y1^-1, Y3^2 * Y2^4 * Y1^-2 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 12, 60, 22, 70, 15, 63)(4, 52, 11, 59, 23, 71, 17, 65)(6, 54, 10, 58, 24, 72, 19, 67)(7, 55, 9, 57, 25, 73, 18, 66)(13, 61, 29, 77, 40, 88, 33, 81)(14, 62, 30, 78, 41, 89, 34, 82)(16, 64, 28, 76, 42, 90, 35, 83)(20, 68, 26, 74, 43, 91, 36, 84)(21, 69, 27, 75, 44, 92, 37, 85)(31, 79, 48, 96, 38, 86, 46, 94)(32, 80, 47, 95, 39, 87, 45, 93)(97, 145, 99, 147, 109, 157, 127, 175, 139, 187, 120, 168, 104, 152, 118, 166, 136, 184, 134, 182, 116, 164, 102, 150)(98, 146, 105, 153, 122, 170, 141, 189, 129, 177, 113, 161, 101, 149, 114, 162, 132, 180, 143, 191, 125, 173, 107, 155)(100, 148, 110, 158, 128, 176, 140, 188, 121, 169, 138, 186, 119, 167, 137, 185, 135, 183, 117, 165, 103, 151, 112, 160)(106, 154, 123, 171, 142, 190, 130, 178, 111, 159, 131, 179, 115, 163, 133, 181, 144, 192, 126, 174, 108, 156, 124, 172) L = (1, 100)(2, 106)(3, 110)(4, 109)(5, 115)(6, 112)(7, 97)(8, 119)(9, 123)(10, 122)(11, 124)(12, 98)(13, 128)(14, 127)(15, 101)(16, 99)(17, 131)(18, 133)(19, 132)(20, 103)(21, 102)(22, 137)(23, 136)(24, 138)(25, 104)(26, 142)(27, 141)(28, 105)(29, 108)(30, 107)(31, 140)(32, 139)(33, 111)(34, 113)(35, 114)(36, 144)(37, 143)(38, 117)(39, 116)(40, 135)(41, 134)(42, 118)(43, 121)(44, 120)(45, 130)(46, 129)(47, 126)(48, 125)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ), ( 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 E23.515 Graph:: bipartite v = 16 e = 96 f = 36 degree seq :: [ 8^12, 24^4 ] E23.527 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = (C3 : C4) : C4 (small group id <48, 12>) Aut = (C2 x C4 x S3) : C2 (small group id <96, 91>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y3^2 * Y2^-1, (Y3, Y2), (R * Y3)^2, Y1^-1 * Y3^-1 * Y1 * Y2^-1, (R * Y1)^2, Y1^4, Y2 * Y1 * Y3 * Y1^-1, (R * Y2)^2, Y2^2 * Y1 * Y2^2 * Y1^-1, Y3^2 * Y2^3 * Y1^-1 * Y2^-1 * Y1^-1, Y3^-1 * Y2 * Y1^-2 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1, Y2 * Y1^-1 * Y2^-5 * Y1^-1 ] Map:: non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 12, 60, 22, 70, 15, 63)(4, 52, 11, 59, 23, 71, 17, 65)(6, 54, 10, 58, 24, 72, 19, 67)(7, 55, 9, 57, 25, 73, 18, 66)(13, 61, 29, 77, 40, 88, 33, 81)(14, 62, 30, 78, 41, 89, 34, 82)(16, 64, 28, 76, 42, 90, 35, 83)(20, 68, 26, 74, 43, 91, 36, 84)(21, 69, 27, 75, 44, 92, 37, 85)(31, 79, 48, 96, 39, 87, 45, 93)(32, 80, 47, 95, 38, 86, 46, 94)(97, 145, 99, 147, 109, 157, 127, 175, 140, 188, 121, 169, 138, 186, 119, 167, 137, 185, 134, 182, 116, 164, 102, 150)(98, 146, 105, 153, 122, 170, 141, 189, 130, 178, 111, 159, 131, 179, 115, 163, 133, 181, 143, 191, 125, 173, 107, 155)(100, 148, 110, 158, 128, 176, 139, 187, 120, 168, 104, 152, 118, 166, 136, 184, 135, 183, 117, 165, 103, 151, 112, 160)(101, 149, 114, 162, 132, 180, 144, 192, 126, 174, 108, 156, 124, 172, 106, 154, 123, 171, 142, 190, 129, 177, 113, 161) L = (1, 100)(2, 106)(3, 110)(4, 109)(5, 115)(6, 112)(7, 97)(8, 119)(9, 123)(10, 122)(11, 124)(12, 98)(13, 128)(14, 127)(15, 101)(16, 99)(17, 131)(18, 133)(19, 132)(20, 103)(21, 102)(22, 137)(23, 136)(24, 138)(25, 104)(26, 142)(27, 141)(28, 105)(29, 108)(30, 107)(31, 139)(32, 140)(33, 111)(34, 113)(35, 114)(36, 143)(37, 144)(38, 117)(39, 116)(40, 134)(41, 135)(42, 118)(43, 121)(44, 120)(45, 129)(46, 130)(47, 126)(48, 125)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ), ( 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 E23.518 Graph:: bipartite v = 16 e = 96 f = 36 degree seq :: [ 8^12, 24^4 ] E23.528 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = (C3 : C4) : C4 (small group id <48, 12>) Aut = (C2 x C4 x S3) : C2 (small group id <96, 91>) |r| :: 2 Presentation :: [ R^2, (Y3, Y2), Y2 * Y3^-1 * Y1^2, (Y2^-1 * Y3)^2, (R * Y3)^2, Y3^-2 * Y2^2, (R * Y2)^2, (R * Y1)^2, Y1 * Y2^-1 * Y3 * Y1, Y2 * Y3^-1 * Y1^-2, Y3^-3 * Y2^-3, Y3^-1 * Y1 * Y2^-1 * Y3^-1 * Y1^-1 * Y2^-1, (Y2^-1 * Y1)^4, Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 4, 52, 16, 64)(6, 54, 17, 65, 7, 55, 18, 66)(9, 57, 21, 69, 10, 58, 24, 72)(11, 59, 25, 73, 12, 60, 26, 74)(14, 62, 27, 75, 15, 63, 28, 76)(19, 67, 22, 70, 20, 68, 23, 71)(29, 77, 37, 85, 30, 78, 38, 86)(31, 79, 43, 91, 32, 80, 44, 92)(33, 81, 45, 93, 34, 82, 46, 94)(35, 83, 39, 87, 36, 84, 40, 88)(41, 89, 47, 95, 42, 90, 48, 96)(97, 145, 99, 147, 110, 158, 129, 177, 116, 164, 103, 151, 104, 152, 100, 148, 111, 159, 130, 178, 115, 163, 102, 150)(98, 146, 105, 153, 118, 166, 137, 185, 124, 172, 108, 156, 101, 149, 106, 154, 119, 167, 138, 186, 123, 171, 107, 155)(109, 157, 125, 173, 113, 161, 131, 179, 142, 190, 128, 176, 112, 160, 126, 174, 114, 162, 132, 180, 141, 189, 127, 175)(117, 165, 133, 181, 121, 169, 139, 187, 144, 192, 136, 184, 120, 168, 134, 182, 122, 170, 140, 188, 143, 191, 135, 183) L = (1, 100)(2, 106)(3, 111)(4, 110)(5, 105)(6, 104)(7, 97)(8, 99)(9, 119)(10, 118)(11, 101)(12, 98)(13, 126)(14, 130)(15, 129)(16, 125)(17, 132)(18, 131)(19, 103)(20, 102)(21, 134)(22, 138)(23, 137)(24, 133)(25, 140)(26, 139)(27, 108)(28, 107)(29, 114)(30, 113)(31, 112)(32, 109)(33, 115)(34, 116)(35, 141)(36, 142)(37, 122)(38, 121)(39, 120)(40, 117)(41, 123)(42, 124)(43, 143)(44, 144)(45, 128)(46, 127)(47, 136)(48, 135)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ), ( 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 E23.516 Graph:: bipartite v = 16 e = 96 f = 36 degree seq :: [ 8^12, 24^4 ] E23.529 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = (C3 : C4) : C4 (small group id <48, 12>) Aut = (C2 x C4 x S3) : C2 (small group id <96, 91>) |r| :: 2 Presentation :: [ R^2, (Y3^-1 * Y2)^2, (Y3, Y2^-1), Y2^2 * Y3^-2, (R * Y2)^2, (R * Y1)^2, Y3 * Y1^-1 * Y2 * Y1^-1, (R * Y3)^2, Y1^4, Y1^-1 * Y2^-1 * Y1^-1 * Y3^-1, Y3^2 * Y1 * Y3^2 * Y1^-1, Y3^4 * Y2 * Y3 ] Map:: non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 22, 70, 12, 60)(4, 52, 17, 65, 23, 71, 11, 59)(6, 54, 19, 67, 24, 72, 10, 58)(7, 55, 18, 66, 25, 73, 9, 57)(14, 62, 29, 77, 38, 86, 33, 81)(15, 63, 30, 78, 39, 87, 32, 80)(16, 64, 28, 76, 40, 88, 31, 79)(20, 68, 26, 74, 41, 89, 36, 84)(21, 69, 27, 75, 42, 90, 37, 85)(34, 82, 45, 93, 47, 95, 43, 91)(35, 83, 46, 94, 48, 96, 44, 92)(97, 145, 99, 147, 110, 158, 130, 178, 117, 165, 103, 151, 112, 160, 100, 148, 111, 159, 131, 179, 116, 164, 102, 150)(98, 146, 105, 153, 122, 170, 139, 187, 126, 174, 108, 156, 124, 172, 106, 154, 123, 171, 140, 188, 125, 173, 107, 155)(101, 149, 114, 162, 132, 180, 141, 189, 128, 176, 109, 157, 127, 175, 115, 163, 133, 181, 142, 190, 129, 177, 113, 161)(104, 152, 118, 166, 134, 182, 143, 191, 138, 186, 121, 169, 136, 184, 119, 167, 135, 183, 144, 192, 137, 185, 120, 168) L = (1, 100)(2, 106)(3, 111)(4, 110)(5, 115)(6, 112)(7, 97)(8, 119)(9, 123)(10, 122)(11, 124)(12, 98)(13, 101)(14, 131)(15, 130)(16, 99)(17, 127)(18, 133)(19, 132)(20, 103)(21, 102)(22, 135)(23, 134)(24, 136)(25, 104)(26, 140)(27, 139)(28, 105)(29, 108)(30, 107)(31, 114)(32, 113)(33, 109)(34, 116)(35, 117)(36, 142)(37, 141)(38, 144)(39, 143)(40, 118)(41, 121)(42, 120)(43, 125)(44, 126)(45, 129)(46, 128)(47, 137)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ), ( 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 E23.519 Graph:: bipartite v = 16 e = 96 f = 36 degree seq :: [ 8^12, 24^4 ] E23.530 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = (C3 : C4) : C4 (small group id <48, 12>) Aut = (C2 x C4 x S3) : C2 (small group id <96, 91>) |r| :: 2 Presentation :: [ R^2, (Y2, Y3), (Y3^-1 * Y2)^2, (R * Y1)^2, Y1^4, (R * Y3)^2, Y3^2 * Y2^-2, Y2^-1 * Y1 * Y3^-1 * Y1, (R * Y2)^2, Y1^-1 * Y2^-1 * Y1^-1 * Y3^-1, Y2 * Y1^-1 * Y2 * Y3^-1 * Y1 * Y3^-1, Y3^2 * Y1^-1 * Y3^-4 * Y1^-1, Y2 * Y1^-1 * Y2^-1 * Y3^-2 * Y2^-1 * Y1^-1 * Y2 ] Map:: polytopal non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 22, 70, 12, 60)(4, 52, 17, 65, 23, 71, 11, 59)(6, 54, 19, 67, 24, 72, 10, 58)(7, 55, 18, 66, 25, 73, 9, 57)(14, 62, 29, 77, 40, 88, 33, 81)(15, 63, 30, 78, 41, 89, 32, 80)(16, 64, 28, 76, 42, 90, 31, 79)(20, 68, 26, 74, 43, 91, 36, 84)(21, 69, 27, 75, 44, 92, 37, 85)(34, 82, 46, 94, 38, 86, 48, 96)(35, 83, 45, 93, 39, 87, 47, 95)(97, 145, 99, 147, 110, 158, 130, 178, 139, 187, 120, 168, 104, 152, 118, 166, 136, 184, 134, 182, 116, 164, 102, 150)(98, 146, 105, 153, 122, 170, 141, 189, 129, 177, 113, 161, 101, 149, 114, 162, 132, 180, 143, 191, 125, 173, 107, 155)(100, 148, 111, 159, 131, 179, 140, 188, 121, 169, 138, 186, 119, 167, 137, 185, 135, 183, 117, 165, 103, 151, 112, 160)(106, 154, 123, 171, 142, 190, 128, 176, 109, 157, 127, 175, 115, 163, 133, 181, 144, 192, 126, 174, 108, 156, 124, 172) L = (1, 100)(2, 106)(3, 111)(4, 110)(5, 115)(6, 112)(7, 97)(8, 119)(9, 123)(10, 122)(11, 124)(12, 98)(13, 101)(14, 131)(15, 130)(16, 99)(17, 127)(18, 133)(19, 132)(20, 103)(21, 102)(22, 137)(23, 136)(24, 138)(25, 104)(26, 142)(27, 141)(28, 105)(29, 108)(30, 107)(31, 114)(32, 113)(33, 109)(34, 140)(35, 139)(36, 144)(37, 143)(38, 117)(39, 116)(40, 135)(41, 134)(42, 118)(43, 121)(44, 120)(45, 128)(46, 129)(47, 126)(48, 125)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ), ( 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 E23.514 Graph:: bipartite v = 16 e = 96 f = 36 degree seq :: [ 8^12, 24^4 ] E23.531 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = (C3 : C4) : C4 (small group id <48, 12>) Aut = (C2 x C4 x S3) : C2 (small group id <96, 91>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-2 * Y2^-1, Y2^-1 * Y1^2 * Y3, Y1^4, Y2^2 * Y3^-2, (Y3^-1 * Y2)^2, Y1 * Y3^-1 * Y2 * Y1, Y3^-1 * Y1^2 * Y2, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y3 * Y1 * Y2^-1 * Y3 * Y1^-1 * Y2^-1, Y2 * Y3 * Y1^-1 * Y3^2 * Y1^-1, Y3 * Y1^-1 * Y2^-1 * Y3^-1 * Y2^-3 * Y1^-1, Y2^5 * Y1 * Y3^-1 * Y1^-1, Y2^-2 * Y3^-1 * Y1^-1 * Y3 * Y2^2 * Y1^-1, Y3 * Y1^-1 * Y3 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 4, 52, 16, 64)(6, 54, 17, 65, 7, 55, 18, 66)(9, 57, 21, 69, 10, 58, 24, 72)(11, 59, 25, 73, 12, 60, 26, 74)(14, 62, 27, 75, 15, 63, 28, 76)(19, 67, 22, 70, 20, 68, 23, 71)(29, 77, 39, 87, 30, 78, 40, 88)(31, 79, 45, 93, 32, 80, 46, 94)(33, 81, 44, 92, 34, 82, 43, 91)(35, 83, 41, 89, 36, 84, 42, 90)(37, 85, 48, 96, 38, 86, 47, 95)(97, 145, 99, 147, 110, 158, 129, 177, 137, 185, 117, 165, 135, 183, 121, 169, 141, 189, 133, 181, 115, 163, 102, 150)(98, 146, 105, 153, 118, 166, 139, 187, 128, 176, 112, 160, 126, 174, 114, 162, 132, 180, 143, 191, 123, 171, 107, 155)(100, 148, 111, 159, 130, 178, 138, 186, 120, 168, 136, 184, 122, 170, 142, 190, 134, 182, 116, 164, 103, 151, 104, 152)(101, 149, 106, 154, 119, 167, 140, 188, 127, 175, 109, 157, 125, 173, 113, 161, 131, 179, 144, 192, 124, 172, 108, 156) L = (1, 100)(2, 106)(3, 111)(4, 110)(5, 105)(6, 104)(7, 97)(8, 99)(9, 119)(10, 118)(11, 101)(12, 98)(13, 126)(14, 130)(15, 129)(16, 125)(17, 132)(18, 131)(19, 103)(20, 102)(21, 136)(22, 140)(23, 139)(24, 135)(25, 142)(26, 141)(27, 108)(28, 107)(29, 114)(30, 113)(31, 112)(32, 109)(33, 138)(34, 137)(35, 143)(36, 144)(37, 116)(38, 115)(39, 122)(40, 121)(41, 120)(42, 117)(43, 127)(44, 128)(45, 134)(46, 133)(47, 124)(48, 123)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ), ( 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 E23.517 Graph:: bipartite v = 16 e = 96 f = 36 degree seq :: [ 8^12, 24^4 ] E23.532 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = C12 : C4 (small group id <48, 13>) Aut = (C12 x C2 x C2) : C2 (small group id <96, 137>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3 * Y2 * Y3 * Y2^-1, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y1 * Y2 * Y1, Y2^4, Y3 * Y1 * Y3^-1 * Y1, (R * Y2 * Y3^-1)^2, Y3^6 * Y1, Y3^2 * Y1 * Y2^-1 * Y3^2 * Y1 * Y2 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 8, 56)(5, 53, 9, 57)(6, 54, 10, 58)(11, 59, 18, 66)(12, 60, 19, 67)(13, 61, 20, 68)(14, 62, 21, 69)(15, 63, 22, 70)(16, 64, 23, 71)(17, 65, 24, 72)(25, 73, 33, 81)(26, 74, 34, 82)(27, 75, 35, 83)(28, 76, 36, 84)(29, 77, 32, 80)(30, 78, 37, 85)(31, 79, 38, 86)(39, 87, 45, 93)(40, 88, 46, 94)(41, 89, 42, 90)(43, 91, 44, 92)(47, 95, 48, 96)(97, 145, 99, 147, 107, 155, 101, 149)(98, 146, 103, 151, 114, 162, 105, 153)(100, 148, 109, 157, 121, 169, 111, 159)(102, 150, 108, 156, 122, 170, 112, 160)(104, 152, 116, 164, 129, 177, 118, 166)(106, 154, 115, 163, 130, 178, 119, 167)(110, 158, 124, 172, 135, 183, 126, 174)(113, 161, 123, 171, 136, 184, 127, 175)(117, 165, 132, 180, 141, 189, 133, 181)(120, 168, 131, 179, 142, 190, 134, 182)(125, 173, 138, 186, 143, 191, 139, 187)(128, 176, 137, 185, 144, 192, 140, 188) L = (1, 100)(2, 104)(3, 108)(4, 110)(5, 112)(6, 97)(7, 115)(8, 117)(9, 119)(10, 98)(11, 121)(12, 123)(13, 99)(14, 125)(15, 101)(16, 127)(17, 102)(18, 129)(19, 131)(20, 103)(21, 128)(22, 105)(23, 134)(24, 106)(25, 135)(26, 107)(27, 137)(28, 109)(29, 120)(30, 111)(31, 140)(32, 113)(33, 141)(34, 114)(35, 138)(36, 116)(37, 118)(38, 139)(39, 143)(40, 122)(41, 132)(42, 124)(43, 126)(44, 133)(45, 144)(46, 130)(47, 142)(48, 136)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24 ) } Outer automorphisms :: reflexible Dual of E23.535 Graph:: simple bipartite v = 36 e = 96 f = 16 degree seq :: [ 4^24, 8^12 ] E23.533 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = C12 : C4 (small group id <48, 13>) Aut = (C12 x C2 x C2) : C2 (small group id <96, 137>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2 * Y1 * Y2, Y3 * Y1 * Y3^-1 * Y1, (R * Y3)^2, Y2 * Y3^-1 * Y2^-1 * Y3^-1, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^12 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 5, 53)(4, 52, 7, 55)(6, 54, 8, 56)(9, 57, 13, 61)(10, 58, 12, 60)(11, 59, 15, 63)(14, 62, 16, 64)(17, 65, 21, 69)(18, 66, 20, 68)(19, 67, 23, 71)(22, 70, 24, 72)(25, 73, 29, 77)(26, 74, 28, 76)(27, 75, 31, 79)(30, 78, 32, 80)(33, 81, 37, 85)(34, 82, 36, 84)(35, 83, 39, 87)(38, 86, 40, 88)(41, 89, 45, 93)(42, 90, 44, 92)(43, 91, 46, 94)(47, 95, 48, 96)(97, 145, 99, 147, 98, 146, 101, 149)(100, 148, 106, 154, 103, 151, 108, 156)(102, 150, 105, 153, 104, 152, 109, 157)(107, 155, 114, 162, 111, 159, 116, 164)(110, 158, 113, 161, 112, 160, 117, 165)(115, 163, 122, 170, 119, 167, 124, 172)(118, 166, 121, 169, 120, 168, 125, 173)(123, 171, 130, 178, 127, 175, 132, 180)(126, 174, 129, 177, 128, 176, 133, 181)(131, 179, 138, 186, 135, 183, 140, 188)(134, 182, 137, 185, 136, 184, 141, 189)(139, 187, 143, 191, 142, 190, 144, 192) L = (1, 100)(2, 103)(3, 105)(4, 107)(5, 109)(6, 97)(7, 111)(8, 98)(9, 113)(10, 99)(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, 142)(40, 128)(41, 143)(42, 130)(43, 134)(44, 132)(45, 144)(46, 136)(47, 138)(48, 140)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24 ) } Outer automorphisms :: reflexible Dual of E23.536 Graph:: bipartite v = 36 e = 96 f = 16 degree seq :: [ 4^24, 8^12 ] E23.534 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = C12 : C4 (small group id <48, 13>) Aut = (C12 x C2 x C2) : C2 (small group id <96, 137>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3 * Y2 * Y3 * Y2^-1, (R * Y1)^2, (R * Y3)^2, Y2^4, Y1 * Y2 * Y1 * Y2^-1, Y3 * Y1 * Y3^-1 * Y1, (R * Y2 * Y3^-1)^2, Y2^-1 * Y1 * Y2^-1 * Y3^6 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 8, 56)(5, 53, 9, 57)(6, 54, 10, 58)(11, 59, 18, 66)(12, 60, 19, 67)(13, 61, 20, 68)(14, 62, 21, 69)(15, 63, 22, 70)(16, 64, 23, 71)(17, 65, 24, 72)(25, 73, 33, 81)(26, 74, 34, 82)(27, 75, 35, 83)(28, 76, 36, 84)(29, 77, 37, 85)(30, 78, 38, 86)(31, 79, 39, 87)(32, 80, 40, 88)(41, 89, 48, 96)(42, 90, 45, 93)(43, 91, 46, 94)(44, 92, 47, 95)(97, 145, 99, 147, 107, 155, 101, 149)(98, 146, 103, 151, 114, 162, 105, 153)(100, 148, 109, 157, 121, 169, 111, 159)(102, 150, 108, 156, 122, 170, 112, 160)(104, 152, 116, 164, 129, 177, 118, 166)(106, 154, 115, 163, 130, 178, 119, 167)(110, 158, 124, 172, 137, 185, 126, 174)(113, 161, 123, 171, 138, 186, 127, 175)(117, 165, 132, 180, 144, 192, 134, 182)(120, 168, 131, 179, 141, 189, 135, 183)(125, 173, 140, 188, 136, 184, 142, 190)(128, 176, 139, 187, 133, 181, 143, 191) L = (1, 100)(2, 104)(3, 108)(4, 110)(5, 112)(6, 97)(7, 115)(8, 117)(9, 119)(10, 98)(11, 121)(12, 123)(13, 99)(14, 125)(15, 101)(16, 127)(17, 102)(18, 129)(19, 131)(20, 103)(21, 133)(22, 105)(23, 135)(24, 106)(25, 137)(26, 107)(27, 139)(28, 109)(29, 141)(30, 111)(31, 143)(32, 113)(33, 144)(34, 114)(35, 142)(36, 116)(37, 138)(38, 118)(39, 140)(40, 120)(41, 136)(42, 122)(43, 134)(44, 124)(45, 130)(46, 126)(47, 132)(48, 128)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24 ) } Outer automorphisms :: reflexible Dual of E23.537 Graph:: simple bipartite v = 36 e = 96 f = 16 degree seq :: [ 4^24, 8^12 ] E23.535 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = C12 : C4 (small group id <48, 13>) Aut = (C12 x C2 x C2) : C2 (small group id <96, 137>) |r| :: 2 Presentation :: [ R^2, (Y3^-1 * Y2)^2, (Y3, Y2^-1), Y2^2 * Y3^-2, (R * Y3)^2, Y2 * Y1 * Y2 * Y1^-1, (R * Y2^-1)^2, Y3^-1 * Y1 * Y3^-1 * Y1^-1, (R * Y1)^2, Y1^4, Y3^-2 * Y2^-1 * Y3^-1 * Y2^-2 ] Map:: non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 11, 59, 22, 70, 15, 63)(4, 52, 12, 60, 23, 71, 17, 65)(6, 54, 9, 57, 24, 72, 18, 66)(7, 55, 10, 58, 25, 73, 19, 67)(13, 61, 29, 77, 38, 86, 33, 81)(14, 62, 30, 78, 39, 87, 34, 82)(16, 64, 28, 76, 40, 88, 35, 83)(20, 68, 26, 74, 41, 89, 36, 84)(21, 69, 27, 75, 42, 90, 37, 85)(31, 79, 44, 92, 47, 95, 45, 93)(32, 80, 43, 91, 48, 96, 46, 94)(97, 145, 99, 147, 109, 157, 127, 175, 117, 165, 103, 151, 112, 160, 100, 148, 110, 158, 128, 176, 116, 164, 102, 150)(98, 146, 105, 153, 122, 170, 139, 187, 126, 174, 108, 156, 124, 172, 106, 154, 123, 171, 140, 188, 125, 173, 107, 155)(101, 149, 114, 162, 132, 180, 142, 190, 130, 178, 113, 161, 131, 179, 115, 163, 133, 181, 141, 189, 129, 177, 111, 159)(104, 152, 118, 166, 134, 182, 143, 191, 138, 186, 121, 169, 136, 184, 119, 167, 135, 183, 144, 192, 137, 185, 120, 168) L = (1, 100)(2, 106)(3, 110)(4, 109)(5, 115)(6, 112)(7, 97)(8, 119)(9, 123)(10, 122)(11, 124)(12, 98)(13, 128)(14, 127)(15, 131)(16, 99)(17, 101)(18, 133)(19, 132)(20, 103)(21, 102)(22, 135)(23, 134)(24, 136)(25, 104)(26, 140)(27, 139)(28, 105)(29, 108)(30, 107)(31, 116)(32, 117)(33, 113)(34, 111)(35, 114)(36, 141)(37, 142)(38, 144)(39, 143)(40, 118)(41, 121)(42, 120)(43, 125)(44, 126)(45, 130)(46, 129)(47, 137)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ), ( 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 E23.532 Graph:: bipartite v = 16 e = 96 f = 36 degree seq :: [ 8^12, 24^4 ] E23.536 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = C12 : C4 (small group id <48, 13>) Aut = (C12 x C2 x C2) : C2 (small group id <96, 137>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1 * Y3 * Y1^-1, Y3^-1 * Y1^-2 * Y2, Y1^-1 * Y3^-1 * Y2 * Y1^-1, Y3^-1 * Y1^2 * Y2, Y1^4, Y2 * Y1^-1 * Y3 * Y1^-1, Y3^-1 * Y2 * Y1^2, Y3^-1 * Y1^-1 * Y2^-1 * Y1^-1, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y2^5 * Y1 * Y2^5 * Y1^-1, Y2^12 ] Map:: non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 11, 59, 4, 52, 12, 60)(6, 54, 9, 57, 7, 55, 10, 58)(13, 61, 19, 67, 14, 62, 20, 68)(15, 63, 17, 65, 16, 64, 18, 66)(21, 69, 27, 75, 22, 70, 28, 76)(23, 71, 25, 73, 24, 72, 26, 74)(29, 77, 35, 83, 30, 78, 36, 84)(31, 79, 33, 81, 32, 80, 34, 82)(37, 85, 43, 91, 38, 86, 44, 92)(39, 87, 41, 89, 40, 88, 42, 90)(45, 93, 47, 95, 46, 94, 48, 96)(97, 145, 99, 147, 109, 157, 117, 165, 125, 173, 133, 181, 141, 189, 135, 183, 127, 175, 119, 167, 111, 159, 102, 150)(98, 146, 105, 153, 113, 161, 121, 169, 129, 177, 137, 185, 143, 191, 139, 187, 131, 179, 123, 171, 115, 163, 107, 155)(100, 148, 110, 158, 118, 166, 126, 174, 134, 182, 142, 190, 136, 184, 128, 176, 120, 168, 112, 160, 103, 151, 104, 152)(101, 149, 106, 154, 114, 162, 122, 170, 130, 178, 138, 186, 144, 192, 140, 188, 132, 180, 124, 172, 116, 164, 108, 156) L = (1, 100)(2, 106)(3, 110)(4, 109)(5, 105)(6, 104)(7, 97)(8, 99)(9, 114)(10, 113)(11, 101)(12, 98)(13, 118)(14, 117)(15, 103)(16, 102)(17, 122)(18, 121)(19, 108)(20, 107)(21, 126)(22, 125)(23, 112)(24, 111)(25, 130)(26, 129)(27, 116)(28, 115)(29, 134)(30, 133)(31, 120)(32, 119)(33, 138)(34, 137)(35, 124)(36, 123)(37, 142)(38, 141)(39, 128)(40, 127)(41, 144)(42, 143)(43, 132)(44, 131)(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) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ), ( 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 E23.533 Graph:: bipartite v = 16 e = 96 f = 36 degree seq :: [ 8^12, 24^4 ] E23.537 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = C12 : C4 (small group id <48, 13>) Aut = (C12 x C2 x C2) : C2 (small group id <96, 137>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y3^2 * Y2^-1, Y3^-1 * Y1 * Y3^-1 * Y1^-1, (Y3, Y2), (R * Y3)^2, (R * Y1)^2, Y1^4, Y2^-1 * Y1^-1 * Y2^-1 * Y1, (R * Y2^-1)^2, Y3^-1 * Y2 * Y1 * Y3 * Y2^-1 * Y1^-1, Y1^2 * Y3 * Y2^5, Y3^2 * Y2^2 * Y3 * Y2 * Y1^-2, Y3^2 * Y2 * Y1^-1 * Y3^-2 * Y1^-1 * Y3 ] Map:: non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 11, 59, 22, 70, 15, 63)(4, 52, 12, 60, 23, 71, 17, 65)(6, 54, 9, 57, 24, 72, 18, 66)(7, 55, 10, 58, 25, 73, 19, 67)(13, 61, 29, 77, 40, 88, 33, 81)(14, 62, 30, 78, 41, 89, 34, 82)(16, 64, 28, 76, 42, 90, 35, 83)(20, 68, 26, 74, 43, 91, 36, 84)(21, 69, 27, 75, 44, 92, 37, 85)(31, 79, 47, 95, 39, 87, 46, 94)(32, 80, 48, 96, 38, 86, 45, 93)(97, 145, 99, 147, 109, 157, 127, 175, 140, 188, 121, 169, 138, 186, 119, 167, 137, 185, 134, 182, 116, 164, 102, 150)(98, 146, 105, 153, 122, 170, 141, 189, 130, 178, 113, 161, 131, 179, 115, 163, 133, 181, 143, 191, 125, 173, 107, 155)(100, 148, 110, 158, 128, 176, 139, 187, 120, 168, 104, 152, 118, 166, 136, 184, 135, 183, 117, 165, 103, 151, 112, 160)(101, 149, 114, 162, 132, 180, 144, 192, 126, 174, 108, 156, 124, 172, 106, 154, 123, 171, 142, 190, 129, 177, 111, 159) L = (1, 100)(2, 106)(3, 110)(4, 109)(5, 115)(6, 112)(7, 97)(8, 119)(9, 123)(10, 122)(11, 124)(12, 98)(13, 128)(14, 127)(15, 131)(16, 99)(17, 101)(18, 133)(19, 132)(20, 103)(21, 102)(22, 137)(23, 136)(24, 138)(25, 104)(26, 142)(27, 141)(28, 105)(29, 108)(30, 107)(31, 139)(32, 140)(33, 113)(34, 111)(35, 114)(36, 143)(37, 144)(38, 117)(39, 116)(40, 134)(41, 135)(42, 118)(43, 121)(44, 120)(45, 129)(46, 130)(47, 126)(48, 125)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ), ( 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 E23.534 Graph:: bipartite v = 16 e = 96 f = 36 degree seq :: [ 8^12, 24^4 ] E23.538 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = C2 x (C3 : Q8) (small group id <48, 34>) Aut = C2 x ((C12 x C2) : C2) (small group id <96, 208>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^4, Y3^-1 * Y2^-1 * Y3^-1 * Y2, (R * Y3)^2, Y3 * Y1 * Y3^-1 * Y1, (R * Y1)^2, Y2^-1 * Y1 * Y2 * Y1, (R * Y2 * Y3^-1)^2, Y3^5 * Y2^-1 * Y3^-1 * Y2^-1 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 8, 56)(5, 53, 9, 57)(6, 54, 10, 58)(11, 59, 18, 66)(12, 60, 19, 67)(13, 61, 20, 68)(14, 62, 21, 69)(15, 63, 22, 70)(16, 64, 23, 71)(17, 65, 24, 72)(25, 73, 33, 81)(26, 74, 34, 82)(27, 75, 35, 83)(28, 76, 36, 84)(29, 77, 37, 85)(30, 78, 38, 86)(31, 79, 39, 87)(32, 80, 40, 88)(41, 89, 45, 93)(42, 90, 46, 94)(43, 91, 47, 95)(44, 92, 48, 96)(97, 145, 99, 147, 107, 155, 101, 149)(98, 146, 103, 151, 114, 162, 105, 153)(100, 148, 109, 157, 121, 169, 111, 159)(102, 150, 108, 156, 122, 170, 112, 160)(104, 152, 116, 164, 129, 177, 118, 166)(106, 154, 115, 163, 130, 178, 119, 167)(110, 158, 124, 172, 137, 185, 126, 174)(113, 161, 123, 171, 138, 186, 127, 175)(117, 165, 132, 180, 141, 189, 134, 182)(120, 168, 131, 179, 142, 190, 135, 183)(125, 173, 140, 188, 128, 176, 139, 187)(133, 181, 144, 192, 136, 184, 143, 191) L = (1, 100)(2, 104)(3, 108)(4, 110)(5, 112)(6, 97)(7, 115)(8, 117)(9, 119)(10, 98)(11, 121)(12, 123)(13, 99)(14, 125)(15, 101)(16, 127)(17, 102)(18, 129)(19, 131)(20, 103)(21, 133)(22, 105)(23, 135)(24, 106)(25, 137)(26, 107)(27, 139)(28, 109)(29, 138)(30, 111)(31, 140)(32, 113)(33, 141)(34, 114)(35, 143)(36, 116)(37, 142)(38, 118)(39, 144)(40, 120)(41, 128)(42, 122)(43, 126)(44, 124)(45, 136)(46, 130)(47, 134)(48, 132)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24 ) } Outer automorphisms :: reflexible Dual of E23.539 Graph:: simple bipartite v = 36 e = 96 f = 16 degree seq :: [ 4^24, 8^12 ] E23.539 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = C2 x (C3 : Q8) (small group id <48, 34>) Aut = C2 x ((C12 x C2) : C2) (small group id <96, 208>) |r| :: 2 Presentation :: [ R^2, Y2^-1 * Y3^2 * Y2^-1, Y1^4, (Y3, Y2), Y2^-1 * Y1^-1 * Y2^-1 * Y1, (R * Y1)^2, (R * Y2^-1)^2, (R * Y3)^2, Y3^-1 * Y1 * Y3^-1 * Y1^-1, Y3 * Y1^-1 * Y3^-3 * Y2^-2 * Y1^-1, Y3^2 * Y2^4 * Y1^-2 ] Map:: non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 11, 59, 22, 70, 15, 63)(4, 52, 12, 60, 23, 71, 17, 65)(6, 54, 9, 57, 24, 72, 18, 66)(7, 55, 10, 58, 25, 73, 19, 67)(13, 61, 29, 77, 40, 88, 33, 81)(14, 62, 30, 78, 41, 89, 34, 82)(16, 64, 28, 76, 42, 90, 35, 83)(20, 68, 26, 74, 43, 91, 36, 84)(21, 69, 27, 75, 44, 92, 37, 85)(31, 79, 47, 95, 38, 86, 45, 93)(32, 80, 48, 96, 39, 87, 46, 94)(97, 145, 99, 147, 109, 157, 127, 175, 139, 187, 120, 168, 104, 152, 118, 166, 136, 184, 134, 182, 116, 164, 102, 150)(98, 146, 105, 153, 122, 170, 141, 189, 129, 177, 111, 159, 101, 149, 114, 162, 132, 180, 143, 191, 125, 173, 107, 155)(100, 148, 110, 158, 128, 176, 140, 188, 121, 169, 138, 186, 119, 167, 137, 185, 135, 183, 117, 165, 103, 151, 112, 160)(106, 154, 123, 171, 142, 190, 130, 178, 113, 161, 131, 179, 115, 163, 133, 181, 144, 192, 126, 174, 108, 156, 124, 172) L = (1, 100)(2, 106)(3, 110)(4, 109)(5, 115)(6, 112)(7, 97)(8, 119)(9, 123)(10, 122)(11, 124)(12, 98)(13, 128)(14, 127)(15, 131)(16, 99)(17, 101)(18, 133)(19, 132)(20, 103)(21, 102)(22, 137)(23, 136)(24, 138)(25, 104)(26, 142)(27, 141)(28, 105)(29, 108)(30, 107)(31, 140)(32, 139)(33, 113)(34, 111)(35, 114)(36, 144)(37, 143)(38, 117)(39, 116)(40, 135)(41, 134)(42, 118)(43, 121)(44, 120)(45, 130)(46, 129)(47, 126)(48, 125)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ), ( 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 E23.538 Graph:: bipartite v = 16 e = 96 f = 36 degree seq :: [ 8^12, 24^4 ] E23.540 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = (C12 x C2) : C2 (small group id <48, 37>) Aut = (C6 x D8) : C2 (small group id <96, 211>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y2^-1 * Y3 * Y2^-1, Y2 * Y3^-2 * Y2, Y3^-2 * Y2^-2, (R * Y1)^2, Y3^-1 * Y2^-1 * Y3^-1 * Y2, (R * Y3)^2, R * Y2 * R * Y2^-1, Y2^4, Y3 * Y1 * Y3^-1 * Y2^-1 * Y1 * Y2^-1, Y2^-1 * Y1 * Y2^2 * Y1 * Y2^-1, Y3 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1, (Y3^-1 * Y1)^12 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 11, 59)(4, 52, 15, 63)(5, 53, 16, 64)(6, 54, 17, 65)(7, 55, 18, 66)(8, 56, 22, 70)(9, 57, 23, 71)(10, 58, 24, 72)(12, 60, 19, 67)(13, 61, 21, 69)(14, 62, 20, 68)(25, 73, 33, 81)(26, 74, 34, 82)(27, 75, 35, 83)(28, 76, 36, 84)(29, 77, 37, 85)(30, 78, 38, 86)(31, 79, 39, 87)(32, 80, 40, 88)(41, 89, 47, 95)(42, 90, 46, 94)(43, 91, 45, 93)(44, 92, 48, 96)(97, 145, 99, 147, 108, 156, 101, 149)(98, 146, 103, 151, 115, 163, 105, 153)(100, 148, 110, 158, 102, 150, 109, 157)(104, 152, 117, 165, 106, 154, 116, 164)(107, 155, 121, 169, 112, 160, 123, 171)(111, 159, 122, 170, 113, 161, 124, 172)(114, 162, 125, 173, 119, 167, 127, 175)(118, 166, 126, 174, 120, 168, 128, 176)(129, 177, 137, 185, 131, 179, 139, 187)(130, 178, 138, 186, 132, 180, 140, 188)(133, 181, 141, 189, 135, 183, 143, 191)(134, 182, 142, 190, 136, 184, 144, 192) L = (1, 100)(2, 104)(3, 109)(4, 108)(5, 110)(6, 97)(7, 116)(8, 115)(9, 117)(10, 98)(11, 122)(12, 102)(13, 101)(14, 99)(15, 123)(16, 124)(17, 121)(18, 126)(19, 106)(20, 105)(21, 103)(22, 127)(23, 128)(24, 125)(25, 111)(26, 112)(27, 113)(28, 107)(29, 118)(30, 119)(31, 120)(32, 114)(33, 138)(34, 139)(35, 140)(36, 137)(37, 142)(38, 143)(39, 144)(40, 141)(41, 130)(42, 131)(43, 132)(44, 129)(45, 134)(46, 135)(47, 136)(48, 133)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24 ) } Outer automorphisms :: reflexible Dual of E23.561 Graph:: simple bipartite v = 36 e = 96 f = 16 degree seq :: [ 4^24, 8^12 ] E23.541 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = (C2 x (C3 : C4)) : C2 (small group id <48, 39>) Aut = (C6 x D8) : C2 (small group id <96, 211>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3 * Y2^-1 * Y3 * Y2, (R * Y1)^2, (R * Y3)^2, Y2^4, Y2 * Y1 * Y2^-1 * Y1, (R * Y2 * Y3^-1)^2, Y2^-2 * Y3^-1 * Y1 * Y3 * Y1, (Y3 * Y2 * Y1)^2, Y3^2 * Y1 * Y3^-2 * Y1, (Y3^-1 * Y2^-1 * Y1)^2, Y3^6, R * Y3^-1 * Y2^-1 * Y1 * Y2^-1 * R * Y3^-1 * Y1, Y3^-1 * Y2^-1 * Y3^2 * Y2^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 14, 62)(5, 53, 9, 57)(6, 54, 18, 66)(8, 56, 23, 71)(10, 58, 27, 75)(11, 59, 20, 68)(12, 60, 26, 74)(13, 61, 25, 73)(15, 63, 24, 72)(16, 64, 22, 70)(17, 65, 21, 69)(19, 67, 28, 76)(29, 77, 36, 84)(30, 78, 37, 85)(31, 79, 38, 86)(32, 80, 44, 92)(33, 81, 40, 88)(34, 82, 41, 89)(35, 83, 42, 90)(39, 87, 47, 95)(43, 91, 48, 96)(45, 93, 46, 94)(97, 145, 99, 147, 107, 155, 101, 149)(98, 146, 103, 151, 116, 164, 105, 153)(100, 148, 109, 157, 119, 167, 112, 160)(102, 150, 108, 156, 123, 171, 113, 161)(104, 152, 118, 166, 110, 158, 121, 169)(106, 154, 117, 165, 114, 162, 122, 170)(111, 159, 126, 174, 134, 182, 129, 177)(115, 163, 125, 173, 138, 186, 130, 178)(120, 168, 133, 181, 127, 175, 136, 184)(124, 172, 132, 180, 131, 179, 137, 185)(128, 176, 139, 187, 143, 191, 141, 189)(135, 183, 142, 190, 140, 188, 144, 192) L = (1, 100)(2, 104)(3, 108)(4, 111)(5, 113)(6, 97)(7, 117)(8, 120)(9, 122)(10, 98)(11, 119)(12, 125)(13, 99)(14, 127)(15, 128)(16, 101)(17, 130)(18, 116)(19, 102)(20, 110)(21, 132)(22, 103)(23, 134)(24, 135)(25, 105)(26, 137)(27, 107)(28, 106)(29, 139)(30, 109)(31, 140)(32, 115)(33, 112)(34, 141)(35, 114)(36, 142)(37, 118)(38, 143)(39, 124)(40, 121)(41, 144)(42, 123)(43, 126)(44, 131)(45, 129)(46, 133)(47, 138)(48, 136)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24 ) } Outer automorphisms :: reflexible Dual of E23.563 Graph:: simple bipartite v = 36 e = 96 f = 16 degree seq :: [ 4^24, 8^12 ] E23.542 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = (C2 x (C3 : C4)) : C2 (small group id <48, 39>) Aut = (C6 x D8) : C2 (small group id <96, 211>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y2 * Y1)^2, Y3^-1 * Y2 * Y3^-1 * Y2^-1, (R * Y3)^2, Y2^4, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2^-1 * Y1 * Y3^-1 * Y2 * Y1, Y3^6, Y3 * Y1 * Y2^2 * Y3^-1 * Y1, Y3^2 * Y1 * Y3^-2 * Y1, Y2 * R * Y3^-1 * Y1 * Y3 * R * Y2^-1 * Y1, Y3 * Y2 * Y3^-2 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y2^-1 * Y3 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 9, 57)(4, 52, 14, 62)(5, 53, 7, 55)(6, 54, 18, 66)(8, 56, 23, 71)(10, 58, 27, 75)(11, 59, 20, 68)(12, 60, 21, 69)(13, 61, 22, 70)(15, 63, 24, 72)(16, 64, 25, 73)(17, 65, 26, 74)(19, 67, 28, 76)(29, 77, 41, 89)(30, 78, 40, 88)(31, 79, 38, 86)(32, 80, 44, 92)(33, 81, 37, 85)(34, 82, 36, 84)(35, 83, 42, 90)(39, 87, 47, 95)(43, 91, 46, 94)(45, 93, 48, 96)(97, 145, 99, 147, 107, 155, 101, 149)(98, 146, 103, 151, 116, 164, 105, 153)(100, 148, 109, 157, 119, 167, 112, 160)(102, 150, 108, 156, 123, 171, 113, 161)(104, 152, 118, 166, 110, 158, 121, 169)(106, 154, 117, 165, 114, 162, 122, 170)(111, 159, 126, 174, 134, 182, 129, 177)(115, 163, 125, 173, 138, 186, 130, 178)(120, 168, 133, 181, 127, 175, 136, 184)(124, 172, 132, 180, 131, 179, 137, 185)(128, 176, 139, 187, 143, 191, 141, 189)(135, 183, 142, 190, 140, 188, 144, 192) L = (1, 100)(2, 104)(3, 108)(4, 111)(5, 113)(6, 97)(7, 117)(8, 120)(9, 122)(10, 98)(11, 119)(12, 125)(13, 99)(14, 127)(15, 128)(16, 101)(17, 130)(18, 116)(19, 102)(20, 110)(21, 132)(22, 103)(23, 134)(24, 135)(25, 105)(26, 137)(27, 107)(28, 106)(29, 139)(30, 109)(31, 140)(32, 115)(33, 112)(34, 141)(35, 114)(36, 142)(37, 118)(38, 143)(39, 124)(40, 121)(41, 144)(42, 123)(43, 126)(44, 131)(45, 129)(46, 133)(47, 138)(48, 136)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24 ) } Outer automorphisms :: reflexible Dual of E23.562 Graph:: simple bipartite v = 36 e = 96 f = 16 degree seq :: [ 4^24, 8^12 ] E23.543 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = Q8 x S3 (small group id <48, 40>) Aut = ((C4 x C2) : C2) x S3 (small group id <96, 215>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^4, Y2^-1 * Y3^2 * Y2^-1, Y3^2 * Y2^2, Y3^-1 * Y2^-1 * Y3 * Y2^-1, Y2 * Y1 * Y2^-1 * Y1, (R * Y3)^2, R * Y2 * R * Y2^-1, Y3^-1 * Y2 * Y3^-1 * Y2^-1, (R * Y1)^2, (Y3^-1 * Y1 * Y3^-1)^2, (Y1 * Y3^-1 * Y1 * Y3)^3 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 14, 62)(5, 53, 9, 57)(6, 54, 15, 63)(8, 56, 19, 67)(10, 58, 20, 68)(11, 59, 16, 64)(12, 60, 21, 69)(13, 61, 22, 70)(17, 65, 25, 73)(18, 66, 26, 74)(23, 71, 31, 79)(24, 72, 32, 80)(27, 75, 35, 83)(28, 76, 36, 84)(29, 77, 37, 85)(30, 78, 38, 86)(33, 81, 41, 89)(34, 82, 42, 90)(39, 87, 43, 91)(40, 88, 44, 92)(45, 93, 47, 95)(46, 94, 48, 96)(97, 145, 99, 147, 107, 155, 101, 149)(98, 146, 103, 151, 112, 160, 105, 153)(100, 148, 109, 157, 102, 150, 108, 156)(104, 152, 114, 162, 106, 154, 113, 161)(110, 158, 118, 166, 111, 159, 117, 165)(115, 163, 122, 170, 116, 164, 121, 169)(119, 167, 125, 173, 120, 168, 126, 174)(123, 171, 129, 177, 124, 172, 130, 178)(127, 175, 133, 181, 128, 176, 134, 182)(131, 179, 137, 185, 132, 180, 138, 186)(135, 183, 142, 190, 136, 184, 141, 189)(139, 187, 144, 192, 140, 188, 143, 191) L = (1, 100)(2, 104)(3, 108)(4, 107)(5, 109)(6, 97)(7, 113)(8, 112)(9, 114)(10, 98)(11, 102)(12, 101)(13, 99)(14, 119)(15, 120)(16, 106)(17, 105)(18, 103)(19, 123)(20, 124)(21, 125)(22, 126)(23, 111)(24, 110)(25, 129)(26, 130)(27, 116)(28, 115)(29, 118)(30, 117)(31, 135)(32, 136)(33, 122)(34, 121)(35, 139)(36, 140)(37, 141)(38, 142)(39, 128)(40, 127)(41, 143)(42, 144)(43, 132)(44, 131)(45, 134)(46, 133)(47, 138)(48, 137)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24 ) } Outer automorphisms :: reflexible Dual of E23.565 Graph:: simple bipartite v = 36 e = 96 f = 16 degree seq :: [ 4^24, 8^12 ] E23.544 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = Q8 x S3 (small group id <48, 40>) Aut = ((C4 x C2) : C2) x S3 (small group id <96, 215>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^-1 * Y3^-2 * Y2^-1, Y3 * Y2^-2 * Y3, (R * Y3)^2, Y3^-1 * Y2^-1 * Y3 * Y2^-1, Y2 * Y3 * Y2^-1 * Y3, R * Y2 * R * Y2^-1, (R * Y1)^2, Y2^-1 * Y1 * Y3^-2 * Y1 * Y2^-1, Y3 * Y2 * Y1 * Y3^-1 * Y2 * Y1, Y2 * Y1 * Y2^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1, (Y3^-1 * Y1)^12 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 11, 59)(4, 52, 15, 63)(5, 53, 16, 64)(6, 54, 17, 65)(7, 55, 18, 66)(8, 56, 22, 70)(9, 57, 23, 71)(10, 58, 24, 72)(12, 60, 19, 67)(13, 61, 20, 68)(14, 62, 21, 69)(25, 73, 33, 81)(26, 74, 34, 82)(27, 75, 35, 83)(28, 76, 36, 84)(29, 77, 37, 85)(30, 78, 38, 86)(31, 79, 39, 87)(32, 80, 40, 88)(41, 89, 45, 93)(42, 90, 46, 94)(43, 91, 47, 95)(44, 92, 48, 96)(97, 145, 99, 147, 108, 156, 101, 149)(98, 146, 103, 151, 115, 163, 105, 153)(100, 148, 110, 158, 102, 150, 109, 157)(104, 152, 117, 165, 106, 154, 116, 164)(107, 155, 121, 169, 112, 160, 123, 171)(111, 159, 124, 172, 113, 161, 122, 170)(114, 162, 125, 173, 119, 167, 127, 175)(118, 166, 128, 176, 120, 168, 126, 174)(129, 177, 137, 185, 131, 179, 139, 187)(130, 178, 140, 188, 132, 180, 138, 186)(133, 181, 141, 189, 135, 183, 143, 191)(134, 182, 144, 192, 136, 184, 142, 190) L = (1, 100)(2, 104)(3, 109)(4, 108)(5, 110)(6, 97)(7, 116)(8, 115)(9, 117)(10, 98)(11, 122)(12, 102)(13, 101)(14, 99)(15, 121)(16, 124)(17, 123)(18, 126)(19, 106)(20, 105)(21, 103)(22, 125)(23, 128)(24, 127)(25, 113)(26, 112)(27, 111)(28, 107)(29, 120)(30, 119)(31, 118)(32, 114)(33, 138)(34, 137)(35, 140)(36, 139)(37, 142)(38, 141)(39, 144)(40, 143)(41, 132)(42, 131)(43, 130)(44, 129)(45, 136)(46, 135)(47, 134)(48, 133)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24 ) } Outer automorphisms :: reflexible Dual of E23.564 Graph:: simple bipartite v = 36 e = 96 f = 16 degree seq :: [ 4^24, 8^12 ] E23.545 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = (C12 x C2) : C2 (small group id <48, 37>) Aut = (D8 x S3) : C2 (small group id <96, 216>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^4, Y2^-1 * Y3^2 * Y2^-1, Y3^2 * Y2^2, (R * Y3)^2, Y3^-1 * Y2 * Y3^-1 * Y2^-1, Y3^-1 * Y2^-1 * Y3 * Y2^-1, (R * Y1)^2, (Y2 * Y1)^2, R * Y2 * R * Y2^-1, (Y3^-1 * Y1 * Y3^-1)^2, (Y1 * Y3^-1 * Y1 * Y3)^3 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 9, 57)(4, 52, 14, 62)(5, 53, 7, 55)(6, 54, 15, 63)(8, 56, 19, 67)(10, 58, 20, 68)(11, 59, 16, 64)(12, 60, 21, 69)(13, 61, 22, 70)(17, 65, 25, 73)(18, 66, 26, 74)(23, 71, 31, 79)(24, 72, 32, 80)(27, 75, 35, 83)(28, 76, 36, 84)(29, 77, 37, 85)(30, 78, 38, 86)(33, 81, 41, 89)(34, 82, 42, 90)(39, 87, 43, 91)(40, 88, 44, 92)(45, 93, 48, 96)(46, 94, 47, 95)(97, 145, 99, 147, 107, 155, 101, 149)(98, 146, 103, 151, 112, 160, 105, 153)(100, 148, 109, 157, 102, 150, 108, 156)(104, 152, 114, 162, 106, 154, 113, 161)(110, 158, 117, 165, 111, 159, 118, 166)(115, 163, 121, 169, 116, 164, 122, 170)(119, 167, 126, 174, 120, 168, 125, 173)(123, 171, 130, 178, 124, 172, 129, 177)(127, 175, 133, 181, 128, 176, 134, 182)(131, 179, 137, 185, 132, 180, 138, 186)(135, 183, 142, 190, 136, 184, 141, 189)(139, 187, 144, 192, 140, 188, 143, 191) L = (1, 100)(2, 104)(3, 108)(4, 107)(5, 109)(6, 97)(7, 113)(8, 112)(9, 114)(10, 98)(11, 102)(12, 101)(13, 99)(14, 119)(15, 120)(16, 106)(17, 105)(18, 103)(19, 123)(20, 124)(21, 125)(22, 126)(23, 111)(24, 110)(25, 129)(26, 130)(27, 116)(28, 115)(29, 118)(30, 117)(31, 135)(32, 136)(33, 122)(34, 121)(35, 139)(36, 140)(37, 141)(38, 142)(39, 128)(40, 127)(41, 143)(42, 144)(43, 132)(44, 131)(45, 134)(46, 133)(47, 138)(48, 137)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24 ) } Outer automorphisms :: reflexible Dual of E23.570 Graph:: simple bipartite v = 36 e = 96 f = 16 degree seq :: [ 4^24, 8^12 ] E23.546 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = (C12 x C2) : C2 (small group id <48, 37>) Aut = (D8 x S3) : C2 (small group id <96, 216>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, Y2^4, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y3 * Y2 * Y3, Y2^-1 * Y1 * Y2 * Y1, (Y3 * Y2 * Y1 * Y3 * Y1 * Y3 * Y1)^2 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 6, 54)(4, 52, 11, 59)(5, 53, 8, 56)(7, 55, 15, 63)(9, 57, 13, 61)(10, 58, 18, 66)(12, 60, 20, 68)(14, 62, 22, 70)(16, 64, 24, 72)(17, 65, 25, 73)(19, 67, 27, 75)(21, 69, 29, 77)(23, 71, 31, 79)(26, 74, 34, 82)(28, 76, 36, 84)(30, 78, 38, 86)(32, 80, 40, 88)(33, 81, 41, 89)(35, 83, 43, 91)(37, 85, 45, 93)(39, 87, 47, 95)(42, 90, 48, 96)(44, 92, 46, 94)(97, 145, 99, 147, 105, 153, 101, 149)(98, 146, 102, 150, 109, 157, 104, 152)(100, 148, 106, 154, 113, 161, 108, 156)(103, 151, 110, 158, 117, 165, 112, 160)(107, 155, 114, 162, 121, 169, 116, 164)(111, 159, 118, 166, 125, 173, 120, 168)(115, 163, 122, 170, 129, 177, 124, 172)(119, 167, 126, 174, 133, 181, 128, 176)(123, 171, 130, 178, 137, 185, 132, 180)(127, 175, 134, 182, 141, 189, 136, 184)(131, 179, 138, 186, 143, 191, 140, 188)(135, 183, 142, 190, 139, 187, 144, 192) L = (1, 100)(2, 103)(3, 106)(4, 97)(5, 108)(6, 110)(7, 98)(8, 112)(9, 113)(10, 99)(11, 115)(12, 101)(13, 117)(14, 102)(15, 119)(16, 104)(17, 105)(18, 122)(19, 107)(20, 124)(21, 109)(22, 126)(23, 111)(24, 128)(25, 129)(26, 114)(27, 131)(28, 116)(29, 133)(30, 118)(31, 135)(32, 120)(33, 121)(34, 138)(35, 123)(36, 140)(37, 125)(38, 142)(39, 127)(40, 144)(41, 143)(42, 130)(43, 141)(44, 132)(45, 139)(46, 134)(47, 137)(48, 136)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24 ) } Outer automorphisms :: reflexible Dual of E23.567 Graph:: simple bipartite v = 36 e = 96 f = 16 degree seq :: [ 4^24, 8^12 ] E23.547 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = (C4 x S3) : C2 (small group id <48, 41>) Aut = (D8 x S3) : C2 (small group id <96, 216>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, (R * Y2)^2, Y3 * Y2 * Y3 * Y2^-1, (R * Y1)^2, (Y2^-1 * Y1)^2, (R * Y3)^2, Y2^4, Y3 * Y2 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y2^-1 * Y1 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 8, 56)(4, 52, 11, 59)(5, 53, 6, 54)(7, 55, 15, 63)(9, 57, 13, 61)(10, 58, 18, 66)(12, 60, 19, 67)(14, 62, 22, 70)(16, 64, 23, 71)(17, 65, 25, 73)(20, 68, 28, 76)(21, 69, 29, 77)(24, 72, 32, 80)(26, 74, 34, 82)(27, 75, 35, 83)(30, 78, 38, 86)(31, 79, 39, 87)(33, 81, 41, 89)(36, 84, 44, 92)(37, 85, 45, 93)(40, 88, 48, 96)(42, 90, 46, 94)(43, 91, 47, 95)(97, 145, 99, 147, 105, 153, 101, 149)(98, 146, 102, 150, 109, 157, 104, 152)(100, 148, 106, 154, 113, 161, 108, 156)(103, 151, 110, 158, 117, 165, 112, 160)(107, 155, 115, 163, 121, 169, 114, 162)(111, 159, 119, 167, 125, 173, 118, 166)(116, 164, 123, 171, 129, 177, 122, 170)(120, 168, 127, 175, 133, 181, 126, 174)(124, 172, 130, 178, 137, 185, 131, 179)(128, 176, 134, 182, 141, 189, 135, 183)(132, 180, 138, 186, 144, 192, 139, 187)(136, 184, 142, 190, 140, 188, 143, 191) L = (1, 100)(2, 103)(3, 106)(4, 97)(5, 108)(6, 110)(7, 98)(8, 112)(9, 113)(10, 99)(11, 116)(12, 101)(13, 117)(14, 102)(15, 120)(16, 104)(17, 105)(18, 122)(19, 123)(20, 107)(21, 109)(22, 126)(23, 127)(24, 111)(25, 129)(26, 114)(27, 115)(28, 132)(29, 133)(30, 118)(31, 119)(32, 136)(33, 121)(34, 138)(35, 139)(36, 124)(37, 125)(38, 142)(39, 143)(40, 128)(41, 144)(42, 130)(43, 131)(44, 141)(45, 140)(46, 134)(47, 135)(48, 137)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24 ) } Outer automorphisms :: reflexible Dual of E23.569 Graph:: simple bipartite v = 36 e = 96 f = 16 degree seq :: [ 4^24, 8^12 ] E23.548 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = (C12 x C2) : C2 (small group id <48, 37>) Aut = (D8 x S3) : C2 (small group id <96, 216>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, Y2^-1 * Y3 * Y2 * Y3, (R * Y1)^2, Y2^4, (R * Y3)^2, (R * Y2)^2, Y3 * Y1 * Y2 * Y3 * Y1 * Y2^-1, (Y2^-1 * Y1 * Y2^-1)^2, Y2^-1 * Y1 * Y2^-1 * Y1 * Y3 * Y1 * Y2 * Y1 * Y3 * Y1 * Y2^-1 * Y1, (Y3 * Y1)^12 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 9, 57)(4, 52, 12, 60)(5, 53, 14, 62)(6, 54, 15, 63)(7, 55, 18, 66)(8, 56, 20, 68)(10, 58, 16, 64)(11, 59, 17, 65)(13, 61, 19, 67)(21, 69, 31, 79)(22, 70, 33, 81)(23, 71, 34, 82)(24, 72, 32, 80)(25, 73, 35, 83)(26, 74, 36, 84)(27, 75, 38, 86)(28, 76, 39, 87)(29, 77, 37, 85)(30, 78, 40, 88)(41, 89, 47, 95)(42, 90, 48, 96)(43, 91, 45, 93)(44, 92, 46, 94)(97, 145, 99, 147, 106, 154, 101, 149)(98, 146, 102, 150, 112, 160, 104, 152)(100, 148, 107, 155, 120, 168, 109, 157)(103, 151, 113, 161, 125, 173, 115, 163)(105, 153, 117, 165, 110, 158, 119, 167)(108, 156, 118, 166, 128, 176, 121, 169)(111, 159, 122, 170, 116, 164, 124, 172)(114, 162, 123, 171, 133, 181, 126, 174)(127, 175, 137, 185, 130, 178, 139, 187)(129, 177, 138, 186, 131, 179, 140, 188)(132, 180, 141, 189, 135, 183, 143, 191)(134, 182, 142, 190, 136, 184, 144, 192) L = (1, 100)(2, 103)(3, 107)(4, 97)(5, 109)(6, 113)(7, 98)(8, 115)(9, 118)(10, 120)(11, 99)(12, 119)(13, 101)(14, 121)(15, 123)(16, 125)(17, 102)(18, 124)(19, 104)(20, 126)(21, 128)(22, 105)(23, 108)(24, 106)(25, 110)(26, 133)(27, 111)(28, 114)(29, 112)(30, 116)(31, 138)(32, 117)(33, 139)(34, 140)(35, 137)(36, 142)(37, 122)(38, 143)(39, 144)(40, 141)(41, 131)(42, 127)(43, 129)(44, 130)(45, 136)(46, 132)(47, 134)(48, 135)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24 ) } Outer automorphisms :: reflexible Dual of E23.566 Graph:: simple bipartite v = 36 e = 96 f = 16 degree seq :: [ 4^24, 8^12 ] E23.549 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = (C4 x S3) : C2 (small group id <48, 41>) Aut = (D8 x S3) : C2 (small group id <96, 216>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, Y3 * Y2 * Y3 * Y2^-1, (R * Y3)^2, Y2^4, (R * Y2)^2, (R * Y1)^2, Y3 * Y1 * Y3 * Y2^-1 * Y1 * Y2^-1, Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y2^-1 * Y1 * Y3 * Y1 * Y2^-1 * Y1, (Y2 * Y1)^12 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 9, 57)(4, 52, 12, 60)(5, 53, 14, 62)(6, 54, 15, 63)(7, 55, 18, 66)(8, 56, 20, 68)(10, 58, 16, 64)(11, 59, 19, 67)(13, 61, 17, 65)(21, 69, 31, 79)(22, 70, 32, 80)(23, 71, 34, 82)(24, 72, 33, 81)(25, 73, 35, 83)(26, 74, 36, 84)(27, 75, 37, 85)(28, 76, 39, 87)(29, 77, 38, 86)(30, 78, 40, 88)(41, 89, 45, 93)(42, 90, 48, 96)(43, 91, 47, 95)(44, 92, 46, 94)(97, 145, 99, 147, 106, 154, 101, 149)(98, 146, 102, 150, 112, 160, 104, 152)(100, 148, 107, 155, 120, 168, 109, 157)(103, 151, 113, 161, 125, 173, 115, 163)(105, 153, 117, 165, 110, 158, 119, 167)(108, 156, 121, 169, 129, 177, 118, 166)(111, 159, 122, 170, 116, 164, 124, 172)(114, 162, 126, 174, 134, 182, 123, 171)(127, 175, 137, 185, 130, 178, 139, 187)(128, 176, 140, 188, 131, 179, 138, 186)(132, 180, 141, 189, 135, 183, 143, 191)(133, 181, 144, 192, 136, 184, 142, 190) L = (1, 100)(2, 103)(3, 107)(4, 97)(5, 109)(6, 113)(7, 98)(8, 115)(9, 118)(10, 120)(11, 99)(12, 117)(13, 101)(14, 121)(15, 123)(16, 125)(17, 102)(18, 122)(19, 104)(20, 126)(21, 108)(22, 105)(23, 129)(24, 106)(25, 110)(26, 114)(27, 111)(28, 134)(29, 112)(30, 116)(31, 138)(32, 137)(33, 119)(34, 140)(35, 139)(36, 142)(37, 141)(38, 124)(39, 144)(40, 143)(41, 128)(42, 127)(43, 131)(44, 130)(45, 133)(46, 132)(47, 136)(48, 135)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24 ) } Outer automorphisms :: reflexible Dual of E23.568 Graph:: simple bipartite v = 36 e = 96 f = 16 degree seq :: [ 4^24, 8^12 ] E23.550 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = (C12 x C2) : C2 (small group id <48, 37>) Aut = (D8 x S3) : C2 (small group id <96, 216>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2 * Y3^-1 * Y2^-1 * Y3^-1, Y3 * Y1 * Y3^-1 * Y1, (Y2 * Y1)^2, (R * Y3)^2, (R * Y1)^2, Y2^4, (Y2^-1 * Y3^-1 * Y1)^2, (R * Y2 * Y3^-1)^2, Y2^-1 * Y3^-6 * Y2^-1, Y2 * R * Y2^-2 * Y1 * R * Y2^-1 * Y1 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 9, 57)(4, 52, 8, 56)(5, 53, 7, 55)(6, 54, 10, 58)(11, 59, 18, 66)(12, 60, 23, 71)(13, 61, 22, 70)(14, 62, 21, 69)(15, 63, 20, 68)(16, 64, 19, 67)(17, 65, 24, 72)(25, 73, 33, 81)(26, 74, 34, 82)(27, 75, 39, 87)(28, 76, 38, 86)(29, 77, 37, 85)(30, 78, 36, 84)(31, 79, 35, 83)(32, 80, 40, 88)(41, 89, 45, 93)(42, 90, 46, 94)(43, 91, 48, 96)(44, 92, 47, 95)(97, 145, 99, 147, 107, 155, 101, 149)(98, 146, 103, 151, 114, 162, 105, 153)(100, 148, 109, 157, 121, 169, 111, 159)(102, 150, 108, 156, 122, 170, 112, 160)(104, 152, 116, 164, 129, 177, 118, 166)(106, 154, 115, 163, 130, 178, 119, 167)(110, 158, 124, 172, 137, 185, 126, 174)(113, 161, 123, 171, 138, 186, 127, 175)(117, 165, 132, 180, 141, 189, 134, 182)(120, 168, 131, 179, 142, 190, 135, 183)(125, 173, 140, 188, 128, 176, 139, 187)(133, 181, 144, 192, 136, 184, 143, 191) L = (1, 100)(2, 104)(3, 108)(4, 110)(5, 112)(6, 97)(7, 115)(8, 117)(9, 119)(10, 98)(11, 121)(12, 123)(13, 99)(14, 125)(15, 101)(16, 127)(17, 102)(18, 129)(19, 131)(20, 103)(21, 133)(22, 105)(23, 135)(24, 106)(25, 137)(26, 107)(27, 139)(28, 109)(29, 138)(30, 111)(31, 140)(32, 113)(33, 141)(34, 114)(35, 143)(36, 116)(37, 142)(38, 118)(39, 144)(40, 120)(41, 128)(42, 122)(43, 126)(44, 124)(45, 136)(46, 130)(47, 134)(48, 132)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8, 24, 8, 24 ), ( 8, 24, 8, 24, 8, 24, 8, 24 ) } Outer automorphisms :: reflexible Dual of E23.571 Graph:: simple bipartite v = 36 e = 96 f = 16 degree seq :: [ 4^24, 8^12 ] E23.551 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = (C2 x (C3 : C4)) : C2 (small group id <48, 39>) Aut = (C6 x D8) : C2 (small group id <96, 211>) |r| :: 2 Presentation :: [ Y3^2, R^2, Y1 * Y2^-2 * Y1, Y1^2 * Y2^2, Y1^4, (Y3 * Y1)^2, Y1 * Y2^-2 * Y1, Y2^4, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y1 * Y3 * Y2 * Y3 * Y1^-1, (R * Y2 * Y3)^2, Y2^-1 * R * Y1^2 * R * Y2^-1, Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2 * Y1^-1 * Y2^-1 * Y1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, Y1^-1 * 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 ] Map:: non-degenerate R = (1, 49, 2, 50, 7, 55, 5, 53)(3, 51, 11, 59, 6, 54, 13, 61)(4, 52, 14, 62, 18, 66, 9, 57)(8, 56, 19, 67, 10, 58, 21, 69)(12, 60, 23, 71, 17, 65, 22, 70)(15, 63, 24, 72, 16, 64, 20, 68)(25, 73, 33, 81, 26, 74, 35, 83)(27, 75, 36, 84, 28, 76, 34, 82)(29, 77, 37, 85, 30, 78, 39, 87)(31, 79, 40, 88, 32, 80, 38, 86)(41, 89, 45, 93, 42, 90, 46, 94)(43, 91, 48, 96, 44, 92, 47, 95)(97, 145, 99, 147, 103, 151, 102, 150)(98, 146, 104, 152, 101, 149, 106, 154)(100, 148, 111, 159, 114, 162, 112, 160)(105, 153, 118, 166, 110, 158, 119, 167)(107, 155, 121, 169, 109, 157, 122, 170)(108, 156, 123, 171, 113, 161, 124, 172)(115, 163, 125, 173, 117, 165, 126, 174)(116, 164, 127, 175, 120, 168, 128, 176)(129, 177, 137, 185, 131, 179, 138, 186)(130, 178, 139, 187, 132, 180, 140, 188)(133, 181, 141, 189, 135, 183, 142, 190)(134, 182, 143, 191, 136, 184, 144, 192) L = (1, 100)(2, 105)(3, 108)(4, 97)(5, 110)(6, 113)(7, 114)(8, 116)(9, 98)(10, 120)(11, 118)(12, 99)(13, 119)(14, 101)(15, 117)(16, 115)(17, 102)(18, 103)(19, 112)(20, 104)(21, 111)(22, 107)(23, 109)(24, 106)(25, 130)(26, 132)(27, 131)(28, 129)(29, 134)(30, 136)(31, 135)(32, 133)(33, 124)(34, 121)(35, 123)(36, 122)(37, 128)(38, 125)(39, 127)(40, 126)(41, 143)(42, 144)(43, 142)(44, 141)(45, 140)(46, 139)(47, 137)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E23.556 Graph:: bipartite v = 24 e = 96 f = 28 degree seq :: [ 8^24 ] E23.552 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = Q8 x S3 (small group id <48, 40>) Aut = ((C4 x C2) : C2) x S3 (small group id <96, 215>) |r| :: 2 Presentation :: [ R^2, Y1^4, Y2 * Y1 * Y2 * Y1^-1, Y2^4, Y2^-1 * Y1^-1 * Y2 * Y1^-1, Y1 * Y2^2 * Y1, (Y3 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, R * Y2 * R * Y2^-1, Y2^-1 * Y3 * Y2^-1 * Y3^-1, Y3 * Y2 * Y1 * Y3 * Y2 * Y1^-1, Y2^-1 * Y3^6 * Y2^-1 ] Map:: non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 11, 59, 6, 54, 9, 57)(4, 52, 15, 63, 21, 69, 12, 60)(7, 55, 18, 66, 22, 70, 10, 58)(13, 61, 24, 72, 16, 64, 27, 75)(14, 62, 23, 71, 19, 67, 25, 73)(17, 65, 28, 76, 37, 85, 31, 79)(20, 68, 26, 74, 38, 86, 34, 82)(29, 77, 43, 91, 32, 80, 40, 88)(30, 78, 41, 89, 35, 83, 39, 87)(33, 81, 42, 90, 36, 84, 44, 92)(45, 93, 48, 96, 46, 94, 47, 95)(97, 145, 99, 147, 104, 152, 102, 150)(98, 146, 105, 153, 101, 149, 107, 155)(100, 148, 112, 160, 117, 165, 109, 157)(103, 151, 115, 163, 118, 166, 110, 158)(106, 154, 121, 169, 114, 162, 119, 167)(108, 156, 123, 171, 111, 159, 120, 168)(113, 161, 125, 173, 133, 181, 128, 176)(116, 164, 126, 174, 134, 182, 131, 179)(122, 170, 135, 183, 130, 178, 137, 185)(124, 172, 136, 184, 127, 175, 139, 187)(129, 177, 142, 190, 132, 180, 141, 189)(138, 186, 144, 192, 140, 188, 143, 191) L = (1, 100)(2, 106)(3, 109)(4, 113)(5, 114)(6, 112)(7, 97)(8, 117)(9, 119)(10, 122)(11, 121)(12, 98)(13, 125)(14, 99)(15, 101)(16, 128)(17, 129)(18, 130)(19, 102)(20, 103)(21, 133)(22, 104)(23, 135)(24, 105)(25, 137)(26, 138)(27, 107)(28, 108)(29, 141)(30, 110)(31, 111)(32, 142)(33, 134)(34, 140)(35, 115)(36, 116)(37, 132)(38, 118)(39, 143)(40, 120)(41, 144)(42, 127)(43, 123)(44, 124)(45, 131)(46, 126)(47, 139)(48, 136)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E23.557 Graph:: bipartite v = 24 e = 96 f = 28 degree seq :: [ 8^24 ] E23.553 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = (C12 x C2) : C2 (small group id <48, 37>) Aut = (D8 x S3) : C2 (small group id <96, 216>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y2^-2 * Y1^-1, Y1^4, Y1^-1 * Y2^2 * Y1^-1, (R * Y2)^2, Y2 * Y1^-1 * Y2^-1 * Y1^-1, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, (R * Y1)^2, (Y3 * Y1^-1)^2, (Y2, Y3^-1), Y3^6, Y3^-2 * Y2 * Y1 * Y3^-2 * Y2 * Y1^-1, Y2^-12 ] Map:: non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 11, 59, 6, 54, 9, 57)(4, 52, 15, 63, 21, 69, 12, 60)(7, 55, 18, 66, 22, 70, 10, 58)(13, 61, 24, 72, 17, 65, 27, 75)(14, 62, 23, 71, 19, 67, 26, 74)(16, 64, 28, 76, 36, 84, 31, 79)(20, 68, 25, 73, 37, 85, 34, 82)(29, 77, 42, 90, 33, 81, 39, 87)(30, 78, 41, 89, 35, 83, 38, 86)(32, 80, 44, 92, 46, 94, 40, 88)(43, 91, 47, 95, 45, 93, 48, 96)(97, 145, 99, 147, 104, 152, 102, 150)(98, 146, 105, 153, 101, 149, 107, 155)(100, 148, 109, 157, 117, 165, 113, 161)(103, 151, 110, 158, 118, 166, 115, 163)(106, 154, 119, 167, 114, 162, 122, 170)(108, 156, 120, 168, 111, 159, 123, 171)(112, 160, 125, 173, 132, 180, 129, 177)(116, 164, 126, 174, 133, 181, 131, 179)(121, 169, 134, 182, 130, 178, 137, 185)(124, 172, 135, 183, 127, 175, 138, 186)(128, 176, 139, 187, 142, 190, 141, 189)(136, 184, 143, 191, 140, 188, 144, 192) L = (1, 100)(2, 106)(3, 109)(4, 112)(5, 114)(6, 113)(7, 97)(8, 117)(9, 119)(10, 121)(11, 122)(12, 98)(13, 125)(14, 99)(15, 101)(16, 128)(17, 129)(18, 130)(19, 102)(20, 103)(21, 132)(22, 104)(23, 134)(24, 105)(25, 136)(26, 137)(27, 107)(28, 108)(29, 139)(30, 110)(31, 111)(32, 116)(33, 141)(34, 140)(35, 115)(36, 142)(37, 118)(38, 143)(39, 120)(40, 124)(41, 144)(42, 123)(43, 126)(44, 127)(45, 131)(46, 133)(47, 135)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E23.558 Graph:: bipartite v = 24 e = 96 f = 28 degree seq :: [ 8^24 ] E23.554 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = (C12 x C2) : C2 (small group id <48, 37>) Aut = (D8 x S3) : C2 (small group id <96, 216>) |r| :: 2 Presentation :: [ R^2, Y2^-2 * Y1^2, (Y2, Y1^-1), Y2^2 * Y1^2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, Y1^4, (Y3 * Y1^-1)^2, (Y2, Y3^-1), Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1^-1, Y3^6, Y2^-12 ] Map:: non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 9, 57, 6, 54, 11, 59)(4, 52, 15, 63, 21, 69, 12, 60)(7, 55, 18, 66, 22, 70, 10, 58)(13, 61, 27, 75, 17, 65, 24, 72)(14, 62, 26, 74, 19, 67, 23, 71)(16, 64, 28, 76, 36, 84, 31, 79)(20, 68, 25, 73, 37, 85, 34, 82)(29, 77, 39, 87, 33, 81, 42, 90)(30, 78, 38, 86, 35, 83, 41, 89)(32, 80, 44, 92, 46, 94, 40, 88)(43, 91, 48, 96, 45, 93, 47, 95)(97, 145, 99, 147, 104, 152, 102, 150)(98, 146, 105, 153, 101, 149, 107, 155)(100, 148, 109, 157, 117, 165, 113, 161)(103, 151, 110, 158, 118, 166, 115, 163)(106, 154, 119, 167, 114, 162, 122, 170)(108, 156, 120, 168, 111, 159, 123, 171)(112, 160, 125, 173, 132, 180, 129, 177)(116, 164, 126, 174, 133, 181, 131, 179)(121, 169, 134, 182, 130, 178, 137, 185)(124, 172, 135, 183, 127, 175, 138, 186)(128, 176, 139, 187, 142, 190, 141, 189)(136, 184, 143, 191, 140, 188, 144, 192) L = (1, 100)(2, 106)(3, 109)(4, 112)(5, 114)(6, 113)(7, 97)(8, 117)(9, 119)(10, 121)(11, 122)(12, 98)(13, 125)(14, 99)(15, 101)(16, 128)(17, 129)(18, 130)(19, 102)(20, 103)(21, 132)(22, 104)(23, 134)(24, 105)(25, 136)(26, 137)(27, 107)(28, 108)(29, 139)(30, 110)(31, 111)(32, 116)(33, 141)(34, 140)(35, 115)(36, 142)(37, 118)(38, 143)(39, 120)(40, 124)(41, 144)(42, 123)(43, 126)(44, 127)(45, 131)(46, 133)(47, 135)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E23.560 Graph:: bipartite v = 24 e = 96 f = 28 degree seq :: [ 8^24 ] E23.555 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = (C4 x S3) : C2 (small group id <48, 41>) Aut = (D8 x S3) : C2 (small group id <96, 216>) |r| :: 2 Presentation :: [ R^2, Y1^4, (Y2^-1 * Y1^-1)^2, Y2^4, Y2^-1 * Y3 * Y2^-1 * Y3^-1, (R * Y1)^2, (R * Y3)^2, R * Y2 * R * Y2^-1, (Y3 * Y1^-1)^2, Y1 * Y2^2 * Y1, (Y2 * Y1^-1)^2, (Y3^-1 * Y1^-1)^2, (R * Y3^-1 * Y2)^2, Y2^-1 * Y3^6 * Y2^-1 ] Map:: non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 9, 57, 6, 54, 11, 59)(4, 52, 15, 63, 21, 69, 12, 60)(7, 55, 18, 66, 22, 70, 10, 58)(13, 61, 27, 75, 16, 64, 24, 72)(14, 62, 25, 73, 19, 67, 23, 71)(17, 65, 28, 76, 37, 85, 31, 79)(20, 68, 26, 74, 38, 86, 34, 82)(29, 77, 40, 88, 32, 80, 43, 91)(30, 78, 39, 87, 35, 83, 41, 89)(33, 81, 42, 90, 36, 84, 44, 92)(45, 93, 47, 95, 46, 94, 48, 96)(97, 145, 99, 147, 104, 152, 102, 150)(98, 146, 105, 153, 101, 149, 107, 155)(100, 148, 112, 160, 117, 165, 109, 157)(103, 151, 115, 163, 118, 166, 110, 158)(106, 154, 121, 169, 114, 162, 119, 167)(108, 156, 123, 171, 111, 159, 120, 168)(113, 161, 125, 173, 133, 181, 128, 176)(116, 164, 126, 174, 134, 182, 131, 179)(122, 170, 135, 183, 130, 178, 137, 185)(124, 172, 136, 184, 127, 175, 139, 187)(129, 177, 142, 190, 132, 180, 141, 189)(138, 186, 144, 192, 140, 188, 143, 191) L = (1, 100)(2, 106)(3, 109)(4, 113)(5, 114)(6, 112)(7, 97)(8, 117)(9, 119)(10, 122)(11, 121)(12, 98)(13, 125)(14, 99)(15, 101)(16, 128)(17, 129)(18, 130)(19, 102)(20, 103)(21, 133)(22, 104)(23, 135)(24, 105)(25, 137)(26, 138)(27, 107)(28, 108)(29, 141)(30, 110)(31, 111)(32, 142)(33, 134)(34, 140)(35, 115)(36, 116)(37, 132)(38, 118)(39, 143)(40, 120)(41, 144)(42, 127)(43, 123)(44, 124)(45, 131)(46, 126)(47, 139)(48, 136)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E23.559 Graph:: bipartite v = 24 e = 96 f = 28 degree seq :: [ 8^24 ] E23.556 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = (C2 x (C3 : C4)) : C2 (small group id <48, 39>) Aut = (C6 x D8) : C2 (small group id <96, 211>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (R * Y3)^2, (R * Y1)^2, Y3 * Y2 * Y1^-1 * Y2 * Y3 * Y1^-1, Y2 * Y3 * Y1^-1 * Y2 * Y1 * Y3, Y3 * Y1 * Y2 * Y1^-1 * Y3 * Y2, (Y1^-1 * R * Y2)^2, (R * Y2 * Y3)^2, Y1^-1 * Y2 * Y3 * Y2 * Y1^-1 * Y3, (Y3 * Y1^-2)^2, Y3 * Y1 * Y3 * Y1^-5, (Y1^-1 * Y2 * Y1 * Y2)^2 ] Map:: non-degenerate R = (1, 49, 2, 50, 6, 54, 18, 66, 36, 84, 29, 77, 44, 92, 27, 75, 43, 91, 35, 83, 17, 65, 5, 53)(3, 51, 9, 57, 19, 67, 39, 87, 33, 81, 15, 63, 23, 71, 7, 55, 21, 69, 37, 85, 31, 79, 11, 59)(4, 52, 12, 60, 32, 80, 38, 86, 26, 74, 8, 56, 24, 72, 16, 64, 34, 82, 42, 90, 20, 68, 14, 62)(10, 58, 28, 76, 45, 93, 48, 96, 41, 89, 25, 73, 13, 61, 30, 78, 46, 94, 47, 95, 40, 88, 22, 70)(97, 145, 99, 147)(98, 146, 103, 151)(100, 148, 109, 157)(101, 149, 111, 159)(102, 150, 115, 163)(104, 152, 121, 169)(105, 153, 123, 171)(106, 154, 120, 168)(107, 155, 125, 173)(108, 156, 124, 172)(110, 158, 118, 166)(112, 160, 126, 174)(113, 161, 127, 175)(114, 162, 133, 181)(116, 164, 137, 185)(117, 165, 139, 187)(119, 167, 140, 188)(122, 170, 136, 184)(128, 176, 142, 190)(129, 177, 132, 180)(130, 178, 141, 189)(131, 179, 135, 183)(134, 182, 144, 192)(138, 186, 143, 191) L = (1, 100)(2, 104)(3, 106)(4, 97)(5, 112)(6, 116)(7, 118)(8, 98)(9, 121)(10, 99)(11, 126)(12, 125)(13, 119)(14, 123)(15, 124)(16, 101)(17, 128)(18, 134)(19, 136)(20, 102)(21, 137)(22, 103)(23, 109)(24, 140)(25, 105)(26, 139)(27, 110)(28, 111)(29, 108)(30, 107)(31, 141)(32, 113)(33, 142)(34, 132)(35, 138)(36, 130)(37, 143)(38, 114)(39, 144)(40, 115)(41, 117)(42, 131)(43, 122)(44, 120)(45, 127)(46, 129)(47, 133)(48, 135)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8^4 ), ( 8^24 ) } Outer automorphisms :: reflexible Dual of E23.551 Graph:: simple bipartite v = 28 e = 96 f = 24 degree seq :: [ 4^24, 24^4 ] E23.557 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = Q8 x S3 (small group id <48, 40>) Aut = ((C4 x C2) : C2) x S3 (small group id <96, 215>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y2 * Y3 * Y2 * Y3^-1, (R * Y2)^2, (R * Y3)^2, Y3 * Y1^-1 * Y3^-1 * Y1^-1, Y3^4, (R * Y1)^2, Y1 * Y3 * Y2 * Y1^-1 * Y2 * Y3, Y1 * Y3^2 * Y2 * Y1 * Y2, (Y1^2 * Y2)^2, Y1^-2 * Y2 * Y1 * Y2 * Y1^-3 ] Map:: non-degenerate R = (1, 49, 2, 50, 7, 55, 20, 68, 37, 85, 30, 78, 16, 64, 28, 76, 44, 92, 35, 83, 18, 66, 5, 53)(3, 51, 11, 59, 29, 77, 38, 86, 26, 74, 8, 56, 24, 72, 17, 65, 34, 82, 42, 90, 21, 69, 13, 61)(4, 52, 15, 63, 33, 81, 40, 88, 23, 71, 10, 58, 6, 54, 19, 67, 36, 84, 39, 87, 22, 70, 9, 57)(12, 60, 27, 75, 41, 89, 48, 96, 46, 94, 32, 80, 14, 62, 25, 73, 43, 91, 47, 95, 45, 93, 31, 79)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 108, 156)(101, 149, 113, 161)(102, 150, 110, 158)(103, 151, 117, 165)(105, 153, 121, 169)(106, 154, 123, 171)(107, 155, 126, 174)(109, 157, 124, 172)(111, 159, 128, 176)(112, 160, 120, 168)(114, 162, 125, 173)(115, 163, 127, 175)(116, 164, 134, 182)(118, 166, 137, 185)(119, 167, 139, 187)(122, 170, 140, 188)(129, 177, 141, 189)(130, 178, 133, 181)(131, 179, 138, 186)(132, 180, 142, 190)(135, 183, 143, 191)(136, 184, 144, 192) L = (1, 100)(2, 105)(3, 108)(4, 112)(5, 111)(6, 97)(7, 118)(8, 121)(9, 124)(10, 98)(11, 127)(12, 120)(13, 123)(14, 99)(15, 126)(16, 102)(17, 128)(18, 129)(19, 101)(20, 135)(21, 137)(22, 140)(23, 103)(24, 110)(25, 109)(26, 139)(27, 104)(28, 106)(29, 141)(30, 115)(31, 113)(32, 107)(33, 133)(34, 142)(35, 136)(36, 114)(37, 132)(38, 143)(39, 131)(40, 116)(41, 122)(42, 144)(43, 117)(44, 119)(45, 130)(46, 125)(47, 138)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8^4 ), ( 8^24 ) } Outer automorphisms :: reflexible Dual of E23.552 Graph:: simple bipartite v = 28 e = 96 f = 24 degree seq :: [ 4^24, 24^4 ] E23.558 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = (C12 x C2) : C2 (small group id <48, 37>) Aut = (D8 x S3) : C2 (small group id <96, 216>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (R * Y3)^2, (R * Y1)^2, Y3 * Y2 * Y3 * Y1^-1 * Y2 * Y1^-1, Y3 * R * Y2 * R * Y3 * Y2, Y1^-1 * Y2 * Y3 * Y1 * Y3 * Y2, Y2 * Y3 * Y2 * Y1^-1 * Y3 * Y1^-1, Y2 * Y1^3 * Y2 * Y1^-3, Y3 * Y1^3 * Y3 * Y1^-3, Y1^12 ] Map:: non-degenerate R = (1, 49, 2, 50, 6, 54, 18, 66, 36, 84, 28, 76, 43, 91, 31, 79, 44, 92, 35, 83, 17, 65, 5, 53)(3, 51, 9, 57, 27, 75, 37, 85, 23, 71, 7, 55, 21, 69, 15, 63, 33, 81, 40, 88, 19, 67, 11, 59)(4, 52, 12, 60, 32, 80, 38, 86, 26, 74, 8, 56, 24, 72, 16, 64, 34, 82, 42, 90, 20, 68, 14, 62)(10, 58, 22, 70, 39, 87, 47, 95, 46, 94, 29, 77, 13, 61, 25, 73, 41, 89, 48, 96, 45, 93, 30, 78)(97, 145, 99, 147)(98, 146, 103, 151)(100, 148, 109, 157)(101, 149, 111, 159)(102, 150, 115, 163)(104, 152, 121, 169)(105, 153, 124, 172)(106, 154, 120, 168)(107, 155, 127, 175)(108, 156, 126, 174)(110, 158, 118, 166)(112, 160, 125, 173)(113, 161, 123, 171)(114, 162, 133, 181)(116, 164, 137, 185)(117, 165, 139, 187)(119, 167, 140, 188)(122, 170, 135, 183)(128, 176, 142, 190)(129, 177, 132, 180)(130, 178, 141, 189)(131, 179, 136, 184)(134, 182, 144, 192)(138, 186, 143, 191) L = (1, 100)(2, 104)(3, 106)(4, 97)(5, 112)(6, 116)(7, 118)(8, 98)(9, 125)(10, 99)(11, 121)(12, 124)(13, 117)(14, 127)(15, 126)(16, 101)(17, 128)(18, 134)(19, 135)(20, 102)(21, 109)(22, 103)(23, 137)(24, 139)(25, 107)(26, 140)(27, 141)(28, 108)(29, 105)(30, 111)(31, 110)(32, 113)(33, 142)(34, 132)(35, 138)(36, 130)(37, 143)(38, 114)(39, 115)(40, 144)(41, 119)(42, 131)(43, 120)(44, 122)(45, 123)(46, 129)(47, 133)(48, 136)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8^4 ), ( 8^24 ) } Outer automorphisms :: reflexible Dual of E23.553 Graph:: simple bipartite v = 28 e = 96 f = 24 degree seq :: [ 4^24, 24^4 ] E23.559 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = (C4 x S3) : C2 (small group id <48, 41>) Aut = (D8 x S3) : C2 (small group id <96, 216>) |r| :: 2 Presentation :: [ Y3^2, Y2^2, R^2, (Y2 * Y1^-1)^2, (R * Y3)^2, (R * Y1)^2, Y3 * Y2 * Y1 * Y3 * Y1 * Y2, (R * Y2 * Y3)^2, (Y1^2 * Y3)^2, (Y3 * Y1^-1)^4, Y1^-2 * Y3 * Y1 * Y3 * Y1^-3, Y1 * Y3 * Y2 * Y1^-2 * Y3 * Y2 * Y3 * Y1^-1 * Y3 ] Map:: non-degenerate R = (1, 49, 2, 50, 6, 54, 16, 64, 32, 80, 27, 75, 38, 86, 29, 77, 40, 88, 31, 79, 15, 63, 5, 53)(3, 51, 9, 57, 23, 71, 41, 89, 48, 96, 39, 87, 28, 76, 44, 92, 45, 93, 33, 81, 17, 65, 7, 55)(4, 52, 11, 59, 26, 74, 34, 82, 22, 70, 8, 56, 20, 68, 14, 62, 30, 78, 37, 85, 18, 66, 13, 61)(10, 58, 21, 69, 35, 83, 47, 95, 43, 91, 24, 72, 12, 60, 19, 67, 36, 84, 46, 94, 42, 90, 25, 73)(97, 145, 99, 147)(98, 146, 103, 151)(100, 148, 108, 156)(101, 149, 105, 153)(102, 150, 113, 161)(104, 152, 117, 165)(106, 154, 116, 164)(107, 155, 120, 168)(109, 157, 115, 163)(110, 158, 121, 169)(111, 159, 119, 167)(112, 160, 129, 177)(114, 162, 132, 180)(118, 166, 131, 179)(122, 170, 139, 187)(123, 171, 140, 188)(124, 172, 134, 182)(125, 173, 135, 183)(126, 174, 138, 186)(127, 175, 137, 185)(128, 176, 141, 189)(130, 178, 143, 191)(133, 181, 142, 190)(136, 184, 144, 192) L = (1, 100)(2, 104)(3, 106)(4, 97)(5, 110)(6, 114)(7, 115)(8, 98)(9, 120)(10, 99)(11, 123)(12, 124)(13, 125)(14, 101)(15, 122)(16, 130)(17, 131)(18, 102)(19, 103)(20, 134)(21, 135)(22, 136)(23, 138)(24, 105)(25, 140)(26, 111)(27, 107)(28, 108)(29, 109)(30, 128)(31, 133)(32, 126)(33, 142)(34, 112)(35, 113)(36, 144)(37, 127)(38, 116)(39, 117)(40, 118)(41, 143)(42, 119)(43, 141)(44, 121)(45, 139)(46, 129)(47, 137)(48, 132)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8^4 ), ( 8^24 ) } Outer automorphisms :: reflexible Dual of E23.555 Graph:: simple bipartite v = 28 e = 96 f = 24 degree seq :: [ 4^24, 24^4 ] E23.560 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = (C12 x C2) : C2 (small group id <48, 37>) Aut = (D8 x S3) : C2 (small group id <96, 216>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3 * Y1^-1 * Y3^-1 * Y1^-1, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, (Y1^-1 * Y2)^2, Y3^-1 * Y2 * Y3 * Y2, Y3^4, Y1^-1 * Y3 * Y1^2 * Y3 * Y1^-3 ] Map:: non-degenerate R = (1, 49, 2, 50, 7, 55, 18, 66, 33, 81, 30, 78, 15, 63, 24, 72, 39, 87, 31, 79, 16, 64, 5, 53)(3, 51, 11, 59, 25, 73, 41, 89, 48, 96, 40, 88, 28, 76, 44, 92, 45, 93, 34, 82, 19, 67, 8, 56)(4, 52, 14, 62, 29, 77, 36, 84, 21, 69, 10, 58, 6, 54, 17, 65, 32, 80, 35, 83, 20, 68, 9, 57)(12, 60, 22, 70, 37, 85, 46, 94, 43, 91, 27, 75, 13, 61, 23, 71, 38, 86, 47, 95, 42, 90, 26, 74)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 108, 156)(101, 149, 107, 155)(102, 150, 109, 157)(103, 151, 115, 163)(105, 153, 118, 166)(106, 154, 119, 167)(110, 158, 122, 170)(111, 159, 124, 172)(112, 160, 121, 169)(113, 161, 123, 171)(114, 162, 130, 178)(116, 164, 133, 181)(117, 165, 134, 182)(120, 168, 136, 184)(125, 173, 138, 186)(126, 174, 140, 188)(127, 175, 137, 185)(128, 176, 139, 187)(129, 177, 141, 189)(131, 179, 142, 190)(132, 180, 143, 191)(135, 183, 144, 192) L = (1, 100)(2, 105)(3, 108)(4, 111)(5, 110)(6, 97)(7, 116)(8, 118)(9, 120)(10, 98)(11, 122)(12, 124)(13, 99)(14, 126)(15, 102)(16, 125)(17, 101)(18, 131)(19, 133)(20, 135)(21, 103)(22, 136)(23, 104)(24, 106)(25, 138)(26, 140)(27, 107)(28, 109)(29, 129)(30, 113)(31, 132)(32, 112)(33, 128)(34, 142)(35, 127)(36, 114)(37, 144)(38, 115)(39, 117)(40, 119)(41, 143)(42, 141)(43, 121)(44, 123)(45, 139)(46, 137)(47, 130)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8^4 ), ( 8^24 ) } Outer automorphisms :: reflexible Dual of E23.554 Graph:: simple bipartite v = 28 e = 96 f = 24 degree seq :: [ 4^24, 24^4 ] E23.561 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = (C12 x C2) : C2 (small group id <48, 37>) Aut = (C6 x D8) : C2 (small group id <96, 211>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1 * Y3^-1 * Y1^-1, Y3^2 * Y1^2, Y3^-1 * Y1^-1 * Y3 * Y1^-1, (Y2^-1, Y1), (R * Y3)^2, (Y3 * Y2^-1)^2, (Y2^-1 * Y3^-1)^2, (R * Y1)^2, Y1^4, Y2^-1 * Y1 * R * Y2 * R * Y1, (R * Y2 * Y3^-1)^2, Y2^6 * Y1^2, Y1^-1 * Y3^-1 * Y2^2 * Y3^-1 * Y1^-1 * Y2^2 ] Map:: non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 9, 57, 21, 69, 15, 63)(4, 52, 12, 60, 7, 55, 10, 58)(6, 54, 11, 59, 22, 70, 18, 66)(13, 61, 23, 71, 37, 85, 31, 79)(14, 62, 25, 73, 16, 64, 24, 72)(17, 65, 27, 75, 19, 67, 26, 74)(20, 68, 28, 76, 38, 86, 34, 82)(29, 77, 39, 87, 36, 84, 44, 92)(30, 78, 41, 89, 32, 80, 40, 88)(33, 81, 43, 91, 35, 83, 42, 90)(45, 93, 48, 96, 46, 94, 47, 95)(97, 145, 99, 147, 109, 157, 125, 173, 134, 182, 118, 166, 104, 152, 117, 165, 133, 181, 132, 180, 116, 164, 102, 150)(98, 146, 105, 153, 119, 167, 135, 183, 130, 178, 114, 162, 101, 149, 111, 159, 127, 175, 140, 188, 124, 172, 107, 155)(100, 148, 113, 161, 129, 177, 141, 189, 128, 176, 110, 158, 103, 151, 115, 163, 131, 179, 142, 190, 126, 174, 112, 160)(106, 154, 122, 170, 138, 186, 143, 191, 137, 185, 120, 168, 108, 156, 123, 171, 139, 187, 144, 192, 136, 184, 121, 169) L = (1, 100)(2, 106)(3, 110)(4, 104)(5, 108)(6, 115)(7, 97)(8, 103)(9, 120)(10, 101)(11, 123)(12, 98)(13, 126)(14, 117)(15, 121)(16, 99)(17, 102)(18, 122)(19, 118)(20, 129)(21, 112)(22, 113)(23, 136)(24, 111)(25, 105)(26, 107)(27, 114)(28, 138)(29, 141)(30, 133)(31, 137)(32, 109)(33, 134)(34, 139)(35, 116)(36, 142)(37, 128)(38, 131)(39, 143)(40, 127)(41, 119)(42, 130)(43, 124)(44, 144)(45, 132)(46, 125)(47, 140)(48, 135)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ), ( 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 E23.540 Graph:: bipartite v = 16 e = 96 f = 36 degree seq :: [ 8^12, 24^4 ] E23.562 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = (C2 x (C3 : C4)) : C2 (small group id <48, 39>) Aut = (C6 x D8) : C2 (small group id <96, 211>) |r| :: 2 Presentation :: [ R^2, (Y2 * Y1)^2, (R * Y3)^2, Y3 * Y1^-1 * Y3 * Y1, (Y2 * Y1^-1)^2, (Y3 * Y2^-1)^2, (R * Y1)^2, Y1^4, Y1^-1 * Y2 * Y3^-1 * Y2^-1 * Y1^-1 * Y3^-1, Y2^-1 * Y3^-1 * Y2 * Y3 * Y1^-2, Y3^-1 * Y2^-1 * Y3^-3 * Y2^-1, Y3 * Y2 * Y3 * Y2^-3, Y3^6, Y1^-1 * Y2^-1 * Y3^2 * Y2^-1 * Y1^-1, (R * Y2 * Y3^-1)^2, Y1^-1 * R * Y2 * R * Y2 * Y1^-1, (Y2^-1 * Y3^-1 * Y2^-1)^2 ] Map:: non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 27, 75, 11, 59)(4, 52, 12, 60, 28, 76, 19, 67)(6, 54, 20, 68, 29, 77, 9, 57)(7, 55, 10, 58, 30, 78, 21, 69)(14, 62, 37, 85, 18, 66, 40, 88)(15, 63, 39, 87, 17, 65, 38, 86)(16, 64, 33, 81, 22, 70, 36, 84)(23, 71, 31, 79, 26, 74, 35, 83)(24, 72, 34, 82, 25, 73, 32, 80)(41, 89, 45, 93, 44, 92, 48, 96)(42, 90, 46, 94, 43, 91, 47, 95)(97, 145, 99, 147, 110, 158, 137, 185, 122, 170, 125, 173, 104, 152, 123, 171, 114, 162, 140, 188, 119, 167, 102, 150)(98, 146, 105, 153, 127, 175, 141, 189, 136, 184, 109, 157, 101, 149, 116, 164, 131, 179, 144, 192, 133, 181, 107, 155)(100, 148, 113, 161, 138, 186, 121, 169, 103, 151, 118, 166, 124, 172, 111, 159, 139, 187, 120, 168, 126, 174, 112, 160)(106, 154, 130, 178, 142, 190, 135, 183, 108, 156, 132, 180, 117, 165, 128, 176, 143, 191, 134, 182, 115, 163, 129, 177) L = (1, 100)(2, 106)(3, 111)(4, 114)(5, 117)(6, 118)(7, 97)(8, 124)(9, 128)(10, 131)(11, 132)(12, 98)(13, 129)(14, 138)(15, 140)(16, 99)(17, 137)(18, 139)(19, 101)(20, 130)(21, 127)(22, 123)(23, 126)(24, 102)(25, 125)(26, 103)(27, 113)(28, 110)(29, 112)(30, 104)(31, 142)(32, 144)(33, 105)(34, 141)(35, 143)(36, 116)(37, 115)(38, 107)(39, 109)(40, 108)(41, 120)(42, 119)(43, 122)(44, 121)(45, 134)(46, 133)(47, 136)(48, 135)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ), ( 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 E23.542 Graph:: bipartite v = 16 e = 96 f = 36 degree seq :: [ 8^12, 24^4 ] E23.563 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = (C2 x (C3 : C4)) : C2 (small group id <48, 39>) Aut = (C6 x D8) : C2 (small group id <96, 211>) |r| :: 2 Presentation :: [ R^2, Y2 * Y1^-1 * Y2 * Y1, (Y2 * Y3^-1)^2, Y3^-1 * Y1 * Y3^-1 * Y1^-1, (R * Y3)^2, Y1^4, (R * Y1)^2, Y3^-1 * Y2 * R * Y2^-1 * R * Y3^-1, Y2 * Y1^-1 * Y3^2 * Y2^-1 * Y1^-1, (R * Y2 * Y3^-1)^2, Y3^3 * Y2^-1 * Y3^-1 * Y2^-1, Y3 * Y2 * Y3 * Y2 * Y3^2, Y2 * Y1^-1 * Y2^-1 * Y3^2 * Y1^-1, Y1^-1 * Y3^-1 * Y2^-1 * Y3 * Y1^-1 * Y2^-1, Y1^-1 * Y3^-2 * Y2^2 * Y1^-1, Y3^6, Y2^-3 * Y3^-2 * Y2^-1, Y2 * Y3^-2 * Y2 * Y1^-2, Y3 * Y2^-2 * Y1^-1 * Y3^-1 * Y1^-1, Y2 * Y3^2 * Y1^-1 * Y3^-2 * Y2^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 11, 59, 27, 75, 15, 63)(4, 52, 12, 60, 28, 76, 19, 67)(6, 54, 9, 57, 29, 77, 20, 68)(7, 55, 10, 58, 30, 78, 21, 69)(13, 61, 37, 85, 18, 66, 40, 88)(14, 62, 38, 86, 17, 65, 39, 87)(16, 64, 36, 84, 22, 70, 33, 81)(23, 71, 31, 79, 26, 74, 35, 83)(24, 72, 32, 80, 25, 73, 34, 82)(41, 89, 48, 96, 44, 92, 45, 93)(42, 90, 46, 94, 43, 91, 47, 95)(97, 145, 99, 147, 109, 157, 137, 185, 122, 170, 125, 173, 104, 152, 123, 171, 114, 162, 140, 188, 119, 167, 102, 150)(98, 146, 105, 153, 127, 175, 141, 189, 136, 184, 111, 159, 101, 149, 116, 164, 131, 179, 144, 192, 133, 181, 107, 155)(100, 148, 113, 161, 138, 186, 121, 169, 103, 151, 118, 166, 124, 172, 110, 158, 139, 187, 120, 168, 126, 174, 112, 160)(106, 154, 130, 178, 142, 190, 135, 183, 108, 156, 132, 180, 117, 165, 128, 176, 143, 191, 134, 182, 115, 163, 129, 177) L = (1, 100)(2, 106)(3, 110)(4, 114)(5, 117)(6, 118)(7, 97)(8, 124)(9, 128)(10, 131)(11, 132)(12, 98)(13, 138)(14, 140)(15, 129)(16, 99)(17, 137)(18, 139)(19, 101)(20, 130)(21, 127)(22, 123)(23, 126)(24, 102)(25, 125)(26, 103)(27, 113)(28, 109)(29, 112)(30, 104)(31, 142)(32, 144)(33, 105)(34, 141)(35, 143)(36, 116)(37, 115)(38, 107)(39, 111)(40, 108)(41, 120)(42, 119)(43, 122)(44, 121)(45, 134)(46, 133)(47, 136)(48, 135)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ), ( 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 E23.541 Graph:: bipartite v = 16 e = 96 f = 36 degree seq :: [ 8^12, 24^4 ] E23.564 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = Q8 x S3 (small group id <48, 40>) Aut = ((C4 x C2) : C2) x S3 (small group id <96, 215>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^-2 * Y1, Y1 * Y3^-1 * Y1 * Y3, Y2^-1 * Y1^-1 * Y2 * Y1^-1, Y3^-1 * Y1 * Y3^-1 * Y1^-1, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2^-1)^2, Y1^4, (Y3^-1 * Y2^-1)^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3^-1 * Y2^2 * Y3^-1 * Y1^-1 * Y2^2, Y2^2 * Y1^-1 * Y2^4 * Y1^-1 ] Map:: non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 21, 69, 9, 57)(4, 52, 12, 60, 7, 55, 10, 58)(6, 54, 18, 66, 22, 70, 11, 59)(14, 62, 23, 71, 37, 85, 29, 77)(15, 63, 24, 72, 16, 64, 25, 73)(17, 65, 26, 74, 19, 67, 27, 75)(20, 68, 28, 76, 38, 86, 34, 82)(30, 78, 44, 92, 36, 84, 39, 87)(31, 79, 41, 89, 32, 80, 40, 88)(33, 81, 43, 91, 35, 83, 42, 90)(45, 93, 47, 95, 46, 94, 48, 96)(97, 145, 99, 147, 110, 158, 126, 174, 134, 182, 118, 166, 104, 152, 117, 165, 133, 181, 132, 180, 116, 164, 102, 150)(98, 146, 105, 153, 119, 167, 135, 183, 130, 178, 114, 162, 101, 149, 109, 157, 125, 173, 140, 188, 124, 172, 107, 155)(100, 148, 113, 161, 129, 177, 141, 189, 128, 176, 111, 159, 103, 151, 115, 163, 131, 179, 142, 190, 127, 175, 112, 160)(106, 154, 122, 170, 138, 186, 143, 191, 137, 185, 120, 168, 108, 156, 123, 171, 139, 187, 144, 192, 136, 184, 121, 169) L = (1, 100)(2, 106)(3, 111)(4, 104)(5, 108)(6, 115)(7, 97)(8, 103)(9, 120)(10, 101)(11, 123)(12, 98)(13, 121)(14, 127)(15, 117)(16, 99)(17, 102)(18, 122)(19, 118)(20, 129)(21, 112)(22, 113)(23, 136)(24, 109)(25, 105)(26, 107)(27, 114)(28, 138)(29, 137)(30, 141)(31, 133)(32, 110)(33, 134)(34, 139)(35, 116)(36, 142)(37, 128)(38, 131)(39, 143)(40, 125)(41, 119)(42, 130)(43, 124)(44, 144)(45, 132)(46, 126)(47, 140)(48, 135)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ), ( 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 E23.544 Graph:: bipartite v = 16 e = 96 f = 36 degree seq :: [ 8^12, 24^4 ] E23.565 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = Q8 x S3 (small group id <48, 40>) Aut = ((C4 x C2) : C2) x S3 (small group id <96, 215>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1 * Y3 * Y1^-1, Y1 * Y3^2 * Y1, Y1^-1 * Y3 * Y1 * Y3, Y2^-1 * Y1^-1 * Y2^-1 * Y1, (R * Y1)^2, Y1^4, (Y3^-1 * Y2^-1)^2, (Y3 * Y2^-1)^2, (R * Y3)^2, Y3^-1 * Y2 * Y3 * Y1^-1 * Y2^-1 * Y1^-1, (R * Y2 * Y3^-1)^2, Y2^2 * Y1^-1 * Y3 * Y2^-2 * Y3 * Y1^-1, Y2^-1 * Y3^-1 * Y2^2 * Y3^-1 * Y2^-3 ] Map:: non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 11, 59, 21, 69, 15, 63)(4, 52, 12, 60, 7, 55, 10, 58)(6, 54, 9, 57, 22, 70, 18, 66)(13, 61, 28, 76, 37, 85, 31, 79)(14, 62, 26, 74, 16, 64, 27, 75)(17, 65, 24, 72, 19, 67, 25, 73)(20, 68, 23, 71, 38, 86, 34, 82)(29, 77, 44, 92, 36, 84, 39, 87)(30, 78, 43, 91, 32, 80, 42, 90)(33, 81, 41, 89, 35, 83, 40, 88)(45, 93, 47, 95, 46, 94, 48, 96)(97, 145, 99, 147, 109, 157, 125, 173, 134, 182, 118, 166, 104, 152, 117, 165, 133, 181, 132, 180, 116, 164, 102, 150)(98, 146, 105, 153, 119, 167, 135, 183, 127, 175, 111, 159, 101, 149, 114, 162, 130, 178, 140, 188, 124, 172, 107, 155)(100, 148, 113, 161, 129, 177, 141, 189, 128, 176, 110, 158, 103, 151, 115, 163, 131, 179, 142, 190, 126, 174, 112, 160)(106, 154, 122, 170, 138, 186, 143, 191, 137, 185, 120, 168, 108, 156, 123, 171, 139, 187, 144, 192, 136, 184, 121, 169) L = (1, 100)(2, 106)(3, 110)(4, 104)(5, 108)(6, 115)(7, 97)(8, 103)(9, 120)(10, 101)(11, 123)(12, 98)(13, 126)(14, 117)(15, 122)(16, 99)(17, 102)(18, 121)(19, 118)(20, 129)(21, 112)(22, 113)(23, 136)(24, 114)(25, 105)(26, 107)(27, 111)(28, 138)(29, 141)(30, 133)(31, 139)(32, 109)(33, 134)(34, 137)(35, 116)(36, 142)(37, 128)(38, 131)(39, 143)(40, 130)(41, 119)(42, 127)(43, 124)(44, 144)(45, 132)(46, 125)(47, 140)(48, 135)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ), ( 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 E23.543 Graph:: bipartite v = 16 e = 96 f = 36 degree seq :: [ 8^12, 24^4 ] E23.566 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = (C12 x C2) : C2 (small group id <48, 37>) Aut = (D8 x S3) : C2 (small group id <96, 216>) |r| :: 2 Presentation :: [ R^2, Y3^2, R * Y2 * R * Y2^-1, Y1^4, (R * Y1)^2, (Y2^-1 * Y3)^2, Y1 * Y3 * Y1^-1 * Y3, (R * Y3)^2, (Y2^-1, Y1^-1), Y2^6 * Y1^2, Y2^-2 * Y1 * Y3 * Y2^-2 * Y3 * Y1^-1 ] Map:: non-degenerate R = (1, 49, 2, 50, 7, 55, 5, 53)(3, 51, 8, 56, 18, 66, 13, 61)(4, 52, 9, 57, 19, 67, 15, 63)(6, 54, 10, 58, 20, 68, 16, 64)(11, 59, 21, 69, 33, 81, 27, 75)(12, 60, 22, 70, 34, 82, 28, 76)(14, 62, 23, 71, 35, 83, 30, 78)(17, 65, 24, 72, 36, 84, 31, 79)(25, 73, 37, 85, 32, 80, 40, 88)(26, 74, 38, 86, 45, 93, 42, 90)(29, 77, 39, 87, 46, 94, 44, 92)(41, 89, 47, 95, 43, 91, 48, 96)(97, 145, 99, 147, 107, 155, 121, 169, 132, 180, 116, 164, 103, 151, 114, 162, 129, 177, 128, 176, 113, 161, 102, 150)(98, 146, 104, 152, 117, 165, 133, 181, 127, 175, 112, 160, 101, 149, 109, 157, 123, 171, 136, 184, 120, 168, 106, 154)(100, 148, 110, 158, 125, 173, 139, 187, 141, 189, 130, 178, 115, 163, 131, 179, 142, 190, 137, 185, 122, 170, 108, 156)(105, 153, 119, 167, 135, 183, 144, 192, 138, 186, 124, 172, 111, 159, 126, 174, 140, 188, 143, 191, 134, 182, 118, 166) L = (1, 100)(2, 105)(3, 108)(4, 97)(5, 111)(6, 110)(7, 115)(8, 118)(9, 98)(10, 119)(11, 122)(12, 99)(13, 124)(14, 102)(15, 101)(16, 126)(17, 125)(18, 130)(19, 103)(20, 131)(21, 134)(22, 104)(23, 106)(24, 135)(25, 137)(26, 107)(27, 138)(28, 109)(29, 113)(30, 112)(31, 140)(32, 139)(33, 141)(34, 114)(35, 116)(36, 142)(37, 143)(38, 117)(39, 120)(40, 144)(41, 121)(42, 123)(43, 128)(44, 127)(45, 129)(46, 132)(47, 133)(48, 136)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ), ( 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 E23.548 Graph:: bipartite v = 16 e = 96 f = 36 degree seq :: [ 8^12, 24^4 ] E23.567 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = (C12 x C2) : C2 (small group id <48, 37>) Aut = (D8 x S3) : C2 (small group id <96, 216>) |r| :: 2 Presentation :: [ R^2, Y3^2, R * Y2 * R * Y2^-1, Y2^-1 * Y1^-1 * Y2^-1 * Y1, (R * Y1)^2, Y1 * Y3 * Y1^-1 * Y3, Y1^4, (R * Y3)^2, (Y2^-1 * Y3)^2, Y1^-1 * Y2^-6 * Y1^-1 ] Map:: non-degenerate R = (1, 49, 2, 50, 7, 55, 5, 53)(3, 51, 10, 58, 18, 66, 13, 61)(4, 52, 9, 57, 19, 67, 15, 63)(6, 54, 8, 56, 20, 68, 16, 64)(11, 59, 24, 72, 33, 81, 27, 75)(12, 60, 23, 71, 34, 82, 28, 76)(14, 62, 22, 70, 35, 83, 30, 78)(17, 65, 21, 69, 36, 84, 31, 79)(25, 73, 40, 88, 32, 80, 37, 85)(26, 74, 39, 87, 45, 93, 42, 90)(29, 77, 38, 86, 46, 94, 44, 92)(41, 89, 48, 96, 43, 91, 47, 95)(97, 145, 99, 147, 107, 155, 121, 169, 132, 180, 116, 164, 103, 151, 114, 162, 129, 177, 128, 176, 113, 161, 102, 150)(98, 146, 104, 152, 117, 165, 133, 181, 123, 171, 109, 157, 101, 149, 112, 160, 127, 175, 136, 184, 120, 168, 106, 154)(100, 148, 110, 158, 125, 173, 139, 187, 141, 189, 130, 178, 115, 163, 131, 179, 142, 190, 137, 185, 122, 170, 108, 156)(105, 153, 119, 167, 135, 183, 144, 192, 140, 188, 126, 174, 111, 159, 124, 172, 138, 186, 143, 191, 134, 182, 118, 166) L = (1, 100)(2, 105)(3, 108)(4, 97)(5, 111)(6, 110)(7, 115)(8, 118)(9, 98)(10, 119)(11, 122)(12, 99)(13, 124)(14, 102)(15, 101)(16, 126)(17, 125)(18, 130)(19, 103)(20, 131)(21, 134)(22, 104)(23, 106)(24, 135)(25, 137)(26, 107)(27, 138)(28, 109)(29, 113)(30, 112)(31, 140)(32, 139)(33, 141)(34, 114)(35, 116)(36, 142)(37, 143)(38, 117)(39, 120)(40, 144)(41, 121)(42, 123)(43, 128)(44, 127)(45, 129)(46, 132)(47, 133)(48, 136)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ), ( 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 E23.546 Graph:: bipartite v = 16 e = 96 f = 36 degree seq :: [ 8^12, 24^4 ] E23.568 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = (C4 x S3) : C2 (small group id <48, 41>) Aut = (D8 x S3) : C2 (small group id <96, 216>) |r| :: 2 Presentation :: [ Y3^2, R^2, R * Y2 * R * Y2^-1, Y1^-1 * Y3 * Y1 * Y3, (R * Y3)^2, (R * Y1)^2, (Y2^-1 * Y3)^2, Y1^4, Y2 * Y1^-1 * Y2^-1 * Y1^-1, (Y2^-1 * Y1 * Y3)^2, (Y3 * Y2^-3)^2, Y2^5 * Y1^2 * Y2 ] Map:: non-degenerate R = (1, 49, 2, 50, 7, 55, 5, 53)(3, 51, 11, 59, 18, 66, 8, 56)(4, 52, 9, 57, 19, 67, 15, 63)(6, 54, 16, 64, 20, 68, 10, 58)(12, 60, 21, 69, 33, 81, 25, 73)(13, 61, 26, 74, 34, 82, 22, 70)(14, 62, 29, 77, 35, 83, 23, 71)(17, 65, 24, 72, 36, 84, 31, 79)(27, 75, 40, 88, 32, 80, 37, 85)(28, 76, 38, 86, 45, 93, 41, 89)(30, 78, 39, 87, 46, 94, 43, 91)(42, 90, 48, 96, 44, 92, 47, 95)(97, 145, 99, 147, 108, 156, 123, 171, 132, 180, 116, 164, 103, 151, 114, 162, 129, 177, 128, 176, 113, 161, 102, 150)(98, 146, 104, 152, 117, 165, 133, 181, 127, 175, 112, 160, 101, 149, 107, 155, 121, 169, 136, 184, 120, 168, 106, 154)(100, 148, 110, 158, 126, 174, 140, 188, 141, 189, 130, 178, 115, 163, 131, 179, 142, 190, 138, 186, 124, 172, 109, 157)(105, 153, 119, 167, 135, 183, 144, 192, 137, 185, 122, 170, 111, 159, 125, 173, 139, 187, 143, 191, 134, 182, 118, 166) L = (1, 100)(2, 105)(3, 109)(4, 97)(5, 111)(6, 110)(7, 115)(8, 118)(9, 98)(10, 119)(11, 122)(12, 124)(13, 99)(14, 102)(15, 101)(16, 125)(17, 126)(18, 130)(19, 103)(20, 131)(21, 134)(22, 104)(23, 106)(24, 135)(25, 137)(26, 107)(27, 138)(28, 108)(29, 112)(30, 113)(31, 139)(32, 140)(33, 141)(34, 114)(35, 116)(36, 142)(37, 143)(38, 117)(39, 120)(40, 144)(41, 121)(42, 123)(43, 127)(44, 128)(45, 129)(46, 132)(47, 133)(48, 136)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ), ( 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 E23.549 Graph:: bipartite v = 16 e = 96 f = 36 degree seq :: [ 8^12, 24^4 ] E23.569 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = (C4 x S3) : C2 (small group id <48, 41>) Aut = (D8 x S3) : C2 (small group id <96, 216>) |r| :: 2 Presentation :: [ Y3^2, R^2, R * Y2 * R * Y2^-1, Y3 * Y1 * Y3 * Y1^-1, (R * Y3)^2, (R * Y1)^2, Y1^4, (Y2^-1 * Y3)^2, (Y2^-1 * Y1^-1)^2, (Y2 * Y1^-1)^2, Y1^-1 * Y2 * Y1^2 * Y2^-1 * Y1^-1, Y2^2 * Y1^-1 * Y2^-4 * Y1^-1 ] Map:: non-degenerate R = (1, 49, 2, 50, 7, 55, 5, 53)(3, 51, 11, 59, 18, 66, 10, 58)(4, 52, 9, 57, 19, 67, 15, 63)(6, 54, 16, 64, 20, 68, 8, 56)(12, 60, 24, 72, 33, 81, 26, 74)(13, 61, 25, 73, 34, 82, 23, 71)(14, 62, 29, 77, 35, 83, 22, 70)(17, 65, 21, 69, 36, 84, 31, 79)(27, 75, 37, 85, 32, 80, 40, 88)(28, 76, 39, 87, 45, 93, 41, 89)(30, 78, 38, 86, 46, 94, 43, 91)(42, 90, 47, 95, 44, 92, 48, 96)(97, 145, 99, 147, 108, 156, 123, 171, 132, 180, 116, 164, 103, 151, 114, 162, 129, 177, 128, 176, 113, 161, 102, 150)(98, 146, 104, 152, 117, 165, 133, 181, 122, 170, 107, 155, 101, 149, 112, 160, 127, 175, 136, 184, 120, 168, 106, 154)(100, 148, 110, 158, 126, 174, 140, 188, 141, 189, 130, 178, 115, 163, 131, 179, 142, 190, 138, 186, 124, 172, 109, 157)(105, 153, 119, 167, 135, 183, 144, 192, 139, 187, 125, 173, 111, 159, 121, 169, 137, 185, 143, 191, 134, 182, 118, 166) L = (1, 100)(2, 105)(3, 109)(4, 97)(5, 111)(6, 110)(7, 115)(8, 118)(9, 98)(10, 119)(11, 121)(12, 124)(13, 99)(14, 102)(15, 101)(16, 125)(17, 126)(18, 130)(19, 103)(20, 131)(21, 134)(22, 104)(23, 106)(24, 135)(25, 107)(26, 137)(27, 138)(28, 108)(29, 112)(30, 113)(31, 139)(32, 140)(33, 141)(34, 114)(35, 116)(36, 142)(37, 143)(38, 117)(39, 120)(40, 144)(41, 122)(42, 123)(43, 127)(44, 128)(45, 129)(46, 132)(47, 133)(48, 136)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ), ( 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 E23.547 Graph:: bipartite v = 16 e = 96 f = 36 degree seq :: [ 8^12, 24^4 ] E23.570 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = (C12 x C2) : C2 (small group id <48, 37>) Aut = (D8 x S3) : C2 (small group id <96, 216>) |r| :: 2 Presentation :: [ R^2, Y3^-2 * Y1^2, Y1^-1 * Y3^-2 * Y1^-1, Y1^4, Y3 * Y1^-1 * Y3^-1 * Y1^-1, (Y2 * Y1^-1)^2, (R * Y3)^2, Y3 * Y1 * Y3 * Y1^-1, (Y2^-1 * Y1^-1)^2, (R * Y1)^2, (Y3^-1 * Y2^-1)^2, (Y3 * Y2^-1)^2, Y2 * Y3^-1 * Y1 * Y2^-1 * Y1^-1 * Y3, (R * Y2 * Y3^-1)^2, Y2^5 * Y1 * Y2^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 21, 69, 11, 59)(4, 52, 12, 60, 7, 55, 10, 58)(6, 54, 18, 66, 22, 70, 9, 57)(14, 62, 28, 76, 37, 85, 29, 77)(15, 63, 27, 75, 16, 64, 26, 74)(17, 65, 25, 73, 19, 67, 24, 72)(20, 68, 23, 71, 38, 86, 34, 82)(30, 78, 39, 87, 36, 84, 44, 92)(31, 79, 43, 91, 32, 80, 42, 90)(33, 81, 41, 89, 35, 83, 40, 88)(45, 93, 48, 96, 46, 94, 47, 95)(97, 145, 99, 147, 110, 158, 126, 174, 134, 182, 118, 166, 104, 152, 117, 165, 133, 181, 132, 180, 116, 164, 102, 150)(98, 146, 105, 153, 119, 167, 135, 183, 125, 173, 109, 157, 101, 149, 114, 162, 130, 178, 140, 188, 124, 172, 107, 155)(100, 148, 113, 161, 129, 177, 141, 189, 128, 176, 111, 159, 103, 151, 115, 163, 131, 179, 142, 190, 127, 175, 112, 160)(106, 154, 122, 170, 138, 186, 143, 191, 137, 185, 120, 168, 108, 156, 123, 171, 139, 187, 144, 192, 136, 184, 121, 169) L = (1, 100)(2, 106)(3, 111)(4, 104)(5, 108)(6, 115)(7, 97)(8, 103)(9, 120)(10, 101)(11, 123)(12, 98)(13, 122)(14, 127)(15, 117)(16, 99)(17, 102)(18, 121)(19, 118)(20, 129)(21, 112)(22, 113)(23, 136)(24, 114)(25, 105)(26, 107)(27, 109)(28, 138)(29, 139)(30, 141)(31, 133)(32, 110)(33, 134)(34, 137)(35, 116)(36, 142)(37, 128)(38, 131)(39, 143)(40, 130)(41, 119)(42, 125)(43, 124)(44, 144)(45, 132)(46, 126)(47, 140)(48, 135)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ), ( 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 E23.545 Graph:: bipartite v = 16 e = 96 f = 36 degree seq :: [ 8^12, 24^4 ] E23.571 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 4, 12}) Quotient :: dipole Aut^+ = (C12 x C2) : C2 (small group id <48, 37>) Aut = (D8 x S3) : C2 (small group id <96, 216>) |r| :: 2 Presentation :: [ R^2, (Y3^-1 * Y2)^2, Y2^-1 * Y3^2 * Y2^-1, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, (Y3, Y2), (Y1^-1 * Y2^-1)^2, Y3^-1 * Y1 * Y3^-1 * Y1^-1, Y1^4, (Y2 * Y1^-1)^2, Y3^-1 * Y2 * Y1^-1 * Y3 * Y2^-1 * Y1^-1, Y3^2 * Y2 * Y3^2 * Y2 * Y1^-2, Y1^-1 * Y2^-6 * Y1^-1, Y3^3 * Y1^-1 * Y3^-1 * Y2^-2 * Y1^-1 ] Map:: non-degenerate R = (1, 49, 2, 50, 8, 56, 5, 53)(3, 51, 13, 61, 22, 70, 11, 59)(4, 52, 12, 60, 23, 71, 17, 65)(6, 54, 18, 66, 24, 72, 9, 57)(7, 55, 10, 58, 25, 73, 19, 67)(14, 62, 29, 77, 40, 88, 32, 80)(15, 63, 33, 81, 41, 89, 30, 78)(16, 64, 31, 79, 42, 90, 28, 76)(20, 68, 26, 74, 43, 91, 36, 84)(21, 69, 37, 85, 44, 92, 27, 75)(34, 82, 45, 93, 38, 86, 47, 95)(35, 83, 48, 96, 39, 87, 46, 94)(97, 145, 99, 147, 110, 158, 130, 178, 139, 187, 120, 168, 104, 152, 118, 166, 136, 184, 134, 182, 116, 164, 102, 150)(98, 146, 105, 153, 122, 170, 141, 189, 128, 176, 109, 157, 101, 149, 114, 162, 132, 180, 143, 191, 125, 173, 107, 155)(100, 148, 111, 159, 131, 179, 140, 188, 121, 169, 138, 186, 119, 167, 137, 185, 135, 183, 117, 165, 103, 151, 112, 160)(106, 154, 123, 171, 142, 190, 129, 177, 113, 161, 127, 175, 115, 163, 133, 181, 144, 192, 126, 174, 108, 156, 124, 172) L = (1, 100)(2, 106)(3, 111)(4, 110)(5, 115)(6, 112)(7, 97)(8, 119)(9, 123)(10, 122)(11, 124)(12, 98)(13, 127)(14, 131)(15, 130)(16, 99)(17, 101)(18, 133)(19, 132)(20, 103)(21, 102)(22, 137)(23, 136)(24, 138)(25, 104)(26, 142)(27, 141)(28, 105)(29, 108)(30, 107)(31, 114)(32, 113)(33, 109)(34, 140)(35, 139)(36, 144)(37, 143)(38, 117)(39, 116)(40, 135)(41, 134)(42, 118)(43, 121)(44, 120)(45, 129)(46, 128)(47, 126)(48, 125)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8 ), ( 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 E23.550 Graph:: bipartite v = 16 e = 96 f = 36 degree seq :: [ 8^12, 24^4 ] E23.572 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 12}) Quotient :: dipole Aut^+ = SL(2,3) : C2 (small group id <48, 33>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^3, Y2^3, (R * Y3)^2, (R * Y1)^2, Y1 * Y2^-1 * Y1 * Y3 * Y2 * Y3^-1, Y1 * Y3^-1 * Y1 * Y2^-1 * Y3 * Y2, Y1 * Y3^-1 * Y1 * Y3^-1 * Y2^-1 * Y3, Y2 * Y3 * Y2^-1 * Y3 * Y2 * Y3^-1, (Y2^-1 * Y1 * Y3^-1)^2, (R * Y2 * Y3^-1)^2 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 11, 59)(4, 52, 14, 62)(5, 53, 17, 65)(6, 54, 20, 68)(7, 55, 23, 71)(8, 56, 26, 74)(9, 57, 29, 77)(10, 58, 32, 80)(12, 60, 34, 82)(13, 61, 38, 86)(15, 63, 27, 75)(16, 64, 43, 91)(18, 66, 41, 89)(19, 67, 31, 79)(21, 69, 36, 84)(22, 70, 24, 72)(25, 73, 45, 93)(28, 76, 37, 85)(30, 78, 46, 94)(33, 81, 42, 90)(35, 83, 44, 92)(39, 87, 40, 88)(47, 95, 48, 96)(97, 145, 99, 147, 101, 149)(98, 146, 103, 151, 105, 153)(100, 148, 111, 159, 112, 160)(102, 150, 117, 165, 118, 166)(104, 152, 123, 171, 124, 172)(106, 154, 129, 177, 130, 178)(107, 155, 121, 169, 131, 179)(108, 156, 133, 181, 125, 173)(109, 157, 135, 183, 119, 167)(110, 158, 136, 184, 126, 174)(113, 161, 120, 168, 139, 187)(114, 162, 122, 170, 140, 188)(115, 163, 128, 176, 141, 189)(116, 164, 134, 182, 127, 175)(132, 180, 143, 191, 137, 185)(138, 186, 144, 192, 142, 190) L = (1, 100)(2, 104)(3, 108)(4, 102)(5, 114)(6, 97)(7, 120)(8, 106)(9, 126)(10, 98)(11, 123)(12, 109)(13, 99)(14, 137)(15, 138)(16, 140)(17, 124)(18, 115)(19, 101)(20, 131)(21, 128)(22, 122)(23, 111)(24, 121)(25, 103)(26, 142)(27, 132)(28, 136)(29, 112)(30, 127)(31, 105)(32, 135)(33, 116)(34, 110)(35, 129)(36, 107)(37, 144)(38, 139)(39, 117)(40, 113)(41, 130)(42, 119)(43, 143)(44, 125)(45, 133)(46, 118)(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) :: { ( 12, 24, 12, 24 ), ( 12, 24, 12, 24, 12, 24 ) } Outer automorphisms :: reflexible Dual of E23.578 Graph:: simple bipartite v = 40 e = 96 f = 12 degree seq :: [ 4^24, 6^16 ] E23.573 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 12}) Quotient :: dipole Aut^+ = SL(2,3) : C2 (small group id <48, 33>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^3, Y3 * Y2^-1 * Y3, (Y3^-1 * Y2^-1)^2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y2 * Y1 * Y3)^2, (Y3^-1 * Y2^-1 * Y1)^2, Y1 * Y3 * Y1 * Y2 * Y1 * Y3 * Y1 * Y3^-1, (Y3^-1 * Y1)^12 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 11, 59)(4, 52, 13, 61)(5, 53, 14, 62)(6, 54, 15, 63)(7, 55, 16, 64)(8, 56, 18, 66)(9, 57, 19, 67)(10, 58, 20, 68)(12, 60, 17, 65)(21, 69, 37, 85)(22, 70, 31, 79)(23, 71, 30, 78)(24, 72, 38, 86)(25, 73, 36, 84)(26, 74, 39, 87)(27, 75, 40, 88)(28, 76, 33, 81)(29, 77, 41, 89)(32, 80, 42, 90)(34, 82, 43, 91)(35, 83, 44, 92)(45, 93, 47, 95)(46, 94, 48, 96)(97, 145, 99, 147, 101, 149)(98, 146, 103, 151, 105, 153)(100, 148, 108, 156, 102, 150)(104, 152, 113, 161, 106, 154)(107, 155, 117, 165, 119, 167)(109, 157, 121, 169, 123, 171)(110, 158, 124, 172, 122, 170)(111, 159, 120, 168, 118, 166)(112, 160, 125, 173, 127, 175)(114, 162, 129, 177, 131, 179)(115, 163, 132, 180, 130, 178)(116, 164, 128, 176, 126, 174)(133, 181, 141, 189, 136, 184)(134, 182, 142, 190, 135, 183)(137, 185, 143, 191, 140, 188)(138, 186, 144, 192, 139, 187) L = (1, 100)(2, 104)(3, 108)(4, 99)(5, 102)(6, 97)(7, 113)(8, 103)(9, 106)(10, 98)(11, 118)(12, 101)(13, 122)(14, 123)(15, 119)(16, 126)(17, 105)(18, 130)(19, 131)(20, 127)(21, 111)(22, 117)(23, 120)(24, 107)(25, 110)(26, 121)(27, 124)(28, 109)(29, 116)(30, 125)(31, 128)(32, 112)(33, 115)(34, 129)(35, 132)(36, 114)(37, 135)(38, 136)(39, 141)(40, 142)(41, 139)(42, 140)(43, 143)(44, 144)(45, 134)(46, 133)(47, 138)(48, 137)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 12, 24, 12, 24 ), ( 12, 24, 12, 24, 12, 24 ) } Outer automorphisms :: reflexible Dual of E23.579 Graph:: simple bipartite v = 40 e = 96 f = 12 degree seq :: [ 4^24, 6^16 ] E23.574 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 12}) Quotient :: dipole Aut^+ = SL(2,3) : C2 (small group id <48, 33>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y2 * Y3^-1, Y1^3, (Y3 * Y1)^2, (Y1 * Y3)^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y3^-1 * Y2^-1 * Y3^-1 * Y2^2, Y2 * Y1^-1 * Y2^-2 * Y1^-1, Y2^2 * Y1 * Y2^-1 * Y1, Y2^6, Y3^-1 * Y1 * Y2 * Y3 * Y1^-1 * Y2^-1, (Y2^-1 * Y1^-1)^3 ] Map:: non-degenerate R = (1, 49, 2, 50, 5, 53)(3, 51, 12, 60, 15, 63)(4, 52, 16, 64, 17, 65)(6, 54, 21, 69, 22, 70)(7, 55, 25, 73, 9, 57)(8, 56, 26, 74, 28, 76)(10, 58, 23, 71, 29, 77)(11, 59, 32, 80, 19, 67)(13, 61, 18, 66, 37, 85)(14, 62, 27, 75, 38, 86)(20, 68, 30, 78, 33, 81)(24, 72, 31, 79, 41, 89)(34, 82, 44, 92, 40, 88)(35, 83, 39, 87, 43, 91)(36, 84, 42, 90, 48, 96)(45, 93, 47, 95, 46, 94)(97, 145, 99, 147, 109, 157, 131, 179, 119, 167, 102, 150)(98, 146, 104, 152, 111, 159, 135, 183, 126, 174, 106, 154)(100, 148, 110, 158, 132, 180, 141, 189, 120, 168, 103, 151)(101, 149, 114, 162, 124, 172, 139, 187, 117, 165, 116, 164)(105, 153, 123, 171, 136, 184, 144, 192, 127, 175, 107, 155)(108, 156, 129, 177, 133, 181, 125, 173, 122, 170, 118, 166)(112, 160, 115, 163, 134, 182, 143, 191, 140, 188, 137, 185)(113, 161, 138, 186, 128, 176, 142, 190, 121, 169, 130, 178) L = (1, 100)(2, 105)(3, 110)(4, 99)(5, 115)(6, 103)(7, 97)(8, 123)(9, 104)(10, 107)(11, 98)(12, 113)(13, 132)(14, 109)(15, 136)(16, 101)(17, 129)(18, 134)(19, 114)(20, 112)(21, 137)(22, 130)(23, 120)(24, 102)(25, 118)(26, 121)(27, 111)(28, 143)(29, 142)(30, 127)(31, 106)(32, 125)(33, 138)(34, 108)(35, 141)(36, 131)(37, 128)(38, 124)(39, 144)(40, 135)(41, 116)(42, 133)(43, 140)(44, 117)(45, 119)(46, 122)(47, 139)(48, 126)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 24, 4, 24, 4, 24 ), ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E23.576 Graph:: simple bipartite v = 24 e = 96 f = 28 degree seq :: [ 6^16, 12^8 ] E23.575 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 12}) Quotient :: dipole Aut^+ = SL(2,3) : C2 (small group id <48, 33>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ R^2, Y1^3, (Y3^-1 * Y2^-1)^2, (Y3^-1 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, Y1 * Y3 * Y2 * Y1 * Y3^-1, Y3^-1 * Y2^-2 * Y3 * Y1^-1, Y2^2 * Y1 * Y2^-1 * Y1, Y3^4 * Y2^-1 * Y1^-1, (Y1^-1 * R * Y2^-1)^2, (R * Y2 * Y3^-1)^2, Y2^6, (Y1^-1 * Y2^-1)^3, Y3 * Y1^-1 * Y2 * Y3^-2 * Y2 * Y1^-1 * Y3 ] Map:: non-degenerate R = (1, 49, 2, 50, 5, 53)(3, 51, 12, 60, 15, 63)(4, 52, 17, 65, 20, 68)(6, 54, 25, 73, 27, 75)(7, 55, 29, 77, 9, 57)(8, 56, 32, 80, 34, 82)(10, 58, 28, 76, 38, 86)(11, 59, 18, 66, 23, 71)(13, 61, 22, 70, 19, 67)(14, 62, 26, 74, 44, 92)(16, 64, 35, 83, 40, 88)(21, 69, 36, 84, 47, 95)(24, 72, 31, 79, 39, 87)(30, 78, 42, 90, 48, 96)(33, 81, 37, 85, 46, 94)(41, 89, 45, 93, 43, 91)(97, 145, 99, 147, 109, 157, 137, 185, 124, 172, 102, 150)(98, 146, 104, 152, 111, 159, 141, 189, 127, 175, 106, 154)(100, 148, 114, 162, 136, 184, 140, 188, 138, 186, 117, 165)(101, 149, 118, 166, 130, 178, 139, 187, 121, 169, 120, 168)(103, 151, 126, 174, 113, 161, 129, 177, 107, 155, 110, 158)(105, 153, 116, 164, 112, 160, 142, 190, 122, 170, 132, 180)(108, 156, 135, 183, 115, 163, 134, 182, 128, 176, 123, 171)(119, 167, 125, 173, 131, 179, 144, 192, 133, 181, 143, 191) L = (1, 100)(2, 105)(3, 110)(4, 115)(5, 119)(6, 122)(7, 97)(8, 129)(9, 108)(10, 133)(11, 98)(12, 136)(13, 116)(14, 139)(15, 125)(16, 99)(17, 101)(18, 102)(19, 131)(20, 106)(21, 121)(22, 126)(23, 128)(24, 138)(25, 107)(26, 111)(27, 143)(28, 113)(29, 120)(30, 141)(31, 103)(32, 112)(33, 137)(34, 114)(35, 104)(36, 124)(37, 130)(38, 117)(39, 132)(40, 118)(41, 140)(42, 109)(43, 144)(44, 123)(45, 142)(46, 134)(47, 127)(48, 135)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 24, 4, 24, 4, 24 ), ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E23.577 Graph:: simple bipartite v = 24 e = 96 f = 28 degree seq :: [ 6^16, 12^8 ] E23.576 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 12}) Quotient :: dipole Aut^+ = SL(2,3) : C2 (small group id <48, 33>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3 * Y1^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2)^3, (Y1^-1 * Y2)^3, Y2 * Y1^3 * Y2 * Y1^-3, Y1^12, (Y3^-1 * Y1^-1)^6 ] Map:: non-degenerate R = (1, 49, 2, 50, 5, 53, 11, 59, 21, 69, 33, 81, 43, 91, 42, 90, 32, 80, 20, 68, 10, 58, 4, 52)(3, 51, 7, 55, 15, 63, 22, 70, 35, 83, 45, 93, 48, 96, 46, 94, 38, 86, 30, 78, 17, 65, 8, 56)(6, 54, 13, 61, 25, 73, 34, 82, 27, 75, 39, 87, 47, 95, 41, 89, 31, 79, 19, 67, 26, 74, 14, 62)(9, 57, 18, 66, 24, 72, 12, 60, 23, 71, 36, 84, 44, 92, 37, 85, 29, 77, 40, 88, 28, 76, 16, 64)(97, 145, 99, 147)(98, 146, 102, 150)(100, 148, 105, 153)(101, 149, 108, 156)(103, 151, 112, 160)(104, 152, 109, 157)(106, 154, 115, 163)(107, 155, 118, 166)(110, 158, 119, 167)(111, 159, 123, 171)(113, 161, 125, 173)(114, 162, 127, 175)(116, 164, 126, 174)(117, 165, 130, 178)(120, 168, 131, 179)(121, 169, 133, 181)(122, 170, 134, 182)(124, 172, 135, 183)(128, 176, 136, 184)(129, 177, 140, 188)(132, 180, 142, 190)(137, 185, 141, 189)(138, 186, 143, 191)(139, 187, 144, 192) L = (1, 98)(2, 101)(3, 103)(4, 97)(5, 107)(6, 109)(7, 111)(8, 99)(9, 114)(10, 100)(11, 117)(12, 119)(13, 121)(14, 102)(15, 118)(16, 105)(17, 104)(18, 120)(19, 122)(20, 106)(21, 129)(22, 131)(23, 132)(24, 108)(25, 130)(26, 110)(27, 135)(28, 112)(29, 136)(30, 113)(31, 115)(32, 116)(33, 139)(34, 123)(35, 141)(36, 140)(37, 125)(38, 126)(39, 143)(40, 124)(41, 127)(42, 128)(43, 138)(44, 133)(45, 144)(46, 134)(47, 137)(48, 142)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 6, 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 E23.574 Graph:: bipartite v = 28 e = 96 f = 24 degree seq :: [ 4^24, 24^4 ] E23.577 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 12}) Quotient :: dipole Aut^+ = SL(2,3) : C2 (small group id <48, 33>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ R^2, Y2^2, (R * Y3)^2, (R * Y1)^2, (Y2 * Y1^-1)^3, (R * Y2 * Y3^-1)^2, Y3^2 * Y2 * Y1 * Y3 * Y1^-1, Y3^-1 * Y1 * Y3^-1 * Y2 * Y3^-1 * Y1^-1, Y1^-1 * Y3 * Y1 * Y2 * Y3^-1 * Y2, Y3^-1 * Y2 * Y1^2 * Y2 * Y1^-1, Y2 * Y3^-1 * Y2 * Y3^2 * Y1^-1, Y3 * Y1^-3 * Y2 * Y1^-1, Y2 * Y1 * Y3 * Y1 * Y3 * Y1^-1, Y3^-1 * Y2 * Y1^-2 * Y3 * Y1^-1, (Y1^-1 * R * Y2)^2, Y3 * Y2 * Y3^3 * Y1^-1, Y3 * Y2 * Y1 * Y2 * Y3^-1 * Y1^-1, (Y1^-1 * Y3^-1 * Y1^-1)^2, (Y3 * Y2)^3, Y2 * Y1 * Y2 * Y3 * Y1^-2, Y3 * Y2 * Y3^-1 * Y1 * Y2 * Y1^-1, Y2 * Y3^2 * Y2 * Y3^-1 * Y1^-1 ] Map:: non-degenerate R = (1, 49, 2, 50, 7, 55, 27, 75, 16, 64, 36, 84, 47, 95, 45, 93, 14, 62, 34, 82, 21, 69, 5, 53)(3, 51, 11, 59, 32, 80, 20, 68, 43, 91, 17, 65, 29, 77, 25, 73, 6, 54, 23, 71, 44, 92, 13, 61)(4, 52, 15, 63, 37, 85, 26, 74, 41, 89, 10, 58, 39, 87, 24, 72, 33, 81, 8, 56, 31, 79, 18, 66)(9, 57, 35, 83, 22, 70, 42, 90, 48, 96, 30, 78, 19, 67, 40, 88, 12, 60, 28, 76, 46, 94, 38, 86)(97, 145, 99, 147)(98, 146, 104, 152)(100, 148, 112, 160)(101, 149, 115, 163)(102, 150, 120, 168)(103, 151, 124, 172)(105, 153, 132, 180)(106, 154, 136, 184)(107, 155, 126, 174)(108, 156, 139, 187)(109, 157, 127, 175)(110, 158, 138, 186)(111, 159, 128, 176)(113, 161, 137, 185)(114, 162, 131, 179)(116, 164, 123, 171)(117, 165, 135, 183)(118, 166, 140, 188)(119, 167, 130, 178)(121, 169, 134, 182)(122, 170, 141, 189)(125, 173, 143, 191)(129, 177, 142, 190)(133, 181, 144, 192) L = (1, 100)(2, 105)(3, 108)(4, 113)(5, 116)(6, 97)(7, 125)(8, 128)(9, 133)(10, 98)(11, 137)(12, 132)(13, 123)(14, 99)(15, 136)(16, 138)(17, 130)(18, 141)(19, 129)(20, 134)(21, 124)(22, 101)(23, 126)(24, 131)(25, 127)(26, 102)(27, 122)(28, 114)(29, 118)(30, 103)(31, 144)(32, 143)(33, 112)(34, 104)(35, 107)(36, 119)(37, 117)(38, 110)(39, 109)(40, 121)(41, 142)(42, 106)(43, 120)(44, 111)(45, 115)(46, 140)(47, 135)(48, 139)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 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 E23.575 Graph:: bipartite v = 28 e = 96 f = 24 degree seq :: [ 4^24, 24^4 ] E23.578 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 12}) Quotient :: dipole Aut^+ = SL(2,3) : C2 (small group id <48, 33>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ R^2, Y3^3, (R * Y3)^2, (R * Y1)^2, (Y2 * Y1^-1)^2, (Y3 * Y2^-1)^2, Y3 * Y2 * Y3 * Y1 * Y2^-1, Y1 * Y2 * Y3 * Y2^-1 * Y1, Y1 * Y3 * Y1^-1 * Y3 * Y1, (R * Y2 * Y3^-1)^2, R * Y3^-1 * Y1 * Y2^-1 * R * Y2^-1, Y2^-4 * Y3^-1 * Y1^-1, Y1^6, (Y3^-1 * Y1^-1)^3 ] Map:: non-degenerate R = (1, 49, 2, 50, 8, 56, 32, 80, 22, 70, 5, 53)(3, 51, 13, 61, 42, 90, 36, 84, 39, 87, 11, 59)(4, 52, 17, 65, 12, 60, 41, 89, 40, 88, 19, 67)(6, 54, 20, 68, 31, 79, 45, 93, 16, 64, 26, 74)(7, 55, 29, 77, 27, 75, 46, 94, 21, 69, 30, 78)(9, 57, 35, 83, 23, 71, 15, 63, 25, 73, 33, 81)(10, 58, 37, 85, 34, 82, 14, 62, 43, 91, 24, 72)(18, 66, 38, 86, 48, 96, 47, 95, 44, 92, 28, 76)(97, 145, 99, 147, 110, 158, 140, 188, 126, 174, 141, 189, 128, 176, 132, 180, 106, 154, 134, 182, 123, 171, 102, 150)(98, 146, 105, 153, 117, 165, 124, 172, 113, 161, 138, 186, 118, 166, 111, 159, 125, 173, 144, 192, 136, 184, 107, 155)(100, 148, 114, 162, 133, 181, 119, 167, 101, 149, 116, 164, 137, 185, 143, 191, 139, 187, 129, 177, 104, 152, 112, 160)(103, 151, 121, 169, 120, 168, 135, 183, 115, 163, 122, 170, 142, 190, 131, 179, 130, 178, 109, 157, 108, 156, 127, 175) L = (1, 100)(2, 106)(3, 111)(4, 103)(5, 117)(6, 121)(7, 97)(8, 125)(9, 116)(10, 108)(11, 127)(12, 98)(13, 134)(14, 115)(15, 112)(16, 99)(17, 139)(18, 107)(19, 118)(20, 132)(21, 120)(22, 110)(23, 135)(24, 101)(25, 124)(26, 143)(27, 113)(28, 102)(29, 130)(30, 136)(31, 114)(32, 137)(33, 109)(34, 104)(35, 144)(36, 105)(37, 126)(38, 129)(39, 140)(40, 133)(41, 142)(42, 122)(43, 123)(44, 119)(45, 131)(46, 128)(47, 138)(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, 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 E23.572 Graph:: bipartite v = 12 e = 96 f = 40 degree seq :: [ 12^8, 24^4 ] E23.579 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 12}) Quotient :: dipole Aut^+ = SL(2,3) : C2 (small group id <48, 33>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1^-1, (Y3 * Y2^-1)^2, (R * Y3)^2, (Y2^-1 * Y1)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3^-1 * Y1^-1)^3, Y1^6, (Y2 * Y1^2)^2, Y2 * Y1 * Y2 * Y1 * Y2^-2 * Y1, Y2^12 ] Map:: non-degenerate R = (1, 49, 2, 50, 6, 54, 16, 64, 12, 60, 4, 52)(3, 51, 9, 57, 23, 71, 36, 84, 21, 69, 8, 56)(5, 53, 11, 59, 28, 76, 37, 85, 17, 65, 14, 62)(7, 55, 19, 67, 13, 61, 30, 78, 39, 87, 18, 66)(10, 58, 26, 74, 42, 90, 47, 95, 31, 79, 25, 73)(15, 63, 32, 80, 20, 68, 40, 88, 46, 94, 34, 82)(22, 70, 33, 81, 38, 86, 44, 92, 24, 72, 29, 77)(27, 75, 41, 89, 48, 96, 35, 83, 43, 91, 45, 93)(97, 145, 99, 147, 106, 154, 123, 171, 136, 184, 133, 181, 112, 160, 132, 180, 143, 191, 131, 179, 111, 159, 101, 149)(98, 146, 103, 151, 116, 164, 137, 185, 140, 188, 119, 167, 108, 156, 126, 174, 130, 178, 139, 187, 118, 166, 104, 152)(100, 148, 107, 155, 125, 173, 141, 189, 122, 170, 114, 162, 102, 150, 113, 161, 134, 182, 144, 192, 127, 175, 109, 157)(105, 153, 120, 168, 124, 172, 142, 190, 135, 183, 138, 186, 117, 165, 129, 177, 110, 158, 128, 176, 115, 163, 121, 169) L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 107)(6, 112)(7, 115)(8, 99)(9, 119)(10, 122)(11, 124)(12, 100)(13, 126)(14, 101)(15, 128)(16, 108)(17, 110)(18, 103)(19, 109)(20, 136)(21, 104)(22, 129)(23, 132)(24, 125)(25, 106)(26, 138)(27, 137)(28, 133)(29, 118)(30, 135)(31, 121)(32, 116)(33, 134)(34, 111)(35, 139)(36, 117)(37, 113)(38, 140)(39, 114)(40, 142)(41, 144)(42, 143)(43, 141)(44, 120)(45, 123)(46, 130)(47, 127)(48, 131)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 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 E23.573 Graph:: bipartite v = 12 e = 96 f = 40 degree seq :: [ 12^8, 24^4 ] E23.580 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 12}) Quotient :: dipole Aut^+ = SL(2,3) : C2 (small group id <48, 33>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^3, (R * Y1)^2, (R * Y3)^2, Y3^-1 * Y1 * Y3^-1 * Y1 * Y2, Y3^-1 * Y2^-1 * Y3^-1 * Y2^2, Y3 * Y2 * Y1 * Y2^-1 * Y3^-1 * Y1, Y2^6, Y2^-1 * Y1 * Y2^2 * Y3 * Y1, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^3 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 11, 59)(4, 52, 15, 63)(5, 53, 18, 66)(6, 54, 22, 70)(7, 55, 25, 73)(8, 56, 14, 62)(9, 57, 29, 77)(10, 58, 17, 65)(12, 60, 33, 81)(13, 61, 34, 82)(16, 64, 28, 76)(19, 67, 31, 79)(20, 68, 30, 78)(21, 69, 32, 80)(23, 71, 26, 74)(24, 72, 27, 75)(35, 83, 44, 92)(36, 84, 42, 90)(37, 85, 45, 93)(38, 86, 46, 94)(39, 87, 47, 95)(40, 88, 41, 89)(43, 91, 48, 96)(97, 145, 99, 147, 108, 156, 133, 181, 116, 164, 101, 149)(98, 146, 103, 151, 122, 170, 141, 189, 127, 175, 105, 153)(100, 148, 112, 160, 136, 184, 140, 188, 117, 165, 113, 161)(102, 150, 119, 167, 109, 157, 134, 182, 125, 173, 120, 168)(104, 152, 124, 172, 142, 190, 144, 192, 128, 176, 118, 166)(106, 154, 129, 177, 123, 171, 137, 185, 114, 162, 130, 178)(107, 155, 131, 179, 143, 191, 126, 174, 111, 159, 132, 180)(110, 158, 135, 183, 121, 169, 139, 187, 138, 186, 115, 163) L = (1, 100)(2, 104)(3, 109)(4, 102)(5, 115)(6, 97)(7, 123)(8, 106)(9, 126)(10, 98)(11, 124)(12, 121)(13, 110)(14, 99)(15, 103)(16, 108)(17, 135)(18, 118)(19, 117)(20, 120)(21, 101)(22, 132)(23, 136)(24, 139)(25, 112)(26, 107)(27, 111)(28, 122)(29, 113)(30, 128)(31, 130)(32, 105)(33, 142)(34, 131)(35, 127)(36, 114)(37, 140)(38, 133)(39, 125)(40, 138)(41, 141)(42, 119)(43, 116)(44, 134)(45, 144)(46, 143)(47, 129)(48, 137)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 6, 24, 6, 24 ), ( 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24 ) } Outer automorphisms :: reflexible Dual of E23.582 Graph:: simple bipartite v = 32 e = 96 f = 20 degree seq :: [ 4^24, 12^8 ] E23.581 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 12}) Quotient :: dipole Aut^+ = SL(2,3) : C2 (small group id <48, 33>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y2^-1, (R * Y1)^2, (R * Y3)^2, (Y2 * Y3^-1 * Y2)^2, Y2^6, Y3 * Y1 * Y2^-1 * Y3 * Y2^-1 * Y1 * Y3 * Y2^-1, (Y2^-3 * Y1)^2, Y3^2 * Y1 * Y2 * Y3^-2 * Y1 * Y2^-1, Y3 * Y1 * Y2 * Y1 * Y2 * Y3^-1 * Y1 * Y3^-1 * Y1, Y2 * Y1 * Y2 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1, (Y3^-2 * Y1 * Y3^-1 * Y1 * Y3^-1)^3 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 9, 57)(5, 53, 11, 59)(6, 54, 13, 61)(8, 56, 17, 65)(10, 58, 21, 69)(12, 60, 24, 72)(14, 62, 28, 76)(15, 63, 29, 77)(16, 64, 31, 79)(18, 66, 25, 73)(19, 67, 35, 83)(20, 68, 36, 84)(22, 70, 37, 85)(23, 71, 30, 78)(26, 74, 33, 81)(27, 75, 40, 88)(32, 80, 42, 90)(34, 82, 43, 91)(38, 86, 46, 94)(39, 87, 47, 95)(41, 89, 45, 93)(44, 92, 48, 96)(97, 145, 99, 147, 104, 152, 114, 162, 106, 154, 100, 148)(98, 146, 101, 149, 108, 156, 121, 169, 110, 158, 102, 150)(103, 151, 111, 159, 126, 174, 117, 165, 128, 176, 112, 160)(105, 153, 115, 163, 130, 178, 113, 161, 129, 177, 116, 164)(107, 155, 118, 166, 127, 175, 124, 172, 134, 182, 119, 167)(109, 157, 122, 170, 135, 183, 120, 168, 131, 179, 123, 171)(125, 173, 137, 185, 139, 187, 138, 186, 140, 188, 132, 180)(133, 181, 141, 189, 143, 191, 142, 190, 144, 192, 136, 184) L = (1, 100)(2, 102)(3, 97)(4, 106)(5, 98)(6, 110)(7, 112)(8, 99)(9, 116)(10, 114)(11, 119)(12, 101)(13, 123)(14, 121)(15, 103)(16, 128)(17, 130)(18, 104)(19, 105)(20, 129)(21, 126)(22, 107)(23, 134)(24, 135)(25, 108)(26, 109)(27, 131)(28, 127)(29, 132)(30, 111)(31, 118)(32, 117)(33, 113)(34, 115)(35, 120)(36, 140)(37, 136)(38, 124)(39, 122)(40, 144)(41, 125)(42, 139)(43, 137)(44, 138)(45, 133)(46, 143)(47, 141)(48, 142)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 6, 24, 6, 24 ), ( 6, 24, 6, 24, 6, 24, 6, 24, 6, 24, 6, 24 ) } Outer automorphisms :: reflexible Dual of E23.583 Graph:: bipartite v = 32 e = 96 f = 20 degree seq :: [ 4^24, 12^8 ] E23.582 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 12}) Quotient :: dipole Aut^+ = SL(2,3) : C2 (small group id <48, 33>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y2^-1, Y1^3, Y3 * Y1 * Y2^-1 * Y1, (R * Y3)^2, (R * Y1)^2, Y3 * Y1^-1 * Y2 * Y3^-3 * Y1^-1 * Y2^-1, Y2^3 * Y3^-1 * Y1^-1 * Y2^-2 * Y1^-1, Y1 * Y2 * Y1 * Y2^2 * Y3^-2 * Y1 * Y3^-1, Y2^12, (Y3 * Y2^-1)^6 ] Map:: non-degenerate R = (1, 49, 2, 50, 5, 53)(3, 51, 8, 56, 7, 55)(4, 52, 10, 58, 12, 60)(6, 54, 14, 62, 13, 61)(9, 57, 19, 67, 18, 66)(11, 59, 22, 70, 24, 72)(15, 63, 29, 77, 28, 76)(16, 64, 17, 65, 32, 80)(20, 68, 30, 78, 36, 84)(21, 69, 37, 85, 25, 73)(23, 71, 31, 79, 39, 87)(26, 74, 27, 75, 38, 86)(33, 81, 42, 90, 43, 91)(34, 82, 35, 83, 40, 88)(41, 89, 45, 93, 46, 94)(44, 92, 48, 96, 47, 95)(97, 145, 99, 147, 105, 153, 116, 164, 125, 173, 138, 186, 144, 192, 142, 190, 134, 182, 119, 167, 107, 155, 100, 148)(98, 146, 102, 150, 111, 159, 126, 174, 133, 181, 141, 189, 143, 191, 136, 184, 120, 168, 127, 175, 112, 160, 103, 151)(101, 149, 106, 154, 117, 165, 132, 180, 115, 163, 131, 179, 140, 188, 139, 187, 128, 176, 135, 183, 122, 170, 109, 157)(104, 152, 113, 161, 129, 177, 124, 172, 110, 158, 123, 171, 137, 185, 121, 169, 108, 156, 118, 166, 130, 178, 114, 162) L = (1, 100)(2, 103)(3, 97)(4, 107)(5, 109)(6, 98)(7, 112)(8, 114)(9, 99)(10, 101)(11, 119)(12, 121)(13, 122)(14, 124)(15, 102)(16, 127)(17, 104)(18, 130)(19, 132)(20, 105)(21, 106)(22, 108)(23, 134)(24, 136)(25, 137)(26, 135)(27, 110)(28, 129)(29, 116)(30, 111)(31, 120)(32, 139)(33, 113)(34, 118)(35, 115)(36, 117)(37, 126)(38, 142)(39, 128)(40, 143)(41, 123)(42, 125)(43, 140)(44, 131)(45, 133)(46, 144)(47, 141)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 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 E23.580 Graph:: bipartite v = 20 e = 96 f = 32 degree seq :: [ 6^16, 24^4 ] E23.583 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 3, 6, 12}) Quotient :: dipole Aut^+ = SL(2,3) : C2 (small group id <48, 33>) Aut = (SL(2,3) : C2) : C2 (small group id <96, 193>) |r| :: 2 Presentation :: [ R^2, Y1^3, (Y3^-1 * Y1^-1)^2, (R * Y3)^2, (R * Y1)^2, (Y2 * Y1^-1)^2, Y2 * Y3^-1 * Y2 * Y3^-1 * Y1^-1, R * Y2 * Y1 * R * Y2^-1, Y2^2 * Y3 * Y2 * Y1, Y1 * Y3^-1 * Y2^-1 * Y3^-2, (Y2^-1 * Y1^-1 * Y3)^2, Y2^12 ] Map:: non-degenerate R = (1, 49, 2, 50, 5, 53)(3, 51, 12, 60, 10, 58)(4, 52, 16, 64, 19, 67)(6, 54, 21, 69, 25, 73)(7, 55, 28, 76, 9, 57)(8, 56, 32, 80, 23, 71)(11, 59, 39, 87, 22, 70)(13, 61, 40, 88, 33, 81)(14, 62, 38, 86, 31, 79)(15, 63, 34, 82, 20, 68)(17, 65, 26, 74, 35, 83)(18, 66, 36, 84, 41, 89)(24, 72, 37, 85, 30, 78)(27, 75, 44, 92, 29, 77)(42, 90, 48, 96, 47, 95)(43, 91, 46, 94, 45, 93)(97, 145, 99, 147, 109, 157, 138, 186, 140, 188, 124, 172, 130, 178, 118, 166, 132, 180, 142, 190, 122, 170, 102, 150)(98, 146, 104, 152, 123, 171, 144, 192, 127, 175, 135, 183, 116, 164, 100, 148, 113, 161, 141, 189, 133, 181, 106, 154)(101, 149, 117, 165, 134, 182, 143, 191, 136, 184, 115, 163, 111, 159, 105, 153, 120, 168, 139, 187, 137, 185, 119, 167)(103, 151, 125, 173, 128, 176, 114, 162, 107, 155, 110, 158, 121, 169, 131, 179, 112, 160, 129, 177, 108, 156, 126, 174) L = (1, 100)(2, 105)(3, 110)(4, 114)(5, 118)(6, 120)(7, 97)(8, 129)(9, 131)(10, 132)(11, 98)(12, 116)(13, 119)(14, 139)(15, 99)(16, 101)(17, 124)(18, 138)(19, 123)(20, 117)(21, 125)(22, 126)(23, 113)(24, 135)(25, 130)(26, 128)(27, 102)(28, 134)(29, 141)(30, 143)(31, 103)(32, 111)(33, 142)(34, 104)(35, 144)(36, 115)(37, 121)(38, 106)(39, 109)(40, 107)(41, 108)(42, 133)(43, 140)(44, 112)(45, 136)(46, 127)(47, 122)(48, 137)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 12, 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E23.581 Graph:: bipartite v = 20 e = 96 f = 32 degree seq :: [ 6^16, 24^4 ] E23.584 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 24, 24}) Quotient :: halfedge^2 Aut^+ = C8 x S3 (small group id <48, 4>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y3 * Y2, (R * Y1)^2, R * Y3 * R * Y2, Y1^-3 * Y2 * Y1^3 * Y2, Y1^-1 * Y2 * Y1^-1 * Y2 * Y1 * Y2 * Y1 * Y2, Y1^-7 * Y2 * Y1^-1 * Y2 ] Map:: R = (1, 50, 2, 53, 5, 59, 11, 71, 23, 87, 39, 81, 33, 65, 17, 77, 29, 92, 44, 79, 31, 93, 45, 96, 48, 95, 47, 82, 34, 94, 46, 80, 32, 64, 16, 76, 28, 91, 43, 86, 38, 70, 22, 58, 10, 52, 4, 49)(3, 55, 7, 63, 15, 72, 24, 89, 41, 84, 36, 68, 20, 57, 9, 67, 19, 74, 26, 60, 12, 73, 25, 90, 42, 85, 37, 69, 21, 78, 30, 62, 14, 54, 6, 61, 13, 75, 27, 88, 40, 83, 35, 66, 18, 56, 8, 51) 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, 47)(37, 39)(38, 41)(42, 48)(49, 51)(50, 54)(52, 57)(53, 60)(55, 64)(56, 65)(58, 69)(59, 72)(61, 76)(62, 77)(63, 79)(66, 82)(67, 80)(68, 81)(70, 83)(71, 88)(73, 91)(74, 92)(75, 93)(78, 94)(84, 95)(85, 87)(86, 89)(90, 96) local type(s) :: { ( 48^48 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 48 f = 2 degree seq :: [ 48^2 ] E23.585 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 24, 24}) Quotient :: halfedge^2 Aut^+ = C3 x D16 (small group id <48, 25>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y3 * Y2, R * Y2 * R * Y3, (R * Y1)^2, (Y1^-3 * Y2)^2, Y2 * Y1 * Y3 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1, Y1^-3 * Y2 * Y1 * Y2 * Y1^-4 ] Map:: R = (1, 50, 2, 53, 5, 59, 11, 71, 23, 87, 39, 81, 33, 64, 16, 76, 28, 90, 42, 83, 35, 94, 46, 96, 48, 95, 47, 80, 32, 93, 45, 82, 34, 65, 17, 77, 29, 91, 43, 86, 38, 70, 22, 58, 10, 52, 4, 49)(3, 55, 7, 63, 15, 79, 31, 88, 40, 78, 30, 62, 14, 54, 6, 61, 13, 75, 27, 69, 21, 85, 37, 92, 44, 74, 26, 60, 12, 73, 25, 68, 20, 57, 9, 67, 19, 84, 36, 89, 41, 72, 24, 66, 18, 56, 8, 51) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 35)(19, 33)(20, 34)(22, 31)(23, 40)(25, 42)(26, 43)(27, 45)(30, 46)(36, 47)(37, 39)(38, 41)(44, 48)(49, 51)(50, 54)(52, 57)(53, 60)(55, 64)(56, 65)(58, 69)(59, 72)(61, 76)(62, 77)(63, 80)(66, 83)(67, 81)(68, 82)(70, 79)(71, 88)(73, 90)(74, 91)(75, 93)(78, 94)(84, 95)(85, 87)(86, 89)(92, 96) local type(s) :: { ( 48^48 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 48 f = 2 degree seq :: [ 48^2 ] E23.586 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 24, 24}) Quotient :: halfedge^2 Aut^+ = C3 x D16 (small group id <48, 25>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (Y3 * Y2)^2, (R * Y1)^2, R * Y3 * R * Y2, Y3 * Y1 * Y2 * Y3 * Y1^-1 * Y2, Y1^2 * Y2 * Y1^-2 * Y3, Y2 * Y1^2 * Y3 * Y1^-2, (Y1^-2 * Y2 * Y1^-1)^2, Y2 * Y1^-1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1, (Y1^-2 * Y3 * Y1^-1)^2, Y1^24 ] Map:: non-degenerate R = (1, 50, 2, 54, 6, 65, 17, 83, 35, 77, 29, 92, 44, 73, 25, 89, 41, 96, 48, 93, 45, 75, 27, 58, 10, 69, 21, 87, 39, 95, 47, 94, 46, 76, 28, 91, 43, 74, 26, 90, 42, 82, 34, 64, 16, 53, 5, 49)(3, 57, 9, 67, 19, 88, 40, 81, 33, 63, 15, 70, 22, 55, 7, 68, 20, 85, 37, 79, 31, 61, 13, 52, 4, 60, 12, 66, 18, 86, 38, 80, 32, 62, 14, 72, 24, 56, 8, 71, 23, 84, 36, 78, 30, 59, 11, 51) L = (1, 3)(2, 7)(4, 10)(5, 14)(6, 18)(8, 21)(9, 25)(11, 28)(12, 26)(13, 29)(15, 27)(16, 31)(17, 36)(19, 39)(20, 41)(22, 43)(23, 42)(24, 44)(30, 45)(32, 46)(33, 35)(34, 40)(37, 47)(38, 48)(49, 52)(50, 56)(51, 58)(53, 63)(54, 67)(55, 69)(57, 74)(59, 77)(60, 73)(61, 76)(62, 75)(64, 78)(65, 85)(66, 87)(68, 90)(70, 92)(71, 89)(72, 91)(79, 93)(80, 83)(81, 94)(82, 86)(84, 95)(88, 96) local type(s) :: { ( 48^48 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 48 f = 2 degree seq :: [ 48^2 ] E23.587 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 24, 24}) Quotient :: halfedge^2 Aut^+ = C8 x S3 (small group id <48, 4>) Aut = (C8 x S3) : C2 (small group id <96, 126>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (Y2 * Y3)^2, (R * Y1)^2, Y2 * Y1 * Y3 * Y2 * Y1^-1 * Y3, Y3 * Y1 * Y2 * Y3 * Y1^-1 * Y2, Y1^-1 * Y3 * Y1^-2 * Y2 * Y1^-1, Y1^-1 * Y3 * Y1^5 * Y2, Y2 * Y1^-1 * Y3 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1, Y2 * Y3 * Y2 * Y1^-1 * Y3 * Y2 * Y1^-1 * Y3 * Y2 * Y1^-1 * Y3 * Y2 * Y1^-1 * Y3 * Y1^-2 * Y3 * Y2 * Y1^-2 ] Map:: non-degenerate R = (1, 50, 2, 54, 6, 65, 17, 83, 35, 75, 27, 90, 42, 77, 29, 91, 43, 96, 48, 93, 45, 76, 28, 58, 10, 69, 21, 86, 38, 95, 47, 94, 46, 74, 26, 89, 41, 78, 30, 92, 44, 82, 34, 64, 16, 53, 5, 49)(3, 57, 9, 73, 25, 84, 36, 72, 24, 56, 8, 71, 23, 62, 14, 80, 32, 87, 39, 66, 18, 61, 13, 52, 4, 60, 12, 79, 31, 85, 37, 70, 22, 55, 7, 68, 20, 63, 15, 81, 33, 88, 40, 67, 19, 59, 11, 51) L = (1, 3)(2, 7)(4, 10)(5, 14)(6, 18)(8, 21)(9, 26)(11, 29)(12, 27)(13, 30)(15, 28)(16, 31)(17, 36)(19, 38)(20, 41)(22, 43)(23, 42)(24, 44)(25, 45)(32, 46)(33, 35)(34, 40)(37, 47)(39, 48)(49, 52)(50, 56)(51, 58)(53, 63)(54, 67)(55, 69)(57, 75)(59, 78)(60, 74)(61, 77)(62, 76)(64, 73)(65, 85)(66, 86)(68, 90)(70, 92)(71, 89)(72, 91)(79, 93)(80, 83)(81, 94)(82, 87)(84, 95)(88, 96) local type(s) :: { ( 48^48 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 48 f = 2 degree seq :: [ 48^2 ] E23.588 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 24, 24}) Quotient :: edge^2 Aut^+ = C8 x S3 (small group id <48, 4>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y1, R * Y2 * R * Y1, (R * Y3)^2, Y3^-1 * Y1 * Y3^3 * Y1 * Y3^-2, Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1, (Y3^-1 * Y1 * Y3^-3)^2, Y3^24 ] Map:: R = (1, 49, 3, 51, 8, 56, 18, 66, 35, 83, 44, 92, 28, 76, 13, 61, 27, 75, 42, 90, 25, 73, 41, 89, 48, 96, 45, 93, 29, 77, 40, 88, 24, 72, 11, 59, 23, 71, 39, 87, 38, 86, 22, 70, 10, 58, 4, 52)(2, 50, 5, 53, 12, 60, 26, 74, 43, 91, 36, 84, 20, 68, 9, 57, 19, 67, 34, 82, 17, 65, 33, 81, 47, 95, 37, 85, 21, 69, 32, 80, 16, 64, 7, 55, 15, 63, 31, 79, 46, 94, 30, 78, 14, 62, 6, 54)(97, 98)(99, 103)(100, 105)(101, 107)(102, 109)(104, 113)(106, 117)(108, 121)(110, 125)(111, 119)(112, 123)(114, 122)(115, 120)(116, 124)(118, 126)(127, 137)(128, 136)(129, 135)(130, 138)(131, 142)(132, 141)(133, 140)(134, 139)(143, 144)(145, 146)(147, 151)(148, 153)(149, 155)(150, 157)(152, 161)(154, 165)(156, 169)(158, 173)(159, 167)(160, 171)(162, 170)(163, 168)(164, 172)(166, 174)(175, 185)(176, 184)(177, 183)(178, 186)(179, 190)(180, 189)(181, 188)(182, 187)(191, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 96, 96 ), ( 96^48 ) } Outer automorphisms :: reflexible Dual of E23.597 Graph:: simple bipartite v = 50 e = 96 f = 2 degree seq :: [ 2^48, 48^2 ] E23.589 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 24, 24}) Quotient :: edge^2 Aut^+ = C3 x D16 (small group id <48, 25>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y1, (R * Y3)^2, R * Y2 * R * Y1, (Y3^-3 * Y1)^2, Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1, Y3 * Y1 * Y3^-7 * Y1, (Y3^2 * Y1 * Y3^-2 * Y1)^2 ] Map:: R = (1, 49, 3, 51, 8, 56, 18, 66, 35, 83, 40, 88, 24, 72, 11, 59, 23, 71, 39, 87, 29, 77, 45, 93, 48, 96, 42, 90, 25, 73, 41, 89, 28, 76, 13, 61, 27, 75, 44, 92, 38, 86, 22, 70, 10, 58, 4, 52)(2, 50, 5, 53, 12, 60, 26, 74, 43, 91, 32, 80, 16, 64, 7, 55, 15, 63, 31, 79, 21, 69, 37, 85, 47, 95, 34, 82, 17, 65, 33, 81, 20, 68, 9, 57, 19, 67, 36, 84, 46, 94, 30, 78, 14, 62, 6, 54)(97, 98)(99, 103)(100, 105)(101, 107)(102, 109)(104, 113)(106, 117)(108, 121)(110, 125)(111, 119)(112, 123)(114, 126)(115, 120)(116, 124)(118, 122)(127, 137)(128, 141)(129, 135)(130, 140)(131, 139)(132, 138)(133, 136)(134, 142)(143, 144)(145, 146)(147, 151)(148, 153)(149, 155)(150, 157)(152, 161)(154, 165)(156, 169)(158, 173)(159, 167)(160, 171)(162, 174)(163, 168)(164, 172)(166, 170)(175, 185)(176, 189)(177, 183)(178, 188)(179, 187)(180, 186)(181, 184)(182, 190)(191, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 96, 96 ), ( 96^48 ) } Outer automorphisms :: reflexible Dual of E23.598 Graph:: simple bipartite v = 50 e = 96 f = 2 degree seq :: [ 2^48, 48^2 ] E23.590 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 24, 24}) Quotient :: edge^2 Aut^+ = C3 x D16 (small group id <48, 25>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y1 * Y2)^2, R * Y2 * R * Y1, (R * Y3)^2, Y2 * Y3^-1 * Y1 * Y2 * Y3 * Y1, Y3^2 * Y2 * Y3^-2 * Y1, Y3^-1 * Y2 * Y3^2 * Y1 * Y3^-1, Y3 * Y1 * Y3 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y1, (Y3 * Y2 * Y3^2)^2, (Y3 * Y1 * Y3^2)^2, Y3^24 ] Map:: R = (1, 49, 4, 52, 13, 61, 31, 79, 43, 91, 23, 71, 38, 86, 19, 67, 37, 85, 48, 96, 36, 84, 18, 66, 6, 54, 17, 65, 35, 83, 47, 95, 42, 90, 22, 70, 40, 88, 20, 68, 39, 87, 34, 82, 16, 64, 5, 53)(2, 50, 7, 55, 21, 69, 41, 89, 33, 81, 15, 63, 28, 76, 11, 59, 27, 75, 46, 94, 26, 74, 10, 58, 3, 51, 9, 57, 25, 73, 45, 93, 32, 80, 14, 62, 30, 78, 12, 60, 29, 77, 44, 92, 24, 72, 8, 56)(97, 98)(99, 102)(100, 107)(101, 110)(103, 115)(104, 118)(105, 116)(106, 119)(108, 113)(109, 121)(111, 114)(112, 122)(117, 131)(120, 132)(123, 133)(124, 136)(125, 135)(126, 134)(127, 140)(128, 138)(129, 139)(130, 137)(141, 144)(142, 143)(145, 147)(146, 150)(148, 156)(149, 159)(151, 164)(152, 167)(153, 163)(154, 166)(155, 161)(157, 165)(158, 162)(160, 168)(169, 179)(170, 180)(171, 183)(172, 182)(173, 181)(174, 184)(175, 190)(176, 187)(177, 186)(178, 189)(185, 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) :: { ( 96, 96 ), ( 96^48 ) } Outer automorphisms :: reflexible Dual of E23.599 Graph:: simple bipartite v = 50 e = 96 f = 2 degree seq :: [ 2^48, 48^2 ] E23.591 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 24, 24}) Quotient :: edge^2 Aut^+ = C8 x S3 (small group id <48, 4>) Aut = (C8 x S3) : C2 (small group id <96, 126>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y2 * Y1)^2, (R * Y3)^2, R * Y2 * R * Y1, Y3 * Y2 * Y1 * Y3^-1 * Y2 * Y1, Y3 * Y2 * Y1 * Y3^-1 * Y2 * Y1, Y1 * Y3^-2 * Y2 * Y3^-2, Y3 * Y1 * Y3^-5 * Y2, Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y2 * Y3^-1 * Y1 ] Map:: R = (1, 49, 4, 52, 13, 61, 31, 79, 40, 88, 20, 68, 39, 87, 22, 70, 42, 90, 48, 96, 36, 84, 18, 66, 6, 54, 17, 65, 35, 83, 47, 95, 38, 86, 19, 67, 37, 85, 23, 71, 43, 91, 34, 82, 16, 64, 5, 53)(2, 50, 7, 55, 21, 69, 41, 89, 30, 78, 12, 60, 29, 77, 14, 62, 32, 80, 46, 94, 26, 74, 10, 58, 3, 51, 9, 57, 25, 73, 45, 93, 28, 76, 11, 59, 27, 75, 15, 63, 33, 81, 44, 92, 24, 72, 8, 56)(97, 98)(99, 102)(100, 107)(101, 110)(103, 115)(104, 118)(105, 116)(106, 119)(108, 113)(109, 122)(111, 114)(112, 121)(117, 132)(120, 131)(123, 133)(124, 138)(125, 135)(126, 139)(127, 137)(128, 134)(129, 136)(130, 140)(141, 143)(142, 144)(145, 147)(146, 150)(148, 156)(149, 159)(151, 164)(152, 167)(153, 163)(154, 166)(155, 161)(157, 168)(158, 162)(160, 165)(169, 180)(170, 179)(171, 183)(172, 187)(173, 181)(174, 186)(175, 189)(176, 184)(177, 182)(178, 190)(185, 191)(188, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 96, 96 ), ( 96^48 ) } Outer automorphisms :: reflexible Dual of E23.600 Graph:: simple bipartite v = 50 e = 96 f = 2 degree seq :: [ 2^48, 48^2 ] E23.592 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 24, 24}) Quotient :: edge^2 Aut^+ = C8 x S3 (small group id <48, 4>) Aut = C2 x C8 x S3 (small group id <96, 106>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, R * Y2 * R * Y1, (R * Y3)^2, Y1^2 * Y2^-1 * Y1^-2 * Y2, Y3 * Y2^-1 * Y1^2 * Y3 * Y1^-3, Y3 * Y2^2 * Y1^-1 * Y3 * Y2^-3, Y3 * Y1 * Y3 * Y2 * Y3 * Y1^-1 * Y3 * Y2^-1, Y3 * Y2 * Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1, Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1^-1, Y2^2 * Y3 * Y2^2 * Y1^-2 * Y3 * Y1^-2, Y3 * Y2^2 * Y1^-1 * Y2 * Y3 * Y1^-4, Y2^24, Y1^24 ] Map:: non-degenerate R = (1, 49, 4, 52)(2, 50, 6, 54)(3, 51, 8, 56)(5, 53, 12, 60)(7, 55, 16, 64)(9, 57, 20, 68)(10, 58, 22, 70)(11, 59, 24, 72)(13, 61, 28, 76)(14, 62, 30, 78)(15, 63, 32, 80)(17, 65, 34, 82)(18, 66, 36, 84)(19, 67, 37, 85)(21, 69, 38, 86)(23, 71, 40, 88)(25, 73, 43, 91)(26, 74, 44, 92)(27, 75, 45, 93)(29, 77, 46, 94)(31, 79, 41, 89)(33, 81, 39, 87)(35, 83, 47, 95)(42, 90, 48, 96)(97, 98, 101, 107, 119, 135, 132, 118, 126, 140, 133, 141, 144, 143, 134, 142, 130, 116, 124, 139, 127, 111, 103, 99)(100, 105, 115, 120, 137, 131, 114, 104, 113, 122, 108, 121, 138, 129, 112, 125, 110, 102, 109, 123, 136, 128, 117, 106)(145, 147, 151, 159, 175, 187, 172, 164, 178, 190, 182, 191, 192, 189, 181, 188, 174, 166, 180, 183, 167, 155, 149, 146)(148, 154, 165, 176, 184, 171, 157, 150, 158, 173, 160, 177, 186, 169, 156, 170, 161, 152, 162, 179, 185, 168, 163, 153) 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) :: { ( 8^4 ), ( 8^24 ) } Outer automorphisms :: reflexible Dual of E23.601 Graph:: simple bipartite v = 28 e = 96 f = 24 degree seq :: [ 4^24, 24^4 ] E23.593 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 24, 24}) Quotient :: edge^2 Aut^+ = C8 x S3 (small group id <48, 4>) Aut = (C8 : C2) x S3 (small group id <96, 113>) |r| :: 2 Presentation :: [ R^2, Y3^2, (Y2, Y1^-1), (Y1^-1 * Y2^-1)^2, Y1^2 * Y2^2, (Y1^-1, Y2), (R * Y3)^2, R * Y1 * R * Y2, Y3 * Y1 * Y2 * Y3 * Y2^-1 * Y1^-1, Y2^-2 * Y3 * Y1 * Y2^-1 * Y3, Y2^-1 * Y3 * Y2 * Y1 * Y3 * Y1^-1, Y1^-1 * Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y1 * Y3, Y1^-3 * Y2 * Y1^-1 * Y3 * Y1 * Y3, Y2^24, Y1^24 ] Map:: polytopal non-degenerate R = (1, 49, 4, 52)(2, 50, 9, 57)(3, 51, 12, 60)(5, 53, 18, 66)(6, 54, 19, 67)(7, 55, 21, 69)(8, 56, 23, 71)(10, 58, 28, 76)(11, 59, 30, 78)(13, 61, 34, 82)(14, 62, 35, 83)(15, 63, 36, 84)(16, 64, 37, 85)(17, 65, 38, 86)(20, 68, 40, 88)(22, 70, 44, 92)(24, 72, 45, 93)(25, 73, 46, 94)(26, 74, 47, 95)(27, 75, 48, 96)(29, 77, 43, 91)(31, 79, 42, 90)(32, 80, 39, 87)(33, 81, 41, 89)(97, 98, 103, 116, 135, 134, 144, 133, 143, 125, 109, 99, 104, 102, 106, 118, 137, 131, 141, 132, 142, 127, 107, 101)(100, 110, 130, 136, 121, 115, 123, 114, 129, 139, 117, 111, 119, 113, 126, 140, 122, 105, 120, 108, 128, 138, 124, 112)(145, 147, 155, 173, 190, 181, 189, 182, 185, 164, 154, 146, 152, 149, 157, 175, 191, 180, 192, 179, 183, 166, 151, 150)(148, 159, 172, 187, 176, 162, 168, 163, 170, 184, 174, 158, 167, 160, 165, 186, 177, 156, 171, 153, 169, 188, 178, 161) 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) :: { ( 8^4 ), ( 8^24 ) } Outer automorphisms :: reflexible Dual of E23.602 Graph:: simple bipartite v = 28 e = 96 f = 24 degree seq :: [ 4^24, 24^4 ] E23.594 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 24, 24}) Quotient :: edge^2 Aut^+ = C24 : C2 (small group id <48, 5>) Aut = (C8 : C2) x S3 (small group id <96, 113>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^2 * Y1^2, (Y2, Y1^-1), R * Y1 * R * Y2, (R * Y3)^2, Y2^-1 * Y3 * Y2 * Y1 * Y3 * Y1^-1, Y1 * Y3 * Y2^-1 * Y1 * Y3 * Y1, (Y1^-1 * Y3 * Y2^-1)^2, Y3 * Y1 * Y3 * Y1^-5, Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1, Y2^24 ] Map:: polytopal non-degenerate R = (1, 49, 4, 52)(2, 50, 9, 57)(3, 51, 12, 60)(5, 53, 18, 66)(6, 54, 19, 67)(7, 55, 21, 69)(8, 56, 23, 71)(10, 58, 28, 76)(11, 59, 30, 78)(13, 61, 34, 82)(14, 62, 35, 83)(15, 63, 36, 84)(16, 64, 37, 85)(17, 65, 38, 86)(20, 68, 40, 88)(22, 70, 44, 92)(24, 72, 45, 93)(25, 73, 46, 94)(26, 74, 47, 95)(27, 75, 48, 96)(29, 77, 42, 90)(31, 79, 43, 91)(32, 80, 41, 89)(33, 81, 39, 87)(97, 98, 103, 116, 135, 131, 141, 132, 142, 125, 109, 99, 104, 102, 106, 118, 137, 134, 144, 133, 143, 127, 107, 101)(100, 110, 130, 140, 122, 105, 120, 108, 128, 139, 117, 111, 119, 113, 126, 136, 121, 115, 123, 114, 129, 138, 124, 112)(145, 147, 155, 173, 191, 180, 192, 179, 185, 164, 154, 146, 152, 149, 157, 175, 190, 181, 189, 182, 183, 166, 151, 150)(148, 159, 172, 187, 177, 156, 171, 153, 169, 188, 174, 158, 167, 160, 165, 186, 176, 162, 168, 163, 170, 184, 178, 161) 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) :: { ( 8^4 ), ( 8^24 ) } Outer automorphisms :: reflexible Dual of E23.603 Graph:: simple bipartite v = 28 e = 96 f = 24 degree seq :: [ 4^24, 24^4 ] E23.595 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 24, 24}) Quotient :: edge^2 Aut^+ = D48 (small group id <48, 7>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ R^2, Y3^2, R * Y2 * R * Y1, (R * Y3)^2, (Y1, Y2), (Y3 * Y1^-1)^2, (Y3 * Y2^-1)^2, Y1^-3 * Y2^-3, (Y3 * Y1 * Y2^-1)^2, Y1^-4 * Y2^4, Y1 * Y3 * Y2^2 * Y3 * Y1^-1 * Y2^2, Y1^24, Y2^24 ] Map:: polytopal non-degenerate R = (1, 49, 4, 52)(2, 50, 9, 57)(3, 51, 12, 60)(5, 53, 14, 62)(6, 54, 15, 63)(7, 55, 21, 69)(8, 56, 24, 72)(10, 58, 25, 73)(11, 59, 28, 76)(13, 61, 30, 78)(16, 64, 32, 80)(17, 65, 33, 81)(18, 66, 34, 82)(19, 67, 36, 84)(20, 68, 38, 86)(22, 70, 39, 87)(23, 71, 41, 89)(26, 74, 42, 90)(27, 75, 43, 91)(29, 77, 44, 92)(31, 79, 45, 93)(35, 83, 46, 94)(37, 85, 47, 95)(40, 88, 48, 96)(97, 98, 103, 115, 131, 127, 109, 99, 104, 116, 114, 122, 136, 125, 107, 119, 113, 102, 106, 118, 133, 123, 112, 101)(100, 110, 128, 139, 143, 135, 121, 111, 129, 137, 124, 140, 144, 138, 130, 134, 120, 108, 126, 141, 142, 132, 117, 105)(145, 147, 155, 171, 179, 170, 154, 146, 152, 167, 160, 175, 184, 166, 151, 164, 161, 149, 157, 173, 181, 163, 162, 150)(148, 159, 178, 180, 191, 188, 174, 158, 177, 182, 165, 183, 192, 189, 176, 185, 168, 153, 169, 186, 190, 187, 172, 156) 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) :: { ( 8^4 ), ( 8^24 ) } Outer automorphisms :: reflexible Dual of E23.604 Graph:: simple bipartite v = 28 e = 96 f = 24 degree seq :: [ 4^24, 24^4 ] E23.596 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 24, 24}) Quotient :: edge^2 Aut^+ = C24 : C2 (small group id <48, 6>) Aut = QD16 x S3 (small group id <96, 120>) |r| :: 2 Presentation :: [ R^2, Y3^2, (Y1, Y2^-1), (R * Y3)^2, R * Y1 * R * Y2, Y1^-3 * Y2^-3, Y3 * Y2^-1 * Y1 * Y2^-1 * Y3 * Y1^-1, (Y2 * Y3 * Y2)^2, (Y1 * Y3 * Y1)^2, Y1^-1 * Y3 * Y1^-1 * Y2^-1 * Y3 * Y2^-1, Y3 * Y2 * Y1^-1 * Y3 * Y1^-1 * Y2, Y1^-1 * Y3 * Y2^-1 * Y3 * Y2 * Y1^-1, Y1^24, Y2^24 ] Map:: polytopal non-degenerate R = (1, 49, 4, 52)(2, 50, 9, 57)(3, 51, 12, 60)(5, 53, 18, 66)(6, 54, 21, 69)(7, 55, 25, 73)(8, 56, 28, 76)(10, 58, 33, 81)(11, 59, 31, 79)(13, 61, 30, 78)(14, 62, 34, 82)(15, 63, 37, 85)(16, 64, 36, 84)(17, 65, 26, 74)(19, 67, 38, 86)(20, 68, 39, 87)(22, 70, 40, 88)(23, 71, 43, 91)(24, 72, 45, 93)(27, 75, 46, 94)(29, 77, 48, 96)(32, 80, 44, 92)(35, 83, 47, 95)(41, 89, 42, 90)(97, 98, 103, 119, 138, 133, 109, 99, 104, 120, 118, 130, 144, 132, 107, 123, 116, 102, 106, 122, 140, 131, 115, 101)(100, 110, 134, 141, 128, 108, 129, 111, 135, 139, 127, 105, 125, 114, 136, 143, 124, 113, 126, 117, 137, 142, 121, 112)(145, 147, 155, 179, 186, 178, 154, 146, 152, 171, 163, 181, 192, 170, 151, 168, 164, 149, 157, 180, 188, 167, 166, 150)(148, 159, 184, 190, 176, 153, 174, 158, 183, 191, 169, 156, 173, 165, 182, 187, 172, 160, 177, 162, 185, 189, 175, 161) 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) :: { ( 8^4 ), ( 8^24 ) } Outer automorphisms :: reflexible Dual of E23.605 Graph:: simple bipartite v = 28 e = 96 f = 24 degree seq :: [ 4^24, 24^4 ] E23.597 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 24, 24}) Quotient :: loop^2 Aut^+ = C8 x S3 (small group id <48, 4>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y1, R * Y2 * R * Y1, (R * Y3)^2, Y3^-1 * Y1 * Y3^3 * Y1 * Y3^-2, Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1, (Y3^-1 * Y1 * Y3^-3)^2, Y3^24 ] Map:: R = (1, 49, 97, 145, 3, 51, 99, 147, 8, 56, 104, 152, 18, 66, 114, 162, 35, 83, 131, 179, 44, 92, 140, 188, 28, 76, 124, 172, 13, 61, 109, 157, 27, 75, 123, 171, 42, 90, 138, 186, 25, 73, 121, 169, 41, 89, 137, 185, 48, 96, 144, 192, 45, 93, 141, 189, 29, 77, 125, 173, 40, 88, 136, 184, 24, 72, 120, 168, 11, 59, 107, 155, 23, 71, 119, 167, 39, 87, 135, 183, 38, 86, 134, 182, 22, 70, 118, 166, 10, 58, 106, 154, 4, 52, 100, 148)(2, 50, 98, 146, 5, 53, 101, 149, 12, 60, 108, 156, 26, 74, 122, 170, 43, 91, 139, 187, 36, 84, 132, 180, 20, 68, 116, 164, 9, 57, 105, 153, 19, 67, 115, 163, 34, 82, 130, 178, 17, 65, 113, 161, 33, 81, 129, 177, 47, 95, 143, 191, 37, 85, 133, 181, 21, 69, 117, 165, 32, 80, 128, 176, 16, 64, 112, 160, 7, 55, 103, 151, 15, 63, 111, 159, 31, 79, 127, 175, 46, 94, 142, 190, 30, 78, 126, 174, 14, 62, 110, 158, 6, 54, 102, 150) L = (1, 50)(2, 49)(3, 55)(4, 57)(5, 59)(6, 61)(7, 51)(8, 65)(9, 52)(10, 69)(11, 53)(12, 73)(13, 54)(14, 77)(15, 71)(16, 75)(17, 56)(18, 74)(19, 72)(20, 76)(21, 58)(22, 78)(23, 63)(24, 67)(25, 60)(26, 66)(27, 64)(28, 68)(29, 62)(30, 70)(31, 89)(32, 88)(33, 87)(34, 90)(35, 94)(36, 93)(37, 92)(38, 91)(39, 81)(40, 80)(41, 79)(42, 82)(43, 86)(44, 85)(45, 84)(46, 83)(47, 96)(48, 95)(97, 146)(98, 145)(99, 151)(100, 153)(101, 155)(102, 157)(103, 147)(104, 161)(105, 148)(106, 165)(107, 149)(108, 169)(109, 150)(110, 173)(111, 167)(112, 171)(113, 152)(114, 170)(115, 168)(116, 172)(117, 154)(118, 174)(119, 159)(120, 163)(121, 156)(122, 162)(123, 160)(124, 164)(125, 158)(126, 166)(127, 185)(128, 184)(129, 183)(130, 186)(131, 190)(132, 189)(133, 188)(134, 187)(135, 177)(136, 176)(137, 175)(138, 178)(139, 182)(140, 181)(141, 180)(142, 179)(143, 192)(144, 191) 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 E23.588 Transitivity :: VT+ Graph:: bipartite v = 2 e = 96 f = 50 degree seq :: [ 96^2 ] E23.598 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 24, 24}) Quotient :: loop^2 Aut^+ = C3 x D16 (small group id <48, 25>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y1, (R * Y3)^2, R * Y2 * R * Y1, (Y3^-3 * Y1)^2, Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1, Y3 * Y1 * Y3^-7 * Y1, (Y3^2 * Y1 * Y3^-2 * Y1)^2 ] Map:: R = (1, 49, 97, 145, 3, 51, 99, 147, 8, 56, 104, 152, 18, 66, 114, 162, 35, 83, 131, 179, 40, 88, 136, 184, 24, 72, 120, 168, 11, 59, 107, 155, 23, 71, 119, 167, 39, 87, 135, 183, 29, 77, 125, 173, 45, 93, 141, 189, 48, 96, 144, 192, 42, 90, 138, 186, 25, 73, 121, 169, 41, 89, 137, 185, 28, 76, 124, 172, 13, 61, 109, 157, 27, 75, 123, 171, 44, 92, 140, 188, 38, 86, 134, 182, 22, 70, 118, 166, 10, 58, 106, 154, 4, 52, 100, 148)(2, 50, 98, 146, 5, 53, 101, 149, 12, 60, 108, 156, 26, 74, 122, 170, 43, 91, 139, 187, 32, 80, 128, 176, 16, 64, 112, 160, 7, 55, 103, 151, 15, 63, 111, 159, 31, 79, 127, 175, 21, 69, 117, 165, 37, 85, 133, 181, 47, 95, 143, 191, 34, 82, 130, 178, 17, 65, 113, 161, 33, 81, 129, 177, 20, 68, 116, 164, 9, 57, 105, 153, 19, 67, 115, 163, 36, 84, 132, 180, 46, 94, 142, 190, 30, 78, 126, 174, 14, 62, 110, 158, 6, 54, 102, 150) L = (1, 50)(2, 49)(3, 55)(4, 57)(5, 59)(6, 61)(7, 51)(8, 65)(9, 52)(10, 69)(11, 53)(12, 73)(13, 54)(14, 77)(15, 71)(16, 75)(17, 56)(18, 78)(19, 72)(20, 76)(21, 58)(22, 74)(23, 63)(24, 67)(25, 60)(26, 70)(27, 64)(28, 68)(29, 62)(30, 66)(31, 89)(32, 93)(33, 87)(34, 92)(35, 91)(36, 90)(37, 88)(38, 94)(39, 81)(40, 85)(41, 79)(42, 84)(43, 83)(44, 82)(45, 80)(46, 86)(47, 96)(48, 95)(97, 146)(98, 145)(99, 151)(100, 153)(101, 155)(102, 157)(103, 147)(104, 161)(105, 148)(106, 165)(107, 149)(108, 169)(109, 150)(110, 173)(111, 167)(112, 171)(113, 152)(114, 174)(115, 168)(116, 172)(117, 154)(118, 170)(119, 159)(120, 163)(121, 156)(122, 166)(123, 160)(124, 164)(125, 158)(126, 162)(127, 185)(128, 189)(129, 183)(130, 188)(131, 187)(132, 186)(133, 184)(134, 190)(135, 177)(136, 181)(137, 175)(138, 180)(139, 179)(140, 178)(141, 176)(142, 182)(143, 192)(144, 191) 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 E23.589 Transitivity :: VT+ Graph:: bipartite v = 2 e = 96 f = 50 degree seq :: [ 96^2 ] E23.599 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 24, 24}) Quotient :: loop^2 Aut^+ = C3 x D16 (small group id <48, 25>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y1 * Y2)^2, R * Y2 * R * Y1, (R * Y3)^2, Y2 * Y3^-1 * Y1 * Y2 * Y3 * Y1, Y3^2 * Y2 * Y3^-2 * Y1, Y3^-1 * Y2 * Y3^2 * Y1 * Y3^-1, Y3 * Y1 * Y3 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y1, (Y3 * Y2 * Y3^2)^2, (Y3 * Y1 * Y3^2)^2, Y3^24 ] Map:: R = (1, 49, 97, 145, 4, 52, 100, 148, 13, 61, 109, 157, 31, 79, 127, 175, 43, 91, 139, 187, 23, 71, 119, 167, 38, 86, 134, 182, 19, 67, 115, 163, 37, 85, 133, 181, 48, 96, 144, 192, 36, 84, 132, 180, 18, 66, 114, 162, 6, 54, 102, 150, 17, 65, 113, 161, 35, 83, 131, 179, 47, 95, 143, 191, 42, 90, 138, 186, 22, 70, 118, 166, 40, 88, 136, 184, 20, 68, 116, 164, 39, 87, 135, 183, 34, 82, 130, 178, 16, 64, 112, 160, 5, 53, 101, 149)(2, 50, 98, 146, 7, 55, 103, 151, 21, 69, 117, 165, 41, 89, 137, 185, 33, 81, 129, 177, 15, 63, 111, 159, 28, 76, 124, 172, 11, 59, 107, 155, 27, 75, 123, 171, 46, 94, 142, 190, 26, 74, 122, 170, 10, 58, 106, 154, 3, 51, 99, 147, 9, 57, 105, 153, 25, 73, 121, 169, 45, 93, 141, 189, 32, 80, 128, 176, 14, 62, 110, 158, 30, 78, 126, 174, 12, 60, 108, 156, 29, 77, 125, 173, 44, 92, 140, 188, 24, 72, 120, 168, 8, 56, 104, 152) L = (1, 50)(2, 49)(3, 54)(4, 59)(5, 62)(6, 51)(7, 67)(8, 70)(9, 68)(10, 71)(11, 52)(12, 65)(13, 73)(14, 53)(15, 66)(16, 74)(17, 60)(18, 63)(19, 55)(20, 57)(21, 83)(22, 56)(23, 58)(24, 84)(25, 61)(26, 64)(27, 85)(28, 88)(29, 87)(30, 86)(31, 92)(32, 90)(33, 91)(34, 89)(35, 69)(36, 72)(37, 75)(38, 78)(39, 77)(40, 76)(41, 82)(42, 80)(43, 81)(44, 79)(45, 96)(46, 95)(47, 94)(48, 93)(97, 147)(98, 150)(99, 145)(100, 156)(101, 159)(102, 146)(103, 164)(104, 167)(105, 163)(106, 166)(107, 161)(108, 148)(109, 165)(110, 162)(111, 149)(112, 168)(113, 155)(114, 158)(115, 153)(116, 151)(117, 157)(118, 154)(119, 152)(120, 160)(121, 179)(122, 180)(123, 183)(124, 182)(125, 181)(126, 184)(127, 190)(128, 187)(129, 186)(130, 189)(131, 169)(132, 170)(133, 173)(134, 172)(135, 171)(136, 174)(137, 192)(138, 177)(139, 176)(140, 191)(141, 178)(142, 175)(143, 188)(144, 185) 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 E23.590 Transitivity :: VT+ Graph:: bipartite v = 2 e = 96 f = 50 degree seq :: [ 96^2 ] E23.600 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 24, 24}) Quotient :: loop^2 Aut^+ = C8 x S3 (small group id <48, 4>) Aut = (C8 x S3) : C2 (small group id <96, 126>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y2 * Y1)^2, (R * Y3)^2, R * Y2 * R * Y1, Y3 * Y2 * Y1 * Y3^-1 * Y2 * Y1, Y3 * Y2 * Y1 * Y3^-1 * Y2 * Y1, Y1 * Y3^-2 * Y2 * Y3^-2, Y3 * Y1 * Y3^-5 * Y2, Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y2 * Y3^-1 * Y1 ] Map:: R = (1, 49, 97, 145, 4, 52, 100, 148, 13, 61, 109, 157, 31, 79, 127, 175, 40, 88, 136, 184, 20, 68, 116, 164, 39, 87, 135, 183, 22, 70, 118, 166, 42, 90, 138, 186, 48, 96, 144, 192, 36, 84, 132, 180, 18, 66, 114, 162, 6, 54, 102, 150, 17, 65, 113, 161, 35, 83, 131, 179, 47, 95, 143, 191, 38, 86, 134, 182, 19, 67, 115, 163, 37, 85, 133, 181, 23, 71, 119, 167, 43, 91, 139, 187, 34, 82, 130, 178, 16, 64, 112, 160, 5, 53, 101, 149)(2, 50, 98, 146, 7, 55, 103, 151, 21, 69, 117, 165, 41, 89, 137, 185, 30, 78, 126, 174, 12, 60, 108, 156, 29, 77, 125, 173, 14, 62, 110, 158, 32, 80, 128, 176, 46, 94, 142, 190, 26, 74, 122, 170, 10, 58, 106, 154, 3, 51, 99, 147, 9, 57, 105, 153, 25, 73, 121, 169, 45, 93, 141, 189, 28, 76, 124, 172, 11, 59, 107, 155, 27, 75, 123, 171, 15, 63, 111, 159, 33, 81, 129, 177, 44, 92, 140, 188, 24, 72, 120, 168, 8, 56, 104, 152) L = (1, 50)(2, 49)(3, 54)(4, 59)(5, 62)(6, 51)(7, 67)(8, 70)(9, 68)(10, 71)(11, 52)(12, 65)(13, 74)(14, 53)(15, 66)(16, 73)(17, 60)(18, 63)(19, 55)(20, 57)(21, 84)(22, 56)(23, 58)(24, 83)(25, 64)(26, 61)(27, 85)(28, 90)(29, 87)(30, 91)(31, 89)(32, 86)(33, 88)(34, 92)(35, 72)(36, 69)(37, 75)(38, 80)(39, 77)(40, 81)(41, 79)(42, 76)(43, 78)(44, 82)(45, 95)(46, 96)(47, 93)(48, 94)(97, 147)(98, 150)(99, 145)(100, 156)(101, 159)(102, 146)(103, 164)(104, 167)(105, 163)(106, 166)(107, 161)(108, 148)(109, 168)(110, 162)(111, 149)(112, 165)(113, 155)(114, 158)(115, 153)(116, 151)(117, 160)(118, 154)(119, 152)(120, 157)(121, 180)(122, 179)(123, 183)(124, 187)(125, 181)(126, 186)(127, 189)(128, 184)(129, 182)(130, 190)(131, 170)(132, 169)(133, 173)(134, 177)(135, 171)(136, 176)(137, 191)(138, 174)(139, 172)(140, 192)(141, 175)(142, 178)(143, 185)(144, 188) 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 E23.591 Transitivity :: VT+ Graph:: bipartite v = 2 e = 96 f = 50 degree seq :: [ 96^2 ] E23.601 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 24, 24}) Quotient :: loop^2 Aut^+ = C8 x S3 (small group id <48, 4>) Aut = C2 x C8 x S3 (small group id <96, 106>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, R * Y2 * R * Y1, (R * Y3)^2, Y1^2 * Y2^-1 * Y1^-2 * Y2, Y3 * Y2^-1 * Y1^2 * Y3 * Y1^-3, Y3 * Y2^2 * Y1^-1 * Y3 * Y2^-3, Y3 * Y1 * Y3 * Y2 * Y3 * Y1^-1 * Y3 * Y2^-1, Y3 * Y2 * Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1, Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1^-1, Y2^2 * Y3 * Y2^2 * Y1^-2 * Y3 * Y1^-2, Y3 * Y2^2 * Y1^-1 * Y2 * Y3 * Y1^-4, Y2^24, Y1^24 ] Map:: non-degenerate R = (1, 49, 97, 145, 4, 52, 100, 148)(2, 50, 98, 146, 6, 54, 102, 150)(3, 51, 99, 147, 8, 56, 104, 152)(5, 53, 101, 149, 12, 60, 108, 156)(7, 55, 103, 151, 16, 64, 112, 160)(9, 57, 105, 153, 20, 68, 116, 164)(10, 58, 106, 154, 22, 70, 118, 166)(11, 59, 107, 155, 24, 72, 120, 168)(13, 61, 109, 157, 28, 76, 124, 172)(14, 62, 110, 158, 30, 78, 126, 174)(15, 63, 111, 159, 32, 80, 128, 176)(17, 65, 113, 161, 34, 82, 130, 178)(18, 66, 114, 162, 36, 84, 132, 180)(19, 67, 115, 163, 37, 85, 133, 181)(21, 69, 117, 165, 38, 86, 134, 182)(23, 71, 119, 167, 40, 88, 136, 184)(25, 73, 121, 169, 43, 91, 139, 187)(26, 74, 122, 170, 44, 92, 140, 188)(27, 75, 123, 171, 45, 93, 141, 189)(29, 77, 125, 173, 46, 94, 142, 190)(31, 79, 127, 175, 41, 89, 137, 185)(33, 81, 129, 177, 39, 87, 135, 183)(35, 83, 131, 179, 47, 95, 143, 191)(42, 90, 138, 186, 48, 96, 144, 192) L = (1, 50)(2, 53)(3, 49)(4, 57)(5, 59)(6, 61)(7, 51)(8, 65)(9, 67)(10, 52)(11, 71)(12, 73)(13, 75)(14, 54)(15, 55)(16, 77)(17, 74)(18, 56)(19, 72)(20, 76)(21, 58)(22, 78)(23, 87)(24, 89)(25, 90)(26, 60)(27, 88)(28, 91)(29, 62)(30, 92)(31, 63)(32, 69)(33, 64)(34, 68)(35, 66)(36, 70)(37, 93)(38, 94)(39, 84)(40, 80)(41, 83)(42, 81)(43, 79)(44, 85)(45, 96)(46, 82)(47, 86)(48, 95)(97, 147)(98, 145)(99, 151)(100, 154)(101, 146)(102, 158)(103, 159)(104, 162)(105, 148)(106, 165)(107, 149)(108, 170)(109, 150)(110, 173)(111, 175)(112, 177)(113, 152)(114, 179)(115, 153)(116, 178)(117, 176)(118, 180)(119, 155)(120, 163)(121, 156)(122, 161)(123, 157)(124, 164)(125, 160)(126, 166)(127, 187)(128, 184)(129, 186)(130, 190)(131, 185)(132, 183)(133, 188)(134, 191)(135, 167)(136, 171)(137, 168)(138, 169)(139, 172)(140, 174)(141, 181)(142, 182)(143, 192)(144, 189) local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E23.592 Transitivity :: VT+ Graph:: bipartite v = 24 e = 96 f = 28 degree seq :: [ 8^24 ] E23.602 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 24, 24}) Quotient :: loop^2 Aut^+ = C8 x S3 (small group id <48, 4>) Aut = (C8 : C2) x S3 (small group id <96, 113>) |r| :: 2 Presentation :: [ R^2, Y3^2, (Y2, Y1^-1), (Y1^-1 * Y2^-1)^2, Y1^2 * Y2^2, (Y1^-1, Y2), (R * Y3)^2, R * Y1 * R * Y2, Y3 * Y1 * Y2 * Y3 * Y2^-1 * Y1^-1, Y2^-2 * Y3 * Y1 * Y2^-1 * Y3, Y2^-1 * Y3 * Y2 * Y1 * Y3 * Y1^-1, Y1^-1 * Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y1 * Y3, Y1^-3 * Y2 * Y1^-1 * Y3 * Y1 * Y3, Y2^24, Y1^24 ] Map:: polytopal non-degenerate R = (1, 49, 97, 145, 4, 52, 100, 148)(2, 50, 98, 146, 9, 57, 105, 153)(3, 51, 99, 147, 12, 60, 108, 156)(5, 53, 101, 149, 18, 66, 114, 162)(6, 54, 102, 150, 19, 67, 115, 163)(7, 55, 103, 151, 21, 69, 117, 165)(8, 56, 104, 152, 23, 71, 119, 167)(10, 58, 106, 154, 28, 76, 124, 172)(11, 59, 107, 155, 30, 78, 126, 174)(13, 61, 109, 157, 34, 82, 130, 178)(14, 62, 110, 158, 35, 83, 131, 179)(15, 63, 111, 159, 36, 84, 132, 180)(16, 64, 112, 160, 37, 85, 133, 181)(17, 65, 113, 161, 38, 86, 134, 182)(20, 68, 116, 164, 40, 88, 136, 184)(22, 70, 118, 166, 44, 92, 140, 188)(24, 72, 120, 168, 45, 93, 141, 189)(25, 73, 121, 169, 46, 94, 142, 190)(26, 74, 122, 170, 47, 95, 143, 191)(27, 75, 123, 171, 48, 96, 144, 192)(29, 77, 125, 173, 43, 91, 139, 187)(31, 79, 127, 175, 42, 90, 138, 186)(32, 80, 128, 176, 39, 87, 135, 183)(33, 81, 129, 177, 41, 89, 137, 185) L = (1, 50)(2, 55)(3, 56)(4, 62)(5, 49)(6, 58)(7, 68)(8, 54)(9, 72)(10, 70)(11, 53)(12, 80)(13, 51)(14, 82)(15, 71)(16, 52)(17, 78)(18, 81)(19, 75)(20, 87)(21, 63)(22, 89)(23, 65)(24, 60)(25, 67)(26, 57)(27, 66)(28, 64)(29, 61)(30, 92)(31, 59)(32, 90)(33, 91)(34, 88)(35, 93)(36, 94)(37, 95)(38, 96)(39, 86)(40, 73)(41, 83)(42, 76)(43, 69)(44, 74)(45, 84)(46, 79)(47, 77)(48, 85)(97, 147)(98, 152)(99, 155)(100, 159)(101, 157)(102, 145)(103, 150)(104, 149)(105, 169)(106, 146)(107, 173)(108, 171)(109, 175)(110, 167)(111, 172)(112, 165)(113, 148)(114, 168)(115, 170)(116, 154)(117, 186)(118, 151)(119, 160)(120, 163)(121, 188)(122, 184)(123, 153)(124, 187)(125, 190)(126, 158)(127, 191)(128, 162)(129, 156)(130, 161)(131, 183)(132, 192)(133, 189)(134, 185)(135, 166)(136, 174)(137, 164)(138, 177)(139, 176)(140, 178)(141, 182)(142, 181)(143, 180)(144, 179) local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E23.593 Transitivity :: VT+ Graph:: simple bipartite v = 24 e = 96 f = 28 degree seq :: [ 8^24 ] E23.603 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 24, 24}) Quotient :: loop^2 Aut^+ = C24 : C2 (small group id <48, 5>) Aut = (C8 : C2) x S3 (small group id <96, 113>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^2 * Y1^2, (Y2, Y1^-1), R * Y1 * R * Y2, (R * Y3)^2, Y2^-1 * Y3 * Y2 * Y1 * Y3 * Y1^-1, Y1 * Y3 * Y2^-1 * Y1 * Y3 * Y1, (Y1^-1 * Y3 * Y2^-1)^2, Y3 * Y1 * Y3 * Y1^-5, Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1, Y2^24 ] Map:: polytopal non-degenerate R = (1, 49, 97, 145, 4, 52, 100, 148)(2, 50, 98, 146, 9, 57, 105, 153)(3, 51, 99, 147, 12, 60, 108, 156)(5, 53, 101, 149, 18, 66, 114, 162)(6, 54, 102, 150, 19, 67, 115, 163)(7, 55, 103, 151, 21, 69, 117, 165)(8, 56, 104, 152, 23, 71, 119, 167)(10, 58, 106, 154, 28, 76, 124, 172)(11, 59, 107, 155, 30, 78, 126, 174)(13, 61, 109, 157, 34, 82, 130, 178)(14, 62, 110, 158, 35, 83, 131, 179)(15, 63, 111, 159, 36, 84, 132, 180)(16, 64, 112, 160, 37, 85, 133, 181)(17, 65, 113, 161, 38, 86, 134, 182)(20, 68, 116, 164, 40, 88, 136, 184)(22, 70, 118, 166, 44, 92, 140, 188)(24, 72, 120, 168, 45, 93, 141, 189)(25, 73, 121, 169, 46, 94, 142, 190)(26, 74, 122, 170, 47, 95, 143, 191)(27, 75, 123, 171, 48, 96, 144, 192)(29, 77, 125, 173, 42, 90, 138, 186)(31, 79, 127, 175, 43, 91, 139, 187)(32, 80, 128, 176, 41, 89, 137, 185)(33, 81, 129, 177, 39, 87, 135, 183) L = (1, 50)(2, 55)(3, 56)(4, 62)(5, 49)(6, 58)(7, 68)(8, 54)(9, 72)(10, 70)(11, 53)(12, 80)(13, 51)(14, 82)(15, 71)(16, 52)(17, 78)(18, 81)(19, 75)(20, 87)(21, 63)(22, 89)(23, 65)(24, 60)(25, 67)(26, 57)(27, 66)(28, 64)(29, 61)(30, 88)(31, 59)(32, 91)(33, 90)(34, 92)(35, 93)(36, 94)(37, 95)(38, 96)(39, 83)(40, 73)(41, 86)(42, 76)(43, 69)(44, 74)(45, 84)(46, 77)(47, 79)(48, 85)(97, 147)(98, 152)(99, 155)(100, 159)(101, 157)(102, 145)(103, 150)(104, 149)(105, 169)(106, 146)(107, 173)(108, 171)(109, 175)(110, 167)(111, 172)(112, 165)(113, 148)(114, 168)(115, 170)(116, 154)(117, 186)(118, 151)(119, 160)(120, 163)(121, 188)(122, 184)(123, 153)(124, 187)(125, 191)(126, 158)(127, 190)(128, 162)(129, 156)(130, 161)(131, 185)(132, 192)(133, 189)(134, 183)(135, 166)(136, 178)(137, 164)(138, 176)(139, 177)(140, 174)(141, 182)(142, 181)(143, 180)(144, 179) local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E23.594 Transitivity :: VT+ Graph:: simple bipartite v = 24 e = 96 f = 28 degree seq :: [ 8^24 ] E23.604 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 24, 24}) Quotient :: loop^2 Aut^+ = D48 (small group id <48, 7>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ R^2, Y3^2, R * Y2 * R * Y1, (R * Y3)^2, (Y1, Y2), (Y3 * Y1^-1)^2, (Y3 * Y2^-1)^2, Y1^-3 * Y2^-3, (Y3 * Y1 * Y2^-1)^2, Y1^-4 * Y2^4, Y1 * Y3 * Y2^2 * Y3 * Y1^-1 * Y2^2, Y1^24, Y2^24 ] Map:: polytopal non-degenerate R = (1, 49, 97, 145, 4, 52, 100, 148)(2, 50, 98, 146, 9, 57, 105, 153)(3, 51, 99, 147, 12, 60, 108, 156)(5, 53, 101, 149, 14, 62, 110, 158)(6, 54, 102, 150, 15, 63, 111, 159)(7, 55, 103, 151, 21, 69, 117, 165)(8, 56, 104, 152, 24, 72, 120, 168)(10, 58, 106, 154, 25, 73, 121, 169)(11, 59, 107, 155, 28, 76, 124, 172)(13, 61, 109, 157, 30, 78, 126, 174)(16, 64, 112, 160, 32, 80, 128, 176)(17, 65, 113, 161, 33, 81, 129, 177)(18, 66, 114, 162, 34, 82, 130, 178)(19, 67, 115, 163, 36, 84, 132, 180)(20, 68, 116, 164, 38, 86, 134, 182)(22, 70, 118, 166, 39, 87, 135, 183)(23, 71, 119, 167, 41, 89, 137, 185)(26, 74, 122, 170, 42, 90, 138, 186)(27, 75, 123, 171, 43, 91, 139, 187)(29, 77, 125, 173, 44, 92, 140, 188)(31, 79, 127, 175, 45, 93, 141, 189)(35, 83, 131, 179, 46, 94, 142, 190)(37, 85, 133, 181, 47, 95, 143, 191)(40, 88, 136, 184, 48, 96, 144, 192) L = (1, 50)(2, 55)(3, 56)(4, 62)(5, 49)(6, 58)(7, 67)(8, 68)(9, 52)(10, 70)(11, 71)(12, 78)(13, 51)(14, 80)(15, 81)(16, 53)(17, 54)(18, 74)(19, 83)(20, 66)(21, 57)(22, 85)(23, 65)(24, 60)(25, 63)(26, 88)(27, 64)(28, 92)(29, 59)(30, 93)(31, 61)(32, 91)(33, 89)(34, 86)(35, 79)(36, 69)(37, 75)(38, 72)(39, 73)(40, 77)(41, 76)(42, 82)(43, 95)(44, 96)(45, 94)(46, 84)(47, 87)(48, 90)(97, 147)(98, 152)(99, 155)(100, 159)(101, 157)(102, 145)(103, 164)(104, 167)(105, 169)(106, 146)(107, 171)(108, 148)(109, 173)(110, 177)(111, 178)(112, 175)(113, 149)(114, 150)(115, 162)(116, 161)(117, 183)(118, 151)(119, 160)(120, 153)(121, 186)(122, 154)(123, 179)(124, 156)(125, 181)(126, 158)(127, 184)(128, 185)(129, 182)(130, 180)(131, 170)(132, 191)(133, 163)(134, 165)(135, 192)(136, 166)(137, 168)(138, 190)(139, 172)(140, 174)(141, 176)(142, 187)(143, 188)(144, 189) local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E23.595 Transitivity :: VT+ Graph:: bipartite v = 24 e = 96 f = 28 degree seq :: [ 8^24 ] E23.605 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 24, 24}) Quotient :: loop^2 Aut^+ = C24 : C2 (small group id <48, 6>) Aut = QD16 x S3 (small group id <96, 120>) |r| :: 2 Presentation :: [ R^2, Y3^2, (Y1, Y2^-1), (R * Y3)^2, R * Y1 * R * Y2, Y1^-3 * Y2^-3, Y3 * Y2^-1 * Y1 * Y2^-1 * Y3 * Y1^-1, (Y2 * Y3 * Y2)^2, (Y1 * Y3 * Y1)^2, Y1^-1 * Y3 * Y1^-1 * Y2^-1 * Y3 * Y2^-1, Y3 * Y2 * Y1^-1 * Y3 * Y1^-1 * Y2, Y1^-1 * Y3 * Y2^-1 * Y3 * Y2 * Y1^-1, Y1^24, Y2^24 ] Map:: polytopal non-degenerate R = (1, 49, 97, 145, 4, 52, 100, 148)(2, 50, 98, 146, 9, 57, 105, 153)(3, 51, 99, 147, 12, 60, 108, 156)(5, 53, 101, 149, 18, 66, 114, 162)(6, 54, 102, 150, 21, 69, 117, 165)(7, 55, 103, 151, 25, 73, 121, 169)(8, 56, 104, 152, 28, 76, 124, 172)(10, 58, 106, 154, 33, 81, 129, 177)(11, 59, 107, 155, 31, 79, 127, 175)(13, 61, 109, 157, 30, 78, 126, 174)(14, 62, 110, 158, 34, 82, 130, 178)(15, 63, 111, 159, 37, 85, 133, 181)(16, 64, 112, 160, 36, 84, 132, 180)(17, 65, 113, 161, 26, 74, 122, 170)(19, 67, 115, 163, 38, 86, 134, 182)(20, 68, 116, 164, 39, 87, 135, 183)(22, 70, 118, 166, 40, 88, 136, 184)(23, 71, 119, 167, 43, 91, 139, 187)(24, 72, 120, 168, 45, 93, 141, 189)(27, 75, 123, 171, 46, 94, 142, 190)(29, 77, 125, 173, 48, 96, 144, 192)(32, 80, 128, 176, 44, 92, 140, 188)(35, 83, 131, 179, 47, 95, 143, 191)(41, 89, 137, 185, 42, 90, 138, 186) L = (1, 50)(2, 55)(3, 56)(4, 62)(5, 49)(6, 58)(7, 71)(8, 72)(9, 77)(10, 74)(11, 75)(12, 81)(13, 51)(14, 86)(15, 87)(16, 52)(17, 78)(18, 88)(19, 53)(20, 54)(21, 89)(22, 82)(23, 90)(24, 70)(25, 64)(26, 92)(27, 68)(28, 65)(29, 66)(30, 69)(31, 57)(32, 60)(33, 63)(34, 96)(35, 67)(36, 59)(37, 61)(38, 93)(39, 91)(40, 95)(41, 94)(42, 85)(43, 79)(44, 83)(45, 80)(46, 73)(47, 76)(48, 84)(97, 147)(98, 152)(99, 155)(100, 159)(101, 157)(102, 145)(103, 168)(104, 171)(105, 174)(106, 146)(107, 179)(108, 173)(109, 180)(110, 183)(111, 184)(112, 177)(113, 148)(114, 185)(115, 181)(116, 149)(117, 182)(118, 150)(119, 166)(120, 164)(121, 156)(122, 151)(123, 163)(124, 160)(125, 165)(126, 158)(127, 161)(128, 153)(129, 162)(130, 154)(131, 186)(132, 188)(133, 192)(134, 187)(135, 191)(136, 190)(137, 189)(138, 178)(139, 172)(140, 167)(141, 175)(142, 176)(143, 169)(144, 170) local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E23.596 Transitivity :: VT+ Graph:: simple bipartite v = 24 e = 96 f = 28 degree seq :: [ 8^24 ] E23.606 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 24, 24}) Quotient :: dipole Aut^+ = C8 x S3 (small group id <48, 4>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y1^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1)^2, (R * Y2 * Y3^-1)^2, Y2^3 * Y1 * Y2^-3 * Y1, Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1, (Y2^-1 * Y1 * Y2^-3)^2, (Y3 * Y2^-1)^24 ] Map:: R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 9, 57)(5, 53, 11, 59)(6, 54, 13, 61)(8, 56, 17, 65)(10, 58, 21, 69)(12, 60, 25, 73)(14, 62, 29, 77)(15, 63, 23, 71)(16, 64, 27, 75)(18, 66, 26, 74)(19, 67, 24, 72)(20, 68, 28, 76)(22, 70, 30, 78)(31, 79, 41, 89)(32, 80, 40, 88)(33, 81, 39, 87)(34, 82, 42, 90)(35, 83, 46, 94)(36, 84, 45, 93)(37, 85, 44, 92)(38, 86, 43, 91)(47, 95, 48, 96)(97, 145, 99, 147, 104, 152, 114, 162, 131, 179, 140, 188, 124, 172, 109, 157, 123, 171, 138, 186, 121, 169, 137, 185, 144, 192, 141, 189, 125, 173, 136, 184, 120, 168, 107, 155, 119, 167, 135, 183, 134, 182, 118, 166, 106, 154, 100, 148)(98, 146, 101, 149, 108, 156, 122, 170, 139, 187, 132, 180, 116, 164, 105, 153, 115, 163, 130, 178, 113, 161, 129, 177, 143, 191, 133, 181, 117, 165, 128, 176, 112, 160, 103, 151, 111, 159, 127, 175, 142, 190, 126, 174, 110, 158, 102, 150) 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, 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 = 26 e = 96 f = 26 degree seq :: [ 4^24, 48^2 ] E23.607 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 24, 24}) Quotient :: dipole Aut^+ = C3 x D16 (small group id <48, 25>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y1^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1)^2, (R * Y2 * Y3^-1)^2, (Y2^3 * Y1)^2, Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1, Y2^4 * Y1 * Y2^-4 * Y1, (Y2^-2 * Y1 * Y2^2 * Y1)^2, (Y3 * Y2^-1)^24 ] Map:: R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 9, 57)(5, 53, 11, 59)(6, 54, 13, 61)(8, 56, 17, 65)(10, 58, 21, 69)(12, 60, 25, 73)(14, 62, 29, 77)(15, 63, 23, 71)(16, 64, 27, 75)(18, 66, 30, 78)(19, 67, 24, 72)(20, 68, 28, 76)(22, 70, 26, 74)(31, 79, 41, 89)(32, 80, 45, 93)(33, 81, 39, 87)(34, 82, 44, 92)(35, 83, 43, 91)(36, 84, 42, 90)(37, 85, 40, 88)(38, 86, 46, 94)(47, 95, 48, 96)(97, 145, 99, 147, 104, 152, 114, 162, 131, 179, 136, 184, 120, 168, 107, 155, 119, 167, 135, 183, 125, 173, 141, 189, 144, 192, 138, 186, 121, 169, 137, 185, 124, 172, 109, 157, 123, 171, 140, 188, 134, 182, 118, 166, 106, 154, 100, 148)(98, 146, 101, 149, 108, 156, 122, 170, 139, 187, 128, 176, 112, 160, 103, 151, 111, 159, 127, 175, 117, 165, 133, 181, 143, 191, 130, 178, 113, 161, 129, 177, 116, 164, 105, 153, 115, 163, 132, 180, 142, 190, 126, 174, 110, 158, 102, 150) 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, 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 = 26 e = 96 f = 26 degree seq :: [ 4^24, 48^2 ] E23.608 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 24, 24}) Quotient :: dipole Aut^+ = C8 x S3 (small group id <48, 4>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, Y2^-1 * Y3 * Y2 * Y3, (Y1 * Y3)^2, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y3 * Y2^2 * Y1 * Y2^2 * Y1, Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1, Y1 * Y2^3 * Y1 * Y2^-3, Y2^24 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 9, 57)(4, 52, 7, 55)(5, 53, 13, 61)(6, 54, 15, 63)(8, 56, 19, 67)(10, 58, 24, 72)(11, 59, 22, 70)(12, 60, 27, 75)(14, 62, 31, 79)(16, 64, 28, 76)(17, 65, 34, 82)(18, 66, 37, 85)(20, 68, 26, 74)(21, 69, 33, 81)(23, 71, 38, 86)(25, 73, 36, 84)(29, 77, 35, 83)(30, 78, 39, 87)(32, 80, 40, 88)(41, 89, 48, 96)(42, 90, 45, 93)(43, 91, 47, 95)(44, 92, 46, 94)(97, 145, 99, 147, 106, 154, 121, 169, 140, 188, 130, 178, 135, 183, 115, 163, 134, 182, 143, 191, 124, 172, 108, 156, 100, 148, 107, 155, 122, 170, 141, 189, 131, 179, 111, 159, 129, 177, 133, 181, 144, 192, 128, 176, 110, 158, 101, 149)(98, 146, 102, 150, 112, 160, 132, 180, 137, 185, 118, 166, 126, 174, 109, 157, 125, 173, 139, 187, 120, 168, 114, 162, 103, 151, 113, 161, 127, 175, 138, 186, 119, 167, 105, 153, 117, 165, 123, 171, 142, 190, 136, 184, 116, 164, 104, 152) L = (1, 100)(2, 103)(3, 107)(4, 97)(5, 108)(6, 113)(7, 98)(8, 114)(9, 118)(10, 122)(11, 99)(12, 101)(13, 123)(14, 124)(15, 130)(16, 127)(17, 102)(18, 104)(19, 133)(20, 120)(21, 126)(22, 105)(23, 137)(24, 116)(25, 141)(26, 106)(27, 109)(28, 110)(29, 142)(30, 117)(31, 112)(32, 143)(33, 135)(34, 111)(35, 140)(36, 138)(37, 115)(38, 144)(39, 129)(40, 139)(41, 119)(42, 132)(43, 136)(44, 131)(45, 121)(46, 125)(47, 128)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 48, 4, 48 ), ( 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 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 = 26 e = 96 f = 26 degree seq :: [ 4^24, 48^2 ] E23.609 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 24, 24}) Quotient :: dipole Aut^+ = C3 x D16 (small group id <48, 25>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, Y2 * Y3 * Y2^-1 * Y3, (Y3 * Y1)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3 * Y1 * Y2^2 * Y1 * Y2^-2, (Y1 * Y2^-3)^2, Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1, Y2^24 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 9, 57)(4, 52, 7, 55)(5, 53, 13, 61)(6, 54, 15, 63)(8, 56, 19, 67)(10, 58, 24, 72)(11, 59, 22, 70)(12, 60, 27, 75)(14, 62, 31, 79)(16, 64, 26, 74)(17, 65, 34, 82)(18, 66, 37, 85)(20, 68, 28, 76)(21, 69, 33, 81)(23, 71, 38, 86)(25, 73, 40, 88)(29, 77, 35, 83)(30, 78, 39, 87)(32, 80, 36, 84)(41, 89, 45, 93)(42, 90, 48, 96)(43, 91, 47, 95)(44, 92, 46, 94)(97, 145, 99, 147, 106, 154, 121, 169, 140, 188, 133, 181, 131, 179, 111, 159, 129, 177, 143, 191, 124, 172, 108, 156, 100, 148, 107, 155, 122, 170, 141, 189, 135, 183, 115, 163, 134, 182, 130, 178, 144, 192, 128, 176, 110, 158, 101, 149)(98, 146, 102, 150, 112, 160, 132, 180, 142, 190, 123, 171, 119, 167, 105, 153, 117, 165, 137, 185, 127, 175, 114, 162, 103, 151, 113, 161, 120, 168, 139, 187, 126, 174, 109, 157, 125, 173, 118, 166, 138, 186, 136, 184, 116, 164, 104, 152) L = (1, 100)(2, 103)(3, 107)(4, 97)(5, 108)(6, 113)(7, 98)(8, 114)(9, 118)(10, 122)(11, 99)(12, 101)(13, 123)(14, 124)(15, 130)(16, 120)(17, 102)(18, 104)(19, 133)(20, 127)(21, 138)(22, 105)(23, 125)(24, 112)(25, 141)(26, 106)(27, 109)(28, 110)(29, 119)(30, 142)(31, 116)(32, 143)(33, 144)(34, 111)(35, 134)(36, 139)(37, 115)(38, 131)(39, 140)(40, 137)(41, 136)(42, 117)(43, 132)(44, 135)(45, 121)(46, 126)(47, 128)(48, 129)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 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 = 26 e = 96 f = 26 degree seq :: [ 4^24, 48^2 ] E23.610 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 24, 24}) Quotient :: dipole Aut^+ = C8 x S3 (small group id <48, 4>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^3, (Y3^-1, Y2^-1), (R * Y3)^2, (Y1 * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2 * Y3^-1 * Y1 * Y2^-1 * Y1, Y3 * Y2^-8, (Y2^4 * Y1)^2, 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 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 11, 59)(4, 52, 10, 58)(5, 53, 16, 64)(6, 54, 8, 56)(7, 55, 14, 62)(9, 57, 15, 63)(12, 60, 24, 72)(13, 61, 20, 68)(17, 65, 30, 78)(18, 66, 22, 70)(19, 67, 26, 74)(21, 69, 32, 80)(23, 71, 27, 75)(25, 73, 33, 81)(28, 76, 29, 77)(31, 79, 34, 82)(35, 83, 38, 86)(36, 84, 39, 87)(37, 85, 46, 94)(40, 88, 42, 90)(41, 89, 44, 92)(43, 91, 45, 93)(47, 95, 48, 96)(97, 145, 99, 147, 108, 156, 121, 169, 133, 181, 136, 184, 124, 172, 111, 159, 100, 148, 109, 157, 122, 170, 134, 182, 144, 192, 140, 188, 128, 176, 114, 162, 102, 150, 110, 158, 123, 171, 135, 183, 139, 187, 127, 175, 113, 161, 101, 149)(98, 146, 103, 151, 115, 163, 129, 177, 141, 189, 137, 185, 125, 173, 112, 160, 104, 152, 116, 164, 120, 168, 132, 180, 143, 191, 138, 186, 126, 174, 118, 166, 106, 154, 107, 155, 119, 167, 131, 179, 142, 190, 130, 178, 117, 165, 105, 153) L = (1, 100)(2, 104)(3, 109)(4, 102)(5, 111)(6, 97)(7, 116)(8, 106)(9, 112)(10, 98)(11, 103)(12, 122)(13, 110)(14, 99)(15, 114)(16, 118)(17, 124)(18, 101)(19, 120)(20, 107)(21, 125)(22, 105)(23, 115)(24, 119)(25, 134)(26, 123)(27, 108)(28, 128)(29, 126)(30, 117)(31, 136)(32, 113)(33, 132)(34, 137)(35, 129)(36, 131)(37, 144)(38, 135)(39, 121)(40, 140)(41, 138)(42, 130)(43, 133)(44, 127)(45, 143)(46, 141)(47, 142)(48, 139)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 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 = 26 e = 96 f = 26 degree seq :: [ 4^24, 48^2 ] E23.611 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 24, 24}) Quotient :: dipole Aut^+ = C3 x D16 (small group id <48, 25>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y1)^2, (R * Y2)^2, (Y3^-1 * Y1)^2, Y3^4, (R * Y3)^2, (Y2, Y3^-1), Y1 * Y3 * Y2 * Y1 * Y2^-1, Y2^6 * Y3^-1, Y2^-1 * Y3^2 * Y1 * Y2 * Y3^-1 * Y1, (Y1 * Y2^-3)^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 * Y2^2 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 11, 59)(4, 52, 10, 58)(5, 53, 17, 65)(6, 54, 8, 56)(7, 55, 13, 61)(9, 57, 19, 67)(12, 60, 27, 75)(14, 62, 26, 74)(15, 63, 22, 70)(16, 64, 33, 81)(18, 66, 36, 84)(20, 68, 39, 87)(21, 69, 31, 79)(23, 71, 32, 80)(24, 72, 43, 91)(25, 73, 29, 77)(28, 76, 44, 92)(30, 78, 41, 89)(34, 82, 42, 90)(35, 83, 38, 86)(37, 85, 40, 88)(45, 93, 48, 96)(46, 94, 47, 95)(97, 145, 99, 147, 108, 156, 124, 172, 130, 178, 112, 160, 100, 148, 109, 157, 125, 173, 143, 191, 139, 187, 128, 176, 111, 159, 127, 175, 135, 183, 144, 192, 134, 182, 115, 163, 102, 150, 110, 158, 126, 174, 133, 181, 114, 162, 101, 149)(98, 146, 103, 151, 116, 164, 136, 184, 138, 186, 119, 167, 104, 152, 107, 155, 121, 169, 141, 189, 132, 180, 129, 177, 118, 166, 122, 170, 123, 171, 142, 190, 131, 179, 113, 161, 106, 154, 117, 165, 137, 185, 140, 188, 120, 168, 105, 153) L = (1, 100)(2, 104)(3, 109)(4, 111)(5, 112)(6, 97)(7, 107)(8, 118)(9, 119)(10, 98)(11, 122)(12, 125)(13, 127)(14, 99)(15, 102)(16, 128)(17, 105)(18, 130)(19, 101)(20, 121)(21, 103)(22, 106)(23, 129)(24, 138)(25, 123)(26, 117)(27, 137)(28, 143)(29, 135)(30, 108)(31, 110)(32, 115)(33, 113)(34, 139)(35, 120)(36, 131)(37, 124)(38, 114)(39, 126)(40, 141)(41, 116)(42, 132)(43, 134)(44, 136)(45, 142)(46, 140)(47, 144)(48, 133)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 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 = 26 e = 96 f = 26 degree seq :: [ 4^24, 48^2 ] E23.612 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 24, 24}) Quotient :: dipole Aut^+ = C3 x D16 (small group id <48, 25>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y2)^2, (R * Y3)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, Y3^4, (Y3^-1, Y2^-1), Y3^-1 * Y1 * Y2^-1 * Y1 * Y2, Y3 * Y2^6, (Y1 * Y2^-3)^2, Y1 * Y2^2 * Y3 * Y1 * Y2^-2 * Y3^-1, Y3^2 * Y2^-2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 11, 59)(4, 52, 10, 58)(5, 53, 17, 65)(6, 54, 8, 56)(7, 55, 14, 62)(9, 57, 16, 64)(12, 60, 27, 75)(13, 61, 26, 74)(15, 63, 22, 70)(18, 66, 36, 84)(19, 67, 34, 82)(20, 68, 39, 87)(21, 69, 31, 79)(23, 71, 42, 90)(24, 72, 32, 80)(25, 73, 30, 78)(28, 76, 43, 91)(29, 77, 41, 89)(33, 81, 35, 83)(37, 85, 40, 88)(38, 86, 44, 92)(45, 93, 48, 96)(46, 94, 47, 95)(97, 145, 99, 147, 108, 156, 124, 172, 134, 182, 115, 163, 102, 150, 110, 158, 126, 174, 143, 191, 138, 186, 128, 176, 111, 159, 127, 175, 135, 183, 144, 192, 129, 177, 112, 160, 100, 148, 109, 157, 125, 173, 133, 181, 114, 162, 101, 149)(98, 146, 103, 151, 116, 164, 136, 184, 140, 188, 120, 168, 106, 154, 107, 155, 121, 169, 141, 189, 132, 180, 130, 178, 118, 166, 122, 170, 123, 171, 142, 190, 131, 179, 113, 161, 104, 152, 117, 165, 137, 185, 139, 187, 119, 167, 105, 153) L = (1, 100)(2, 104)(3, 109)(4, 111)(5, 112)(6, 97)(7, 117)(8, 118)(9, 113)(10, 98)(11, 103)(12, 125)(13, 127)(14, 99)(15, 102)(16, 128)(17, 130)(18, 129)(19, 101)(20, 137)(21, 122)(22, 106)(23, 131)(24, 105)(25, 116)(26, 107)(27, 121)(28, 133)(29, 135)(30, 108)(31, 110)(32, 115)(33, 138)(34, 120)(35, 132)(36, 140)(37, 144)(38, 114)(39, 126)(40, 139)(41, 123)(42, 134)(43, 142)(44, 119)(45, 136)(46, 141)(47, 124)(48, 143)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 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 = 26 e = 96 f = 26 degree seq :: [ 4^24, 48^2 ] E23.613 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 24, 24}) Quotient :: dipole Aut^+ = C8 x S3 (small group id <48, 4>) Aut = D16 x S3 (small group id <96, 117>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y2^-1, Y3^-1), (R * Y2)^2, (Y3 * Y1)^2, (R * Y3)^2, (R * Y1)^2, Y2^4 * Y3, Y2^-1 * Y1 * Y2 * Y3^2 * Y1, Y3^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y3^-1, Y3^6, Y2^2 * Y1 * Y3 * Y2^-2 * Y1 * Y3^-1, (Y2^-1 * Y3)^24 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 11, 59)(4, 52, 10, 58)(5, 53, 17, 65)(6, 54, 8, 56)(7, 55, 21, 69)(9, 57, 27, 75)(12, 60, 33, 81)(13, 61, 23, 71)(14, 62, 32, 80)(15, 63, 30, 78)(16, 64, 38, 86)(18, 66, 41, 89)(19, 67, 29, 77)(20, 68, 25, 73)(22, 70, 43, 91)(24, 72, 42, 90)(26, 74, 47, 95)(28, 76, 48, 96)(31, 79, 39, 87)(34, 82, 40, 88)(35, 83, 44, 92)(36, 84, 45, 93)(37, 85, 46, 94)(97, 145, 99, 147, 108, 156, 115, 163, 102, 150, 110, 158, 130, 178, 123, 171, 116, 164, 131, 179, 139, 187, 143, 191, 132, 180, 138, 186, 144, 192, 133, 181, 111, 159, 117, 165, 135, 183, 112, 160, 100, 148, 109, 157, 114, 162, 101, 149)(98, 146, 103, 151, 118, 166, 125, 173, 106, 154, 120, 168, 136, 184, 113, 161, 126, 174, 140, 188, 129, 177, 134, 182, 141, 189, 128, 176, 137, 185, 142, 190, 121, 169, 107, 155, 127, 175, 122, 170, 104, 152, 119, 167, 124, 172, 105, 153) L = (1, 100)(2, 104)(3, 109)(4, 111)(5, 112)(6, 97)(7, 119)(8, 121)(9, 122)(10, 98)(11, 128)(12, 114)(13, 117)(14, 99)(15, 132)(16, 133)(17, 125)(18, 135)(19, 101)(20, 102)(21, 138)(22, 124)(23, 107)(24, 103)(25, 141)(26, 142)(27, 115)(28, 127)(29, 105)(30, 106)(31, 137)(32, 140)(33, 136)(34, 108)(35, 110)(36, 116)(37, 143)(38, 113)(39, 144)(40, 118)(41, 129)(42, 131)(43, 130)(44, 120)(45, 126)(46, 134)(47, 123)(48, 139)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 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 = 26 e = 96 f = 26 degree seq :: [ 4^24, 48^2 ] E23.614 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 24, 24}) Quotient :: halfedge^2 Aut^+ = C3 x QD16 (small group id <48, 26>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y3 * Y2, R * Y2 * R * Y3, (R * Y1)^2, Y1^-4 * Y2 * Y1^-1 * Y2 * Y1^-1, (Y2 * Y1^2 * Y2 * Y1^-2)^2 ] Map:: R = (1, 50, 2, 53, 5, 59, 11, 71, 23, 65, 17, 77, 29, 87, 39, 94, 46, 91, 43, 82, 34, 90, 42, 96, 48, 92, 44, 80, 32, 89, 41, 95, 47, 93, 45, 81, 33, 64, 16, 76, 28, 70, 22, 58, 10, 52, 4, 49)(3, 55, 7, 63, 15, 79, 31, 68, 20, 57, 9, 67, 19, 83, 35, 85, 37, 72, 24, 69, 21, 84, 36, 88, 40, 74, 26, 60, 12, 73, 25, 86, 38, 78, 30, 62, 14, 54, 6, 61, 13, 75, 27, 66, 18, 56, 8, 51) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 34)(19, 33)(20, 23)(22, 25)(26, 39)(27, 41)(30, 42)(31, 43)(35, 44)(36, 45)(37, 46)(38, 47)(40, 48)(49, 51)(50, 54)(52, 57)(53, 60)(55, 64)(56, 65)(58, 69)(59, 72)(61, 76)(62, 77)(63, 80)(66, 82)(67, 81)(68, 71)(70, 73)(74, 87)(75, 89)(78, 90)(79, 91)(83, 92)(84, 93)(85, 94)(86, 95)(88, 96) local type(s) :: { ( 48^48 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 48 f = 2 degree seq :: [ 48^2 ] E23.615 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 24, 24}) Quotient :: halfedge^2 Aut^+ = C3 x QD16 (small group id <48, 26>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (Y3 * Y2)^2, R * Y3 * R * Y2, (R * Y1)^2, Y2 * Y1^-1 * Y2 * Y3 * Y1 * Y3, Y1^-1 * Y3 * Y1^2 * Y2 * Y1^-1, Y1 * Y3 * Y1^-2 * Y2 * Y1, Y3 * Y1 * Y3 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1, Y2 * Y1^-1 * Y2 * Y1^-5 ] Map:: non-degenerate R = (1, 50, 2, 54, 6, 65, 17, 83, 35, 76, 28, 91, 43, 74, 26, 90, 42, 96, 48, 93, 45, 75, 27, 58, 10, 69, 21, 87, 39, 95, 47, 94, 46, 77, 29, 92, 44, 73, 25, 89, 41, 82, 34, 64, 16, 53, 5, 49)(3, 57, 9, 67, 19, 88, 40, 80, 32, 62, 14, 72, 24, 56, 8, 71, 23, 84, 36, 79, 31, 61, 13, 52, 4, 60, 12, 66, 18, 86, 38, 81, 33, 63, 15, 70, 22, 55, 7, 68, 20, 85, 37, 78, 30, 59, 11, 51) L = (1, 3)(2, 7)(4, 10)(5, 14)(6, 18)(8, 21)(9, 25)(11, 28)(12, 26)(13, 29)(15, 27)(16, 31)(17, 36)(19, 39)(20, 41)(22, 43)(23, 42)(24, 44)(30, 45)(32, 35)(33, 46)(34, 38)(37, 47)(40, 48)(49, 52)(50, 56)(51, 58)(53, 63)(54, 67)(55, 69)(57, 74)(59, 77)(60, 73)(61, 76)(62, 75)(64, 78)(65, 85)(66, 87)(68, 90)(70, 92)(71, 89)(72, 91)(79, 93)(80, 94)(81, 83)(82, 88)(84, 95)(86, 96) local type(s) :: { ( 48^48 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 48 f = 2 degree seq :: [ 48^2 ] E23.616 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 24, 24}) Quotient :: halfedge^2 Aut^+ = C24 : C2 (small group id <48, 5>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y2 * Y3, (R * Y1)^2, R * Y3 * R * Y2, Y1^-1 * Y3 * Y1 * Y2 * Y1^-4, Y1^-3 * Y3 * Y1 * Y2 * Y1^-2, Y2 * Y1^-1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1, Y2 * Y1^-3 * Y3 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-3 ] Map:: R = (1, 50, 2, 53, 5, 59, 11, 71, 23, 64, 16, 76, 28, 87, 39, 94, 46, 91, 43, 79, 31, 89, 41, 95, 47, 93, 45, 81, 33, 90, 42, 96, 48, 92, 44, 80, 32, 65, 17, 77, 29, 70, 22, 58, 10, 52, 4, 49)(3, 55, 7, 63, 15, 78, 30, 62, 14, 54, 6, 61, 13, 75, 27, 88, 40, 74, 26, 60, 12, 73, 25, 86, 38, 84, 36, 69, 21, 72, 24, 85, 37, 83, 35, 68, 20, 57, 9, 67, 19, 82, 34, 66, 18, 56, 8, 51) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 31)(18, 33)(19, 23)(20, 32)(22, 26)(25, 39)(27, 41)(30, 42)(34, 43)(35, 45)(36, 44)(37, 46)(38, 47)(40, 48)(49, 51)(50, 54)(52, 57)(53, 60)(55, 64)(56, 65)(58, 69)(59, 72)(61, 76)(62, 77)(63, 79)(66, 81)(67, 71)(68, 80)(70, 74)(73, 87)(75, 89)(78, 90)(82, 91)(83, 93)(84, 92)(85, 94)(86, 95)(88, 96) local type(s) :: { ( 48^48 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 48 f = 2 degree seq :: [ 48^2 ] E23.617 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 24, 24}) Quotient :: halfedge^2 Aut^+ = C24 : C2 (small group id <48, 5>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (R * Y1)^2, Y2 * Y1^-2 * Y3 * Y1^2, Y3 * Y1 * Y3 * Y2 * Y1^-1 * Y2, (Y3 * Y2)^3, Y3 * Y1^-3 * Y2 * Y1^-1, (Y2 * Y1 * Y3 * Y1^-1)^2, Y3 * Y2 * Y3 * Y1^2 * Y3 * Y1^-2, Y1^-1 * Y3 * Y1^-1 * Y2 * Y3 * Y2 * Y1^-2 ] Map:: non-degenerate R = (1, 50, 2, 54, 6, 66, 18, 86, 38, 76, 28, 92, 44, 79, 31, 58, 10, 70, 22, 89, 41, 84, 36, 96, 48, 77, 29, 93, 45, 83, 35, 61, 13, 73, 25, 90, 42, 80, 32, 95, 47, 82, 34, 65, 17, 53, 5, 49)(3, 57, 9, 75, 27, 64, 16, 71, 23, 55, 7, 69, 21, 62, 14, 52, 4, 60, 12, 67, 19, 88, 40, 74, 26, 56, 8, 72, 24, 87, 39, 78, 30, 91, 43, 68, 20, 63, 15, 85, 37, 94, 46, 81, 33, 59, 11, 51) L = (1, 3)(2, 7)(4, 13)(5, 15)(6, 19)(8, 25)(9, 28)(10, 30)(11, 32)(12, 34)(14, 36)(16, 35)(17, 24)(18, 39)(20, 42)(21, 44)(22, 46)(23, 47)(26, 48)(27, 41)(29, 43)(31, 40)(33, 45)(37, 38)(49, 52)(50, 56)(51, 58)(53, 64)(54, 68)(55, 70)(57, 77)(59, 66)(60, 76)(61, 78)(62, 80)(63, 79)(65, 81)(67, 89)(69, 93)(71, 86)(72, 92)(73, 94)(74, 95)(75, 90)(82, 91)(83, 88)(84, 87)(85, 96) local type(s) :: { ( 48^48 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 48 f = 2 degree seq :: [ 48^2 ] E23.618 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 24, 24}) Quotient :: edge^2 Aut^+ = C3 x QD16 (small group id <48, 26>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y1 * Y2, R * Y2 * R * Y1, (R * Y3)^2, Y3 * Y2 * Y3 * Y1 * Y3^4, Y3^-3 * Y2 * Y3^-1 * Y1 * Y3^-2, Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1, (Y3^2 * Y1 * Y3^-2 * Y1)^2 ] Map:: R = (1, 49, 3, 51, 8, 56, 18, 66, 28, 76, 13, 61, 27, 75, 41, 89, 48, 96, 40, 88, 29, 77, 42, 90, 47, 95, 39, 87, 25, 73, 38, 86, 46, 94, 37, 85, 24, 72, 11, 59, 23, 71, 22, 70, 10, 58, 4, 52)(2, 50, 5, 53, 12, 60, 26, 74, 20, 68, 9, 57, 19, 67, 35, 83, 45, 93, 34, 82, 21, 69, 36, 84, 44, 92, 33, 81, 17, 65, 32, 80, 43, 91, 31, 79, 16, 64, 7, 55, 15, 63, 30, 78, 14, 62, 6, 54)(97, 98)(99, 103)(100, 105)(101, 107)(102, 109)(104, 113)(106, 117)(108, 121)(110, 125)(111, 119)(112, 123)(114, 130)(115, 120)(116, 124)(118, 128)(122, 136)(126, 134)(127, 138)(129, 137)(131, 135)(132, 133)(139, 142)(140, 143)(141, 144)(145, 146)(147, 151)(148, 153)(149, 155)(150, 157)(152, 161)(154, 165)(156, 169)(158, 173)(159, 167)(160, 171)(162, 178)(163, 168)(164, 172)(166, 176)(170, 184)(174, 182)(175, 186)(177, 185)(179, 183)(180, 181)(187, 190)(188, 191)(189, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 96, 96 ), ( 96^48 ) } Outer automorphisms :: reflexible Dual of E23.625 Graph:: simple bipartite v = 50 e = 96 f = 2 degree seq :: [ 2^48, 48^2 ] E23.619 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 24, 24}) Quotient :: edge^2 Aut^+ = C3 x QD16 (small group id <48, 26>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y2 * Y1)^2, R * Y2 * R * Y1, (R * Y3)^2, Y2 * Y3^-1 * Y1 * Y2 * Y3 * Y1, Y3^2 * Y2 * Y3^-2 * Y1, Y3^-1 * Y2 * Y3^2 * Y1 * Y3^-1, Y3^-1 * Y2 * Y3 * Y2 * Y3^-1 * Y2 * Y3 * Y1, Y3 * Y2 * Y3^5 * Y2 ] Map:: R = (1, 49, 4, 52, 13, 61, 31, 79, 42, 90, 22, 70, 40, 88, 20, 68, 39, 87, 48, 96, 36, 84, 18, 66, 6, 54, 17, 65, 35, 83, 47, 95, 43, 91, 23, 71, 38, 86, 19, 67, 37, 85, 34, 82, 16, 64, 5, 53)(2, 50, 7, 55, 21, 69, 41, 89, 32, 80, 14, 62, 30, 78, 12, 60, 29, 77, 46, 94, 26, 74, 10, 58, 3, 51, 9, 57, 25, 73, 45, 93, 33, 81, 15, 63, 28, 76, 11, 59, 27, 75, 44, 92, 24, 72, 8, 56)(97, 98)(99, 102)(100, 107)(101, 110)(103, 115)(104, 118)(105, 116)(106, 119)(108, 113)(109, 121)(111, 114)(112, 122)(117, 131)(120, 132)(123, 133)(124, 136)(125, 135)(126, 134)(127, 142)(128, 138)(129, 139)(130, 141)(137, 144)(140, 143)(145, 147)(146, 150)(148, 156)(149, 159)(151, 164)(152, 167)(153, 163)(154, 166)(155, 161)(157, 165)(158, 162)(160, 168)(169, 179)(170, 180)(171, 183)(172, 182)(173, 181)(174, 184)(175, 188)(176, 187)(177, 186)(178, 185)(189, 192)(190, 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) :: { ( 96, 96 ), ( 96^48 ) } Outer automorphisms :: reflexible Dual of E23.626 Graph:: simple bipartite v = 50 e = 96 f = 2 degree seq :: [ 2^48, 48^2 ] E23.620 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 24, 24}) Quotient :: edge^2 Aut^+ = C24 : C2 (small group id <48, 5>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y1, R * Y2 * R * Y1, (R * Y3)^2, Y3^-1 * Y1 * Y3 * Y2 * Y3^-4, Y3 * Y2 * Y3 * Y1 * Y3^-1 * Y2 * Y3^-1 * Y1, Y3^-1 * Y1 * Y3^-1 * Y2 * Y3 * Y1 * Y3 * Y1, Y3 * Y1 * Y3 * Y2 * Y3^-1 * Y1 * Y3^-1 * Y1, Y2 * Y3 * Y1 * Y3^2 * Y1 * Y3^3 * Y2 * Y3^2 ] Map:: R = (1, 49, 3, 51, 8, 56, 18, 66, 24, 72, 11, 59, 23, 71, 37, 85, 46, 94, 39, 87, 25, 73, 38, 86, 47, 95, 42, 90, 29, 77, 40, 88, 48, 96, 41, 89, 28, 76, 13, 61, 27, 75, 22, 70, 10, 58, 4, 52)(2, 50, 5, 53, 12, 60, 26, 74, 16, 64, 7, 55, 15, 63, 31, 79, 43, 91, 33, 81, 17, 65, 32, 80, 44, 92, 36, 84, 21, 69, 34, 82, 45, 93, 35, 83, 20, 68, 9, 57, 19, 67, 30, 78, 14, 62, 6, 54)(97, 98)(99, 103)(100, 105)(101, 107)(102, 109)(104, 113)(106, 117)(108, 121)(110, 125)(111, 119)(112, 123)(114, 130)(115, 120)(116, 124)(118, 129)(122, 136)(126, 135)(127, 134)(128, 133)(131, 138)(132, 137)(139, 144)(140, 143)(141, 142)(145, 146)(147, 151)(148, 153)(149, 155)(150, 157)(152, 161)(154, 165)(156, 169)(158, 173)(159, 167)(160, 171)(162, 178)(163, 168)(164, 172)(166, 177)(170, 184)(174, 183)(175, 182)(176, 181)(179, 186)(180, 185)(187, 192)(188, 191)(189, 190) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 96, 96 ), ( 96^48 ) } Outer automorphisms :: reflexible Dual of E23.627 Graph:: simple bipartite v = 50 e = 96 f = 2 degree seq :: [ 2^48, 48^2 ] E23.621 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 24, 24}) Quotient :: edge^2 Aut^+ = C24 : C2 (small group id <48, 5>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, Y3 * Y2 * Y3^-2 * Y1 * Y3, Y3^-3 * Y2 * Y3^-1 * Y1, (Y2 * Y1)^3, Y3^-1 * Y2 * Y1 * Y3 * Y1 * Y2, Y2 * Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3, (Y3^-1 * Y2 * Y3 * Y1)^2, Y2 * Y3^2 * Y2 * Y3 * Y2 * Y3 * Y1, Y3^-16 * Y1 * Y2 ] Map:: R = (1, 49, 4, 52, 14, 62, 31, 79, 45, 93, 21, 69, 44, 92, 28, 76, 9, 57, 27, 75, 47, 95, 25, 73, 48, 96, 29, 77, 43, 91, 20, 68, 6, 54, 19, 67, 41, 89, 24, 72, 46, 94, 22, 70, 17, 65, 5, 53)(2, 50, 7, 55, 23, 71, 42, 90, 34, 82, 12, 60, 33, 81, 39, 87, 18, 66, 38, 86, 36, 84, 16, 64, 37, 85, 40, 88, 32, 80, 11, 59, 3, 51, 10, 58, 30, 78, 15, 63, 35, 83, 13, 61, 26, 74, 8, 56)(97, 98)(99, 105)(100, 108)(101, 111)(102, 114)(103, 117)(104, 120)(106, 125)(107, 127)(109, 123)(110, 132)(112, 124)(113, 128)(115, 136)(116, 138)(118, 134)(119, 143)(121, 135)(122, 139)(126, 137)(129, 140)(130, 142)(131, 141)(133, 144)(145, 147)(146, 150)(148, 157)(149, 160)(151, 166)(152, 169)(153, 162)(154, 165)(155, 168)(156, 163)(158, 167)(159, 164)(161, 177)(170, 188)(171, 184)(172, 186)(173, 182)(174, 191)(175, 183)(176, 187)(178, 192)(179, 190)(180, 185)(181, 189) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 96, 96 ), ( 96^48 ) } Outer automorphisms :: reflexible Dual of E23.628 Graph:: simple bipartite v = 50 e = 96 f = 2 degree seq :: [ 2^48, 48^2 ] E23.622 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 24, 24}) Quotient :: edge^2 Aut^+ = C24 : C2 (small group id <48, 5>) Aut = C2 x (C24 : C2) (small group id <96, 107>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1 * Y2, (R * Y3)^2, R * Y1 * R * Y2, Y1 * Y3 * Y2^2 * Y1^-3 * Y3, Y3 * Y1 * Y3 * Y2^-1 * Y3 * Y2 * Y3 * Y1^-1, Y2^2 * Y1^-1 * Y3 * Y1 * Y3 * Y1^-2, Y2^24, Y1^24 ] Map:: non-degenerate R = (1, 49, 4, 52)(2, 50, 6, 54)(3, 51, 8, 56)(5, 53, 12, 60)(7, 55, 16, 64)(9, 57, 20, 68)(10, 58, 22, 70)(11, 59, 24, 72)(13, 61, 28, 76)(14, 62, 30, 78)(15, 63, 26, 74)(17, 65, 23, 71)(18, 66, 34, 82)(19, 67, 35, 83)(21, 69, 36, 84)(25, 73, 39, 87)(27, 75, 41, 89)(29, 77, 42, 90)(31, 79, 43, 91)(32, 80, 44, 92)(33, 81, 45, 93)(37, 85, 46, 94)(38, 86, 47, 95)(40, 88, 48, 96)(97, 98, 101, 107, 119, 116, 124, 135, 142, 140, 131, 137, 143, 141, 132, 138, 144, 139, 130, 118, 126, 111, 103, 99)(100, 105, 115, 125, 110, 102, 109, 123, 136, 122, 108, 121, 134, 127, 112, 120, 133, 129, 114, 104, 113, 128, 117, 106)(145, 147, 151, 159, 174, 166, 178, 187, 192, 186, 180, 189, 191, 185, 179, 188, 190, 183, 172, 164, 167, 155, 149, 146)(148, 154, 165, 176, 161, 152, 162, 177, 181, 168, 160, 175, 182, 169, 156, 170, 184, 171, 157, 150, 158, 173, 163, 153) 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) :: { ( 8^4 ), ( 8^24 ) } Outer automorphisms :: reflexible Dual of E23.629 Graph:: simple bipartite v = 28 e = 96 f = 24 degree seq :: [ 4^24, 24^4 ] E23.623 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 24, 24}) Quotient :: edge^2 Aut^+ = C24 : C2 (small group id <48, 6>) Aut = (D8 x S3) : C2 (small group id <96, 118>) |r| :: 2 Presentation :: [ R^2, Y3^2, (Y2, Y1), R * Y1 * R * Y2, (R * Y3)^2, Y1^-1 * Y3 * Y2 * Y3 * Y2^-1 * Y1^-1, Y2^-1 * Y3 * Y2 * Y1^2 * Y3, Y3 * Y2^2 * Y1 * Y3 * Y1^-1, Y2 * Y1^-3 * Y2^2, (Y3 * Y2^-2)^2, Y3 * Y1^-1 * Y2^-1 * Y3 * Y2^-1 * Y1^-1, Y1^-1 * Y2 * Y3 * Y2^-1 * Y1 * Y3 * Y1^-1 * Y2, Y2^3 * Y1^21 ] Map:: polytopal non-degenerate R = (1, 49, 4, 52)(2, 50, 9, 57)(3, 51, 12, 60)(5, 53, 18, 66)(6, 54, 21, 69)(7, 55, 25, 73)(8, 56, 28, 76)(10, 58, 33, 81)(11, 59, 35, 83)(13, 61, 38, 86)(14, 62, 27, 75)(15, 63, 24, 72)(16, 64, 39, 87)(17, 65, 40, 88)(19, 67, 37, 85)(20, 68, 32, 80)(22, 70, 31, 79)(23, 71, 44, 92)(26, 74, 48, 96)(29, 77, 45, 93)(30, 78, 43, 91)(34, 82, 47, 95)(36, 84, 42, 90)(41, 89, 46, 94)(97, 98, 103, 119, 138, 136, 116, 102, 106, 122, 107, 123, 141, 135, 118, 130, 109, 99, 104, 120, 139, 137, 115, 101)(100, 110, 133, 144, 126, 117, 124, 113, 134, 140, 127, 105, 125, 114, 131, 142, 129, 111, 128, 108, 132, 143, 121, 112)(145, 147, 155, 167, 187, 183, 164, 149, 157, 170, 151, 168, 189, 184, 163, 178, 154, 146, 152, 171, 186, 185, 166, 150)(148, 159, 175, 192, 180, 162, 172, 160, 177, 188, 181, 156, 173, 165, 169, 190, 182, 158, 176, 153, 174, 191, 179, 161) 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) :: { ( 8^4 ), ( 8^24 ) } Outer automorphisms :: reflexible Dual of E23.630 Graph:: simple bipartite v = 28 e = 96 f = 24 degree seq :: [ 4^24, 24^4 ] E23.624 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 24, 24}) Quotient :: edge^2 Aut^+ = D48 (small group id <48, 7>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ R^2, Y3^2, R * Y2 * R * Y1, (Y2^-1, Y1^-1), (Y3 * Y1^-1)^2, (Y3 * Y2^-1)^2, (R * Y3)^2, Y1^-1 * Y2 * Y1^-4, (Y3 * Y1 * Y2^-1)^2, Y2^4 * Y1^-1 * Y2, (Y2 * Y3 * Y1^-1)^2 ] Map:: polytopal non-degenerate R = (1, 49, 4, 52)(2, 50, 9, 57)(3, 51, 12, 60)(5, 53, 14, 62)(6, 54, 15, 63)(7, 55, 21, 69)(8, 56, 24, 72)(10, 58, 25, 73)(11, 59, 27, 75)(13, 61, 29, 77)(16, 64, 30, 78)(17, 65, 31, 79)(18, 66, 32, 80)(19, 67, 36, 84)(20, 68, 38, 86)(22, 70, 39, 87)(23, 71, 41, 89)(26, 74, 42, 90)(28, 76, 43, 91)(33, 81, 44, 92)(34, 82, 45, 93)(35, 83, 46, 94)(37, 85, 47, 95)(40, 88, 48, 96)(97, 98, 103, 115, 109, 99, 104, 116, 131, 124, 107, 119, 133, 130, 114, 122, 136, 129, 113, 102, 106, 118, 112, 101)(100, 110, 126, 135, 121, 111, 127, 140, 144, 138, 128, 141, 143, 137, 123, 139, 142, 134, 120, 108, 125, 132, 117, 105)(145, 147, 155, 170, 154, 146, 152, 167, 184, 166, 151, 164, 181, 177, 160, 163, 179, 178, 161, 149, 157, 172, 162, 150)(148, 159, 176, 187, 173, 158, 175, 189, 190, 180, 174, 188, 191, 182, 165, 183, 192, 185, 168, 153, 169, 186, 171, 156) 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) :: { ( 8^4 ), ( 8^24 ) } Outer automorphisms :: reflexible Dual of E23.631 Graph:: simple bipartite v = 28 e = 96 f = 24 degree seq :: [ 4^24, 24^4 ] E23.625 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 24, 24}) Quotient :: loop^2 Aut^+ = C3 x QD16 (small group id <48, 26>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y1 * Y2, R * Y2 * R * Y1, (R * Y3)^2, Y3 * Y2 * Y3 * Y1 * Y3^4, Y3^-3 * Y2 * Y3^-1 * Y1 * Y3^-2, Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1, (Y3^2 * Y1 * Y3^-2 * Y1)^2 ] Map:: R = (1, 49, 97, 145, 3, 51, 99, 147, 8, 56, 104, 152, 18, 66, 114, 162, 28, 76, 124, 172, 13, 61, 109, 157, 27, 75, 123, 171, 41, 89, 137, 185, 48, 96, 144, 192, 40, 88, 136, 184, 29, 77, 125, 173, 42, 90, 138, 186, 47, 95, 143, 191, 39, 87, 135, 183, 25, 73, 121, 169, 38, 86, 134, 182, 46, 94, 142, 190, 37, 85, 133, 181, 24, 72, 120, 168, 11, 59, 107, 155, 23, 71, 119, 167, 22, 70, 118, 166, 10, 58, 106, 154, 4, 52, 100, 148)(2, 50, 98, 146, 5, 53, 101, 149, 12, 60, 108, 156, 26, 74, 122, 170, 20, 68, 116, 164, 9, 57, 105, 153, 19, 67, 115, 163, 35, 83, 131, 179, 45, 93, 141, 189, 34, 82, 130, 178, 21, 69, 117, 165, 36, 84, 132, 180, 44, 92, 140, 188, 33, 81, 129, 177, 17, 65, 113, 161, 32, 80, 128, 176, 43, 91, 139, 187, 31, 79, 127, 175, 16, 64, 112, 160, 7, 55, 103, 151, 15, 63, 111, 159, 30, 78, 126, 174, 14, 62, 110, 158, 6, 54, 102, 150) L = (1, 50)(2, 49)(3, 55)(4, 57)(5, 59)(6, 61)(7, 51)(8, 65)(9, 52)(10, 69)(11, 53)(12, 73)(13, 54)(14, 77)(15, 71)(16, 75)(17, 56)(18, 82)(19, 72)(20, 76)(21, 58)(22, 80)(23, 63)(24, 67)(25, 60)(26, 88)(27, 64)(28, 68)(29, 62)(30, 86)(31, 90)(32, 70)(33, 89)(34, 66)(35, 87)(36, 85)(37, 84)(38, 78)(39, 83)(40, 74)(41, 81)(42, 79)(43, 94)(44, 95)(45, 96)(46, 91)(47, 92)(48, 93)(97, 146)(98, 145)(99, 151)(100, 153)(101, 155)(102, 157)(103, 147)(104, 161)(105, 148)(106, 165)(107, 149)(108, 169)(109, 150)(110, 173)(111, 167)(112, 171)(113, 152)(114, 178)(115, 168)(116, 172)(117, 154)(118, 176)(119, 159)(120, 163)(121, 156)(122, 184)(123, 160)(124, 164)(125, 158)(126, 182)(127, 186)(128, 166)(129, 185)(130, 162)(131, 183)(132, 181)(133, 180)(134, 174)(135, 179)(136, 170)(137, 177)(138, 175)(139, 190)(140, 191)(141, 192)(142, 187)(143, 188)(144, 189) 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 E23.618 Transitivity :: VT+ Graph:: bipartite v = 2 e = 96 f = 50 degree seq :: [ 96^2 ] E23.626 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 24, 24}) Quotient :: loop^2 Aut^+ = C3 x QD16 (small group id <48, 26>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y2 * Y1)^2, R * Y2 * R * Y1, (R * Y3)^2, Y2 * Y3^-1 * Y1 * Y2 * Y3 * Y1, Y3^2 * Y2 * Y3^-2 * Y1, Y3^-1 * Y2 * Y3^2 * Y1 * Y3^-1, Y3^-1 * Y2 * Y3 * Y2 * Y3^-1 * Y2 * Y3 * Y1, Y3 * Y2 * Y3^5 * Y2 ] Map:: R = (1, 49, 97, 145, 4, 52, 100, 148, 13, 61, 109, 157, 31, 79, 127, 175, 42, 90, 138, 186, 22, 70, 118, 166, 40, 88, 136, 184, 20, 68, 116, 164, 39, 87, 135, 183, 48, 96, 144, 192, 36, 84, 132, 180, 18, 66, 114, 162, 6, 54, 102, 150, 17, 65, 113, 161, 35, 83, 131, 179, 47, 95, 143, 191, 43, 91, 139, 187, 23, 71, 119, 167, 38, 86, 134, 182, 19, 67, 115, 163, 37, 85, 133, 181, 34, 82, 130, 178, 16, 64, 112, 160, 5, 53, 101, 149)(2, 50, 98, 146, 7, 55, 103, 151, 21, 69, 117, 165, 41, 89, 137, 185, 32, 80, 128, 176, 14, 62, 110, 158, 30, 78, 126, 174, 12, 60, 108, 156, 29, 77, 125, 173, 46, 94, 142, 190, 26, 74, 122, 170, 10, 58, 106, 154, 3, 51, 99, 147, 9, 57, 105, 153, 25, 73, 121, 169, 45, 93, 141, 189, 33, 81, 129, 177, 15, 63, 111, 159, 28, 76, 124, 172, 11, 59, 107, 155, 27, 75, 123, 171, 44, 92, 140, 188, 24, 72, 120, 168, 8, 56, 104, 152) L = (1, 50)(2, 49)(3, 54)(4, 59)(5, 62)(6, 51)(7, 67)(8, 70)(9, 68)(10, 71)(11, 52)(12, 65)(13, 73)(14, 53)(15, 66)(16, 74)(17, 60)(18, 63)(19, 55)(20, 57)(21, 83)(22, 56)(23, 58)(24, 84)(25, 61)(26, 64)(27, 85)(28, 88)(29, 87)(30, 86)(31, 94)(32, 90)(33, 91)(34, 93)(35, 69)(36, 72)(37, 75)(38, 78)(39, 77)(40, 76)(41, 96)(42, 80)(43, 81)(44, 95)(45, 82)(46, 79)(47, 92)(48, 89)(97, 147)(98, 150)(99, 145)(100, 156)(101, 159)(102, 146)(103, 164)(104, 167)(105, 163)(106, 166)(107, 161)(108, 148)(109, 165)(110, 162)(111, 149)(112, 168)(113, 155)(114, 158)(115, 153)(116, 151)(117, 157)(118, 154)(119, 152)(120, 160)(121, 179)(122, 180)(123, 183)(124, 182)(125, 181)(126, 184)(127, 188)(128, 187)(129, 186)(130, 185)(131, 169)(132, 170)(133, 173)(134, 172)(135, 171)(136, 174)(137, 178)(138, 177)(139, 176)(140, 175)(141, 192)(142, 191)(143, 190)(144, 189) 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 E23.619 Transitivity :: VT+ Graph:: bipartite v = 2 e = 96 f = 50 degree seq :: [ 96^2 ] E23.627 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 24, 24}) Quotient :: loop^2 Aut^+ = C24 : C2 (small group id <48, 5>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y1, R * Y2 * R * Y1, (R * Y3)^2, Y3^-1 * Y1 * Y3 * Y2 * Y3^-4, Y3 * Y2 * Y3 * Y1 * Y3^-1 * Y2 * Y3^-1 * Y1, Y3^-1 * Y1 * Y3^-1 * Y2 * Y3 * Y1 * Y3 * Y1, Y3 * Y1 * Y3 * Y2 * Y3^-1 * Y1 * Y3^-1 * Y1, Y2 * Y3 * Y1 * Y3^2 * Y1 * Y3^3 * Y2 * Y3^2 ] Map:: R = (1, 49, 97, 145, 3, 51, 99, 147, 8, 56, 104, 152, 18, 66, 114, 162, 24, 72, 120, 168, 11, 59, 107, 155, 23, 71, 119, 167, 37, 85, 133, 181, 46, 94, 142, 190, 39, 87, 135, 183, 25, 73, 121, 169, 38, 86, 134, 182, 47, 95, 143, 191, 42, 90, 138, 186, 29, 77, 125, 173, 40, 88, 136, 184, 48, 96, 144, 192, 41, 89, 137, 185, 28, 76, 124, 172, 13, 61, 109, 157, 27, 75, 123, 171, 22, 70, 118, 166, 10, 58, 106, 154, 4, 52, 100, 148)(2, 50, 98, 146, 5, 53, 101, 149, 12, 60, 108, 156, 26, 74, 122, 170, 16, 64, 112, 160, 7, 55, 103, 151, 15, 63, 111, 159, 31, 79, 127, 175, 43, 91, 139, 187, 33, 81, 129, 177, 17, 65, 113, 161, 32, 80, 128, 176, 44, 92, 140, 188, 36, 84, 132, 180, 21, 69, 117, 165, 34, 82, 130, 178, 45, 93, 141, 189, 35, 83, 131, 179, 20, 68, 116, 164, 9, 57, 105, 153, 19, 67, 115, 163, 30, 78, 126, 174, 14, 62, 110, 158, 6, 54, 102, 150) L = (1, 50)(2, 49)(3, 55)(4, 57)(5, 59)(6, 61)(7, 51)(8, 65)(9, 52)(10, 69)(11, 53)(12, 73)(13, 54)(14, 77)(15, 71)(16, 75)(17, 56)(18, 82)(19, 72)(20, 76)(21, 58)(22, 81)(23, 63)(24, 67)(25, 60)(26, 88)(27, 64)(28, 68)(29, 62)(30, 87)(31, 86)(32, 85)(33, 70)(34, 66)(35, 90)(36, 89)(37, 80)(38, 79)(39, 78)(40, 74)(41, 84)(42, 83)(43, 96)(44, 95)(45, 94)(46, 93)(47, 92)(48, 91)(97, 146)(98, 145)(99, 151)(100, 153)(101, 155)(102, 157)(103, 147)(104, 161)(105, 148)(106, 165)(107, 149)(108, 169)(109, 150)(110, 173)(111, 167)(112, 171)(113, 152)(114, 178)(115, 168)(116, 172)(117, 154)(118, 177)(119, 159)(120, 163)(121, 156)(122, 184)(123, 160)(124, 164)(125, 158)(126, 183)(127, 182)(128, 181)(129, 166)(130, 162)(131, 186)(132, 185)(133, 176)(134, 175)(135, 174)(136, 170)(137, 180)(138, 179)(139, 192)(140, 191)(141, 190)(142, 189)(143, 188)(144, 187) 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 E23.620 Transitivity :: VT+ Graph:: bipartite v = 2 e = 96 f = 50 degree seq :: [ 96^2 ] E23.628 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 24, 24}) Quotient :: loop^2 Aut^+ = C24 : C2 (small group id <48, 5>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, Y3 * Y2 * Y3^-2 * Y1 * Y3, Y3^-3 * Y2 * Y3^-1 * Y1, (Y2 * Y1)^3, Y3^-1 * Y2 * Y1 * Y3 * Y1 * Y2, Y2 * Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3, (Y3^-1 * Y2 * Y3 * Y1)^2, Y2 * Y3^2 * Y2 * Y3 * Y2 * Y3 * Y1, Y3^-16 * Y1 * Y2 ] Map:: R = (1, 49, 97, 145, 4, 52, 100, 148, 14, 62, 110, 158, 31, 79, 127, 175, 45, 93, 141, 189, 21, 69, 117, 165, 44, 92, 140, 188, 28, 76, 124, 172, 9, 57, 105, 153, 27, 75, 123, 171, 47, 95, 143, 191, 25, 73, 121, 169, 48, 96, 144, 192, 29, 77, 125, 173, 43, 91, 139, 187, 20, 68, 116, 164, 6, 54, 102, 150, 19, 67, 115, 163, 41, 89, 137, 185, 24, 72, 120, 168, 46, 94, 142, 190, 22, 70, 118, 166, 17, 65, 113, 161, 5, 53, 101, 149)(2, 50, 98, 146, 7, 55, 103, 151, 23, 71, 119, 167, 42, 90, 138, 186, 34, 82, 130, 178, 12, 60, 108, 156, 33, 81, 129, 177, 39, 87, 135, 183, 18, 66, 114, 162, 38, 86, 134, 182, 36, 84, 132, 180, 16, 64, 112, 160, 37, 85, 133, 181, 40, 88, 136, 184, 32, 80, 128, 176, 11, 59, 107, 155, 3, 51, 99, 147, 10, 58, 106, 154, 30, 78, 126, 174, 15, 63, 111, 159, 35, 83, 131, 179, 13, 61, 109, 157, 26, 74, 122, 170, 8, 56, 104, 152) L = (1, 50)(2, 49)(3, 57)(4, 60)(5, 63)(6, 66)(7, 69)(8, 72)(9, 51)(10, 77)(11, 79)(12, 52)(13, 75)(14, 84)(15, 53)(16, 76)(17, 80)(18, 54)(19, 88)(20, 90)(21, 55)(22, 86)(23, 95)(24, 56)(25, 87)(26, 91)(27, 61)(28, 64)(29, 58)(30, 89)(31, 59)(32, 65)(33, 92)(34, 94)(35, 93)(36, 62)(37, 96)(38, 70)(39, 73)(40, 67)(41, 78)(42, 68)(43, 74)(44, 81)(45, 83)(46, 82)(47, 71)(48, 85)(97, 147)(98, 150)(99, 145)(100, 157)(101, 160)(102, 146)(103, 166)(104, 169)(105, 162)(106, 165)(107, 168)(108, 163)(109, 148)(110, 167)(111, 164)(112, 149)(113, 177)(114, 153)(115, 156)(116, 159)(117, 154)(118, 151)(119, 158)(120, 155)(121, 152)(122, 188)(123, 184)(124, 186)(125, 182)(126, 191)(127, 183)(128, 187)(129, 161)(130, 192)(131, 190)(132, 185)(133, 189)(134, 173)(135, 175)(136, 171)(137, 180)(138, 172)(139, 176)(140, 170)(141, 181)(142, 179)(143, 174)(144, 178) 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 E23.621 Transitivity :: VT+ Graph:: bipartite v = 2 e = 96 f = 50 degree seq :: [ 96^2 ] E23.629 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 24, 24}) Quotient :: loop^2 Aut^+ = C24 : C2 (small group id <48, 5>) Aut = C2 x (C24 : C2) (small group id <96, 107>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1 * Y2, (R * Y3)^2, R * Y1 * R * Y2, Y1 * Y3 * Y2^2 * Y1^-3 * Y3, Y3 * Y1 * Y3 * Y2^-1 * Y3 * Y2 * Y3 * Y1^-1, Y2^2 * Y1^-1 * Y3 * Y1 * Y3 * Y1^-2, Y2^24, Y1^24 ] Map:: non-degenerate R = (1, 49, 97, 145, 4, 52, 100, 148)(2, 50, 98, 146, 6, 54, 102, 150)(3, 51, 99, 147, 8, 56, 104, 152)(5, 53, 101, 149, 12, 60, 108, 156)(7, 55, 103, 151, 16, 64, 112, 160)(9, 57, 105, 153, 20, 68, 116, 164)(10, 58, 106, 154, 22, 70, 118, 166)(11, 59, 107, 155, 24, 72, 120, 168)(13, 61, 109, 157, 28, 76, 124, 172)(14, 62, 110, 158, 30, 78, 126, 174)(15, 63, 111, 159, 26, 74, 122, 170)(17, 65, 113, 161, 23, 71, 119, 167)(18, 66, 114, 162, 34, 82, 130, 178)(19, 67, 115, 163, 35, 83, 131, 179)(21, 69, 117, 165, 36, 84, 132, 180)(25, 73, 121, 169, 39, 87, 135, 183)(27, 75, 123, 171, 41, 89, 137, 185)(29, 77, 125, 173, 42, 90, 138, 186)(31, 79, 127, 175, 43, 91, 139, 187)(32, 80, 128, 176, 44, 92, 140, 188)(33, 81, 129, 177, 45, 93, 141, 189)(37, 85, 133, 181, 46, 94, 142, 190)(38, 86, 134, 182, 47, 95, 143, 191)(40, 88, 136, 184, 48, 96, 144, 192) L = (1, 50)(2, 53)(3, 49)(4, 57)(5, 59)(6, 61)(7, 51)(8, 65)(9, 67)(10, 52)(11, 71)(12, 73)(13, 75)(14, 54)(15, 55)(16, 72)(17, 80)(18, 56)(19, 77)(20, 76)(21, 58)(22, 78)(23, 68)(24, 85)(25, 86)(26, 60)(27, 88)(28, 87)(29, 62)(30, 63)(31, 64)(32, 69)(33, 66)(34, 70)(35, 89)(36, 90)(37, 81)(38, 79)(39, 94)(40, 74)(41, 95)(42, 96)(43, 82)(44, 83)(45, 84)(46, 92)(47, 93)(48, 91)(97, 147)(98, 145)(99, 151)(100, 154)(101, 146)(102, 158)(103, 159)(104, 162)(105, 148)(106, 165)(107, 149)(108, 170)(109, 150)(110, 173)(111, 174)(112, 175)(113, 152)(114, 177)(115, 153)(116, 167)(117, 176)(118, 178)(119, 155)(120, 160)(121, 156)(122, 184)(123, 157)(124, 164)(125, 163)(126, 166)(127, 182)(128, 161)(129, 181)(130, 187)(131, 188)(132, 189)(133, 168)(134, 169)(135, 172)(136, 171)(137, 179)(138, 180)(139, 192)(140, 190)(141, 191)(142, 183)(143, 185)(144, 186) local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E23.622 Transitivity :: VT+ Graph:: bipartite v = 24 e = 96 f = 28 degree seq :: [ 8^24 ] E23.630 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 24, 24}) Quotient :: loop^2 Aut^+ = C24 : C2 (small group id <48, 6>) Aut = (D8 x S3) : C2 (small group id <96, 118>) |r| :: 2 Presentation :: [ R^2, Y3^2, (Y2, Y1), R * Y1 * R * Y2, (R * Y3)^2, Y1^-1 * Y3 * Y2 * Y3 * Y2^-1 * Y1^-1, Y2^-1 * Y3 * Y2 * Y1^2 * Y3, Y3 * Y2^2 * Y1 * Y3 * Y1^-1, Y2 * Y1^-3 * Y2^2, (Y3 * Y2^-2)^2, Y3 * Y1^-1 * Y2^-1 * Y3 * Y2^-1 * Y1^-1, Y1^-1 * Y2 * Y3 * Y2^-1 * Y1 * Y3 * Y1^-1 * Y2, Y2^3 * Y1^21 ] Map:: polytopal non-degenerate R = (1, 49, 97, 145, 4, 52, 100, 148)(2, 50, 98, 146, 9, 57, 105, 153)(3, 51, 99, 147, 12, 60, 108, 156)(5, 53, 101, 149, 18, 66, 114, 162)(6, 54, 102, 150, 21, 69, 117, 165)(7, 55, 103, 151, 25, 73, 121, 169)(8, 56, 104, 152, 28, 76, 124, 172)(10, 58, 106, 154, 33, 81, 129, 177)(11, 59, 107, 155, 35, 83, 131, 179)(13, 61, 109, 157, 38, 86, 134, 182)(14, 62, 110, 158, 27, 75, 123, 171)(15, 63, 111, 159, 24, 72, 120, 168)(16, 64, 112, 160, 39, 87, 135, 183)(17, 65, 113, 161, 40, 88, 136, 184)(19, 67, 115, 163, 37, 85, 133, 181)(20, 68, 116, 164, 32, 80, 128, 176)(22, 70, 118, 166, 31, 79, 127, 175)(23, 71, 119, 167, 44, 92, 140, 188)(26, 74, 122, 170, 48, 96, 144, 192)(29, 77, 125, 173, 45, 93, 141, 189)(30, 78, 126, 174, 43, 91, 139, 187)(34, 82, 130, 178, 47, 95, 143, 191)(36, 84, 132, 180, 42, 90, 138, 186)(41, 89, 137, 185, 46, 94, 142, 190) L = (1, 50)(2, 55)(3, 56)(4, 62)(5, 49)(6, 58)(7, 71)(8, 72)(9, 77)(10, 74)(11, 75)(12, 84)(13, 51)(14, 85)(15, 80)(16, 52)(17, 86)(18, 83)(19, 53)(20, 54)(21, 76)(22, 82)(23, 90)(24, 91)(25, 64)(26, 59)(27, 93)(28, 65)(29, 66)(30, 69)(31, 57)(32, 60)(33, 63)(34, 61)(35, 94)(36, 95)(37, 96)(38, 92)(39, 70)(40, 68)(41, 67)(42, 88)(43, 89)(44, 79)(45, 87)(46, 81)(47, 73)(48, 78)(97, 147)(98, 152)(99, 155)(100, 159)(101, 157)(102, 145)(103, 168)(104, 171)(105, 174)(106, 146)(107, 167)(108, 173)(109, 170)(110, 176)(111, 175)(112, 177)(113, 148)(114, 172)(115, 178)(116, 149)(117, 169)(118, 150)(119, 187)(120, 189)(121, 190)(122, 151)(123, 186)(124, 160)(125, 165)(126, 191)(127, 192)(128, 153)(129, 188)(130, 154)(131, 161)(132, 162)(133, 156)(134, 158)(135, 164)(136, 163)(137, 166)(138, 185)(139, 183)(140, 181)(141, 184)(142, 182)(143, 179)(144, 180) local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E23.623 Transitivity :: VT+ Graph:: simple bipartite v = 24 e = 96 f = 28 degree seq :: [ 8^24 ] E23.631 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 24, 24}) Quotient :: loop^2 Aut^+ = D48 (small group id <48, 7>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ R^2, Y3^2, R * Y2 * R * Y1, (Y2^-1, Y1^-1), (Y3 * Y1^-1)^2, (Y3 * Y2^-1)^2, (R * Y3)^2, Y1^-1 * Y2 * Y1^-4, (Y3 * Y1 * Y2^-1)^2, Y2^4 * Y1^-1 * Y2, (Y2 * Y3 * Y1^-1)^2 ] Map:: polytopal non-degenerate R = (1, 49, 97, 145, 4, 52, 100, 148)(2, 50, 98, 146, 9, 57, 105, 153)(3, 51, 99, 147, 12, 60, 108, 156)(5, 53, 101, 149, 14, 62, 110, 158)(6, 54, 102, 150, 15, 63, 111, 159)(7, 55, 103, 151, 21, 69, 117, 165)(8, 56, 104, 152, 24, 72, 120, 168)(10, 58, 106, 154, 25, 73, 121, 169)(11, 59, 107, 155, 27, 75, 123, 171)(13, 61, 109, 157, 29, 77, 125, 173)(16, 64, 112, 160, 30, 78, 126, 174)(17, 65, 113, 161, 31, 79, 127, 175)(18, 66, 114, 162, 32, 80, 128, 176)(19, 67, 115, 163, 36, 84, 132, 180)(20, 68, 116, 164, 38, 86, 134, 182)(22, 70, 118, 166, 39, 87, 135, 183)(23, 71, 119, 167, 41, 89, 137, 185)(26, 74, 122, 170, 42, 90, 138, 186)(28, 76, 124, 172, 43, 91, 139, 187)(33, 81, 129, 177, 44, 92, 140, 188)(34, 82, 130, 178, 45, 93, 141, 189)(35, 83, 131, 179, 46, 94, 142, 190)(37, 85, 133, 181, 47, 95, 143, 191)(40, 88, 136, 184, 48, 96, 144, 192) L = (1, 50)(2, 55)(3, 56)(4, 62)(5, 49)(6, 58)(7, 67)(8, 68)(9, 52)(10, 70)(11, 71)(12, 77)(13, 51)(14, 78)(15, 79)(16, 53)(17, 54)(18, 74)(19, 61)(20, 83)(21, 57)(22, 64)(23, 85)(24, 60)(25, 63)(26, 88)(27, 91)(28, 59)(29, 84)(30, 87)(31, 92)(32, 93)(33, 65)(34, 66)(35, 76)(36, 69)(37, 82)(38, 72)(39, 73)(40, 81)(41, 75)(42, 80)(43, 94)(44, 96)(45, 95)(46, 86)(47, 89)(48, 90)(97, 147)(98, 152)(99, 155)(100, 159)(101, 157)(102, 145)(103, 164)(104, 167)(105, 169)(106, 146)(107, 170)(108, 148)(109, 172)(110, 175)(111, 176)(112, 163)(113, 149)(114, 150)(115, 179)(116, 181)(117, 183)(118, 151)(119, 184)(120, 153)(121, 186)(122, 154)(123, 156)(124, 162)(125, 158)(126, 188)(127, 189)(128, 187)(129, 160)(130, 161)(131, 178)(132, 174)(133, 177)(134, 165)(135, 192)(136, 166)(137, 168)(138, 171)(139, 173)(140, 191)(141, 190)(142, 180)(143, 182)(144, 185) local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E23.624 Transitivity :: VT+ Graph:: bipartite v = 24 e = 96 f = 28 degree seq :: [ 8^24 ] E23.632 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 24, 24}) Quotient :: dipole Aut^+ = C3 x QD16 (small group id <48, 26>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y1^2, (Y3^-1 * Y1)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2^-5 * Y1 * Y2^-1 * Y1, (Y2^2 * Y1 * Y2^-2 * Y1)^2, (Y3 * Y2^-1)^24 ] Map:: R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 9, 57)(5, 53, 11, 59)(6, 54, 13, 61)(8, 56, 17, 65)(10, 58, 21, 69)(12, 60, 25, 73)(14, 62, 29, 77)(15, 63, 23, 71)(16, 64, 27, 75)(18, 66, 34, 82)(19, 67, 24, 72)(20, 68, 28, 76)(22, 70, 32, 80)(26, 74, 40, 88)(30, 78, 38, 86)(31, 79, 42, 90)(33, 81, 41, 89)(35, 83, 39, 87)(36, 84, 37, 85)(43, 91, 46, 94)(44, 92, 47, 95)(45, 93, 48, 96)(97, 145, 99, 147, 104, 152, 114, 162, 124, 172, 109, 157, 123, 171, 137, 185, 144, 192, 136, 184, 125, 173, 138, 186, 143, 191, 135, 183, 121, 169, 134, 182, 142, 190, 133, 181, 120, 168, 107, 155, 119, 167, 118, 166, 106, 154, 100, 148)(98, 146, 101, 149, 108, 156, 122, 170, 116, 164, 105, 153, 115, 163, 131, 179, 141, 189, 130, 178, 117, 165, 132, 180, 140, 188, 129, 177, 113, 161, 128, 176, 139, 187, 127, 175, 112, 160, 103, 151, 111, 159, 126, 174, 110, 158, 102, 150) 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, 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 = 26 e = 96 f = 26 degree seq :: [ 4^24, 48^2 ] E23.633 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 24, 24}) Quotient :: dipole Aut^+ = C24 : C2 (small group id <48, 5>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y1^2, (Y3^-1 * Y1)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2^5 * Y1 * Y2^-1 * Y1, (Y3 * Y2^-1)^24 ] Map:: R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 9, 57)(5, 53, 11, 59)(6, 54, 13, 61)(8, 56, 17, 65)(10, 58, 21, 69)(12, 60, 25, 73)(14, 62, 29, 77)(15, 63, 23, 71)(16, 64, 27, 75)(18, 66, 34, 82)(19, 67, 24, 72)(20, 68, 28, 76)(22, 70, 33, 81)(26, 74, 40, 88)(30, 78, 39, 87)(31, 79, 38, 86)(32, 80, 37, 85)(35, 83, 42, 90)(36, 84, 41, 89)(43, 91, 48, 96)(44, 92, 47, 95)(45, 93, 46, 94)(97, 145, 99, 147, 104, 152, 114, 162, 120, 168, 107, 155, 119, 167, 133, 181, 142, 190, 135, 183, 121, 169, 134, 182, 143, 191, 138, 186, 125, 173, 136, 184, 144, 192, 137, 185, 124, 172, 109, 157, 123, 171, 118, 166, 106, 154, 100, 148)(98, 146, 101, 149, 108, 156, 122, 170, 112, 160, 103, 151, 111, 159, 127, 175, 139, 187, 129, 177, 113, 161, 128, 176, 140, 188, 132, 180, 117, 165, 130, 178, 141, 189, 131, 179, 116, 164, 105, 153, 115, 163, 126, 174, 110, 158, 102, 150) 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, 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 = 26 e = 96 f = 26 degree seq :: [ 4^24, 48^2 ] E23.634 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 24, 24}) Quotient :: dipole Aut^+ = C3 x QD16 (small group id <48, 26>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, Y3 * Y2^-1 * Y3 * Y2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y3 * Y1)^2, Y2 * Y1 * Y2^-2 * Y1 * Y3 * Y2, Y2^5 * Y1 * Y2 * Y1, Y2 * Y3 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 9, 57)(4, 52, 7, 55)(5, 53, 13, 61)(6, 54, 15, 63)(8, 56, 19, 67)(10, 58, 24, 72)(11, 59, 22, 70)(12, 60, 27, 75)(14, 62, 31, 79)(16, 64, 26, 74)(17, 65, 34, 82)(18, 66, 37, 85)(20, 68, 28, 76)(21, 69, 33, 81)(23, 71, 38, 86)(25, 73, 43, 91)(29, 77, 35, 83)(30, 78, 39, 87)(32, 80, 42, 90)(36, 84, 46, 94)(40, 88, 44, 92)(41, 89, 47, 95)(45, 93, 48, 96)(97, 145, 99, 147, 106, 154, 121, 169, 135, 183, 115, 163, 134, 182, 130, 178, 143, 191, 142, 190, 124, 172, 108, 156, 100, 148, 107, 155, 122, 170, 140, 188, 144, 192, 133, 181, 131, 179, 111, 159, 129, 177, 128, 176, 110, 158, 101, 149)(98, 146, 102, 150, 112, 160, 132, 180, 126, 174, 109, 157, 125, 173, 118, 166, 137, 185, 139, 187, 127, 175, 114, 162, 103, 151, 113, 161, 120, 168, 138, 186, 141, 189, 123, 171, 119, 167, 105, 153, 117, 165, 136, 184, 116, 164, 104, 152) L = (1, 100)(2, 103)(3, 107)(4, 97)(5, 108)(6, 113)(7, 98)(8, 114)(9, 118)(10, 122)(11, 99)(12, 101)(13, 123)(14, 124)(15, 130)(16, 120)(17, 102)(18, 104)(19, 133)(20, 127)(21, 137)(22, 105)(23, 125)(24, 112)(25, 140)(26, 106)(27, 109)(28, 110)(29, 119)(30, 141)(31, 116)(32, 142)(33, 143)(34, 111)(35, 134)(36, 138)(37, 115)(38, 131)(39, 144)(40, 139)(41, 117)(42, 132)(43, 136)(44, 121)(45, 126)(46, 128)(47, 129)(48, 135)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 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 = 26 e = 96 f = 26 degree seq :: [ 4^24, 48^2 ] E23.635 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 24, 24}) Quotient :: dipole Aut^+ = C24 : C2 (small group id <48, 5>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, Y2^-1 * Y3 * Y2 * Y3, (R * Y3)^2, (R * Y2)^2, (Y3 * Y1)^2, (R * Y1)^2, Y2 * Y1 * Y2^2 * Y1 * Y3 * Y2, Y2^-5 * Y1 * Y2 * Y1 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 9, 57)(4, 52, 7, 55)(5, 53, 13, 61)(6, 54, 15, 63)(8, 56, 19, 67)(10, 58, 24, 72)(11, 59, 22, 70)(12, 60, 27, 75)(14, 62, 31, 79)(16, 64, 28, 76)(17, 65, 34, 82)(18, 66, 37, 85)(20, 68, 26, 74)(21, 69, 33, 81)(23, 71, 38, 86)(25, 73, 43, 91)(29, 77, 35, 83)(30, 78, 39, 87)(32, 80, 42, 90)(36, 84, 44, 92)(40, 88, 46, 94)(41, 89, 48, 96)(45, 93, 47, 95)(97, 145, 99, 147, 106, 154, 121, 169, 131, 179, 111, 159, 129, 177, 133, 181, 144, 192, 142, 190, 124, 172, 108, 156, 100, 148, 107, 155, 122, 170, 140, 188, 143, 191, 130, 178, 135, 183, 115, 163, 134, 182, 128, 176, 110, 158, 101, 149)(98, 146, 102, 150, 112, 160, 132, 180, 119, 167, 105, 153, 117, 165, 123, 171, 141, 189, 138, 186, 120, 168, 114, 162, 103, 151, 113, 161, 127, 175, 139, 187, 137, 185, 118, 166, 126, 174, 109, 157, 125, 173, 136, 184, 116, 164, 104, 152) L = (1, 100)(2, 103)(3, 107)(4, 97)(5, 108)(6, 113)(7, 98)(8, 114)(9, 118)(10, 122)(11, 99)(12, 101)(13, 123)(14, 124)(15, 130)(16, 127)(17, 102)(18, 104)(19, 133)(20, 120)(21, 126)(22, 105)(23, 137)(24, 116)(25, 140)(26, 106)(27, 109)(28, 110)(29, 141)(30, 117)(31, 112)(32, 142)(33, 135)(34, 111)(35, 143)(36, 139)(37, 115)(38, 144)(39, 129)(40, 138)(41, 119)(42, 136)(43, 132)(44, 121)(45, 125)(46, 128)(47, 131)(48, 134)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 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 = 26 e = 96 f = 26 degree seq :: [ 4^24, 48^2 ] E23.636 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 24, 24}) Quotient :: dipole Aut^+ = C24 : C2 (small group id <48, 5>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^3, (Y3, Y2), (R * Y2)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y3)^2, Y2 * Y1 * Y3^-1 * Y2^-2 * Y1 * Y2, Y3^-1 * Y1 * Y2^-3 * Y1 * Y2^-1, Y2^24 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 11, 59)(4, 52, 10, 58)(5, 53, 16, 64)(6, 54, 8, 56)(7, 55, 19, 67)(9, 57, 24, 72)(12, 60, 31, 79)(13, 61, 30, 78)(14, 62, 28, 76)(15, 63, 35, 83)(17, 65, 40, 88)(18, 66, 38, 86)(20, 68, 33, 81)(21, 69, 41, 89)(22, 70, 43, 91)(23, 71, 45, 93)(25, 73, 42, 90)(26, 74, 32, 80)(27, 75, 36, 84)(29, 77, 46, 94)(34, 82, 39, 87)(37, 85, 44, 92)(47, 95, 48, 96)(97, 145, 99, 147, 108, 156, 128, 176, 140, 188, 115, 163, 132, 180, 111, 159, 100, 148, 109, 157, 129, 177, 141, 189, 144, 192, 139, 187, 138, 186, 114, 162, 102, 150, 110, 158, 130, 178, 120, 168, 142, 190, 137, 185, 113, 161, 101, 149)(98, 146, 103, 151, 116, 164, 134, 182, 125, 173, 107, 155, 123, 171, 119, 167, 104, 152, 117, 165, 127, 175, 131, 179, 143, 191, 124, 172, 136, 184, 122, 170, 106, 154, 118, 166, 135, 183, 112, 160, 133, 181, 126, 174, 121, 169, 105, 153) L = (1, 100)(2, 104)(3, 109)(4, 102)(5, 111)(6, 97)(7, 117)(8, 106)(9, 119)(10, 98)(11, 124)(12, 129)(13, 110)(14, 99)(15, 114)(16, 134)(17, 132)(18, 101)(19, 139)(20, 127)(21, 118)(22, 103)(23, 122)(24, 128)(25, 123)(26, 105)(27, 136)(28, 126)(29, 143)(30, 107)(31, 135)(32, 141)(33, 130)(34, 108)(35, 112)(36, 138)(37, 125)(38, 131)(39, 116)(40, 121)(41, 115)(42, 113)(43, 137)(44, 144)(45, 120)(46, 140)(47, 133)(48, 142)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 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 = 26 e = 96 f = 26 degree seq :: [ 4^24, 48^2 ] E23.637 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 24, 24}) Quotient :: dipole Aut^+ = C3 x QD16 (small group id <48, 26>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y3 * Y1)^2, (Y3, Y2^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3^4, Y3 * Y1 * Y2^-1 * Y1 * Y2, Y3^-1 * Y2^-6, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 11, 59)(4, 52, 10, 58)(5, 53, 17, 65)(6, 54, 8, 56)(7, 55, 13, 61)(9, 57, 19, 67)(12, 60, 27, 75)(14, 62, 26, 74)(15, 63, 22, 70)(16, 64, 33, 81)(18, 66, 36, 84)(20, 68, 39, 87)(21, 69, 31, 79)(23, 71, 32, 80)(24, 72, 43, 91)(25, 73, 29, 77)(28, 76, 46, 94)(30, 78, 41, 89)(34, 82, 42, 90)(35, 83, 38, 86)(37, 85, 45, 93)(40, 88, 47, 95)(44, 92, 48, 96)(97, 145, 99, 147, 108, 156, 124, 172, 134, 182, 115, 163, 102, 150, 110, 158, 126, 174, 143, 191, 139, 187, 128, 176, 111, 159, 127, 175, 135, 183, 144, 192, 130, 178, 112, 160, 100, 148, 109, 157, 125, 173, 133, 181, 114, 162, 101, 149)(98, 146, 103, 151, 116, 164, 136, 184, 131, 179, 113, 161, 106, 154, 117, 165, 137, 185, 142, 190, 132, 180, 129, 177, 118, 166, 122, 170, 123, 171, 141, 189, 138, 186, 119, 167, 104, 152, 107, 155, 121, 169, 140, 188, 120, 168, 105, 153) L = (1, 100)(2, 104)(3, 109)(4, 111)(5, 112)(6, 97)(7, 107)(8, 118)(9, 119)(10, 98)(11, 122)(12, 125)(13, 127)(14, 99)(15, 102)(16, 128)(17, 105)(18, 130)(19, 101)(20, 121)(21, 103)(22, 106)(23, 129)(24, 138)(25, 123)(26, 117)(27, 137)(28, 133)(29, 135)(30, 108)(31, 110)(32, 115)(33, 113)(34, 139)(35, 120)(36, 131)(37, 144)(38, 114)(39, 126)(40, 140)(41, 116)(42, 132)(43, 134)(44, 141)(45, 142)(46, 136)(47, 124)(48, 143)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 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 = 26 e = 96 f = 26 degree seq :: [ 4^24, 48^2 ] E23.638 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 24, 24}) Quotient :: dipole Aut^+ = C3 x QD16 (small group id <48, 26>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1)^2, Y3^4, (Y3, Y2), (R * Y2)^2, Y3 * Y1 * Y2 * Y1 * Y2^-1, Y3 * Y2^-6, Y3 * Y2 * Y3 * Y1 * Y2^-1 * Y3^-1 * Y1, Y3^2 * Y2^2 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 11, 59)(4, 52, 10, 58)(5, 53, 17, 65)(6, 54, 8, 56)(7, 55, 14, 62)(9, 57, 16, 64)(12, 60, 27, 75)(13, 61, 26, 74)(15, 63, 22, 70)(18, 66, 36, 84)(19, 67, 34, 82)(20, 68, 39, 87)(21, 69, 31, 79)(23, 71, 42, 90)(24, 72, 32, 80)(25, 73, 30, 78)(28, 76, 46, 94)(29, 77, 41, 89)(33, 81, 35, 83)(37, 85, 45, 93)(38, 86, 44, 92)(40, 88, 47, 95)(43, 91, 48, 96)(97, 145, 99, 147, 108, 156, 124, 172, 129, 177, 112, 160, 100, 148, 109, 157, 125, 173, 143, 191, 138, 186, 128, 176, 111, 159, 127, 175, 135, 183, 144, 192, 134, 182, 115, 163, 102, 150, 110, 158, 126, 174, 133, 181, 114, 162, 101, 149)(98, 146, 103, 151, 116, 164, 136, 184, 131, 179, 113, 161, 104, 152, 117, 165, 137, 185, 142, 190, 132, 180, 130, 178, 118, 166, 122, 170, 123, 171, 141, 189, 140, 188, 120, 168, 106, 154, 107, 155, 121, 169, 139, 187, 119, 167, 105, 153) L = (1, 100)(2, 104)(3, 109)(4, 111)(5, 112)(6, 97)(7, 117)(8, 118)(9, 113)(10, 98)(11, 103)(12, 125)(13, 127)(14, 99)(15, 102)(16, 128)(17, 130)(18, 129)(19, 101)(20, 137)(21, 122)(22, 106)(23, 131)(24, 105)(25, 116)(26, 107)(27, 121)(28, 143)(29, 135)(30, 108)(31, 110)(32, 115)(33, 138)(34, 120)(35, 132)(36, 140)(37, 124)(38, 114)(39, 126)(40, 142)(41, 123)(42, 134)(43, 136)(44, 119)(45, 139)(46, 141)(47, 144)(48, 133)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 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 = 26 e = 96 f = 26 degree seq :: [ 4^24, 48^2 ] E23.639 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 24, 24}) Quotient :: dipole Aut^+ = C24 : C2 (small group id <48, 5>) Aut = (D8 x S3) : C2 (small group id <96, 121>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y3^-1, Y2^-1), (R * Y1)^2, (Y3^-1 * Y1)^2, (R * Y2)^2, (R * Y3)^2, Y3 * Y2^4, Y1 * Y3 * Y2^-1 * Y1 * Y2, Y3^6, Y1 * Y3^-1 * Y2^-1 * Y1 * Y3^-2 * Y2, Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-2 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 11, 59)(4, 52, 10, 58)(5, 53, 17, 65)(6, 54, 8, 56)(7, 55, 14, 62)(9, 57, 16, 64)(12, 60, 29, 77)(13, 61, 28, 76)(15, 63, 26, 74)(18, 66, 38, 86)(19, 67, 36, 84)(20, 68, 23, 71)(21, 69, 40, 88)(22, 70, 32, 80)(24, 72, 43, 91)(25, 73, 34, 82)(27, 75, 30, 78)(31, 79, 45, 93)(33, 81, 42, 90)(35, 83, 37, 85)(39, 87, 46, 94)(41, 89, 47, 95)(44, 92, 48, 96)(97, 145, 99, 147, 108, 156, 115, 163, 102, 150, 110, 158, 126, 174, 135, 183, 116, 164, 128, 176, 136, 184, 144, 192, 129, 177, 143, 191, 139, 187, 130, 178, 111, 159, 127, 175, 131, 179, 112, 160, 100, 148, 109, 157, 114, 162, 101, 149)(98, 146, 103, 151, 117, 165, 121, 169, 106, 154, 107, 155, 123, 171, 140, 188, 122, 170, 124, 172, 125, 173, 142, 190, 138, 186, 141, 189, 134, 182, 132, 180, 119, 167, 137, 185, 133, 181, 113, 161, 104, 152, 118, 166, 120, 168, 105, 153) L = (1, 100)(2, 104)(3, 109)(4, 111)(5, 112)(6, 97)(7, 118)(8, 119)(9, 113)(10, 98)(11, 103)(12, 114)(13, 127)(14, 99)(15, 129)(16, 130)(17, 132)(18, 131)(19, 101)(20, 102)(21, 120)(22, 137)(23, 138)(24, 133)(25, 105)(26, 106)(27, 117)(28, 107)(29, 123)(30, 108)(31, 143)(32, 110)(33, 116)(34, 144)(35, 139)(36, 142)(37, 134)(38, 125)(39, 115)(40, 126)(41, 141)(42, 122)(43, 136)(44, 121)(45, 124)(46, 140)(47, 128)(48, 135)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 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 = 26 e = 96 f = 26 degree seq :: [ 4^24, 48^2 ] E23.640 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 24, 24}) Quotient :: halfedge^2 Aut^+ = C3 x (C8 : C2) (small group id <48, 24>) Aut = (C2 x D24) : C2 (small group id <96, 115>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y3 * Y2, R * Y2 * R * Y3, (R * Y1)^2, Y1 * Y2 * Y1^-2 * Y2 * Y1, (Y1 * Y2 * Y1^-1 * Y2)^2, Y1^-4 * Y2 * Y1^-7 * Y2 * Y1^-1, (Y2 * Y1^3 * Y2 * Y1)^3 ] Map:: R = (1, 50, 2, 53, 5, 59, 11, 68, 20, 77, 29, 85, 37, 93, 45, 89, 41, 81, 33, 73, 25, 64, 16, 72, 24, 63, 15, 71, 23, 80, 32, 88, 40, 96, 48, 92, 44, 84, 36, 76, 28, 67, 19, 58, 10, 52, 4, 49)(3, 55, 7, 60, 12, 70, 22, 78, 30, 87, 39, 94, 46, 91, 43, 83, 35, 75, 27, 66, 18, 57, 9, 62, 14, 54, 6, 61, 13, 69, 21, 79, 31, 86, 38, 95, 47, 90, 42, 82, 34, 74, 26, 65, 17, 56, 8, 51) 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, 45)(44, 47)(49, 51)(50, 54)(52, 57)(53, 60)(55, 63)(56, 64)(58, 65)(59, 69)(61, 71)(62, 72)(66, 73)(67, 75)(68, 78)(70, 80)(74, 81)(76, 82)(77, 86)(79, 88)(83, 89)(84, 91)(85, 94)(87, 96)(90, 93)(92, 95) local type(s) :: { ( 48^48 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 48 f = 2 degree seq :: [ 48^2 ] E23.641 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 24, 24}) Quotient :: halfedge^2 Aut^+ = C24 : C2 (small group id <48, 6>) Aut = (C2 x D24) : C2 (small group id <96, 115>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y2 * Y3, R * Y2 * R * Y3, (R * Y1)^2, (Y1^-2 * Y2)^2, Y1 * Y3 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2, Y1^-4 * Y2 * Y1 * Y2 * Y1^-7 ] Map:: R = (1, 50, 2, 53, 5, 59, 11, 68, 20, 77, 29, 85, 37, 93, 45, 90, 42, 82, 34, 74, 26, 64, 16, 71, 23, 65, 17, 72, 24, 80, 32, 88, 40, 96, 48, 92, 44, 84, 36, 76, 28, 67, 19, 58, 10, 52, 4, 49)(3, 55, 7, 63, 15, 73, 25, 81, 33, 89, 41, 95, 47, 86, 38, 79, 31, 69, 21, 62, 14, 54, 6, 61, 13, 57, 9, 66, 18, 75, 27, 83, 35, 91, 43, 94, 46, 87, 39, 78, 30, 70, 22, 60, 12, 56, 8, 51) 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, 45)(44, 47)(49, 51)(50, 54)(52, 57)(53, 60)(55, 64)(56, 65)(58, 63)(59, 69)(61, 71)(62, 72)(66, 74)(67, 75)(68, 78)(70, 80)(73, 82)(76, 81)(77, 86)(79, 88)(83, 90)(84, 91)(85, 94)(87, 96)(89, 93)(92, 95) local type(s) :: { ( 48^48 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 48 f = 2 degree seq :: [ 48^2 ] E23.642 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 24, 24}) Quotient :: halfedge^2 Aut^+ = C24 : C2 (small group id <48, 6>) Aut = (C2 x D24) : C2 (small group id <96, 115>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (Y2 * Y3)^2, Y3 * Y1^-1 * Y2 * Y1^-1, (R * Y1)^2, R * Y3 * R * Y2, Y2 * Y1^4 * Y3 * Y2 * Y1^-4 * Y3, Y1^-1 * Y3 * Y1^4 * Y2 * Y1^-7 ] Map:: non-degenerate R = (1, 50, 2, 54, 6, 61, 13, 69, 21, 77, 29, 85, 37, 93, 45, 90, 42, 82, 34, 74, 26, 66, 18, 58, 10, 64, 16, 72, 24, 80, 32, 88, 40, 96, 48, 92, 44, 84, 36, 76, 28, 68, 20, 60, 12, 53, 5, 49)(3, 57, 9, 65, 17, 73, 25, 81, 33, 89, 41, 95, 47, 86, 38, 79, 31, 70, 22, 63, 15, 55, 7, 52, 4, 59, 11, 67, 19, 75, 27, 83, 35, 91, 43, 94, 46, 87, 39, 78, 30, 71, 23, 62, 14, 56, 8, 51) L = (1, 3)(2, 7)(4, 10)(5, 11)(6, 14)(8, 16)(9, 18)(12, 17)(13, 22)(15, 24)(19, 26)(20, 27)(21, 30)(23, 32)(25, 34)(28, 33)(29, 38)(31, 40)(35, 42)(36, 43)(37, 46)(39, 48)(41, 45)(44, 47)(49, 52)(50, 56)(51, 58)(53, 57)(54, 63)(55, 64)(59, 66)(60, 67)(61, 71)(62, 72)(65, 74)(68, 73)(69, 79)(70, 80)(75, 82)(76, 83)(77, 87)(78, 88)(81, 90)(84, 89)(85, 95)(86, 96)(91, 93)(92, 94) local type(s) :: { ( 48^48 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 48 f = 2 degree seq :: [ 48^2 ] E23.643 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 24, 24}) Quotient :: halfedge^2 Aut^+ = C24 : C2 (small group id <48, 6>) Aut = (C2 x D24) : C2 (small group id <96, 115>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (R * Y1)^2, (Y1^-1 * Y2 * Y1^-1)^2, Y3 * Y2 * Y1 * Y2 * Y3 * Y1^-1, Y2 * Y1^-1 * Y3 * Y1^3, (Y3 * Y2)^3, (Y3 * Y1^-2)^2, Y2 * Y1 * Y3 * Y2 * Y3 * Y1^-3, Y1^16 * Y2 * Y3 ] Map:: non-degenerate R = (1, 50, 2, 54, 6, 66, 18, 85, 37, 83, 35, 94, 46, 79, 31, 58, 10, 70, 22, 87, 39, 76, 28, 90, 42, 80, 32, 93, 45, 82, 34, 61, 13, 73, 25, 88, 40, 77, 29, 91, 43, 81, 33, 65, 17, 53, 5, 49)(3, 57, 9, 75, 27, 92, 44, 96, 48, 89, 41, 68, 20, 62, 14, 52, 4, 60, 12, 71, 23, 55, 7, 69, 21, 63, 15, 84, 36, 95, 47, 78, 30, 86, 38, 74, 26, 56, 8, 72, 24, 64, 16, 67, 19, 59, 11, 51) L = (1, 3)(2, 7)(4, 13)(5, 15)(6, 19)(8, 25)(9, 28)(10, 30)(11, 32)(12, 18)(14, 35)(16, 34)(17, 27)(20, 40)(21, 42)(22, 44)(23, 45)(24, 37)(26, 46)(29, 38)(31, 41)(33, 47)(36, 39)(43, 48)(49, 52)(50, 56)(51, 58)(53, 64)(54, 68)(55, 70)(57, 77)(59, 81)(60, 76)(61, 78)(62, 80)(63, 79)(65, 71)(66, 86)(67, 87)(69, 91)(72, 90)(73, 92)(74, 93)(75, 94)(82, 89)(83, 95)(84, 88)(85, 96) local type(s) :: { ( 48^48 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 48 f = 2 degree seq :: [ 48^2 ] E23.644 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 24, 24}) Quotient :: halfedge^2 Aut^+ = C24 : C2 (small group id <48, 6>) Aut = (C2 x D24) : C2 (small group id <96, 115>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (R * Y1)^2, Y1^-4 * Y3 * Y2, (Y2 * Y1^-2)^2, (Y1^-1 * Y3 * Y1^-1)^2, Y3 * Y2 * Y1^-1 * Y2 * Y3 * Y1, Y1^-1 * Y2 * Y3 * Y2 * Y1 * Y3 * Y1^-2, Y2 * Y1^-1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1, Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1, Y2 * Y1^-1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y1^-1 ] Map:: non-degenerate R = (1, 50, 2, 54, 6, 66, 18, 61, 13, 73, 25, 87, 39, 77, 29, 90, 42, 81, 33, 93, 45, 76, 28, 89, 41, 80, 32, 92, 44, 82, 34, 94, 46, 84, 36, 96, 48, 79, 31, 58, 10, 70, 22, 65, 17, 53, 5, 49)(3, 57, 9, 75, 27, 95, 47, 78, 30, 86, 38, 74, 26, 56, 8, 72, 24, 64, 16, 71, 23, 55, 7, 69, 21, 63, 15, 85, 37, 91, 43, 83, 35, 88, 40, 68, 20, 62, 14, 52, 4, 60, 12, 67, 19, 59, 11, 51) L = (1, 3)(2, 7)(4, 13)(5, 15)(6, 19)(8, 25)(9, 28)(10, 30)(11, 32)(12, 34)(14, 36)(16, 18)(17, 27)(20, 39)(21, 41)(22, 43)(23, 44)(24, 46)(26, 48)(29, 38)(31, 40)(33, 47)(35, 42)(37, 45)(49, 52)(50, 56)(51, 58)(53, 64)(54, 68)(55, 70)(57, 77)(59, 81)(60, 76)(61, 83)(62, 80)(63, 79)(65, 67)(66, 86)(69, 90)(71, 93)(72, 89)(73, 95)(74, 92)(75, 96)(78, 94)(82, 88)(84, 91)(85, 87) local type(s) :: { ( 48^48 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 48 f = 2 degree seq :: [ 48^2 ] E23.645 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 24, 24}) Quotient :: edge^2 Aut^+ = C3 x (C8 : C2) (small group id <48, 24>) Aut = (C2 x D24) : C2 (small group id <96, 115>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y1, (R * Y3)^2, R * Y1 * R * Y2, Y3^-2 * Y1 * Y3^2 * Y1, Y3^-1 * Y2 * Y3^2 * Y2 * Y3^-1, (Y3^-1 * Y1 * Y3 * Y1)^2, Y3^11 * Y1 * Y3 * Y1 ] Map:: R = (1, 49, 3, 51, 8, 56, 17, 65, 26, 74, 34, 82, 42, 90, 47, 95, 39, 87, 31, 79, 23, 71, 13, 61, 21, 69, 11, 59, 20, 68, 29, 77, 37, 85, 45, 93, 44, 92, 36, 84, 28, 76, 19, 67, 10, 58, 4, 52)(2, 50, 5, 53, 12, 60, 22, 70, 30, 78, 38, 86, 46, 94, 43, 91, 35, 83, 27, 75, 18, 66, 9, 57, 16, 64, 7, 55, 15, 63, 25, 73, 33, 81, 41, 89, 48, 96, 40, 88, 32, 80, 24, 72, 14, 62, 6, 54)(97, 98)(99, 103)(100, 105)(101, 107)(102, 109)(104, 108)(106, 110)(111, 116)(112, 117)(113, 121)(114, 119)(115, 123)(118, 125)(120, 127)(122, 126)(124, 128)(129, 133)(130, 137)(131, 135)(132, 139)(134, 141)(136, 143)(138, 142)(140, 144)(145, 146)(147, 151)(148, 153)(149, 155)(150, 157)(152, 156)(154, 158)(159, 164)(160, 165)(161, 169)(162, 167)(163, 171)(166, 173)(168, 175)(170, 174)(172, 176)(177, 181)(178, 185)(179, 183)(180, 187)(182, 189)(184, 191)(186, 190)(188, 192) 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 ), ( 96^48 ) } Outer automorphisms :: reflexible Dual of E23.653 Graph:: simple bipartite v = 50 e = 96 f = 2 degree seq :: [ 2^48, 48^2 ] E23.646 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 24, 24}) Quotient :: edge^2 Aut^+ = C24 : C2 (small group id <48, 6>) Aut = (C2 x D24) : C2 (small group id <96, 115>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y1 * Y2, R * Y1 * R * Y2, (R * Y3)^2, Y3^-2 * Y2 * Y3^-2 * Y1, Y3^-1 * Y1 * Y3^-1 * Y2 * Y3^-1 * Y1 * Y3^-1 * Y1, Y3^3 * Y2 * Y3^-9 * Y1 ] Map:: R = (1, 49, 3, 51, 8, 56, 17, 65, 26, 74, 34, 82, 42, 90, 45, 93, 37, 85, 29, 77, 21, 69, 11, 59, 20, 68, 13, 61, 23, 71, 31, 79, 39, 87, 47, 95, 44, 92, 36, 84, 28, 76, 19, 67, 10, 58, 4, 52)(2, 50, 5, 53, 12, 60, 22, 70, 30, 78, 38, 86, 46, 94, 41, 89, 33, 81, 25, 73, 16, 64, 7, 55, 15, 63, 9, 57, 18, 66, 27, 75, 35, 83, 43, 91, 48, 96, 40, 88, 32, 80, 24, 72, 14, 62, 6, 54)(97, 98)(99, 103)(100, 105)(101, 107)(102, 109)(104, 110)(106, 108)(111, 116)(112, 119)(113, 121)(114, 117)(115, 123)(118, 125)(120, 127)(122, 128)(124, 126)(129, 135)(130, 137)(131, 133)(132, 139)(134, 141)(136, 143)(138, 144)(140, 142)(145, 146)(147, 151)(148, 153)(149, 155)(150, 157)(152, 158)(154, 156)(159, 164)(160, 167)(161, 169)(162, 165)(163, 171)(166, 173)(168, 175)(170, 176)(172, 174)(177, 183)(178, 185)(179, 181)(180, 187)(182, 189)(184, 191)(186, 192)(188, 190) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 96, 96 ), ( 96^48 ) } Outer automorphisms :: reflexible Dual of E23.654 Graph:: simple bipartite v = 50 e = 96 f = 2 degree seq :: [ 2^48, 48^2 ] E23.647 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 24, 24}) Quotient :: edge^2 Aut^+ = C24 : C2 (small group id <48, 6>) Aut = (C2 x D24) : C2 (small group id <96, 115>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y2 * Y1)^2, (R * Y3)^2, Y3^-1 * Y1 * Y3^-1 * Y2, R * Y2 * R * Y1, Y3^5 * Y1 * Y3^-7 * Y1 ] Map:: R = (1, 49, 4, 52, 11, 59, 19, 67, 27, 75, 35, 83, 43, 91, 46, 94, 38, 86, 30, 78, 22, 70, 14, 62, 6, 54, 13, 61, 21, 69, 29, 77, 37, 85, 45, 93, 44, 92, 36, 84, 28, 76, 20, 68, 12, 60, 5, 53)(2, 50, 7, 55, 15, 63, 23, 71, 31, 79, 39, 87, 47, 95, 42, 90, 34, 82, 26, 74, 18, 66, 10, 58, 3, 51, 9, 57, 17, 65, 25, 73, 33, 81, 41, 89, 48, 96, 40, 88, 32, 80, 24, 72, 16, 64, 8, 56)(97, 98)(99, 102)(100, 106)(101, 105)(103, 110)(104, 109)(107, 112)(108, 111)(113, 118)(114, 117)(115, 122)(116, 121)(119, 126)(120, 125)(123, 128)(124, 127)(129, 134)(130, 133)(131, 138)(132, 137)(135, 142)(136, 141)(139, 144)(140, 143)(145, 147)(146, 150)(148, 152)(149, 151)(153, 158)(154, 157)(155, 162)(156, 161)(159, 166)(160, 165)(163, 168)(164, 167)(169, 174)(170, 173)(171, 178)(172, 177)(175, 182)(176, 181)(179, 184)(180, 183)(185, 190)(186, 189)(187, 191)(188, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 96, 96 ), ( 96^48 ) } Outer automorphisms :: reflexible Dual of E23.655 Graph:: simple bipartite v = 50 e = 96 f = 2 degree seq :: [ 2^48, 48^2 ] E23.648 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 24, 24}) Quotient :: edge^2 Aut^+ = C24 : C2 (small group id <48, 6>) Aut = (C2 x D24) : C2 (small group id <96, 115>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3^2 * Y1)^2, Y3^-1 * Y2 * Y1 * Y3 * Y1 * Y2, (Y2 * Y1)^3, Y3^-1 * Y1 * Y3 * Y2 * Y3^-2, (Y3^2 * Y2)^2, Y3^-1 * Y2 * Y3 * Y1 * Y2 * Y3^2 * Y1, Y3^-1 * Y2 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y2, (Y3^-1 * Y1 * Y2)^8 ] Map:: R = (1, 49, 4, 52, 14, 62, 22, 70, 45, 93, 25, 73, 46, 94, 28, 76, 9, 57, 27, 75, 44, 92, 21, 69, 43, 91, 24, 72, 42, 90, 20, 68, 6, 54, 19, 67, 40, 88, 29, 77, 47, 95, 31, 79, 17, 65, 5, 53)(2, 50, 7, 55, 23, 71, 13, 61, 35, 83, 16, 64, 36, 84, 38, 86, 18, 66, 37, 85, 34, 82, 12, 60, 33, 81, 15, 63, 32, 80, 11, 59, 3, 51, 10, 58, 30, 78, 39, 87, 48, 96, 41, 89, 26, 74, 8, 56)(97, 98)(99, 105)(100, 108)(101, 111)(102, 114)(103, 117)(104, 120)(106, 125)(107, 127)(109, 123)(110, 122)(112, 124)(113, 119)(115, 135)(116, 137)(118, 133)(121, 134)(126, 142)(128, 140)(129, 139)(130, 138)(131, 143)(132, 136)(141, 144)(145, 147)(146, 150)(148, 157)(149, 160)(151, 166)(152, 169)(153, 162)(154, 165)(155, 168)(156, 163)(158, 176)(159, 164)(161, 174)(167, 186)(170, 184)(171, 183)(172, 185)(173, 181)(175, 182)(177, 189)(178, 190)(179, 187)(180, 188)(191, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 96, 96 ), ( 96^48 ) } Outer automorphisms :: reflexible Dual of E23.656 Graph:: simple bipartite v = 50 e = 96 f = 2 degree seq :: [ 2^48, 48^2 ] E23.649 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 24, 24}) Quotient :: edge^2 Aut^+ = C24 : C2 (small group id <48, 6>) Aut = (C2 x D24) : C2 (small group id <96, 115>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y1 * Y3^2)^2, Y3^-1 * Y1 * Y2 * Y3^-3, Y3^-1 * Y1 * Y2 * Y3 * Y2 * Y1, Y3^-1 * Y1 * Y3^2 * Y2 * Y3^-1, Y2 * Y3 * Y1 * Y2 * Y1 * Y3 * Y2 * Y1, Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 ] Map:: R = (1, 49, 4, 52, 14, 62, 20, 68, 6, 54, 19, 67, 42, 90, 30, 78, 38, 86, 32, 80, 45, 93, 21, 69, 44, 92, 24, 72, 47, 95, 22, 70, 46, 94, 25, 73, 48, 96, 29, 77, 9, 57, 28, 76, 17, 65, 5, 53)(2, 50, 7, 55, 23, 71, 11, 59, 3, 51, 10, 58, 31, 79, 41, 89, 27, 75, 43, 91, 34, 82, 12, 60, 33, 81, 15, 63, 36, 84, 13, 61, 35, 83, 16, 64, 37, 85, 40, 88, 18, 66, 39, 87, 26, 74, 8, 56)(97, 98)(99, 105)(100, 108)(101, 111)(102, 114)(103, 117)(104, 120)(106, 126)(107, 128)(109, 124)(110, 122)(112, 125)(113, 119)(115, 137)(116, 139)(118, 135)(121, 136)(123, 142)(127, 144)(129, 140)(130, 143)(131, 134)(132, 141)(133, 138)(145, 147)(146, 150)(148, 157)(149, 160)(151, 166)(152, 169)(153, 171)(154, 165)(155, 168)(156, 163)(158, 167)(159, 164)(161, 175)(162, 182)(170, 186)(172, 184)(173, 183)(174, 187)(176, 185)(177, 190)(178, 192)(179, 188)(180, 191)(181, 189) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 96, 96 ), ( 96^48 ) } Outer automorphisms :: reflexible Dual of E23.657 Graph:: simple bipartite v = 50 e = 96 f = 2 degree seq :: [ 2^48, 48^2 ] E23.650 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 24, 24}) Quotient :: edge^2 Aut^+ = C24 : C2 (small group id <48, 6>) Aut = C2 x (C24 : C2) (small group id <96, 109>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, R * Y2 * R * Y1, (R * Y3)^2, Y3 * Y2^2 * Y3 * Y1^-2, Y3 * Y1^-1 * Y2 * Y3 * Y2 * Y1^-1, Y3 * Y2^-1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2^-1, Y2^4 * Y3 * Y2^-1 * Y1 * Y2^-1 * Y3 * Y1^-3 * Y2 * Y1^-1, Y2^24, Y1^24 ] Map:: non-degenerate R = (1, 49, 4, 52)(2, 50, 6, 54)(3, 51, 8, 56)(5, 53, 12, 60)(7, 55, 16, 64)(9, 57, 18, 66)(10, 58, 19, 67)(11, 59, 21, 69)(13, 61, 23, 71)(14, 62, 24, 72)(15, 63, 26, 74)(17, 65, 28, 76)(20, 68, 30, 78)(22, 70, 32, 80)(25, 73, 34, 82)(27, 75, 36, 84)(29, 77, 38, 86)(31, 79, 40, 88)(33, 81, 42, 90)(35, 83, 44, 92)(37, 85, 46, 94)(39, 87, 48, 96)(41, 89, 47, 95)(43, 91, 45, 93)(97, 98, 101, 107, 116, 125, 133, 141, 140, 132, 124, 114, 119, 115, 120, 128, 136, 144, 137, 129, 121, 111, 103, 99)(100, 105, 112, 123, 130, 139, 143, 134, 127, 117, 110, 102, 109, 104, 113, 122, 131, 138, 142, 135, 126, 118, 108, 106)(145, 147, 151, 159, 169, 177, 185, 192, 184, 176, 168, 163, 167, 162, 172, 180, 188, 189, 181, 173, 164, 155, 149, 146)(148, 154, 156, 166, 174, 183, 190, 186, 179, 170, 161, 152, 157, 150, 158, 165, 175, 182, 191, 187, 178, 171, 160, 153) 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) :: { ( 8^4 ), ( 8^24 ) } Outer automorphisms :: reflexible Dual of E23.658 Graph:: simple bipartite v = 28 e = 96 f = 24 degree seq :: [ 4^24, 24^4 ] E23.651 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 24, 24}) Quotient :: edge^2 Aut^+ = C24 : C2 (small group id <48, 6>) Aut = (C2 x D24) : C2 (small group id <96, 115>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^2 * Y1^2, Y2^2 * Y1^2, (Y1^-1 * Y2^-1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), R * Y2 * R * Y1, Y3 * Y2 * Y3 * Y1^-1, (Y3 * Y2^-2)^2, Y2^-6 * Y1^-6, Y2^10 * Y1^-1 * Y2 ] Map:: polytopal non-degenerate R = (1, 49, 4, 52)(2, 50, 9, 57)(3, 51, 12, 60)(5, 53, 15, 63)(6, 54, 14, 62)(7, 55, 17, 65)(8, 56, 19, 67)(10, 58, 20, 68)(11, 59, 22, 70)(13, 61, 24, 72)(16, 64, 26, 74)(18, 66, 28, 76)(21, 69, 30, 78)(23, 71, 32, 80)(25, 73, 34, 82)(27, 75, 36, 84)(29, 77, 38, 86)(31, 79, 40, 88)(33, 81, 42, 90)(35, 83, 44, 92)(37, 85, 45, 93)(39, 87, 46, 94)(41, 89, 47, 95)(43, 91, 48, 96)(97, 98, 103, 112, 121, 129, 137, 133, 127, 117, 109, 99, 104, 102, 106, 114, 123, 131, 139, 135, 125, 119, 107, 101)(100, 108, 118, 126, 134, 141, 144, 138, 132, 122, 116, 105, 115, 111, 120, 128, 136, 142, 143, 140, 130, 124, 113, 110)(145, 147, 155, 165, 173, 181, 187, 177, 171, 160, 154, 146, 152, 149, 157, 167, 175, 183, 185, 179, 169, 162, 151, 150)(148, 153, 161, 170, 178, 186, 191, 189, 184, 174, 168, 156, 163, 158, 164, 172, 180, 188, 192, 190, 182, 176, 166, 159) 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) :: { ( 8^4 ), ( 8^24 ) } Outer automorphisms :: reflexible Dual of E23.659 Graph:: simple bipartite v = 28 e = 96 f = 24 degree seq :: [ 4^24, 24^4 ] E23.652 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 24, 24}) Quotient :: edge^2 Aut^+ = D48 (small group id <48, 7>) Aut = (C2 x D24) : C2 (small group id <96, 115>) |r| :: 2 Presentation :: [ R^2, Y3^2, (Y2^-1, Y1^-1), (Y2^-1 * Y1^-1)^2, (Y3 * Y1)^2, Y2^2 * Y1^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y2^-1)^2, Y1^2 * Y2^-1 * Y1 * Y2^2 * Y1^-1 * Y2, Y2 * Y1^-1 * Y2^2 * Y1^-1 * Y2^2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 49, 4, 52)(2, 50, 9, 57)(3, 51, 12, 60)(5, 53, 14, 62)(6, 54, 15, 63)(7, 55, 17, 65)(8, 56, 19, 67)(10, 58, 20, 68)(11, 59, 22, 70)(13, 61, 24, 72)(16, 64, 26, 74)(18, 66, 28, 76)(21, 69, 30, 78)(23, 71, 32, 80)(25, 73, 34, 82)(27, 75, 36, 84)(29, 77, 38, 86)(31, 79, 40, 88)(33, 81, 42, 90)(35, 83, 44, 92)(37, 85, 45, 93)(39, 87, 46, 94)(41, 89, 47, 95)(43, 91, 48, 96)(97, 98, 103, 112, 121, 129, 137, 133, 127, 117, 109, 99, 104, 102, 106, 114, 123, 131, 139, 135, 125, 119, 107, 101)(100, 110, 118, 128, 134, 142, 144, 140, 132, 124, 116, 111, 115, 108, 120, 126, 136, 141, 143, 138, 130, 122, 113, 105)(145, 147, 155, 165, 173, 181, 187, 177, 171, 160, 154, 146, 152, 149, 157, 167, 175, 183, 185, 179, 169, 162, 151, 150)(148, 159, 161, 172, 178, 188, 191, 190, 184, 176, 168, 158, 163, 153, 164, 170, 180, 186, 192, 189, 182, 174, 166, 156) 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) :: { ( 8^4 ), ( 8^24 ) } Outer automorphisms :: reflexible Dual of E23.660 Graph:: simple bipartite v = 28 e = 96 f = 24 degree seq :: [ 4^24, 24^4 ] E23.653 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 24, 24}) Quotient :: loop^2 Aut^+ = C3 x (C8 : C2) (small group id <48, 24>) Aut = (C2 x D24) : C2 (small group id <96, 115>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y1, (R * Y3)^2, R * Y1 * R * Y2, Y3^-2 * Y1 * Y3^2 * Y1, Y3^-1 * Y2 * Y3^2 * Y2 * Y3^-1, (Y3^-1 * Y1 * Y3 * Y1)^2, Y3^11 * Y1 * Y3 * Y1 ] Map:: R = (1, 49, 97, 145, 3, 51, 99, 147, 8, 56, 104, 152, 17, 65, 113, 161, 26, 74, 122, 170, 34, 82, 130, 178, 42, 90, 138, 186, 47, 95, 143, 191, 39, 87, 135, 183, 31, 79, 127, 175, 23, 71, 119, 167, 13, 61, 109, 157, 21, 69, 117, 165, 11, 59, 107, 155, 20, 68, 116, 164, 29, 77, 125, 173, 37, 85, 133, 181, 45, 93, 141, 189, 44, 92, 140, 188, 36, 84, 132, 180, 28, 76, 124, 172, 19, 67, 115, 163, 10, 58, 106, 154, 4, 52, 100, 148)(2, 50, 98, 146, 5, 53, 101, 149, 12, 60, 108, 156, 22, 70, 118, 166, 30, 78, 126, 174, 38, 86, 134, 182, 46, 94, 142, 190, 43, 91, 139, 187, 35, 83, 131, 179, 27, 75, 123, 171, 18, 66, 114, 162, 9, 57, 105, 153, 16, 64, 112, 160, 7, 55, 103, 151, 15, 63, 111, 159, 25, 73, 121, 169, 33, 81, 129, 177, 41, 89, 137, 185, 48, 96, 144, 192, 40, 88, 136, 184, 32, 80, 128, 176, 24, 72, 120, 168, 14, 62, 110, 158, 6, 54, 102, 150) L = (1, 50)(2, 49)(3, 55)(4, 57)(5, 59)(6, 61)(7, 51)(8, 60)(9, 52)(10, 62)(11, 53)(12, 56)(13, 54)(14, 58)(15, 68)(16, 69)(17, 73)(18, 71)(19, 75)(20, 63)(21, 64)(22, 77)(23, 66)(24, 79)(25, 65)(26, 78)(27, 67)(28, 80)(29, 70)(30, 74)(31, 72)(32, 76)(33, 85)(34, 89)(35, 87)(36, 91)(37, 81)(38, 93)(39, 83)(40, 95)(41, 82)(42, 94)(43, 84)(44, 96)(45, 86)(46, 90)(47, 88)(48, 92)(97, 146)(98, 145)(99, 151)(100, 153)(101, 155)(102, 157)(103, 147)(104, 156)(105, 148)(106, 158)(107, 149)(108, 152)(109, 150)(110, 154)(111, 164)(112, 165)(113, 169)(114, 167)(115, 171)(116, 159)(117, 160)(118, 173)(119, 162)(120, 175)(121, 161)(122, 174)(123, 163)(124, 176)(125, 166)(126, 170)(127, 168)(128, 172)(129, 181)(130, 185)(131, 183)(132, 187)(133, 177)(134, 189)(135, 179)(136, 191)(137, 178)(138, 190)(139, 180)(140, 192)(141, 182)(142, 186)(143, 184)(144, 188) 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 E23.645 Transitivity :: VT+ Graph:: bipartite v = 2 e = 96 f = 50 degree seq :: [ 96^2 ] E23.654 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 24, 24}) Quotient :: loop^2 Aut^+ = C24 : C2 (small group id <48, 6>) Aut = (C2 x D24) : C2 (small group id <96, 115>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y1 * Y2, R * Y1 * R * Y2, (R * Y3)^2, Y3^-2 * Y2 * Y3^-2 * Y1, Y3^-1 * Y1 * Y3^-1 * Y2 * Y3^-1 * Y1 * Y3^-1 * Y1, Y3^3 * Y2 * Y3^-9 * Y1 ] Map:: R = (1, 49, 97, 145, 3, 51, 99, 147, 8, 56, 104, 152, 17, 65, 113, 161, 26, 74, 122, 170, 34, 82, 130, 178, 42, 90, 138, 186, 45, 93, 141, 189, 37, 85, 133, 181, 29, 77, 125, 173, 21, 69, 117, 165, 11, 59, 107, 155, 20, 68, 116, 164, 13, 61, 109, 157, 23, 71, 119, 167, 31, 79, 127, 175, 39, 87, 135, 183, 47, 95, 143, 191, 44, 92, 140, 188, 36, 84, 132, 180, 28, 76, 124, 172, 19, 67, 115, 163, 10, 58, 106, 154, 4, 52, 100, 148)(2, 50, 98, 146, 5, 53, 101, 149, 12, 60, 108, 156, 22, 70, 118, 166, 30, 78, 126, 174, 38, 86, 134, 182, 46, 94, 142, 190, 41, 89, 137, 185, 33, 81, 129, 177, 25, 73, 121, 169, 16, 64, 112, 160, 7, 55, 103, 151, 15, 63, 111, 159, 9, 57, 105, 153, 18, 66, 114, 162, 27, 75, 123, 171, 35, 83, 131, 179, 43, 91, 139, 187, 48, 96, 144, 192, 40, 88, 136, 184, 32, 80, 128, 176, 24, 72, 120, 168, 14, 62, 110, 158, 6, 54, 102, 150) L = (1, 50)(2, 49)(3, 55)(4, 57)(5, 59)(6, 61)(7, 51)(8, 62)(9, 52)(10, 60)(11, 53)(12, 58)(13, 54)(14, 56)(15, 68)(16, 71)(17, 73)(18, 69)(19, 75)(20, 63)(21, 66)(22, 77)(23, 64)(24, 79)(25, 65)(26, 80)(27, 67)(28, 78)(29, 70)(30, 76)(31, 72)(32, 74)(33, 87)(34, 89)(35, 85)(36, 91)(37, 83)(38, 93)(39, 81)(40, 95)(41, 82)(42, 96)(43, 84)(44, 94)(45, 86)(46, 92)(47, 88)(48, 90)(97, 146)(98, 145)(99, 151)(100, 153)(101, 155)(102, 157)(103, 147)(104, 158)(105, 148)(106, 156)(107, 149)(108, 154)(109, 150)(110, 152)(111, 164)(112, 167)(113, 169)(114, 165)(115, 171)(116, 159)(117, 162)(118, 173)(119, 160)(120, 175)(121, 161)(122, 176)(123, 163)(124, 174)(125, 166)(126, 172)(127, 168)(128, 170)(129, 183)(130, 185)(131, 181)(132, 187)(133, 179)(134, 189)(135, 177)(136, 191)(137, 178)(138, 192)(139, 180)(140, 190)(141, 182)(142, 188)(143, 184)(144, 186) 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 E23.646 Transitivity :: VT+ Graph:: bipartite v = 2 e = 96 f = 50 degree seq :: [ 96^2 ] E23.655 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 24, 24}) Quotient :: loop^2 Aut^+ = C24 : C2 (small group id <48, 6>) Aut = (C2 x D24) : C2 (small group id <96, 115>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y2 * Y1)^2, (R * Y3)^2, Y3^-1 * Y1 * Y3^-1 * Y2, R * Y2 * R * Y1, Y3^5 * Y1 * Y3^-7 * Y1 ] Map:: R = (1, 49, 97, 145, 4, 52, 100, 148, 11, 59, 107, 155, 19, 67, 115, 163, 27, 75, 123, 171, 35, 83, 131, 179, 43, 91, 139, 187, 46, 94, 142, 190, 38, 86, 134, 182, 30, 78, 126, 174, 22, 70, 118, 166, 14, 62, 110, 158, 6, 54, 102, 150, 13, 61, 109, 157, 21, 69, 117, 165, 29, 77, 125, 173, 37, 85, 133, 181, 45, 93, 141, 189, 44, 92, 140, 188, 36, 84, 132, 180, 28, 76, 124, 172, 20, 68, 116, 164, 12, 60, 108, 156, 5, 53, 101, 149)(2, 50, 98, 146, 7, 55, 103, 151, 15, 63, 111, 159, 23, 71, 119, 167, 31, 79, 127, 175, 39, 87, 135, 183, 47, 95, 143, 191, 42, 90, 138, 186, 34, 82, 130, 178, 26, 74, 122, 170, 18, 66, 114, 162, 10, 58, 106, 154, 3, 51, 99, 147, 9, 57, 105, 153, 17, 65, 113, 161, 25, 73, 121, 169, 33, 81, 129, 177, 41, 89, 137, 185, 48, 96, 144, 192, 40, 88, 136, 184, 32, 80, 128, 176, 24, 72, 120, 168, 16, 64, 112, 160, 8, 56, 104, 152) L = (1, 50)(2, 49)(3, 54)(4, 58)(5, 57)(6, 51)(7, 62)(8, 61)(9, 53)(10, 52)(11, 64)(12, 63)(13, 56)(14, 55)(15, 60)(16, 59)(17, 70)(18, 69)(19, 74)(20, 73)(21, 66)(22, 65)(23, 78)(24, 77)(25, 68)(26, 67)(27, 80)(28, 79)(29, 72)(30, 71)(31, 76)(32, 75)(33, 86)(34, 85)(35, 90)(36, 89)(37, 82)(38, 81)(39, 94)(40, 93)(41, 84)(42, 83)(43, 96)(44, 95)(45, 88)(46, 87)(47, 92)(48, 91)(97, 147)(98, 150)(99, 145)(100, 152)(101, 151)(102, 146)(103, 149)(104, 148)(105, 158)(106, 157)(107, 162)(108, 161)(109, 154)(110, 153)(111, 166)(112, 165)(113, 156)(114, 155)(115, 168)(116, 167)(117, 160)(118, 159)(119, 164)(120, 163)(121, 174)(122, 173)(123, 178)(124, 177)(125, 170)(126, 169)(127, 182)(128, 181)(129, 172)(130, 171)(131, 184)(132, 183)(133, 176)(134, 175)(135, 180)(136, 179)(137, 190)(138, 189)(139, 191)(140, 192)(141, 186)(142, 185)(143, 187)(144, 188) 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 E23.647 Transitivity :: VT+ Graph:: bipartite v = 2 e = 96 f = 50 degree seq :: [ 96^2 ] E23.656 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 24, 24}) Quotient :: loop^2 Aut^+ = C24 : C2 (small group id <48, 6>) Aut = (C2 x D24) : C2 (small group id <96, 115>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3^2 * Y1)^2, Y3^-1 * Y2 * Y1 * Y3 * Y1 * Y2, (Y2 * Y1)^3, Y3^-1 * Y1 * Y3 * Y2 * Y3^-2, (Y3^2 * Y2)^2, Y3^-1 * Y2 * Y3 * Y1 * Y2 * Y3^2 * Y1, Y3^-1 * Y2 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y2, (Y3^-1 * Y1 * Y2)^8 ] Map:: R = (1, 49, 97, 145, 4, 52, 100, 148, 14, 62, 110, 158, 22, 70, 118, 166, 45, 93, 141, 189, 25, 73, 121, 169, 46, 94, 142, 190, 28, 76, 124, 172, 9, 57, 105, 153, 27, 75, 123, 171, 44, 92, 140, 188, 21, 69, 117, 165, 43, 91, 139, 187, 24, 72, 120, 168, 42, 90, 138, 186, 20, 68, 116, 164, 6, 54, 102, 150, 19, 67, 115, 163, 40, 88, 136, 184, 29, 77, 125, 173, 47, 95, 143, 191, 31, 79, 127, 175, 17, 65, 113, 161, 5, 53, 101, 149)(2, 50, 98, 146, 7, 55, 103, 151, 23, 71, 119, 167, 13, 61, 109, 157, 35, 83, 131, 179, 16, 64, 112, 160, 36, 84, 132, 180, 38, 86, 134, 182, 18, 66, 114, 162, 37, 85, 133, 181, 34, 82, 130, 178, 12, 60, 108, 156, 33, 81, 129, 177, 15, 63, 111, 159, 32, 80, 128, 176, 11, 59, 107, 155, 3, 51, 99, 147, 10, 58, 106, 154, 30, 78, 126, 174, 39, 87, 135, 183, 48, 96, 144, 192, 41, 89, 137, 185, 26, 74, 122, 170, 8, 56, 104, 152) L = (1, 50)(2, 49)(3, 57)(4, 60)(5, 63)(6, 66)(7, 69)(8, 72)(9, 51)(10, 77)(11, 79)(12, 52)(13, 75)(14, 74)(15, 53)(16, 76)(17, 71)(18, 54)(19, 87)(20, 89)(21, 55)(22, 85)(23, 65)(24, 56)(25, 86)(26, 62)(27, 61)(28, 64)(29, 58)(30, 94)(31, 59)(32, 92)(33, 91)(34, 90)(35, 95)(36, 88)(37, 70)(38, 73)(39, 67)(40, 84)(41, 68)(42, 82)(43, 81)(44, 80)(45, 96)(46, 78)(47, 83)(48, 93)(97, 147)(98, 150)(99, 145)(100, 157)(101, 160)(102, 146)(103, 166)(104, 169)(105, 162)(106, 165)(107, 168)(108, 163)(109, 148)(110, 176)(111, 164)(112, 149)(113, 174)(114, 153)(115, 156)(116, 159)(117, 154)(118, 151)(119, 186)(120, 155)(121, 152)(122, 184)(123, 183)(124, 185)(125, 181)(126, 161)(127, 182)(128, 158)(129, 189)(130, 190)(131, 187)(132, 188)(133, 173)(134, 175)(135, 171)(136, 170)(137, 172)(138, 167)(139, 179)(140, 180)(141, 177)(142, 178)(143, 192)(144, 191) 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 E23.648 Transitivity :: VT+ Graph:: bipartite v = 2 e = 96 f = 50 degree seq :: [ 96^2 ] E23.657 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 24, 24}) Quotient :: loop^2 Aut^+ = C24 : C2 (small group id <48, 6>) Aut = (C2 x D24) : C2 (small group id <96, 115>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y1 * Y3^2)^2, Y3^-1 * Y1 * Y2 * Y3^-3, Y3^-1 * Y1 * Y2 * Y3 * Y2 * Y1, Y3^-1 * Y1 * Y3^2 * Y2 * Y3^-1, Y2 * Y3 * Y1 * Y2 * Y1 * Y3 * Y2 * Y1, Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 ] Map:: R = (1, 49, 97, 145, 4, 52, 100, 148, 14, 62, 110, 158, 20, 68, 116, 164, 6, 54, 102, 150, 19, 67, 115, 163, 42, 90, 138, 186, 30, 78, 126, 174, 38, 86, 134, 182, 32, 80, 128, 176, 45, 93, 141, 189, 21, 69, 117, 165, 44, 92, 140, 188, 24, 72, 120, 168, 47, 95, 143, 191, 22, 70, 118, 166, 46, 94, 142, 190, 25, 73, 121, 169, 48, 96, 144, 192, 29, 77, 125, 173, 9, 57, 105, 153, 28, 76, 124, 172, 17, 65, 113, 161, 5, 53, 101, 149)(2, 50, 98, 146, 7, 55, 103, 151, 23, 71, 119, 167, 11, 59, 107, 155, 3, 51, 99, 147, 10, 58, 106, 154, 31, 79, 127, 175, 41, 89, 137, 185, 27, 75, 123, 171, 43, 91, 139, 187, 34, 82, 130, 178, 12, 60, 108, 156, 33, 81, 129, 177, 15, 63, 111, 159, 36, 84, 132, 180, 13, 61, 109, 157, 35, 83, 131, 179, 16, 64, 112, 160, 37, 85, 133, 181, 40, 88, 136, 184, 18, 66, 114, 162, 39, 87, 135, 183, 26, 74, 122, 170, 8, 56, 104, 152) L = (1, 50)(2, 49)(3, 57)(4, 60)(5, 63)(6, 66)(7, 69)(8, 72)(9, 51)(10, 78)(11, 80)(12, 52)(13, 76)(14, 74)(15, 53)(16, 77)(17, 71)(18, 54)(19, 89)(20, 91)(21, 55)(22, 87)(23, 65)(24, 56)(25, 88)(26, 62)(27, 94)(28, 61)(29, 64)(30, 58)(31, 96)(32, 59)(33, 92)(34, 95)(35, 86)(36, 93)(37, 90)(38, 83)(39, 70)(40, 73)(41, 67)(42, 85)(43, 68)(44, 81)(45, 84)(46, 75)(47, 82)(48, 79)(97, 147)(98, 150)(99, 145)(100, 157)(101, 160)(102, 146)(103, 166)(104, 169)(105, 171)(106, 165)(107, 168)(108, 163)(109, 148)(110, 167)(111, 164)(112, 149)(113, 175)(114, 182)(115, 156)(116, 159)(117, 154)(118, 151)(119, 158)(120, 155)(121, 152)(122, 186)(123, 153)(124, 184)(125, 183)(126, 187)(127, 161)(128, 185)(129, 190)(130, 192)(131, 188)(132, 191)(133, 189)(134, 162)(135, 173)(136, 172)(137, 176)(138, 170)(139, 174)(140, 179)(141, 181)(142, 177)(143, 180)(144, 178) 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 E23.649 Transitivity :: VT+ Graph:: bipartite v = 2 e = 96 f = 50 degree seq :: [ 96^2 ] E23.658 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 24, 24}) Quotient :: loop^2 Aut^+ = C24 : C2 (small group id <48, 6>) Aut = C2 x (C24 : C2) (small group id <96, 109>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, R * Y2 * R * Y1, (R * Y3)^2, Y3 * Y2^2 * Y3 * Y1^-2, Y3 * Y1^-1 * Y2 * Y3 * Y2 * Y1^-1, Y3 * Y2^-1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2^-1, Y2^4 * Y3 * Y2^-1 * Y1 * Y2^-1 * Y3 * Y1^-3 * Y2 * Y1^-1, Y2^24, Y1^24 ] Map:: non-degenerate R = (1, 49, 97, 145, 4, 52, 100, 148)(2, 50, 98, 146, 6, 54, 102, 150)(3, 51, 99, 147, 8, 56, 104, 152)(5, 53, 101, 149, 12, 60, 108, 156)(7, 55, 103, 151, 16, 64, 112, 160)(9, 57, 105, 153, 18, 66, 114, 162)(10, 58, 106, 154, 19, 67, 115, 163)(11, 59, 107, 155, 21, 69, 117, 165)(13, 61, 109, 157, 23, 71, 119, 167)(14, 62, 110, 158, 24, 72, 120, 168)(15, 63, 111, 159, 26, 74, 122, 170)(17, 65, 113, 161, 28, 76, 124, 172)(20, 68, 116, 164, 30, 78, 126, 174)(22, 70, 118, 166, 32, 80, 128, 176)(25, 73, 121, 169, 34, 82, 130, 178)(27, 75, 123, 171, 36, 84, 132, 180)(29, 77, 125, 173, 38, 86, 134, 182)(31, 79, 127, 175, 40, 88, 136, 184)(33, 81, 129, 177, 42, 90, 138, 186)(35, 83, 131, 179, 44, 92, 140, 188)(37, 85, 133, 181, 46, 94, 142, 190)(39, 87, 135, 183, 48, 96, 144, 192)(41, 89, 137, 185, 47, 95, 143, 191)(43, 91, 139, 187, 45, 93, 141, 189) L = (1, 50)(2, 53)(3, 49)(4, 57)(5, 59)(6, 61)(7, 51)(8, 65)(9, 64)(10, 52)(11, 68)(12, 58)(13, 56)(14, 54)(15, 55)(16, 75)(17, 74)(18, 71)(19, 72)(20, 77)(21, 62)(22, 60)(23, 67)(24, 80)(25, 63)(26, 83)(27, 82)(28, 66)(29, 85)(30, 70)(31, 69)(32, 88)(33, 73)(34, 91)(35, 90)(36, 76)(37, 93)(38, 79)(39, 78)(40, 96)(41, 81)(42, 94)(43, 95)(44, 84)(45, 92)(46, 87)(47, 86)(48, 89)(97, 147)(98, 145)(99, 151)(100, 154)(101, 146)(102, 158)(103, 159)(104, 157)(105, 148)(106, 156)(107, 149)(108, 166)(109, 150)(110, 165)(111, 169)(112, 153)(113, 152)(114, 172)(115, 167)(116, 155)(117, 175)(118, 174)(119, 162)(120, 163)(121, 177)(122, 161)(123, 160)(124, 180)(125, 164)(126, 183)(127, 182)(128, 168)(129, 185)(130, 171)(131, 170)(132, 188)(133, 173)(134, 191)(135, 190)(136, 176)(137, 192)(138, 179)(139, 178)(140, 189)(141, 181)(142, 186)(143, 187)(144, 184) local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E23.650 Transitivity :: VT+ Graph:: bipartite v = 24 e = 96 f = 28 degree seq :: [ 8^24 ] E23.659 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 24, 24}) Quotient :: loop^2 Aut^+ = C24 : C2 (small group id <48, 6>) Aut = (C2 x D24) : C2 (small group id <96, 115>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^2 * Y1^2, Y2^2 * Y1^2, (Y1^-1 * Y2^-1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), R * Y2 * R * Y1, Y3 * Y2 * Y3 * Y1^-1, (Y3 * Y2^-2)^2, Y2^-6 * Y1^-6, Y2^10 * Y1^-1 * Y2 ] Map:: polytopal non-degenerate R = (1, 49, 97, 145, 4, 52, 100, 148)(2, 50, 98, 146, 9, 57, 105, 153)(3, 51, 99, 147, 12, 60, 108, 156)(5, 53, 101, 149, 15, 63, 111, 159)(6, 54, 102, 150, 14, 62, 110, 158)(7, 55, 103, 151, 17, 65, 113, 161)(8, 56, 104, 152, 19, 67, 115, 163)(10, 58, 106, 154, 20, 68, 116, 164)(11, 59, 107, 155, 22, 70, 118, 166)(13, 61, 109, 157, 24, 72, 120, 168)(16, 64, 112, 160, 26, 74, 122, 170)(18, 66, 114, 162, 28, 76, 124, 172)(21, 69, 117, 165, 30, 78, 126, 174)(23, 71, 119, 167, 32, 80, 128, 176)(25, 73, 121, 169, 34, 82, 130, 178)(27, 75, 123, 171, 36, 84, 132, 180)(29, 77, 125, 173, 38, 86, 134, 182)(31, 79, 127, 175, 40, 88, 136, 184)(33, 81, 129, 177, 42, 90, 138, 186)(35, 83, 131, 179, 44, 92, 140, 188)(37, 85, 133, 181, 45, 93, 141, 189)(39, 87, 135, 183, 46, 94, 142, 190)(41, 89, 137, 185, 47, 95, 143, 191)(43, 91, 139, 187, 48, 96, 144, 192) L = (1, 50)(2, 55)(3, 56)(4, 60)(5, 49)(6, 58)(7, 64)(8, 54)(9, 67)(10, 66)(11, 53)(12, 70)(13, 51)(14, 52)(15, 72)(16, 73)(17, 62)(18, 75)(19, 63)(20, 57)(21, 61)(22, 78)(23, 59)(24, 80)(25, 81)(26, 68)(27, 83)(28, 65)(29, 71)(30, 86)(31, 69)(32, 88)(33, 89)(34, 76)(35, 91)(36, 74)(37, 79)(38, 93)(39, 77)(40, 94)(41, 85)(42, 84)(43, 87)(44, 82)(45, 96)(46, 95)(47, 92)(48, 90)(97, 147)(98, 152)(99, 155)(100, 153)(101, 157)(102, 145)(103, 150)(104, 149)(105, 161)(106, 146)(107, 165)(108, 163)(109, 167)(110, 164)(111, 148)(112, 154)(113, 170)(114, 151)(115, 158)(116, 172)(117, 173)(118, 159)(119, 175)(120, 156)(121, 162)(122, 178)(123, 160)(124, 180)(125, 181)(126, 168)(127, 183)(128, 166)(129, 171)(130, 186)(131, 169)(132, 188)(133, 187)(134, 176)(135, 185)(136, 174)(137, 179)(138, 191)(139, 177)(140, 192)(141, 184)(142, 182)(143, 189)(144, 190) local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E23.651 Transitivity :: VT+ Graph:: bipartite v = 24 e = 96 f = 28 degree seq :: [ 8^24 ] E23.660 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 24, 24}) Quotient :: loop^2 Aut^+ = D48 (small group id <48, 7>) Aut = (C2 x D24) : C2 (small group id <96, 115>) |r| :: 2 Presentation :: [ R^2, Y3^2, (Y2^-1, Y1^-1), (Y2^-1 * Y1^-1)^2, (Y3 * Y1)^2, Y2^2 * Y1^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y2^-1)^2, Y1^2 * Y2^-1 * Y1 * Y2^2 * Y1^-1 * Y2, Y2 * Y1^-1 * Y2^2 * Y1^-1 * Y2^2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 49, 97, 145, 4, 52, 100, 148)(2, 50, 98, 146, 9, 57, 105, 153)(3, 51, 99, 147, 12, 60, 108, 156)(5, 53, 101, 149, 14, 62, 110, 158)(6, 54, 102, 150, 15, 63, 111, 159)(7, 55, 103, 151, 17, 65, 113, 161)(8, 56, 104, 152, 19, 67, 115, 163)(10, 58, 106, 154, 20, 68, 116, 164)(11, 59, 107, 155, 22, 70, 118, 166)(13, 61, 109, 157, 24, 72, 120, 168)(16, 64, 112, 160, 26, 74, 122, 170)(18, 66, 114, 162, 28, 76, 124, 172)(21, 69, 117, 165, 30, 78, 126, 174)(23, 71, 119, 167, 32, 80, 128, 176)(25, 73, 121, 169, 34, 82, 130, 178)(27, 75, 123, 171, 36, 84, 132, 180)(29, 77, 125, 173, 38, 86, 134, 182)(31, 79, 127, 175, 40, 88, 136, 184)(33, 81, 129, 177, 42, 90, 138, 186)(35, 83, 131, 179, 44, 92, 140, 188)(37, 85, 133, 181, 45, 93, 141, 189)(39, 87, 135, 183, 46, 94, 142, 190)(41, 89, 137, 185, 47, 95, 143, 191)(43, 91, 139, 187, 48, 96, 144, 192) L = (1, 50)(2, 55)(3, 56)(4, 62)(5, 49)(6, 58)(7, 64)(8, 54)(9, 52)(10, 66)(11, 53)(12, 72)(13, 51)(14, 70)(15, 67)(16, 73)(17, 57)(18, 75)(19, 60)(20, 63)(21, 61)(22, 80)(23, 59)(24, 78)(25, 81)(26, 65)(27, 83)(28, 68)(29, 71)(30, 88)(31, 69)(32, 86)(33, 89)(34, 74)(35, 91)(36, 76)(37, 79)(38, 94)(39, 77)(40, 93)(41, 85)(42, 82)(43, 87)(44, 84)(45, 95)(46, 96)(47, 90)(48, 92)(97, 147)(98, 152)(99, 155)(100, 159)(101, 157)(102, 145)(103, 150)(104, 149)(105, 164)(106, 146)(107, 165)(108, 148)(109, 167)(110, 163)(111, 161)(112, 154)(113, 172)(114, 151)(115, 153)(116, 170)(117, 173)(118, 156)(119, 175)(120, 158)(121, 162)(122, 180)(123, 160)(124, 178)(125, 181)(126, 166)(127, 183)(128, 168)(129, 171)(130, 188)(131, 169)(132, 186)(133, 187)(134, 174)(135, 185)(136, 176)(137, 179)(138, 192)(139, 177)(140, 191)(141, 182)(142, 184)(143, 190)(144, 189) local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E23.652 Transitivity :: VT+ Graph:: bipartite v = 24 e = 96 f = 28 degree seq :: [ 8^24 ] E23.661 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 24, 24}) Quotient :: dipole Aut^+ = C3 x (C8 : C2) (small group id <48, 24>) Aut = (C2 x D24) : C2 (small group id <96, 115>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y1^2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1)^2, (R * Y2 * Y3^-1)^2, Y2^2 * Y1 * Y2^-2 * Y1, (Y2 * Y1 * Y2^-1 * Y1)^2, Y2^11 * Y1 * Y2 * Y1, (Y3 * Y2^-1)^24 ] Map:: R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 9, 57)(5, 53, 11, 59)(6, 54, 13, 61)(8, 56, 12, 60)(10, 58, 14, 62)(15, 63, 20, 68)(16, 64, 21, 69)(17, 65, 25, 73)(18, 66, 23, 71)(19, 67, 27, 75)(22, 70, 29, 77)(24, 72, 31, 79)(26, 74, 30, 78)(28, 76, 32, 80)(33, 81, 37, 85)(34, 82, 41, 89)(35, 83, 39, 87)(36, 84, 43, 91)(38, 86, 45, 93)(40, 88, 47, 95)(42, 90, 46, 94)(44, 92, 48, 96)(97, 145, 99, 147, 104, 152, 113, 161, 122, 170, 130, 178, 138, 186, 143, 191, 135, 183, 127, 175, 119, 167, 109, 157, 117, 165, 107, 155, 116, 164, 125, 173, 133, 181, 141, 189, 140, 188, 132, 180, 124, 172, 115, 163, 106, 154, 100, 148)(98, 146, 101, 149, 108, 156, 118, 166, 126, 174, 134, 182, 142, 190, 139, 187, 131, 179, 123, 171, 114, 162, 105, 153, 112, 160, 103, 151, 111, 159, 121, 169, 129, 177, 137, 185, 144, 192, 136, 184, 128, 176, 120, 168, 110, 158, 102, 150) 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, 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 = 26 e = 96 f = 26 degree seq :: [ 4^24, 48^2 ] E23.662 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 24, 24}) Quotient :: dipole Aut^+ = C24 : C2 (small group id <48, 6>) Aut = (C2 x D24) : C2 (small group id <96, 115>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y1^2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1)^2, (R * Y2 * Y3^-1)^2, (Y2^2 * Y1)^2, (Y2^-1 * Y1)^4, Y2^3 * Y1 * Y2^-9 * Y1, (Y3 * Y2^-1)^24 ] Map:: R = (1, 49, 2, 50)(3, 51, 7, 55)(4, 52, 9, 57)(5, 53, 11, 59)(6, 54, 13, 61)(8, 56, 14, 62)(10, 58, 12, 60)(15, 63, 20, 68)(16, 64, 23, 71)(17, 65, 25, 73)(18, 66, 21, 69)(19, 67, 27, 75)(22, 70, 29, 77)(24, 72, 31, 79)(26, 74, 32, 80)(28, 76, 30, 78)(33, 81, 39, 87)(34, 82, 41, 89)(35, 83, 37, 85)(36, 84, 43, 91)(38, 86, 45, 93)(40, 88, 47, 95)(42, 90, 48, 96)(44, 92, 46, 94)(97, 145, 99, 147, 104, 152, 113, 161, 122, 170, 130, 178, 138, 186, 141, 189, 133, 181, 125, 173, 117, 165, 107, 155, 116, 164, 109, 157, 119, 167, 127, 175, 135, 183, 143, 191, 140, 188, 132, 180, 124, 172, 115, 163, 106, 154, 100, 148)(98, 146, 101, 149, 108, 156, 118, 166, 126, 174, 134, 182, 142, 190, 137, 185, 129, 177, 121, 169, 112, 160, 103, 151, 111, 159, 105, 153, 114, 162, 123, 171, 131, 179, 139, 187, 144, 192, 136, 184, 128, 176, 120, 168, 110, 158, 102, 150) 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, 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 = 26 e = 96 f = 26 degree seq :: [ 4^24, 48^2 ] E23.663 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 24, 24}) Quotient :: dipole Aut^+ = C3 x (C8 : C2) (small group id <48, 24>) Aut = (C2 x D24) : C2 (small group id <96, 115>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, (Y3 * Y1)^2, Y3 * Y2 * Y3 * Y2^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3 * Y1 * Y2^-1 * Y1 * Y2, Y3 * Y2^12 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 9, 57)(4, 52, 7, 55)(5, 53, 13, 61)(6, 54, 11, 59)(8, 56, 12, 60)(10, 58, 15, 63)(14, 62, 16, 64)(17, 65, 19, 67)(18, 66, 25, 73)(20, 68, 21, 69)(22, 70, 29, 77)(23, 71, 27, 75)(24, 72, 28, 76)(26, 74, 31, 79)(30, 78, 32, 80)(33, 81, 35, 83)(34, 82, 41, 89)(36, 84, 37, 85)(38, 86, 45, 93)(39, 87, 43, 91)(40, 88, 44, 92)(42, 90, 47, 95)(46, 94, 48, 96)(97, 145, 99, 147, 106, 154, 114, 162, 122, 170, 130, 178, 138, 186, 140, 188, 132, 180, 124, 172, 116, 164, 108, 156, 100, 148, 107, 155, 115, 163, 123, 171, 131, 179, 139, 187, 142, 190, 134, 182, 126, 174, 118, 166, 110, 158, 101, 149)(98, 146, 102, 150, 111, 159, 119, 167, 127, 175, 135, 183, 143, 191, 141, 189, 133, 181, 125, 173, 117, 165, 109, 157, 103, 151, 105, 153, 113, 161, 121, 169, 129, 177, 137, 185, 144, 192, 136, 184, 128, 176, 120, 168, 112, 160, 104, 152) L = (1, 100)(2, 103)(3, 107)(4, 97)(5, 108)(6, 105)(7, 98)(8, 109)(9, 102)(10, 115)(11, 99)(12, 101)(13, 104)(14, 116)(15, 113)(16, 117)(17, 111)(18, 123)(19, 106)(20, 110)(21, 112)(22, 124)(23, 121)(24, 125)(25, 119)(26, 131)(27, 114)(28, 118)(29, 120)(30, 132)(31, 129)(32, 133)(33, 127)(34, 139)(35, 122)(36, 126)(37, 128)(38, 140)(39, 137)(40, 141)(41, 135)(42, 142)(43, 130)(44, 134)(45, 136)(46, 138)(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) :: { ( 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 = 26 e = 96 f = 26 degree seq :: [ 4^24, 48^2 ] E23.664 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 24, 24}) Quotient :: dipole Aut^+ = C24 : C2 (small group id <48, 6>) Aut = (C2 x D24) : C2 (small group id <96, 115>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, (Y3 * Y1)^2, Y3 * Y2 * Y3 * Y2^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3 * Y1 * Y2^-1 * Y1 * Y2^-1, Y3 * Y2^-12 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 9, 57)(4, 52, 7, 55)(5, 53, 13, 61)(6, 54, 12, 60)(8, 56, 11, 59)(10, 58, 16, 64)(14, 62, 15, 63)(17, 65, 19, 67)(18, 66, 25, 73)(20, 68, 21, 69)(22, 70, 29, 77)(23, 71, 28, 76)(24, 72, 27, 75)(26, 74, 32, 80)(30, 78, 31, 79)(33, 81, 35, 83)(34, 82, 41, 89)(36, 84, 37, 85)(38, 86, 45, 93)(39, 87, 44, 92)(40, 88, 43, 91)(42, 90, 48, 96)(46, 94, 47, 95)(97, 145, 99, 147, 106, 154, 114, 162, 122, 170, 130, 178, 138, 186, 140, 188, 132, 180, 124, 172, 116, 164, 108, 156, 100, 148, 107, 155, 115, 163, 123, 171, 131, 179, 139, 187, 142, 190, 134, 182, 126, 174, 118, 166, 110, 158, 101, 149)(98, 146, 102, 150, 111, 159, 119, 167, 127, 175, 135, 183, 143, 191, 137, 185, 129, 177, 121, 169, 113, 161, 105, 153, 103, 151, 109, 157, 117, 165, 125, 173, 133, 181, 141, 189, 144, 192, 136, 184, 128, 176, 120, 168, 112, 160, 104, 152) L = (1, 100)(2, 103)(3, 107)(4, 97)(5, 108)(6, 109)(7, 98)(8, 105)(9, 104)(10, 115)(11, 99)(12, 101)(13, 102)(14, 116)(15, 117)(16, 113)(17, 112)(18, 123)(19, 106)(20, 110)(21, 111)(22, 124)(23, 125)(24, 121)(25, 120)(26, 131)(27, 114)(28, 118)(29, 119)(30, 132)(31, 133)(32, 129)(33, 128)(34, 139)(35, 122)(36, 126)(37, 127)(38, 140)(39, 141)(40, 137)(41, 136)(42, 142)(43, 130)(44, 134)(45, 135)(46, 138)(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) :: { ( 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 = 26 e = 96 f = 26 degree seq :: [ 4^24, 48^2 ] E23.665 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 24, 24}) Quotient :: dipole Aut^+ = C3 x (C8 : C2) (small group id <48, 24>) Aut = (C2 x D24) : C2 (small group id <96, 115>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y1)^2, Y2^-1 * Y1 * Y2 * Y1, Y3 * Y1 * Y2^-1 * Y3 * Y2, R * Y2 * R * Y1 * Y2, Y2^12 * Y1, (Y1 * Y2^-2)^12 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 6, 54)(4, 52, 7, 55)(5, 53, 8, 56)(9, 57, 15, 63)(10, 58, 11, 59)(12, 60, 13, 61)(14, 62, 16, 64)(17, 65, 23, 71)(18, 66, 19, 67)(20, 68, 21, 69)(22, 70, 24, 72)(25, 73, 31, 79)(26, 74, 27, 75)(28, 76, 29, 77)(30, 78, 32, 80)(33, 81, 39, 87)(34, 82, 35, 83)(36, 84, 37, 85)(38, 86, 40, 88)(41, 89, 46, 94)(42, 90, 43, 91)(44, 92, 45, 93)(47, 95, 48, 96)(97, 145, 99, 147, 105, 153, 113, 161, 121, 169, 129, 177, 137, 185, 136, 184, 128, 176, 120, 168, 112, 160, 104, 152, 98, 146, 102, 150, 111, 159, 119, 167, 127, 175, 135, 183, 142, 190, 134, 182, 126, 174, 118, 166, 110, 158, 101, 149)(100, 148, 107, 155, 114, 162, 123, 171, 130, 178, 139, 187, 143, 191, 141, 189, 133, 181, 125, 173, 117, 165, 109, 157, 103, 151, 106, 154, 115, 163, 122, 170, 131, 179, 138, 186, 144, 192, 140, 188, 132, 180, 124, 172, 116, 164, 108, 156) L = (1, 100)(2, 103)(3, 106)(4, 97)(5, 109)(6, 107)(7, 98)(8, 108)(9, 114)(10, 99)(11, 102)(12, 104)(13, 101)(14, 116)(15, 115)(16, 117)(17, 122)(18, 105)(19, 111)(20, 110)(21, 112)(22, 125)(23, 123)(24, 124)(25, 130)(26, 113)(27, 119)(28, 120)(29, 118)(30, 132)(31, 131)(32, 133)(33, 138)(34, 121)(35, 127)(36, 126)(37, 128)(38, 141)(39, 139)(40, 140)(41, 143)(42, 129)(43, 135)(44, 136)(45, 134)(46, 144)(47, 137)(48, 142)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 48, 4, 48 ), ( 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48 ) } Outer automorphisms :: reflexible Dual of E23.666 Graph:: bipartite v = 26 e = 96 f = 26 degree seq :: [ 4^24, 48^2 ] E23.666 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 24, 24}) Quotient :: dipole Aut^+ = C3 x (C8 : C2) (small group id <48, 24>) Aut = (C2 x D24) : C2 (small group id <96, 115>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^2, Y2^-1 * Y3 * Y2 * Y1, Y2 * Y3 * Y2^-1 * Y1, (Y3 * Y1)^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3)^2, Y2^11 * Y1 * Y2 * Y1, (Y2^-1 * Y1)^24 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 9, 57)(4, 52, 7, 55)(5, 53, 11, 59)(6, 54, 13, 61)(8, 56, 15, 63)(10, 58, 14, 62)(12, 60, 16, 64)(17, 65, 21, 69)(18, 66, 25, 73)(19, 67, 23, 71)(20, 68, 27, 75)(22, 70, 29, 77)(24, 72, 31, 79)(26, 74, 30, 78)(28, 76, 32, 80)(33, 81, 37, 85)(34, 82, 41, 89)(35, 83, 39, 87)(36, 84, 43, 91)(38, 86, 45, 93)(40, 88, 47, 95)(42, 90, 46, 94)(44, 92, 48, 96)(97, 145, 99, 147, 106, 154, 114, 162, 122, 170, 130, 178, 138, 186, 143, 191, 135, 183, 127, 175, 119, 167, 111, 159, 103, 151, 109, 157, 117, 165, 125, 173, 133, 181, 141, 189, 140, 188, 132, 180, 124, 172, 116, 164, 108, 156, 101, 149)(98, 146, 102, 150, 110, 158, 118, 166, 126, 174, 134, 182, 142, 190, 139, 187, 131, 179, 123, 171, 115, 163, 107, 155, 100, 148, 105, 153, 113, 161, 121, 169, 129, 177, 137, 185, 144, 192, 136, 184, 128, 176, 120, 168, 112, 160, 104, 152) L = (1, 100)(2, 103)(3, 102)(4, 97)(5, 104)(6, 99)(7, 98)(8, 101)(9, 109)(10, 113)(11, 111)(12, 115)(13, 105)(14, 117)(15, 107)(16, 119)(17, 106)(18, 118)(19, 108)(20, 120)(21, 110)(22, 114)(23, 112)(24, 116)(25, 125)(26, 129)(27, 127)(28, 131)(29, 121)(30, 133)(31, 123)(32, 135)(33, 122)(34, 134)(35, 124)(36, 136)(37, 126)(38, 130)(39, 128)(40, 132)(41, 141)(42, 144)(43, 143)(44, 142)(45, 137)(46, 140)(47, 139)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 48, 4, 48 ), ( 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48 ) } Outer automorphisms :: reflexible Dual of E23.665 Graph:: bipartite v = 26 e = 96 f = 26 degree seq :: [ 4^24, 48^2 ] E23.667 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 24, 24}) Quotient :: dipole Aut^+ = C24 : C2 (small group id <48, 6>) Aut = (C2 x D24) : C2 (small group id <96, 115>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^3, (R * Y3)^2, (Y1 * Y3^-1)^2, (R * Y2)^2, (Y3^-1, Y2^-1), (R * Y1)^2, (Y2^-1 * Y1 * Y2^-1)^2, Y2 * Y1 * Y3^-1 * Y2^-1 * Y1 * Y2^2, Y2^24 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 11, 59)(4, 52, 10, 58)(5, 53, 16, 64)(6, 54, 8, 56)(7, 55, 19, 67)(9, 57, 24, 72)(12, 60, 25, 73)(13, 61, 30, 78)(14, 62, 28, 76)(15, 63, 34, 82)(17, 65, 20, 68)(18, 66, 37, 85)(21, 69, 31, 79)(22, 70, 41, 89)(23, 71, 43, 91)(26, 74, 38, 86)(27, 75, 40, 88)(29, 77, 39, 87)(32, 80, 36, 84)(33, 81, 44, 92)(35, 83, 42, 90)(45, 93, 47, 95)(46, 94, 48, 96)(97, 145, 99, 147, 108, 156, 127, 175, 143, 191, 139, 187, 131, 179, 111, 159, 100, 148, 109, 157, 128, 176, 115, 163, 136, 184, 120, 168, 135, 183, 114, 162, 102, 150, 110, 158, 129, 177, 137, 185, 144, 192, 134, 182, 113, 161, 101, 149)(98, 146, 103, 151, 116, 164, 126, 174, 142, 190, 130, 178, 140, 188, 119, 167, 104, 152, 117, 165, 125, 173, 107, 155, 123, 171, 112, 160, 132, 180, 122, 170, 106, 154, 118, 166, 138, 186, 124, 172, 141, 189, 133, 181, 121, 169, 105, 153) L = (1, 100)(2, 104)(3, 109)(4, 102)(5, 111)(6, 97)(7, 117)(8, 106)(9, 119)(10, 98)(11, 124)(12, 128)(13, 110)(14, 99)(15, 114)(16, 133)(17, 131)(18, 101)(19, 137)(20, 125)(21, 118)(22, 103)(23, 122)(24, 134)(25, 140)(26, 105)(27, 141)(28, 126)(29, 138)(30, 107)(31, 115)(32, 129)(33, 108)(34, 112)(35, 135)(36, 121)(37, 130)(38, 139)(39, 113)(40, 144)(41, 127)(42, 116)(43, 120)(44, 132)(45, 142)(46, 123)(47, 136)(48, 143)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 48, 4, 48 ), ( 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 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 = 26 e = 96 f = 26 degree seq :: [ 4^24, 48^2 ] E23.668 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 24, 24}) Quotient :: dipole Aut^+ = C24 : C2 (small group id <48, 6>) Aut = (C2 x D24) : C2 (small group id <96, 115>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^4, (Y2, Y3^-1), (Y1 * Y3^-1)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2^-1 * Y3^2 * Y1 * Y2^-1 * Y1, Y2^-1 * Y1 * Y3^-2 * Y2^-1 * Y1, Y2^6 * Y3, Y1 * Y2^3 * Y3^-1 * Y1 * Y2^-3, Y1 * Y2 * Y1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 11, 59)(4, 52, 10, 58)(5, 53, 17, 65)(6, 54, 8, 56)(7, 55, 20, 68)(9, 57, 26, 74)(12, 60, 27, 75)(13, 61, 25, 73)(14, 62, 28, 76)(15, 63, 24, 72)(16, 64, 22, 70)(18, 66, 21, 69)(19, 67, 23, 71)(29, 77, 42, 90)(30, 78, 45, 93)(31, 79, 44, 92)(32, 80, 41, 89)(33, 81, 40, 88)(34, 82, 37, 85)(35, 83, 48, 96)(36, 84, 39, 87)(38, 86, 46, 94)(43, 91, 47, 95)(97, 145, 99, 147, 108, 156, 126, 174, 132, 180, 115, 163, 102, 150, 110, 158, 128, 176, 142, 190, 133, 181, 116, 164, 111, 159, 122, 170, 138, 186, 143, 191, 129, 177, 112, 160, 100, 148, 109, 157, 127, 175, 131, 179, 114, 162, 101, 149)(98, 146, 103, 151, 117, 165, 134, 182, 140, 188, 124, 172, 106, 154, 119, 167, 136, 184, 141, 189, 125, 173, 107, 155, 120, 168, 113, 161, 130, 178, 144, 192, 137, 185, 121, 169, 104, 152, 118, 166, 135, 183, 139, 187, 123, 171, 105, 153) L = (1, 100)(2, 104)(3, 109)(4, 111)(5, 112)(6, 97)(7, 118)(8, 120)(9, 121)(10, 98)(11, 124)(12, 127)(13, 122)(14, 99)(15, 102)(16, 116)(17, 119)(18, 129)(19, 101)(20, 115)(21, 135)(22, 113)(23, 103)(24, 106)(25, 107)(26, 110)(27, 137)(28, 105)(29, 140)(30, 131)(31, 138)(32, 108)(33, 133)(34, 136)(35, 143)(36, 114)(37, 132)(38, 139)(39, 130)(40, 117)(41, 125)(42, 128)(43, 144)(44, 123)(45, 134)(46, 126)(47, 142)(48, 141)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 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 = 26 e = 96 f = 26 degree seq :: [ 4^24, 48^2 ] E23.669 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 24, 24}) Quotient :: dipole Aut^+ = C24 : C2 (small group id <48, 6>) Aut = (C2 x D24) : C2 (small group id <96, 115>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y3 * Y1)^2, (Y2^-1, Y3), (R * Y2)^2, Y3^4, (R * Y3)^2, (R * Y1)^2, (Y1 * Y2^-2)^2, Y1 * Y3^2 * Y2 * Y1 * Y2, Y2 * Y3 * Y1 * Y3^-1 * Y2 * Y1, Y3^-1 * Y2^6, 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 * Y3^2 * Y2^2 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 11, 59)(4, 52, 10, 58)(5, 53, 17, 65)(6, 54, 8, 56)(7, 55, 20, 68)(9, 57, 26, 74)(12, 60, 27, 75)(13, 61, 25, 73)(14, 62, 28, 76)(15, 63, 24, 72)(16, 64, 22, 70)(18, 66, 21, 69)(19, 67, 23, 71)(29, 77, 42, 90)(30, 78, 45, 93)(31, 79, 44, 92)(32, 80, 41, 89)(33, 81, 40, 88)(34, 82, 37, 85)(35, 83, 47, 95)(36, 84, 39, 87)(38, 86, 46, 94)(43, 91, 48, 96)(97, 145, 99, 147, 108, 156, 126, 174, 129, 177, 112, 160, 100, 148, 109, 157, 127, 175, 142, 190, 133, 181, 116, 164, 111, 159, 122, 170, 138, 186, 144, 192, 132, 180, 115, 163, 102, 150, 110, 158, 128, 176, 131, 179, 114, 162, 101, 149)(98, 146, 103, 151, 117, 165, 134, 182, 137, 185, 121, 169, 104, 152, 118, 166, 135, 183, 141, 189, 125, 173, 107, 155, 120, 168, 113, 161, 130, 178, 143, 191, 140, 188, 124, 172, 106, 154, 119, 167, 136, 184, 139, 187, 123, 171, 105, 153) L = (1, 100)(2, 104)(3, 109)(4, 111)(5, 112)(6, 97)(7, 118)(8, 120)(9, 121)(10, 98)(11, 124)(12, 127)(13, 122)(14, 99)(15, 102)(16, 116)(17, 119)(18, 129)(19, 101)(20, 115)(21, 135)(22, 113)(23, 103)(24, 106)(25, 107)(26, 110)(27, 137)(28, 105)(29, 140)(30, 142)(31, 138)(32, 108)(33, 133)(34, 136)(35, 126)(36, 114)(37, 132)(38, 141)(39, 130)(40, 117)(41, 125)(42, 128)(43, 134)(44, 123)(45, 143)(46, 144)(47, 139)(48, 131)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 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 = 26 e = 96 f = 26 degree seq :: [ 4^24, 48^2 ] E23.670 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 24, 24}) Quotient :: dipole Aut^+ = C24 : C2 (small group id <48, 6>) Aut = (C2 x D24) : C2 (small group id <96, 115>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y2, Y3), (R * Y1)^2, (Y3^-1 * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y2^4 * Y3, (Y2 * Y1 * Y2)^2, Y3^6, Y1 * Y3^2 * Y2^-1 * Y1 * Y3^-1 * Y2^-1, Y3^-1 * Y1 * Y3 * Y2^-1 * Y1 * Y2^-1 * Y3^-1, Y3 * Y2 * Y3^2 * Y1 * Y2 * 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 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 11, 59)(4, 52, 10, 58)(5, 53, 17, 65)(6, 54, 8, 56)(7, 55, 21, 69)(9, 57, 27, 75)(12, 60, 28, 76)(13, 61, 34, 82)(14, 62, 32, 80)(15, 63, 30, 78)(16, 64, 40, 88)(18, 66, 22, 70)(19, 67, 43, 91)(20, 68, 25, 73)(23, 71, 39, 87)(24, 72, 44, 92)(26, 74, 36, 84)(29, 77, 37, 85)(31, 79, 38, 86)(33, 81, 48, 96)(35, 83, 47, 95)(41, 89, 46, 94)(42, 90, 45, 93)(97, 145, 99, 147, 108, 156, 115, 163, 102, 150, 110, 158, 131, 179, 140, 188, 116, 164, 133, 181, 141, 189, 117, 165, 134, 182, 123, 171, 144, 192, 135, 183, 111, 159, 132, 180, 137, 185, 112, 160, 100, 148, 109, 157, 114, 162, 101, 149)(98, 146, 103, 151, 118, 166, 125, 173, 106, 154, 120, 168, 142, 190, 128, 176, 126, 174, 139, 187, 129, 177, 107, 155, 127, 175, 113, 161, 138, 186, 130, 178, 121, 169, 136, 184, 143, 191, 122, 170, 104, 152, 119, 167, 124, 172, 105, 153) L = (1, 100)(2, 104)(3, 109)(4, 111)(5, 112)(6, 97)(7, 119)(8, 121)(9, 122)(10, 98)(11, 128)(12, 114)(13, 132)(14, 99)(15, 134)(16, 135)(17, 139)(18, 137)(19, 101)(20, 102)(21, 140)(22, 124)(23, 136)(24, 103)(25, 127)(26, 130)(27, 133)(28, 143)(29, 105)(30, 106)(31, 126)(32, 125)(33, 142)(34, 107)(35, 108)(36, 123)(37, 110)(38, 116)(39, 117)(40, 113)(41, 144)(42, 129)(43, 120)(44, 115)(45, 131)(46, 118)(47, 138)(48, 141)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 48, 4, 48 ), ( 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 26 e = 96 f = 26 degree seq :: [ 4^24, 48^2 ] E23.671 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 24, 24}) Quotient :: dipole Aut^+ = C24 : C2 (small group id <48, 6>) Aut = (C2 x D24) : C2 (small group id <96, 115>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2 * Y3^-1 * Y2, (Y1 * Y3)^2, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, R * Y1 * Y2 * R * Y2^-1 * Y1 * Y3^-1, Y1 * Y2 * Y3^2 * Y2^-1 * Y3^-1 * Y1 * Y3, Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1, Y3 * Y2 * Y1 * Y2^-1 * Y3^-4 * Y1 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 11, 59)(4, 52, 10, 58)(5, 53, 14, 62)(6, 54, 8, 56)(7, 55, 17, 65)(9, 57, 20, 68)(12, 60, 25, 73)(13, 61, 22, 70)(15, 63, 29, 77)(16, 64, 19, 67)(18, 66, 34, 82)(21, 69, 38, 86)(23, 71, 32, 80)(24, 72, 37, 85)(26, 74, 42, 90)(27, 75, 40, 88)(28, 76, 33, 81)(30, 78, 46, 94)(31, 79, 36, 84)(35, 83, 43, 91)(39, 87, 47, 95)(41, 89, 48, 96)(44, 92, 45, 93)(97, 145, 99, 147, 100, 148, 108, 156, 109, 157, 122, 170, 123, 171, 139, 187, 140, 188, 130, 178, 129, 177, 113, 161, 128, 176, 116, 164, 133, 181, 134, 182, 144, 192, 143, 191, 127, 175, 126, 174, 112, 160, 111, 159, 102, 150, 101, 149)(98, 146, 103, 151, 104, 152, 114, 162, 115, 163, 131, 179, 132, 180, 138, 186, 137, 185, 121, 169, 120, 168, 107, 155, 119, 167, 110, 158, 124, 172, 125, 173, 141, 189, 142, 190, 136, 184, 135, 183, 118, 166, 117, 165, 106, 154, 105, 153) L = (1, 100)(2, 104)(3, 108)(4, 109)(5, 99)(6, 97)(7, 114)(8, 115)(9, 103)(10, 98)(11, 110)(12, 122)(13, 123)(14, 125)(15, 101)(16, 102)(17, 116)(18, 131)(19, 132)(20, 134)(21, 105)(22, 106)(23, 124)(24, 119)(25, 107)(26, 139)(27, 140)(28, 141)(29, 142)(30, 111)(31, 112)(32, 133)(33, 128)(34, 113)(35, 138)(36, 137)(37, 144)(38, 143)(39, 117)(40, 118)(41, 120)(42, 121)(43, 130)(44, 129)(45, 136)(46, 135)(47, 126)(48, 127)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 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 = 26 e = 96 f = 26 degree seq :: [ 4^24, 48^2 ] E23.672 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 24, 24}) Quotient :: dipole Aut^+ = C24 : C2 (small group id <48, 6>) Aut = (C2 x D24) : C2 (small group id <96, 115>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y3^-1, Y2), (Y3^-1 * Y1)^2, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y3 * Y1 * Y2 * Y1 * Y2^-1, (Y2^-2 * Y3)^2, (Y2^-2 * Y1)^2, Y3^2 * Y2 * Y3^3 * Y2, Y2^8 * Y3 * Y2^2 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 11, 59)(4, 52, 10, 58)(5, 53, 17, 65)(6, 54, 8, 56)(7, 55, 14, 62)(9, 57, 16, 64)(12, 60, 24, 72)(13, 61, 28, 76)(15, 63, 26, 74)(18, 66, 21, 69)(19, 67, 35, 83)(20, 68, 23, 71)(22, 70, 33, 81)(25, 73, 29, 77)(27, 75, 31, 79)(30, 78, 42, 90)(32, 80, 45, 93)(34, 82, 44, 92)(36, 84, 39, 87)(37, 85, 48, 96)(38, 86, 41, 89)(40, 88, 47, 95)(43, 91, 46, 94)(97, 145, 99, 147, 108, 156, 125, 173, 111, 159, 128, 176, 134, 182, 143, 191, 132, 180, 115, 163, 102, 150, 110, 158, 127, 175, 112, 160, 100, 148, 109, 157, 126, 174, 142, 190, 130, 178, 133, 181, 116, 164, 129, 177, 114, 162, 101, 149)(98, 146, 103, 151, 117, 165, 131, 179, 119, 167, 136, 184, 140, 188, 141, 189, 138, 186, 121, 169, 106, 154, 107, 155, 123, 171, 113, 161, 104, 152, 118, 166, 135, 183, 144, 192, 137, 185, 139, 187, 122, 170, 124, 172, 120, 168, 105, 153) L = (1, 100)(2, 104)(3, 109)(4, 111)(5, 112)(6, 97)(7, 118)(8, 119)(9, 113)(10, 98)(11, 103)(12, 126)(13, 128)(14, 99)(15, 130)(16, 125)(17, 131)(18, 127)(19, 101)(20, 102)(21, 135)(22, 136)(23, 137)(24, 123)(25, 105)(26, 106)(27, 117)(28, 107)(29, 142)(30, 134)(31, 108)(32, 133)(33, 110)(34, 132)(35, 144)(36, 114)(37, 115)(38, 116)(39, 140)(40, 139)(41, 138)(42, 120)(43, 121)(44, 122)(45, 124)(46, 143)(47, 129)(48, 141)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 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 = 26 e = 96 f = 26 degree seq :: [ 4^24, 48^2 ] E23.673 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 24, 24}) Quotient :: halfedge^2 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, Y3 * Y2, R * Y3 * R * Y2, (R * Y1)^2, (Y1^-1 * Y2)^2, Y1^24 ] Map:: R = (1, 50, 2, 53, 5, 57, 9, 61, 13, 65, 17, 69, 21, 73, 25, 77, 29, 81, 33, 85, 37, 89, 41, 93, 45, 92, 44, 88, 40, 84, 36, 80, 32, 76, 28, 72, 24, 68, 20, 64, 16, 60, 12, 56, 8, 52, 4, 49)(3, 55, 7, 59, 11, 63, 15, 67, 19, 71, 23, 75, 27, 79, 31, 83, 35, 87, 39, 91, 43, 95, 47, 96, 48, 94, 46, 90, 42, 86, 38, 82, 34, 78, 30, 74, 26, 70, 22, 66, 18, 62, 14, 58, 10, 54, 6, 51) 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)(49, 51)(50, 54)(52, 55)(53, 58)(56, 59)(57, 62)(60, 63)(61, 66)(64, 67)(65, 70)(68, 71)(69, 74)(72, 75)(73, 78)(76, 79)(77, 82)(80, 83)(81, 86)(84, 87)(85, 90)(88, 91)(89, 94)(92, 95)(93, 96) local type(s) :: { ( 48^48 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 48 f = 2 degree seq :: [ 48^2 ] E23.674 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 24, 24}) Quotient :: halfedge^2 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 * Y3 * R * Y2, (Y3 * Y1^-1)^2, (R * Y1)^2, (Y3 * Y2)^2, (Y1^-1 * Y2)^2, Y2 * Y1^4 * Y3 * Y2 * Y1^-4 * Y3, Y1^-4 * Y3 * Y2 * Y1^-8, Y1^-1 * Y3 * Y1^4 * Y2 * Y1^-7 ] Map:: non-degenerate R = (1, 50, 2, 54, 6, 61, 13, 69, 21, 77, 29, 85, 37, 93, 45, 90, 42, 82, 34, 74, 26, 66, 18, 58, 10, 64, 16, 72, 24, 80, 32, 88, 40, 96, 48, 92, 44, 84, 36, 76, 28, 68, 20, 60, 12, 53, 5, 49)(3, 57, 9, 65, 17, 73, 25, 81, 33, 89, 41, 95, 47, 87, 39, 79, 31, 71, 23, 63, 15, 56, 8, 52, 4, 59, 11, 67, 19, 75, 27, 83, 35, 91, 43, 94, 46, 86, 38, 78, 30, 70, 22, 62, 14, 55, 7, 51) 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, 30)(23, 32)(27, 34)(28, 33)(29, 38)(31, 40)(35, 42)(36, 41)(37, 46)(39, 48)(43, 45)(44, 47)(49, 52)(50, 56)(51, 58)(53, 59)(54, 63)(55, 64)(57, 66)(60, 67)(61, 71)(62, 72)(65, 74)(68, 75)(69, 79)(70, 80)(73, 82)(76, 83)(77, 87)(78, 88)(81, 90)(84, 91)(85, 95)(86, 96)(89, 93)(92, 94) local type(s) :: { ( 48^48 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 48 f = 2 degree seq :: [ 48^2 ] E23.675 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 24, 24}) Quotient :: halfedge^2 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, (Y1 * Y3)^2, R * Y3 * R * Y2, (Y2 * Y1)^2, (R * Y1)^2, (Y2 * Y3)^3, Y1^-4 * Y2 * Y3 * Y1^-4, Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^3 ] Map:: non-degenerate R = (1, 50, 2, 54, 6, 62, 14, 73, 25, 85, 37, 80, 32, 68, 20, 58, 10, 65, 17, 76, 28, 88, 40, 95, 47, 93, 45, 83, 35, 71, 23, 60, 12, 66, 18, 77, 29, 89, 41, 84, 36, 72, 24, 61, 13, 53, 5, 49)(3, 57, 9, 67, 19, 79, 31, 87, 39, 75, 27, 64, 16, 56, 8, 52, 4, 59, 11, 70, 22, 82, 34, 92, 44, 96, 48, 90, 42, 78, 30, 69, 21, 81, 33, 91, 43, 94, 46, 86, 38, 74, 26, 63, 15, 55, 7, 51) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 15)(8, 18)(10, 21)(11, 23)(13, 19)(14, 26)(16, 29)(17, 30)(20, 33)(22, 35)(24, 31)(25, 38)(27, 41)(28, 42)(32, 43)(34, 45)(36, 39)(37, 46)(40, 48)(44, 47)(49, 52)(50, 56)(51, 58)(53, 59)(54, 64)(55, 65)(57, 68)(60, 69)(61, 70)(62, 75)(63, 76)(66, 78)(67, 80)(71, 81)(72, 82)(73, 87)(74, 88)(77, 90)(79, 85)(83, 91)(84, 92)(86, 95)(89, 96)(93, 94) local type(s) :: { ( 48^48 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 48 f = 2 degree seq :: [ 48^2 ] E23.676 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 24, 24}) Quotient :: halfedge^2 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, (Y3 * Y1)^2, R * Y3 * R * Y2, (R * Y1)^2, (Y2 * Y1)^2, Y1 * Y2 * Y1^-2 * Y3 * Y1, (Y3 * Y2)^6, Y2 * Y1 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 * Y1^-1 * Y2 * Y3 ] Map:: non-degenerate R = (1, 50, 2, 54, 6, 62, 14, 60, 12, 66, 18, 72, 24, 79, 31, 78, 30, 82, 34, 88, 40, 94, 46, 93, 45, 96, 48, 91, 43, 84, 36, 77, 29, 81, 33, 75, 27, 68, 20, 58, 10, 65, 17, 61, 13, 53, 5, 49)(3, 57, 9, 67, 19, 73, 25, 69, 21, 76, 28, 83, 35, 89, 41, 85, 37, 92, 44, 95, 47, 90, 42, 86, 38, 87, 39, 80, 32, 74, 26, 70, 22, 71, 23, 64, 16, 56, 8, 52, 4, 59, 11, 63, 15, 55, 7, 51) L = (1, 3)(2, 7)(4, 12)(5, 9)(6, 15)(8, 18)(10, 21)(11, 14)(13, 19)(16, 24)(17, 25)(20, 28)(22, 30)(23, 31)(26, 34)(27, 35)(29, 37)(32, 40)(33, 41)(36, 44)(38, 45)(39, 46)(42, 48)(43, 47)(49, 52)(50, 56)(51, 58)(53, 59)(54, 64)(55, 65)(57, 68)(60, 70)(61, 63)(62, 71)(66, 74)(67, 75)(69, 77)(72, 80)(73, 81)(76, 84)(78, 86)(79, 87)(82, 90)(83, 91)(85, 93)(88, 95)(89, 96)(92, 94) local type(s) :: { ( 48^48 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: bipartite v = 2 e = 48 f = 2 degree seq :: [ 48^2 ] E23.677 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 24, 24}) Quotient :: edge^2 Aut^+ = D48 (small group id <48, 7>) Aut = C2 x D48 (small group id <96, 110>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y1 * Y2, R * Y2 * R * Y1, (Y3 * Y2)^2, (Y3^-1 * Y1)^2, (R * Y3)^2, Y3^24 ] 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, 44, 92, 40, 88, 36, 84, 32, 80, 28, 76, 24, 72, 20, 68, 16, 64, 12, 60, 8, 56, 4, 52)(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, 46, 94, 42, 90, 38, 86, 34, 82, 30, 78, 26, 74, 22, 70, 18, 66, 14, 62, 10, 58, 6, 54)(97, 98)(99, 102)(100, 101)(103, 106)(104, 105)(107, 110)(108, 109)(111, 114)(112, 113)(115, 118)(116, 117)(119, 122)(120, 121)(123, 126)(124, 125)(127, 130)(128, 129)(131, 134)(132, 133)(135, 138)(136, 137)(139, 142)(140, 141)(143, 144)(145, 146)(147, 150)(148, 149)(151, 154)(152, 153)(155, 158)(156, 157)(159, 162)(160, 161)(163, 166)(164, 165)(167, 170)(168, 169)(171, 174)(172, 173)(175, 178)(176, 177)(179, 182)(180, 181)(183, 186)(184, 185)(187, 190)(188, 189)(191, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 96, 96 ), ( 96^48 ) } Outer automorphisms :: reflexible Dual of E23.682 Graph:: simple bipartite v = 50 e = 96 f = 2 degree seq :: [ 2^48, 48^2 ] E23.678 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 24, 24}) Quotient :: edge^2 Aut^+ = D48 (small group id <48, 7>) Aut = C2 x D48 (small group id <96, 110>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3^-1 * Y2)^2, (Y2 * Y1)^2, (Y3 * Y1)^2, Y3^-1 * Y2 * Y1 * Y3 * Y2 * Y1, Y3^5 * Y2 * Y3^-7 * Y1, Y3^2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * 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, 49, 4, 52, 11, 59, 19, 67, 27, 75, 35, 83, 43, 91, 46, 94, 38, 86, 30, 78, 22, 70, 14, 62, 6, 54, 13, 61, 21, 69, 29, 77, 37, 85, 45, 93, 44, 92, 36, 84, 28, 76, 20, 68, 12, 60, 5, 53)(2, 50, 7, 55, 15, 63, 23, 71, 31, 79, 39, 87, 47, 95, 42, 90, 34, 82, 26, 74, 18, 66, 10, 58, 3, 51, 9, 57, 17, 65, 25, 73, 33, 81, 41, 89, 48, 96, 40, 88, 32, 80, 24, 72, 16, 64, 8, 56)(97, 98)(99, 102)(100, 104)(101, 103)(105, 110)(106, 109)(107, 112)(108, 111)(113, 118)(114, 117)(115, 120)(116, 119)(121, 126)(122, 125)(123, 128)(124, 127)(129, 134)(130, 133)(131, 136)(132, 135)(137, 142)(138, 141)(139, 144)(140, 143)(145, 147)(146, 150)(148, 154)(149, 153)(151, 158)(152, 157)(155, 162)(156, 161)(159, 166)(160, 165)(163, 170)(164, 169)(167, 174)(168, 173)(171, 178)(172, 177)(175, 182)(176, 181)(179, 186)(180, 185)(183, 190)(184, 189)(187, 191)(188, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 96, 96 ), ( 96^48 ) } Outer automorphisms :: reflexible Dual of E23.683 Graph:: simple bipartite v = 50 e = 96 f = 2 degree seq :: [ 2^48, 48^2 ] E23.679 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 24, 24}) Quotient :: edge^2 Aut^+ = D48 (small group id <48, 7>) Aut = C2 x D48 (small group id <96, 110>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y1)^2, (Y3 * Y2)^2, (Y2 * Y1)^3, Y3^6 * Y1 * Y3^-2 * Y2, Y3^-2 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-2 ] Map:: R = (1, 49, 4, 52, 12, 60, 23, 71, 35, 83, 44, 92, 32, 80, 20, 68, 9, 57, 19, 67, 31, 79, 43, 91, 48, 96, 40, 88, 28, 76, 16, 64, 6, 54, 15, 63, 27, 75, 39, 87, 36, 84, 24, 72, 13, 61, 5, 53)(2, 50, 7, 55, 17, 65, 29, 77, 41, 89, 47, 95, 38, 86, 26, 74, 14, 62, 25, 73, 37, 85, 46, 94, 45, 93, 34, 82, 22, 70, 11, 59, 3, 51, 10, 58, 21, 69, 33, 81, 42, 90, 30, 78, 18, 66, 8, 56)(97, 98)(99, 105)(100, 104)(101, 103)(102, 110)(106, 116)(107, 115)(108, 114)(109, 113)(111, 122)(112, 121)(117, 128)(118, 127)(119, 126)(120, 125)(123, 134)(124, 133)(129, 140)(130, 139)(131, 138)(132, 137)(135, 143)(136, 142)(141, 144)(145, 147)(146, 150)(148, 155)(149, 154)(151, 160)(152, 159)(153, 158)(156, 166)(157, 165)(161, 172)(162, 171)(163, 170)(164, 169)(167, 178)(168, 177)(173, 184)(174, 183)(175, 182)(176, 181)(179, 189)(180, 186)(185, 192)(187, 191)(188, 190) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 96, 96 ), ( 96^48 ) } Outer automorphisms :: reflexible Dual of E23.684 Graph:: simple bipartite v = 50 e = 96 f = 2 degree seq :: [ 2^48, 48^2 ] E23.680 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 24, 24}) Quotient :: edge^2 Aut^+ = D48 (small group id <48, 7>) Aut = C2 x D48 (small group id <96, 110>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3^-1 * Y1)^2, (Y3^-1 * Y2)^2, Y3 * Y2 * Y3^-3 * Y1, (Y2 * Y1)^6, (Y3 * Y1 * Y2)^24 ] Map:: R = (1, 49, 4, 52, 12, 60, 16, 64, 6, 54, 15, 63, 26, 74, 33, 81, 23, 71, 32, 80, 42, 90, 47, 95, 39, 87, 46, 94, 45, 93, 37, 85, 27, 75, 36, 84, 30, 78, 21, 69, 9, 57, 20, 68, 13, 61, 5, 53)(2, 50, 7, 55, 17, 65, 11, 59, 3, 51, 10, 58, 22, 70, 29, 77, 19, 67, 28, 76, 38, 86, 44, 92, 35, 83, 43, 91, 48, 96, 41, 89, 31, 79, 40, 88, 34, 82, 25, 73, 14, 62, 24, 72, 18, 66, 8, 56)(97, 98)(99, 105)(100, 104)(101, 103)(102, 110)(106, 117)(107, 116)(108, 114)(109, 113)(111, 121)(112, 120)(115, 123)(118, 126)(119, 127)(122, 130)(124, 133)(125, 132)(128, 137)(129, 136)(131, 135)(134, 141)(138, 144)(139, 143)(140, 142)(145, 147)(146, 150)(148, 155)(149, 154)(151, 160)(152, 159)(153, 163)(156, 161)(157, 166)(158, 167)(162, 170)(164, 173)(165, 172)(168, 177)(169, 176)(171, 179)(174, 182)(175, 183)(178, 186)(180, 188)(181, 187)(184, 191)(185, 190)(189, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 96, 96 ), ( 96^48 ) } Outer automorphisms :: reflexible Dual of E23.685 Graph:: simple bipartite v = 50 e = 96 f = 2 degree seq :: [ 2^48, 48^2 ] E23.681 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 24, 24}) Quotient :: edge^2 Aut^+ = D48 (small group id <48, 7>) Aut = C2 x D48 (small group id <96, 110>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, R * Y2 * R * Y1, (R * Y3)^2, Y3 * Y1 * Y3 * Y2^-1, Y2^24, Y1^24 ] Map:: non-degenerate R = (1, 49, 4, 52)(2, 50, 6, 54)(3, 51, 8, 56)(5, 53, 10, 58)(7, 55, 12, 60)(9, 57, 14, 62)(11, 59, 16, 64)(13, 61, 18, 66)(15, 63, 20, 68)(17, 65, 22, 70)(19, 67, 24, 72)(21, 69, 26, 74)(23, 71, 28, 76)(25, 73, 30, 78)(27, 75, 32, 80)(29, 77, 34, 82)(31, 79, 36, 84)(33, 81, 38, 86)(35, 83, 40, 88)(37, 85, 42, 90)(39, 87, 44, 92)(41, 89, 46, 94)(43, 91, 47, 95)(45, 93, 48, 96)(97, 98, 101, 105, 109, 113, 117, 121, 125, 129, 133, 137, 141, 139, 135, 131, 127, 123, 119, 115, 111, 107, 103, 99)(100, 104, 108, 112, 116, 120, 124, 128, 132, 136, 140, 143, 144, 142, 138, 134, 130, 126, 122, 118, 114, 110, 106, 102)(145, 147, 151, 155, 159, 163, 167, 171, 175, 179, 183, 187, 189, 185, 181, 177, 173, 169, 165, 161, 157, 153, 149, 146)(148, 150, 154, 158, 162, 166, 170, 174, 178, 182, 186, 190, 192, 191, 188, 184, 180, 176, 172, 168, 164, 160, 156, 152) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8^4 ), ( 8^24 ) } Outer automorphisms :: reflexible Dual of E23.686 Graph:: simple bipartite v = 28 e = 96 f = 24 degree seq :: [ 4^24, 24^4 ] E23.682 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 24, 24}) Quotient :: loop^2 Aut^+ = D48 (small group id <48, 7>) Aut = C2 x D48 (small group id <96, 110>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y1 * Y2, R * Y2 * R * Y1, (Y3 * Y2)^2, (Y3^-1 * Y1)^2, (R * Y3)^2, Y3^24 ] Map:: R = (1, 49, 97, 145, 3, 51, 99, 147, 7, 55, 103, 151, 11, 59, 107, 155, 15, 63, 111, 159, 19, 67, 115, 163, 23, 71, 119, 167, 27, 75, 123, 171, 31, 79, 127, 175, 35, 83, 131, 179, 39, 87, 135, 183, 43, 91, 139, 187, 47, 95, 143, 191, 44, 92, 140, 188, 40, 88, 136, 184, 36, 84, 132, 180, 32, 80, 128, 176, 28, 76, 124, 172, 24, 72, 120, 168, 20, 68, 116, 164, 16, 64, 112, 160, 12, 60, 108, 156, 8, 56, 104, 152, 4, 52, 100, 148)(2, 50, 98, 146, 5, 53, 101, 149, 9, 57, 105, 153, 13, 61, 109, 157, 17, 65, 113, 161, 21, 69, 117, 165, 25, 73, 121, 169, 29, 77, 125, 173, 33, 81, 129, 177, 37, 85, 133, 181, 41, 89, 137, 185, 45, 93, 141, 189, 48, 96, 144, 192, 46, 94, 142, 190, 42, 90, 138, 186, 38, 86, 134, 182, 34, 82, 130, 178, 30, 78, 126, 174, 26, 74, 122, 170, 22, 70, 118, 166, 18, 66, 114, 162, 14, 62, 110, 158, 10, 58, 106, 154, 6, 54, 102, 150) L = (1, 50)(2, 49)(3, 54)(4, 53)(5, 52)(6, 51)(7, 58)(8, 57)(9, 56)(10, 55)(11, 62)(12, 61)(13, 60)(14, 59)(15, 66)(16, 65)(17, 64)(18, 63)(19, 70)(20, 69)(21, 68)(22, 67)(23, 74)(24, 73)(25, 72)(26, 71)(27, 78)(28, 77)(29, 76)(30, 75)(31, 82)(32, 81)(33, 80)(34, 79)(35, 86)(36, 85)(37, 84)(38, 83)(39, 90)(40, 89)(41, 88)(42, 87)(43, 94)(44, 93)(45, 92)(46, 91)(47, 96)(48, 95)(97, 146)(98, 145)(99, 150)(100, 149)(101, 148)(102, 147)(103, 154)(104, 153)(105, 152)(106, 151)(107, 158)(108, 157)(109, 156)(110, 155)(111, 162)(112, 161)(113, 160)(114, 159)(115, 166)(116, 165)(117, 164)(118, 163)(119, 170)(120, 169)(121, 168)(122, 167)(123, 174)(124, 173)(125, 172)(126, 171)(127, 178)(128, 177)(129, 176)(130, 175)(131, 182)(132, 181)(133, 180)(134, 179)(135, 186)(136, 185)(137, 184)(138, 183)(139, 190)(140, 189)(141, 188)(142, 187)(143, 192)(144, 191) 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 E23.677 Transitivity :: VT+ Graph:: bipartite v = 2 e = 96 f = 50 degree seq :: [ 96^2 ] E23.683 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 24, 24}) Quotient :: loop^2 Aut^+ = D48 (small group id <48, 7>) Aut = C2 x D48 (small group id <96, 110>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3^-1 * Y2)^2, (Y2 * Y1)^2, (Y3 * Y1)^2, Y3^-1 * Y2 * Y1 * Y3 * Y2 * Y1, Y3^5 * Y2 * Y3^-7 * Y1, Y3^2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * 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, 49, 97, 145, 4, 52, 100, 148, 11, 59, 107, 155, 19, 67, 115, 163, 27, 75, 123, 171, 35, 83, 131, 179, 43, 91, 139, 187, 46, 94, 142, 190, 38, 86, 134, 182, 30, 78, 126, 174, 22, 70, 118, 166, 14, 62, 110, 158, 6, 54, 102, 150, 13, 61, 109, 157, 21, 69, 117, 165, 29, 77, 125, 173, 37, 85, 133, 181, 45, 93, 141, 189, 44, 92, 140, 188, 36, 84, 132, 180, 28, 76, 124, 172, 20, 68, 116, 164, 12, 60, 108, 156, 5, 53, 101, 149)(2, 50, 98, 146, 7, 55, 103, 151, 15, 63, 111, 159, 23, 71, 119, 167, 31, 79, 127, 175, 39, 87, 135, 183, 47, 95, 143, 191, 42, 90, 138, 186, 34, 82, 130, 178, 26, 74, 122, 170, 18, 66, 114, 162, 10, 58, 106, 154, 3, 51, 99, 147, 9, 57, 105, 153, 17, 65, 113, 161, 25, 73, 121, 169, 33, 81, 129, 177, 41, 89, 137, 185, 48, 96, 144, 192, 40, 88, 136, 184, 32, 80, 128, 176, 24, 72, 120, 168, 16, 64, 112, 160, 8, 56, 104, 152) L = (1, 50)(2, 49)(3, 54)(4, 56)(5, 55)(6, 51)(7, 53)(8, 52)(9, 62)(10, 61)(11, 64)(12, 63)(13, 58)(14, 57)(15, 60)(16, 59)(17, 70)(18, 69)(19, 72)(20, 71)(21, 66)(22, 65)(23, 68)(24, 67)(25, 78)(26, 77)(27, 80)(28, 79)(29, 74)(30, 73)(31, 76)(32, 75)(33, 86)(34, 85)(35, 88)(36, 87)(37, 82)(38, 81)(39, 84)(40, 83)(41, 94)(42, 93)(43, 96)(44, 95)(45, 90)(46, 89)(47, 92)(48, 91)(97, 147)(98, 150)(99, 145)(100, 154)(101, 153)(102, 146)(103, 158)(104, 157)(105, 149)(106, 148)(107, 162)(108, 161)(109, 152)(110, 151)(111, 166)(112, 165)(113, 156)(114, 155)(115, 170)(116, 169)(117, 160)(118, 159)(119, 174)(120, 173)(121, 164)(122, 163)(123, 178)(124, 177)(125, 168)(126, 167)(127, 182)(128, 181)(129, 172)(130, 171)(131, 186)(132, 185)(133, 176)(134, 175)(135, 190)(136, 189)(137, 180)(138, 179)(139, 191)(140, 192)(141, 184)(142, 183)(143, 187)(144, 188) 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 E23.678 Transitivity :: VT+ Graph:: bipartite v = 2 e = 96 f = 50 degree seq :: [ 96^2 ] E23.684 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 24, 24}) Quotient :: loop^2 Aut^+ = D48 (small group id <48, 7>) Aut = C2 x D48 (small group id <96, 110>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3 * Y1)^2, (Y3 * Y2)^2, (Y2 * Y1)^3, Y3^6 * Y1 * Y3^-2 * Y2, Y3^-2 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-2 ] Map:: R = (1, 49, 97, 145, 4, 52, 100, 148, 12, 60, 108, 156, 23, 71, 119, 167, 35, 83, 131, 179, 44, 92, 140, 188, 32, 80, 128, 176, 20, 68, 116, 164, 9, 57, 105, 153, 19, 67, 115, 163, 31, 79, 127, 175, 43, 91, 139, 187, 48, 96, 144, 192, 40, 88, 136, 184, 28, 76, 124, 172, 16, 64, 112, 160, 6, 54, 102, 150, 15, 63, 111, 159, 27, 75, 123, 171, 39, 87, 135, 183, 36, 84, 132, 180, 24, 72, 120, 168, 13, 61, 109, 157, 5, 53, 101, 149)(2, 50, 98, 146, 7, 55, 103, 151, 17, 65, 113, 161, 29, 77, 125, 173, 41, 89, 137, 185, 47, 95, 143, 191, 38, 86, 134, 182, 26, 74, 122, 170, 14, 62, 110, 158, 25, 73, 121, 169, 37, 85, 133, 181, 46, 94, 142, 190, 45, 93, 141, 189, 34, 82, 130, 178, 22, 70, 118, 166, 11, 59, 107, 155, 3, 51, 99, 147, 10, 58, 106, 154, 21, 69, 117, 165, 33, 81, 129, 177, 42, 90, 138, 186, 30, 78, 126, 174, 18, 66, 114, 162, 8, 56, 104, 152) L = (1, 50)(2, 49)(3, 57)(4, 56)(5, 55)(6, 62)(7, 53)(8, 52)(9, 51)(10, 68)(11, 67)(12, 66)(13, 65)(14, 54)(15, 74)(16, 73)(17, 61)(18, 60)(19, 59)(20, 58)(21, 80)(22, 79)(23, 78)(24, 77)(25, 64)(26, 63)(27, 86)(28, 85)(29, 72)(30, 71)(31, 70)(32, 69)(33, 92)(34, 91)(35, 90)(36, 89)(37, 76)(38, 75)(39, 95)(40, 94)(41, 84)(42, 83)(43, 82)(44, 81)(45, 96)(46, 88)(47, 87)(48, 93)(97, 147)(98, 150)(99, 145)(100, 155)(101, 154)(102, 146)(103, 160)(104, 159)(105, 158)(106, 149)(107, 148)(108, 166)(109, 165)(110, 153)(111, 152)(112, 151)(113, 172)(114, 171)(115, 170)(116, 169)(117, 157)(118, 156)(119, 178)(120, 177)(121, 164)(122, 163)(123, 162)(124, 161)(125, 184)(126, 183)(127, 182)(128, 181)(129, 168)(130, 167)(131, 189)(132, 186)(133, 176)(134, 175)(135, 174)(136, 173)(137, 192)(138, 180)(139, 191)(140, 190)(141, 179)(142, 188)(143, 187)(144, 185) 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 E23.679 Transitivity :: VT+ Graph:: bipartite v = 2 e = 96 f = 50 degree seq :: [ 96^2 ] E23.685 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 24, 24}) Quotient :: loop^2 Aut^+ = D48 (small group id <48, 7>) Aut = C2 x D48 (small group id <96, 110>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, R * Y2 * R * Y1, (R * Y3)^2, (Y3^-1 * Y1)^2, (Y3^-1 * Y2)^2, Y3 * Y2 * Y3^-3 * Y1, (Y2 * Y1)^6, (Y3 * Y1 * Y2)^24 ] Map:: R = (1, 49, 97, 145, 4, 52, 100, 148, 12, 60, 108, 156, 16, 64, 112, 160, 6, 54, 102, 150, 15, 63, 111, 159, 26, 74, 122, 170, 33, 81, 129, 177, 23, 71, 119, 167, 32, 80, 128, 176, 42, 90, 138, 186, 47, 95, 143, 191, 39, 87, 135, 183, 46, 94, 142, 190, 45, 93, 141, 189, 37, 85, 133, 181, 27, 75, 123, 171, 36, 84, 132, 180, 30, 78, 126, 174, 21, 69, 117, 165, 9, 57, 105, 153, 20, 68, 116, 164, 13, 61, 109, 157, 5, 53, 101, 149)(2, 50, 98, 146, 7, 55, 103, 151, 17, 65, 113, 161, 11, 59, 107, 155, 3, 51, 99, 147, 10, 58, 106, 154, 22, 70, 118, 166, 29, 77, 125, 173, 19, 67, 115, 163, 28, 76, 124, 172, 38, 86, 134, 182, 44, 92, 140, 188, 35, 83, 131, 179, 43, 91, 139, 187, 48, 96, 144, 192, 41, 89, 137, 185, 31, 79, 127, 175, 40, 88, 136, 184, 34, 82, 130, 178, 25, 73, 121, 169, 14, 62, 110, 158, 24, 72, 120, 168, 18, 66, 114, 162, 8, 56, 104, 152) L = (1, 50)(2, 49)(3, 57)(4, 56)(5, 55)(6, 62)(7, 53)(8, 52)(9, 51)(10, 69)(11, 68)(12, 66)(13, 65)(14, 54)(15, 73)(16, 72)(17, 61)(18, 60)(19, 75)(20, 59)(21, 58)(22, 78)(23, 79)(24, 64)(25, 63)(26, 82)(27, 67)(28, 85)(29, 84)(30, 70)(31, 71)(32, 89)(33, 88)(34, 74)(35, 87)(36, 77)(37, 76)(38, 93)(39, 83)(40, 81)(41, 80)(42, 96)(43, 95)(44, 94)(45, 86)(46, 92)(47, 91)(48, 90)(97, 147)(98, 150)(99, 145)(100, 155)(101, 154)(102, 146)(103, 160)(104, 159)(105, 163)(106, 149)(107, 148)(108, 161)(109, 166)(110, 167)(111, 152)(112, 151)(113, 156)(114, 170)(115, 153)(116, 173)(117, 172)(118, 157)(119, 158)(120, 177)(121, 176)(122, 162)(123, 179)(124, 165)(125, 164)(126, 182)(127, 183)(128, 169)(129, 168)(130, 186)(131, 171)(132, 188)(133, 187)(134, 174)(135, 175)(136, 191)(137, 190)(138, 178)(139, 181)(140, 180)(141, 192)(142, 185)(143, 184)(144, 189) 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 E23.680 Transitivity :: VT+ Graph:: bipartite v = 2 e = 96 f = 50 degree seq :: [ 96^2 ] E23.686 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 24, 24}) Quotient :: loop^2 Aut^+ = D48 (small group id <48, 7>) Aut = C2 x D48 (small group id <96, 110>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, R * Y2 * R * Y1, (R * Y3)^2, Y3 * Y1 * Y3 * Y2^-1, Y2^24, Y1^24 ] Map:: non-degenerate R = (1, 49, 97, 145, 4, 52, 100, 148)(2, 50, 98, 146, 6, 54, 102, 150)(3, 51, 99, 147, 8, 56, 104, 152)(5, 53, 101, 149, 10, 58, 106, 154)(7, 55, 103, 151, 12, 60, 108, 156)(9, 57, 105, 153, 14, 62, 110, 158)(11, 59, 107, 155, 16, 64, 112, 160)(13, 61, 109, 157, 18, 66, 114, 162)(15, 63, 111, 159, 20, 68, 116, 164)(17, 65, 113, 161, 22, 70, 118, 166)(19, 67, 115, 163, 24, 72, 120, 168)(21, 69, 117, 165, 26, 74, 122, 170)(23, 71, 119, 167, 28, 76, 124, 172)(25, 73, 121, 169, 30, 78, 126, 174)(27, 75, 123, 171, 32, 80, 128, 176)(29, 77, 125, 173, 34, 82, 130, 178)(31, 79, 127, 175, 36, 84, 132, 180)(33, 81, 129, 177, 38, 86, 134, 182)(35, 83, 131, 179, 40, 88, 136, 184)(37, 85, 133, 181, 42, 90, 138, 186)(39, 87, 135, 183, 44, 92, 140, 188)(41, 89, 137, 185, 46, 94, 142, 190)(43, 91, 139, 187, 47, 95, 143, 191)(45, 93, 141, 189, 48, 96, 144, 192) L = (1, 50)(2, 53)(3, 49)(4, 56)(5, 57)(6, 52)(7, 51)(8, 60)(9, 61)(10, 54)(11, 55)(12, 64)(13, 65)(14, 58)(15, 59)(16, 68)(17, 69)(18, 62)(19, 63)(20, 72)(21, 73)(22, 66)(23, 67)(24, 76)(25, 77)(26, 70)(27, 71)(28, 80)(29, 81)(30, 74)(31, 75)(32, 84)(33, 85)(34, 78)(35, 79)(36, 88)(37, 89)(38, 82)(39, 83)(40, 92)(41, 93)(42, 86)(43, 87)(44, 95)(45, 91)(46, 90)(47, 96)(48, 94)(97, 147)(98, 145)(99, 151)(100, 150)(101, 146)(102, 154)(103, 155)(104, 148)(105, 149)(106, 158)(107, 159)(108, 152)(109, 153)(110, 162)(111, 163)(112, 156)(113, 157)(114, 166)(115, 167)(116, 160)(117, 161)(118, 170)(119, 171)(120, 164)(121, 165)(122, 174)(123, 175)(124, 168)(125, 169)(126, 178)(127, 179)(128, 172)(129, 173)(130, 182)(131, 183)(132, 176)(133, 177)(134, 186)(135, 187)(136, 180)(137, 181)(138, 190)(139, 189)(140, 184)(141, 185)(142, 192)(143, 188)(144, 191) local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E23.681 Transitivity :: VT+ Graph:: bipartite v = 24 e = 96 f = 28 degree seq :: [ 8^24 ] E23.687 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 24, 24}) Quotient :: dipole Aut^+ = C24 x C2 (small group id <48, 23>) Aut = C2 x D48 (small group id <96, 110>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y1^2, (R * Y1)^2, (Y3^-1 * Y1)^2, (R * Y3)^2, Y2 * Y1 * Y2^-1 * Y1, (R * Y2 * Y3^-1)^2, Y2^24, (Y3 * Y2^-1)^24 ] 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, 140, 188, 136, 184, 132, 180, 128, 176, 124, 172, 120, 168, 116, 164, 112, 160, 108, 156, 104, 152, 100, 148)(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, 142, 190, 138, 186, 134, 182, 130, 178, 126, 174, 122, 170, 118, 166, 114, 162, 110, 158, 106, 154, 102, 150) 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, 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 = 26 e = 96 f = 26 degree seq :: [ 4^24, 48^2 ] E23.688 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 24, 24}) Quotient :: dipole Aut^+ = D48 (small group id <48, 7>) Aut = C2 x D48 (small group id <96, 110>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y1^2, (R * Y1)^2, (Y3^-1 * Y1)^2, (R * Y3)^2, (Y2 * Y1)^2, (R * Y2 * Y3^-1)^2, Y2^24, (Y3 * Y2^-1)^24 ] Map:: R = (1, 49, 2, 50)(3, 51, 6, 54)(4, 52, 5, 53)(7, 55, 10, 58)(8, 56, 9, 57)(11, 59, 14, 62)(12, 60, 13, 61)(15, 63, 18, 66)(16, 64, 17, 65)(19, 67, 22, 70)(20, 68, 21, 69)(23, 71, 26, 74)(24, 72, 25, 73)(27, 75, 30, 78)(28, 76, 29, 77)(31, 79, 34, 82)(32, 80, 33, 81)(35, 83, 38, 86)(36, 84, 37, 85)(39, 87, 42, 90)(40, 88, 41, 89)(43, 91, 46, 94)(44, 92, 45, 93)(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, 140, 188, 136, 184, 132, 180, 128, 176, 124, 172, 120, 168, 116, 164, 112, 160, 108, 156, 104, 152, 100, 148)(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, 142, 190, 138, 186, 134, 182, 130, 178, 126, 174, 122, 170, 118, 166, 114, 162, 110, 158, 106, 154, 102, 150) 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, 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 = 26 e = 96 f = 26 degree seq :: [ 4^24, 48^2 ] E23.689 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 24, 24}) Quotient :: dipole Aut^+ = C24 x C2 (small group id <48, 23>) Aut = C2 x D48 (small group id <96, 110>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, (R * Y3)^2, (Y3 * Y1)^2, Y3 * Y2 * Y3 * Y2^-1, (R * Y1)^2, (R * Y2)^2, Y2 * Y1 * Y2^-1 * Y1, Y2^12 * Y1 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 6, 54)(4, 52, 7, 55)(5, 53, 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, 44, 92)(42, 90, 45, 93)(43, 91, 46, 94)(47, 95, 48, 96)(97, 145, 99, 147, 105, 153, 113, 161, 121, 169, 129, 177, 137, 185, 136, 184, 128, 176, 120, 168, 112, 160, 104, 152, 98, 146, 102, 150, 109, 157, 117, 165, 125, 173, 133, 181, 140, 188, 132, 180, 124, 172, 116, 164, 108, 156, 101, 149)(100, 148, 106, 154, 114, 162, 122, 170, 130, 178, 138, 186, 143, 191, 142, 190, 135, 183, 127, 175, 119, 167, 111, 159, 103, 151, 110, 158, 118, 166, 126, 174, 134, 182, 141, 189, 144, 192, 139, 187, 131, 179, 123, 171, 115, 163, 107, 155) L = (1, 100)(2, 103)(3, 106)(4, 97)(5, 107)(6, 110)(7, 98)(8, 111)(9, 114)(10, 99)(11, 101)(12, 115)(13, 118)(14, 102)(15, 104)(16, 119)(17, 122)(18, 105)(19, 108)(20, 123)(21, 126)(22, 109)(23, 112)(24, 127)(25, 130)(26, 113)(27, 116)(28, 131)(29, 134)(30, 117)(31, 120)(32, 135)(33, 138)(34, 121)(35, 124)(36, 139)(37, 141)(38, 125)(39, 128)(40, 142)(41, 143)(42, 129)(43, 132)(44, 144)(45, 133)(46, 136)(47, 137)(48, 140)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 48, 4, 48 ), ( 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48 ) } Outer automorphisms :: reflexible Dual of E23.690 Graph:: bipartite v = 26 e = 96 f = 26 degree seq :: [ 4^24, 48^2 ] E23.690 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 24, 24}) Quotient :: dipole Aut^+ = C24 x C2 (small group id <48, 23>) Aut = C2 x D48 (small group id <96, 110>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, (Y3 * Y1)^2, Y3 * Y2 * Y3 * Y2^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2 * Y1 * Y2^-1 * Y1, Y2^2 * Y3 * Y1 * Y2^-2 * Y3 * Y1, Y2^10 * Y3 * Y2^2 * Y1 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 6, 54)(4, 52, 7, 55)(5, 53, 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)(97, 145, 99, 147, 105, 153, 113, 161, 121, 169, 129, 177, 137, 185, 143, 191, 135, 183, 127, 175, 119, 167, 111, 159, 103, 151, 110, 158, 118, 166, 126, 174, 134, 182, 142, 190, 140, 188, 132, 180, 124, 172, 116, 164, 108, 156, 101, 149)(98, 146, 102, 150, 109, 157, 117, 165, 125, 173, 133, 181, 141, 189, 139, 187, 131, 179, 123, 171, 115, 163, 107, 155, 100, 148, 106, 154, 114, 162, 122, 170, 130, 178, 138, 186, 144, 192, 136, 184, 128, 176, 120, 168, 112, 160, 104, 152) L = (1, 100)(2, 103)(3, 106)(4, 97)(5, 107)(6, 110)(7, 98)(8, 111)(9, 114)(10, 99)(11, 101)(12, 115)(13, 118)(14, 102)(15, 104)(16, 119)(17, 122)(18, 105)(19, 108)(20, 123)(21, 126)(22, 109)(23, 112)(24, 127)(25, 130)(26, 113)(27, 116)(28, 131)(29, 134)(30, 117)(31, 120)(32, 135)(33, 138)(34, 121)(35, 124)(36, 139)(37, 142)(38, 125)(39, 128)(40, 143)(41, 144)(42, 129)(43, 132)(44, 141)(45, 140)(46, 133)(47, 136)(48, 137)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 48, 4, 48 ), ( 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48, 4, 48 ) } Outer automorphisms :: reflexible Dual of E23.689 Graph:: bipartite v = 26 e = 96 f = 26 degree seq :: [ 4^24, 48^2 ] E23.691 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 24, 24}) Quotient :: dipole Aut^+ = C24 x C2 (small group id <48, 23>) Aut = C2 x D48 (small group id <96, 110>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, (Y3 * Y1)^2, Y3 * Y2 * Y3 * Y2^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2^-1 * Y1 * Y2 * Y1, Y3 * Y2^12 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 6, 54)(4, 52, 7, 55)(5, 53, 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)(97, 145, 99, 147, 105, 153, 113, 161, 121, 169, 129, 177, 137, 185, 139, 187, 131, 179, 123, 171, 115, 163, 107, 155, 100, 148, 106, 154, 114, 162, 122, 170, 130, 178, 138, 186, 140, 188, 132, 180, 124, 172, 116, 164, 108, 156, 101, 149)(98, 146, 102, 150, 109, 157, 117, 165, 125, 173, 133, 181, 141, 189, 143, 191, 135, 183, 127, 175, 119, 167, 111, 159, 103, 151, 110, 158, 118, 166, 126, 174, 134, 182, 142, 190, 144, 192, 136, 184, 128, 176, 120, 168, 112, 160, 104, 152) L = (1, 100)(2, 103)(3, 106)(4, 97)(5, 107)(6, 110)(7, 98)(8, 111)(9, 114)(10, 99)(11, 101)(12, 115)(13, 118)(14, 102)(15, 104)(16, 119)(17, 122)(18, 105)(19, 108)(20, 123)(21, 126)(22, 109)(23, 112)(24, 127)(25, 130)(26, 113)(27, 116)(28, 131)(29, 134)(30, 117)(31, 120)(32, 135)(33, 138)(34, 121)(35, 124)(36, 139)(37, 142)(38, 125)(39, 128)(40, 143)(41, 140)(42, 129)(43, 132)(44, 137)(45, 144)(46, 133)(47, 136)(48, 141)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 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 = 26 e = 96 f = 26 degree seq :: [ 4^24, 48^2 ] E23.692 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 24, 24}) Quotient :: dipole Aut^+ = D48 (small group id <48, 7>) Aut = C2 x D48 (small group id <96, 110>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, (Y3 * Y1)^2, Y3 * Y2 * Y3 * Y2^-1, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y2^-1 * Y1)^2, Y3 * Y2^12 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 8, 56)(4, 52, 7, 55)(5, 53, 6, 54)(9, 57, 16, 64)(10, 58, 15, 63)(11, 59, 14, 62)(12, 60, 13, 61)(17, 65, 24, 72)(18, 66, 23, 71)(19, 67, 22, 70)(20, 68, 21, 69)(25, 73, 32, 80)(26, 74, 31, 79)(27, 75, 30, 78)(28, 76, 29, 77)(33, 81, 40, 88)(34, 82, 39, 87)(35, 83, 38, 86)(36, 84, 37, 85)(41, 89, 48, 96)(42, 90, 47, 95)(43, 91, 46, 94)(44, 92, 45, 93)(97, 145, 99, 147, 105, 153, 113, 161, 121, 169, 129, 177, 137, 185, 139, 187, 131, 179, 123, 171, 115, 163, 107, 155, 100, 148, 106, 154, 114, 162, 122, 170, 130, 178, 138, 186, 140, 188, 132, 180, 124, 172, 116, 164, 108, 156, 101, 149)(98, 146, 102, 150, 109, 157, 117, 165, 125, 173, 133, 181, 141, 189, 143, 191, 135, 183, 127, 175, 119, 167, 111, 159, 103, 151, 110, 158, 118, 166, 126, 174, 134, 182, 142, 190, 144, 192, 136, 184, 128, 176, 120, 168, 112, 160, 104, 152) L = (1, 100)(2, 103)(3, 106)(4, 97)(5, 107)(6, 110)(7, 98)(8, 111)(9, 114)(10, 99)(11, 101)(12, 115)(13, 118)(14, 102)(15, 104)(16, 119)(17, 122)(18, 105)(19, 108)(20, 123)(21, 126)(22, 109)(23, 112)(24, 127)(25, 130)(26, 113)(27, 116)(28, 131)(29, 134)(30, 117)(31, 120)(32, 135)(33, 138)(34, 121)(35, 124)(36, 139)(37, 142)(38, 125)(39, 128)(40, 143)(41, 140)(42, 129)(43, 132)(44, 137)(45, 144)(46, 133)(47, 136)(48, 141)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 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 = 26 e = 96 f = 26 degree seq :: [ 4^24, 48^2 ] E23.693 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 24, 24}) Quotient :: dipole Aut^+ = D48 (small group id <48, 7>) Aut = C2 x D48 (small group id <96, 110>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^3, (R * Y2)^2, (R * Y3)^2, (Y3, Y2^-1), (Y2 * Y1)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, Y3^-1 * Y2^8, (Y2^-1 * Y3)^24 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 9, 57)(4, 52, 10, 58)(5, 53, 7, 55)(6, 54, 8, 56)(11, 59, 21, 69)(12, 60, 22, 70)(13, 61, 20, 68)(14, 62, 19, 67)(15, 63, 17, 65)(16, 64, 18, 66)(23, 71, 33, 81)(24, 72, 34, 82)(25, 73, 32, 80)(26, 74, 31, 79)(27, 75, 29, 77)(28, 76, 30, 78)(35, 83, 45, 93)(36, 84, 46, 94)(37, 85, 44, 92)(38, 86, 43, 91)(39, 87, 41, 89)(40, 88, 42, 90)(47, 95, 48, 96)(97, 145, 99, 147, 107, 155, 119, 167, 131, 179, 134, 182, 122, 170, 110, 158, 100, 148, 108, 156, 120, 168, 132, 180, 143, 191, 136, 184, 124, 172, 112, 160, 102, 150, 109, 157, 121, 169, 133, 181, 135, 183, 123, 171, 111, 159, 101, 149)(98, 146, 103, 151, 113, 161, 125, 173, 137, 185, 140, 188, 128, 176, 116, 164, 104, 152, 114, 162, 126, 174, 138, 186, 144, 192, 142, 190, 130, 178, 118, 166, 106, 154, 115, 163, 127, 175, 139, 187, 141, 189, 129, 177, 117, 165, 105, 153) L = (1, 100)(2, 104)(3, 108)(4, 102)(5, 110)(6, 97)(7, 114)(8, 106)(9, 116)(10, 98)(11, 120)(12, 109)(13, 99)(14, 112)(15, 122)(16, 101)(17, 126)(18, 115)(19, 103)(20, 118)(21, 128)(22, 105)(23, 132)(24, 121)(25, 107)(26, 124)(27, 134)(28, 111)(29, 138)(30, 127)(31, 113)(32, 130)(33, 140)(34, 117)(35, 143)(36, 133)(37, 119)(38, 136)(39, 131)(40, 123)(41, 144)(42, 139)(43, 125)(44, 142)(45, 137)(46, 129)(47, 135)(48, 141)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 4, 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 = 26 e = 96 f = 26 degree seq :: [ 4^24, 48^2 ] E23.694 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 24, 24}) Quotient :: dipole Aut^+ = D48 (small group id <48, 7>) Aut = C2 x D48 (small group id <96, 110>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^4, (Y3^-1, Y2^-1), (Y3^-1 * Y1)^2, (R * Y1)^2, (Y2^-1 * Y1)^2, (R * Y3)^2, (R * Y2)^2, Y3 * Y2^6, 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 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 9, 57)(4, 52, 10, 58)(5, 53, 7, 55)(6, 54, 8, 56)(11, 59, 23, 71)(12, 60, 24, 72)(13, 61, 22, 70)(14, 62, 21, 69)(15, 63, 20, 68)(16, 64, 18, 66)(17, 65, 19, 67)(25, 73, 39, 87)(26, 74, 40, 88)(27, 75, 38, 86)(28, 76, 37, 85)(29, 77, 36, 84)(30, 78, 35, 83)(31, 79, 33, 81)(32, 80, 34, 82)(41, 89, 48, 96)(42, 90, 47, 95)(43, 91, 46, 94)(44, 92, 45, 93)(97, 145, 99, 147, 107, 155, 121, 169, 128, 176, 113, 161, 102, 150, 109, 157, 123, 171, 137, 185, 139, 187, 125, 173, 110, 158, 124, 172, 138, 186, 140, 188, 126, 174, 111, 159, 100, 148, 108, 156, 122, 170, 127, 175, 112, 160, 101, 149)(98, 146, 103, 151, 114, 162, 129, 177, 136, 184, 120, 168, 106, 154, 116, 164, 131, 179, 141, 189, 143, 191, 133, 181, 117, 165, 132, 180, 142, 190, 144, 192, 134, 182, 118, 166, 104, 152, 115, 163, 130, 178, 135, 183, 119, 167, 105, 153) L = (1, 100)(2, 104)(3, 108)(4, 110)(5, 111)(6, 97)(7, 115)(8, 117)(9, 118)(10, 98)(11, 122)(12, 124)(13, 99)(14, 102)(15, 125)(16, 126)(17, 101)(18, 130)(19, 132)(20, 103)(21, 106)(22, 133)(23, 134)(24, 105)(25, 127)(26, 138)(27, 107)(28, 109)(29, 113)(30, 139)(31, 140)(32, 112)(33, 135)(34, 142)(35, 114)(36, 116)(37, 120)(38, 143)(39, 144)(40, 119)(41, 121)(42, 123)(43, 128)(44, 137)(45, 129)(46, 131)(47, 136)(48, 141)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 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 = 26 e = 96 f = 26 degree seq :: [ 4^24, 48^2 ] E23.695 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 24, 24}) Quotient :: dipole Aut^+ = D48 (small group id <48, 7>) Aut = C2 x D48 (small group id <96, 110>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^4, (Y3^-1, Y2^-1), (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y3)^2, (Y2 * Y1)^2, (R * Y2)^2, Y3^-1 * Y2^6, Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^2 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 9, 57)(4, 52, 10, 58)(5, 53, 7, 55)(6, 54, 8, 56)(11, 59, 23, 71)(12, 60, 24, 72)(13, 61, 22, 70)(14, 62, 21, 69)(15, 63, 20, 68)(16, 64, 18, 66)(17, 65, 19, 67)(25, 73, 39, 87)(26, 74, 40, 88)(27, 75, 38, 86)(28, 76, 37, 85)(29, 77, 36, 84)(30, 78, 35, 83)(31, 79, 33, 81)(32, 80, 34, 82)(41, 89, 48, 96)(42, 90, 47, 95)(43, 91, 46, 94)(44, 92, 45, 93)(97, 145, 99, 147, 107, 155, 121, 169, 126, 174, 111, 159, 100, 148, 108, 156, 122, 170, 137, 185, 139, 187, 125, 173, 110, 158, 124, 172, 138, 186, 140, 188, 128, 176, 113, 161, 102, 150, 109, 157, 123, 171, 127, 175, 112, 160, 101, 149)(98, 146, 103, 151, 114, 162, 129, 177, 134, 182, 118, 166, 104, 152, 115, 163, 130, 178, 141, 189, 143, 191, 133, 181, 117, 165, 132, 180, 142, 190, 144, 192, 136, 184, 120, 168, 106, 154, 116, 164, 131, 179, 135, 183, 119, 167, 105, 153) L = (1, 100)(2, 104)(3, 108)(4, 110)(5, 111)(6, 97)(7, 115)(8, 117)(9, 118)(10, 98)(11, 122)(12, 124)(13, 99)(14, 102)(15, 125)(16, 126)(17, 101)(18, 130)(19, 132)(20, 103)(21, 106)(22, 133)(23, 134)(24, 105)(25, 137)(26, 138)(27, 107)(28, 109)(29, 113)(30, 139)(31, 121)(32, 112)(33, 141)(34, 142)(35, 114)(36, 116)(37, 120)(38, 143)(39, 129)(40, 119)(41, 140)(42, 123)(43, 128)(44, 127)(45, 144)(46, 131)(47, 136)(48, 135)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 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 = 26 e = 96 f = 26 degree seq :: [ 4^24, 48^2 ] E23.696 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 24, 24}) Quotient :: dipole Aut^+ = D48 (small group id <48, 7>) Aut = C2 x D48 (small group id <96, 110>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1)^2, (Y2, Y3^-1), (R * Y2)^2, (Y2^-1 * Y1)^2, Y3 * Y2^4, Y3^6, Y3^2 * Y2^-2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 9, 57)(4, 52, 10, 58)(5, 53, 7, 55)(6, 54, 8, 56)(11, 59, 24, 72)(12, 60, 25, 73)(13, 61, 23, 71)(14, 62, 26, 74)(15, 63, 21, 69)(16, 64, 19, 67)(17, 65, 20, 68)(18, 66, 22, 70)(27, 75, 39, 87)(28, 76, 40, 88)(29, 77, 38, 86)(30, 78, 37, 85)(31, 79, 36, 84)(32, 80, 34, 82)(33, 81, 35, 83)(41, 89, 48, 96)(42, 90, 47, 95)(43, 91, 46, 94)(44, 92, 45, 93)(97, 145, 99, 147, 107, 155, 113, 161, 102, 150, 109, 157, 123, 171, 129, 177, 114, 162, 125, 173, 137, 185, 139, 187, 126, 174, 138, 186, 140, 188, 127, 175, 110, 158, 124, 172, 128, 176, 111, 159, 100, 148, 108, 156, 112, 160, 101, 149)(98, 146, 103, 151, 115, 163, 121, 169, 106, 154, 117, 165, 130, 178, 136, 184, 122, 170, 132, 180, 141, 189, 143, 191, 133, 181, 142, 190, 144, 192, 134, 182, 118, 166, 131, 179, 135, 183, 119, 167, 104, 152, 116, 164, 120, 168, 105, 153) L = (1, 100)(2, 104)(3, 108)(4, 110)(5, 111)(6, 97)(7, 116)(8, 118)(9, 119)(10, 98)(11, 112)(12, 124)(13, 99)(14, 126)(15, 127)(16, 128)(17, 101)(18, 102)(19, 120)(20, 131)(21, 103)(22, 133)(23, 134)(24, 135)(25, 105)(26, 106)(27, 107)(28, 138)(29, 109)(30, 114)(31, 139)(32, 140)(33, 113)(34, 115)(35, 142)(36, 117)(37, 122)(38, 143)(39, 144)(40, 121)(41, 123)(42, 125)(43, 129)(44, 137)(45, 130)(46, 132)(47, 136)(48, 141)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 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 = 26 e = 96 f = 26 degree seq :: [ 4^24, 48^2 ] E23.697 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 24, 24}) Quotient :: dipole Aut^+ = D48 (small group id <48, 7>) Aut = C2 x D48 (small group id <96, 110>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^2 * Y3^-1, (R * Y1)^2, (R * Y2)^2, (Y3^-1 * Y1)^2, (R * Y3)^2, (Y2 * Y1)^2, Y3^12 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 9, 57)(4, 52, 10, 58)(5, 53, 7, 55)(6, 54, 8, 56)(11, 59, 17, 65)(12, 60, 18, 66)(13, 61, 15, 63)(14, 62, 16, 64)(19, 67, 25, 73)(20, 68, 26, 74)(21, 69, 23, 71)(22, 70, 24, 72)(27, 75, 33, 81)(28, 76, 34, 82)(29, 77, 31, 79)(30, 78, 32, 80)(35, 83, 41, 89)(36, 84, 42, 90)(37, 85, 39, 87)(38, 86, 40, 88)(43, 91, 48, 96)(44, 92, 47, 95)(45, 93, 46, 94)(97, 145, 99, 147, 100, 148, 107, 155, 108, 156, 115, 163, 116, 164, 123, 171, 124, 172, 131, 179, 132, 180, 139, 187, 140, 188, 141, 189, 134, 182, 133, 181, 126, 174, 125, 173, 118, 166, 117, 165, 110, 158, 109, 157, 102, 150, 101, 149)(98, 146, 103, 151, 104, 152, 111, 159, 112, 160, 119, 167, 120, 168, 127, 175, 128, 176, 135, 183, 136, 184, 142, 190, 143, 191, 144, 192, 138, 186, 137, 185, 130, 178, 129, 177, 122, 170, 121, 169, 114, 162, 113, 161, 106, 154, 105, 153) L = (1, 100)(2, 104)(3, 107)(4, 108)(5, 99)(6, 97)(7, 111)(8, 112)(9, 103)(10, 98)(11, 115)(12, 116)(13, 101)(14, 102)(15, 119)(16, 120)(17, 105)(18, 106)(19, 123)(20, 124)(21, 109)(22, 110)(23, 127)(24, 128)(25, 113)(26, 114)(27, 131)(28, 132)(29, 117)(30, 118)(31, 135)(32, 136)(33, 121)(34, 122)(35, 139)(36, 140)(37, 125)(38, 126)(39, 142)(40, 143)(41, 129)(42, 130)(43, 141)(44, 134)(45, 133)(46, 144)(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) :: { ( 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 = 26 e = 96 f = 26 degree seq :: [ 4^24, 48^2 ] E23.698 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 24, 24}) Quotient :: dipole Aut^+ = D48 (small group id <48, 7>) Aut = C2 x D48 (small group id <96, 110>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y3^-1, Y2), (R * Y3)^2, (R * Y2)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, (Y2 * Y1)^2, Y2^-1 * Y3 * Y2^-3 * Y3, Y3^2 * Y2 * Y3^3 * Y2 ] Map:: non-degenerate R = (1, 49, 2, 50)(3, 51, 9, 57)(4, 52, 10, 58)(5, 53, 7, 55)(6, 54, 8, 56)(11, 59, 24, 72)(12, 60, 25, 73)(13, 61, 23, 71)(14, 62, 26, 74)(15, 63, 21, 69)(16, 64, 19, 67)(17, 65, 20, 68)(18, 66, 22, 70)(27, 75, 40, 88)(28, 76, 42, 90)(29, 77, 38, 86)(30, 78, 43, 91)(31, 79, 36, 84)(32, 80, 44, 92)(33, 81, 37, 85)(34, 82, 39, 87)(35, 83, 41, 89)(45, 93, 48, 96)(46, 94, 47, 95)(97, 145, 99, 147, 107, 155, 123, 171, 110, 158, 126, 174, 131, 179, 142, 190, 129, 177, 113, 161, 102, 150, 109, 157, 125, 173, 111, 159, 100, 148, 108, 156, 124, 172, 141, 189, 128, 176, 130, 178, 114, 162, 127, 175, 112, 160, 101, 149)(98, 146, 103, 151, 115, 163, 132, 180, 118, 166, 135, 183, 140, 188, 144, 192, 138, 186, 121, 169, 106, 154, 117, 165, 134, 182, 119, 167, 104, 152, 116, 164, 133, 181, 143, 191, 137, 185, 139, 187, 122, 170, 136, 184, 120, 168, 105, 153) L = (1, 100)(2, 104)(3, 108)(4, 110)(5, 111)(6, 97)(7, 116)(8, 118)(9, 119)(10, 98)(11, 124)(12, 126)(13, 99)(14, 128)(15, 123)(16, 125)(17, 101)(18, 102)(19, 133)(20, 135)(21, 103)(22, 137)(23, 132)(24, 134)(25, 105)(26, 106)(27, 141)(28, 131)(29, 107)(30, 130)(31, 109)(32, 129)(33, 112)(34, 113)(35, 114)(36, 143)(37, 140)(38, 115)(39, 139)(40, 117)(41, 138)(42, 120)(43, 121)(44, 122)(45, 142)(46, 127)(47, 144)(48, 136)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 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 = 26 e = 96 f = 26 degree seq :: [ 4^24, 48^2 ] E23.699 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 24, 24}) Quotient :: edge^2 Aut^+ = C3 x (C8 : C2) (small group id <48, 24>) Aut = C6 x (C8 : C2) (small group id <96, 177>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, (R * Y3)^2, R * Y1 * R * Y2, Y3 * Y2^-1 * Y1 * Y3 * Y2 * Y1^-1, Y3 * Y2^2 * Y3 * Y2^-2, Y3 * Y1^2 * Y3 * Y1^-2, Y3 * Y1^-1 * Y3 * Y2 * Y3 * Y1 * Y3 * Y2^-1, Y2^3 * Y3 * Y1^-1 * Y3 * Y2 * Y1^-1 * Y2 * Y1^-3 * Y2 * Y1^-1, Y1^24, Y2^24 ] Map:: non-degenerate R = (1, 49, 4, 52)(2, 50, 6, 54)(3, 51, 8, 56)(5, 53, 12, 60)(7, 55, 16, 64)(9, 57, 18, 66)(10, 58, 19, 67)(11, 59, 21, 69)(13, 61, 23, 71)(14, 62, 24, 72)(15, 63, 26, 74)(17, 65, 28, 76)(20, 68, 30, 78)(22, 70, 32, 80)(25, 73, 34, 82)(27, 75, 36, 84)(29, 77, 38, 86)(31, 79, 40, 88)(33, 81, 42, 90)(35, 83, 44, 92)(37, 85, 46, 94)(39, 87, 48, 96)(41, 89, 47, 95)(43, 91, 45, 93)(97, 98, 101, 107, 116, 125, 133, 141, 140, 132, 124, 115, 120, 114, 119, 128, 136, 144, 137, 129, 121, 111, 103, 99)(100, 105, 108, 118, 126, 135, 142, 138, 131, 122, 113, 104, 110, 102, 109, 117, 127, 134, 143, 139, 130, 123, 112, 106)(145, 147, 151, 159, 169, 177, 185, 192, 184, 176, 167, 162, 168, 163, 172, 180, 188, 189, 181, 173, 164, 155, 149, 146)(148, 154, 160, 171, 178, 187, 191, 182, 175, 165, 157, 150, 158, 152, 161, 170, 179, 186, 190, 183, 174, 166, 156, 153) 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) :: { ( 8^4 ), ( 8^24 ) } Outer automorphisms :: reflexible Dual of E23.702 Graph:: simple bipartite v = 28 e = 96 f = 24 degree seq :: [ 4^24, 24^4 ] E23.700 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 24, 24}) Quotient :: edge^2 Aut^+ = C3 x D16 (small group id <48, 25>) Aut = C6 x D16 (small group id <96, 179>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1 * Y2, R * Y1 * R * Y2, (R * Y3)^2, Y3 * Y1^-1 * Y2^2 * Y3 * Y1^-3, Y3 * Y2 * Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1, Y3 * Y2 * Y3 * Y1 * Y3 * Y2^-1 * Y3 * Y1^-1, Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1^-1, Y2 * Y3 * Y2^2 * Y1^-1 * Y3 * Y1^-2, Y3 * Y1^2 * Y2^-1 * Y3 * Y2^-3, Y3 * Y1^2 * Y2^-1 * Y1 * Y3 * Y1^-4, Y2^2 * Y3 * Y1^2 * Y2^-2 * Y3 * Y1^-2, Y2^24, Y1^24 ] Map:: non-degenerate R = (1, 49, 4, 52)(2, 50, 6, 54)(3, 51, 8, 56)(5, 53, 12, 60)(7, 55, 16, 64)(9, 57, 20, 68)(10, 58, 22, 70)(11, 59, 24, 72)(13, 61, 28, 76)(14, 62, 30, 78)(15, 63, 32, 80)(17, 65, 35, 83)(18, 66, 36, 84)(19, 67, 37, 85)(21, 69, 38, 86)(23, 71, 40, 88)(25, 73, 42, 90)(26, 74, 44, 92)(27, 75, 45, 93)(29, 77, 46, 94)(31, 79, 41, 89)(33, 81, 39, 87)(34, 82, 47, 95)(43, 91, 48, 96)(97, 98, 101, 107, 119, 135, 131, 116, 124, 138, 134, 142, 144, 143, 133, 141, 132, 118, 126, 140, 127, 111, 103, 99)(100, 105, 115, 128, 136, 125, 110, 102, 109, 123, 112, 129, 139, 122, 108, 121, 114, 104, 113, 130, 137, 120, 117, 106)(145, 147, 151, 159, 175, 188, 174, 166, 180, 189, 181, 191, 192, 190, 182, 186, 172, 164, 179, 183, 167, 155, 149, 146)(148, 154, 165, 168, 185, 178, 161, 152, 162, 169, 156, 170, 187, 177, 160, 171, 157, 150, 158, 173, 184, 176, 163, 153) 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) :: { ( 8^4 ), ( 8^24 ) } Outer automorphisms :: reflexible Dual of E23.703 Graph:: simple bipartite v = 28 e = 96 f = 24 degree seq :: [ 4^24, 24^4 ] E23.701 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 24, 24}) Quotient :: edge^2 Aut^+ = C3 x QD16 (small group id <48, 26>) Aut = C6 x QD16 (small group id <96, 180>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1^-1 * Y2^-1, Y1^-2 * Y2^-2, R * Y1 * R * Y2, (R * Y3)^2, Y2 * Y3 * Y1^-1 * Y3 * Y2^2 * Y1^-2, Y1^2 * Y2^-3 * Y3 * Y2^-1 * Y3, Y3 * Y1 * Y3 * Y2 * Y3 * Y1^-1 * Y3 * Y2^-1, Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1^-1, Y3 * Y2 * Y3 * Y1^19, Y2^24 ] Map:: non-degenerate R = (1, 49, 4, 52)(2, 50, 6, 54)(3, 51, 8, 56)(5, 53, 12, 60)(7, 55, 16, 64)(9, 57, 20, 68)(10, 58, 22, 70)(11, 59, 24, 72)(13, 61, 28, 76)(14, 62, 30, 78)(15, 63, 25, 73)(17, 65, 33, 81)(18, 66, 23, 71)(19, 67, 35, 83)(21, 69, 36, 84)(26, 74, 40, 88)(27, 75, 41, 89)(29, 77, 42, 90)(31, 79, 43, 91)(32, 80, 44, 92)(34, 82, 45, 93)(37, 85, 46, 94)(38, 86, 47, 95)(39, 87, 48, 96)(97, 98, 101, 107, 119, 118, 126, 136, 142, 141, 132, 138, 144, 140, 131, 137, 143, 139, 129, 116, 124, 111, 103, 99)(100, 105, 115, 130, 114, 104, 113, 128, 133, 120, 112, 127, 135, 122, 108, 121, 134, 125, 110, 102, 109, 123, 117, 106)(145, 147, 151, 159, 172, 164, 177, 187, 191, 185, 179, 188, 192, 186, 180, 189, 190, 184, 174, 166, 167, 155, 149, 146)(148, 154, 165, 171, 157, 150, 158, 173, 182, 169, 156, 170, 183, 175, 160, 168, 181, 176, 161, 152, 162, 178, 163, 153) 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) :: { ( 8^4 ), ( 8^24 ) } Outer automorphisms :: reflexible Dual of E23.704 Graph:: simple bipartite v = 28 e = 96 f = 24 degree seq :: [ 4^24, 24^4 ] E23.702 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 24, 24}) Quotient :: loop^2 Aut^+ = C3 x (C8 : C2) (small group id <48, 24>) Aut = C6 x (C8 : C2) (small group id <96, 177>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, (R * Y3)^2, R * Y1 * R * Y2, Y3 * Y2^-1 * Y1 * Y3 * Y2 * Y1^-1, Y3 * Y2^2 * Y3 * Y2^-2, Y3 * Y1^2 * Y3 * Y1^-2, Y3 * Y1^-1 * Y3 * Y2 * Y3 * Y1 * Y3 * Y2^-1, Y2^3 * Y3 * Y1^-1 * Y3 * Y2 * Y1^-1 * Y2 * Y1^-3 * Y2 * Y1^-1, Y1^24, Y2^24 ] Map:: non-degenerate R = (1, 49, 97, 145, 4, 52, 100, 148)(2, 50, 98, 146, 6, 54, 102, 150)(3, 51, 99, 147, 8, 56, 104, 152)(5, 53, 101, 149, 12, 60, 108, 156)(7, 55, 103, 151, 16, 64, 112, 160)(9, 57, 105, 153, 18, 66, 114, 162)(10, 58, 106, 154, 19, 67, 115, 163)(11, 59, 107, 155, 21, 69, 117, 165)(13, 61, 109, 157, 23, 71, 119, 167)(14, 62, 110, 158, 24, 72, 120, 168)(15, 63, 111, 159, 26, 74, 122, 170)(17, 65, 113, 161, 28, 76, 124, 172)(20, 68, 116, 164, 30, 78, 126, 174)(22, 70, 118, 166, 32, 80, 128, 176)(25, 73, 121, 169, 34, 82, 130, 178)(27, 75, 123, 171, 36, 84, 132, 180)(29, 77, 125, 173, 38, 86, 134, 182)(31, 79, 127, 175, 40, 88, 136, 184)(33, 81, 129, 177, 42, 90, 138, 186)(35, 83, 131, 179, 44, 92, 140, 188)(37, 85, 133, 181, 46, 94, 142, 190)(39, 87, 135, 183, 48, 96, 144, 192)(41, 89, 137, 185, 47, 95, 143, 191)(43, 91, 139, 187, 45, 93, 141, 189) L = (1, 50)(2, 53)(3, 49)(4, 57)(5, 59)(6, 61)(7, 51)(8, 62)(9, 60)(10, 52)(11, 68)(12, 70)(13, 69)(14, 54)(15, 55)(16, 58)(17, 56)(18, 71)(19, 72)(20, 77)(21, 79)(22, 78)(23, 80)(24, 66)(25, 63)(26, 65)(27, 64)(28, 67)(29, 85)(30, 87)(31, 86)(32, 88)(33, 73)(34, 75)(35, 74)(36, 76)(37, 93)(38, 95)(39, 94)(40, 96)(41, 81)(42, 83)(43, 82)(44, 84)(45, 92)(46, 90)(47, 91)(48, 89)(97, 147)(98, 145)(99, 151)(100, 154)(101, 146)(102, 158)(103, 159)(104, 161)(105, 148)(106, 160)(107, 149)(108, 153)(109, 150)(110, 152)(111, 169)(112, 171)(113, 170)(114, 168)(115, 172)(116, 155)(117, 157)(118, 156)(119, 162)(120, 163)(121, 177)(122, 179)(123, 178)(124, 180)(125, 164)(126, 166)(127, 165)(128, 167)(129, 185)(130, 187)(131, 186)(132, 188)(133, 173)(134, 175)(135, 174)(136, 176)(137, 192)(138, 190)(139, 191)(140, 189)(141, 181)(142, 183)(143, 182)(144, 184) local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E23.699 Transitivity :: VT+ Graph:: bipartite v = 24 e = 96 f = 28 degree seq :: [ 8^24 ] E23.703 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 24, 24}) Quotient :: loop^2 Aut^+ = C3 x D16 (small group id <48, 25>) Aut = C6 x D16 (small group id <96, 179>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1 * Y2, R * Y1 * R * Y2, (R * Y3)^2, Y3 * Y1^-1 * Y2^2 * Y3 * Y1^-3, Y3 * Y2 * Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1, Y3 * Y2 * Y3 * Y1 * Y3 * Y2^-1 * Y3 * Y1^-1, Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1^-1, Y2 * Y3 * Y2^2 * Y1^-1 * Y3 * Y1^-2, Y3 * Y1^2 * Y2^-1 * Y3 * Y2^-3, Y3 * Y1^2 * Y2^-1 * Y1 * Y3 * Y1^-4, Y2^2 * Y3 * Y1^2 * Y2^-2 * Y3 * Y1^-2, Y2^24, Y1^24 ] Map:: non-degenerate R = (1, 49, 97, 145, 4, 52, 100, 148)(2, 50, 98, 146, 6, 54, 102, 150)(3, 51, 99, 147, 8, 56, 104, 152)(5, 53, 101, 149, 12, 60, 108, 156)(7, 55, 103, 151, 16, 64, 112, 160)(9, 57, 105, 153, 20, 68, 116, 164)(10, 58, 106, 154, 22, 70, 118, 166)(11, 59, 107, 155, 24, 72, 120, 168)(13, 61, 109, 157, 28, 76, 124, 172)(14, 62, 110, 158, 30, 78, 126, 174)(15, 63, 111, 159, 32, 80, 128, 176)(17, 65, 113, 161, 35, 83, 131, 179)(18, 66, 114, 162, 36, 84, 132, 180)(19, 67, 115, 163, 37, 85, 133, 181)(21, 69, 117, 165, 38, 86, 134, 182)(23, 71, 119, 167, 40, 88, 136, 184)(25, 73, 121, 169, 42, 90, 138, 186)(26, 74, 122, 170, 44, 92, 140, 188)(27, 75, 123, 171, 45, 93, 141, 189)(29, 77, 125, 173, 46, 94, 142, 190)(31, 79, 127, 175, 41, 89, 137, 185)(33, 81, 129, 177, 39, 87, 135, 183)(34, 82, 130, 178, 47, 95, 143, 191)(43, 91, 139, 187, 48, 96, 144, 192) L = (1, 50)(2, 53)(3, 49)(4, 57)(5, 59)(6, 61)(7, 51)(8, 65)(9, 67)(10, 52)(11, 71)(12, 73)(13, 75)(14, 54)(15, 55)(16, 81)(17, 82)(18, 56)(19, 80)(20, 76)(21, 58)(22, 78)(23, 87)(24, 69)(25, 66)(26, 60)(27, 64)(28, 90)(29, 62)(30, 92)(31, 63)(32, 88)(33, 91)(34, 89)(35, 68)(36, 70)(37, 93)(38, 94)(39, 83)(40, 77)(41, 72)(42, 86)(43, 74)(44, 79)(45, 84)(46, 96)(47, 85)(48, 95)(97, 147)(98, 145)(99, 151)(100, 154)(101, 146)(102, 158)(103, 159)(104, 162)(105, 148)(106, 165)(107, 149)(108, 170)(109, 150)(110, 173)(111, 175)(112, 171)(113, 152)(114, 169)(115, 153)(116, 179)(117, 168)(118, 180)(119, 155)(120, 185)(121, 156)(122, 187)(123, 157)(124, 164)(125, 184)(126, 166)(127, 188)(128, 163)(129, 160)(130, 161)(131, 183)(132, 189)(133, 191)(134, 186)(135, 167)(136, 176)(137, 178)(138, 172)(139, 177)(140, 174)(141, 181)(142, 182)(143, 192)(144, 190) local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E23.700 Transitivity :: VT+ Graph:: bipartite v = 24 e = 96 f = 28 degree seq :: [ 8^24 ] E23.704 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 24, 24}) Quotient :: loop^2 Aut^+ = C3 x QD16 (small group id <48, 26>) Aut = C6 x QD16 (small group id <96, 180>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1^-1 * Y2^-1, Y1^-2 * Y2^-2, R * Y1 * R * Y2, (R * Y3)^2, Y2 * Y3 * Y1^-1 * Y3 * Y2^2 * Y1^-2, Y1^2 * Y2^-3 * Y3 * Y2^-1 * Y3, Y3 * Y1 * Y3 * Y2 * Y3 * Y1^-1 * Y3 * Y2^-1, Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1^-1, Y3 * Y2 * Y3 * Y1^19, Y2^24 ] Map:: non-degenerate R = (1, 49, 97, 145, 4, 52, 100, 148)(2, 50, 98, 146, 6, 54, 102, 150)(3, 51, 99, 147, 8, 56, 104, 152)(5, 53, 101, 149, 12, 60, 108, 156)(7, 55, 103, 151, 16, 64, 112, 160)(9, 57, 105, 153, 20, 68, 116, 164)(10, 58, 106, 154, 22, 70, 118, 166)(11, 59, 107, 155, 24, 72, 120, 168)(13, 61, 109, 157, 28, 76, 124, 172)(14, 62, 110, 158, 30, 78, 126, 174)(15, 63, 111, 159, 25, 73, 121, 169)(17, 65, 113, 161, 33, 81, 129, 177)(18, 66, 114, 162, 23, 71, 119, 167)(19, 67, 115, 163, 35, 83, 131, 179)(21, 69, 117, 165, 36, 84, 132, 180)(26, 74, 122, 170, 40, 88, 136, 184)(27, 75, 123, 171, 41, 89, 137, 185)(29, 77, 125, 173, 42, 90, 138, 186)(31, 79, 127, 175, 43, 91, 139, 187)(32, 80, 128, 176, 44, 92, 140, 188)(34, 82, 130, 178, 45, 93, 141, 189)(37, 85, 133, 181, 46, 94, 142, 190)(38, 86, 134, 182, 47, 95, 143, 191)(39, 87, 135, 183, 48, 96, 144, 192) L = (1, 50)(2, 53)(3, 49)(4, 57)(5, 59)(6, 61)(7, 51)(8, 65)(9, 67)(10, 52)(11, 71)(12, 73)(13, 75)(14, 54)(15, 55)(16, 79)(17, 80)(18, 56)(19, 82)(20, 76)(21, 58)(22, 78)(23, 70)(24, 64)(25, 86)(26, 60)(27, 69)(28, 63)(29, 62)(30, 88)(31, 87)(32, 85)(33, 68)(34, 66)(35, 89)(36, 90)(37, 72)(38, 77)(39, 74)(40, 94)(41, 95)(42, 96)(43, 81)(44, 83)(45, 84)(46, 93)(47, 91)(48, 92)(97, 147)(98, 145)(99, 151)(100, 154)(101, 146)(102, 158)(103, 159)(104, 162)(105, 148)(106, 165)(107, 149)(108, 170)(109, 150)(110, 173)(111, 172)(112, 168)(113, 152)(114, 178)(115, 153)(116, 177)(117, 171)(118, 167)(119, 155)(120, 181)(121, 156)(122, 183)(123, 157)(124, 164)(125, 182)(126, 166)(127, 160)(128, 161)(129, 187)(130, 163)(131, 188)(132, 189)(133, 176)(134, 169)(135, 175)(136, 174)(137, 179)(138, 180)(139, 191)(140, 192)(141, 190)(142, 184)(143, 185)(144, 186) local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E23.701 Transitivity :: VT+ Graph:: bipartite v = 24 e = 96 f = 28 degree seq :: [ 8^24 ] E23.705 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 24, 24}) Quotient :: edge^2 Aut^+ = C3 x D16 (small group id <48, 25>) Aut = C3 x ((C2 x D8) : C2) (small group id <96, 183>) |r| :: 2 Presentation :: [ R^2, Y3^2, (Y2, Y1), (R * Y3)^2, Y1^-1 * Y2^-2 * Y1^-1, (Y1 * Y2)^2, R * Y1 * R * Y2, Y1 * Y3 * Y1^-1 * Y2^-1 * Y3 * Y2, Y3 * Y2^-2 * Y3 * Y2 * Y1^-1, Y3 * Y1 * Y2 * Y3 * Y2^-1 * Y1^-1, Y1 * Y3 * Y1^-2 * Y3 * Y2^-1, Y1^-2 * Y2 * Y3 * Y1^-1 * Y3 * Y1^-2, Y3 * Y1 * Y3 * Y2 * Y3 * Y1 * Y3 * Y1^-1, Y2 * Y3 * Y2^2 * Y1^-1 * Y3 * Y2 * Y1^-1, Y3 * Y1^-1 * Y3 * Y1^7, Y1^-2 * Y2^22 ] Map:: polytopal non-degenerate R = (1, 49, 4, 52)(2, 50, 9, 57)(3, 51, 12, 60)(5, 53, 18, 66)(6, 54, 19, 67)(7, 55, 21, 69)(8, 56, 23, 71)(10, 58, 28, 76)(11, 59, 30, 78)(13, 61, 34, 82)(14, 62, 35, 83)(15, 63, 36, 84)(16, 64, 37, 85)(17, 65, 38, 86)(20, 68, 40, 88)(22, 70, 44, 92)(24, 72, 45, 93)(25, 73, 46, 94)(26, 74, 47, 95)(27, 75, 48, 96)(29, 77, 42, 90)(31, 79, 43, 91)(32, 80, 41, 89)(33, 81, 39, 87)(97, 98, 103, 116, 135, 132, 142, 131, 141, 125, 109, 99, 104, 102, 106, 118, 137, 133, 143, 134, 144, 127, 107, 101)(100, 110, 124, 139, 129, 108, 122, 105, 120, 140, 126, 111, 119, 113, 117, 138, 128, 114, 121, 115, 123, 136, 130, 112)(145, 147, 155, 173, 192, 179, 191, 180, 185, 164, 154, 146, 152, 149, 157, 175, 189, 182, 190, 181, 183, 166, 151, 150)(148, 159, 178, 188, 171, 153, 169, 156, 176, 187, 165, 158, 167, 160, 174, 184, 168, 163, 170, 162, 177, 186, 172, 161) 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) :: { ( 8^4 ), ( 8^24 ) } Outer automorphisms :: reflexible Dual of E23.707 Graph:: simple bipartite v = 28 e = 96 f = 24 degree seq :: [ 4^24, 24^4 ] E23.706 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 24, 24}) Quotient :: edge^2 Aut^+ = C3 x QD16 (small group id <48, 26>) Aut = C3 x ((C2 x D8) : C2) (small group id <96, 183>) |r| :: 2 Presentation :: [ R^2, Y3^2, (Y1, Y2^-1), (R * Y3)^2, R * Y1 * R * Y2, (Y1 * Y2)^2, Y2^-1 * Y1^-2 * Y2^-1, Y3 * Y1 * Y2^-1 * Y3 * Y1^-2, Y3 * Y1^2 * Y3 * Y2 * Y1^-1, Y3 * Y2^-2 * Y3 * Y2 * Y1^-1, Y1 * Y3 * Y1^-2 * Y3 * Y2^-1, Y1^-1 * Y3 * Y1 * Y2 * Y3 * Y2^-1, Y1 * Y3 * Y1^-1 * Y2^-1 * Y3 * Y2, Y3 * Y1 * Y3 * Y2 * Y3 * Y1 * Y3 * Y1^-1, Y3 * Y2^2 * Y1^-1 * Y3 * Y2^3, Y2 * Y3 * Y1^-3 * Y3 * Y1^-2, Y2^-2 * Y1^22, Y1^-2 * Y2^22 ] Map:: polytopal non-degenerate R = (1, 49, 4, 52)(2, 50, 9, 57)(3, 51, 12, 60)(5, 53, 18, 66)(6, 54, 19, 67)(7, 55, 21, 69)(8, 56, 23, 71)(10, 58, 28, 76)(11, 59, 30, 78)(13, 61, 34, 82)(14, 62, 35, 83)(15, 63, 36, 84)(16, 64, 37, 85)(17, 65, 38, 86)(20, 68, 40, 88)(22, 70, 44, 92)(24, 72, 45, 93)(25, 73, 46, 94)(26, 74, 47, 95)(27, 75, 48, 96)(29, 77, 43, 91)(31, 79, 42, 90)(32, 80, 39, 87)(33, 81, 41, 89)(97, 98, 103, 116, 135, 133, 143, 134, 144, 125, 109, 99, 104, 102, 106, 118, 137, 132, 142, 131, 141, 127, 107, 101)(100, 110, 124, 139, 128, 114, 121, 115, 123, 136, 126, 111, 119, 113, 117, 138, 129, 108, 122, 105, 120, 140, 130, 112)(145, 147, 155, 173, 189, 182, 190, 181, 185, 164, 154, 146, 152, 149, 157, 175, 192, 179, 191, 180, 183, 166, 151, 150)(148, 159, 178, 184, 168, 163, 170, 162, 177, 187, 165, 158, 167, 160, 174, 188, 171, 153, 169, 156, 176, 186, 172, 161) 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) :: { ( 8^4 ), ( 8^24 ) } Outer automorphisms :: reflexible Dual of E23.708 Graph:: simple bipartite v = 28 e = 96 f = 24 degree seq :: [ 4^24, 24^4 ] E23.707 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 24, 24}) Quotient :: loop^2 Aut^+ = C3 x D16 (small group id <48, 25>) Aut = C3 x ((C2 x D8) : C2) (small group id <96, 183>) |r| :: 2 Presentation :: [ R^2, Y3^2, (Y2, Y1), (R * Y3)^2, Y1^-1 * Y2^-2 * Y1^-1, (Y1 * Y2)^2, R * Y1 * R * Y2, Y1 * Y3 * Y1^-1 * Y2^-1 * Y3 * Y2, Y3 * Y2^-2 * Y3 * Y2 * Y1^-1, Y3 * Y1 * Y2 * Y3 * Y2^-1 * Y1^-1, Y1 * Y3 * Y1^-2 * Y3 * Y2^-1, Y1^-2 * Y2 * Y3 * Y1^-1 * Y3 * Y1^-2, Y3 * Y1 * Y3 * Y2 * Y3 * Y1 * Y3 * Y1^-1, Y2 * Y3 * Y2^2 * Y1^-1 * Y3 * Y2 * Y1^-1, Y3 * Y1^-1 * Y3 * Y1^7, Y1^-2 * Y2^22 ] Map:: polytopal non-degenerate R = (1, 49, 97, 145, 4, 52, 100, 148)(2, 50, 98, 146, 9, 57, 105, 153)(3, 51, 99, 147, 12, 60, 108, 156)(5, 53, 101, 149, 18, 66, 114, 162)(6, 54, 102, 150, 19, 67, 115, 163)(7, 55, 103, 151, 21, 69, 117, 165)(8, 56, 104, 152, 23, 71, 119, 167)(10, 58, 106, 154, 28, 76, 124, 172)(11, 59, 107, 155, 30, 78, 126, 174)(13, 61, 109, 157, 34, 82, 130, 178)(14, 62, 110, 158, 35, 83, 131, 179)(15, 63, 111, 159, 36, 84, 132, 180)(16, 64, 112, 160, 37, 85, 133, 181)(17, 65, 113, 161, 38, 86, 134, 182)(20, 68, 116, 164, 40, 88, 136, 184)(22, 70, 118, 166, 44, 92, 140, 188)(24, 72, 120, 168, 45, 93, 141, 189)(25, 73, 121, 169, 46, 94, 142, 190)(26, 74, 122, 170, 47, 95, 143, 191)(27, 75, 123, 171, 48, 96, 144, 192)(29, 77, 125, 173, 42, 90, 138, 186)(31, 79, 127, 175, 43, 91, 139, 187)(32, 80, 128, 176, 41, 89, 137, 185)(33, 81, 129, 177, 39, 87, 135, 183) L = (1, 50)(2, 55)(3, 56)(4, 62)(5, 49)(6, 58)(7, 68)(8, 54)(9, 72)(10, 70)(11, 53)(12, 74)(13, 51)(14, 76)(15, 71)(16, 52)(17, 69)(18, 73)(19, 75)(20, 87)(21, 90)(22, 89)(23, 65)(24, 92)(25, 67)(26, 57)(27, 88)(28, 91)(29, 61)(30, 63)(31, 59)(32, 66)(33, 60)(34, 64)(35, 93)(36, 94)(37, 95)(38, 96)(39, 84)(40, 82)(41, 85)(42, 80)(43, 81)(44, 78)(45, 77)(46, 83)(47, 86)(48, 79)(97, 147)(98, 152)(99, 155)(100, 159)(101, 157)(102, 145)(103, 150)(104, 149)(105, 169)(106, 146)(107, 173)(108, 176)(109, 175)(110, 167)(111, 178)(112, 174)(113, 148)(114, 177)(115, 170)(116, 154)(117, 158)(118, 151)(119, 160)(120, 163)(121, 156)(122, 162)(123, 153)(124, 161)(125, 192)(126, 184)(127, 189)(128, 187)(129, 186)(130, 188)(131, 191)(132, 185)(133, 183)(134, 190)(135, 166)(136, 168)(137, 164)(138, 172)(139, 165)(140, 171)(141, 182)(142, 181)(143, 180)(144, 179) local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E23.705 Transitivity :: VT+ Graph:: simple bipartite v = 24 e = 96 f = 28 degree seq :: [ 8^24 ] E23.708 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 24, 24}) Quotient :: loop^2 Aut^+ = C3 x QD16 (small group id <48, 26>) Aut = C3 x ((C2 x D8) : C2) (small group id <96, 183>) |r| :: 2 Presentation :: [ R^2, Y3^2, (Y1, Y2^-1), (R * Y3)^2, R * Y1 * R * Y2, (Y1 * Y2)^2, Y2^-1 * Y1^-2 * Y2^-1, Y3 * Y1 * Y2^-1 * Y3 * Y1^-2, Y3 * Y1^2 * Y3 * Y2 * Y1^-1, Y3 * Y2^-2 * Y3 * Y2 * Y1^-1, Y1 * Y3 * Y1^-2 * Y3 * Y2^-1, Y1^-1 * Y3 * Y1 * Y2 * Y3 * Y2^-1, Y1 * Y3 * Y1^-1 * Y2^-1 * Y3 * Y2, Y3 * Y1 * Y3 * Y2 * Y3 * Y1 * Y3 * Y1^-1, Y3 * Y2^2 * Y1^-1 * Y3 * Y2^3, Y2 * Y3 * Y1^-3 * Y3 * Y1^-2, Y2^-2 * Y1^22, Y1^-2 * Y2^22 ] Map:: polytopal non-degenerate R = (1, 49, 97, 145, 4, 52, 100, 148)(2, 50, 98, 146, 9, 57, 105, 153)(3, 51, 99, 147, 12, 60, 108, 156)(5, 53, 101, 149, 18, 66, 114, 162)(6, 54, 102, 150, 19, 67, 115, 163)(7, 55, 103, 151, 21, 69, 117, 165)(8, 56, 104, 152, 23, 71, 119, 167)(10, 58, 106, 154, 28, 76, 124, 172)(11, 59, 107, 155, 30, 78, 126, 174)(13, 61, 109, 157, 34, 82, 130, 178)(14, 62, 110, 158, 35, 83, 131, 179)(15, 63, 111, 159, 36, 84, 132, 180)(16, 64, 112, 160, 37, 85, 133, 181)(17, 65, 113, 161, 38, 86, 134, 182)(20, 68, 116, 164, 40, 88, 136, 184)(22, 70, 118, 166, 44, 92, 140, 188)(24, 72, 120, 168, 45, 93, 141, 189)(25, 73, 121, 169, 46, 94, 142, 190)(26, 74, 122, 170, 47, 95, 143, 191)(27, 75, 123, 171, 48, 96, 144, 192)(29, 77, 125, 173, 43, 91, 139, 187)(31, 79, 127, 175, 42, 90, 138, 186)(32, 80, 128, 176, 39, 87, 135, 183)(33, 81, 129, 177, 41, 89, 137, 185) L = (1, 50)(2, 55)(3, 56)(4, 62)(5, 49)(6, 58)(7, 68)(8, 54)(9, 72)(10, 70)(11, 53)(12, 74)(13, 51)(14, 76)(15, 71)(16, 52)(17, 69)(18, 73)(19, 75)(20, 87)(21, 90)(22, 89)(23, 65)(24, 92)(25, 67)(26, 57)(27, 88)(28, 91)(29, 61)(30, 63)(31, 59)(32, 66)(33, 60)(34, 64)(35, 93)(36, 94)(37, 95)(38, 96)(39, 85)(40, 78)(41, 84)(42, 81)(43, 80)(44, 82)(45, 79)(46, 83)(47, 86)(48, 77)(97, 147)(98, 152)(99, 155)(100, 159)(101, 157)(102, 145)(103, 150)(104, 149)(105, 169)(106, 146)(107, 173)(108, 176)(109, 175)(110, 167)(111, 178)(112, 174)(113, 148)(114, 177)(115, 170)(116, 154)(117, 158)(118, 151)(119, 160)(120, 163)(121, 156)(122, 162)(123, 153)(124, 161)(125, 189)(126, 188)(127, 192)(128, 186)(129, 187)(130, 184)(131, 191)(132, 183)(133, 185)(134, 190)(135, 166)(136, 168)(137, 164)(138, 172)(139, 165)(140, 171)(141, 182)(142, 181)(143, 180)(144, 179) local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E23.706 Transitivity :: VT+ Graph:: simple bipartite v = 24 e = 96 f = 28 degree seq :: [ 8^24 ] E23.709 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {24, 48, 48}) Quotient :: edge Aut^+ = C48 (small group id <48, 2>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ F^2, T1 * T2^2, (F * T1)^2, (F * T2)^2, T1^24 ] Map:: non-degenerate R = (1, 3, 4, 8, 9, 12, 13, 16, 17, 20, 21, 24, 25, 28, 29, 32, 33, 36, 37, 40, 41, 44, 45, 48, 46, 47, 42, 43, 38, 39, 34, 35, 30, 31, 26, 27, 22, 23, 18, 19, 14, 15, 10, 11, 6, 7, 2, 5)(49, 50, 54, 58, 62, 66, 70, 74, 78, 82, 86, 90, 94, 93, 89, 85, 81, 77, 73, 69, 65, 61, 57, 52)(51, 53, 55, 59, 63, 67, 71, 75, 79, 83, 87, 91, 95, 96, 92, 88, 84, 80, 76, 72, 68, 64, 60, 56) 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) :: { ( 96^24 ), ( 96^48 ) } Outer automorphisms :: reflexible Dual of E23.714 Transitivity :: ET+ Graph:: bipartite v = 3 e = 48 f = 1 degree seq :: [ 24^2, 48 ] E23.710 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {24, 48, 48}) Quotient :: edge Aut^+ = C48 (small group id <48, 2>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T2^-2 * T1^5, T2^9 * T1^-1 * T2, T1^-1 * T2^-1 * T1^-1 * T2^-2 * T1^-1 * T2^-5 * T1^-1, (T1^-1 * T2^-1)^48 ] Map:: non-degenerate R = (1, 3, 9, 19, 30, 40, 39, 29, 18, 8, 2, 7, 17, 28, 38, 48, 42, 32, 22, 16, 6, 15, 27, 37, 47, 43, 33, 23, 11, 21, 14, 26, 36, 46, 44, 34, 24, 12, 4, 10, 20, 31, 41, 45, 35, 25, 13, 5)(49, 50, 54, 62, 68, 57, 65, 75, 84, 89, 78, 86, 95, 92, 83, 87, 90, 81, 72, 61, 66, 70, 59, 52)(51, 55, 63, 74, 79, 67, 76, 85, 94, 93, 88, 96, 91, 82, 73, 77, 80, 71, 60, 53, 56, 64, 69, 58) 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) :: { ( 96^24 ), ( 96^48 ) } Outer automorphisms :: reflexible Dual of E23.716 Transitivity :: ET+ Graph:: bipartite v = 3 e = 48 f = 1 degree seq :: [ 24^2, 48 ] E23.711 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {24, 48, 48}) Quotient :: edge Aut^+ = C48 (small group id <48, 2>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ F^2, (T1^-1, T2), (F * T2)^2, (F * T1)^2, T1^-1 * T2 * T1^-1 * T2^5 * T1^-1, T1^6 * T2^2 * T1, T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^4 ] Map:: non-degenerate R = (1, 3, 9, 19, 33, 28, 14, 27, 37, 45, 47, 40, 24, 12, 4, 10, 20, 34, 30, 16, 6, 15, 29, 43, 48, 46, 39, 23, 11, 21, 35, 32, 18, 8, 2, 7, 17, 31, 44, 42, 26, 38, 22, 36, 41, 25, 13, 5)(49, 50, 54, 62, 74, 87, 72, 61, 66, 78, 81, 92, 96, 95, 89, 83, 68, 57, 65, 77, 85, 70, 59, 52)(51, 55, 63, 75, 86, 71, 60, 53, 56, 64, 76, 90, 94, 88, 73, 80, 82, 67, 79, 91, 93, 84, 69, 58) 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) :: { ( 96^24 ), ( 96^48 ) } Outer automorphisms :: reflexible Dual of E23.715 Transitivity :: ET+ Graph:: bipartite v = 3 e = 48 f = 1 degree seq :: [ 24^2, 48 ] E23.712 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {24, 48, 48}) Quotient :: edge Aut^+ = C48 (small group id <48, 2>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (T1, T2^-1), (F * T1)^2, T1^-2 * T2^-4, T1^11 * T2^-2 ] Map:: non-degenerate R = (1, 3, 9, 19, 11, 21, 28, 35, 30, 37, 44, 48, 46, 41, 31, 40, 34, 25, 14, 24, 18, 8, 2, 7, 17, 12, 4, 10, 20, 27, 22, 29, 36, 43, 38, 45, 39, 47, 42, 33, 23, 32, 26, 16, 6, 15, 13, 5)(49, 50, 54, 62, 71, 79, 87, 92, 84, 76, 68, 57, 65, 61, 66, 74, 82, 90, 94, 86, 78, 70, 59, 52)(51, 55, 63, 72, 80, 88, 95, 96, 91, 83, 75, 67, 60, 53, 56, 64, 73, 81, 89, 93, 85, 77, 69, 58) 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) :: { ( 96^24 ), ( 96^48 ) } Outer automorphisms :: reflexible Dual of E23.717 Transitivity :: ET+ Graph:: bipartite v = 3 e = 48 f = 1 degree seq :: [ 24^2, 48 ] E23.713 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {24, 48, 48}) Quotient :: edge Aut^+ = C48 (small group id <48, 2>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ F^2, (T2^-1, T1), (F * T2)^2, (F * T1)^2, T2^-4 * T1^4, T2^-5 * T1^-7, 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, T2^48, T1^129 * T2^3 ] Map:: non-degenerate R = (1, 3, 9, 19, 26, 38, 47, 43, 34, 22, 32, 18, 8, 2, 7, 17, 31, 37, 46, 44, 35, 23, 11, 21, 30, 16, 6, 15, 29, 40, 45, 41, 36, 24, 12, 4, 10, 20, 28, 14, 27, 39, 48, 42, 33, 25, 13, 5)(49, 50, 54, 62, 74, 85, 93, 90, 82, 71, 60, 53, 56, 64, 76, 67, 79, 88, 96, 91, 83, 72, 61, 66, 78, 68, 57, 65, 77, 87, 95, 92, 84, 73, 80, 69, 58, 51, 55, 63, 75, 86, 94, 89, 81, 70, 59, 52) 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) :: { ( 48^48 ) } Outer automorphisms :: reflexible Dual of E23.718 Transitivity :: ET+ Graph:: bipartite v = 2 e = 48 f = 2 degree seq :: [ 48^2 ] E23.714 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {24, 48, 48}) Quotient :: loop Aut^+ = C48 (small group id <48, 2>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ F^2, T1 * T2^2, (F * T1)^2, (F * T2)^2, T1^24 ] Map:: non-degenerate R = (1, 49, 3, 51, 4, 52, 8, 56, 9, 57, 12, 60, 13, 61, 16, 64, 17, 65, 20, 68, 21, 69, 24, 72, 25, 73, 28, 76, 29, 77, 32, 80, 33, 81, 36, 84, 37, 85, 40, 88, 41, 89, 44, 92, 45, 93, 48, 96, 46, 94, 47, 95, 42, 90, 43, 91, 38, 86, 39, 87, 34, 82, 35, 83, 30, 78, 31, 79, 26, 74, 27, 75, 22, 70, 23, 71, 18, 66, 19, 67, 14, 62, 15, 63, 10, 58, 11, 59, 6, 54, 7, 55, 2, 50, 5, 53) L = (1, 50)(2, 54)(3, 53)(4, 49)(5, 55)(6, 58)(7, 59)(8, 51)(9, 52)(10, 62)(11, 63)(12, 56)(13, 57)(14, 66)(15, 67)(16, 60)(17, 61)(18, 70)(19, 71)(20, 64)(21, 65)(22, 74)(23, 75)(24, 68)(25, 69)(26, 78)(27, 79)(28, 72)(29, 73)(30, 82)(31, 83)(32, 76)(33, 77)(34, 86)(35, 87)(36, 80)(37, 81)(38, 90)(39, 91)(40, 84)(41, 85)(42, 94)(43, 95)(44, 88)(45, 89)(46, 93)(47, 96)(48, 92) local type(s) :: { ( 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48 ) } Outer automorphisms :: reflexible Dual of E23.709 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 48 f = 3 degree seq :: [ 96 ] E23.715 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {24, 48, 48}) Quotient :: loop Aut^+ = C48 (small group id <48, 2>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T2^-2 * T1^5, T2^9 * T1^-1 * T2, T1^-1 * T2^-1 * T1^-1 * T2^-2 * T1^-1 * T2^-5 * T1^-1, (T1^-1 * T2^-1)^48 ] Map:: non-degenerate R = (1, 49, 3, 51, 9, 57, 19, 67, 30, 78, 40, 88, 39, 87, 29, 77, 18, 66, 8, 56, 2, 50, 7, 55, 17, 65, 28, 76, 38, 86, 48, 96, 42, 90, 32, 80, 22, 70, 16, 64, 6, 54, 15, 63, 27, 75, 37, 85, 47, 95, 43, 91, 33, 81, 23, 71, 11, 59, 21, 69, 14, 62, 26, 74, 36, 84, 46, 94, 44, 92, 34, 82, 24, 72, 12, 60, 4, 52, 10, 58, 20, 68, 31, 79, 41, 89, 45, 93, 35, 83, 25, 73, 13, 61, 5, 53) L = (1, 50)(2, 54)(3, 55)(4, 49)(5, 56)(6, 62)(7, 63)(8, 64)(9, 65)(10, 51)(11, 52)(12, 53)(13, 66)(14, 68)(15, 74)(16, 69)(17, 75)(18, 70)(19, 76)(20, 57)(21, 58)(22, 59)(23, 60)(24, 61)(25, 77)(26, 79)(27, 84)(28, 85)(29, 80)(30, 86)(31, 67)(32, 71)(33, 72)(34, 73)(35, 87)(36, 89)(37, 94)(38, 95)(39, 90)(40, 96)(41, 78)(42, 81)(43, 82)(44, 83)(45, 88)(46, 93)(47, 92)(48, 91) local type(s) :: { ( 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48 ) } Outer automorphisms :: reflexible Dual of E23.711 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 48 f = 3 degree seq :: [ 96 ] E23.716 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {24, 48, 48}) Quotient :: loop Aut^+ = C48 (small group id <48, 2>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ F^2, (T1^-1, T2), (F * T2)^2, (F * T1)^2, T1^-1 * T2 * T1^-1 * T2^5 * T1^-1, T1^6 * T2^2 * T1, T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^4 ] Map:: non-degenerate R = (1, 49, 3, 51, 9, 57, 19, 67, 33, 81, 28, 76, 14, 62, 27, 75, 37, 85, 45, 93, 47, 95, 40, 88, 24, 72, 12, 60, 4, 52, 10, 58, 20, 68, 34, 82, 30, 78, 16, 64, 6, 54, 15, 63, 29, 77, 43, 91, 48, 96, 46, 94, 39, 87, 23, 71, 11, 59, 21, 69, 35, 83, 32, 80, 18, 66, 8, 56, 2, 50, 7, 55, 17, 65, 31, 79, 44, 92, 42, 90, 26, 74, 38, 86, 22, 70, 36, 84, 41, 89, 25, 73, 13, 61, 5, 53) L = (1, 50)(2, 54)(3, 55)(4, 49)(5, 56)(6, 62)(7, 63)(8, 64)(9, 65)(10, 51)(11, 52)(12, 53)(13, 66)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 57)(21, 58)(22, 59)(23, 60)(24, 61)(25, 80)(26, 87)(27, 86)(28, 90)(29, 85)(30, 81)(31, 91)(32, 82)(33, 92)(34, 67)(35, 68)(36, 69)(37, 70)(38, 71)(39, 72)(40, 73)(41, 83)(42, 94)(43, 93)(44, 96)(45, 84)(46, 88)(47, 89)(48, 95) local type(s) :: { ( 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48 ) } Outer automorphisms :: reflexible Dual of E23.710 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 48 f = 3 degree seq :: [ 96 ] E23.717 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {24, 48, 48}) Quotient :: loop Aut^+ = C48 (small group id <48, 2>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (T1, T2^-1), (F * T1)^2, T1^-2 * T2^-4, T1^11 * T2^-2 ] Map:: non-degenerate R = (1, 49, 3, 51, 9, 57, 19, 67, 11, 59, 21, 69, 28, 76, 35, 83, 30, 78, 37, 85, 44, 92, 48, 96, 46, 94, 41, 89, 31, 79, 40, 88, 34, 82, 25, 73, 14, 62, 24, 72, 18, 66, 8, 56, 2, 50, 7, 55, 17, 65, 12, 60, 4, 52, 10, 58, 20, 68, 27, 75, 22, 70, 29, 77, 36, 84, 43, 91, 38, 86, 45, 93, 39, 87, 47, 95, 42, 90, 33, 81, 23, 71, 32, 80, 26, 74, 16, 64, 6, 54, 15, 63, 13, 61, 5, 53) L = (1, 50)(2, 54)(3, 55)(4, 49)(5, 56)(6, 62)(7, 63)(8, 64)(9, 65)(10, 51)(11, 52)(12, 53)(13, 66)(14, 71)(15, 72)(16, 73)(17, 61)(18, 74)(19, 60)(20, 57)(21, 58)(22, 59)(23, 79)(24, 80)(25, 81)(26, 82)(27, 67)(28, 68)(29, 69)(30, 70)(31, 87)(32, 88)(33, 89)(34, 90)(35, 75)(36, 76)(37, 77)(38, 78)(39, 92)(40, 95)(41, 93)(42, 94)(43, 83)(44, 84)(45, 85)(46, 86)(47, 96)(48, 91) local type(s) :: { ( 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48, 24, 48 ) } Outer automorphisms :: reflexible Dual of E23.712 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 48 f = 3 degree seq :: [ 96 ] E23.718 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {24, 48, 48}) Quotient :: loop Aut^+ = C48 (small group id <48, 2>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T2^-3 * T1 * T2^-1 * T1 * T2^-1, T1^8 * T2^-1 * T1^2, (T1^-1 * T2^-1)^48 ] Map:: non-degenerate R = (1, 49, 3, 51, 9, 57, 19, 67, 16, 64, 6, 54, 15, 63, 29, 77, 40, 88, 38, 86, 26, 74, 37, 85, 47, 95, 43, 91, 32, 80, 41, 89, 45, 93, 34, 82, 23, 71, 11, 59, 21, 69, 25, 73, 13, 61, 5, 53)(2, 50, 7, 55, 17, 65, 30, 78, 28, 76, 14, 62, 27, 75, 39, 87, 48, 96, 42, 90, 36, 84, 46, 94, 44, 92, 33, 81, 22, 70, 31, 79, 35, 83, 24, 72, 12, 60, 4, 52, 10, 58, 20, 68, 18, 66, 8, 56) L = (1, 50)(2, 54)(3, 55)(4, 49)(5, 56)(6, 62)(7, 63)(8, 64)(9, 65)(10, 51)(11, 52)(12, 53)(13, 66)(14, 74)(15, 75)(16, 76)(17, 77)(18, 67)(19, 78)(20, 57)(21, 58)(22, 59)(23, 60)(24, 61)(25, 68)(26, 84)(27, 85)(28, 86)(29, 87)(30, 88)(31, 69)(32, 70)(33, 71)(34, 72)(35, 73)(36, 89)(37, 94)(38, 90)(39, 95)(40, 96)(41, 79)(42, 80)(43, 81)(44, 82)(45, 83)(46, 93)(47, 92)(48, 91) local type(s) :: { ( 48^48 ) } Outer automorphisms :: reflexible Dual of E23.713 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 48 f = 2 degree seq :: [ 48^2 ] E23.719 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {24, 48, 48}) Quotient :: dipole Aut^+ = C48 (small group id <48, 2>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y2^2 * Y3^-1, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y3^24, Y1^24 ] Map:: R = (1, 49, 2, 50, 6, 54, 10, 58, 14, 62, 18, 66, 22, 70, 26, 74, 30, 78, 34, 82, 38, 86, 42, 90, 46, 94, 45, 93, 41, 89, 37, 85, 33, 81, 29, 77, 25, 73, 21, 69, 17, 65, 13, 61, 9, 57, 4, 52)(3, 51, 5, 53, 7, 55, 11, 59, 15, 63, 19, 67, 23, 71, 27, 75, 31, 79, 35, 83, 39, 87, 43, 91, 47, 95, 48, 96, 44, 92, 40, 88, 36, 84, 32, 80, 28, 76, 24, 72, 20, 68, 16, 64, 12, 60, 8, 56)(97, 145, 99, 147, 100, 148, 104, 152, 105, 153, 108, 156, 109, 157, 112, 160, 113, 161, 116, 164, 117, 165, 120, 168, 121, 169, 124, 172, 125, 173, 128, 176, 129, 177, 132, 180, 133, 181, 136, 184, 137, 185, 140, 188, 141, 189, 144, 192, 142, 190, 143, 191, 138, 186, 139, 187, 134, 182, 135, 183, 130, 178, 131, 179, 126, 174, 127, 175, 122, 170, 123, 171, 118, 166, 119, 167, 114, 162, 115, 163, 110, 158, 111, 159, 106, 154, 107, 155, 102, 150, 103, 151, 98, 146, 101, 149) L = (1, 100)(2, 97)(3, 104)(4, 105)(5, 99)(6, 98)(7, 101)(8, 108)(9, 109)(10, 102)(11, 103)(12, 112)(13, 113)(14, 106)(15, 107)(16, 116)(17, 117)(18, 110)(19, 111)(20, 120)(21, 121)(22, 114)(23, 115)(24, 124)(25, 125)(26, 118)(27, 119)(28, 128)(29, 129)(30, 122)(31, 123)(32, 132)(33, 133)(34, 126)(35, 127)(36, 136)(37, 137)(38, 130)(39, 131)(40, 140)(41, 141)(42, 134)(43, 135)(44, 144)(45, 142)(46, 138)(47, 139)(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, 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 E23.725 Graph:: bipartite v = 3 e = 96 f = 49 degree seq :: [ 48^2, 96 ] E23.720 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {24, 48, 48}) Quotient :: dipole Aut^+ = C48 (small group id <48, 2>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y2)^2, (Y3^-1, Y2^-1), (Y1^-1, Y2), (R * Y3)^2, (R * Y1)^2, Y2^-2 * Y1^2 * Y3^-3, Y1^4 * Y2^-2 * Y3^-1, Y2^-9 * Y3^-1 * Y2^-1, Y3 * Y2^-1 * Y3 * Y2^-2 * Y3 * Y2^-5 * Y1^-1, Y2 * Y3 * Y2^-5 * Y3 * Y2^2 * Y3 * Y2^2 * Y3 * Y2^2 * Y3, Y2 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y1 * Y2^2 ] Map:: R = (1, 49, 2, 50, 6, 54, 14, 62, 20, 68, 9, 57, 17, 65, 27, 75, 36, 84, 41, 89, 30, 78, 38, 86, 47, 95, 44, 92, 35, 83, 39, 87, 42, 90, 33, 81, 24, 72, 13, 61, 18, 66, 22, 70, 11, 59, 4, 52)(3, 51, 7, 55, 15, 63, 26, 74, 31, 79, 19, 67, 28, 76, 37, 85, 46, 94, 45, 93, 40, 88, 48, 96, 43, 91, 34, 82, 25, 73, 29, 77, 32, 80, 23, 71, 12, 60, 5, 53, 8, 56, 16, 64, 21, 69, 10, 58)(97, 145, 99, 147, 105, 153, 115, 163, 126, 174, 136, 184, 135, 183, 125, 173, 114, 162, 104, 152, 98, 146, 103, 151, 113, 161, 124, 172, 134, 182, 144, 192, 138, 186, 128, 176, 118, 166, 112, 160, 102, 150, 111, 159, 123, 171, 133, 181, 143, 191, 139, 187, 129, 177, 119, 167, 107, 155, 117, 165, 110, 158, 122, 170, 132, 180, 142, 190, 140, 188, 130, 178, 120, 168, 108, 156, 100, 148, 106, 154, 116, 164, 127, 175, 137, 185, 141, 189, 131, 179, 121, 169, 109, 157, 101, 149) L = (1, 100)(2, 97)(3, 106)(4, 107)(5, 108)(6, 98)(7, 99)(8, 101)(9, 116)(10, 117)(11, 118)(12, 119)(13, 120)(14, 102)(15, 103)(16, 104)(17, 105)(18, 109)(19, 127)(20, 110)(21, 112)(22, 114)(23, 128)(24, 129)(25, 130)(26, 111)(27, 113)(28, 115)(29, 121)(30, 137)(31, 122)(32, 125)(33, 138)(34, 139)(35, 140)(36, 123)(37, 124)(38, 126)(39, 131)(40, 141)(41, 132)(42, 135)(43, 144)(44, 143)(45, 142)(46, 133)(47, 134)(48, 136)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 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, 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 E23.727 Graph:: bipartite v = 3 e = 96 f = 49 degree seq :: [ 48^2, 96 ] E23.721 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {24, 48, 48}) Quotient :: dipole Aut^+ = C48 (small group id <48, 2>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, Y3 * Y2^-1 * Y1 * Y2, Y2^-1 * Y3^-1 * Y2 * Y1^-1, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y1^3 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-2, Y1 * Y2^-1 * Y3^-1 * Y2^-1 * Y1 * Y2^-4, Y3^2 * Y2^-2 * Y3^2 * Y2^-2 * Y3^2 * Y2^2 * Y1^-1, Y3^24, Y2^-3 * Y1^-1 * Y2^-1 * Y1^3 * Y2^-1 * Y3^-1 * Y1^3 * Y2^-1 * Y3^-1 * Y1^3 * Y2^-1 * Y3^-1 * Y1^3 * Y2^-1 * Y3^-1 * Y1^3 * Y2^-1 * Y3^-1 * Y1^3 * Y2^-1 * Y3^-1 * Y1^3 * Y2^-1 * Y3^-1 * Y1^3 * Y2^-1 * Y3^-1 * Y1^3 * Y2^-1 * Y3^-1 * Y1^3 * Y2^-1 * Y3^-1 * Y1^3 * Y2^-1 * Y3^-1 * Y1^3 * Y2^-1 * Y3^-1 * Y1^3 * Y2^-1 * Y3^-1 * Y1^3 * Y2^-1 * Y3^-1 * Y1^2 ] Map:: R = (1, 49, 2, 50, 6, 54, 14, 62, 26, 74, 39, 87, 24, 72, 13, 61, 18, 66, 30, 78, 33, 81, 44, 92, 48, 96, 47, 95, 41, 89, 35, 83, 20, 68, 9, 57, 17, 65, 29, 77, 37, 85, 22, 70, 11, 59, 4, 52)(3, 51, 7, 55, 15, 63, 27, 75, 38, 86, 23, 71, 12, 60, 5, 53, 8, 56, 16, 64, 28, 76, 42, 90, 46, 94, 40, 88, 25, 73, 32, 80, 34, 82, 19, 67, 31, 79, 43, 91, 45, 93, 36, 84, 21, 69, 10, 58)(97, 145, 99, 147, 105, 153, 115, 163, 129, 177, 124, 172, 110, 158, 123, 171, 133, 181, 141, 189, 143, 191, 136, 184, 120, 168, 108, 156, 100, 148, 106, 154, 116, 164, 130, 178, 126, 174, 112, 160, 102, 150, 111, 159, 125, 173, 139, 187, 144, 192, 142, 190, 135, 183, 119, 167, 107, 155, 117, 165, 131, 179, 128, 176, 114, 162, 104, 152, 98, 146, 103, 151, 113, 161, 127, 175, 140, 188, 138, 186, 122, 170, 134, 182, 118, 166, 132, 180, 137, 185, 121, 169, 109, 157, 101, 149) L = (1, 100)(2, 97)(3, 106)(4, 107)(5, 108)(6, 98)(7, 99)(8, 101)(9, 116)(10, 117)(11, 118)(12, 119)(13, 120)(14, 102)(15, 103)(16, 104)(17, 105)(18, 109)(19, 130)(20, 131)(21, 132)(22, 133)(23, 134)(24, 135)(25, 136)(26, 110)(27, 111)(28, 112)(29, 113)(30, 114)(31, 115)(32, 121)(33, 126)(34, 128)(35, 137)(36, 141)(37, 125)(38, 123)(39, 122)(40, 142)(41, 143)(42, 124)(43, 127)(44, 129)(45, 139)(46, 138)(47, 144)(48, 140)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 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, 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 E23.726 Graph:: bipartite v = 3 e = 96 f = 49 degree seq :: [ 48^2, 96 ] E23.722 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {24, 48, 48}) Quotient :: dipole Aut^+ = C48 (small group id <48, 2>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, Y1 * Y3, (Y2, Y1^-1), (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, Y1^-1 * Y2^-4 * Y1^-1, Y3^-3 * Y2 * Y3^3 * Y2^-1, Y1^3 * Y2^-1 * Y3^-2 * Y2^-1 * Y3^-6, Y1^3 * Y2^-1 * Y3^-2 * Y1 * Y3^-5 * Y2^-1, Y1^7 * Y3^-4 * Y2^-2, Y2^2 * Y3^2 * Y2 * Y1^-2 * Y2 * Y3^3 * Y2 * Y1^-1 * Y2 * Y3, Y3^24, Y3 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 ] Map:: R = (1, 49, 2, 50, 6, 54, 14, 62, 23, 71, 31, 79, 39, 87, 44, 92, 36, 84, 28, 76, 20, 68, 9, 57, 17, 65, 13, 61, 18, 66, 26, 74, 34, 82, 42, 90, 46, 94, 38, 86, 30, 78, 22, 70, 11, 59, 4, 52)(3, 51, 7, 55, 15, 63, 24, 72, 32, 80, 40, 88, 47, 95, 48, 96, 43, 91, 35, 83, 27, 75, 19, 67, 12, 60, 5, 53, 8, 56, 16, 64, 25, 73, 33, 81, 41, 89, 45, 93, 37, 85, 29, 77, 21, 69, 10, 58)(97, 145, 99, 147, 105, 153, 115, 163, 107, 155, 117, 165, 124, 172, 131, 179, 126, 174, 133, 181, 140, 188, 144, 192, 142, 190, 137, 185, 127, 175, 136, 184, 130, 178, 121, 169, 110, 158, 120, 168, 114, 162, 104, 152, 98, 146, 103, 151, 113, 161, 108, 156, 100, 148, 106, 154, 116, 164, 123, 171, 118, 166, 125, 173, 132, 180, 139, 187, 134, 182, 141, 189, 135, 183, 143, 191, 138, 186, 129, 177, 119, 167, 128, 176, 122, 170, 112, 160, 102, 150, 111, 159, 109, 157, 101, 149) L = (1, 100)(2, 97)(3, 106)(4, 107)(5, 108)(6, 98)(7, 99)(8, 101)(9, 116)(10, 117)(11, 118)(12, 115)(13, 113)(14, 102)(15, 103)(16, 104)(17, 105)(18, 109)(19, 123)(20, 124)(21, 125)(22, 126)(23, 110)(24, 111)(25, 112)(26, 114)(27, 131)(28, 132)(29, 133)(30, 134)(31, 119)(32, 120)(33, 121)(34, 122)(35, 139)(36, 140)(37, 141)(38, 142)(39, 127)(40, 128)(41, 129)(42, 130)(43, 144)(44, 135)(45, 137)(46, 138)(47, 136)(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, 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 E23.728 Graph:: bipartite v = 3 e = 96 f = 49 degree seq :: [ 48^2, 96 ] E23.723 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {24, 48, 48}) Quotient :: dipole Aut^+ = C48 (small group id <48, 2>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (Y2^-1, Y1), (R * Y3)^2, Y2^2 * Y1^-1 * Y2 * Y1^-3 * Y2, Y2^-10 * Y1^-1 * Y2^-1, Y1^-3 * Y2^-1 * Y1^-1 * Y2^-2 * Y1^-5, (Y3^-1 * Y1^-1)^24 ] Map:: R = (1, 49, 2, 50, 6, 54, 14, 62, 26, 74, 37, 85, 45, 93, 44, 92, 36, 84, 25, 73, 32, 80, 21, 69, 10, 58, 3, 51, 7, 55, 15, 63, 27, 75, 38, 86, 46, 94, 43, 91, 35, 83, 24, 72, 13, 61, 18, 66, 30, 78, 20, 68, 9, 57, 17, 65, 29, 77, 39, 87, 47, 95, 42, 90, 34, 82, 23, 71, 12, 60, 5, 53, 8, 56, 16, 64, 28, 76, 19, 67, 31, 79, 40, 88, 48, 96, 41, 89, 33, 81, 22, 70, 11, 59, 4, 52)(97, 145, 99, 147, 105, 153, 115, 163, 122, 170, 134, 182, 143, 191, 137, 185, 132, 180, 120, 168, 108, 156, 100, 148, 106, 154, 116, 164, 124, 172, 110, 158, 123, 171, 135, 183, 144, 192, 140, 188, 131, 179, 119, 167, 107, 155, 117, 165, 126, 174, 112, 160, 102, 150, 111, 159, 125, 173, 136, 184, 141, 189, 139, 187, 130, 178, 118, 166, 128, 176, 114, 162, 104, 152, 98, 146, 103, 151, 113, 161, 127, 175, 133, 181, 142, 190, 138, 186, 129, 177, 121, 169, 109, 157, 101, 149) L = (1, 99)(2, 103)(3, 105)(4, 106)(5, 97)(6, 111)(7, 113)(8, 98)(9, 115)(10, 116)(11, 117)(12, 100)(13, 101)(14, 123)(15, 125)(16, 102)(17, 127)(18, 104)(19, 122)(20, 124)(21, 126)(22, 128)(23, 107)(24, 108)(25, 109)(26, 134)(27, 135)(28, 110)(29, 136)(30, 112)(31, 133)(32, 114)(33, 121)(34, 118)(35, 119)(36, 120)(37, 142)(38, 143)(39, 144)(40, 141)(41, 132)(42, 129)(43, 130)(44, 131)(45, 139)(46, 138)(47, 137)(48, 140)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 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 E23.724 Graph:: bipartite v = 2 e = 96 f = 50 degree seq :: [ 96^2 ] E23.724 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {24, 48, 48}) Quotient :: dipole Aut^+ = C48 (small group id <48, 2>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ Y1, R^2, (Y3^-1, Y2^-1), (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y2^3 * Y3 * Y2 * Y3 * Y2, Y2 * Y3^-1 * Y2^2 * Y3^4 * Y2^2 * Y3^-1, Y3 * Y2 * Y3^9, Y3^4 * Y2^-1 * Y3^4 * Y2^-3, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1, (Y3^-1 * Y1^-1)^48 ] 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, 110, 158, 120, 168, 109, 157, 114, 162, 123, 171, 132, 180, 140, 188, 131, 179, 135, 183, 143, 191, 137, 185, 126, 174, 134, 182, 139, 187, 128, 176, 116, 164, 105, 153, 113, 161, 118, 166, 107, 155, 100, 148)(99, 147, 103, 151, 111, 159, 119, 167, 108, 156, 101, 149, 104, 152, 112, 160, 122, 170, 130, 178, 121, 169, 125, 173, 133, 181, 142, 190, 136, 184, 141, 189, 144, 192, 138, 186, 127, 175, 115, 163, 124, 172, 129, 177, 117, 165, 106, 154) L = (1, 99)(2, 103)(3, 105)(4, 106)(5, 97)(6, 111)(7, 113)(8, 98)(9, 115)(10, 116)(11, 117)(12, 100)(13, 101)(14, 119)(15, 118)(16, 102)(17, 124)(18, 104)(19, 126)(20, 127)(21, 128)(22, 129)(23, 107)(24, 108)(25, 109)(26, 110)(27, 112)(28, 134)(29, 114)(30, 136)(31, 137)(32, 138)(33, 139)(34, 120)(35, 121)(36, 122)(37, 123)(38, 141)(39, 125)(40, 140)(41, 142)(42, 143)(43, 144)(44, 130)(45, 131)(46, 132)(47, 133)(48, 135)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 96, 96 ), ( 96^48 ) } Outer automorphisms :: reflexible Dual of E23.723 Graph:: simple bipartite v = 50 e = 96 f = 2 degree seq :: [ 2^48, 48^2 ] E23.725 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {24, 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 * Y1^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^24, (Y3 * Y2^-1)^24 ] Map:: R = (1, 49, 2, 50, 5, 53, 6, 54, 9, 57, 10, 58, 13, 61, 14, 62, 17, 65, 18, 66, 21, 69, 22, 70, 25, 73, 26, 74, 29, 77, 30, 78, 33, 81, 34, 82, 37, 85, 38, 86, 41, 89, 42, 90, 45, 93, 46, 94, 47, 95, 48, 96, 43, 91, 44, 92, 39, 87, 40, 88, 35, 83, 36, 84, 31, 79, 32, 80, 27, 75, 28, 76, 23, 71, 24, 72, 19, 67, 20, 68, 15, 63, 16, 64, 11, 59, 12, 60, 7, 55, 8, 56, 3, 51, 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, 100)(3, 103)(4, 104)(5, 97)(6, 98)(7, 107)(8, 108)(9, 101)(10, 102)(11, 111)(12, 112)(13, 105)(14, 106)(15, 115)(16, 116)(17, 109)(18, 110)(19, 119)(20, 120)(21, 113)(22, 114)(23, 123)(24, 124)(25, 117)(26, 118)(27, 127)(28, 128)(29, 121)(30, 122)(31, 131)(32, 132)(33, 125)(34, 126)(35, 135)(36, 136)(37, 129)(38, 130)(39, 139)(40, 140)(41, 133)(42, 134)(43, 143)(44, 144)(45, 137)(46, 138)(47, 141)(48, 142)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 48, 96 ), ( 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96 ) } Outer automorphisms :: reflexible Dual of E23.719 Graph:: bipartite v = 49 e = 96 f = 3 degree seq :: [ 2^48, 96 ] E23.726 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {24, 48, 48}) Quotient :: dipole Aut^+ = C48 (small group id <48, 2>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y1, Y3^-1), (R * Y2 * Y3^-1)^2, Y3^-3 * Y1 * Y3^-1 * Y1 * Y3^-1, Y1^2 * Y3^-1 * Y1^8, (Y3 * Y2^-1)^24, (Y1^-1 * Y3^-1)^48 ] Map:: R = (1, 49, 2, 50, 6, 54, 14, 62, 26, 74, 36, 84, 41, 89, 31, 79, 21, 69, 10, 58, 3, 51, 7, 55, 15, 63, 27, 75, 37, 85, 46, 94, 45, 93, 35, 83, 25, 73, 20, 68, 9, 57, 17, 65, 29, 77, 39, 87, 47, 95, 44, 92, 34, 82, 24, 72, 13, 61, 18, 66, 19, 67, 30, 78, 40, 88, 48, 96, 43, 91, 33, 81, 23, 71, 12, 60, 5, 53, 8, 56, 16, 64, 28, 76, 38, 86, 42, 90, 32, 80, 22, 70, 11, 59, 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, 103)(3, 105)(4, 106)(5, 97)(6, 111)(7, 113)(8, 98)(9, 115)(10, 116)(11, 117)(12, 100)(13, 101)(14, 123)(15, 125)(16, 102)(17, 126)(18, 104)(19, 112)(20, 114)(21, 121)(22, 127)(23, 107)(24, 108)(25, 109)(26, 133)(27, 135)(28, 110)(29, 136)(30, 124)(31, 131)(32, 137)(33, 118)(34, 119)(35, 120)(36, 142)(37, 143)(38, 122)(39, 144)(40, 134)(41, 141)(42, 132)(43, 128)(44, 129)(45, 130)(46, 140)(47, 139)(48, 138)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 48, 96 ), ( 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96 ) } Outer automorphisms :: reflexible Dual of E23.721 Graph:: bipartite v = 49 e = 96 f = 3 degree seq :: [ 2^48, 96 ] E23.727 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {24, 48, 48}) Quotient :: dipole Aut^+ = C48 (small group id <48, 2>) Aut = D96 (small group id <96, 6>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y1, Y3^-1), (R * Y2 * Y3^-1)^2, Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1^4, Y3 * Y1 * Y3^2 * Y1 * Y3^4, Y3^4 * Y1^-1 * Y3^-2 * Y1^-2 * Y3^-2 * Y1^-2 * Y3^-2 * Y1^-2 * Y3^-2 * Y1^-1, (Y3 * Y2^-1)^24, (Y1^-1 * Y3^-1)^48 ] Map:: R = (1, 49, 2, 50, 6, 54, 14, 62, 26, 74, 34, 82, 19, 67, 31, 79, 41, 89, 44, 92, 46, 94, 38, 86, 23, 71, 12, 60, 5, 53, 8, 56, 16, 64, 28, 76, 35, 83, 20, 68, 9, 57, 17, 65, 29, 77, 43, 91, 48, 96, 47, 95, 39, 87, 24, 72, 13, 61, 18, 66, 30, 78, 36, 84, 21, 69, 10, 58, 3, 51, 7, 55, 15, 63, 27, 75, 42, 90, 45, 93, 33, 81, 40, 88, 25, 73, 32, 80, 37, 85, 22, 70, 11, 59, 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, 103)(3, 105)(4, 106)(5, 97)(6, 111)(7, 113)(8, 98)(9, 115)(10, 116)(11, 117)(12, 100)(13, 101)(14, 123)(15, 125)(16, 102)(17, 127)(18, 104)(19, 129)(20, 130)(21, 131)(22, 132)(23, 107)(24, 108)(25, 109)(26, 138)(27, 139)(28, 110)(29, 137)(30, 112)(31, 136)(32, 114)(33, 135)(34, 141)(35, 122)(36, 124)(37, 126)(38, 118)(39, 119)(40, 120)(41, 121)(42, 144)(43, 140)(44, 128)(45, 143)(46, 133)(47, 134)(48, 142)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 48, 96 ), ( 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96 ) } Outer automorphisms :: reflexible Dual of E23.720 Graph:: bipartite v = 49 e = 96 f = 3 degree seq :: [ 2^48, 96 ] E23.728 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {24, 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, Y1), (R * Y3)^2, (R * Y1)^2, Y3^-2 * Y1^-4, (R * Y2 * Y3^-1)^2, Y3^-11 * Y1^2, (Y3 * Y2^-1)^24 ] Map:: R = (1, 49, 2, 50, 6, 54, 14, 62, 13, 61, 18, 66, 24, 72, 31, 79, 30, 78, 34, 82, 40, 88, 47, 95, 46, 94, 44, 92, 35, 83, 41, 89, 37, 85, 28, 76, 19, 67, 25, 73, 21, 69, 10, 58, 3, 51, 7, 55, 15, 63, 12, 60, 5, 53, 8, 56, 16, 64, 23, 71, 22, 70, 26, 74, 32, 80, 39, 87, 38, 86, 42, 90, 43, 91, 48, 96, 45, 93, 36, 84, 27, 75, 33, 81, 29, 77, 20, 68, 9, 57, 17, 65, 11, 59, 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, 103)(3, 105)(4, 106)(5, 97)(6, 111)(7, 113)(8, 98)(9, 115)(10, 116)(11, 117)(12, 100)(13, 101)(14, 108)(15, 107)(16, 102)(17, 121)(18, 104)(19, 123)(20, 124)(21, 125)(22, 109)(23, 110)(24, 112)(25, 129)(26, 114)(27, 131)(28, 132)(29, 133)(30, 118)(31, 119)(32, 120)(33, 137)(34, 122)(35, 139)(36, 140)(37, 141)(38, 126)(39, 127)(40, 128)(41, 144)(42, 130)(43, 136)(44, 138)(45, 142)(46, 134)(47, 135)(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) :: { ( 48, 96 ), ( 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96, 48, 96 ) } Outer automorphisms :: reflexible Dual of E23.722 Graph:: bipartite v = 49 e = 96 f = 3 degree seq :: [ 2^48, 96 ] E23.729 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {8, 14, 56}) Quotient :: edge Aut^+ = C56 (small group id <56, 2>) Aut = D112 (small group id <112, 6>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^8, T1^4 * T2^7 ] Map:: non-degenerate R = (1, 3, 9, 19, 33, 49, 42, 26, 41, 56, 40, 25, 13, 5)(2, 7, 17, 31, 47, 53, 37, 22, 36, 52, 48, 32, 18, 8)(4, 10, 20, 34, 50, 44, 28, 14, 27, 43, 55, 39, 24, 12)(6, 15, 29, 45, 54, 38, 23, 11, 21, 35, 51, 46, 30, 16)(57, 58, 62, 70, 82, 78, 67, 60)(59, 63, 71, 83, 97, 92, 77, 66)(61, 64, 72, 84, 98, 93, 79, 68)(65, 73, 85, 99, 112, 108, 91, 76)(69, 74, 86, 100, 105, 109, 94, 80)(75, 87, 101, 111, 96, 104, 107, 90)(81, 88, 102, 106, 89, 103, 110, 95) L = (1, 57)(2, 58)(3, 59)(4, 60)(5, 61)(6, 62)(7, 63)(8, 64)(9, 65)(10, 66)(11, 67)(12, 68)(13, 69)(14, 70)(15, 71)(16, 72)(17, 73)(18, 74)(19, 75)(20, 76)(21, 77)(22, 78)(23, 79)(24, 80)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112) local type(s) :: { ( 112^8 ), ( 112^14 ) } Outer automorphisms :: reflexible Dual of E23.733 Transitivity :: ET+ Graph:: bipartite v = 11 e = 56 f = 1 degree seq :: [ 8^7, 14^4 ] E23.730 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {8, 14, 56}) Quotient :: edge Aut^+ = C56 (small group id <56, 2>) Aut = D112 (small group id <112, 6>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^-3 * T2^4, T1^14, T1^14, (T1^-1 * T2^-1)^8 ] Map:: non-degenerate R = (1, 3, 9, 19, 14, 27, 36, 45, 42, 51, 55, 47, 38, 41, 32, 23, 11, 21, 18, 8, 2, 7, 17, 29, 26, 35, 44, 53, 50, 56, 48, 39, 30, 33, 24, 12, 4, 10, 20, 16, 6, 15, 28, 37, 34, 43, 52, 54, 46, 49, 40, 31, 22, 25, 13, 5)(57, 58, 62, 70, 82, 90, 98, 106, 102, 94, 86, 78, 67, 60)(59, 63, 71, 83, 91, 99, 107, 112, 105, 97, 89, 81, 77, 66)(61, 64, 72, 75, 85, 93, 101, 109, 110, 103, 95, 87, 79, 68)(65, 73, 84, 92, 100, 108, 111, 104, 96, 88, 80, 69, 74, 76) 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) :: { ( 16^14 ), ( 16^56 ) } Outer automorphisms :: reflexible Dual of E23.734 Transitivity :: ET+ Graph:: bipartite v = 5 e = 56 f = 7 degree seq :: [ 14^4, 56 ] E23.731 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {8, 14, 56}) Quotient :: edge Aut^+ = C56 (small group id <56, 2>) Aut = D112 (small group id <112, 6>) |r| :: 2 Presentation :: [ F^2, (T2, T1), (F * T2)^2, (F * T1)^2, T2^8, T2^8, T2^-3 * T1^-7, T2^3 * T1^-1 * T2 * T1^-1 * T2^3 * T1 * T2 * T1, (T1^-1 * T2^-1)^14 ] Map:: non-degenerate R = (1, 3, 9, 19, 33, 25, 13, 5)(2, 7, 17, 31, 48, 32, 18, 8)(4, 10, 20, 34, 49, 40, 24, 12)(6, 15, 29, 46, 56, 47, 30, 16)(11, 21, 35, 50, 53, 41, 39, 23)(14, 27, 44, 37, 52, 55, 45, 28)(22, 36, 51, 54, 43, 26, 42, 38)(57, 58, 62, 70, 82, 97, 96, 81, 88, 103, 111, 107, 91, 76, 65, 73, 85, 100, 94, 79, 68, 61, 64, 72, 84, 99, 109, 105, 89, 104, 112, 108, 92, 77, 66, 59, 63, 71, 83, 98, 95, 80, 69, 74, 86, 101, 110, 106, 90, 75, 87, 102, 93, 78, 67, 60) L = (1, 57)(2, 58)(3, 59)(4, 60)(5, 61)(6, 62)(7, 63)(8, 64)(9, 65)(10, 66)(11, 67)(12, 68)(13, 69)(14, 70)(15, 71)(16, 72)(17, 73)(18, 74)(19, 75)(20, 76)(21, 77)(22, 78)(23, 79)(24, 80)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112) local type(s) :: { ( 28^8 ), ( 28^56 ) } Outer automorphisms :: reflexible Dual of E23.732 Transitivity :: ET+ Graph:: bipartite v = 8 e = 56 f = 4 degree seq :: [ 8^7, 56 ] E23.732 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {8, 14, 56}) Quotient :: loop Aut^+ = C56 (small group id <56, 2>) Aut = D112 (small group id <112, 6>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^8, T1^4 * T2^7 ] Map:: non-degenerate R = (1, 57, 3, 59, 9, 65, 19, 75, 33, 89, 49, 105, 42, 98, 26, 82, 41, 97, 56, 112, 40, 96, 25, 81, 13, 69, 5, 61)(2, 58, 7, 63, 17, 73, 31, 87, 47, 103, 53, 109, 37, 93, 22, 78, 36, 92, 52, 108, 48, 104, 32, 88, 18, 74, 8, 64)(4, 60, 10, 66, 20, 76, 34, 90, 50, 106, 44, 100, 28, 84, 14, 70, 27, 83, 43, 99, 55, 111, 39, 95, 24, 80, 12, 68)(6, 62, 15, 71, 29, 85, 45, 101, 54, 110, 38, 94, 23, 79, 11, 67, 21, 77, 35, 91, 51, 107, 46, 102, 30, 86, 16, 72) L = (1, 58)(2, 62)(3, 63)(4, 57)(5, 64)(6, 70)(7, 71)(8, 72)(9, 73)(10, 59)(11, 60)(12, 61)(13, 74)(14, 82)(15, 83)(16, 84)(17, 85)(18, 86)(19, 87)(20, 65)(21, 66)(22, 67)(23, 68)(24, 69)(25, 88)(26, 78)(27, 97)(28, 98)(29, 99)(30, 100)(31, 101)(32, 102)(33, 103)(34, 75)(35, 76)(36, 77)(37, 79)(38, 80)(39, 81)(40, 104)(41, 92)(42, 93)(43, 112)(44, 105)(45, 111)(46, 106)(47, 110)(48, 107)(49, 109)(50, 89)(51, 90)(52, 91)(53, 94)(54, 95)(55, 96)(56, 108) local type(s) :: { ( 8, 56, 8, 56, 8, 56, 8, 56, 8, 56, 8, 56, 8, 56, 8, 56, 8, 56, 8, 56, 8, 56, 8, 56, 8, 56, 8, 56 ) } Outer automorphisms :: reflexible Dual of E23.731 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 4 e = 56 f = 8 degree seq :: [ 28^4 ] E23.733 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {8, 14, 56}) Quotient :: loop Aut^+ = C56 (small group id <56, 2>) Aut = D112 (small group id <112, 6>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T1, T2^-1), T1^-3 * T2^4, T1^14, T1^14, (T1^-1 * T2^-1)^8 ] Map:: non-degenerate R = (1, 57, 3, 59, 9, 65, 19, 75, 14, 70, 27, 83, 36, 92, 45, 101, 42, 98, 51, 107, 55, 111, 47, 103, 38, 94, 41, 97, 32, 88, 23, 79, 11, 67, 21, 77, 18, 74, 8, 64, 2, 58, 7, 63, 17, 73, 29, 85, 26, 82, 35, 91, 44, 100, 53, 109, 50, 106, 56, 112, 48, 104, 39, 95, 30, 86, 33, 89, 24, 80, 12, 68, 4, 60, 10, 66, 20, 76, 16, 72, 6, 62, 15, 71, 28, 84, 37, 93, 34, 90, 43, 99, 52, 108, 54, 110, 46, 102, 49, 105, 40, 96, 31, 87, 22, 78, 25, 81, 13, 69, 5, 61) L = (1, 58)(2, 62)(3, 63)(4, 57)(5, 64)(6, 70)(7, 71)(8, 72)(9, 73)(10, 59)(11, 60)(12, 61)(13, 74)(14, 82)(15, 83)(16, 75)(17, 84)(18, 76)(19, 85)(20, 65)(21, 66)(22, 67)(23, 68)(24, 69)(25, 77)(26, 90)(27, 91)(28, 92)(29, 93)(30, 78)(31, 79)(32, 80)(33, 81)(34, 98)(35, 99)(36, 100)(37, 101)(38, 86)(39, 87)(40, 88)(41, 89)(42, 106)(43, 107)(44, 108)(45, 109)(46, 94)(47, 95)(48, 96)(49, 97)(50, 102)(51, 112)(52, 111)(53, 110)(54, 103)(55, 104)(56, 105) local type(s) :: { ( 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14, 8, 14 ) } Outer automorphisms :: reflexible Dual of E23.729 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 56 f = 11 degree seq :: [ 112 ] E23.734 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {8, 14, 56}) Quotient :: loop Aut^+ = C56 (small group id <56, 2>) Aut = D112 (small group id <112, 6>) |r| :: 2 Presentation :: [ F^2, (T2, T1), (F * T2)^2, (F * T1)^2, T2^8, T2^8, T2^-3 * T1^-7, T2^3 * T1^-1 * T2 * T1^-1 * T2^3 * T1 * T2 * T1, (T1^-1 * T2^-1)^14 ] Map:: non-degenerate R = (1, 57, 3, 59, 9, 65, 19, 75, 33, 89, 25, 81, 13, 69, 5, 61)(2, 58, 7, 63, 17, 73, 31, 87, 48, 104, 32, 88, 18, 74, 8, 64)(4, 60, 10, 66, 20, 76, 34, 90, 49, 105, 40, 96, 24, 80, 12, 68)(6, 62, 15, 71, 29, 85, 46, 102, 56, 112, 47, 103, 30, 86, 16, 72)(11, 67, 21, 77, 35, 91, 50, 106, 53, 109, 41, 97, 39, 95, 23, 79)(14, 70, 27, 83, 44, 100, 37, 93, 52, 108, 55, 111, 45, 101, 28, 84)(22, 78, 36, 92, 51, 107, 54, 110, 43, 99, 26, 82, 42, 98, 38, 94) L = (1, 58)(2, 62)(3, 63)(4, 57)(5, 64)(6, 70)(7, 71)(8, 72)(9, 73)(10, 59)(11, 60)(12, 61)(13, 74)(14, 82)(15, 83)(16, 84)(17, 85)(18, 86)(19, 87)(20, 65)(21, 66)(22, 67)(23, 68)(24, 69)(25, 88)(26, 97)(27, 98)(28, 99)(29, 100)(30, 101)(31, 102)(32, 103)(33, 104)(34, 75)(35, 76)(36, 77)(37, 78)(38, 79)(39, 80)(40, 81)(41, 96)(42, 95)(43, 109)(44, 94)(45, 110)(46, 93)(47, 111)(48, 112)(49, 89)(50, 90)(51, 91)(52, 92)(53, 105)(54, 106)(55, 107)(56, 108) local type(s) :: { ( 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56, 14, 56 ) } Outer automorphisms :: reflexible Dual of E23.730 Transitivity :: ET+ VT+ AT Graph:: v = 7 e = 56 f = 5 degree seq :: [ 16^7 ] E23.735 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 14, 56}) Quotient :: dipole Aut^+ = C56 (small group id <56, 2>) Aut = D112 (small group id <112, 6>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, (Y2, Y1^-1), (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y3^-1, Y2^-1), Y1 * Y2 * Y3^2 * Y2^-1 * Y1, Y2^2 * Y3^2 * Y2^-1 * Y1 * Y2^-1 * Y1, (Y1^-1 * Y3^3)^2, Y1^8, Y2^-7 * Y1^4, Y2 * Y1 * Y2^2 * Y1 * Y2^4 * Y1 * Y3^-1, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 57, 2, 58, 6, 62, 14, 70, 26, 82, 22, 78, 11, 67, 4, 60)(3, 59, 7, 63, 15, 71, 27, 83, 41, 97, 36, 92, 21, 77, 10, 66)(5, 61, 8, 64, 16, 72, 28, 84, 42, 98, 37, 93, 23, 79, 12, 68)(9, 65, 17, 73, 29, 85, 43, 99, 56, 112, 52, 108, 35, 91, 20, 76)(13, 69, 18, 74, 30, 86, 44, 100, 49, 105, 53, 109, 38, 94, 24, 80)(19, 75, 31, 87, 45, 101, 55, 111, 40, 96, 48, 104, 51, 107, 34, 90)(25, 81, 32, 88, 46, 102, 50, 106, 33, 89, 47, 103, 54, 110, 39, 95)(113, 169, 115, 171, 121, 177, 131, 187, 145, 201, 161, 217, 154, 210, 138, 194, 153, 209, 168, 224, 152, 208, 137, 193, 125, 181, 117, 173)(114, 170, 119, 175, 129, 185, 143, 199, 159, 215, 165, 221, 149, 205, 134, 190, 148, 204, 164, 220, 160, 216, 144, 200, 130, 186, 120, 176)(116, 172, 122, 178, 132, 188, 146, 202, 162, 218, 156, 212, 140, 196, 126, 182, 139, 195, 155, 211, 167, 223, 151, 207, 136, 192, 124, 180)(118, 174, 127, 183, 141, 197, 157, 213, 166, 222, 150, 206, 135, 191, 123, 179, 133, 189, 147, 203, 163, 219, 158, 214, 142, 198, 128, 184) L = (1, 116)(2, 113)(3, 122)(4, 123)(5, 124)(6, 114)(7, 115)(8, 117)(9, 132)(10, 133)(11, 134)(12, 135)(13, 136)(14, 118)(15, 119)(16, 120)(17, 121)(18, 125)(19, 146)(20, 147)(21, 148)(22, 138)(23, 149)(24, 150)(25, 151)(26, 126)(27, 127)(28, 128)(29, 129)(30, 130)(31, 131)(32, 137)(33, 162)(34, 163)(35, 164)(36, 153)(37, 154)(38, 165)(39, 166)(40, 167)(41, 139)(42, 140)(43, 141)(44, 142)(45, 143)(46, 144)(47, 145)(48, 152)(49, 156)(50, 158)(51, 160)(52, 168)(53, 161)(54, 159)(55, 157)(56, 155)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224) local type(s) :: { ( 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112 ), ( 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112, 2, 112 ) } Outer automorphisms :: reflexible Dual of E23.738 Graph:: bipartite v = 11 e = 112 f = 57 degree seq :: [ 16^7, 28^4 ] E23.736 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 14, 56}) Quotient :: dipole Aut^+ = C56 (small group id <56, 2>) Aut = D112 (small group id <112, 6>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y2^-1, Y1^-1), Y2^4 * Y1^-3, Y1^14, Y1^14, (Y3^-1 * Y1^-1)^8 ] Map:: R = (1, 57, 2, 58, 6, 62, 14, 70, 26, 82, 34, 90, 42, 98, 50, 106, 46, 102, 38, 94, 30, 86, 22, 78, 11, 67, 4, 60)(3, 59, 7, 63, 15, 71, 27, 83, 35, 91, 43, 99, 51, 107, 56, 112, 49, 105, 41, 97, 33, 89, 25, 81, 21, 77, 10, 66)(5, 61, 8, 64, 16, 72, 19, 75, 29, 85, 37, 93, 45, 101, 53, 109, 54, 110, 47, 103, 39, 95, 31, 87, 23, 79, 12, 68)(9, 65, 17, 73, 28, 84, 36, 92, 44, 100, 52, 108, 55, 111, 48, 104, 40, 96, 32, 88, 24, 80, 13, 69, 18, 74, 20, 76)(113, 169, 115, 171, 121, 177, 131, 187, 126, 182, 139, 195, 148, 204, 157, 213, 154, 210, 163, 219, 167, 223, 159, 215, 150, 206, 153, 209, 144, 200, 135, 191, 123, 179, 133, 189, 130, 186, 120, 176, 114, 170, 119, 175, 129, 185, 141, 197, 138, 194, 147, 203, 156, 212, 165, 221, 162, 218, 168, 224, 160, 216, 151, 207, 142, 198, 145, 201, 136, 192, 124, 180, 116, 172, 122, 178, 132, 188, 128, 184, 118, 174, 127, 183, 140, 196, 149, 205, 146, 202, 155, 211, 164, 220, 166, 222, 158, 214, 161, 217, 152, 208, 143, 199, 134, 190, 137, 193, 125, 181, 117, 173) L = (1, 115)(2, 119)(3, 121)(4, 122)(5, 113)(6, 127)(7, 129)(8, 114)(9, 131)(10, 132)(11, 133)(12, 116)(13, 117)(14, 139)(15, 140)(16, 118)(17, 141)(18, 120)(19, 126)(20, 128)(21, 130)(22, 137)(23, 123)(24, 124)(25, 125)(26, 147)(27, 148)(28, 149)(29, 138)(30, 145)(31, 134)(32, 135)(33, 136)(34, 155)(35, 156)(36, 157)(37, 146)(38, 153)(39, 142)(40, 143)(41, 144)(42, 163)(43, 164)(44, 165)(45, 154)(46, 161)(47, 150)(48, 151)(49, 152)(50, 168)(51, 167)(52, 166)(53, 162)(54, 158)(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) :: { ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ), ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 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 E23.737 Graph:: bipartite v = 5 e = 112 f = 63 degree seq :: [ 28^4, 112 ] E23.737 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 14, 56}) Quotient :: dipole Aut^+ = C56 (small group id <56, 2>) Aut = D112 (small group id <112, 6>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2, Y3^-1), Y2^-8, Y2^8, Y2^3 * Y3^-7, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1, (Y3^-1 * Y1^-1)^56 ] Map:: R = (1, 57)(2, 58)(3, 59)(4, 60)(5, 61)(6, 62)(7, 63)(8, 64)(9, 65)(10, 66)(11, 67)(12, 68)(13, 69)(14, 70)(15, 71)(16, 72)(17, 73)(18, 74)(19, 75)(20, 76)(21, 77)(22, 78)(23, 79)(24, 80)(25, 81)(26, 82)(27, 83)(28, 84)(29, 85)(30, 86)(31, 87)(32, 88)(33, 89)(34, 90)(35, 91)(36, 92)(37, 93)(38, 94)(39, 95)(40, 96)(41, 97)(42, 98)(43, 99)(44, 100)(45, 101)(46, 102)(47, 103)(48, 104)(49, 105)(50, 106)(51, 107)(52, 108)(53, 109)(54, 110)(55, 111)(56, 112)(113, 169, 114, 170, 118, 174, 126, 182, 138, 194, 134, 190, 123, 179, 116, 172)(115, 171, 119, 175, 127, 183, 139, 195, 153, 209, 148, 204, 133, 189, 122, 178)(117, 173, 120, 176, 128, 184, 140, 196, 154, 210, 149, 205, 135, 191, 124, 180)(121, 177, 129, 185, 141, 197, 155, 211, 165, 221, 161, 217, 147, 203, 132, 188)(125, 181, 130, 186, 142, 198, 156, 212, 166, 222, 162, 218, 150, 206, 136, 192)(131, 187, 143, 199, 157, 213, 167, 223, 164, 220, 152, 208, 160, 216, 146, 202)(137, 193, 144, 200, 158, 214, 145, 201, 159, 215, 168, 224, 163, 219, 151, 207) L = (1, 115)(2, 119)(3, 121)(4, 122)(5, 113)(6, 127)(7, 129)(8, 114)(9, 131)(10, 132)(11, 133)(12, 116)(13, 117)(14, 139)(15, 141)(16, 118)(17, 143)(18, 120)(19, 145)(20, 146)(21, 147)(22, 148)(23, 123)(24, 124)(25, 125)(26, 153)(27, 155)(28, 126)(29, 157)(30, 128)(31, 159)(32, 130)(33, 156)(34, 158)(35, 160)(36, 161)(37, 134)(38, 135)(39, 136)(40, 137)(41, 165)(42, 138)(43, 167)(44, 140)(45, 168)(46, 142)(47, 166)(48, 144)(49, 152)(50, 149)(51, 150)(52, 151)(53, 164)(54, 154)(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) :: { ( 28, 112 ), ( 28, 112, 28, 112, 28, 112, 28, 112, 28, 112, 28, 112, 28, 112, 28, 112 ) } Outer automorphisms :: reflexible Dual of E23.736 Graph:: simple bipartite v = 63 e = 112 f = 5 degree seq :: [ 2^56, 16^7 ] E23.738 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 14, 56}) Quotient :: dipole Aut^+ = C56 (small group id <56, 2>) Aut = D112 (small group id <112, 6>) |r| :: 2 Presentation :: [ Y2, R^2, (Y3, Y1), (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^8, Y3^-3 * Y1^-7, (Y3 * Y2^-1)^8, (Y1^-1 * Y3^-1)^14 ] Map:: R = (1, 57, 2, 58, 6, 62, 14, 70, 26, 82, 41, 97, 40, 96, 25, 81, 32, 88, 47, 103, 55, 111, 51, 107, 35, 91, 20, 76, 9, 65, 17, 73, 29, 85, 44, 100, 38, 94, 23, 79, 12, 68, 5, 61, 8, 64, 16, 72, 28, 84, 43, 99, 53, 109, 49, 105, 33, 89, 48, 104, 56, 112, 52, 108, 36, 92, 21, 77, 10, 66, 3, 59, 7, 63, 15, 71, 27, 83, 42, 98, 39, 95, 24, 80, 13, 69, 18, 74, 30, 86, 45, 101, 54, 110, 50, 106, 34, 90, 19, 75, 31, 87, 46, 102, 37, 93, 22, 78, 11, 67, 4, 60)(113, 169)(114, 170)(115, 171)(116, 172)(117, 173)(118, 174)(119, 175)(120, 176)(121, 177)(122, 178)(123, 179)(124, 180)(125, 181)(126, 182)(127, 183)(128, 184)(129, 185)(130, 186)(131, 187)(132, 188)(133, 189)(134, 190)(135, 191)(136, 192)(137, 193)(138, 194)(139, 195)(140, 196)(141, 197)(142, 198)(143, 199)(144, 200)(145, 201)(146, 202)(147, 203)(148, 204)(149, 205)(150, 206)(151, 207)(152, 208)(153, 209)(154, 210)(155, 211)(156, 212)(157, 213)(158, 214)(159, 215)(160, 216)(161, 217)(162, 218)(163, 219)(164, 220)(165, 221)(166, 222)(167, 223)(168, 224) L = (1, 115)(2, 119)(3, 121)(4, 122)(5, 113)(6, 127)(7, 129)(8, 114)(9, 131)(10, 132)(11, 133)(12, 116)(13, 117)(14, 139)(15, 141)(16, 118)(17, 143)(18, 120)(19, 145)(20, 146)(21, 147)(22, 148)(23, 123)(24, 124)(25, 125)(26, 154)(27, 156)(28, 126)(29, 158)(30, 128)(31, 160)(32, 130)(33, 137)(34, 161)(35, 162)(36, 163)(37, 164)(38, 134)(39, 135)(40, 136)(41, 151)(42, 150)(43, 138)(44, 149)(45, 140)(46, 168)(47, 142)(48, 144)(49, 152)(50, 165)(51, 166)(52, 167)(53, 153)(54, 155)(55, 157)(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) :: { ( 16, 28 ), ( 16, 28, 16, 28, 16, 28, 16, 28, 16, 28, 16, 28, 16, 28, 16, 28, 16, 28, 16, 28, 16, 28, 16, 28, 16, 28, 16, 28, 16, 28, 16, 28, 16, 28, 16, 28, 16, 28, 16, 28, 16, 28, 16, 28, 16, 28, 16, 28, 16, 28, 16, 28, 16, 28, 16, 28, 16, 28, 16, 28, 16, 28, 16, 28, 16, 28, 16, 28, 16, 28, 16, 28, 16, 28, 16, 28, 16, 28, 16, 28, 16, 28, 16, 28, 16, 28, 16, 28, 16, 28, 16, 28, 16, 28, 16, 28, 16, 28, 16, 28, 16, 28, 16, 28, 16, 28, 16, 28, 16, 28, 16, 28 ) } Outer automorphisms :: reflexible Dual of E23.735 Graph:: bipartite v = 57 e = 112 f = 11 degree seq :: [ 2^56, 112 ] E23.739 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 14, 56}) Quotient :: dipole Aut^+ = C56 (small group id <56, 2>) Aut = D112 (small group id <112, 6>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, Y1^-1 * Y3^-1, (R * Y3)^2, (Y3^-1, Y2^-1), (R * Y2)^2, (R * Y1)^2, (Y2, Y1^-1), Y1^7 * Y3^-1, Y1^8, Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-5, Y2^2 * Y3 * Y2 * Y3 * Y2^4 * Y1^-3, Y2^-1 * Y3^2 * Y2^-1 * Y3^2 * Y2 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1, Y3^2 * Y2^49 * Y3 ] Map:: R = (1, 57, 2, 58, 6, 62, 14, 70, 26, 82, 22, 78, 11, 67, 4, 60)(3, 59, 7, 63, 15, 71, 27, 83, 41, 97, 36, 92, 21, 77, 10, 66)(5, 61, 8, 64, 16, 72, 28, 84, 42, 98, 37, 93, 23, 79, 12, 68)(9, 65, 17, 73, 29, 85, 43, 99, 53, 109, 52, 108, 35, 91, 20, 76)(13, 69, 18, 74, 30, 86, 44, 100, 54, 110, 49, 105, 38, 94, 24, 80)(19, 75, 31, 87, 45, 101, 40, 96, 48, 104, 56, 112, 51, 107, 34, 90)(25, 81, 32, 88, 46, 102, 55, 111, 50, 106, 33, 89, 47, 103, 39, 95)(113, 169, 115, 171, 121, 177, 131, 187, 145, 201, 161, 217, 149, 205, 134, 190, 148, 204, 164, 220, 168, 224, 158, 214, 142, 198, 128, 184, 118, 174, 127, 183, 141, 197, 157, 213, 151, 207, 136, 192, 124, 180, 116, 172, 122, 178, 132, 188, 146, 202, 162, 218, 166, 222, 154, 210, 138, 194, 153, 209, 165, 221, 160, 216, 144, 200, 130, 186, 120, 176, 114, 170, 119, 175, 129, 185, 143, 199, 159, 215, 150, 206, 135, 191, 123, 179, 133, 189, 147, 203, 163, 219, 167, 223, 156, 212, 140, 196, 126, 182, 139, 195, 155, 211, 152, 208, 137, 193, 125, 181, 117, 173) L = (1, 116)(2, 113)(3, 122)(4, 123)(5, 124)(6, 114)(7, 115)(8, 117)(9, 132)(10, 133)(11, 134)(12, 135)(13, 136)(14, 118)(15, 119)(16, 120)(17, 121)(18, 125)(19, 146)(20, 147)(21, 148)(22, 138)(23, 149)(24, 150)(25, 151)(26, 126)(27, 127)(28, 128)(29, 129)(30, 130)(31, 131)(32, 137)(33, 162)(34, 163)(35, 164)(36, 153)(37, 154)(38, 161)(39, 159)(40, 157)(41, 139)(42, 140)(43, 141)(44, 142)(45, 143)(46, 144)(47, 145)(48, 152)(49, 166)(50, 167)(51, 168)(52, 165)(53, 155)(54, 156)(55, 158)(56, 160)(57, 169)(58, 170)(59, 171)(60, 172)(61, 173)(62, 174)(63, 175)(64, 176)(65, 177)(66, 178)(67, 179)(68, 180)(69, 181)(70, 182)(71, 183)(72, 184)(73, 185)(74, 186)(75, 187)(76, 188)(77, 189)(78, 190)(79, 191)(80, 192)(81, 193)(82, 194)(83, 195)(84, 196)(85, 197)(86, 198)(87, 199)(88, 200)(89, 201)(90, 202)(91, 203)(92, 204)(93, 205)(94, 206)(95, 207)(96, 208)(97, 209)(98, 210)(99, 211)(100, 212)(101, 213)(102, 214)(103, 215)(104, 216)(105, 217)(106, 218)(107, 219)(108, 220)(109, 221)(110, 222)(111, 223)(112, 224) local type(s) :: { ( 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28 ), ( 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28, 2, 28 ) } Outer automorphisms :: reflexible Dual of E23.740 Graph:: bipartite v = 8 e = 112 f = 60 degree seq :: [ 16^7, 112 ] E23.740 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 14, 56}) Quotient :: dipole Aut^+ = C56 (small group id <56, 2>) Aut = D112 (small group id <112, 6>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y1, Y3^-1), (R * Y2 * Y3^-1)^2, Y1^3 * Y3^-4, Y1^-14, Y1^14, (Y1^-1 * Y3^-1)^8, (Y3 * Y2^-1)^56 ] Map:: R = (1, 57, 2, 58, 6, 62, 14, 70, 26, 82, 34, 90, 42, 98, 50, 106, 46, 102, 38, 94, 30, 86, 22, 78, 11, 67, 4, 60)(3, 59, 7, 63, 15, 71, 27, 83, 35, 91, 43, 99, 51, 107, 56, 112, 49, 105, 41, 97, 33, 89, 25, 81, 21, 77, 10, 66)(5, 61, 8, 64, 16, 72, 19, 75, 29, 85, 37, 93, 45, 101, 53, 109, 54, 110, 47, 103, 39, 95, 31, 87, 23, 79, 12, 68)(9, 65, 17, 73, 28, 84, 36, 92, 44, 100, 52, 108, 55, 111, 48, 104, 40, 96, 32, 88, 24, 80, 13, 69, 18, 74, 20, 76)(113, 169)(114, 170)(115, 171)(116, 172)(117, 173)(118, 174)(119, 175)(120, 176)(121, 177)(122, 178)(123, 179)(124, 180)(125, 181)(126, 182)(127, 183)(128, 184)(129, 185)(130, 186)(131, 187)(132, 188)(133, 189)(134, 190)(135, 191)(136, 192)(137, 193)(138, 194)(139, 195)(140, 196)(141, 197)(142, 198)(143, 199)(144, 200)(145, 201)(146, 202)(147, 203)(148, 204)(149, 205)(150, 206)(151, 207)(152, 208)(153, 209)(154, 210)(155, 211)(156, 212)(157, 213)(158, 214)(159, 215)(160, 216)(161, 217)(162, 218)(163, 219)(164, 220)(165, 221)(166, 222)(167, 223)(168, 224) L = (1, 115)(2, 119)(3, 121)(4, 122)(5, 113)(6, 127)(7, 129)(8, 114)(9, 131)(10, 132)(11, 133)(12, 116)(13, 117)(14, 139)(15, 140)(16, 118)(17, 141)(18, 120)(19, 126)(20, 128)(21, 130)(22, 137)(23, 123)(24, 124)(25, 125)(26, 147)(27, 148)(28, 149)(29, 138)(30, 145)(31, 134)(32, 135)(33, 136)(34, 155)(35, 156)(36, 157)(37, 146)(38, 153)(39, 142)(40, 143)(41, 144)(42, 163)(43, 164)(44, 165)(45, 154)(46, 161)(47, 150)(48, 151)(49, 152)(50, 168)(51, 167)(52, 166)(53, 162)(54, 158)(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) :: { ( 16, 112 ), ( 16, 112, 16, 112, 16, 112, 16, 112, 16, 112, 16, 112, 16, 112, 16, 112, 16, 112, 16, 112, 16, 112, 16, 112, 16, 112, 16, 112 ) } Outer automorphisms :: reflexible Dual of E23.739 Graph:: simple bipartite v = 60 e = 112 f = 8 degree seq :: [ 2^56, 28^4 ] E23.741 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 6, 10}) Quotient :: dipole Aut^+ = S3 x D10 (small group id <60, 8>) Aut = C2 x S3 x D10 (small group id <120, 42>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^2, (Y2 * Y1)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3)^2, (Y3 * Y2 * Y3 * Y1)^2, (Y3 * Y2)^6, Y2 * Y3 * Y1 * Y2 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y2 * Y3 * Y1 ] Map:: polytopal non-degenerate R = (1, 61, 2, 62)(3, 63, 5, 65)(4, 64, 8, 68)(6, 66, 11, 71)(7, 67, 13, 73)(9, 69, 15, 75)(10, 70, 18, 78)(12, 72, 20, 80)(14, 74, 23, 83)(16, 76, 27, 87)(17, 77, 22, 82)(19, 79, 29, 89)(21, 81, 33, 93)(24, 84, 36, 96)(25, 85, 31, 91)(26, 86, 38, 98)(28, 88, 34, 94)(30, 90, 43, 103)(32, 92, 45, 105)(35, 95, 49, 109)(37, 97, 44, 104)(39, 99, 53, 113)(40, 100, 56, 116)(41, 101, 55, 115)(42, 102, 54, 114)(46, 106, 51, 111)(47, 107, 50, 110)(48, 108, 58, 118)(52, 112, 59, 119)(57, 117, 60, 120)(121, 181, 123, 183)(122, 182, 125, 185)(124, 184, 129, 189)(126, 186, 132, 192)(127, 187, 134, 194)(128, 188, 135, 195)(130, 190, 139, 199)(131, 191, 140, 200)(133, 193, 143, 203)(136, 196, 144, 204)(137, 197, 148, 208)(138, 198, 149, 209)(141, 201, 150, 210)(142, 202, 154, 214)(145, 205, 157, 217)(146, 206, 159, 219)(147, 207, 156, 216)(151, 211, 164, 224)(152, 212, 166, 226)(153, 213, 163, 223)(155, 215, 170, 230)(158, 218, 173, 233)(160, 220, 174, 234)(161, 221, 172, 232)(162, 222, 176, 236)(165, 225, 171, 231)(167, 227, 169, 229)(168, 228, 177, 237)(175, 235, 179, 239)(178, 238, 180, 240) L = (1, 124)(2, 126)(3, 127)(4, 121)(5, 130)(6, 122)(7, 123)(8, 136)(9, 137)(10, 125)(11, 141)(12, 142)(13, 144)(14, 145)(15, 146)(16, 128)(17, 129)(18, 150)(19, 151)(20, 152)(21, 131)(22, 132)(23, 155)(24, 133)(25, 134)(26, 135)(27, 160)(28, 161)(29, 162)(30, 138)(31, 139)(32, 140)(33, 167)(34, 168)(35, 143)(36, 171)(37, 172)(38, 174)(39, 175)(40, 147)(41, 148)(42, 149)(43, 173)(44, 177)(45, 169)(46, 178)(47, 153)(48, 154)(49, 165)(50, 179)(51, 156)(52, 157)(53, 163)(54, 158)(55, 159)(56, 180)(57, 164)(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) :: { ( 12, 20, 12, 20 ) } Outer automorphisms :: reflexible Dual of E23.746 Graph:: simple bipartite v = 60 e = 120 f = 16 degree seq :: [ 4^60 ] E23.742 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 6, 10}) Quotient :: dipole Aut^+ = S3 x D10 (small group id <60, 8>) Aut = C2 x S3 x D10 (small group id <120, 42>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, (R * Y3)^2, (Y3 * Y1)^2, (R * Y1)^2, (Y2^-1 * Y1)^2, Y2^-1 * R * Y2^2 * R * Y2^-1, (R * Y2 * Y3)^2, Y2^6, (Y3 * Y2^-2)^2, Y2^-1 * Y3 * Y2^-1 * Y1 * Y2 * Y3 * Y2 * Y1, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y1 * Y3 * Y2^-1 * Y3 * Y2 * Y3 ] Map:: polytopal non-degenerate R = (1, 61, 2, 62)(3, 63, 8, 68)(4, 64, 7, 67)(5, 65, 6, 66)(9, 69, 20, 80)(10, 70, 19, 79)(11, 71, 18, 78)(12, 72, 17, 77)(13, 73, 16, 76)(14, 74, 15, 75)(21, 81, 29, 89)(22, 82, 33, 93)(23, 83, 31, 91)(24, 84, 36, 96)(25, 85, 30, 90)(26, 86, 35, 95)(27, 87, 34, 94)(28, 88, 32, 92)(37, 97, 45, 105)(38, 98, 46, 106)(39, 99, 47, 107)(40, 100, 52, 112)(41, 101, 49, 109)(42, 102, 51, 111)(43, 103, 50, 110)(44, 104, 48, 108)(53, 113, 60, 120)(54, 114, 58, 118)(55, 115, 59, 119)(56, 116, 57, 117)(121, 181, 123, 183, 129, 189, 141, 201, 134, 194, 125, 185)(122, 182, 126, 186, 135, 195, 149, 209, 140, 200, 128, 188)(124, 184, 131, 191, 145, 205, 158, 218, 142, 202, 132, 192)(127, 187, 137, 197, 153, 213, 166, 226, 150, 210, 138, 198)(130, 190, 143, 203, 133, 193, 148, 208, 157, 217, 144, 204)(136, 196, 151, 211, 139, 199, 156, 216, 165, 225, 152, 212)(146, 206, 161, 221, 147, 207, 163, 223, 173, 233, 162, 222)(154, 214, 169, 229, 155, 215, 171, 231, 180, 240, 170, 230)(159, 219, 174, 234, 160, 220, 176, 236, 164, 224, 175, 235)(167, 227, 179, 239, 168, 228, 177, 237, 172, 232, 178, 238) L = (1, 124)(2, 127)(3, 130)(4, 121)(5, 133)(6, 136)(7, 122)(8, 139)(9, 142)(10, 123)(11, 146)(12, 147)(13, 125)(14, 145)(15, 150)(16, 126)(17, 154)(18, 155)(19, 128)(20, 153)(21, 157)(22, 129)(23, 159)(24, 160)(25, 134)(26, 131)(27, 132)(28, 164)(29, 165)(30, 135)(31, 167)(32, 168)(33, 140)(34, 137)(35, 138)(36, 172)(37, 141)(38, 173)(39, 143)(40, 144)(41, 177)(42, 178)(43, 179)(44, 148)(45, 149)(46, 180)(47, 151)(48, 152)(49, 176)(50, 175)(51, 174)(52, 156)(53, 158)(54, 171)(55, 170)(56, 169)(57, 161)(58, 162)(59, 163)(60, 166)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 4, 20, 4, 20 ), ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) } Outer automorphisms :: reflexible Dual of E23.745 Graph:: simple bipartite v = 40 e = 120 f = 36 degree seq :: [ 4^30, 12^10 ] E23.743 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 6, 10}) Quotient :: dipole Aut^+ = S3 x D10 (small group id <60, 8>) Aut = C2 x S3 x D10 (small group id <120, 42>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, (Y3 * Y1)^2, (R * Y1)^2, (R * Y3)^2, (Y1 * Y2 * Y3)^2, (R * Y2 * Y3)^2, Y2^2 * Y1 * Y2^-2 * Y1, (Y3 * Y2^-2)^2, Y2^6, Y2^-1 * Y1 * Y2 * Y3 * Y2 * Y3 * Y2^-1 * Y1 * Y2^-1 * Y1, (Y3 * Y2)^10 ] Map:: polytopal non-degenerate R = (1, 61, 2, 62)(3, 63, 9, 69)(4, 64, 7, 67)(5, 65, 14, 74)(6, 66, 17, 77)(8, 68, 22, 82)(10, 70, 18, 78)(11, 71, 21, 81)(12, 72, 23, 83)(13, 73, 19, 79)(15, 75, 20, 80)(16, 76, 24, 84)(25, 85, 43, 103)(26, 86, 46, 106)(27, 87, 44, 104)(28, 88, 37, 97)(29, 89, 47, 107)(30, 90, 45, 105)(31, 91, 40, 100)(32, 92, 50, 110)(33, 93, 51, 111)(34, 94, 52, 112)(35, 95, 55, 115)(36, 96, 53, 113)(38, 98, 56, 116)(39, 99, 54, 114)(41, 101, 59, 119)(42, 102, 60, 120)(48, 108, 58, 118)(49, 109, 57, 117)(121, 181, 123, 183, 130, 190, 147, 207, 136, 196, 125, 185)(122, 182, 126, 186, 138, 198, 156, 216, 144, 204, 128, 188)(124, 184, 132, 192, 151, 211, 169, 229, 148, 208, 133, 193)(127, 187, 140, 200, 160, 220, 178, 238, 157, 217, 141, 201)(129, 189, 145, 205, 164, 224, 152, 212, 134, 194, 146, 206)(131, 191, 149, 209, 135, 195, 153, 213, 168, 228, 150, 210)(137, 197, 154, 214, 173, 233, 161, 221, 142, 202, 155, 215)(139, 199, 158, 218, 143, 203, 162, 222, 177, 237, 159, 219)(163, 223, 175, 235, 170, 230, 172, 232, 166, 226, 179, 239)(165, 225, 180, 240, 167, 227, 174, 234, 171, 231, 176, 236) L = (1, 124)(2, 127)(3, 131)(4, 121)(5, 135)(6, 139)(7, 122)(8, 143)(9, 141)(10, 148)(11, 123)(12, 142)(13, 137)(14, 140)(15, 125)(16, 151)(17, 133)(18, 157)(19, 126)(20, 134)(21, 129)(22, 132)(23, 128)(24, 160)(25, 165)(26, 167)(27, 168)(28, 130)(29, 166)(30, 163)(31, 136)(32, 171)(33, 170)(34, 174)(35, 176)(36, 177)(37, 138)(38, 175)(39, 172)(40, 144)(41, 180)(42, 179)(43, 150)(44, 178)(45, 145)(46, 149)(47, 146)(48, 147)(49, 173)(50, 153)(51, 152)(52, 159)(53, 169)(54, 154)(55, 158)(56, 155)(57, 156)(58, 164)(59, 162)(60, 161)(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 ) } Outer automorphisms :: reflexible Dual of E23.744 Graph:: simple bipartite v = 40 e = 120 f = 36 degree seq :: [ 4^30, 12^10 ] E23.744 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 6, 10}) Quotient :: dipole Aut^+ = S3 x D10 (small group id <60, 8>) Aut = C2 x S3 x D10 (small group id <120, 42>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (Y3 * Y2)^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y2 * Y1^-1 * Y3)^2, (Y1^-2 * Y3)^2, Y1^-1 * Y2 * Y1^2 * Y2 * Y1^-1, Y1^-1 * Y3 * Y1 * Y2 * Y1 * Y3 * Y1^-2, Y1^10, (Y3 * Y1)^6 ] Map:: polytopal non-degenerate R = (1, 61, 2, 62, 6, 66, 17, 77, 35, 95, 51, 111, 50, 110, 34, 94, 16, 76, 5, 65)(3, 63, 9, 69, 18, 78, 38, 98, 52, 112, 43, 103, 55, 115, 41, 101, 30, 90, 11, 71)(4, 64, 12, 72, 31, 91, 42, 102, 56, 116, 44, 104, 53, 113, 40, 100, 19, 79, 13, 73)(7, 67, 20, 80, 36, 96, 28, 88, 46, 106, 25, 85, 45, 105, 32, 92, 14, 74, 22, 82)(8, 68, 23, 83, 15, 75, 33, 93, 48, 108, 26, 86, 47, 107, 29, 89, 37, 97, 24, 84)(10, 70, 27, 87, 49, 109, 57, 117, 60, 120, 58, 118, 59, 119, 54, 114, 39, 99, 21, 81)(121, 181, 123, 183)(122, 182, 127, 187)(124, 184, 130, 190)(125, 185, 134, 194)(126, 186, 138, 198)(128, 188, 141, 201)(129, 189, 145, 205)(131, 191, 148, 208)(132, 192, 149, 209)(133, 193, 146, 206)(135, 195, 147, 207)(136, 196, 150, 210)(137, 197, 156, 216)(139, 199, 159, 219)(140, 200, 161, 221)(142, 202, 163, 223)(143, 203, 164, 224)(144, 204, 162, 222)(151, 211, 169, 229)(152, 212, 158, 218)(153, 213, 160, 220)(154, 214, 165, 225)(155, 215, 172, 232)(157, 217, 174, 234)(166, 226, 171, 231)(167, 227, 178, 238)(168, 228, 177, 237)(170, 230, 175, 235)(173, 233, 179, 239)(176, 236, 180, 240) L = (1, 124)(2, 128)(3, 130)(4, 121)(5, 135)(6, 139)(7, 141)(8, 122)(9, 146)(10, 123)(11, 149)(12, 148)(13, 145)(14, 147)(15, 125)(16, 151)(17, 157)(18, 159)(19, 126)(20, 162)(21, 127)(22, 164)(23, 163)(24, 161)(25, 133)(26, 129)(27, 134)(28, 132)(29, 131)(30, 169)(31, 136)(32, 160)(33, 158)(34, 168)(35, 173)(36, 174)(37, 137)(38, 153)(39, 138)(40, 152)(41, 144)(42, 140)(43, 143)(44, 142)(45, 177)(46, 178)(47, 171)(48, 154)(49, 150)(50, 176)(51, 167)(52, 179)(53, 155)(54, 156)(55, 180)(56, 170)(57, 165)(58, 166)(59, 172)(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, 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 E23.743 Graph:: simple bipartite v = 36 e = 120 f = 40 degree seq :: [ 4^30, 20^6 ] E23.745 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 6, 10}) Quotient :: dipole Aut^+ = S3 x D10 (small group id <60, 8>) Aut = C2 x S3 x D10 (small group id <120, 42>) |r| :: 2 Presentation :: [ Y3^2, Y2^2, R^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y1^-1 * Y2)^2, (Y1^-2 * Y3)^2, Y1^2 * Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1^-1 * Y2, Y1^10, (Y3 * Y1)^6 ] Map:: polytopal non-degenerate R = (1, 61, 2, 62, 6, 66, 15, 75, 30, 90, 51, 111, 50, 110, 29, 89, 14, 74, 5, 65)(3, 63, 9, 69, 21, 81, 39, 99, 57, 117, 60, 120, 52, 112, 31, 91, 16, 76, 7, 67)(4, 64, 11, 71, 25, 85, 44, 104, 59, 119, 54, 114, 53, 113, 34, 94, 17, 77, 12, 72)(8, 68, 19, 79, 13, 73, 28, 88, 48, 108, 42, 102, 58, 118, 43, 103, 32, 92, 20, 80)(10, 70, 23, 83, 33, 93, 49, 109, 56, 116, 37, 97, 55, 115, 38, 98, 40, 100, 24, 84)(18, 78, 35, 95, 46, 106, 26, 86, 45, 105, 27, 87, 47, 107, 41, 101, 22, 82, 36, 96)(121, 181, 123, 183)(122, 182, 127, 187)(124, 184, 130, 190)(125, 185, 129, 189)(126, 186, 136, 196)(128, 188, 138, 198)(131, 191, 144, 204)(132, 192, 143, 203)(133, 193, 142, 202)(134, 194, 141, 201)(135, 195, 151, 211)(137, 197, 153, 213)(139, 199, 156, 216)(140, 200, 155, 215)(145, 205, 160, 220)(146, 206, 163, 223)(147, 207, 162, 222)(148, 208, 161, 221)(149, 209, 159, 219)(150, 210, 172, 232)(152, 212, 166, 226)(154, 214, 169, 229)(157, 217, 174, 234)(158, 218, 164, 224)(165, 225, 178, 238)(167, 227, 168, 228)(170, 230, 177, 237)(171, 231, 180, 240)(173, 233, 176, 236)(175, 235, 179, 239) L = (1, 124)(2, 128)(3, 130)(4, 121)(5, 133)(6, 137)(7, 138)(8, 122)(9, 142)(10, 123)(11, 146)(12, 147)(13, 125)(14, 145)(15, 152)(16, 153)(17, 126)(18, 127)(19, 157)(20, 158)(21, 160)(22, 129)(23, 162)(24, 163)(25, 134)(26, 131)(27, 132)(28, 169)(29, 168)(30, 173)(31, 166)(32, 135)(33, 136)(34, 161)(35, 164)(36, 174)(37, 139)(38, 140)(39, 167)(40, 141)(41, 154)(42, 143)(43, 144)(44, 155)(45, 180)(46, 151)(47, 159)(48, 149)(49, 148)(50, 179)(51, 178)(52, 176)(53, 150)(54, 156)(55, 177)(56, 172)(57, 175)(58, 171)(59, 170)(60, 165)(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, 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 E23.742 Graph:: simple bipartite v = 36 e = 120 f = 40 degree seq :: [ 4^30, 20^6 ] E23.746 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 6, 10}) Quotient :: dipole Aut^+ = S3 x D10 (small group id <60, 8>) Aut = C2 x S3 x D10 (small group id <120, 42>) |r| :: 2 Presentation :: [ R^2, Y3^2, R * Y2 * R * Y2^-1, (Y2^-1 * Y3)^2, (R * Y1)^2, (R * Y3)^2, (Y1^-1 * Y3)^2, (Y1^-1 * Y2^-1)^2, (Y2 * Y1^-1)^2, Y1^6, Y1 * Y2^-1 * Y1^-1 * Y2 * Y1 * Y2^-3 * Y3, Y1^2 * Y2^-1 * Y1^-1 * Y2 * Y3 * Y2^-3, Y2^10 ] Map:: polytopal non-degenerate R = (1, 61, 2, 62, 7, 67, 19, 79, 17, 77, 5, 65)(3, 63, 11, 71, 27, 87, 40, 100, 20, 80, 10, 70)(4, 64, 14, 74, 32, 92, 39, 99, 21, 81, 9, 69)(6, 66, 16, 76, 35, 95, 38, 98, 22, 82, 8, 68)(12, 72, 26, 86, 41, 101, 57, 117, 49, 109, 29, 89)(13, 73, 25, 85, 42, 102, 60, 120, 50, 110, 28, 88)(15, 75, 24, 84, 43, 103, 53, 113, 55, 115, 33, 93)(18, 78, 23, 83, 44, 104, 54, 114, 58, 118, 36, 96)(30, 90, 52, 112, 46, 106, 34, 94, 56, 116, 48, 108)(31, 91, 51, 111, 45, 105, 37, 97, 59, 119, 47, 107)(121, 181, 123, 183, 132, 192, 150, 210, 173, 233, 159, 219, 180, 240, 157, 217, 138, 198, 126, 186)(122, 182, 128, 188, 143, 203, 165, 225, 170, 230, 152, 212, 175, 235, 168, 228, 146, 206, 130, 190)(124, 184, 135, 195, 154, 214, 177, 237, 160, 220, 139, 199, 158, 218, 174, 234, 151, 211, 133, 193)(125, 185, 136, 196, 156, 216, 179, 239, 162, 222, 141, 201, 163, 223, 172, 232, 149, 209, 131, 191)(127, 187, 140, 200, 161, 221, 176, 236, 153, 213, 134, 194, 148, 208, 171, 231, 164, 224, 142, 202)(129, 189, 145, 205, 167, 227, 178, 238, 155, 215, 137, 197, 147, 207, 169, 229, 166, 226, 144, 204) L = (1, 124)(2, 129)(3, 133)(4, 121)(5, 134)(6, 135)(7, 141)(8, 144)(9, 122)(10, 145)(11, 148)(12, 151)(13, 123)(14, 125)(15, 126)(16, 153)(17, 152)(18, 154)(19, 159)(20, 162)(21, 127)(22, 163)(23, 166)(24, 128)(25, 130)(26, 167)(27, 170)(28, 131)(29, 171)(30, 174)(31, 132)(32, 137)(33, 136)(34, 138)(35, 175)(36, 176)(37, 177)(38, 173)(39, 139)(40, 180)(41, 179)(42, 140)(43, 142)(44, 172)(45, 169)(46, 143)(47, 146)(48, 178)(49, 165)(50, 147)(51, 149)(52, 164)(53, 158)(54, 150)(55, 155)(56, 156)(57, 157)(58, 168)(59, 161)(60, 160)(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) :: { ( 4^12 ), ( 4^20 ) } Outer automorphisms :: reflexible Dual of E23.741 Graph:: bipartite v = 16 e = 120 f = 60 degree seq :: [ 12^10, 20^6 ] E23.747 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 6, 10}) Quotient :: dipole Aut^+ = D60 (small group id <60, 12>) Aut = C2 x C2 x D30 (small group id <120, 46>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y1)^2, (Y3, Y2^-1), (Y3^-1 * Y1)^2, (R * Y2)^2, (Y2^-1 * Y1)^2, (R * Y3)^2, Y2^6, Y3^-5 * Y2^2 ] Map:: non-degenerate R = (1, 61, 2, 62)(3, 63, 9, 69)(4, 64, 10, 70)(5, 65, 7, 67)(6, 66, 8, 68)(11, 71, 24, 84)(12, 72, 25, 85)(13, 73, 23, 83)(14, 74, 26, 86)(15, 75, 21, 81)(16, 76, 19, 79)(17, 77, 20, 80)(18, 78, 22, 82)(27, 87, 38, 98)(28, 88, 46, 106)(29, 89, 45, 105)(30, 90, 47, 107)(31, 91, 44, 104)(32, 92, 48, 108)(33, 93, 42, 102)(34, 94, 40, 100)(35, 95, 39, 99)(36, 96, 41, 101)(37, 97, 43, 103)(49, 109, 56, 116)(50, 110, 55, 115)(51, 111, 59, 119)(52, 112, 60, 120)(53, 113, 57, 117)(54, 114, 58, 118)(121, 181, 123, 183, 131, 191, 147, 207, 136, 196, 125, 185)(122, 182, 127, 187, 139, 199, 158, 218, 144, 204, 129, 189)(124, 184, 132, 192, 148, 208, 169, 229, 154, 214, 135, 195)(126, 186, 133, 193, 149, 209, 170, 230, 155, 215, 137, 197)(128, 188, 140, 200, 159, 219, 175, 235, 165, 225, 143, 203)(130, 190, 141, 201, 160, 220, 176, 236, 166, 226, 145, 205)(134, 194, 150, 210, 171, 231, 174, 234, 157, 217, 153, 213)(138, 198, 151, 211, 152, 212, 172, 232, 173, 233, 156, 216)(142, 202, 161, 221, 177, 237, 180, 240, 168, 228, 164, 224)(146, 206, 162, 222, 163, 223, 178, 238, 179, 239, 167, 227) L = (1, 124)(2, 128)(3, 132)(4, 134)(5, 135)(6, 121)(7, 140)(8, 142)(9, 143)(10, 122)(11, 148)(12, 150)(13, 123)(14, 152)(15, 153)(16, 154)(17, 125)(18, 126)(19, 159)(20, 161)(21, 127)(22, 163)(23, 164)(24, 165)(25, 129)(26, 130)(27, 169)(28, 171)(29, 131)(30, 172)(31, 133)(32, 149)(33, 151)(34, 157)(35, 136)(36, 137)(37, 138)(38, 175)(39, 177)(40, 139)(41, 178)(42, 141)(43, 160)(44, 162)(45, 168)(46, 144)(47, 145)(48, 146)(49, 174)(50, 147)(51, 173)(52, 170)(53, 155)(54, 156)(55, 180)(56, 158)(57, 179)(58, 176)(59, 166)(60, 167)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 4, 20, 4, 20 ), ( 4, 20, 4, 20, 4, 20, 4, 20, 4, 20, 4, 20 ) } Outer automorphisms :: reflexible Dual of E23.748 Graph:: simple bipartite v = 40 e = 120 f = 36 degree seq :: [ 4^30, 12^10 ] E23.748 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 6, 10}) Quotient :: dipole Aut^+ = D60 (small group id <60, 12>) Aut = C2 x C2 x D30 (small group id <120, 46>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3 * Y2)^2, (R * Y3)^2, (Y2 * Y1^-1)^2, (R * Y1)^2, (Y3^-1, Y1^-1), Y3^-3 * Y1^2, (R * Y2 * Y3^-1)^2, Y1^10 ] Map:: non-degenerate R = (1, 61, 2, 62, 7, 67, 19, 79, 33, 93, 45, 105, 42, 102, 30, 90, 16, 76, 5, 65)(3, 63, 11, 71, 25, 85, 39, 99, 51, 111, 56, 116, 46, 106, 34, 94, 20, 80, 8, 68)(4, 64, 9, 69, 21, 81, 35, 95, 47, 107, 55, 115, 44, 104, 32, 92, 18, 78, 15, 75)(6, 66, 10, 70, 14, 74, 24, 84, 37, 97, 49, 109, 54, 114, 43, 103, 31, 91, 17, 77)(12, 72, 26, 86, 40, 100, 52, 112, 59, 119, 58, 118, 50, 110, 38, 98, 29, 89, 22, 82)(13, 73, 27, 87, 28, 88, 41, 101, 53, 113, 60, 120, 57, 117, 48, 108, 36, 96, 23, 83)(121, 181, 123, 183)(122, 182, 128, 188)(124, 184, 133, 193)(125, 185, 131, 191)(126, 186, 132, 192)(127, 187, 140, 200)(129, 189, 143, 203)(130, 190, 142, 202)(134, 194, 149, 209)(135, 195, 147, 207)(136, 196, 145, 205)(137, 197, 146, 206)(138, 198, 148, 208)(139, 199, 154, 214)(141, 201, 156, 216)(144, 204, 158, 218)(150, 210, 159, 219)(151, 211, 160, 220)(152, 212, 161, 221)(153, 213, 166, 226)(155, 215, 168, 228)(157, 217, 170, 230)(162, 222, 171, 231)(163, 223, 172, 232)(164, 224, 173, 233)(165, 225, 176, 236)(167, 227, 177, 237)(169, 229, 178, 238)(174, 234, 179, 239)(175, 235, 180, 240) L = (1, 124)(2, 129)(3, 132)(4, 134)(5, 135)(6, 121)(7, 141)(8, 142)(9, 144)(10, 122)(11, 146)(12, 148)(13, 123)(14, 127)(15, 130)(16, 138)(17, 125)(18, 126)(19, 155)(20, 149)(21, 157)(22, 147)(23, 128)(24, 139)(25, 160)(26, 161)(27, 131)(28, 145)(29, 133)(30, 152)(31, 136)(32, 137)(33, 167)(34, 158)(35, 169)(36, 140)(37, 153)(38, 143)(39, 172)(40, 173)(41, 159)(42, 164)(43, 150)(44, 151)(45, 175)(46, 170)(47, 174)(48, 154)(49, 165)(50, 156)(51, 179)(52, 180)(53, 171)(54, 162)(55, 163)(56, 178)(57, 166)(58, 168)(59, 177)(60, 176)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 4, 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 E23.747 Graph:: simple bipartite v = 36 e = 120 f = 40 degree seq :: [ 4^30, 20^6 ] E23.749 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {10, 12, 12}) Quotient :: edge Aut^+ = C3 x (C5 : C4) (small group id <60, 2>) Aut = (C10 x S3) : C2 (small group id <120, 13>) |r| :: 2 Presentation :: [ F^2, T1 * T2 * T1 * T2^-1, (F * T2)^2, (F * T1)^2, T1^10, T1^2 * T2 * T1^-3 * T2^5, T2^12 ] Map:: non-degenerate R = (1, 3, 10, 21, 36, 55, 42, 60, 41, 25, 13, 5)(2, 7, 17, 31, 49, 56, 37, 51, 50, 32, 18, 8)(4, 9, 20, 35, 54, 44, 26, 43, 59, 40, 24, 12)(6, 15, 29, 47, 57, 38, 22, 33, 52, 48, 30, 16)(11, 19, 34, 53, 46, 28, 14, 27, 45, 58, 39, 23)(61, 62, 66, 74, 86, 102, 97, 82, 71, 64)(63, 69, 79, 93, 111, 120, 103, 87, 75, 67)(65, 72, 83, 98, 116, 115, 104, 88, 76, 68)(70, 77, 89, 105, 119, 101, 110, 112, 94, 80)(73, 78, 90, 106, 114, 96, 109, 117, 99, 84)(81, 95, 113, 108, 92, 85, 100, 118, 107, 91) L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 24^10 ), ( 24^12 ) } Outer automorphisms :: reflexible Dual of E23.750 Transitivity :: ET+ Graph:: bipartite v = 11 e = 60 f = 5 degree seq :: [ 10^6, 12^5 ] E23.750 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {10, 12, 12}) Quotient :: loop Aut^+ = C3 x (C5 : C4) (small group id <60, 2>) Aut = (C10 x S3) : C2 (small group id <120, 13>) |r| :: 2 Presentation :: [ F^2, T1 * T2 * T1 * T2^-1, (F * T2)^2, (F * T1)^2, T1^10, T1^2 * T2 * T1^-3 * T2^5, T2^12 ] Map:: non-degenerate R = (1, 61, 3, 63, 10, 70, 21, 81, 36, 96, 55, 115, 42, 102, 60, 120, 41, 101, 25, 85, 13, 73, 5, 65)(2, 62, 7, 67, 17, 77, 31, 91, 49, 109, 56, 116, 37, 97, 51, 111, 50, 110, 32, 92, 18, 78, 8, 68)(4, 64, 9, 69, 20, 80, 35, 95, 54, 114, 44, 104, 26, 86, 43, 103, 59, 119, 40, 100, 24, 84, 12, 72)(6, 66, 15, 75, 29, 89, 47, 107, 57, 117, 38, 98, 22, 82, 33, 93, 52, 112, 48, 108, 30, 90, 16, 76)(11, 71, 19, 79, 34, 94, 53, 113, 46, 106, 28, 88, 14, 74, 27, 87, 45, 105, 58, 118, 39, 99, 23, 83) L = (1, 62)(2, 66)(3, 69)(4, 61)(5, 72)(6, 74)(7, 63)(8, 65)(9, 79)(10, 77)(11, 64)(12, 83)(13, 78)(14, 86)(15, 67)(16, 68)(17, 89)(18, 90)(19, 93)(20, 70)(21, 95)(22, 71)(23, 98)(24, 73)(25, 100)(26, 102)(27, 75)(28, 76)(29, 105)(30, 106)(31, 81)(32, 85)(33, 111)(34, 80)(35, 113)(36, 109)(37, 82)(38, 116)(39, 84)(40, 118)(41, 110)(42, 97)(43, 87)(44, 88)(45, 119)(46, 114)(47, 91)(48, 92)(49, 117)(50, 112)(51, 120)(52, 94)(53, 108)(54, 96)(55, 104)(56, 115)(57, 99)(58, 107)(59, 101)(60, 103) local type(s) :: { ( 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12, 10, 12 ) } Outer automorphisms :: reflexible Dual of E23.749 Transitivity :: ET+ VT+ AT Graph:: v = 5 e = 60 f = 11 degree seq :: [ 24^5 ] E23.751 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {10, 12, 12}) Quotient :: dipole Aut^+ = C3 x (C5 : C4) (small group id <60, 2>) Aut = (C10 x S3) : C2 (small group id <120, 13>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, Y2 * Y3 * Y2^-1 * Y1^-1, Y2^-1 * Y3 * Y2 * Y1^-1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y1^3 * Y2 * Y3^-1 * Y2^-1 * Y1^-3 * Y3^-1, (Y1^-4 * Y3)^2, Y1^10, Y1^3 * Y2 * Y3^2 * Y2^5, Y1 * Y2 * Y3 * Y2^2 * Y3 * Y2^3 * Y3^-2, (Y2^-1 * Y1)^12 ] Map:: R = (1, 61, 2, 62, 6, 66, 14, 74, 26, 86, 42, 102, 37, 97, 22, 82, 11, 71, 4, 64)(3, 63, 9, 69, 19, 79, 33, 93, 51, 111, 60, 120, 43, 103, 27, 87, 15, 75, 7, 67)(5, 65, 12, 72, 23, 83, 38, 98, 56, 116, 55, 115, 44, 104, 28, 88, 16, 76, 8, 68)(10, 70, 17, 77, 29, 89, 45, 105, 59, 119, 41, 101, 50, 110, 52, 112, 34, 94, 20, 80)(13, 73, 18, 78, 30, 90, 46, 106, 54, 114, 36, 96, 49, 109, 57, 117, 39, 99, 24, 84)(21, 81, 35, 95, 53, 113, 48, 108, 32, 92, 25, 85, 40, 100, 58, 118, 47, 107, 31, 91)(121, 181, 123, 183, 130, 190, 141, 201, 156, 216, 175, 235, 162, 222, 180, 240, 161, 221, 145, 205, 133, 193, 125, 185)(122, 182, 127, 187, 137, 197, 151, 211, 169, 229, 176, 236, 157, 217, 171, 231, 170, 230, 152, 212, 138, 198, 128, 188)(124, 184, 129, 189, 140, 200, 155, 215, 174, 234, 164, 224, 146, 206, 163, 223, 179, 239, 160, 220, 144, 204, 132, 192)(126, 186, 135, 195, 149, 209, 167, 227, 177, 237, 158, 218, 142, 202, 153, 213, 172, 232, 168, 228, 150, 210, 136, 196)(131, 191, 139, 199, 154, 214, 173, 233, 166, 226, 148, 208, 134, 194, 147, 207, 165, 225, 178, 238, 159, 219, 143, 203) L = (1, 124)(2, 121)(3, 127)(4, 131)(5, 128)(6, 122)(7, 135)(8, 136)(9, 123)(10, 140)(11, 142)(12, 125)(13, 144)(14, 126)(15, 147)(16, 148)(17, 130)(18, 133)(19, 129)(20, 154)(21, 151)(22, 157)(23, 132)(24, 159)(25, 152)(26, 134)(27, 163)(28, 164)(29, 137)(30, 138)(31, 167)(32, 168)(33, 139)(34, 172)(35, 141)(36, 174)(37, 162)(38, 143)(39, 177)(40, 145)(41, 179)(42, 146)(43, 180)(44, 175)(45, 149)(46, 150)(47, 178)(48, 173)(49, 156)(50, 161)(51, 153)(52, 170)(53, 155)(54, 166)(55, 176)(56, 158)(57, 169)(58, 160)(59, 165)(60, 171)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24 ), ( 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24 ) } Outer automorphisms :: reflexible Dual of E23.752 Graph:: bipartite v = 11 e = 120 f = 65 degree seq :: [ 20^6, 24^5 ] E23.752 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {10, 12, 12}) Quotient :: dipole Aut^+ = C3 x (C5 : C4) (small group id <60, 2>) Aut = (C10 x S3) : C2 (small group id <120, 13>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, Y3 * Y1 * Y3 * Y1^-1, Y1^2 * Y3 * Y1^-2 * Y3^-1, (R * Y2 * Y3^-1)^2, Y1^4 * Y3^-1 * Y1^2 * Y3^-4, Y1^12, (Y3 * Y2^-1)^10 ] Map:: R = (1, 61, 2, 62, 6, 66, 14, 74, 26, 86, 42, 102, 51, 111, 60, 120, 40, 100, 24, 84, 12, 72, 4, 64)(3, 63, 8, 68, 15, 75, 28, 88, 43, 103, 56, 116, 41, 101, 49, 109, 55, 115, 36, 96, 21, 81, 10, 70)(5, 65, 7, 67, 16, 76, 27, 87, 44, 104, 52, 112, 33, 93, 50, 110, 59, 119, 39, 99, 23, 83, 11, 71)(9, 69, 18, 78, 29, 89, 46, 106, 57, 117, 37, 97, 25, 85, 31, 91, 48, 108, 54, 114, 35, 95, 20, 80)(13, 73, 17, 77, 30, 90, 45, 105, 53, 113, 34, 94, 19, 79, 32, 92, 47, 107, 58, 118, 38, 98, 22, 82)(121, 181)(122, 182)(123, 183)(124, 184)(125, 185)(126, 186)(127, 187)(128, 188)(129, 189)(130, 190)(131, 191)(132, 192)(133, 193)(134, 194)(135, 195)(136, 196)(137, 197)(138, 198)(139, 199)(140, 200)(141, 201)(142, 202)(143, 203)(144, 204)(145, 205)(146, 206)(147, 207)(148, 208)(149, 209)(150, 210)(151, 211)(152, 212)(153, 213)(154, 214)(155, 215)(156, 216)(157, 217)(158, 218)(159, 219)(160, 220)(161, 221)(162, 222)(163, 223)(164, 224)(165, 225)(166, 226)(167, 227)(168, 228)(169, 229)(170, 230)(171, 231)(172, 232)(173, 233)(174, 234)(175, 235)(176, 236)(177, 237)(178, 238)(179, 239)(180, 240) L = (1, 123)(2, 127)(3, 129)(4, 131)(5, 121)(6, 135)(7, 137)(8, 122)(9, 139)(10, 124)(11, 142)(12, 141)(13, 125)(14, 147)(15, 149)(16, 126)(17, 151)(18, 128)(19, 153)(20, 130)(21, 155)(22, 157)(23, 132)(24, 159)(25, 133)(26, 163)(27, 165)(28, 134)(29, 167)(30, 136)(31, 169)(32, 138)(33, 171)(34, 140)(35, 173)(36, 144)(37, 176)(38, 143)(39, 178)(40, 175)(41, 145)(42, 172)(43, 177)(44, 146)(45, 174)(46, 148)(47, 179)(48, 150)(49, 180)(50, 152)(51, 161)(52, 154)(53, 164)(54, 156)(55, 168)(56, 162)(57, 158)(58, 166)(59, 160)(60, 170)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 20, 24 ), ( 20, 24, 20, 24, 20, 24, 20, 24, 20, 24, 20, 24, 20, 24, 20, 24, 20, 24, 20, 24, 20, 24, 20, 24 ) } Outer automorphisms :: reflexible Dual of E23.751 Graph:: simple bipartite v = 65 e = 120 f = 11 degree seq :: [ 2^60, 24^5 ] E23.753 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {6, 20, 20}) Quotient :: edge Aut^+ = C5 x (C3 : C4) (small group id <60, 1>) Aut = (C6 x D10) : C2 (small group id <120, 12>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T2 * T1^-1 * T2^-1 * T1^-1, T1^6, T1^-1 * T2^3 * T1^-2 * T2^-3 * T1^-1, T1 * T2^4 * T1^2 * T2^6 ] Map:: non-degenerate R = (1, 3, 10, 21, 33, 45, 57, 50, 38, 26, 14, 25, 37, 49, 60, 48, 36, 24, 13, 5)(2, 7, 17, 29, 41, 53, 58, 46, 34, 22, 11, 19, 31, 43, 55, 54, 42, 30, 18, 8)(4, 9, 20, 32, 44, 56, 52, 40, 28, 16, 6, 15, 27, 39, 51, 59, 47, 35, 23, 12)(61, 62, 66, 74, 71, 64)(63, 69, 79, 85, 75, 67)(65, 72, 82, 86, 76, 68)(70, 77, 87, 97, 91, 80)(73, 78, 88, 98, 94, 83)(81, 92, 103, 109, 99, 89)(84, 95, 106, 110, 100, 90)(93, 101, 111, 120, 115, 104)(96, 102, 112, 117, 118, 107)(105, 116, 114, 108, 119, 113) L = (1, 61)(2, 62)(3, 63)(4, 64)(5, 65)(6, 66)(7, 67)(8, 68)(9, 69)(10, 70)(11, 71)(12, 72)(13, 73)(14, 74)(15, 75)(16, 76)(17, 77)(18, 78)(19, 79)(20, 80)(21, 81)(22, 82)(23, 83)(24, 84)(25, 85)(26, 86)(27, 87)(28, 88)(29, 89)(30, 90)(31, 91)(32, 92)(33, 93)(34, 94)(35, 95)(36, 96)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 103)(44, 104)(45, 105)(46, 106)(47, 107)(48, 108)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 115)(56, 116)(57, 117)(58, 118)(59, 119)(60, 120) local type(s) :: { ( 40^6 ), ( 40^20 ) } Outer automorphisms :: reflexible Dual of E23.754 Transitivity :: ET+ Graph:: bipartite v = 13 e = 60 f = 3 degree seq :: [ 6^10, 20^3 ] E23.754 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {6, 20, 20}) Quotient :: loop Aut^+ = C5 x (C3 : C4) (small group id <60, 1>) Aut = (C6 x D10) : C2 (small group id <120, 12>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T2 * T1^-1 * T2^-1 * T1^-1, T1^6, T1^-1 * T2^3 * T1^-2 * T2^-3 * T1^-1, T1 * T2^4 * T1^2 * T2^6 ] Map:: non-degenerate R = (1, 61, 3, 63, 10, 70, 21, 81, 33, 93, 45, 105, 57, 117, 50, 110, 38, 98, 26, 86, 14, 74, 25, 85, 37, 97, 49, 109, 60, 120, 48, 108, 36, 96, 24, 84, 13, 73, 5, 65)(2, 62, 7, 67, 17, 77, 29, 89, 41, 101, 53, 113, 58, 118, 46, 106, 34, 94, 22, 82, 11, 71, 19, 79, 31, 91, 43, 103, 55, 115, 54, 114, 42, 102, 30, 90, 18, 78, 8, 68)(4, 64, 9, 69, 20, 80, 32, 92, 44, 104, 56, 116, 52, 112, 40, 100, 28, 88, 16, 76, 6, 66, 15, 75, 27, 87, 39, 99, 51, 111, 59, 119, 47, 107, 35, 95, 23, 83, 12, 72) L = (1, 62)(2, 66)(3, 69)(4, 61)(5, 72)(6, 74)(7, 63)(8, 65)(9, 79)(10, 77)(11, 64)(12, 82)(13, 78)(14, 71)(15, 67)(16, 68)(17, 87)(18, 88)(19, 85)(20, 70)(21, 92)(22, 86)(23, 73)(24, 95)(25, 75)(26, 76)(27, 97)(28, 98)(29, 81)(30, 84)(31, 80)(32, 103)(33, 101)(34, 83)(35, 106)(36, 102)(37, 91)(38, 94)(39, 89)(40, 90)(41, 111)(42, 112)(43, 109)(44, 93)(45, 116)(46, 110)(47, 96)(48, 119)(49, 99)(50, 100)(51, 120)(52, 117)(53, 105)(54, 108)(55, 104)(56, 114)(57, 118)(58, 107)(59, 113)(60, 115) local type(s) :: { ( 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20, 6, 20 ) } Outer automorphisms :: reflexible Dual of E23.753 Transitivity :: ET+ VT+ AT Graph:: v = 3 e = 60 f = 13 degree seq :: [ 40^3 ] E23.755 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 20, 20}) Quotient :: dipole Aut^+ = C5 x (C3 : C4) (small group id <60, 1>) Aut = (C6 x D10) : C2 (small group id <120, 12>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y2^-1 * Y3 * Y2 * Y1^-1, (R * Y1)^2, (R * Y3)^2, Y2 * Y3 * Y2^-1 * Y1^-1, (R * Y2 * Y3^-1)^2, Y1^6, Y3 * Y2^3 * Y1^-2 * Y2^-3 * Y3, Y1 * Y2^4 * Y1^2 * Y2^6, Y2 * Y3 * Y2^4 * Y3 * Y2^5 * Y3^-1, (Y2^-1 * Y1)^20 ] Map:: R = (1, 61, 2, 62, 6, 66, 14, 74, 11, 71, 4, 64)(3, 63, 9, 69, 19, 79, 25, 85, 15, 75, 7, 67)(5, 65, 12, 72, 22, 82, 26, 86, 16, 76, 8, 68)(10, 70, 17, 77, 27, 87, 37, 97, 31, 91, 20, 80)(13, 73, 18, 78, 28, 88, 38, 98, 34, 94, 23, 83)(21, 81, 32, 92, 43, 103, 49, 109, 39, 99, 29, 89)(24, 84, 35, 95, 46, 106, 50, 110, 40, 100, 30, 90)(33, 93, 41, 101, 51, 111, 60, 120, 55, 115, 44, 104)(36, 96, 42, 102, 52, 112, 57, 117, 58, 118, 47, 107)(45, 105, 56, 116, 54, 114, 48, 108, 59, 119, 53, 113)(121, 181, 123, 183, 130, 190, 141, 201, 153, 213, 165, 225, 177, 237, 170, 230, 158, 218, 146, 206, 134, 194, 145, 205, 157, 217, 169, 229, 180, 240, 168, 228, 156, 216, 144, 204, 133, 193, 125, 185)(122, 182, 127, 187, 137, 197, 149, 209, 161, 221, 173, 233, 178, 238, 166, 226, 154, 214, 142, 202, 131, 191, 139, 199, 151, 211, 163, 223, 175, 235, 174, 234, 162, 222, 150, 210, 138, 198, 128, 188)(124, 184, 129, 189, 140, 200, 152, 212, 164, 224, 176, 236, 172, 232, 160, 220, 148, 208, 136, 196, 126, 186, 135, 195, 147, 207, 159, 219, 171, 231, 179, 239, 167, 227, 155, 215, 143, 203, 132, 192) L = (1, 124)(2, 121)(3, 127)(4, 131)(5, 128)(6, 122)(7, 135)(8, 136)(9, 123)(10, 140)(11, 134)(12, 125)(13, 143)(14, 126)(15, 145)(16, 146)(17, 130)(18, 133)(19, 129)(20, 151)(21, 149)(22, 132)(23, 154)(24, 150)(25, 139)(26, 142)(27, 137)(28, 138)(29, 159)(30, 160)(31, 157)(32, 141)(33, 164)(34, 158)(35, 144)(36, 167)(37, 147)(38, 148)(39, 169)(40, 170)(41, 153)(42, 156)(43, 152)(44, 175)(45, 173)(46, 155)(47, 178)(48, 174)(49, 163)(50, 166)(51, 161)(52, 162)(53, 179)(54, 176)(55, 180)(56, 165)(57, 172)(58, 177)(59, 168)(60, 171)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40 ), ( 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40 ) } Outer automorphisms :: reflexible Dual of E23.756 Graph:: bipartite v = 13 e = 120 f = 63 degree seq :: [ 12^10, 40^3 ] E23.756 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {6, 20, 20}) Quotient :: dipole Aut^+ = C5 x (C3 : C4) (small group id <60, 1>) Aut = (C6 x D10) : C2 (small group id <120, 12>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y3^-1 * Y1 * Y3^-1, (R * Y2 * Y3^-1)^2, Y3^6, (Y3 * Y2^-1)^6, Y1^4 * Y3^-1 * Y1 * Y3 * Y1^5 * Y3^-1, Y1^8 * Y3^2 * Y1 * Y3^-1 * Y1 ] Map:: R = (1, 61, 2, 62, 6, 66, 14, 74, 25, 85, 37, 97, 49, 109, 55, 115, 43, 103, 31, 91, 19, 79, 30, 90, 42, 102, 54, 114, 60, 120, 48, 108, 36, 96, 24, 84, 12, 72, 4, 64)(3, 63, 8, 68, 15, 75, 27, 87, 38, 98, 51, 111, 58, 118, 46, 106, 34, 94, 22, 82, 13, 73, 17, 77, 29, 89, 40, 100, 53, 113, 57, 117, 45, 105, 33, 93, 21, 81, 10, 70)(5, 65, 7, 67, 16, 76, 26, 86, 39, 99, 50, 110, 56, 116, 44, 104, 32, 92, 20, 80, 9, 69, 18, 78, 28, 88, 41, 101, 52, 112, 59, 119, 47, 107, 35, 95, 23, 83, 11, 71)(121, 181)(122, 182)(123, 183)(124, 184)(125, 185)(126, 186)(127, 187)(128, 188)(129, 189)(130, 190)(131, 191)(132, 192)(133, 193)(134, 194)(135, 195)(136, 196)(137, 197)(138, 198)(139, 199)(140, 200)(141, 201)(142, 202)(143, 203)(144, 204)(145, 205)(146, 206)(147, 207)(148, 208)(149, 209)(150, 210)(151, 211)(152, 212)(153, 213)(154, 214)(155, 215)(156, 216)(157, 217)(158, 218)(159, 219)(160, 220)(161, 221)(162, 222)(163, 223)(164, 224)(165, 225)(166, 226)(167, 227)(168, 228)(169, 229)(170, 230)(171, 231)(172, 232)(173, 233)(174, 234)(175, 235)(176, 236)(177, 237)(178, 238)(179, 239)(180, 240) L = (1, 123)(2, 127)(3, 129)(4, 131)(5, 121)(6, 135)(7, 137)(8, 122)(9, 139)(10, 124)(11, 142)(12, 141)(13, 125)(14, 146)(15, 148)(16, 126)(17, 150)(18, 128)(19, 133)(20, 130)(21, 152)(22, 151)(23, 132)(24, 155)(25, 158)(26, 160)(27, 134)(28, 162)(29, 136)(30, 138)(31, 140)(32, 163)(33, 144)(34, 143)(35, 166)(36, 165)(37, 170)(38, 172)(39, 145)(40, 174)(41, 147)(42, 149)(43, 154)(44, 153)(45, 176)(46, 175)(47, 156)(48, 179)(49, 178)(50, 177)(51, 157)(52, 180)(53, 159)(54, 161)(55, 164)(56, 169)(57, 168)(58, 167)(59, 171)(60, 173)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 12, 40 ), ( 12, 40, 12, 40, 12, 40, 12, 40, 12, 40, 12, 40, 12, 40, 12, 40, 12, 40, 12, 40, 12, 40, 12, 40, 12, 40, 12, 40, 12, 40, 12, 40, 12, 40, 12, 40, 12, 40, 12, 40 ) } Outer automorphisms :: reflexible Dual of E23.755 Graph:: simple bipartite v = 63 e = 120 f = 13 degree seq :: [ 2^60, 40^3 ] E23.757 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = (C16 x C2) : C2 (small group id <64, 38>) Aut = $<128, 916>$ (small group id <128, 916>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^4, (R * Y1)^2, (Y1 * Y2)^2, (R * Y3)^2, Y3 * Y2 * Y3^-1 * Y2, (R * Y2)^2, (Y3^-1 * Y1 * Y3^-1)^2, Y2 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1, Y1 * Y3 * Y1 * Y2 * Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y2 * Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y2 * Y3 ] Map:: non-degenerate R = (1, 65, 2, 66)(3, 67, 6, 70)(4, 68, 11, 75)(5, 69, 13, 77)(7, 71, 16, 80)(8, 72, 18, 82)(9, 73, 19, 83)(10, 74, 21, 85)(12, 76, 17, 81)(14, 78, 24, 88)(15, 79, 26, 90)(20, 84, 25, 89)(22, 86, 31, 95)(23, 87, 32, 96)(27, 91, 35, 99)(28, 92, 36, 100)(29, 93, 37, 101)(30, 94, 38, 102)(33, 97, 41, 105)(34, 98, 42, 106)(39, 103, 47, 111)(40, 104, 48, 112)(43, 107, 51, 115)(44, 108, 52, 116)(45, 109, 53, 117)(46, 110, 54, 118)(49, 113, 57, 121)(50, 114, 58, 122)(55, 119, 63, 127)(56, 120, 64, 128)(59, 123, 61, 125)(60, 124, 62, 126)(129, 193, 131, 195)(130, 194, 134, 198)(132, 196, 137, 201)(133, 197, 138, 202)(135, 199, 142, 206)(136, 200, 143, 207)(139, 203, 147, 211)(140, 204, 148, 212)(141, 205, 149, 213)(144, 208, 152, 216)(145, 209, 153, 217)(146, 210, 154, 218)(150, 214, 157, 221)(151, 215, 158, 222)(155, 219, 161, 225)(156, 220, 162, 226)(159, 223, 165, 229)(160, 224, 166, 230)(163, 227, 169, 233)(164, 228, 170, 234)(167, 231, 173, 237)(168, 232, 174, 238)(171, 235, 177, 241)(172, 236, 178, 242)(175, 239, 181, 245)(176, 240, 182, 246)(179, 243, 185, 249)(180, 244, 186, 250)(183, 247, 189, 253)(184, 248, 190, 254)(187, 251, 191, 255)(188, 252, 192, 256) L = (1, 132)(2, 135)(3, 137)(4, 140)(5, 129)(6, 142)(7, 145)(8, 130)(9, 148)(10, 131)(11, 150)(12, 133)(13, 151)(14, 153)(15, 134)(16, 155)(17, 136)(18, 156)(19, 157)(20, 138)(21, 158)(22, 141)(23, 139)(24, 161)(25, 143)(26, 162)(27, 146)(28, 144)(29, 149)(30, 147)(31, 167)(32, 168)(33, 154)(34, 152)(35, 171)(36, 172)(37, 173)(38, 174)(39, 160)(40, 159)(41, 177)(42, 178)(43, 164)(44, 163)(45, 166)(46, 165)(47, 183)(48, 184)(49, 170)(50, 169)(51, 187)(52, 188)(53, 189)(54, 190)(55, 176)(56, 175)(57, 191)(58, 192)(59, 180)(60, 179)(61, 182)(62, 181)(63, 186)(64, 185)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 8, 32, 8, 32 ) } Outer automorphisms :: reflexible Dual of E23.774 Graph:: simple bipartite v = 64 e = 128 f = 20 degree seq :: [ 4^64 ] E23.758 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = (C16 x C2) : C2 (small group id <64, 38>) Aut = $<128, 916>$ (small group id <128, 916>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y3^-2, (Y1 * Y2)^2, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, (Y3^-1 * Y1)^16 ] Map:: non-degenerate R = (1, 65, 2, 66)(3, 67, 6, 70)(4, 68, 9, 73)(5, 69, 10, 74)(7, 71, 11, 75)(8, 72, 12, 76)(13, 77, 17, 81)(14, 78, 18, 82)(15, 79, 19, 83)(16, 80, 20, 84)(21, 85, 25, 89)(22, 86, 26, 90)(23, 87, 27, 91)(24, 88, 28, 92)(29, 93, 33, 97)(30, 94, 34, 98)(31, 95, 35, 99)(32, 96, 36, 100)(37, 101, 41, 105)(38, 102, 42, 106)(39, 103, 43, 107)(40, 104, 44, 108)(45, 109, 49, 113)(46, 110, 50, 114)(47, 111, 51, 115)(48, 112, 52, 116)(53, 117, 57, 121)(54, 118, 58, 122)(55, 119, 59, 123)(56, 120, 60, 124)(61, 125, 63, 127)(62, 126, 64, 128)(129, 193, 131, 195)(130, 194, 134, 198)(132, 196, 133, 197)(135, 199, 136, 200)(137, 201, 138, 202)(139, 203, 140, 204)(141, 205, 142, 206)(143, 207, 144, 208)(145, 209, 146, 210)(147, 211, 148, 212)(149, 213, 150, 214)(151, 215, 152, 216)(153, 217, 154, 218)(155, 219, 156, 220)(157, 221, 158, 222)(159, 223, 160, 224)(161, 225, 162, 226)(163, 227, 164, 228)(165, 229, 166, 230)(167, 231, 168, 232)(169, 233, 170, 234)(171, 235, 172, 236)(173, 237, 174, 238)(175, 239, 176, 240)(177, 241, 178, 242)(179, 243, 180, 244)(181, 245, 182, 246)(183, 247, 184, 248)(185, 249, 186, 250)(187, 251, 188, 252)(189, 253, 190, 254)(191, 255, 192, 256) L = (1, 132)(2, 135)(3, 133)(4, 131)(5, 129)(6, 136)(7, 134)(8, 130)(9, 141)(10, 142)(11, 143)(12, 144)(13, 138)(14, 137)(15, 140)(16, 139)(17, 149)(18, 150)(19, 151)(20, 152)(21, 146)(22, 145)(23, 148)(24, 147)(25, 157)(26, 158)(27, 159)(28, 160)(29, 154)(30, 153)(31, 156)(32, 155)(33, 165)(34, 166)(35, 167)(36, 168)(37, 162)(38, 161)(39, 164)(40, 163)(41, 173)(42, 174)(43, 175)(44, 176)(45, 170)(46, 169)(47, 172)(48, 171)(49, 181)(50, 182)(51, 183)(52, 184)(53, 178)(54, 177)(55, 180)(56, 179)(57, 189)(58, 190)(59, 191)(60, 192)(61, 186)(62, 185)(63, 188)(64, 187)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 8, 32, 8, 32 ) } Outer automorphisms :: reflexible Dual of E23.772 Graph:: simple bipartite v = 64 e = 128 f = 20 degree seq :: [ 4^64 ] E23.759 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = (C16 x C2) : C2 (small group id <64, 38>) Aut = $<128, 916>$ (small group id <128, 916>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^4, (R * Y1)^2, (Y1 * Y2)^2, (R * Y3)^2, Y3 * Y2 * Y3^-1 * Y2, (R * Y2)^2, (Y3^-1 * Y1 * Y3^-1)^2, Y2 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 ] Map:: polytopal non-degenerate R = (1, 65, 2, 66)(3, 67, 6, 70)(4, 68, 11, 75)(5, 69, 13, 77)(7, 71, 16, 80)(8, 72, 18, 82)(9, 73, 19, 83)(10, 74, 21, 85)(12, 76, 17, 81)(14, 78, 24, 88)(15, 79, 26, 90)(20, 84, 25, 89)(22, 86, 31, 95)(23, 87, 32, 96)(27, 91, 35, 99)(28, 92, 36, 100)(29, 93, 37, 101)(30, 94, 38, 102)(33, 97, 41, 105)(34, 98, 42, 106)(39, 103, 47, 111)(40, 104, 48, 112)(43, 107, 51, 115)(44, 108, 52, 116)(45, 109, 53, 117)(46, 110, 54, 118)(49, 113, 57, 121)(50, 114, 58, 122)(55, 119, 63, 127)(56, 120, 64, 128)(59, 123, 62, 126)(60, 124, 61, 125)(129, 193, 131, 195)(130, 194, 134, 198)(132, 196, 137, 201)(133, 197, 138, 202)(135, 199, 142, 206)(136, 200, 143, 207)(139, 203, 147, 211)(140, 204, 148, 212)(141, 205, 149, 213)(144, 208, 152, 216)(145, 209, 153, 217)(146, 210, 154, 218)(150, 214, 157, 221)(151, 215, 158, 222)(155, 219, 161, 225)(156, 220, 162, 226)(159, 223, 165, 229)(160, 224, 166, 230)(163, 227, 169, 233)(164, 228, 170, 234)(167, 231, 173, 237)(168, 232, 174, 238)(171, 235, 177, 241)(172, 236, 178, 242)(175, 239, 181, 245)(176, 240, 182, 246)(179, 243, 185, 249)(180, 244, 186, 250)(183, 247, 189, 253)(184, 248, 190, 254)(187, 251, 192, 256)(188, 252, 191, 255) L = (1, 132)(2, 135)(3, 137)(4, 140)(5, 129)(6, 142)(7, 145)(8, 130)(9, 148)(10, 131)(11, 150)(12, 133)(13, 151)(14, 153)(15, 134)(16, 155)(17, 136)(18, 156)(19, 157)(20, 138)(21, 158)(22, 141)(23, 139)(24, 161)(25, 143)(26, 162)(27, 146)(28, 144)(29, 149)(30, 147)(31, 167)(32, 168)(33, 154)(34, 152)(35, 171)(36, 172)(37, 173)(38, 174)(39, 160)(40, 159)(41, 177)(42, 178)(43, 164)(44, 163)(45, 166)(46, 165)(47, 183)(48, 184)(49, 170)(50, 169)(51, 187)(52, 188)(53, 189)(54, 190)(55, 176)(56, 175)(57, 192)(58, 191)(59, 180)(60, 179)(61, 182)(62, 181)(63, 185)(64, 186)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 8, 32, 8, 32 ) } Outer automorphisms :: reflexible Dual of E23.773 Graph:: simple bipartite v = 64 e = 128 f = 20 degree seq :: [ 4^64 ] E23.760 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = (C16 x C2) : C2 (small group id <64, 38>) Aut = $<128, 916>$ (small group id <128, 916>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, (Y3 * Y1)^2, (R * Y3)^2, Y2 * Y1 * Y2^-1 * Y1, (R * Y1)^2, Y2^4, (Y2^-1 * R * Y2^-1)^2, (Y2^-1 * Y3 * Y2^-1)^2, (R * Y2 * Y3)^2, Y2 * Y1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3, Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y1 * Y2^-2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y1 ] Map:: non-degenerate R = (1, 65, 2, 66)(3, 67, 6, 70)(4, 68, 7, 71)(5, 69, 8, 72)(9, 73, 14, 78)(10, 74, 15, 79)(11, 75, 16, 80)(12, 76, 17, 81)(13, 77, 18, 82)(19, 83, 24, 88)(20, 84, 25, 89)(21, 85, 26, 90)(22, 86, 27, 91)(23, 87, 28, 92)(29, 93, 33, 97)(30, 94, 34, 98)(31, 95, 35, 99)(32, 96, 36, 100)(37, 101, 41, 105)(38, 102, 42, 106)(39, 103, 43, 107)(40, 104, 44, 108)(45, 109, 49, 113)(46, 110, 50, 114)(47, 111, 51, 115)(48, 112, 52, 116)(53, 117, 57, 121)(54, 118, 58, 122)(55, 119, 59, 123)(56, 120, 60, 124)(61, 125, 63, 127)(62, 126, 64, 128)(129, 193, 131, 195, 137, 201, 133, 197)(130, 194, 134, 198, 142, 206, 136, 200)(132, 196, 139, 203, 147, 211, 140, 204)(135, 199, 144, 208, 152, 216, 145, 209)(138, 202, 148, 212, 141, 205, 149, 213)(143, 207, 153, 217, 146, 210, 154, 218)(150, 214, 159, 223, 151, 215, 160, 224)(155, 219, 163, 227, 156, 220, 164, 228)(157, 221, 165, 229, 158, 222, 166, 230)(161, 225, 169, 233, 162, 226, 170, 234)(167, 231, 175, 239, 168, 232, 176, 240)(171, 235, 179, 243, 172, 236, 180, 244)(173, 237, 181, 245, 174, 238, 182, 246)(177, 241, 185, 249, 178, 242, 186, 250)(183, 247, 191, 255, 184, 248, 192, 256)(187, 251, 189, 253, 188, 252, 190, 254) L = (1, 132)(2, 135)(3, 138)(4, 129)(5, 141)(6, 143)(7, 130)(8, 146)(9, 147)(10, 131)(11, 150)(12, 151)(13, 133)(14, 152)(15, 134)(16, 155)(17, 156)(18, 136)(19, 137)(20, 157)(21, 158)(22, 139)(23, 140)(24, 142)(25, 161)(26, 162)(27, 144)(28, 145)(29, 148)(30, 149)(31, 167)(32, 168)(33, 153)(34, 154)(35, 171)(36, 172)(37, 173)(38, 174)(39, 159)(40, 160)(41, 177)(42, 178)(43, 163)(44, 164)(45, 165)(46, 166)(47, 183)(48, 184)(49, 169)(50, 170)(51, 187)(52, 188)(53, 189)(54, 190)(55, 175)(56, 176)(57, 191)(58, 192)(59, 179)(60, 180)(61, 181)(62, 182)(63, 185)(64, 186)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32 ) } Outer automorphisms :: reflexible Dual of E23.769 Graph:: simple bipartite v = 48 e = 128 f = 36 degree seq :: [ 4^32, 8^16 ] E23.761 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = (C16 x C2) : C2 (small group id <64, 38>) Aut = $<128, 916>$ (small group id <128, 916>) |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^-1)^16 ] Map:: polytopal non-degenerate R = (1, 65, 2, 66)(3, 67, 5, 69)(4, 68, 6, 70)(7, 71, 10, 74)(8, 72, 9, 73)(11, 75, 12, 76)(13, 77, 14, 78)(15, 79, 16, 80)(17, 81, 18, 82)(19, 83, 20, 84)(21, 85, 22, 86)(23, 87, 24, 88)(25, 89, 26, 90)(27, 91, 28, 92)(29, 93, 30, 94)(31, 95, 32, 96)(33, 97, 34, 98)(35, 99, 36, 100)(37, 101, 38, 102)(39, 103, 40, 104)(41, 105, 42, 106)(43, 107, 44, 108)(45, 109, 46, 110)(47, 111, 48, 112)(49, 113, 50, 114)(51, 115, 52, 116)(53, 117, 54, 118)(55, 119, 56, 120)(57, 121, 58, 122)(59, 123, 60, 124)(61, 125, 62, 126)(63, 127, 64, 128)(129, 193, 131, 195, 130, 194, 133, 197)(132, 196, 136, 200, 134, 198, 137, 201)(135, 199, 139, 203, 138, 202, 140, 204)(141, 205, 145, 209, 142, 206, 146, 210)(143, 207, 147, 211, 144, 208, 148, 212)(149, 213, 153, 217, 150, 214, 154, 218)(151, 215, 155, 219, 152, 216, 156, 220)(157, 221, 161, 225, 158, 222, 162, 226)(159, 223, 163, 227, 160, 224, 164, 228)(165, 229, 169, 233, 166, 230, 170, 234)(167, 231, 171, 235, 168, 232, 172, 236)(173, 237, 177, 241, 174, 238, 178, 242)(175, 239, 179, 243, 176, 240, 180, 244)(181, 245, 185, 249, 182, 246, 186, 250)(183, 247, 187, 251, 184, 248, 188, 252)(189, 253, 191, 255, 190, 254, 192, 256) L = (1, 132)(2, 134)(3, 135)(4, 129)(5, 138)(6, 130)(7, 131)(8, 141)(9, 142)(10, 133)(11, 143)(12, 144)(13, 136)(14, 137)(15, 139)(16, 140)(17, 149)(18, 150)(19, 151)(20, 152)(21, 145)(22, 146)(23, 147)(24, 148)(25, 157)(26, 158)(27, 159)(28, 160)(29, 153)(30, 154)(31, 155)(32, 156)(33, 165)(34, 166)(35, 167)(36, 168)(37, 161)(38, 162)(39, 163)(40, 164)(41, 173)(42, 174)(43, 175)(44, 176)(45, 169)(46, 170)(47, 171)(48, 172)(49, 181)(50, 182)(51, 183)(52, 184)(53, 177)(54, 178)(55, 179)(56, 180)(57, 189)(58, 190)(59, 191)(60, 192)(61, 185)(62, 186)(63, 187)(64, 188)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32 ) } Outer automorphisms :: reflexible Dual of E23.770 Graph:: bipartite v = 48 e = 128 f = 36 degree seq :: [ 4^32, 8^16 ] E23.762 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = (C16 x C2) : C2 (small group id <64, 38>) Aut = $<128, 916>$ (small group id <128, 916>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, (Y3 * Y1)^2, (R * Y3)^2, Y2 * Y1 * Y2^-1 * Y1, (R * Y1)^2, Y2^4, (Y2^-1 * R * Y2^-1)^2, (Y2^-1 * Y3 * Y2^-1)^2, (R * Y2 * Y3)^2, Y2 * Y1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3, Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y1 ] Map:: polytopal non-degenerate R = (1, 65, 2, 66)(3, 67, 6, 70)(4, 68, 7, 71)(5, 69, 8, 72)(9, 73, 14, 78)(10, 74, 15, 79)(11, 75, 16, 80)(12, 76, 17, 81)(13, 77, 18, 82)(19, 83, 24, 88)(20, 84, 25, 89)(21, 85, 26, 90)(22, 86, 27, 91)(23, 87, 28, 92)(29, 93, 33, 97)(30, 94, 34, 98)(31, 95, 35, 99)(32, 96, 36, 100)(37, 101, 41, 105)(38, 102, 42, 106)(39, 103, 43, 107)(40, 104, 44, 108)(45, 109, 49, 113)(46, 110, 50, 114)(47, 111, 51, 115)(48, 112, 52, 116)(53, 117, 57, 121)(54, 118, 58, 122)(55, 119, 59, 123)(56, 120, 60, 124)(61, 125, 64, 128)(62, 126, 63, 127)(129, 193, 131, 195, 137, 201, 133, 197)(130, 194, 134, 198, 142, 206, 136, 200)(132, 196, 139, 203, 147, 211, 140, 204)(135, 199, 144, 208, 152, 216, 145, 209)(138, 202, 148, 212, 141, 205, 149, 213)(143, 207, 153, 217, 146, 210, 154, 218)(150, 214, 159, 223, 151, 215, 160, 224)(155, 219, 163, 227, 156, 220, 164, 228)(157, 221, 165, 229, 158, 222, 166, 230)(161, 225, 169, 233, 162, 226, 170, 234)(167, 231, 175, 239, 168, 232, 176, 240)(171, 235, 179, 243, 172, 236, 180, 244)(173, 237, 181, 245, 174, 238, 182, 246)(177, 241, 185, 249, 178, 242, 186, 250)(183, 247, 191, 255, 184, 248, 192, 256)(187, 251, 190, 254, 188, 252, 189, 253) L = (1, 132)(2, 135)(3, 138)(4, 129)(5, 141)(6, 143)(7, 130)(8, 146)(9, 147)(10, 131)(11, 150)(12, 151)(13, 133)(14, 152)(15, 134)(16, 155)(17, 156)(18, 136)(19, 137)(20, 157)(21, 158)(22, 139)(23, 140)(24, 142)(25, 161)(26, 162)(27, 144)(28, 145)(29, 148)(30, 149)(31, 167)(32, 168)(33, 153)(34, 154)(35, 171)(36, 172)(37, 173)(38, 174)(39, 159)(40, 160)(41, 177)(42, 178)(43, 163)(44, 164)(45, 165)(46, 166)(47, 183)(48, 184)(49, 169)(50, 170)(51, 187)(52, 188)(53, 189)(54, 190)(55, 175)(56, 176)(57, 192)(58, 191)(59, 179)(60, 180)(61, 181)(62, 182)(63, 186)(64, 185)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32 ) } Outer automorphisms :: reflexible Dual of E23.771 Graph:: simple bipartite v = 48 e = 128 f = 36 degree seq :: [ 4^32, 8^16 ] E23.763 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = (C16 x C2) : C2 (small group id <64, 38>) Aut = $<128, 916>$ (small group id <128, 916>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, (Y3 * Y1)^2, Y2^4, (R * Y3)^2, (R * Y1)^2, (Y2^-1 * Y3 * Y2^-1)^2, (R * Y2 * Y3)^2, (Y2^-1 * Y1 * Y2^-1)^2, (Y2^-1 * R * Y2^-1)^2, Y2 * Y3 * Y1 * Y2^-1 * Y3 * Y1, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y3 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1, (Y3 * Y2)^16 ] Map:: polytopal non-degenerate R = (1, 65, 2, 66)(3, 67, 9, 73)(4, 68, 7, 71)(5, 69, 14, 78)(6, 70, 16, 80)(8, 72, 21, 85)(10, 74, 17, 81)(11, 75, 19, 83)(12, 76, 18, 82)(13, 77, 22, 86)(15, 79, 20, 84)(23, 87, 33, 97)(24, 88, 35, 99)(25, 89, 30, 94)(26, 90, 34, 98)(27, 91, 36, 100)(28, 92, 37, 101)(29, 93, 39, 103)(31, 95, 38, 102)(32, 96, 40, 104)(41, 105, 49, 113)(42, 106, 51, 115)(43, 107, 50, 114)(44, 108, 52, 116)(45, 109, 53, 117)(46, 110, 55, 119)(47, 111, 54, 118)(48, 112, 56, 120)(57, 121, 63, 127)(58, 122, 64, 128)(59, 123, 61, 125)(60, 124, 62, 126)(129, 193, 131, 195, 138, 202, 133, 197)(130, 194, 134, 198, 145, 209, 136, 200)(132, 196, 140, 204, 153, 217, 141, 205)(135, 199, 147, 211, 158, 222, 148, 212)(137, 201, 151, 215, 142, 206, 152, 216)(139, 203, 154, 218, 143, 207, 155, 219)(144, 208, 156, 220, 149, 213, 157, 221)(146, 210, 159, 223, 150, 214, 160, 224)(161, 225, 169, 233, 163, 227, 170, 234)(162, 226, 171, 235, 164, 228, 172, 236)(165, 229, 173, 237, 167, 231, 174, 238)(166, 230, 175, 239, 168, 232, 176, 240)(177, 241, 185, 249, 179, 243, 186, 250)(178, 242, 187, 251, 180, 244, 188, 252)(181, 245, 189, 253, 183, 247, 190, 254)(182, 246, 191, 255, 184, 248, 192, 256) L = (1, 132)(2, 135)(3, 139)(4, 129)(5, 143)(6, 146)(7, 130)(8, 150)(9, 147)(10, 153)(11, 131)(12, 144)(13, 149)(14, 148)(15, 133)(16, 140)(17, 158)(18, 134)(19, 137)(20, 142)(21, 141)(22, 136)(23, 162)(24, 164)(25, 138)(26, 161)(27, 163)(28, 166)(29, 168)(30, 145)(31, 165)(32, 167)(33, 154)(34, 151)(35, 155)(36, 152)(37, 159)(38, 156)(39, 160)(40, 157)(41, 178)(42, 180)(43, 177)(44, 179)(45, 182)(46, 184)(47, 181)(48, 183)(49, 171)(50, 169)(51, 172)(52, 170)(53, 175)(54, 173)(55, 176)(56, 174)(57, 189)(58, 190)(59, 191)(60, 192)(61, 185)(62, 186)(63, 187)(64, 188)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32 ) } Outer automorphisms :: reflexible Dual of E23.766 Graph:: simple bipartite v = 48 e = 128 f = 36 degree seq :: [ 4^32, 8^16 ] E23.764 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = (C16 x C2) : C2 (small group id <64, 38>) Aut = $<128, 916>$ (small group id <128, 916>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, (Y3 * Y1)^2, Y2^-2 * Y3 * Y1, Y2^-1 * Y1 * Y3 * Y2^-1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3)^2, (Y1 * Y2)^16 ] Map:: non-degenerate R = (1, 65, 2, 66)(3, 67, 9, 73)(4, 68, 7, 71)(5, 69, 10, 74)(6, 70, 11, 75)(8, 72, 12, 76)(13, 77, 17, 81)(14, 78, 18, 82)(15, 79, 19, 83)(16, 80, 20, 84)(21, 85, 25, 89)(22, 86, 26, 90)(23, 87, 27, 91)(24, 88, 28, 92)(29, 93, 33, 97)(30, 94, 34, 98)(31, 95, 35, 99)(32, 96, 36, 100)(37, 101, 41, 105)(38, 102, 42, 106)(39, 103, 43, 107)(40, 104, 44, 108)(45, 109, 49, 113)(46, 110, 50, 114)(47, 111, 51, 115)(48, 112, 52, 116)(53, 117, 57, 121)(54, 118, 58, 122)(55, 119, 59, 123)(56, 120, 60, 124)(61, 125, 63, 127)(62, 126, 64, 128)(129, 193, 131, 195, 135, 199, 133, 197)(130, 194, 134, 198, 132, 196, 136, 200)(137, 201, 141, 205, 138, 202, 142, 206)(139, 203, 143, 207, 140, 204, 144, 208)(145, 209, 149, 213, 146, 210, 150, 214)(147, 211, 151, 215, 148, 212, 152, 216)(153, 217, 157, 221, 154, 218, 158, 222)(155, 219, 159, 223, 156, 220, 160, 224)(161, 225, 165, 229, 162, 226, 166, 230)(163, 227, 167, 231, 164, 228, 168, 232)(169, 233, 173, 237, 170, 234, 174, 238)(171, 235, 175, 239, 172, 236, 176, 240)(177, 241, 181, 245, 178, 242, 182, 246)(179, 243, 183, 247, 180, 244, 184, 248)(185, 249, 189, 253, 186, 250, 190, 254)(187, 251, 191, 255, 188, 252, 192, 256) L = (1, 132)(2, 135)(3, 138)(4, 129)(5, 137)(6, 140)(7, 130)(8, 139)(9, 133)(10, 131)(11, 136)(12, 134)(13, 146)(14, 145)(15, 148)(16, 147)(17, 142)(18, 141)(19, 144)(20, 143)(21, 154)(22, 153)(23, 156)(24, 155)(25, 150)(26, 149)(27, 152)(28, 151)(29, 162)(30, 161)(31, 164)(32, 163)(33, 158)(34, 157)(35, 160)(36, 159)(37, 170)(38, 169)(39, 172)(40, 171)(41, 166)(42, 165)(43, 168)(44, 167)(45, 178)(46, 177)(47, 180)(48, 179)(49, 174)(50, 173)(51, 176)(52, 175)(53, 186)(54, 185)(55, 188)(56, 187)(57, 182)(58, 181)(59, 184)(60, 183)(61, 192)(62, 191)(63, 190)(64, 189)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32 ) } Outer automorphisms :: reflexible Dual of E23.767 Graph:: bipartite v = 48 e = 128 f = 36 degree seq :: [ 4^32, 8^16 ] E23.765 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = (C16 x C2) : C2 (small group id <64, 38>) Aut = $<128, 916>$ (small group id <128, 916>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, (Y3 * Y1)^2, Y2^4, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3)^2, (Y2^-1 * R * Y2^-1)^2, (Y2^-1 * Y1 * Y2^-1)^2, (Y2^-1 * Y3 * Y2^-1)^2, Y2 * Y3 * Y1 * Y2^-1 * Y3 * Y1, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y3 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1, (Y3 * Y2)^16 ] Map:: polytopal non-degenerate R = (1, 65, 2, 66)(3, 67, 9, 73)(4, 68, 7, 71)(5, 69, 14, 78)(6, 70, 16, 80)(8, 72, 21, 85)(10, 74, 17, 81)(11, 75, 19, 83)(12, 76, 18, 82)(13, 77, 22, 86)(15, 79, 20, 84)(23, 87, 33, 97)(24, 88, 35, 99)(25, 89, 30, 94)(26, 90, 34, 98)(27, 91, 36, 100)(28, 92, 37, 101)(29, 93, 39, 103)(31, 95, 38, 102)(32, 96, 40, 104)(41, 105, 49, 113)(42, 106, 51, 115)(43, 107, 50, 114)(44, 108, 52, 116)(45, 109, 53, 117)(46, 110, 55, 119)(47, 111, 54, 118)(48, 112, 56, 120)(57, 121, 64, 128)(58, 122, 63, 127)(59, 123, 62, 126)(60, 124, 61, 125)(129, 193, 131, 195, 138, 202, 133, 197)(130, 194, 134, 198, 145, 209, 136, 200)(132, 196, 140, 204, 153, 217, 141, 205)(135, 199, 147, 211, 158, 222, 148, 212)(137, 201, 151, 215, 142, 206, 152, 216)(139, 203, 154, 218, 143, 207, 155, 219)(144, 208, 156, 220, 149, 213, 157, 221)(146, 210, 159, 223, 150, 214, 160, 224)(161, 225, 169, 233, 163, 227, 170, 234)(162, 226, 171, 235, 164, 228, 172, 236)(165, 229, 173, 237, 167, 231, 174, 238)(166, 230, 175, 239, 168, 232, 176, 240)(177, 241, 185, 249, 179, 243, 186, 250)(178, 242, 187, 251, 180, 244, 188, 252)(181, 245, 189, 253, 183, 247, 190, 254)(182, 246, 191, 255, 184, 248, 192, 256) L = (1, 132)(2, 135)(3, 139)(4, 129)(5, 143)(6, 146)(7, 130)(8, 150)(9, 147)(10, 153)(11, 131)(12, 144)(13, 149)(14, 148)(15, 133)(16, 140)(17, 158)(18, 134)(19, 137)(20, 142)(21, 141)(22, 136)(23, 162)(24, 164)(25, 138)(26, 161)(27, 163)(28, 166)(29, 168)(30, 145)(31, 165)(32, 167)(33, 154)(34, 151)(35, 155)(36, 152)(37, 159)(38, 156)(39, 160)(40, 157)(41, 178)(42, 180)(43, 177)(44, 179)(45, 182)(46, 184)(47, 181)(48, 183)(49, 171)(50, 169)(51, 172)(52, 170)(53, 175)(54, 173)(55, 176)(56, 174)(57, 190)(58, 189)(59, 192)(60, 191)(61, 186)(62, 185)(63, 188)(64, 187)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32 ) } Outer automorphisms :: reflexible Dual of E23.768 Graph:: simple bipartite v = 48 e = 128 f = 36 degree seq :: [ 4^32, 8^16 ] E23.766 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = (C16 x C2) : C2 (small group id <64, 38>) Aut = $<128, 916>$ (small group id <128, 916>) |r| :: 2 Presentation :: [ Y3^2, Y2^2, R^2, (R * Y2)^2, (R * Y3)^2, (Y3 * Y2)^2, (R * Y1)^2, Y1^-1 * Y2 * Y1 * Y2, (Y1^-2 * Y3)^2, (Y3 * Y1)^4, Y1^8 * Y2 ] Map:: polytopal non-degenerate R = (1, 65, 2, 66, 6, 70, 15, 79, 30, 94, 43, 107, 24, 88, 10, 74, 3, 67, 7, 71, 16, 80, 31, 95, 47, 111, 29, 93, 14, 78, 5, 69)(4, 68, 11, 75, 25, 89, 44, 108, 58, 122, 51, 115, 33, 97, 22, 86, 9, 73, 21, 85, 39, 103, 55, 119, 48, 112, 34, 98, 17, 81, 12, 76)(8, 72, 19, 83, 13, 77, 28, 92, 46, 110, 60, 124, 49, 113, 36, 100, 18, 82, 35, 99, 23, 87, 42, 106, 57, 121, 50, 114, 32, 96, 20, 84)(26, 90, 37, 101, 27, 91, 38, 102, 52, 116, 61, 125, 63, 127, 56, 120, 40, 104, 53, 117, 41, 105, 54, 118, 62, 126, 64, 128, 59, 123, 45, 109)(129, 193, 131, 195)(130, 194, 135, 199)(132, 196, 137, 201)(133, 197, 138, 202)(134, 198, 144, 208)(136, 200, 146, 210)(139, 203, 149, 213)(140, 204, 150, 214)(141, 205, 151, 215)(142, 206, 152, 216)(143, 207, 159, 223)(145, 209, 161, 225)(147, 211, 163, 227)(148, 212, 164, 228)(153, 217, 167, 231)(154, 218, 168, 232)(155, 219, 169, 233)(156, 220, 170, 234)(157, 221, 171, 235)(158, 222, 175, 239)(160, 224, 177, 241)(162, 226, 179, 243)(165, 229, 181, 245)(166, 230, 182, 246)(172, 236, 183, 247)(173, 237, 184, 248)(174, 238, 185, 249)(176, 240, 186, 250)(178, 242, 188, 252)(180, 244, 190, 254)(187, 251, 191, 255)(189, 253, 192, 256) L = (1, 132)(2, 136)(3, 137)(4, 129)(5, 141)(6, 145)(7, 146)(8, 130)(9, 131)(10, 151)(11, 154)(12, 155)(13, 133)(14, 153)(15, 160)(16, 161)(17, 134)(18, 135)(19, 165)(20, 166)(21, 168)(22, 169)(23, 138)(24, 167)(25, 142)(26, 139)(27, 140)(28, 173)(29, 174)(30, 176)(31, 177)(32, 143)(33, 144)(34, 180)(35, 181)(36, 182)(37, 147)(38, 148)(39, 152)(40, 149)(41, 150)(42, 184)(43, 185)(44, 187)(45, 156)(46, 157)(47, 186)(48, 158)(49, 159)(50, 189)(51, 190)(52, 162)(53, 163)(54, 164)(55, 191)(56, 170)(57, 171)(58, 175)(59, 172)(60, 192)(61, 178)(62, 179)(63, 183)(64, 188)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 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 E23.763 Graph:: bipartite v = 36 e = 128 f = 48 degree seq :: [ 4^32, 32^4 ] E23.767 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = (C16 x C2) : C2 (small group id <64, 38>) Aut = $<128, 916>$ (small group id <128, 916>) |r| :: 2 Presentation :: [ Y3^2, Y2^2, R^2, (Y3 * Y2)^2, Y1^-1 * Y2 * Y1 * Y2, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y3 * Y2 * Y1 * Y3 * Y1, Y1^16 ] Map:: non-degenerate R = (1, 65, 2, 66, 6, 70, 15, 79, 23, 87, 31, 95, 39, 103, 47, 111, 55, 119, 54, 118, 46, 110, 38, 102, 30, 94, 22, 86, 14, 78, 5, 69)(3, 67, 7, 71, 16, 80, 24, 88, 32, 96, 40, 104, 48, 112, 56, 120, 62, 126, 59, 123, 51, 115, 43, 107, 35, 99, 27, 91, 19, 83, 10, 74)(4, 68, 11, 75, 20, 84, 28, 92, 36, 100, 44, 108, 52, 116, 60, 124, 63, 127, 58, 122, 49, 113, 42, 106, 33, 97, 26, 90, 17, 81, 12, 76)(8, 72, 9, 73, 13, 77, 21, 85, 29, 93, 37, 101, 45, 109, 53, 117, 61, 125, 64, 128, 57, 121, 50, 114, 41, 105, 34, 98, 25, 89, 18, 82)(129, 193, 131, 195)(130, 194, 135, 199)(132, 196, 137, 201)(133, 197, 138, 202)(134, 198, 144, 208)(136, 200, 140, 204)(139, 203, 141, 205)(142, 206, 147, 211)(143, 207, 152, 216)(145, 209, 146, 210)(148, 212, 149, 213)(150, 214, 155, 219)(151, 215, 160, 224)(153, 217, 154, 218)(156, 220, 157, 221)(158, 222, 163, 227)(159, 223, 168, 232)(161, 225, 162, 226)(164, 228, 165, 229)(166, 230, 171, 235)(167, 231, 176, 240)(169, 233, 170, 234)(172, 236, 173, 237)(174, 238, 179, 243)(175, 239, 184, 248)(177, 241, 178, 242)(180, 244, 181, 245)(182, 246, 187, 251)(183, 247, 190, 254)(185, 249, 186, 250)(188, 252, 189, 253)(191, 255, 192, 256) L = (1, 132)(2, 136)(3, 137)(4, 129)(5, 141)(6, 145)(7, 140)(8, 130)(9, 131)(10, 139)(11, 138)(12, 135)(13, 133)(14, 148)(15, 153)(16, 146)(17, 134)(18, 144)(19, 149)(20, 142)(21, 147)(22, 157)(23, 161)(24, 154)(25, 143)(26, 152)(27, 156)(28, 155)(29, 150)(30, 164)(31, 169)(32, 162)(33, 151)(34, 160)(35, 165)(36, 158)(37, 163)(38, 173)(39, 177)(40, 170)(41, 159)(42, 168)(43, 172)(44, 171)(45, 166)(46, 180)(47, 185)(48, 178)(49, 167)(50, 176)(51, 181)(52, 174)(53, 179)(54, 189)(55, 191)(56, 186)(57, 175)(58, 184)(59, 188)(60, 187)(61, 182)(62, 192)(63, 183)(64, 190)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 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 E23.764 Graph:: simple bipartite v = 36 e = 128 f = 48 degree seq :: [ 4^32, 32^4 ] E23.768 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = (C16 x C2) : C2 (small group id <64, 38>) Aut = $<128, 916>$ (small group id <128, 916>) |r| :: 2 Presentation :: [ Y3^2, Y2^2, R^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y1)^2, Y2 * Y1 * Y2 * Y1^-1, (R * Y3)^2, (Y1^-1 * Y3 * Y1^-1)^2, (Y1^-1 * Y3)^4, Y1^5 * Y3 * Y1^-3 * Y2 * Y3 ] Map:: polytopal non-degenerate R = (1, 65, 2, 66, 6, 70, 15, 79, 30, 94, 48, 112, 58, 122, 40, 104, 55, 119, 41, 105, 56, 120, 64, 128, 47, 111, 29, 93, 14, 78, 5, 69)(3, 67, 7, 71, 16, 80, 31, 95, 49, 113, 62, 126, 45, 109, 26, 90, 37, 101, 27, 91, 38, 102, 54, 118, 60, 124, 43, 107, 24, 88, 10, 74)(4, 68, 11, 75, 25, 89, 44, 108, 61, 125, 51, 115, 36, 100, 18, 82, 35, 99, 23, 87, 42, 106, 59, 123, 50, 114, 34, 98, 17, 81, 12, 76)(8, 72, 19, 83, 13, 77, 28, 92, 46, 110, 63, 127, 53, 117, 33, 97, 22, 86, 9, 73, 21, 85, 39, 103, 57, 121, 52, 116, 32, 96, 20, 84)(129, 193, 131, 195)(130, 194, 135, 199)(132, 196, 137, 201)(133, 197, 138, 202)(134, 198, 144, 208)(136, 200, 146, 210)(139, 203, 149, 213)(140, 204, 150, 214)(141, 205, 151, 215)(142, 206, 152, 216)(143, 207, 159, 223)(145, 209, 161, 225)(147, 211, 163, 227)(148, 212, 164, 228)(153, 217, 167, 231)(154, 218, 168, 232)(155, 219, 169, 233)(156, 220, 170, 234)(157, 221, 171, 235)(158, 222, 177, 241)(160, 224, 179, 243)(162, 226, 181, 245)(165, 229, 183, 247)(166, 230, 184, 248)(172, 236, 185, 249)(173, 237, 186, 250)(174, 238, 187, 251)(175, 239, 188, 252)(176, 240, 190, 254)(178, 242, 191, 255)(180, 244, 189, 253)(182, 246, 192, 256) L = (1, 132)(2, 136)(3, 137)(4, 129)(5, 141)(6, 145)(7, 146)(8, 130)(9, 131)(10, 151)(11, 154)(12, 155)(13, 133)(14, 153)(15, 160)(16, 161)(17, 134)(18, 135)(19, 165)(20, 166)(21, 168)(22, 169)(23, 138)(24, 167)(25, 142)(26, 139)(27, 140)(28, 173)(29, 174)(30, 178)(31, 179)(32, 143)(33, 144)(34, 182)(35, 183)(36, 184)(37, 147)(38, 148)(39, 152)(40, 149)(41, 150)(42, 186)(43, 187)(44, 190)(45, 156)(46, 157)(47, 189)(48, 185)(49, 191)(50, 158)(51, 159)(52, 188)(53, 192)(54, 162)(55, 163)(56, 164)(57, 176)(58, 170)(59, 171)(60, 180)(61, 175)(62, 172)(63, 177)(64, 181)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 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 E23.765 Graph:: simple bipartite v = 36 e = 128 f = 48 degree seq :: [ 4^32, 32^4 ] E23.769 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = (C16 x C2) : C2 (small group id <64, 38>) Aut = $<128, 916>$ (small group id <128, 916>) |r| :: 2 Presentation :: [ Y3^2, Y2^2, R^2, (Y2 * Y3)^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y3 * Y1 * Y3 * Y2 * Y1^-1 * Y2, (Y1^-2 * Y2)^2, (Y3 * Y1^-2)^2, Y2 * Y1^-1 * Y2 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1, Y1^-2 * Y2 * Y3 * Y1^-6 ] Map:: non-degenerate R = (1, 65, 2, 66, 6, 70, 17, 81, 35, 99, 53, 117, 46, 110, 28, 92, 10, 74, 21, 85, 38, 102, 56, 120, 52, 116, 34, 98, 16, 80, 5, 69)(3, 67, 9, 73, 25, 89, 45, 109, 55, 119, 40, 104, 19, 83, 13, 77, 4, 68, 12, 76, 31, 95, 49, 113, 54, 118, 39, 103, 18, 82, 11, 75)(7, 71, 20, 84, 14, 78, 32, 96, 50, 114, 58, 122, 37, 101, 24, 88, 8, 72, 23, 87, 15, 79, 33, 97, 51, 115, 57, 121, 36, 100, 22, 86)(26, 90, 41, 105, 29, 93, 43, 107, 59, 123, 63, 127, 62, 126, 48, 112, 27, 91, 42, 106, 30, 94, 44, 108, 60, 124, 64, 128, 61, 125, 47, 111)(129, 193, 131, 195)(130, 194, 135, 199)(132, 196, 138, 202)(133, 197, 142, 206)(134, 198, 146, 210)(136, 200, 149, 213)(137, 201, 154, 218)(139, 203, 157, 221)(140, 204, 155, 219)(141, 205, 158, 222)(143, 207, 156, 220)(144, 208, 153, 217)(145, 209, 164, 228)(147, 211, 166, 230)(148, 212, 169, 233)(150, 214, 171, 235)(151, 215, 170, 234)(152, 216, 172, 236)(159, 223, 174, 238)(160, 224, 175, 239)(161, 225, 176, 240)(162, 226, 178, 242)(163, 227, 182, 246)(165, 229, 184, 248)(167, 231, 187, 251)(168, 232, 188, 252)(173, 237, 189, 253)(177, 241, 190, 254)(179, 243, 181, 245)(180, 244, 183, 247)(185, 249, 191, 255)(186, 250, 192, 256) L = (1, 132)(2, 136)(3, 138)(4, 129)(5, 143)(6, 147)(7, 149)(8, 130)(9, 155)(10, 131)(11, 158)(12, 154)(13, 157)(14, 156)(15, 133)(16, 159)(17, 165)(18, 166)(19, 134)(20, 170)(21, 135)(22, 172)(23, 169)(24, 171)(25, 174)(26, 140)(27, 137)(28, 142)(29, 141)(30, 139)(31, 144)(32, 176)(33, 175)(34, 179)(35, 183)(36, 184)(37, 145)(38, 146)(39, 188)(40, 187)(41, 151)(42, 148)(43, 152)(44, 150)(45, 190)(46, 153)(47, 161)(48, 160)(49, 189)(50, 181)(51, 162)(52, 182)(53, 178)(54, 180)(55, 163)(56, 164)(57, 192)(58, 191)(59, 168)(60, 167)(61, 177)(62, 173)(63, 186)(64, 185)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 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 E23.760 Graph:: bipartite v = 36 e = 128 f = 48 degree seq :: [ 4^32, 32^4 ] E23.770 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = (C16 x C2) : C2 (small group id <64, 38>) Aut = $<128, 916>$ (small group id <128, 916>) |r| :: 2 Presentation :: [ Y3^2, Y2^2, R^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y3)^2, Y2 * Y1^-1 * Y3 * Y1^-1, (R * Y1)^2, Y1^16 ] Map:: polytopal non-degenerate R = (1, 65, 2, 66, 6, 70, 13, 77, 21, 85, 29, 93, 37, 101, 45, 109, 53, 117, 52, 116, 44, 108, 36, 100, 28, 92, 20, 84, 12, 76, 5, 69)(3, 67, 9, 73, 17, 81, 25, 89, 33, 97, 41, 105, 49, 113, 57, 121, 60, 124, 55, 119, 46, 110, 39, 103, 30, 94, 23, 87, 14, 78, 8, 72)(4, 68, 11, 75, 19, 83, 27, 91, 35, 99, 43, 107, 51, 115, 59, 123, 61, 125, 54, 118, 47, 111, 38, 102, 31, 95, 22, 86, 15, 79, 7, 71)(10, 74, 16, 80, 24, 88, 32, 96, 40, 104, 48, 112, 56, 120, 62, 126, 64, 128, 63, 127, 58, 122, 50, 114, 42, 106, 34, 98, 26, 90, 18, 82)(129, 193, 131, 195)(130, 194, 135, 199)(132, 196, 138, 202)(133, 197, 139, 203)(134, 198, 142, 206)(136, 200, 144, 208)(137, 201, 146, 210)(140, 204, 145, 209)(141, 205, 150, 214)(143, 207, 152, 216)(147, 211, 154, 218)(148, 212, 155, 219)(149, 213, 158, 222)(151, 215, 160, 224)(153, 217, 162, 226)(156, 220, 161, 225)(157, 221, 166, 230)(159, 223, 168, 232)(163, 227, 170, 234)(164, 228, 171, 235)(165, 229, 174, 238)(167, 231, 176, 240)(169, 233, 178, 242)(172, 236, 177, 241)(173, 237, 182, 246)(175, 239, 184, 248)(179, 243, 186, 250)(180, 244, 187, 251)(181, 245, 188, 252)(183, 247, 190, 254)(185, 249, 191, 255)(189, 253, 192, 256) L = (1, 132)(2, 136)(3, 138)(4, 129)(5, 137)(6, 143)(7, 144)(8, 130)(9, 133)(10, 131)(11, 146)(12, 147)(13, 151)(14, 152)(15, 134)(16, 135)(17, 154)(18, 139)(19, 140)(20, 153)(21, 159)(22, 160)(23, 141)(24, 142)(25, 148)(26, 145)(27, 162)(28, 163)(29, 167)(30, 168)(31, 149)(32, 150)(33, 170)(34, 155)(35, 156)(36, 169)(37, 175)(38, 176)(39, 157)(40, 158)(41, 164)(42, 161)(43, 178)(44, 179)(45, 183)(46, 184)(47, 165)(48, 166)(49, 186)(50, 171)(51, 172)(52, 185)(53, 189)(54, 190)(55, 173)(56, 174)(57, 180)(58, 177)(59, 191)(60, 192)(61, 181)(62, 182)(63, 187)(64, 188)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 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 E23.761 Graph:: simple bipartite v = 36 e = 128 f = 48 degree seq :: [ 4^32, 32^4 ] E23.771 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = (C16 x C2) : C2 (small group id <64, 38>) Aut = $<128, 916>$ (small group id <128, 916>) |r| :: 2 Presentation :: [ Y3^2, Y2^2, R^2, (R * Y2)^2, (Y2 * Y3)^2, (R * Y3)^2, (R * Y1)^2, Y3 * Y1 * Y2 * Y3 * Y1^-1 * Y2, (Y2 * Y1^-2)^2, (Y3 * Y1^-2)^2, (Y1^-1 * Y2)^4, (Y3 * Y1)^4, Y3 * Y1^5 * Y2 * Y1^-3 ] Map:: polytopal non-degenerate R = (1, 65, 2, 66, 6, 70, 17, 81, 35, 99, 53, 117, 48, 112, 27, 91, 42, 106, 30, 94, 44, 108, 60, 124, 52, 116, 34, 98, 16, 80, 5, 69)(3, 67, 9, 73, 25, 89, 45, 109, 58, 122, 37, 101, 24, 88, 8, 72, 23, 87, 15, 79, 33, 97, 51, 115, 54, 118, 39, 103, 18, 82, 11, 75)(4, 68, 12, 76, 31, 95, 49, 113, 57, 121, 36, 100, 22, 86, 7, 71, 20, 84, 14, 78, 32, 96, 50, 114, 55, 119, 40, 104, 19, 83, 13, 77)(10, 74, 21, 85, 38, 102, 56, 120, 63, 127, 61, 125, 47, 111, 26, 90, 41, 105, 29, 93, 43, 107, 59, 123, 64, 128, 62, 126, 46, 110, 28, 92)(129, 193, 131, 195)(130, 194, 135, 199)(132, 196, 138, 202)(133, 197, 142, 206)(134, 198, 146, 210)(136, 200, 149, 213)(137, 201, 154, 218)(139, 203, 157, 221)(140, 204, 155, 219)(141, 205, 158, 222)(143, 207, 156, 220)(144, 208, 153, 217)(145, 209, 164, 228)(147, 211, 166, 230)(148, 212, 169, 233)(150, 214, 171, 235)(151, 215, 170, 234)(152, 216, 172, 236)(159, 223, 174, 238)(160, 224, 175, 239)(161, 225, 176, 240)(162, 226, 178, 242)(163, 227, 182, 246)(165, 229, 184, 248)(167, 231, 187, 251)(168, 232, 188, 252)(173, 237, 189, 253)(177, 241, 181, 245)(179, 243, 190, 254)(180, 244, 186, 250)(183, 247, 191, 255)(185, 249, 192, 256) L = (1, 132)(2, 136)(3, 138)(4, 129)(5, 143)(6, 147)(7, 149)(8, 130)(9, 155)(10, 131)(11, 158)(12, 154)(13, 157)(14, 156)(15, 133)(16, 159)(17, 165)(18, 166)(19, 134)(20, 170)(21, 135)(22, 172)(23, 169)(24, 171)(25, 174)(26, 140)(27, 137)(28, 142)(29, 141)(30, 139)(31, 144)(32, 176)(33, 175)(34, 179)(35, 183)(36, 184)(37, 145)(38, 146)(39, 188)(40, 187)(41, 151)(42, 148)(43, 152)(44, 150)(45, 181)(46, 153)(47, 161)(48, 160)(49, 189)(50, 190)(51, 162)(52, 185)(53, 173)(54, 191)(55, 163)(56, 164)(57, 180)(58, 192)(59, 168)(60, 167)(61, 177)(62, 178)(63, 182)(64, 186)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 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 E23.762 Graph:: simple bipartite v = 36 e = 128 f = 48 degree seq :: [ 4^32, 32^4 ] E23.772 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = (C16 x C2) : C2 (small group id <64, 38>) Aut = $<128, 916>$ (small group id <128, 916>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1, (Y3 * Y2^-1)^2, (R * Y1)^2, (R * Y3)^2, (Y2 * Y1^-1)^2, (Y2^-1 * Y1^-1)^2, Y1^4, (Y3^-1 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y2^16 ] Map:: non-degenerate R = (1, 65, 2, 66, 6, 70, 4, 68)(3, 67, 9, 73, 13, 77, 8, 72)(5, 69, 11, 75, 14, 78, 7, 71)(10, 74, 16, 80, 21, 85, 17, 81)(12, 76, 15, 79, 22, 86, 19, 83)(18, 82, 25, 89, 29, 93, 24, 88)(20, 84, 27, 91, 30, 94, 23, 87)(26, 90, 32, 96, 37, 101, 33, 97)(28, 92, 31, 95, 38, 102, 35, 99)(34, 98, 41, 105, 45, 109, 40, 104)(36, 100, 43, 107, 46, 110, 39, 103)(42, 106, 48, 112, 53, 117, 49, 113)(44, 108, 47, 111, 54, 118, 51, 115)(50, 114, 57, 121, 60, 124, 56, 120)(52, 116, 59, 123, 61, 125, 55, 119)(58, 122, 62, 126, 64, 128, 63, 127)(129, 193, 131, 195, 138, 202, 146, 210, 154, 218, 162, 226, 170, 234, 178, 242, 186, 250, 180, 244, 172, 236, 164, 228, 156, 220, 148, 212, 140, 204, 133, 197)(130, 194, 135, 199, 143, 207, 151, 215, 159, 223, 167, 231, 175, 239, 183, 247, 190, 254, 184, 248, 176, 240, 168, 232, 160, 224, 152, 216, 144, 208, 136, 200)(132, 196, 139, 203, 147, 211, 155, 219, 163, 227, 171, 235, 179, 243, 187, 251, 191, 255, 185, 249, 177, 241, 169, 233, 161, 225, 153, 217, 145, 209, 137, 201)(134, 198, 141, 205, 149, 213, 157, 221, 165, 229, 173, 237, 181, 245, 188, 252, 192, 256, 189, 253, 182, 246, 174, 238, 166, 230, 158, 222, 150, 214, 142, 206) L = (1, 130)(2, 134)(3, 137)(4, 129)(5, 139)(6, 132)(7, 133)(8, 131)(9, 141)(10, 144)(11, 142)(12, 143)(13, 136)(14, 135)(15, 150)(16, 149)(17, 138)(18, 153)(19, 140)(20, 155)(21, 145)(22, 147)(23, 148)(24, 146)(25, 157)(26, 160)(27, 158)(28, 159)(29, 152)(30, 151)(31, 166)(32, 165)(33, 154)(34, 169)(35, 156)(36, 171)(37, 161)(38, 163)(39, 164)(40, 162)(41, 173)(42, 176)(43, 174)(44, 175)(45, 168)(46, 167)(47, 182)(48, 181)(49, 170)(50, 185)(51, 172)(52, 187)(53, 177)(54, 179)(55, 180)(56, 178)(57, 188)(58, 190)(59, 189)(60, 184)(61, 183)(62, 192)(63, 186)(64, 191)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4^8 ), ( 4^32 ) } Outer automorphisms :: reflexible Dual of E23.758 Graph:: bipartite v = 20 e = 128 f = 64 degree seq :: [ 8^16, 32^4 ] E23.773 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = (C16 x C2) : C2 (small group id <64, 38>) Aut = $<128, 916>$ (small group id <128, 916>) |r| :: 2 Presentation :: [ R^2, (Y3, Y1), Y3^-2 * Y1^2, (R * Y3)^2, Y3^2 * Y1^2, (Y1^-1 * Y2)^2, (R * Y1)^2, Y1^4, (Y3 * Y2^-1)^2, (Y2^-1 * Y1^-1)^2, (Y2^-1 * Y3^-1)^2, Y1^-1 * Y2^-1 * Y3 * Y1 * Y2 * Y3^-1, (R * Y2 * Y3^-1)^2, Y2^4 * Y3 * Y2^-4 * Y1^-1, Y2^16 ] Map:: polytopal non-degenerate R = (1, 65, 2, 66, 8, 72, 5, 69)(3, 67, 13, 77, 21, 85, 11, 75)(4, 68, 10, 74, 7, 71, 12, 76)(6, 70, 18, 82, 22, 86, 9, 73)(14, 78, 28, 92, 37, 101, 29, 93)(15, 79, 26, 90, 16, 80, 27, 91)(17, 81, 24, 88, 19, 83, 25, 89)(20, 84, 23, 87, 38, 102, 34, 98)(30, 94, 45, 109, 53, 117, 44, 108)(31, 95, 42, 106, 32, 96, 43, 107)(33, 97, 40, 104, 35, 99, 41, 105)(36, 100, 50, 114, 54, 118, 39, 103)(46, 110, 60, 124, 63, 127, 61, 125)(47, 111, 58, 122, 48, 112, 59, 123)(49, 113, 56, 120, 51, 115, 57, 121)(52, 116, 55, 119, 64, 128, 62, 126)(129, 193, 131, 195, 142, 206, 158, 222, 174, 238, 184, 248, 169, 233, 152, 216, 140, 204, 155, 219, 171, 235, 187, 251, 180, 244, 164, 228, 148, 212, 134, 198)(130, 194, 137, 201, 151, 215, 167, 231, 183, 247, 176, 240, 159, 223, 144, 208, 132, 196, 145, 209, 161, 225, 177, 241, 188, 252, 172, 236, 156, 220, 139, 203)(133, 197, 146, 210, 162, 226, 178, 242, 190, 254, 175, 239, 160, 224, 143, 207, 135, 199, 147, 211, 163, 227, 179, 243, 189, 253, 173, 237, 157, 221, 141, 205)(136, 200, 149, 213, 165, 229, 181, 245, 191, 255, 185, 249, 168, 232, 153, 217, 138, 202, 154, 218, 170, 234, 186, 250, 192, 256, 182, 246, 166, 230, 150, 214) L = (1, 132)(2, 138)(3, 143)(4, 136)(5, 140)(6, 147)(7, 129)(8, 135)(9, 152)(10, 133)(11, 155)(12, 130)(13, 154)(14, 159)(15, 149)(16, 131)(17, 134)(18, 153)(19, 150)(20, 161)(21, 144)(22, 145)(23, 168)(24, 146)(25, 137)(26, 139)(27, 141)(28, 170)(29, 171)(30, 175)(31, 165)(32, 142)(33, 166)(34, 169)(35, 148)(36, 179)(37, 160)(38, 163)(39, 184)(40, 162)(41, 151)(42, 157)(43, 156)(44, 187)(45, 186)(46, 183)(47, 181)(48, 158)(49, 164)(50, 185)(51, 182)(52, 188)(53, 176)(54, 177)(55, 191)(56, 178)(57, 167)(58, 172)(59, 173)(60, 192)(61, 180)(62, 174)(63, 190)(64, 189)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4^8 ), ( 4^32 ) } Outer automorphisms :: reflexible Dual of E23.759 Graph:: bipartite v = 20 e = 128 f = 64 degree seq :: [ 8^16, 32^4 ] E23.774 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = (C16 x C2) : C2 (small group id <64, 38>) Aut = $<128, 916>$ (small group id <128, 916>) |r| :: 2 Presentation :: [ R^2, Y3^2 * Y1^2, Y3^-2 * Y1^2, (R * Y1)^2, (Y3^-1, Y1^-1), Y1^4, (Y2 * Y1^-1)^2, (R * Y3)^2, (Y2^-1 * Y1^-1)^2, (Y2^-1 * Y3^-1)^2, (Y3 * Y2^-1)^2, Y1^-1 * Y2^-1 * Y3 * Y1 * Y2 * Y3^-1, (R * Y2 * Y3^-1)^2, Y2^4 * Y3^-1 * Y2^-4 * Y1^-1, Y2^-1 * Y3^-1 * Y2^6 * Y1^-1 * Y2^-1 ] Map:: non-degenerate R = (1, 65, 2, 66, 8, 72, 5, 69)(3, 67, 13, 77, 21, 85, 11, 75)(4, 68, 10, 74, 7, 71, 12, 76)(6, 70, 18, 82, 22, 86, 9, 73)(14, 78, 28, 92, 37, 101, 29, 93)(15, 79, 26, 90, 16, 80, 27, 91)(17, 81, 24, 88, 19, 83, 25, 89)(20, 84, 23, 87, 38, 102, 34, 98)(30, 94, 45, 109, 53, 117, 44, 108)(31, 95, 42, 106, 32, 96, 43, 107)(33, 97, 40, 104, 35, 99, 41, 105)(36, 100, 50, 114, 54, 118, 39, 103)(46, 110, 60, 124, 63, 127, 61, 125)(47, 111, 58, 122, 48, 112, 59, 123)(49, 113, 56, 120, 51, 115, 57, 121)(52, 116, 55, 119, 64, 128, 62, 126)(129, 193, 131, 195, 142, 206, 158, 222, 174, 238, 185, 249, 168, 232, 153, 217, 138, 202, 154, 218, 170, 234, 186, 250, 180, 244, 164, 228, 148, 212, 134, 198)(130, 194, 137, 201, 151, 215, 167, 231, 183, 247, 175, 239, 160, 224, 143, 207, 135, 199, 147, 211, 163, 227, 179, 243, 188, 252, 172, 236, 156, 220, 139, 203)(132, 196, 145, 209, 161, 225, 177, 241, 189, 253, 173, 237, 157, 221, 141, 205, 133, 197, 146, 210, 162, 226, 178, 242, 190, 254, 176, 240, 159, 223, 144, 208)(136, 200, 149, 213, 165, 229, 181, 245, 191, 255, 184, 248, 169, 233, 152, 216, 140, 204, 155, 219, 171, 235, 187, 251, 192, 256, 182, 246, 166, 230, 150, 214) L = (1, 132)(2, 138)(3, 143)(4, 136)(5, 140)(6, 147)(7, 129)(8, 135)(9, 152)(10, 133)(11, 155)(12, 130)(13, 154)(14, 159)(15, 149)(16, 131)(17, 134)(18, 153)(19, 150)(20, 161)(21, 144)(22, 145)(23, 168)(24, 146)(25, 137)(26, 139)(27, 141)(28, 170)(29, 171)(30, 175)(31, 165)(32, 142)(33, 166)(34, 169)(35, 148)(36, 179)(37, 160)(38, 163)(39, 184)(40, 162)(41, 151)(42, 157)(43, 156)(44, 187)(45, 186)(46, 190)(47, 181)(48, 158)(49, 164)(50, 185)(51, 182)(52, 189)(53, 176)(54, 177)(55, 174)(56, 178)(57, 167)(58, 172)(59, 173)(60, 180)(61, 192)(62, 191)(63, 183)(64, 188)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4^8 ), ( 4^32 ) } Outer automorphisms :: reflexible Dual of E23.757 Graph:: bipartite v = 20 e = 128 f = 64 degree seq :: [ 8^16, 32^4 ] E23.775 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = (C16 : C2) : C2 (small group id <64, 41>) Aut = $<128, 922>$ (small group id <128, 922>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^4, (R * Y3)^2, (R * Y1)^2, (Y1 * Y2)^2, (R * Y2)^2, Y2 * Y3^-1 * Y2 * Y3, Y3 * Y1 * Y3^2 * Y2 * Y1 * Y3, Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1, (Y3^-1 * Y1)^16 ] Map:: non-degenerate R = (1, 65, 2, 66)(3, 67, 6, 70)(4, 68, 11, 75)(5, 69, 13, 77)(7, 71, 16, 80)(8, 72, 18, 82)(9, 73, 19, 83)(10, 74, 21, 85)(12, 76, 24, 88)(14, 78, 27, 91)(15, 79, 28, 92)(17, 81, 20, 84)(22, 86, 33, 97)(23, 87, 34, 98)(25, 89, 35, 99)(26, 90, 36, 100)(29, 93, 37, 101)(30, 94, 38, 102)(31, 95, 39, 103)(32, 96, 40, 104)(41, 105, 49, 113)(42, 106, 50, 114)(43, 107, 51, 115)(44, 108, 52, 116)(45, 109, 53, 117)(46, 110, 54, 118)(47, 111, 55, 119)(48, 112, 56, 120)(57, 121, 64, 128)(58, 122, 62, 126)(59, 123, 63, 127)(60, 124, 61, 125)(129, 193, 131, 195)(130, 194, 134, 198)(132, 196, 137, 201)(133, 197, 138, 202)(135, 199, 142, 206)(136, 200, 143, 207)(139, 203, 147, 211)(140, 204, 148, 212)(141, 205, 149, 213)(144, 208, 155, 219)(145, 209, 152, 216)(146, 210, 156, 220)(150, 214, 154, 218)(151, 215, 153, 217)(157, 221, 160, 224)(158, 222, 159, 223)(161, 225, 164, 228)(162, 226, 163, 227)(165, 229, 168, 232)(166, 230, 167, 231)(169, 233, 172, 236)(170, 234, 171, 235)(173, 237, 176, 240)(174, 238, 175, 239)(177, 241, 180, 244)(178, 242, 179, 243)(181, 245, 184, 248)(182, 246, 183, 247)(185, 249, 188, 252)(186, 250, 187, 251)(189, 253, 192, 256)(190, 254, 191, 255) L = (1, 132)(2, 135)(3, 137)(4, 140)(5, 129)(6, 142)(7, 145)(8, 130)(9, 148)(10, 131)(11, 150)(12, 133)(13, 153)(14, 152)(15, 134)(16, 157)(17, 136)(18, 159)(19, 154)(20, 138)(21, 151)(22, 149)(23, 139)(24, 143)(25, 147)(26, 141)(27, 160)(28, 158)(29, 156)(30, 144)(31, 155)(32, 146)(33, 169)(34, 171)(35, 170)(36, 172)(37, 173)(38, 175)(39, 174)(40, 176)(41, 163)(42, 161)(43, 164)(44, 162)(45, 167)(46, 165)(47, 168)(48, 166)(49, 185)(50, 187)(51, 186)(52, 188)(53, 189)(54, 191)(55, 190)(56, 192)(57, 179)(58, 177)(59, 180)(60, 178)(61, 183)(62, 181)(63, 184)(64, 182)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 8, 32, 8, 32 ) } Outer automorphisms :: reflexible Dual of E23.788 Graph:: simple bipartite v = 64 e = 128 f = 20 degree seq :: [ 4^64 ] E23.776 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = (C16 : C2) : C2 (small group id <64, 41>) Aut = $<128, 922>$ (small group id <128, 922>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3 * Y2 * Y3, (Y2 * R)^2, (R * Y3)^2, (R * Y1)^2, Y1 * Y3 * Y1 * Y2 * Y1 * Y3^-1 * Y1 * Y2, (Y2 * Y1)^4, Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ] Map:: non-degenerate R = (1, 65, 2, 66)(3, 67, 9, 73)(4, 68, 10, 74)(5, 69, 11, 75)(6, 70, 12, 76)(7, 71, 13, 77)(8, 72, 14, 78)(15, 79, 24, 88)(16, 80, 27, 91)(17, 81, 30, 94)(18, 82, 25, 89)(19, 83, 33, 97)(20, 84, 34, 98)(21, 85, 26, 90)(22, 86, 35, 99)(23, 87, 36, 100)(28, 92, 37, 101)(29, 93, 38, 102)(31, 95, 39, 103)(32, 96, 40, 104)(41, 105, 49, 113)(42, 106, 50, 114)(43, 107, 51, 115)(44, 108, 52, 116)(45, 109, 53, 117)(46, 110, 54, 118)(47, 111, 55, 119)(48, 112, 56, 120)(57, 121, 64, 128)(58, 122, 62, 126)(59, 123, 63, 127)(60, 124, 61, 125)(129, 193, 131, 195)(130, 194, 134, 198)(132, 196, 133, 197)(135, 199, 136, 200)(137, 201, 143, 207)(138, 202, 146, 210)(139, 203, 149, 213)(140, 204, 152, 216)(141, 205, 155, 219)(142, 206, 158, 222)(144, 208, 145, 209)(147, 211, 148, 212)(150, 214, 151, 215)(153, 217, 154, 218)(156, 220, 157, 221)(159, 223, 160, 224)(161, 225, 163, 227)(162, 226, 164, 228)(165, 229, 167, 231)(166, 230, 168, 232)(169, 233, 170, 234)(171, 235, 172, 236)(173, 237, 174, 238)(175, 239, 176, 240)(177, 241, 179, 243)(178, 242, 180, 244)(181, 245, 183, 247)(182, 246, 184, 248)(185, 249, 186, 250)(187, 251, 188, 252)(189, 253, 190, 254)(191, 255, 192, 256) L = (1, 132)(2, 135)(3, 133)(4, 131)(5, 129)(6, 136)(7, 134)(8, 130)(9, 144)(10, 147)(11, 150)(12, 153)(13, 156)(14, 159)(15, 145)(16, 143)(17, 137)(18, 148)(19, 146)(20, 138)(21, 151)(22, 149)(23, 139)(24, 154)(25, 152)(26, 140)(27, 157)(28, 155)(29, 141)(30, 160)(31, 158)(32, 142)(33, 169)(34, 171)(35, 170)(36, 172)(37, 173)(38, 175)(39, 174)(40, 176)(41, 163)(42, 161)(43, 164)(44, 162)(45, 167)(46, 165)(47, 168)(48, 166)(49, 185)(50, 187)(51, 186)(52, 188)(53, 189)(54, 191)(55, 190)(56, 192)(57, 179)(58, 177)(59, 180)(60, 178)(61, 183)(62, 181)(63, 184)(64, 182)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 8, 32, 8, 32 ) } Outer automorphisms :: reflexible Dual of E23.786 Graph:: simple bipartite v = 64 e = 128 f = 20 degree seq :: [ 4^64 ] E23.777 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = (C16 : C2) : C2 (small group id <64, 41>) Aut = $<128, 922>$ (small group id <128, 922>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, Y3^-1 * Y2 * Y3 * Y2, (R * Y2)^2, Y3^4, Y3^-1 * Y1 * Y2 * Y1 * Y3^-1, Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1, (Y3^-1 * Y1)^16 ] Map:: polytopal non-degenerate R = (1, 65, 2, 66)(3, 67, 9, 73)(4, 68, 12, 76)(5, 69, 14, 78)(6, 70, 13, 77)(7, 71, 17, 81)(8, 72, 18, 82)(10, 74, 20, 84)(11, 75, 22, 86)(15, 79, 27, 91)(16, 80, 28, 92)(19, 83, 21, 85)(23, 87, 33, 97)(24, 88, 34, 98)(25, 89, 35, 99)(26, 90, 36, 100)(29, 93, 37, 101)(30, 94, 38, 102)(31, 95, 39, 103)(32, 96, 40, 104)(41, 105, 49, 113)(42, 106, 50, 114)(43, 107, 51, 115)(44, 108, 52, 116)(45, 109, 53, 117)(46, 110, 54, 118)(47, 111, 55, 119)(48, 112, 56, 120)(57, 121, 64, 128)(58, 122, 62, 126)(59, 123, 63, 127)(60, 124, 61, 125)(129, 193, 131, 195)(130, 194, 134, 198)(132, 196, 138, 202)(133, 197, 139, 203)(135, 199, 143, 207)(136, 200, 144, 208)(137, 201, 147, 211)(140, 204, 142, 206)(141, 205, 149, 213)(145, 209, 146, 210)(148, 212, 150, 214)(151, 215, 153, 217)(152, 216, 154, 218)(155, 219, 156, 220)(157, 221, 159, 223)(158, 222, 160, 224)(161, 225, 162, 226)(163, 227, 164, 228)(165, 229, 166, 230)(167, 231, 168, 232)(169, 233, 171, 235)(170, 234, 172, 236)(173, 237, 175, 239)(174, 238, 176, 240)(177, 241, 178, 242)(179, 243, 180, 244)(181, 245, 182, 246)(183, 247, 184, 248)(185, 249, 187, 251)(186, 250, 188, 252)(189, 253, 191, 255)(190, 254, 192, 256) L = (1, 132)(2, 135)(3, 138)(4, 141)(5, 129)(6, 143)(7, 137)(8, 130)(9, 136)(10, 149)(11, 131)(12, 151)(13, 133)(14, 153)(15, 147)(16, 134)(17, 157)(18, 159)(19, 144)(20, 152)(21, 139)(22, 154)(23, 148)(24, 140)(25, 150)(26, 142)(27, 158)(28, 160)(29, 155)(30, 145)(31, 156)(32, 146)(33, 169)(34, 171)(35, 170)(36, 172)(37, 173)(38, 175)(39, 174)(40, 176)(41, 163)(42, 161)(43, 164)(44, 162)(45, 167)(46, 165)(47, 168)(48, 166)(49, 185)(50, 187)(51, 186)(52, 188)(53, 189)(54, 191)(55, 190)(56, 192)(57, 179)(58, 177)(59, 180)(60, 178)(61, 183)(62, 181)(63, 184)(64, 182)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 8, 32, 8, 32 ) } Outer automorphisms :: reflexible Dual of E23.787 Graph:: simple bipartite v = 64 e = 128 f = 20 degree seq :: [ 4^64 ] E23.778 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = (C16 : C2) : C2 (small group id <64, 41>) Aut = $<128, 922>$ (small group id <128, 922>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, Y2^4, Y1 * Y2 * Y1 * Y2^-1, (R * Y3)^2, (R * Y1)^2, (Y3 * Y1)^2, (R * Y2 * Y3)^2, Y2^2 * Y3 * Y2^2 * Y3 * Y1, Y3 * Y2 * Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1, (Y3 * Y2^-1)^16 ] Map:: non-degenerate R = (1, 65, 2, 66)(3, 67, 6, 70)(4, 68, 7, 71)(5, 69, 8, 72)(9, 73, 14, 78)(10, 74, 15, 79)(11, 75, 16, 80)(12, 76, 17, 81)(13, 77, 18, 82)(19, 83, 22, 86)(20, 84, 26, 90)(21, 85, 25, 89)(23, 87, 27, 91)(24, 88, 28, 92)(29, 93, 36, 100)(30, 94, 35, 99)(31, 95, 34, 98)(32, 96, 33, 97)(37, 101, 40, 104)(38, 102, 39, 103)(41, 105, 44, 108)(42, 106, 43, 107)(45, 109, 48, 112)(46, 110, 47, 111)(49, 113, 52, 116)(50, 114, 51, 115)(53, 117, 56, 120)(54, 118, 55, 119)(57, 121, 60, 124)(58, 122, 59, 123)(61, 125, 64, 128)(62, 126, 63, 127)(129, 193, 131, 195, 137, 201, 133, 197)(130, 194, 134, 198, 142, 206, 136, 200)(132, 196, 139, 203, 150, 214, 140, 204)(135, 199, 144, 208, 147, 211, 145, 209)(138, 202, 148, 212, 146, 210, 149, 213)(141, 205, 153, 217, 143, 207, 154, 218)(151, 215, 159, 223, 156, 220, 160, 224)(152, 216, 161, 225, 155, 219, 162, 226)(157, 221, 165, 229, 163, 227, 166, 230)(158, 222, 167, 231, 164, 228, 168, 232)(169, 233, 177, 241, 171, 235, 178, 242)(170, 234, 179, 243, 172, 236, 180, 244)(173, 237, 181, 245, 175, 239, 182, 246)(174, 238, 183, 247, 176, 240, 184, 248)(185, 249, 192, 256, 187, 251, 190, 254)(186, 250, 191, 255, 188, 252, 189, 253) L = (1, 132)(2, 135)(3, 138)(4, 129)(5, 141)(6, 143)(7, 130)(8, 146)(9, 147)(10, 131)(11, 151)(12, 152)(13, 133)(14, 150)(15, 134)(16, 155)(17, 156)(18, 136)(19, 137)(20, 157)(21, 158)(22, 142)(23, 139)(24, 140)(25, 163)(26, 164)(27, 144)(28, 145)(29, 148)(30, 149)(31, 169)(32, 170)(33, 171)(34, 172)(35, 153)(36, 154)(37, 173)(38, 174)(39, 175)(40, 176)(41, 159)(42, 160)(43, 161)(44, 162)(45, 165)(46, 166)(47, 167)(48, 168)(49, 185)(50, 186)(51, 187)(52, 188)(53, 189)(54, 190)(55, 191)(56, 192)(57, 177)(58, 178)(59, 179)(60, 180)(61, 181)(62, 182)(63, 183)(64, 184)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32 ) } Outer automorphisms :: reflexible Dual of E23.785 Graph:: simple bipartite v = 48 e = 128 f = 36 degree seq :: [ 4^32, 8^16 ] E23.779 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = (C16 : C2) : C2 (small group id <64, 41>) Aut = $<128, 922>$ (small group id <128, 922>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, (Y3 * Y1)^2, (R * Y1)^2, (R * Y3)^2, Y2^4, Y2^-2 * Y3 * Y2^-2 * Y1, Y3 * Y2^-1 * Y3 * Y1 * Y2 * Y1, (R * Y2 * Y3)^2, Y2^-1 * Y1 * Y2^-1 * Y1 * Y3 * Y2^-1 * Y1 * Y2^-1, R * Y2 * Y3 * Y2^-2 * R * Y2^-1 * Y1, Y2^2 * R * Y2^-2 * R * Y1 * Y3, Y2 * Y3 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y3 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y3 ] Map:: polytopal non-degenerate R = (1, 65, 2, 66)(3, 67, 9, 73)(4, 68, 7, 71)(5, 69, 14, 78)(6, 70, 16, 80)(8, 72, 21, 85)(10, 74, 25, 89)(11, 75, 19, 83)(12, 76, 18, 82)(13, 77, 22, 86)(15, 79, 20, 84)(17, 81, 30, 94)(23, 87, 33, 97)(24, 88, 35, 99)(26, 90, 34, 98)(27, 91, 36, 100)(28, 92, 37, 101)(29, 93, 39, 103)(31, 95, 38, 102)(32, 96, 40, 104)(41, 105, 49, 113)(42, 106, 51, 115)(43, 107, 50, 114)(44, 108, 52, 116)(45, 109, 53, 117)(46, 110, 55, 119)(47, 111, 54, 118)(48, 112, 56, 120)(57, 121, 63, 127)(58, 122, 62, 126)(59, 123, 61, 125)(60, 124, 64, 128)(129, 193, 131, 195, 138, 202, 133, 197)(130, 194, 134, 198, 145, 209, 136, 200)(132, 196, 140, 204, 153, 217, 141, 205)(135, 199, 147, 211, 158, 222, 148, 212)(137, 201, 151, 215, 143, 207, 152, 216)(139, 203, 154, 218, 142, 206, 155, 219)(144, 208, 156, 220, 150, 214, 157, 221)(146, 210, 159, 223, 149, 213, 160, 224)(161, 225, 169, 233, 164, 228, 170, 234)(162, 226, 171, 235, 163, 227, 172, 236)(165, 229, 173, 237, 168, 232, 174, 238)(166, 230, 175, 239, 167, 231, 176, 240)(177, 241, 185, 249, 180, 244, 186, 250)(178, 242, 187, 251, 179, 243, 188, 252)(181, 245, 189, 253, 184, 248, 190, 254)(182, 246, 191, 255, 183, 247, 192, 256) L = (1, 132)(2, 135)(3, 139)(4, 129)(5, 143)(6, 146)(7, 130)(8, 150)(9, 147)(10, 145)(11, 131)(12, 144)(13, 149)(14, 148)(15, 133)(16, 140)(17, 138)(18, 134)(19, 137)(20, 142)(21, 141)(22, 136)(23, 162)(24, 164)(25, 158)(26, 161)(27, 163)(28, 166)(29, 168)(30, 153)(31, 165)(32, 167)(33, 154)(34, 151)(35, 155)(36, 152)(37, 159)(38, 156)(39, 160)(40, 157)(41, 178)(42, 180)(43, 177)(44, 179)(45, 182)(46, 184)(47, 181)(48, 183)(49, 171)(50, 169)(51, 172)(52, 170)(53, 175)(54, 173)(55, 176)(56, 174)(57, 189)(58, 192)(59, 191)(60, 190)(61, 185)(62, 188)(63, 187)(64, 186)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32 ) } Outer automorphisms :: reflexible Dual of E23.782 Graph:: simple bipartite v = 48 e = 128 f = 36 degree seq :: [ 4^32, 8^16 ] E23.780 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = (C16 : C2) : C2 (small group id <64, 41>) Aut = $<128, 922>$ (small group id <128, 922>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3 * Y2^2 * Y1, (Y1 * Y3)^2, Y2 * Y3^-1 * Y1 * Y2, (R * Y3)^2, (R * Y1)^2, Y3^4, (R * Y2^-1 * Y3^-1)^2, R * Y2^2 * R * Y3 * Y1, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2^-1 * Y3^-2 * Y2^-1 * Y1, Y2^-1 * Y1 * Y2 * Y3 * Y2^-1 * Y3^-1 * Y2 * Y1 * Y2 * Y3 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1, Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * 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, 65, 2, 66)(3, 67, 11, 75)(4, 68, 10, 74)(5, 69, 13, 77)(6, 70, 8, 72)(7, 71, 18, 82)(9, 73, 20, 84)(12, 76, 23, 87)(14, 78, 21, 85)(15, 79, 24, 88)(16, 80, 19, 83)(17, 81, 22, 86)(25, 89, 33, 97)(26, 90, 35, 99)(27, 91, 34, 98)(28, 92, 36, 100)(29, 93, 37, 101)(30, 94, 39, 103)(31, 95, 38, 102)(32, 96, 40, 104)(41, 105, 49, 113)(42, 106, 51, 115)(43, 107, 50, 114)(44, 108, 52, 116)(45, 109, 53, 117)(46, 110, 55, 119)(47, 111, 54, 118)(48, 112, 56, 120)(57, 121, 64, 128)(58, 122, 62, 126)(59, 123, 63, 127)(60, 124, 61, 125)(129, 193, 131, 195, 136, 200, 133, 197)(130, 194, 135, 199, 132, 196, 137, 201)(134, 198, 144, 208, 149, 213, 145, 209)(138, 202, 151, 215, 142, 206, 152, 216)(139, 203, 153, 217, 140, 204, 154, 218)(141, 205, 155, 219, 143, 207, 156, 220)(146, 210, 157, 221, 147, 211, 158, 222)(148, 212, 159, 223, 150, 214, 160, 224)(161, 225, 169, 233, 162, 226, 170, 234)(163, 227, 171, 235, 164, 228, 172, 236)(165, 229, 173, 237, 166, 230, 174, 238)(167, 231, 175, 239, 168, 232, 176, 240)(177, 241, 185, 249, 178, 242, 186, 250)(179, 243, 187, 251, 180, 244, 188, 252)(181, 245, 189, 253, 182, 246, 190, 254)(183, 247, 191, 255, 184, 248, 192, 256) L = (1, 132)(2, 136)(3, 140)(4, 142)(5, 143)(6, 129)(7, 147)(8, 149)(9, 150)(10, 130)(11, 133)(12, 152)(13, 131)(14, 134)(15, 151)(16, 146)(17, 148)(18, 137)(19, 145)(20, 135)(21, 138)(22, 144)(23, 139)(24, 141)(25, 162)(26, 164)(27, 161)(28, 163)(29, 166)(30, 168)(31, 165)(32, 167)(33, 154)(34, 156)(35, 153)(36, 155)(37, 158)(38, 160)(39, 157)(40, 159)(41, 178)(42, 180)(43, 177)(44, 179)(45, 182)(46, 184)(47, 181)(48, 183)(49, 170)(50, 172)(51, 169)(52, 171)(53, 174)(54, 176)(55, 173)(56, 175)(57, 191)(58, 189)(59, 192)(60, 190)(61, 187)(62, 185)(63, 188)(64, 186)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32 ) } Outer automorphisms :: reflexible Dual of E23.783 Graph:: bipartite v = 48 e = 128 f = 36 degree seq :: [ 4^32, 8^16 ] E23.781 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = (C16 : C2) : C2 (small group id <64, 41>) Aut = $<128, 922>$ (small group id <128, 922>) |r| :: 2 Presentation :: [ Y1^2, R^2, (Y1 * Y3^-1)^2, Y3^-1 * Y2^2 * Y1, (R * Y3)^2, (R * Y1)^2, Y2 * Y3 * Y1 * Y2, Y3^4, Y2^-1 * Y1 * Y3 * Y2 * Y3^-1 * Y1, (R * Y2 * Y3^-1)^2, Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3^-1 * Y2^-1 * Y1, Y3 * Y2 * Y1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: polytopal non-degenerate R = (1, 65, 2, 66)(3, 67, 11, 75)(4, 68, 10, 74)(5, 69, 12, 76)(6, 70, 8, 72)(7, 71, 18, 82)(9, 73, 19, 83)(13, 77, 21, 85)(14, 78, 20, 84)(15, 79, 22, 86)(16, 80, 24, 88)(17, 81, 23, 87)(25, 89, 33, 97)(26, 90, 34, 98)(27, 91, 35, 99)(28, 92, 36, 100)(29, 93, 37, 101)(30, 94, 38, 102)(31, 95, 39, 103)(32, 96, 40, 104)(41, 105, 49, 113)(42, 106, 50, 114)(43, 107, 51, 115)(44, 108, 52, 116)(45, 109, 53, 117)(46, 110, 54, 118)(47, 111, 55, 119)(48, 112, 56, 120)(57, 121, 64, 128)(58, 122, 62, 126)(59, 123, 63, 127)(60, 124, 61, 125)(129, 193, 131, 195, 138, 202, 133, 197)(130, 194, 135, 199, 134, 198, 137, 201)(132, 196, 142, 206, 150, 214, 144, 208)(136, 200, 149, 213, 143, 207, 151, 215)(139, 203, 153, 217, 141, 205, 154, 218)(140, 204, 155, 219, 145, 209, 156, 220)(146, 210, 157, 221, 148, 212, 158, 222)(147, 211, 159, 223, 152, 216, 160, 224)(161, 225, 169, 233, 163, 227, 170, 234)(162, 226, 171, 235, 164, 228, 172, 236)(165, 229, 173, 237, 167, 231, 174, 238)(166, 230, 175, 239, 168, 232, 176, 240)(177, 241, 185, 249, 179, 243, 186, 250)(178, 242, 187, 251, 180, 244, 188, 252)(181, 245, 189, 253, 183, 247, 190, 254)(182, 246, 191, 255, 184, 248, 192, 256) L = (1, 132)(2, 136)(3, 140)(4, 143)(5, 139)(6, 129)(7, 147)(8, 150)(9, 146)(10, 130)(11, 149)(12, 151)(13, 131)(14, 152)(15, 134)(16, 148)(17, 133)(18, 142)(19, 144)(20, 135)(21, 145)(22, 138)(23, 141)(24, 137)(25, 162)(26, 161)(27, 164)(28, 163)(29, 166)(30, 165)(31, 168)(32, 167)(33, 155)(34, 156)(35, 153)(36, 154)(37, 159)(38, 160)(39, 157)(40, 158)(41, 178)(42, 177)(43, 180)(44, 179)(45, 182)(46, 181)(47, 184)(48, 183)(49, 171)(50, 172)(51, 169)(52, 170)(53, 175)(54, 176)(55, 173)(56, 174)(57, 190)(58, 192)(59, 189)(60, 191)(61, 186)(62, 188)(63, 185)(64, 187)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32 ) } Outer automorphisms :: reflexible Dual of E23.784 Graph:: simple bipartite v = 48 e = 128 f = 36 degree seq :: [ 4^32, 8^16 ] E23.782 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = (C16 : C2) : C2 (small group id <64, 41>) Aut = $<128, 922>$ (small group id <128, 922>) |r| :: 2 Presentation :: [ Y3^2, Y2^2, R^2, (R * Y2)^2, (Y3 * Y2)^2, Y1 * Y2 * Y1^-1 * Y2, (R * Y1)^2, (R * Y3)^2, Y3 * Y1^2 * Y3 * Y2 * Y1^2, (Y3 * Y1^-1)^4, Y1^-8 * Y2 ] Map:: polytopal non-degenerate R = (1, 65, 2, 66, 6, 70, 15, 79, 33, 97, 44, 108, 24, 88, 10, 74, 3, 67, 7, 71, 16, 80, 34, 98, 54, 118, 32, 96, 14, 78, 5, 69)(4, 68, 11, 75, 25, 89, 45, 109, 58, 122, 36, 100, 17, 81, 22, 86, 9, 73, 21, 85, 31, 95, 52, 116, 55, 119, 49, 113, 28, 92, 12, 76)(8, 72, 19, 83, 23, 87, 43, 107, 53, 117, 56, 120, 35, 99, 37, 101, 18, 82, 30, 94, 13, 77, 29, 93, 50, 114, 60, 124, 40, 104, 20, 84)(26, 90, 46, 110, 42, 106, 39, 103, 59, 123, 63, 127, 61, 125, 51, 115, 41, 105, 38, 102, 27, 91, 48, 112, 57, 121, 64, 128, 62, 126, 47, 111)(129, 193, 131, 195)(130, 194, 135, 199)(132, 196, 137, 201)(133, 197, 138, 202)(134, 198, 144, 208)(136, 200, 146, 210)(139, 203, 149, 213)(140, 204, 150, 214)(141, 205, 151, 215)(142, 206, 152, 216)(143, 207, 162, 226)(145, 209, 156, 220)(147, 211, 158, 222)(148, 212, 165, 229)(153, 217, 159, 223)(154, 218, 169, 233)(155, 219, 170, 234)(157, 221, 171, 235)(160, 224, 172, 236)(161, 225, 182, 246)(163, 227, 168, 232)(164, 228, 177, 241)(166, 230, 174, 238)(167, 231, 176, 240)(173, 237, 180, 244)(175, 239, 179, 243)(178, 242, 181, 245)(183, 247, 186, 250)(184, 248, 188, 252)(185, 249, 187, 251)(189, 253, 190, 254)(191, 255, 192, 256) L = (1, 132)(2, 136)(3, 137)(4, 129)(5, 141)(6, 145)(7, 146)(8, 130)(9, 131)(10, 151)(11, 154)(12, 155)(13, 133)(14, 159)(15, 163)(16, 156)(17, 134)(18, 135)(19, 166)(20, 167)(21, 169)(22, 170)(23, 138)(24, 153)(25, 152)(26, 139)(27, 140)(28, 144)(29, 179)(30, 174)(31, 142)(32, 181)(33, 183)(34, 168)(35, 143)(36, 185)(37, 176)(38, 147)(39, 148)(40, 162)(41, 149)(42, 150)(43, 175)(44, 178)(45, 189)(46, 158)(47, 171)(48, 165)(49, 187)(50, 172)(51, 157)(52, 190)(53, 160)(54, 186)(55, 161)(56, 191)(57, 164)(58, 182)(59, 177)(60, 192)(61, 173)(62, 180)(63, 184)(64, 188)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 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 E23.779 Graph:: bipartite v = 36 e = 128 f = 48 degree seq :: [ 4^32, 32^4 ] E23.783 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = (C16 : C2) : C2 (small group id <64, 41>) Aut = $<128, 922>$ (small group id <128, 922>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3 * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y3^4, Y1 * Y3^-1 * Y2 * Y1 * Y3^-1, Y3 * Y2 * Y1 * Y3 * Y1, (R * Y2 * Y3^-1)^2, Y1^2 * Y2 * Y1^-2 * Y2, (Y1 * Y2 * Y1^-1 * Y2)^2, Y1^-2 * Y2 * Y1^-5 * Y2 * Y1^-1, Y1^-1 * Y3 * Y1^4 * Y3 * Y1^-3 ] Map:: non-degenerate R = (1, 65, 2, 66, 7, 71, 24, 88, 41, 105, 57, 121, 49, 113, 33, 97, 16, 80, 30, 94, 46, 110, 62, 126, 56, 120, 39, 103, 20, 84, 5, 69)(3, 67, 11, 75, 25, 89, 45, 109, 58, 122, 52, 116, 36, 100, 18, 82, 29, 93, 8, 72, 28, 92, 42, 106, 61, 125, 50, 114, 34, 98, 13, 77)(4, 68, 15, 79, 35, 99, 51, 115, 60, 124, 47, 111, 26, 90, 23, 87, 6, 70, 22, 86, 38, 102, 54, 118, 59, 123, 48, 112, 27, 91, 17, 81)(9, 73, 14, 78, 21, 85, 40, 104, 55, 119, 63, 127, 43, 107, 32, 96, 10, 74, 12, 76, 19, 83, 37, 101, 53, 117, 64, 128, 44, 108, 31, 95)(129, 193, 131, 195)(130, 194, 136, 200)(132, 196, 142, 206)(133, 197, 146, 210)(134, 198, 140, 204)(135, 199, 153, 217)(137, 201, 151, 215)(138, 202, 145, 209)(139, 203, 158, 222)(141, 205, 161, 225)(143, 207, 147, 211)(144, 208, 157, 221)(148, 212, 162, 226)(149, 213, 150, 214)(152, 216, 170, 234)(154, 218, 160, 224)(155, 219, 159, 223)(156, 220, 174, 238)(163, 227, 168, 232)(164, 228, 177, 241)(165, 229, 166, 230)(167, 231, 180, 244)(169, 233, 186, 250)(171, 235, 176, 240)(172, 236, 175, 239)(173, 237, 190, 254)(178, 242, 185, 249)(179, 243, 181, 245)(182, 246, 183, 247)(184, 248, 189, 253)(187, 251, 192, 256)(188, 252, 191, 255) L = (1, 132)(2, 137)(3, 140)(4, 144)(5, 147)(6, 129)(7, 154)(8, 145)(9, 158)(10, 130)(11, 151)(12, 157)(13, 143)(14, 131)(15, 146)(16, 134)(17, 139)(18, 150)(19, 161)(20, 166)(21, 133)(22, 141)(23, 136)(24, 171)(25, 159)(26, 174)(27, 135)(28, 160)(29, 142)(30, 138)(31, 156)(32, 153)(33, 149)(34, 168)(35, 148)(36, 165)(37, 162)(38, 177)(39, 183)(40, 164)(41, 187)(42, 175)(43, 190)(44, 152)(45, 176)(46, 155)(47, 173)(48, 170)(49, 163)(50, 182)(51, 178)(52, 179)(53, 167)(54, 180)(55, 185)(56, 188)(57, 181)(58, 191)(59, 184)(60, 169)(61, 192)(62, 172)(63, 189)(64, 186)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 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 E23.780 Graph:: simple bipartite v = 36 e = 128 f = 48 degree seq :: [ 4^32, 32^4 ] E23.784 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = (C16 : C2) : C2 (small group id <64, 41>) Aut = $<128, 922>$ (small group id <128, 922>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y3^4, Y1 * Y3^-1 * Y1 * Y2 * Y3^-1, Y1 * Y3^-1 * Y2 * Y1 * Y3, (R * Y2 * Y3^-1)^2, (Y1^-1 * R * Y2)^2, Y1^2 * Y3 * Y2 * Y1^2 * Y2 * Y3, Y1^-1 * Y3^2 * Y1^-7 ] Map:: polytopal non-degenerate R = (1, 65, 2, 66, 7, 71, 24, 88, 41, 105, 57, 121, 49, 113, 33, 97, 16, 80, 30, 94, 46, 110, 62, 126, 56, 120, 39, 103, 20, 84, 5, 69)(3, 67, 11, 75, 25, 89, 45, 109, 58, 122, 52, 116, 36, 100, 18, 82, 29, 93, 8, 72, 28, 92, 42, 106, 61, 125, 50, 114, 34, 98, 13, 77)(4, 68, 15, 79, 35, 99, 51, 115, 60, 124, 47, 111, 26, 90, 23, 87, 6, 70, 22, 86, 38, 102, 54, 118, 59, 123, 48, 112, 27, 91, 17, 81)(9, 73, 12, 76, 21, 85, 40, 104, 55, 119, 63, 127, 43, 107, 32, 96, 10, 74, 14, 78, 19, 83, 37, 101, 53, 117, 64, 128, 44, 108, 31, 95)(129, 193, 131, 195)(130, 194, 136, 200)(132, 196, 142, 206)(133, 197, 146, 210)(134, 198, 140, 204)(135, 199, 153, 217)(137, 201, 145, 209)(138, 202, 151, 215)(139, 203, 158, 222)(141, 205, 161, 225)(143, 207, 149, 213)(144, 208, 157, 221)(147, 211, 150, 214)(148, 212, 162, 226)(152, 216, 170, 234)(154, 218, 159, 223)(155, 219, 160, 224)(156, 220, 174, 238)(163, 227, 165, 229)(164, 228, 177, 241)(166, 230, 168, 232)(167, 231, 180, 244)(169, 233, 186, 250)(171, 235, 175, 239)(172, 236, 176, 240)(173, 237, 190, 254)(178, 242, 185, 249)(179, 243, 183, 247)(181, 245, 182, 246)(184, 248, 189, 253)(187, 251, 191, 255)(188, 252, 192, 256) L = (1, 132)(2, 137)(3, 140)(4, 144)(5, 147)(6, 129)(7, 154)(8, 151)(9, 158)(10, 130)(11, 145)(12, 157)(13, 150)(14, 131)(15, 141)(16, 134)(17, 136)(18, 143)(19, 161)(20, 166)(21, 133)(22, 146)(23, 139)(24, 171)(25, 160)(26, 174)(27, 135)(28, 159)(29, 142)(30, 138)(31, 153)(32, 156)(33, 149)(34, 165)(35, 148)(36, 168)(37, 164)(38, 177)(39, 183)(40, 162)(41, 187)(42, 176)(43, 190)(44, 152)(45, 175)(46, 155)(47, 170)(48, 173)(49, 163)(50, 179)(51, 180)(52, 182)(53, 167)(54, 178)(55, 185)(56, 188)(57, 181)(58, 192)(59, 184)(60, 169)(61, 191)(62, 172)(63, 186)(64, 189)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 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 E23.781 Graph:: simple bipartite v = 36 e = 128 f = 48 degree seq :: [ 4^32, 32^4 ] E23.785 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = (C16 : C2) : C2 (small group id <64, 41>) Aut = $<128, 922>$ (small group id <128, 922>) |r| :: 2 Presentation :: [ Y3^2, Y2^2, R^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y3 * Y1 * Y3 * Y2 * Y1^-1 * Y2, Y1^-2 * Y3 * Y1^-2 * Y2, Y1^-1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y2, Y1^-2 * Y3 * Y2 * Y1^-6 ] Map:: non-degenerate R = (1, 65, 2, 66, 6, 70, 17, 81, 35, 99, 53, 117, 46, 110, 28, 92, 10, 74, 21, 85, 38, 102, 56, 120, 52, 116, 34, 98, 16, 80, 5, 69)(3, 67, 9, 73, 25, 89, 45, 109, 55, 119, 39, 103, 18, 82, 13, 77, 4, 68, 12, 76, 31, 95, 49, 113, 54, 118, 40, 104, 19, 83, 11, 75)(7, 71, 20, 84, 15, 79, 33, 97, 51, 115, 57, 121, 36, 100, 24, 88, 8, 72, 23, 87, 14, 78, 32, 96, 50, 114, 58, 122, 37, 101, 22, 86)(26, 90, 42, 106, 30, 94, 43, 107, 60, 124, 63, 127, 61, 125, 48, 112, 27, 91, 41, 105, 29, 93, 44, 108, 59, 123, 64, 128, 62, 126, 47, 111)(129, 193, 131, 195)(130, 194, 135, 199)(132, 196, 138, 202)(133, 197, 142, 206)(134, 198, 146, 210)(136, 200, 149, 213)(137, 201, 154, 218)(139, 203, 157, 221)(140, 204, 155, 219)(141, 205, 158, 222)(143, 207, 156, 220)(144, 208, 159, 223)(145, 209, 164, 228)(147, 211, 166, 230)(148, 212, 169, 233)(150, 214, 171, 235)(151, 215, 170, 234)(152, 216, 172, 236)(153, 217, 174, 238)(160, 224, 176, 240)(161, 225, 175, 239)(162, 226, 179, 243)(163, 227, 182, 246)(165, 229, 184, 248)(167, 231, 187, 251)(168, 232, 188, 252)(173, 237, 189, 253)(177, 241, 190, 254)(178, 242, 181, 245)(180, 244, 183, 247)(185, 249, 191, 255)(186, 250, 192, 256) L = (1, 132)(2, 136)(3, 138)(4, 129)(5, 143)(6, 147)(7, 149)(8, 130)(9, 155)(10, 131)(11, 158)(12, 154)(13, 157)(14, 156)(15, 133)(16, 153)(17, 165)(18, 166)(19, 134)(20, 170)(21, 135)(22, 172)(23, 169)(24, 171)(25, 144)(26, 140)(27, 137)(28, 142)(29, 141)(30, 139)(31, 174)(32, 175)(33, 176)(34, 178)(35, 183)(36, 184)(37, 145)(38, 146)(39, 188)(40, 187)(41, 151)(42, 148)(43, 152)(44, 150)(45, 190)(46, 159)(47, 160)(48, 161)(49, 189)(50, 162)(51, 181)(52, 182)(53, 179)(54, 180)(55, 163)(56, 164)(57, 192)(58, 191)(59, 168)(60, 167)(61, 177)(62, 173)(63, 186)(64, 185)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 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 E23.778 Graph:: bipartite v = 36 e = 128 f = 48 degree seq :: [ 4^32, 32^4 ] E23.786 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = (C16 : C2) : C2 (small group id <64, 41>) Aut = $<128, 922>$ (small group id <128, 922>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3^-1, Y1^4, (Y2 * Y1^-1)^2, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, (R * Y2 * Y3^-1)^2, R * Y2^-1 * R * Y1 * Y2^-1 * Y1^-1, Y2^-1 * Y1 * Y2 * R * Y2^-1 * R * Y2^-1 * Y1^-1, Y2^-3 * Y3^-1 * Y2^-3 * Y1^-1, Y2^-2 * Y1^2 * Y2^2 * Y1^-2, Y2^-5 * Y1^-1 * Y2^2 * Y1 * Y2^-1 ] Map:: non-degenerate R = (1, 65, 2, 66, 6, 70, 4, 68)(3, 67, 9, 73, 19, 83, 8, 72)(5, 69, 11, 75, 25, 89, 13, 77)(7, 71, 17, 81, 35, 99, 16, 80)(10, 74, 23, 87, 34, 98, 22, 86)(12, 76, 15, 79, 33, 97, 27, 91)(14, 78, 29, 93, 36, 100, 31, 95)(18, 82, 39, 103, 26, 90, 38, 102)(20, 84, 41, 105, 28, 92, 43, 107)(21, 85, 37, 101, 30, 94, 42, 106)(24, 88, 47, 111, 58, 122, 46, 110)(32, 96, 51, 115, 56, 120, 40, 104)(44, 108, 59, 123, 45, 109, 53, 117)(48, 112, 60, 124, 63, 127, 62, 126)(49, 113, 54, 118, 50, 114, 55, 119)(52, 116, 57, 121, 64, 128, 61, 125)(129, 193, 131, 195, 138, 202, 152, 216, 176, 240, 183, 247, 166, 230, 145, 209, 165, 229, 155, 219, 171, 235, 187, 251, 180, 244, 160, 224, 142, 206, 133, 197)(130, 194, 135, 199, 146, 210, 168, 232, 185, 249, 174, 238, 151, 215, 161, 225, 158, 222, 141, 205, 157, 221, 178, 242, 188, 252, 172, 236, 148, 212, 136, 200)(132, 196, 139, 203, 154, 218, 177, 241, 189, 253, 173, 237, 150, 214, 137, 201, 149, 213, 163, 227, 159, 223, 179, 243, 190, 254, 175, 239, 156, 220, 140, 204)(134, 198, 143, 207, 162, 226, 181, 245, 191, 255, 184, 248, 167, 231, 153, 217, 170, 234, 147, 211, 169, 233, 186, 250, 192, 256, 182, 246, 164, 228, 144, 208) L = (1, 130)(2, 134)(3, 137)(4, 129)(5, 139)(6, 132)(7, 145)(8, 131)(9, 147)(10, 151)(11, 153)(12, 143)(13, 133)(14, 157)(15, 161)(16, 135)(17, 163)(18, 167)(19, 136)(20, 169)(21, 165)(22, 138)(23, 162)(24, 175)(25, 141)(26, 166)(27, 140)(28, 171)(29, 164)(30, 170)(31, 142)(32, 179)(33, 155)(34, 150)(35, 144)(36, 159)(37, 158)(38, 146)(39, 154)(40, 160)(41, 156)(42, 149)(43, 148)(44, 187)(45, 181)(46, 152)(47, 186)(48, 188)(49, 182)(50, 183)(51, 184)(52, 185)(53, 172)(54, 178)(55, 177)(56, 168)(57, 192)(58, 174)(59, 173)(60, 191)(61, 180)(62, 176)(63, 190)(64, 189)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4^8 ), ( 4^32 ) } Outer automorphisms :: reflexible Dual of E23.776 Graph:: bipartite v = 20 e = 128 f = 64 degree seq :: [ 8^16, 32^4 ] E23.787 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = (C16 : C2) : C2 (small group id <64, 41>) Aut = $<128, 922>$ (small group id <128, 922>) |r| :: 2 Presentation :: [ R^2, Y3^-2 * Y1^2, (R * Y1)^2, Y3^2 * Y1^2, (Y2 * Y1^-1)^2, Y1^4, (R * Y3)^2, (Y3^-1, Y1^-1), Y2^-1 * Y1^-1 * Y2^-1 * Y3^-1, (Y3 * Y2^-1)^2, (R * Y2 * Y3^-1)^2, Y2^6 * Y1 * Y2^-2 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 65, 2, 66, 8, 72, 5, 69)(3, 67, 13, 77, 26, 90, 11, 75)(4, 68, 10, 74, 7, 71, 12, 76)(6, 70, 18, 82, 25, 89, 17, 81)(9, 73, 23, 87, 19, 83, 22, 86)(14, 78, 30, 94, 37, 101, 29, 93)(15, 79, 21, 85, 16, 80, 27, 91)(20, 84, 33, 97, 38, 102, 35, 99)(24, 88, 40, 104, 34, 98, 39, 103)(28, 92, 42, 106, 32, 96, 43, 107)(31, 95, 47, 111, 58, 122, 46, 110)(36, 100, 51, 115, 56, 120, 41, 105)(44, 108, 59, 123, 45, 109, 53, 117)(48, 112, 60, 124, 63, 127, 62, 126)(49, 113, 55, 119, 50, 114, 54, 118)(52, 116, 57, 121, 64, 128, 61, 125)(129, 193, 131, 195, 142, 206, 159, 223, 176, 240, 183, 247, 167, 231, 151, 215, 140, 204, 155, 219, 171, 235, 187, 251, 180, 244, 164, 228, 148, 212, 134, 198)(130, 194, 137, 201, 152, 216, 169, 233, 185, 249, 174, 238, 158, 222, 144, 208, 132, 196, 145, 209, 161, 225, 177, 241, 188, 252, 172, 236, 156, 220, 139, 203)(133, 197, 146, 210, 162, 226, 178, 242, 189, 253, 173, 237, 157, 221, 141, 205, 135, 199, 147, 211, 163, 227, 179, 243, 190, 254, 175, 239, 160, 224, 143, 207)(136, 200, 149, 213, 165, 229, 181, 245, 191, 255, 184, 248, 168, 232, 153, 217, 138, 202, 154, 218, 170, 234, 186, 250, 192, 256, 182, 246, 166, 230, 150, 214) L = (1, 132)(2, 138)(3, 143)(4, 136)(5, 140)(6, 147)(7, 129)(8, 135)(9, 134)(10, 133)(11, 155)(12, 130)(13, 149)(14, 156)(15, 154)(16, 131)(17, 151)(18, 150)(19, 153)(20, 152)(21, 139)(22, 145)(23, 146)(24, 166)(25, 137)(26, 144)(27, 141)(28, 165)(29, 171)(30, 170)(31, 173)(32, 142)(33, 168)(34, 148)(35, 167)(36, 178)(37, 160)(38, 162)(39, 161)(40, 163)(41, 183)(42, 157)(43, 158)(44, 159)(45, 186)(46, 187)(47, 181)(48, 185)(49, 164)(50, 184)(51, 182)(52, 188)(53, 174)(54, 169)(55, 179)(56, 177)(57, 191)(58, 172)(59, 175)(60, 192)(61, 176)(62, 180)(63, 189)(64, 190)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4^8 ), ( 4^32 ) } Outer automorphisms :: reflexible Dual of E23.777 Graph:: bipartite v = 20 e = 128 f = 64 degree seq :: [ 8^16, 32^4 ] E23.788 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = (C16 : C2) : C2 (small group id <64, 41>) Aut = $<128, 922>$ (small group id <128, 922>) |r| :: 2 Presentation :: [ R^2, Y3^2 * Y1^2, Y3^-2 * Y1^2, (Y3, Y1^-1), Y1^4, (R * Y1)^2, (Y2^-1 * Y1^-1)^2, (Y3 * Y2^-1)^2, Y2 * Y3 * Y2 * Y1^-1, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2 * Y3^2 * Y2^-1 * Y3^-1 * Y1, Y2^4 * Y3^-1 * Y2^-4 * Y1^-1, Y2^16 ] Map:: non-degenerate R = (1, 65, 2, 66, 8, 72, 5, 69)(3, 67, 13, 77, 27, 91, 15, 79)(4, 68, 10, 74, 7, 71, 12, 76)(6, 70, 17, 81, 24, 88, 9, 73)(11, 75, 26, 90, 16, 80, 21, 85)(14, 78, 30, 94, 37, 101, 32, 96)(18, 82, 22, 86, 19, 83, 25, 89)(20, 84, 35, 99, 38, 102, 33, 97)(23, 87, 39, 103, 34, 98, 41, 105)(28, 92, 43, 107, 29, 93, 42, 106)(31, 95, 47, 111, 59, 123, 44, 108)(36, 100, 50, 114, 55, 119, 51, 115)(40, 104, 56, 120, 49, 113, 54, 118)(45, 109, 53, 117, 46, 110, 58, 122)(48, 112, 60, 124, 63, 127, 61, 125)(52, 116, 57, 121, 64, 128, 62, 126)(129, 193, 131, 195, 142, 206, 159, 223, 176, 240, 184, 248, 169, 233, 153, 217, 138, 202, 154, 218, 170, 234, 186, 250, 180, 244, 164, 228, 148, 212, 134, 198)(130, 194, 137, 201, 151, 215, 168, 232, 185, 249, 174, 238, 158, 222, 143, 207, 135, 199, 147, 211, 163, 227, 179, 243, 188, 252, 172, 236, 156, 220, 139, 203)(132, 196, 145, 209, 161, 225, 177, 241, 189, 253, 173, 237, 157, 221, 141, 205, 133, 197, 146, 210, 162, 226, 178, 242, 190, 254, 175, 239, 160, 224, 144, 208)(136, 200, 149, 213, 165, 229, 181, 245, 191, 255, 183, 247, 167, 231, 152, 216, 140, 204, 155, 219, 171, 235, 187, 251, 192, 256, 182, 246, 166, 230, 150, 214) L = (1, 132)(2, 138)(3, 139)(4, 136)(5, 140)(6, 147)(7, 129)(8, 135)(9, 150)(10, 133)(11, 155)(12, 130)(13, 154)(14, 157)(15, 149)(16, 131)(17, 153)(18, 134)(19, 152)(20, 162)(21, 141)(22, 145)(23, 148)(24, 146)(25, 137)(26, 143)(27, 144)(28, 142)(29, 165)(30, 170)(31, 174)(32, 171)(33, 167)(34, 166)(35, 169)(36, 168)(37, 156)(38, 151)(39, 163)(40, 183)(41, 161)(42, 160)(43, 158)(44, 181)(45, 159)(46, 187)(47, 186)(48, 190)(49, 164)(50, 184)(51, 182)(52, 189)(53, 175)(54, 178)(55, 177)(56, 179)(57, 176)(58, 172)(59, 173)(60, 180)(61, 192)(62, 191)(63, 185)(64, 188)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4^8 ), ( 4^32 ) } Outer automorphisms :: reflexible Dual of E23.775 Graph:: bipartite v = 20 e = 128 f = 64 degree seq :: [ 8^16, 32^4 ] E23.789 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = C2 x QD32 (small group id <64, 187>) Aut = $<128, 2144>$ (small group id <128, 2144>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^4, Y3 * Y2 * Y3^-1 * Y2, (R * Y1)^2, (R * Y3)^2, (Y1 * Y2)^2, (R * Y2)^2, Y3^-1 * Y1 * Y3^2 * Y1 * Y3^-1, Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 ] Map:: polytopal non-degenerate R = (1, 65, 2, 66)(3, 67, 6, 70)(4, 68, 11, 75)(5, 69, 13, 77)(7, 71, 16, 80)(8, 72, 18, 82)(9, 73, 19, 83)(10, 74, 21, 85)(12, 76, 17, 81)(14, 78, 24, 88)(15, 79, 26, 90)(20, 84, 25, 89)(22, 86, 31, 95)(23, 87, 32, 96)(27, 91, 35, 99)(28, 92, 36, 100)(29, 93, 37, 101)(30, 94, 38, 102)(33, 97, 41, 105)(34, 98, 42, 106)(39, 103, 47, 111)(40, 104, 48, 112)(43, 107, 51, 115)(44, 108, 52, 116)(45, 109, 53, 117)(46, 110, 54, 118)(49, 113, 57, 121)(50, 114, 58, 122)(55, 119, 60, 124)(56, 120, 59, 123)(61, 125, 64, 128)(62, 126, 63, 127)(129, 193, 131, 195)(130, 194, 134, 198)(132, 196, 137, 201)(133, 197, 138, 202)(135, 199, 142, 206)(136, 200, 143, 207)(139, 203, 147, 211)(140, 204, 148, 212)(141, 205, 149, 213)(144, 208, 152, 216)(145, 209, 153, 217)(146, 210, 154, 218)(150, 214, 157, 221)(151, 215, 158, 222)(155, 219, 161, 225)(156, 220, 162, 226)(159, 223, 165, 229)(160, 224, 166, 230)(163, 227, 169, 233)(164, 228, 170, 234)(167, 231, 173, 237)(168, 232, 174, 238)(171, 235, 177, 241)(172, 236, 178, 242)(175, 239, 181, 245)(176, 240, 182, 246)(179, 243, 185, 249)(180, 244, 186, 250)(183, 247, 189, 253)(184, 248, 190, 254)(187, 251, 191, 255)(188, 252, 192, 256) L = (1, 132)(2, 135)(3, 137)(4, 140)(5, 129)(6, 142)(7, 145)(8, 130)(9, 148)(10, 131)(11, 150)(12, 133)(13, 151)(14, 153)(15, 134)(16, 155)(17, 136)(18, 156)(19, 157)(20, 138)(21, 158)(22, 141)(23, 139)(24, 161)(25, 143)(26, 162)(27, 146)(28, 144)(29, 149)(30, 147)(31, 167)(32, 168)(33, 154)(34, 152)(35, 171)(36, 172)(37, 173)(38, 174)(39, 160)(40, 159)(41, 177)(42, 178)(43, 164)(44, 163)(45, 166)(46, 165)(47, 183)(48, 184)(49, 170)(50, 169)(51, 187)(52, 188)(53, 189)(54, 190)(55, 176)(56, 175)(57, 191)(58, 192)(59, 180)(60, 179)(61, 182)(62, 181)(63, 186)(64, 185)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 8, 32, 8, 32 ) } Outer automorphisms :: reflexible Dual of E23.813 Graph:: simple bipartite v = 64 e = 128 f = 20 degree seq :: [ 4^64 ] E23.790 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = (C2 x D16) : C2 (small group id <64, 190>) Aut = $<128, 2147>$ (small group id <128, 2147>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^2, (Y1 * Y2)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3)^2, (Y3 * Y1 * Y3 * Y2)^2, (Y3 * Y2)^4, Y3 * Y1 * Y3 * Y2 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y2 * Y3 * Y1 ] Map:: polytopal non-degenerate R = (1, 65, 2, 66)(3, 67, 5, 69)(4, 68, 8, 72)(6, 70, 11, 75)(7, 71, 13, 77)(9, 73, 15, 79)(10, 74, 18, 82)(12, 76, 20, 84)(14, 78, 23, 87)(16, 80, 27, 91)(17, 81, 22, 86)(19, 83, 28, 92)(21, 85, 32, 96)(24, 88, 34, 98)(25, 89, 30, 94)(26, 90, 35, 99)(29, 93, 38, 102)(31, 95, 39, 103)(33, 97, 41, 105)(36, 100, 44, 108)(37, 101, 45, 109)(40, 104, 48, 112)(42, 106, 50, 114)(43, 107, 51, 115)(46, 110, 54, 118)(47, 111, 55, 119)(49, 113, 57, 121)(52, 116, 60, 124)(53, 117, 61, 125)(56, 120, 64, 128)(58, 122, 63, 127)(59, 123, 62, 126)(129, 193, 131, 195)(130, 194, 133, 197)(132, 196, 137, 201)(134, 198, 140, 204)(135, 199, 142, 206)(136, 200, 143, 207)(138, 202, 147, 211)(139, 203, 148, 212)(141, 205, 151, 215)(144, 208, 152, 216)(145, 209, 153, 217)(146, 210, 156, 220)(149, 213, 157, 221)(150, 214, 158, 222)(154, 218, 161, 225)(155, 219, 162, 226)(159, 223, 165, 229)(160, 224, 166, 230)(163, 227, 169, 233)(164, 228, 171, 235)(167, 231, 173, 237)(168, 232, 175, 239)(170, 234, 177, 241)(172, 236, 179, 243)(174, 238, 181, 245)(176, 240, 183, 247)(178, 242, 185, 249)(180, 244, 186, 250)(182, 246, 189, 253)(184, 248, 190, 254)(187, 251, 192, 256)(188, 252, 191, 255) L = (1, 132)(2, 134)(3, 135)(4, 129)(5, 138)(6, 130)(7, 131)(8, 144)(9, 145)(10, 133)(11, 149)(12, 150)(13, 152)(14, 153)(15, 154)(16, 136)(17, 137)(18, 157)(19, 158)(20, 159)(21, 139)(22, 140)(23, 161)(24, 141)(25, 142)(26, 143)(27, 164)(28, 165)(29, 146)(30, 147)(31, 148)(32, 168)(33, 151)(34, 170)(35, 171)(36, 155)(37, 156)(38, 174)(39, 175)(40, 160)(41, 177)(42, 162)(43, 163)(44, 180)(45, 181)(46, 166)(47, 167)(48, 184)(49, 169)(50, 186)(51, 187)(52, 172)(53, 173)(54, 190)(55, 191)(56, 176)(57, 192)(58, 178)(59, 179)(60, 189)(61, 188)(62, 182)(63, 183)(64, 185)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 8, 32, 8, 32 ) } Outer automorphisms :: reflexible Dual of E23.816 Graph:: simple bipartite v = 64 e = 128 f = 20 degree seq :: [ 4^64 ] E23.791 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = (C16 x C2) : C2 (small group id <64, 189>) Aut = $<128, 2147>$ (small group id <128, 2147>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3)^2, Y1 * Y2 * Y1 * Y3 * Y2 * Y3, (Y1 * Y2)^4, Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y2 * Y3 * Y2 * Y1 ] Map:: polytopal non-degenerate R = (1, 65, 2, 66)(3, 67, 7, 71)(4, 68, 9, 73)(5, 69, 11, 75)(6, 70, 13, 77)(8, 72, 16, 80)(10, 74, 19, 83)(12, 76, 21, 85)(14, 78, 24, 88)(15, 79, 20, 84)(17, 81, 26, 90)(18, 82, 27, 91)(22, 86, 30, 94)(23, 87, 31, 95)(25, 89, 33, 97)(28, 92, 36, 100)(29, 93, 37, 101)(32, 96, 40, 104)(34, 98, 42, 106)(35, 99, 43, 107)(38, 102, 46, 110)(39, 103, 47, 111)(41, 105, 49, 113)(44, 108, 52, 116)(45, 109, 53, 117)(48, 112, 56, 120)(50, 114, 58, 122)(51, 115, 59, 123)(54, 118, 62, 126)(55, 119, 63, 127)(57, 121, 61, 125)(60, 124, 64, 128)(129, 193, 131, 195)(130, 194, 133, 197)(132, 196, 138, 202)(134, 198, 142, 206)(135, 199, 143, 207)(136, 200, 145, 209)(137, 201, 144, 208)(139, 203, 148, 212)(140, 204, 150, 214)(141, 205, 149, 213)(146, 210, 156, 220)(147, 211, 154, 218)(151, 215, 160, 224)(152, 216, 158, 222)(153, 217, 162, 226)(155, 219, 161, 225)(157, 221, 166, 230)(159, 223, 165, 229)(163, 227, 172, 236)(164, 228, 170, 234)(167, 231, 176, 240)(168, 232, 174, 238)(169, 233, 178, 242)(171, 235, 177, 241)(173, 237, 182, 246)(175, 239, 181, 245)(179, 243, 188, 252)(180, 244, 186, 250)(183, 247, 192, 256)(184, 248, 190, 254)(185, 249, 191, 255)(187, 251, 189, 253) L = (1, 132)(2, 134)(3, 136)(4, 129)(5, 140)(6, 130)(7, 142)(8, 131)(9, 146)(10, 139)(11, 138)(12, 133)(13, 151)(14, 135)(15, 150)(16, 153)(17, 148)(18, 137)(19, 156)(20, 145)(21, 157)(22, 143)(23, 141)(24, 160)(25, 144)(26, 162)(27, 163)(28, 147)(29, 149)(30, 166)(31, 167)(32, 152)(33, 169)(34, 154)(35, 155)(36, 172)(37, 173)(38, 158)(39, 159)(40, 176)(41, 161)(42, 178)(43, 179)(44, 164)(45, 165)(46, 182)(47, 183)(48, 168)(49, 185)(50, 170)(51, 171)(52, 188)(53, 189)(54, 174)(55, 175)(56, 192)(57, 177)(58, 191)(59, 190)(60, 180)(61, 181)(62, 187)(63, 186)(64, 184)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 8, 32, 8, 32 ) } Outer automorphisms :: reflexible Dual of E23.814 Graph:: simple bipartite v = 64 e = 128 f = 20 degree seq :: [ 4^64 ] E23.792 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = (C2 x D16) : C2 (small group id <64, 190>) Aut = $<128, 2147>$ (small group id <128, 2147>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3)^2, Y3 * Y1 * Y3 * Y2 * Y1 * Y2, Y2 * R * Y3 * Y1 * Y3 * R * Y2 * Y1, (Y3 * Y2)^4, Y3 * Y1 * Y3 * Y1 * Y2 * Y1 * Y3 * Y1 * Y2 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1, (Y2 * Y1)^16 ] Map:: polytopal non-degenerate R = (1, 65, 2, 66)(3, 67, 7, 71)(4, 68, 9, 73)(5, 69, 11, 75)(6, 70, 13, 77)(8, 72, 12, 76)(10, 74, 14, 78)(15, 79, 25, 89)(16, 80, 26, 90)(17, 81, 27, 91)(18, 82, 29, 93)(19, 83, 30, 94)(20, 84, 31, 95)(21, 85, 32, 96)(22, 86, 33, 97)(23, 87, 35, 99)(24, 88, 36, 100)(28, 92, 34, 98)(37, 101, 47, 111)(38, 102, 48, 112)(39, 103, 49, 113)(40, 104, 50, 114)(41, 105, 51, 115)(42, 106, 52, 116)(43, 107, 53, 117)(44, 108, 54, 118)(45, 109, 55, 119)(46, 110, 56, 120)(57, 121, 64, 128)(58, 122, 63, 127)(59, 123, 62, 126)(60, 124, 61, 125)(129, 193, 131, 195)(130, 194, 133, 197)(132, 196, 138, 202)(134, 198, 142, 206)(135, 199, 143, 207)(136, 200, 145, 209)(137, 201, 146, 210)(139, 203, 148, 212)(140, 204, 150, 214)(141, 205, 151, 215)(144, 208, 155, 219)(147, 211, 156, 220)(149, 213, 161, 225)(152, 216, 162, 226)(153, 217, 165, 229)(154, 218, 167, 231)(157, 221, 166, 230)(158, 222, 168, 232)(159, 223, 170, 234)(160, 224, 172, 236)(163, 227, 171, 235)(164, 228, 173, 237)(169, 233, 178, 242)(174, 238, 183, 247)(175, 239, 185, 249)(176, 240, 187, 251)(177, 241, 186, 250)(179, 243, 188, 252)(180, 244, 189, 253)(181, 245, 191, 255)(182, 246, 190, 254)(184, 248, 192, 256) L = (1, 132)(2, 134)(3, 136)(4, 129)(5, 140)(6, 130)(7, 144)(8, 131)(9, 143)(10, 147)(11, 149)(12, 133)(13, 148)(14, 152)(15, 137)(16, 135)(17, 156)(18, 158)(19, 138)(20, 141)(21, 139)(22, 162)(23, 164)(24, 142)(25, 166)(26, 165)(27, 168)(28, 145)(29, 169)(30, 146)(31, 171)(32, 170)(33, 173)(34, 150)(35, 174)(36, 151)(37, 154)(38, 153)(39, 178)(40, 155)(41, 157)(42, 160)(43, 159)(44, 183)(45, 161)(46, 163)(47, 186)(48, 185)(49, 188)(50, 167)(51, 187)(52, 190)(53, 189)(54, 192)(55, 172)(56, 191)(57, 176)(58, 175)(59, 179)(60, 177)(61, 181)(62, 180)(63, 184)(64, 182)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 8, 32, 8, 32 ) } Outer automorphisms :: reflexible Dual of E23.815 Graph:: simple bipartite v = 64 e = 128 f = 20 degree seq :: [ 4^64 ] E23.793 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = C2 x D32 (small group id <64, 186>) Aut = $<128, 2140>$ (small group id <128, 2140>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^-4, (Y2, Y3^-1), (R * Y3)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, (Y2^-1 * Y1)^2, (R * Y2)^2, Y2^2 * Y3^8 ] Map:: non-degenerate R = (1, 65, 2, 66)(3, 67, 9, 73)(4, 68, 10, 74)(5, 69, 7, 71)(6, 70, 8, 72)(11, 75, 18, 82)(12, 76, 23, 87)(13, 77, 22, 86)(14, 78, 24, 88)(15, 79, 20, 84)(16, 80, 19, 83)(17, 81, 21, 85)(25, 89, 34, 98)(26, 90, 33, 97)(27, 91, 39, 103)(28, 92, 38, 102)(29, 93, 40, 104)(30, 94, 36, 100)(31, 95, 35, 99)(32, 96, 37, 101)(41, 105, 50, 114)(42, 106, 49, 113)(43, 107, 55, 119)(44, 108, 54, 118)(45, 109, 56, 120)(46, 110, 52, 116)(47, 111, 51, 115)(48, 112, 53, 117)(57, 121, 62, 126)(58, 122, 61, 125)(59, 123, 63, 127)(60, 124, 64, 128)(129, 193, 131, 195, 139, 203, 133, 197)(130, 194, 135, 199, 146, 210, 137, 201)(132, 196, 140, 204, 153, 217, 143, 207)(134, 198, 141, 205, 154, 218, 144, 208)(136, 200, 147, 211, 161, 225, 150, 214)(138, 202, 148, 212, 162, 226, 151, 215)(142, 206, 155, 219, 169, 233, 158, 222)(145, 209, 156, 220, 170, 234, 159, 223)(149, 213, 163, 227, 177, 241, 166, 230)(152, 216, 164, 228, 178, 242, 167, 231)(157, 221, 171, 235, 185, 249, 174, 238)(160, 224, 172, 236, 186, 250, 175, 239)(165, 229, 179, 243, 189, 253, 182, 246)(168, 232, 180, 244, 190, 254, 183, 247)(173, 237, 187, 251, 176, 240, 188, 252)(181, 245, 191, 255, 184, 248, 192, 256) L = (1, 132)(2, 136)(3, 140)(4, 142)(5, 143)(6, 129)(7, 147)(8, 149)(9, 150)(10, 130)(11, 153)(12, 155)(13, 131)(14, 157)(15, 158)(16, 133)(17, 134)(18, 161)(19, 163)(20, 135)(21, 165)(22, 166)(23, 137)(24, 138)(25, 169)(26, 139)(27, 171)(28, 141)(29, 173)(30, 174)(31, 144)(32, 145)(33, 177)(34, 146)(35, 179)(36, 148)(37, 181)(38, 182)(39, 151)(40, 152)(41, 185)(42, 154)(43, 187)(44, 156)(45, 186)(46, 188)(47, 159)(48, 160)(49, 189)(50, 162)(51, 191)(52, 164)(53, 190)(54, 192)(55, 167)(56, 168)(57, 176)(58, 170)(59, 175)(60, 172)(61, 184)(62, 178)(63, 183)(64, 180)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32 ) } Outer automorphisms :: reflexible Dual of E23.803 Graph:: simple bipartite v = 48 e = 128 f = 36 degree seq :: [ 4^32, 8^16 ] E23.794 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = (C16 x C2) : C2 (small group id <64, 189>) Aut = $<128, 2143>$ (small group id <128, 2143>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y2^-2 * Y3^-1, (Y3 * Y1)^2, Y3^4, (R * Y3)^2, Y2^-1 * Y3^-2 * Y2^-1, (R * Y1)^2, Y3^-2 * Y2^2, Y1 * Y2^-1 * Y3^-1 * Y1 * Y2 * Y3, Y2^-1 * R * Y3^-2 * R * Y2^-1, Y2^-1 * Y1 * Y3^-2 * Y1 * Y2^-1, (R * Y2 * Y3^-1)^2, Y2 * Y1 * Y2 * Y1 * Y2 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1, Y3^-1 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 65, 2, 66)(3, 67, 11, 75)(4, 68, 10, 74)(5, 69, 17, 81)(6, 70, 8, 72)(7, 71, 18, 82)(9, 73, 24, 88)(12, 76, 19, 83)(13, 77, 22, 86)(14, 78, 23, 87)(15, 79, 20, 84)(16, 80, 21, 85)(25, 89, 33, 97)(26, 90, 36, 100)(27, 91, 34, 98)(28, 92, 35, 99)(29, 93, 37, 101)(30, 94, 40, 104)(31, 95, 38, 102)(32, 96, 39, 103)(41, 105, 49, 113)(42, 106, 52, 116)(43, 107, 50, 114)(44, 108, 51, 115)(45, 109, 53, 117)(46, 110, 56, 120)(47, 111, 54, 118)(48, 112, 55, 119)(57, 121, 62, 126)(58, 122, 61, 125)(59, 123, 63, 127)(60, 124, 64, 128)(129, 193, 131, 195, 140, 204, 133, 197)(130, 194, 135, 199, 147, 211, 137, 201)(132, 196, 143, 207, 134, 198, 144, 208)(136, 200, 150, 214, 138, 202, 151, 215)(139, 203, 153, 217, 145, 209, 154, 218)(141, 205, 155, 219, 142, 206, 156, 220)(146, 210, 157, 221, 152, 216, 158, 222)(148, 212, 159, 223, 149, 213, 160, 224)(161, 225, 169, 233, 164, 228, 170, 234)(162, 226, 171, 235, 163, 227, 172, 236)(165, 229, 173, 237, 168, 232, 174, 238)(166, 230, 175, 239, 167, 231, 176, 240)(177, 241, 185, 249, 180, 244, 186, 250)(178, 242, 187, 251, 179, 243, 188, 252)(181, 245, 189, 253, 184, 248, 190, 254)(182, 246, 191, 255, 183, 247, 192, 256) L = (1, 132)(2, 136)(3, 141)(4, 140)(5, 142)(6, 129)(7, 148)(8, 147)(9, 149)(10, 130)(11, 151)(12, 134)(13, 133)(14, 131)(15, 146)(16, 152)(17, 150)(18, 144)(19, 138)(20, 137)(21, 135)(22, 139)(23, 145)(24, 143)(25, 162)(26, 163)(27, 161)(28, 164)(29, 166)(30, 167)(31, 165)(32, 168)(33, 156)(34, 154)(35, 153)(36, 155)(37, 160)(38, 158)(39, 157)(40, 159)(41, 178)(42, 179)(43, 177)(44, 180)(45, 182)(46, 183)(47, 181)(48, 184)(49, 172)(50, 170)(51, 169)(52, 171)(53, 176)(54, 174)(55, 173)(56, 175)(57, 191)(58, 192)(59, 190)(60, 189)(61, 187)(62, 188)(63, 186)(64, 185)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32 ) } Outer automorphisms :: reflexible Dual of E23.804 Graph:: simple bipartite v = 48 e = 128 f = 36 degree seq :: [ 4^32, 8^16 ] E23.795 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = (C2 x D16) : C2 (small group id <64, 190>) Aut = $<128, 2144>$ (small group id <128, 2144>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^-1 * Y3 * Y2^-1 * Y3^-1, R * Y2 * R * Y2^-1, (Y3^-1 * Y1)^2, (R * Y1)^2, Y2^-1 * Y1 * Y2 * Y1, (R * Y3)^2, Y2^4, (Y3^3 * Y2 * Y3)^2, Y3^16 ] Map:: non-degenerate R = (1, 65, 2, 66)(3, 67, 7, 71)(4, 68, 10, 74)(5, 69, 9, 73)(6, 70, 8, 72)(11, 75, 18, 82)(12, 76, 20, 84)(13, 77, 19, 83)(14, 78, 23, 87)(15, 79, 24, 88)(16, 80, 21, 85)(17, 81, 22, 86)(25, 89, 34, 98)(26, 90, 33, 97)(27, 91, 36, 100)(28, 92, 35, 99)(29, 93, 39, 103)(30, 94, 40, 104)(31, 95, 37, 101)(32, 96, 38, 102)(41, 105, 50, 114)(42, 106, 49, 113)(43, 107, 52, 116)(44, 108, 51, 115)(45, 109, 55, 119)(46, 110, 56, 120)(47, 111, 53, 117)(48, 112, 54, 118)(57, 121, 62, 126)(58, 122, 61, 125)(59, 123, 64, 128)(60, 124, 63, 127)(129, 193, 131, 195, 139, 203, 133, 197)(130, 194, 135, 199, 146, 210, 137, 201)(132, 196, 142, 206, 153, 217, 140, 204)(134, 198, 144, 208, 154, 218, 141, 205)(136, 200, 149, 213, 161, 225, 147, 211)(138, 202, 151, 215, 162, 226, 148, 212)(143, 207, 155, 219, 169, 233, 157, 221)(145, 209, 156, 220, 170, 234, 159, 223)(150, 214, 163, 227, 177, 241, 165, 229)(152, 216, 164, 228, 178, 242, 167, 231)(158, 222, 173, 237, 185, 249, 171, 235)(160, 224, 175, 239, 186, 250, 172, 236)(166, 230, 181, 245, 189, 253, 179, 243)(168, 232, 183, 247, 190, 254, 180, 244)(174, 238, 187, 251, 176, 240, 188, 252)(182, 246, 191, 255, 184, 248, 192, 256) L = (1, 132)(2, 136)(3, 140)(4, 143)(5, 142)(6, 129)(7, 147)(8, 150)(9, 149)(10, 130)(11, 153)(12, 155)(13, 131)(14, 157)(15, 158)(16, 133)(17, 134)(18, 161)(19, 163)(20, 135)(21, 165)(22, 166)(23, 137)(24, 138)(25, 169)(26, 139)(27, 171)(28, 141)(29, 173)(30, 174)(31, 144)(32, 145)(33, 177)(34, 146)(35, 179)(36, 148)(37, 181)(38, 182)(39, 151)(40, 152)(41, 185)(42, 154)(43, 187)(44, 156)(45, 188)(46, 186)(47, 159)(48, 160)(49, 189)(50, 162)(51, 191)(52, 164)(53, 192)(54, 190)(55, 167)(56, 168)(57, 176)(58, 170)(59, 175)(60, 172)(61, 184)(62, 178)(63, 183)(64, 180)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32 ) } Outer automorphisms :: reflexible Dual of E23.809 Graph:: simple bipartite v = 48 e = 128 f = 36 degree seq :: [ 4^32, 8^16 ] E23.796 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = C2 x QD32 (small group id <64, 187>) Aut = $<128, 2144>$ (small group id <128, 2144>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, Y2^4, (R * Y1)^2, (Y3 * Y1)^2, Y2 * Y1 * Y2^-1 * Y1, (R * Y3)^2, Y2^-1 * Y3 * Y2^2 * Y3 * Y2^-1, (R * Y2 * Y3)^2, Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2 ] Map:: non-degenerate R = (1, 65, 2, 66)(3, 67, 6, 70)(4, 68, 7, 71)(5, 69, 8, 72)(9, 73, 14, 78)(10, 74, 15, 79)(11, 75, 16, 80)(12, 76, 17, 81)(13, 77, 18, 82)(19, 83, 24, 88)(20, 84, 25, 89)(21, 85, 26, 90)(22, 86, 27, 91)(23, 87, 28, 92)(29, 93, 33, 97)(30, 94, 34, 98)(31, 95, 35, 99)(32, 96, 36, 100)(37, 101, 41, 105)(38, 102, 42, 106)(39, 103, 43, 107)(40, 104, 44, 108)(45, 109, 49, 113)(46, 110, 50, 114)(47, 111, 51, 115)(48, 112, 52, 116)(53, 117, 57, 121)(54, 118, 58, 122)(55, 119, 59, 123)(56, 120, 60, 124)(61, 125, 63, 127)(62, 126, 64, 128)(129, 193, 131, 195, 137, 201, 133, 197)(130, 194, 134, 198, 142, 206, 136, 200)(132, 196, 139, 203, 147, 211, 140, 204)(135, 199, 144, 208, 152, 216, 145, 209)(138, 202, 148, 212, 141, 205, 149, 213)(143, 207, 153, 217, 146, 210, 154, 218)(150, 214, 159, 223, 151, 215, 160, 224)(155, 219, 163, 227, 156, 220, 164, 228)(157, 221, 165, 229, 158, 222, 166, 230)(161, 225, 169, 233, 162, 226, 170, 234)(167, 231, 175, 239, 168, 232, 176, 240)(171, 235, 179, 243, 172, 236, 180, 244)(173, 237, 181, 245, 174, 238, 182, 246)(177, 241, 185, 249, 178, 242, 186, 250)(183, 247, 190, 254, 184, 248, 189, 253)(187, 251, 192, 256, 188, 252, 191, 255) L = (1, 132)(2, 135)(3, 138)(4, 129)(5, 141)(6, 143)(7, 130)(8, 146)(9, 147)(10, 131)(11, 150)(12, 151)(13, 133)(14, 152)(15, 134)(16, 155)(17, 156)(18, 136)(19, 137)(20, 157)(21, 158)(22, 139)(23, 140)(24, 142)(25, 161)(26, 162)(27, 144)(28, 145)(29, 148)(30, 149)(31, 167)(32, 168)(33, 153)(34, 154)(35, 171)(36, 172)(37, 173)(38, 174)(39, 159)(40, 160)(41, 177)(42, 178)(43, 163)(44, 164)(45, 165)(46, 166)(47, 183)(48, 184)(49, 169)(50, 170)(51, 187)(52, 188)(53, 189)(54, 190)(55, 175)(56, 176)(57, 191)(58, 192)(59, 179)(60, 180)(61, 181)(62, 182)(63, 185)(64, 186)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32 ) } Outer automorphisms :: reflexible Dual of E23.808 Graph:: simple bipartite v = 48 e = 128 f = 36 degree seq :: [ 4^32, 8^16 ] E23.797 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = (C2 x D16) : C2 (small group id <64, 190>) Aut = $<128, 2144>$ (small group id <128, 2144>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, Y2^4, (R * Y1)^2, (Y3 * Y1)^2, (Y2^-1 * Y1)^2, (R * Y3)^2, (R * Y2 * Y3)^2, Y2^-1 * Y3 * Y2^2 * Y3 * Y2^-1, Y2 * Y3 * Y2^2 * Y1 * Y3 * Y2^-1 * Y1, Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2 ] Map:: non-degenerate R = (1, 65, 2, 66)(3, 67, 8, 72)(4, 68, 7, 71)(5, 69, 6, 70)(9, 73, 14, 78)(10, 74, 18, 82)(11, 75, 17, 81)(12, 76, 16, 80)(13, 77, 15, 79)(19, 83, 24, 88)(20, 84, 25, 89)(21, 85, 26, 90)(22, 86, 28, 92)(23, 87, 27, 91)(29, 93, 33, 97)(30, 94, 34, 98)(31, 95, 35, 99)(32, 96, 36, 100)(37, 101, 42, 106)(38, 102, 41, 105)(39, 103, 43, 107)(40, 104, 44, 108)(45, 109, 50, 114)(46, 110, 49, 113)(47, 111, 52, 116)(48, 112, 51, 115)(53, 117, 57, 121)(54, 118, 58, 122)(55, 119, 60, 124)(56, 120, 59, 123)(61, 125, 63, 127)(62, 126, 64, 128)(129, 193, 131, 195, 137, 201, 133, 197)(130, 194, 134, 198, 142, 206, 136, 200)(132, 196, 139, 203, 147, 211, 140, 204)(135, 199, 144, 208, 152, 216, 145, 209)(138, 202, 148, 212, 141, 205, 149, 213)(143, 207, 153, 217, 146, 210, 154, 218)(150, 214, 159, 223, 151, 215, 160, 224)(155, 219, 163, 227, 156, 220, 164, 228)(157, 221, 165, 229, 158, 222, 166, 230)(161, 225, 169, 233, 162, 226, 170, 234)(167, 231, 175, 239, 168, 232, 176, 240)(171, 235, 179, 243, 172, 236, 180, 244)(173, 237, 181, 245, 174, 238, 182, 246)(177, 241, 185, 249, 178, 242, 186, 250)(183, 247, 190, 254, 184, 248, 189, 253)(187, 251, 192, 256, 188, 252, 191, 255) L = (1, 132)(2, 135)(3, 138)(4, 129)(5, 141)(6, 143)(7, 130)(8, 146)(9, 147)(10, 131)(11, 150)(12, 151)(13, 133)(14, 152)(15, 134)(16, 155)(17, 156)(18, 136)(19, 137)(20, 157)(21, 158)(22, 139)(23, 140)(24, 142)(25, 161)(26, 162)(27, 144)(28, 145)(29, 148)(30, 149)(31, 167)(32, 168)(33, 153)(34, 154)(35, 171)(36, 172)(37, 173)(38, 174)(39, 159)(40, 160)(41, 177)(42, 178)(43, 163)(44, 164)(45, 165)(46, 166)(47, 183)(48, 184)(49, 169)(50, 170)(51, 187)(52, 188)(53, 189)(54, 190)(55, 175)(56, 176)(57, 191)(58, 192)(59, 179)(60, 180)(61, 181)(62, 182)(63, 185)(64, 186)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32 ) } Outer automorphisms :: reflexible Dual of E23.807 Graph:: simple bipartite v = 48 e = 128 f = 36 degree seq :: [ 4^32, 8^16 ] E23.798 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = C2 x QD32 (small group id <64, 187>) Aut = $<128, 2144>$ (small group id <128, 2144>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, (Y3 * Y1)^2, Y2^4, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3)^2, (Y2^-1 * Y3 * Y2^-1)^2, Y2 * Y3 * Y1 * Y2^-1 * Y3 * Y1, (Y2^-1 * R * Y2^-1)^2, (Y2^-1 * Y1 * Y2^-1)^2, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y3 * Y2 * Y3 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1, (Y3 * Y2)^16 ] Map:: non-degenerate R = (1, 65, 2, 66)(3, 67, 9, 73)(4, 68, 7, 71)(5, 69, 14, 78)(6, 70, 16, 80)(8, 72, 21, 85)(10, 74, 17, 81)(11, 75, 19, 83)(12, 76, 18, 82)(13, 77, 22, 86)(15, 79, 20, 84)(23, 87, 33, 97)(24, 88, 35, 99)(25, 89, 30, 94)(26, 90, 34, 98)(27, 91, 36, 100)(28, 92, 37, 101)(29, 93, 39, 103)(31, 95, 38, 102)(32, 96, 40, 104)(41, 105, 49, 113)(42, 106, 51, 115)(43, 107, 50, 114)(44, 108, 52, 116)(45, 109, 53, 117)(46, 110, 55, 119)(47, 111, 54, 118)(48, 112, 56, 120)(57, 121, 62, 126)(58, 122, 61, 125)(59, 123, 64, 128)(60, 124, 63, 127)(129, 193, 131, 195, 138, 202, 133, 197)(130, 194, 134, 198, 145, 209, 136, 200)(132, 196, 140, 204, 153, 217, 141, 205)(135, 199, 147, 211, 158, 222, 148, 212)(137, 201, 151, 215, 142, 206, 152, 216)(139, 203, 154, 218, 143, 207, 155, 219)(144, 208, 156, 220, 149, 213, 157, 221)(146, 210, 159, 223, 150, 214, 160, 224)(161, 225, 169, 233, 163, 227, 170, 234)(162, 226, 171, 235, 164, 228, 172, 236)(165, 229, 173, 237, 167, 231, 174, 238)(166, 230, 175, 239, 168, 232, 176, 240)(177, 241, 185, 249, 179, 243, 186, 250)(178, 242, 187, 251, 180, 244, 188, 252)(181, 245, 189, 253, 183, 247, 190, 254)(182, 246, 191, 255, 184, 248, 192, 256) L = (1, 132)(2, 135)(3, 139)(4, 129)(5, 143)(6, 146)(7, 130)(8, 150)(9, 147)(10, 153)(11, 131)(12, 144)(13, 149)(14, 148)(15, 133)(16, 140)(17, 158)(18, 134)(19, 137)(20, 142)(21, 141)(22, 136)(23, 162)(24, 164)(25, 138)(26, 161)(27, 163)(28, 166)(29, 168)(30, 145)(31, 165)(32, 167)(33, 154)(34, 151)(35, 155)(36, 152)(37, 159)(38, 156)(39, 160)(40, 157)(41, 178)(42, 180)(43, 177)(44, 179)(45, 182)(46, 184)(47, 181)(48, 183)(49, 171)(50, 169)(51, 172)(52, 170)(53, 175)(54, 173)(55, 176)(56, 174)(57, 192)(58, 191)(59, 190)(60, 189)(61, 188)(62, 187)(63, 186)(64, 185)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32 ) } Outer automorphisms :: reflexible Dual of E23.805 Graph:: simple bipartite v = 48 e = 128 f = 36 degree seq :: [ 4^32, 8^16 ] E23.799 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = (C2 x D16) : C2 (small group id <64, 190>) Aut = $<128, 2144>$ (small group id <128, 2144>) |r| :: 2 Presentation :: [ Y1^2, Y3^2, R^2, (Y1 * Y3)^2, (R * Y1)^2, Y2^4, (R * Y3)^2, Y3 * Y2^-1 * Y3 * Y1 * Y2^-1 * Y1, (R * Y2 * Y3)^2, (Y2^-1 * Y1 * Y2^-1)^2, (Y2^-1 * Y3 * Y2^-1)^2, (Y2^-1 * R * Y2^-1)^2, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1, (Y1 * Y2 * Y1 * Y2^-1)^8 ] Map:: non-degenerate R = (1, 65, 2, 66)(3, 67, 9, 73)(4, 68, 7, 71)(5, 69, 14, 78)(6, 70, 16, 80)(8, 72, 21, 85)(10, 74, 17, 81)(11, 75, 20, 84)(12, 76, 22, 86)(13, 77, 18, 82)(15, 79, 19, 83)(23, 87, 33, 97)(24, 88, 35, 99)(25, 89, 30, 94)(26, 90, 36, 100)(27, 91, 34, 98)(28, 92, 37, 101)(29, 93, 39, 103)(31, 95, 40, 104)(32, 96, 38, 102)(41, 105, 49, 113)(42, 106, 51, 115)(43, 107, 52, 116)(44, 108, 50, 114)(45, 109, 53, 117)(46, 110, 55, 119)(47, 111, 56, 120)(48, 112, 54, 118)(57, 121, 62, 126)(58, 122, 61, 125)(59, 123, 64, 128)(60, 124, 63, 127)(129, 193, 131, 195, 138, 202, 133, 197)(130, 194, 134, 198, 145, 209, 136, 200)(132, 196, 140, 204, 153, 217, 141, 205)(135, 199, 147, 211, 158, 222, 148, 212)(137, 201, 151, 215, 142, 206, 152, 216)(139, 203, 154, 218, 143, 207, 155, 219)(144, 208, 156, 220, 149, 213, 157, 221)(146, 210, 159, 223, 150, 214, 160, 224)(161, 225, 169, 233, 163, 227, 170, 234)(162, 226, 171, 235, 164, 228, 172, 236)(165, 229, 173, 237, 167, 231, 174, 238)(166, 230, 175, 239, 168, 232, 176, 240)(177, 241, 185, 249, 179, 243, 186, 250)(178, 242, 187, 251, 180, 244, 188, 252)(181, 245, 189, 253, 183, 247, 190, 254)(182, 246, 191, 255, 184, 248, 192, 256) L = (1, 132)(2, 135)(3, 139)(4, 129)(5, 143)(6, 146)(7, 130)(8, 150)(9, 148)(10, 153)(11, 131)(12, 149)(13, 144)(14, 147)(15, 133)(16, 141)(17, 158)(18, 134)(19, 142)(20, 137)(21, 140)(22, 136)(23, 162)(24, 164)(25, 138)(26, 163)(27, 161)(28, 166)(29, 168)(30, 145)(31, 167)(32, 165)(33, 155)(34, 151)(35, 154)(36, 152)(37, 160)(38, 156)(39, 159)(40, 157)(41, 178)(42, 180)(43, 179)(44, 177)(45, 182)(46, 184)(47, 183)(48, 181)(49, 172)(50, 169)(51, 171)(52, 170)(53, 176)(54, 173)(55, 175)(56, 174)(57, 191)(58, 192)(59, 189)(60, 190)(61, 187)(62, 188)(63, 185)(64, 186)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32 ) } Outer automorphisms :: reflexible Dual of E23.806 Graph:: simple bipartite v = 48 e = 128 f = 36 degree seq :: [ 4^32, 8^16 ] E23.800 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = (C16 x C2) : C2 (small group id <64, 189>) Aut = $<128, 2147>$ (small group id <128, 2147>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^4, (Y2, Y3^-1), (R * Y3)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, Y2^-1 * Y1 * Y2 * Y1, (R * Y2)^2, Y2^2 * Y3^-8 ] Map:: non-degenerate R = (1, 65, 2, 66)(3, 67, 7, 71)(4, 68, 10, 74)(5, 69, 9, 73)(6, 70, 8, 72)(11, 75, 18, 82)(12, 76, 20, 84)(13, 77, 19, 83)(14, 78, 24, 88)(15, 79, 23, 87)(16, 80, 22, 86)(17, 81, 21, 85)(25, 89, 34, 98)(26, 90, 33, 97)(27, 91, 36, 100)(28, 92, 35, 99)(29, 93, 40, 104)(30, 94, 39, 103)(31, 95, 38, 102)(32, 96, 37, 101)(41, 105, 50, 114)(42, 106, 49, 113)(43, 107, 52, 116)(44, 108, 51, 115)(45, 109, 56, 120)(46, 110, 55, 119)(47, 111, 54, 118)(48, 112, 53, 117)(57, 121, 62, 126)(58, 122, 61, 125)(59, 123, 64, 128)(60, 124, 63, 127)(129, 193, 131, 195, 139, 203, 133, 197)(130, 194, 135, 199, 146, 210, 137, 201)(132, 196, 140, 204, 153, 217, 143, 207)(134, 198, 141, 205, 154, 218, 144, 208)(136, 200, 147, 211, 161, 225, 150, 214)(138, 202, 148, 212, 162, 226, 151, 215)(142, 206, 155, 219, 169, 233, 158, 222)(145, 209, 156, 220, 170, 234, 159, 223)(149, 213, 163, 227, 177, 241, 166, 230)(152, 216, 164, 228, 178, 242, 167, 231)(157, 221, 171, 235, 185, 249, 174, 238)(160, 224, 172, 236, 186, 250, 175, 239)(165, 229, 179, 243, 189, 253, 182, 246)(168, 232, 180, 244, 190, 254, 183, 247)(173, 237, 187, 251, 176, 240, 188, 252)(181, 245, 191, 255, 184, 248, 192, 256) L = (1, 132)(2, 136)(3, 140)(4, 142)(5, 143)(6, 129)(7, 147)(8, 149)(9, 150)(10, 130)(11, 153)(12, 155)(13, 131)(14, 157)(15, 158)(16, 133)(17, 134)(18, 161)(19, 163)(20, 135)(21, 165)(22, 166)(23, 137)(24, 138)(25, 169)(26, 139)(27, 171)(28, 141)(29, 173)(30, 174)(31, 144)(32, 145)(33, 177)(34, 146)(35, 179)(36, 148)(37, 181)(38, 182)(39, 151)(40, 152)(41, 185)(42, 154)(43, 187)(44, 156)(45, 186)(46, 188)(47, 159)(48, 160)(49, 189)(50, 162)(51, 191)(52, 164)(53, 190)(54, 192)(55, 167)(56, 168)(57, 176)(58, 170)(59, 175)(60, 172)(61, 184)(62, 178)(63, 183)(64, 180)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32 ) } Outer automorphisms :: reflexible Dual of E23.811 Graph:: simple bipartite v = 48 e = 128 f = 36 degree seq :: [ 4^32, 8^16 ] E23.801 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = (C2 x D16) : C2 (small group id <64, 190>) Aut = $<128, 2147>$ (small group id <128, 2147>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^-1 * Y3 * Y2^-1 * Y3^-1, R * Y2 * R * Y2^-1, (Y3^-1 * Y1)^2, (R * Y1)^2, (Y2^-1 * Y1)^2, (R * Y3)^2, Y2^4, (Y3^3 * Y2 * Y3)^2, Y3^16 ] Map:: non-degenerate R = (1, 65, 2, 66)(3, 67, 9, 73)(4, 68, 10, 74)(5, 69, 7, 71)(6, 70, 8, 72)(11, 75, 18, 82)(12, 76, 23, 87)(13, 77, 21, 85)(14, 78, 20, 84)(15, 79, 24, 88)(16, 80, 19, 83)(17, 81, 22, 86)(25, 89, 34, 98)(26, 90, 33, 97)(27, 91, 39, 103)(28, 92, 37, 101)(29, 93, 36, 100)(30, 94, 40, 104)(31, 95, 35, 99)(32, 96, 38, 102)(41, 105, 50, 114)(42, 106, 49, 113)(43, 107, 55, 119)(44, 108, 53, 117)(45, 109, 52, 116)(46, 110, 56, 120)(47, 111, 51, 115)(48, 112, 54, 118)(57, 121, 62, 126)(58, 122, 61, 125)(59, 123, 63, 127)(60, 124, 64, 128)(129, 193, 131, 195, 139, 203, 133, 197)(130, 194, 135, 199, 146, 210, 137, 201)(132, 196, 142, 206, 153, 217, 140, 204)(134, 198, 144, 208, 154, 218, 141, 205)(136, 200, 149, 213, 161, 225, 147, 211)(138, 202, 151, 215, 162, 226, 148, 212)(143, 207, 155, 219, 169, 233, 157, 221)(145, 209, 156, 220, 170, 234, 159, 223)(150, 214, 163, 227, 177, 241, 165, 229)(152, 216, 164, 228, 178, 242, 167, 231)(158, 222, 173, 237, 185, 249, 171, 235)(160, 224, 175, 239, 186, 250, 172, 236)(166, 230, 181, 245, 189, 253, 179, 243)(168, 232, 183, 247, 190, 254, 180, 244)(174, 238, 187, 251, 176, 240, 188, 252)(182, 246, 191, 255, 184, 248, 192, 256) L = (1, 132)(2, 136)(3, 140)(4, 143)(5, 142)(6, 129)(7, 147)(8, 150)(9, 149)(10, 130)(11, 153)(12, 155)(13, 131)(14, 157)(15, 158)(16, 133)(17, 134)(18, 161)(19, 163)(20, 135)(21, 165)(22, 166)(23, 137)(24, 138)(25, 169)(26, 139)(27, 171)(28, 141)(29, 173)(30, 174)(31, 144)(32, 145)(33, 177)(34, 146)(35, 179)(36, 148)(37, 181)(38, 182)(39, 151)(40, 152)(41, 185)(42, 154)(43, 187)(44, 156)(45, 188)(46, 186)(47, 159)(48, 160)(49, 189)(50, 162)(51, 191)(52, 164)(53, 192)(54, 190)(55, 167)(56, 168)(57, 176)(58, 170)(59, 175)(60, 172)(61, 184)(62, 178)(63, 183)(64, 180)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32 ) } Outer automorphisms :: reflexible Dual of E23.812 Graph:: simple bipartite v = 48 e = 128 f = 36 degree seq :: [ 4^32, 8^16 ] E23.802 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = (C16 x C2) : C2 (small group id <64, 189>) Aut = $<128, 2147>$ (small group id <128, 2147>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^2 * Y3^-2, (Y3^-1 * Y1)^2, (Y2 * Y1)^2, (R * Y3)^2, Y3^4, (R * Y1)^2, Y3 * Y2^2 * Y3, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1, (Y3 * Y2^-1)^16 ] Map:: non-degenerate R = (1, 65, 2, 66)(3, 67, 9, 73)(4, 68, 10, 74)(5, 69, 7, 71)(6, 70, 8, 72)(11, 75, 16, 80)(12, 76, 17, 81)(13, 77, 18, 82)(14, 78, 19, 83)(15, 79, 20, 84)(21, 85, 26, 90)(22, 86, 25, 89)(23, 87, 28, 92)(24, 88, 27, 91)(29, 93, 33, 97)(30, 94, 34, 98)(31, 95, 35, 99)(32, 96, 36, 100)(37, 101, 42, 106)(38, 102, 41, 105)(39, 103, 44, 108)(40, 104, 43, 107)(45, 109, 49, 113)(46, 110, 50, 114)(47, 111, 51, 115)(48, 112, 52, 116)(53, 117, 58, 122)(54, 118, 57, 121)(55, 119, 60, 124)(56, 120, 59, 123)(61, 125, 63, 127)(62, 126, 64, 128)(129, 193, 131, 195, 139, 203, 133, 197)(130, 194, 135, 199, 144, 208, 137, 201)(132, 196, 142, 206, 134, 198, 143, 207)(136, 200, 147, 211, 138, 202, 148, 212)(140, 204, 149, 213, 141, 205, 150, 214)(145, 209, 153, 217, 146, 210, 154, 218)(151, 215, 159, 223, 152, 216, 160, 224)(155, 219, 163, 227, 156, 220, 164, 228)(157, 221, 165, 229, 158, 222, 166, 230)(161, 225, 169, 233, 162, 226, 170, 234)(167, 231, 175, 239, 168, 232, 176, 240)(171, 235, 179, 243, 172, 236, 180, 244)(173, 237, 181, 245, 174, 238, 182, 246)(177, 241, 185, 249, 178, 242, 186, 250)(183, 247, 190, 254, 184, 248, 189, 253)(187, 251, 192, 256, 188, 252, 191, 255) L = (1, 132)(2, 136)(3, 140)(4, 139)(5, 141)(6, 129)(7, 145)(8, 144)(9, 146)(10, 130)(11, 134)(12, 133)(13, 131)(14, 151)(15, 152)(16, 138)(17, 137)(18, 135)(19, 155)(20, 156)(21, 157)(22, 158)(23, 143)(24, 142)(25, 161)(26, 162)(27, 148)(28, 147)(29, 150)(30, 149)(31, 167)(32, 168)(33, 154)(34, 153)(35, 171)(36, 172)(37, 173)(38, 174)(39, 160)(40, 159)(41, 177)(42, 178)(43, 164)(44, 163)(45, 166)(46, 165)(47, 183)(48, 184)(49, 170)(50, 169)(51, 187)(52, 188)(53, 189)(54, 190)(55, 176)(56, 175)(57, 191)(58, 192)(59, 180)(60, 179)(61, 182)(62, 181)(63, 186)(64, 185)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32 ) } Outer automorphisms :: reflexible Dual of E23.810 Graph:: simple bipartite v = 48 e = 128 f = 36 degree seq :: [ 4^32, 8^16 ] E23.803 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = C2 x D32 (small group id <64, 186>) Aut = $<128, 2140>$ (small group id <128, 2140>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3^-1, Y1), (Y3 * Y2)^2, (R * Y3)^2, (Y2 * Y1^-1)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3 * Y1^-2 * Y3 * Y1^-3, Y3 * Y1^4 * Y3^3, (Y1^-1 * Y3^-1)^4 ] Map:: non-degenerate R = (1, 65, 2, 66, 7, 71, 19, 83, 39, 103, 33, 97, 14, 78, 25, 89, 45, 109, 37, 101, 18, 82, 26, 90, 46, 110, 35, 99, 16, 80, 5, 69)(3, 67, 11, 75, 27, 91, 51, 115, 61, 125, 47, 111, 30, 94, 54, 118, 62, 126, 48, 112, 31, 95, 55, 119, 58, 122, 40, 104, 20, 84, 8, 72)(4, 68, 9, 73, 21, 85, 41, 105, 38, 102, 50, 114, 32, 96, 49, 113, 36, 100, 17, 81, 6, 70, 10, 74, 22, 86, 42, 106, 34, 98, 15, 79)(12, 76, 28, 92, 52, 116, 64, 128, 57, 121, 63, 127, 56, 120, 60, 124, 44, 108, 24, 88, 13, 77, 29, 93, 53, 117, 59, 123, 43, 107, 23, 87)(129, 193, 131, 195)(130, 194, 136, 200)(132, 196, 141, 205)(133, 197, 139, 203)(134, 198, 140, 204)(135, 199, 148, 212)(137, 201, 152, 216)(138, 202, 151, 215)(142, 206, 159, 223)(143, 207, 157, 221)(144, 208, 155, 219)(145, 209, 156, 220)(146, 210, 158, 222)(147, 211, 168, 232)(149, 213, 172, 236)(150, 214, 171, 235)(153, 217, 176, 240)(154, 218, 175, 239)(160, 224, 185, 249)(161, 225, 183, 247)(162, 226, 181, 245)(163, 227, 179, 243)(164, 228, 180, 244)(165, 229, 182, 246)(166, 230, 184, 248)(167, 231, 186, 250)(169, 233, 188, 252)(170, 234, 187, 251)(173, 237, 190, 254)(174, 238, 189, 253)(177, 241, 192, 256)(178, 242, 191, 255) L = (1, 132)(2, 137)(3, 140)(4, 142)(5, 143)(6, 129)(7, 149)(8, 151)(9, 153)(10, 130)(11, 156)(12, 158)(13, 131)(14, 160)(15, 161)(16, 162)(17, 133)(18, 134)(19, 169)(20, 171)(21, 173)(22, 135)(23, 175)(24, 136)(25, 177)(26, 138)(27, 180)(28, 182)(29, 139)(30, 184)(31, 141)(32, 174)(33, 178)(34, 167)(35, 170)(36, 144)(37, 145)(38, 146)(39, 166)(40, 187)(41, 165)(42, 147)(43, 189)(44, 148)(45, 164)(46, 150)(47, 191)(48, 152)(49, 163)(50, 154)(51, 192)(52, 190)(53, 155)(54, 188)(55, 157)(56, 186)(57, 159)(58, 181)(59, 179)(60, 168)(61, 185)(62, 172)(63, 183)(64, 176)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 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 E23.793 Graph:: simple bipartite v = 36 e = 128 f = 48 degree seq :: [ 4^32, 32^4 ] E23.804 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = (C16 x C2) : C2 (small group id <64, 189>) Aut = $<128, 2143>$ (small group id <128, 2143>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3 * Y2)^2, Y1^-1 * Y3 * Y1^-1 * Y3^-1, (R * Y1)^2, Y2 * Y1 * Y2 * Y1^-1, (R * Y3)^2, Y3^4, Y1^-1 * Y3^2 * Y1 * Y3^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3 * Y1^2 * Y3 * Y1^-5, Y3^-1 * Y2 * Y1^4 * Y3 * Y2 * Y1^-4 ] Map:: non-degenerate R = (1, 65, 2, 66, 7, 71, 18, 82, 33, 97, 49, 113, 46, 110, 30, 94, 15, 79, 24, 88, 39, 103, 55, 119, 47, 111, 31, 95, 16, 80, 5, 69)(3, 67, 8, 72, 19, 83, 34, 98, 50, 114, 61, 125, 58, 122, 42, 106, 26, 90, 40, 104, 56, 120, 64, 128, 59, 123, 43, 107, 27, 91, 12, 76)(4, 68, 14, 78, 29, 93, 45, 109, 52, 116, 36, 100, 21, 85, 10, 74, 6, 70, 17, 81, 32, 96, 48, 112, 51, 115, 35, 99, 20, 84, 9, 73)(11, 75, 25, 89, 41, 105, 57, 121, 63, 127, 54, 118, 38, 102, 23, 87, 13, 77, 28, 92, 44, 108, 60, 124, 62, 126, 53, 117, 37, 101, 22, 86)(129, 193, 131, 195)(130, 194, 136, 200)(132, 196, 141, 205)(133, 197, 140, 204)(134, 198, 139, 203)(135, 199, 147, 211)(137, 201, 151, 215)(138, 202, 150, 214)(142, 206, 156, 220)(143, 207, 154, 218)(144, 208, 155, 219)(145, 209, 153, 217)(146, 210, 162, 226)(148, 212, 166, 230)(149, 213, 165, 229)(152, 216, 168, 232)(157, 221, 172, 236)(158, 222, 170, 234)(159, 223, 171, 235)(160, 224, 169, 233)(161, 225, 178, 242)(163, 227, 182, 246)(164, 228, 181, 245)(167, 231, 184, 248)(173, 237, 188, 252)(174, 238, 186, 250)(175, 239, 187, 251)(176, 240, 185, 249)(177, 241, 189, 253)(179, 243, 191, 255)(180, 244, 190, 254)(183, 247, 192, 256) L = (1, 132)(2, 137)(3, 139)(4, 143)(5, 142)(6, 129)(7, 148)(8, 150)(9, 152)(10, 130)(11, 154)(12, 153)(13, 131)(14, 158)(15, 134)(16, 157)(17, 133)(18, 163)(19, 165)(20, 167)(21, 135)(22, 168)(23, 136)(24, 138)(25, 170)(26, 141)(27, 169)(28, 140)(29, 174)(30, 145)(31, 173)(32, 144)(33, 179)(34, 181)(35, 183)(36, 146)(37, 184)(38, 147)(39, 149)(40, 151)(41, 186)(42, 156)(43, 185)(44, 155)(45, 177)(46, 160)(47, 180)(48, 159)(49, 176)(50, 190)(51, 175)(52, 161)(53, 192)(54, 162)(55, 164)(56, 166)(57, 189)(58, 172)(59, 191)(60, 171)(61, 188)(62, 187)(63, 178)(64, 182)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 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 E23.794 Graph:: simple bipartite v = 36 e = 128 f = 48 degree seq :: [ 4^32, 32^4 ] E23.805 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = C2 x QD32 (small group id <64, 187>) Aut = $<128, 2144>$ (small group id <128, 2144>) |r| :: 2 Presentation :: [ Y3^2, Y2^2, R^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y2 * Y1 * Y2 * Y1^-1, (Y1^-2 * Y3)^2, (Y3 * Y1)^4, Y3 * Y1^-1 * Y3 * Y1^7, Y1^-2 * Y3 * Y1^3 * Y3 * Y1^-3 ] Map:: non-degenerate R = (1, 65, 2, 66, 6, 70, 15, 79, 30, 94, 48, 112, 45, 109, 26, 90, 37, 101, 27, 91, 38, 102, 54, 118, 47, 111, 29, 93, 14, 78, 5, 69)(3, 67, 7, 71, 16, 80, 31, 95, 49, 113, 61, 125, 58, 122, 40, 104, 55, 119, 41, 105, 56, 120, 64, 128, 60, 124, 43, 107, 24, 88, 10, 74)(4, 68, 11, 75, 25, 89, 44, 108, 52, 116, 32, 96, 20, 84, 8, 72, 19, 83, 13, 77, 28, 92, 46, 110, 50, 114, 34, 98, 17, 81, 12, 76)(9, 73, 21, 85, 39, 103, 57, 121, 63, 127, 51, 115, 36, 100, 18, 82, 35, 99, 23, 87, 42, 106, 59, 123, 62, 126, 53, 117, 33, 97, 22, 86)(129, 193, 131, 195)(130, 194, 135, 199)(132, 196, 137, 201)(133, 197, 138, 202)(134, 198, 144, 208)(136, 200, 146, 210)(139, 203, 149, 213)(140, 204, 150, 214)(141, 205, 151, 215)(142, 206, 152, 216)(143, 207, 159, 223)(145, 209, 161, 225)(147, 211, 163, 227)(148, 212, 164, 228)(153, 217, 167, 231)(154, 218, 168, 232)(155, 219, 169, 233)(156, 220, 170, 234)(157, 221, 171, 235)(158, 222, 177, 241)(160, 224, 179, 243)(162, 226, 181, 245)(165, 229, 183, 247)(166, 230, 184, 248)(172, 236, 185, 249)(173, 237, 186, 250)(174, 238, 187, 251)(175, 239, 188, 252)(176, 240, 189, 253)(178, 242, 190, 254)(180, 244, 191, 255)(182, 246, 192, 256) L = (1, 132)(2, 136)(3, 137)(4, 129)(5, 141)(6, 145)(7, 146)(8, 130)(9, 131)(10, 151)(11, 154)(12, 155)(13, 133)(14, 153)(15, 160)(16, 161)(17, 134)(18, 135)(19, 165)(20, 166)(21, 168)(22, 169)(23, 138)(24, 167)(25, 142)(26, 139)(27, 140)(28, 173)(29, 174)(30, 178)(31, 179)(32, 143)(33, 144)(34, 182)(35, 183)(36, 184)(37, 147)(38, 148)(39, 152)(40, 149)(41, 150)(42, 186)(43, 187)(44, 176)(45, 156)(46, 157)(47, 180)(48, 172)(49, 190)(50, 158)(51, 159)(52, 175)(53, 192)(54, 162)(55, 163)(56, 164)(57, 189)(58, 170)(59, 171)(60, 191)(61, 185)(62, 177)(63, 188)(64, 181)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 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 E23.798 Graph:: simple bipartite v = 36 e = 128 f = 48 degree seq :: [ 4^32, 32^4 ] E23.806 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = (C2 x D16) : C2 (small group id <64, 190>) Aut = $<128, 2144>$ (small group id <128, 2144>) |r| :: 2 Presentation :: [ Y3^2, Y2^2, R^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2 * Y1^-1)^2, Y2 * Y1^-2 * Y2 * Y1^2, (Y1^-2 * Y3)^2, (Y1^2 * Y3 * Y2)^2, (Y3 * Y1)^4, (Y1 * Y2 * Y1^-1 * Y2)^2, Y1^-2 * Y2 * Y1^-5 * Y2 * Y1^-1 ] Map:: non-degenerate R = (1, 65, 2, 66, 6, 70, 17, 81, 35, 99, 53, 117, 46, 110, 28, 92, 43, 107, 25, 89, 41, 105, 59, 123, 52, 116, 34, 98, 16, 80, 5, 69)(3, 67, 9, 73, 18, 82, 38, 102, 54, 118, 50, 114, 32, 96, 14, 78, 22, 86, 7, 71, 20, 84, 36, 100, 56, 120, 48, 112, 30, 94, 11, 75)(4, 68, 12, 76, 31, 95, 49, 113, 58, 122, 37, 101, 24, 88, 8, 72, 23, 87, 15, 79, 33, 97, 51, 115, 55, 119, 40, 104, 19, 83, 13, 77)(10, 74, 27, 91, 45, 109, 61, 125, 64, 128, 60, 124, 42, 106, 26, 90, 44, 108, 29, 93, 47, 111, 62, 126, 63, 127, 57, 121, 39, 103, 21, 85)(129, 193, 131, 195)(130, 194, 135, 199)(132, 196, 138, 202)(133, 197, 142, 206)(134, 198, 146, 210)(136, 200, 149, 213)(137, 201, 153, 217)(139, 203, 156, 220)(140, 204, 157, 221)(141, 205, 154, 218)(143, 207, 155, 219)(144, 208, 158, 222)(145, 209, 164, 228)(147, 211, 167, 231)(148, 212, 169, 233)(150, 214, 171, 235)(151, 215, 172, 236)(152, 216, 170, 234)(159, 223, 173, 237)(160, 224, 174, 238)(161, 225, 175, 239)(162, 226, 178, 242)(163, 227, 182, 246)(165, 229, 185, 249)(166, 230, 187, 251)(168, 232, 188, 252)(176, 240, 181, 245)(177, 241, 190, 254)(179, 243, 189, 253)(180, 244, 184, 248)(183, 247, 191, 255)(186, 250, 192, 256) L = (1, 132)(2, 136)(3, 138)(4, 129)(5, 143)(6, 147)(7, 149)(8, 130)(9, 154)(10, 131)(11, 157)(12, 156)(13, 153)(14, 155)(15, 133)(16, 159)(17, 165)(18, 167)(19, 134)(20, 170)(21, 135)(22, 172)(23, 171)(24, 169)(25, 141)(26, 137)(27, 142)(28, 140)(29, 139)(30, 173)(31, 144)(32, 175)(33, 174)(34, 179)(35, 183)(36, 185)(37, 145)(38, 188)(39, 146)(40, 187)(41, 152)(42, 148)(43, 151)(44, 150)(45, 158)(46, 161)(47, 160)(48, 190)(49, 181)(50, 189)(51, 162)(52, 186)(53, 177)(54, 191)(55, 163)(56, 192)(57, 164)(58, 180)(59, 168)(60, 166)(61, 178)(62, 176)(63, 182)(64, 184)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 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 E23.799 Graph:: simple bipartite v = 36 e = 128 f = 48 degree seq :: [ 4^32, 32^4 ] E23.807 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = (C2 x D16) : C2 (small group id <64, 190>) Aut = $<128, 2144>$ (small group id <128, 2144>) |r| :: 2 Presentation :: [ Y3^2, Y2^2, R^2, (R * Y2)^2, (Y1^-1 * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2)^2, (Y3 * Y1^2)^2, (Y1^-2 * Y3)^2, (Y3 * Y1)^4, Y3 * Y1^-1 * Y3 * Y1^7 ] Map:: non-degenerate R = (1, 65, 2, 66, 6, 70, 15, 79, 30, 94, 48, 112, 45, 109, 26, 90, 37, 101, 27, 91, 38, 102, 54, 118, 47, 111, 29, 93, 14, 78, 5, 69)(3, 67, 9, 73, 21, 85, 39, 103, 57, 121, 64, 128, 55, 119, 42, 106, 56, 120, 43, 107, 60, 124, 61, 125, 49, 113, 31, 95, 16, 80, 7, 71)(4, 68, 11, 75, 25, 89, 44, 108, 52, 116, 32, 96, 20, 84, 8, 72, 19, 83, 13, 77, 28, 92, 46, 110, 50, 114, 34, 98, 17, 81, 12, 76)(10, 74, 23, 87, 33, 97, 53, 117, 62, 126, 58, 122, 41, 105, 22, 86, 36, 100, 18, 82, 35, 99, 51, 115, 63, 127, 59, 123, 40, 104, 24, 88)(129, 193, 131, 195)(130, 194, 135, 199)(132, 196, 138, 202)(133, 197, 137, 201)(134, 198, 144, 208)(136, 200, 146, 210)(139, 203, 152, 216)(140, 204, 151, 215)(141, 205, 150, 214)(142, 206, 149, 213)(143, 207, 159, 223)(145, 209, 161, 225)(147, 211, 164, 228)(148, 212, 163, 227)(153, 217, 168, 232)(154, 218, 171, 235)(155, 219, 170, 234)(156, 220, 169, 233)(157, 221, 167, 231)(158, 222, 177, 241)(160, 224, 179, 243)(162, 226, 181, 245)(165, 229, 184, 248)(166, 230, 183, 247)(172, 236, 187, 251)(173, 237, 188, 252)(174, 238, 186, 250)(175, 239, 185, 249)(176, 240, 189, 253)(178, 242, 190, 254)(180, 244, 191, 255)(182, 246, 192, 256) L = (1, 132)(2, 136)(3, 138)(4, 129)(5, 141)(6, 145)(7, 146)(8, 130)(9, 150)(10, 131)(11, 154)(12, 155)(13, 133)(14, 153)(15, 160)(16, 161)(17, 134)(18, 135)(19, 165)(20, 166)(21, 168)(22, 137)(23, 170)(24, 171)(25, 142)(26, 139)(27, 140)(28, 173)(29, 174)(30, 178)(31, 179)(32, 143)(33, 144)(34, 182)(35, 183)(36, 184)(37, 147)(38, 148)(39, 186)(40, 149)(41, 188)(42, 151)(43, 152)(44, 176)(45, 156)(46, 157)(47, 180)(48, 172)(49, 190)(50, 158)(51, 159)(52, 175)(53, 192)(54, 162)(55, 163)(56, 164)(57, 191)(58, 167)(59, 189)(60, 169)(61, 187)(62, 177)(63, 185)(64, 181)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 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 E23.797 Graph:: simple bipartite v = 36 e = 128 f = 48 degree seq :: [ 4^32, 32^4 ] E23.808 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = C2 x QD32 (small group id <64, 187>) Aut = $<128, 2144>$ (small group id <128, 2144>) |r| :: 2 Presentation :: [ Y3^2, Y2^2, R^2, (Y3 * Y2)^2, (R * Y1)^2, (R * Y2)^2, (R * Y3)^2, (Y1^-1 * Y3 * Y1^-1)^2, Y3 * Y1 * Y3 * Y2 * Y1^-1 * Y2, (Y2 * Y1^-2)^2, Y1^-1 * Y3 * Y1 * Y3 * Y1 * Y2 * Y1^-1 * Y2, Y1 * Y2 * Y1^-7 * Y2 ] Map:: non-degenerate R = (1, 65, 2, 66, 6, 70, 17, 81, 35, 99, 53, 117, 47, 111, 26, 90, 41, 105, 29, 93, 43, 107, 59, 123, 52, 116, 34, 98, 16, 80, 5, 69)(3, 67, 9, 73, 25, 89, 45, 109, 57, 121, 36, 100, 22, 86, 7, 71, 20, 84, 14, 78, 32, 96, 50, 114, 54, 118, 39, 103, 18, 82, 11, 75)(4, 68, 12, 76, 31, 95, 49, 113, 58, 122, 37, 101, 24, 88, 8, 72, 23, 87, 15, 79, 33, 97, 51, 115, 55, 119, 40, 104, 19, 83, 13, 77)(10, 74, 21, 85, 38, 102, 56, 120, 63, 127, 61, 125, 48, 112, 27, 91, 42, 106, 30, 94, 44, 108, 60, 124, 64, 128, 62, 126, 46, 110, 28, 92)(129, 193, 131, 195)(130, 194, 135, 199)(132, 196, 138, 202)(133, 197, 142, 206)(134, 198, 146, 210)(136, 200, 149, 213)(137, 201, 154, 218)(139, 203, 157, 221)(140, 204, 155, 219)(141, 205, 158, 222)(143, 207, 156, 220)(144, 208, 153, 217)(145, 209, 164, 228)(147, 211, 166, 230)(148, 212, 169, 233)(150, 214, 171, 235)(151, 215, 170, 234)(152, 216, 172, 236)(159, 223, 174, 238)(160, 224, 175, 239)(161, 225, 176, 240)(162, 226, 178, 242)(163, 227, 182, 246)(165, 229, 184, 248)(167, 231, 187, 251)(168, 232, 188, 252)(173, 237, 181, 245)(177, 241, 189, 253)(179, 243, 190, 254)(180, 244, 185, 249)(183, 247, 191, 255)(186, 250, 192, 256) L = (1, 132)(2, 136)(3, 138)(4, 129)(5, 143)(6, 147)(7, 149)(8, 130)(9, 155)(10, 131)(11, 158)(12, 154)(13, 157)(14, 156)(15, 133)(16, 159)(17, 165)(18, 166)(19, 134)(20, 170)(21, 135)(22, 172)(23, 169)(24, 171)(25, 174)(26, 140)(27, 137)(28, 142)(29, 141)(30, 139)(31, 144)(32, 176)(33, 175)(34, 179)(35, 183)(36, 184)(37, 145)(38, 146)(39, 188)(40, 187)(41, 151)(42, 148)(43, 152)(44, 150)(45, 189)(46, 153)(47, 161)(48, 160)(49, 181)(50, 190)(51, 162)(52, 186)(53, 177)(54, 191)(55, 163)(56, 164)(57, 192)(58, 180)(59, 168)(60, 167)(61, 173)(62, 178)(63, 182)(64, 185)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 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 E23.796 Graph:: simple bipartite v = 36 e = 128 f = 48 degree seq :: [ 4^32, 32^4 ] E23.809 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = (C2 x D16) : C2 (small group id <64, 190>) Aut = $<128, 2144>$ (small group id <128, 2144>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^-1 * Y1^-2 * Y3^-1, (Y3^-1 * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y1^-1 * Y3^-1 * Y2 * Y1^-1 * Y2 * Y3, Y1 * Y2 * Y3^-2 * Y2 * Y1, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2 * Y1 * Y3 * Y2 * Y1^-1, Y1^-1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1^-1 * Y3, (Y3 * Y1)^4, Y3 * Y1^-1 * Y3^5 * Y1^-1 ] Map:: non-degenerate R = (1, 65, 2, 66, 7, 71, 21, 85, 44, 108, 40, 104, 55, 119, 32, 96, 50, 114, 35, 99, 53, 117, 43, 107, 56, 120, 39, 103, 16, 80, 5, 69)(3, 67, 11, 75, 31, 95, 57, 121, 63, 127, 45, 109, 26, 90, 8, 72, 24, 88, 18, 82, 41, 105, 60, 124, 61, 125, 48, 112, 22, 86, 13, 77)(4, 68, 15, 79, 6, 70, 20, 84, 23, 87, 49, 113, 42, 106, 19, 83, 29, 93, 9, 73, 28, 92, 10, 74, 30, 94, 46, 110, 38, 102, 17, 81)(12, 76, 27, 91, 14, 78, 37, 101, 58, 122, 64, 128, 54, 118, 36, 100, 51, 115, 33, 97, 52, 116, 34, 98, 59, 123, 62, 126, 47, 111, 25, 89)(129, 193, 131, 195)(130, 194, 136, 200)(132, 196, 142, 206)(133, 197, 146, 210)(134, 198, 140, 204)(135, 199, 150, 214)(137, 201, 155, 219)(138, 202, 153, 217)(139, 203, 160, 224)(141, 205, 163, 227)(143, 207, 161, 225)(144, 208, 159, 223)(145, 209, 162, 226)(147, 211, 165, 229)(148, 212, 164, 228)(149, 213, 173, 237)(151, 215, 175, 239)(152, 216, 178, 242)(154, 218, 181, 245)(156, 220, 179, 243)(157, 221, 180, 244)(158, 222, 182, 246)(166, 230, 186, 250)(167, 231, 188, 252)(168, 232, 185, 249)(169, 233, 183, 247)(170, 234, 187, 251)(171, 235, 176, 240)(172, 236, 189, 253)(174, 238, 190, 254)(177, 241, 192, 256)(184, 248, 191, 255) L = (1, 132)(2, 137)(3, 140)(4, 144)(5, 147)(6, 129)(7, 134)(8, 153)(9, 133)(10, 130)(11, 161)(12, 150)(13, 164)(14, 131)(15, 160)(16, 166)(17, 168)(18, 155)(19, 167)(20, 163)(21, 138)(22, 175)(23, 135)(24, 179)(25, 173)(26, 182)(27, 136)(28, 178)(29, 183)(30, 181)(31, 142)(32, 145)(33, 141)(34, 139)(35, 143)(36, 176)(37, 146)(38, 184)(39, 177)(40, 174)(41, 180)(42, 172)(43, 148)(44, 151)(45, 190)(46, 149)(47, 189)(48, 192)(49, 171)(50, 157)(51, 154)(52, 152)(53, 156)(54, 191)(55, 170)(56, 158)(57, 162)(58, 159)(59, 169)(60, 165)(61, 187)(62, 185)(63, 186)(64, 188)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 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 E23.795 Graph:: simple bipartite v = 36 e = 128 f = 48 degree seq :: [ 4^32, 32^4 ] E23.810 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = (C16 x C2) : C2 (small group id <64, 189>) Aut = $<128, 2147>$ (small group id <128, 2147>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3 * Y2)^2, (R * Y3)^2, Y3^-1 * Y1^-1 * Y3 * Y1^-1, (R * Y1)^2, Y3^4, (Y1^-1 * Y2)^2, Y1 * Y3 * Y2 * Y1^-1 * Y3 * Y2, (R * Y2 * Y3^-1)^2, Y1^-2 * Y3^-1 * Y1^2 * Y3^-1 * Y1^-4 ] Map:: non-degenerate R = (1, 65, 2, 66, 7, 71, 18, 82, 33, 97, 49, 113, 46, 110, 30, 94, 15, 79, 24, 88, 39, 103, 55, 119, 47, 111, 31, 95, 16, 80, 5, 69)(3, 67, 11, 75, 25, 89, 41, 105, 57, 121, 64, 128, 56, 120, 40, 104, 28, 92, 44, 108, 60, 124, 61, 125, 50, 114, 34, 98, 19, 83, 8, 72)(4, 68, 14, 78, 29, 93, 45, 109, 52, 116, 36, 100, 21, 85, 10, 74, 6, 70, 17, 81, 32, 96, 48, 112, 51, 115, 35, 99, 20, 84, 9, 73)(12, 76, 22, 86, 37, 101, 53, 117, 62, 126, 59, 123, 43, 107, 27, 91, 13, 77, 23, 87, 38, 102, 54, 118, 63, 127, 58, 122, 42, 106, 26, 90)(129, 193, 131, 195)(130, 194, 136, 200)(132, 196, 141, 205)(133, 197, 139, 203)(134, 198, 140, 204)(135, 199, 147, 211)(137, 201, 151, 215)(138, 202, 150, 214)(142, 206, 155, 219)(143, 207, 156, 220)(144, 208, 153, 217)(145, 209, 154, 218)(146, 210, 162, 226)(148, 212, 166, 230)(149, 213, 165, 229)(152, 216, 168, 232)(157, 221, 171, 235)(158, 222, 172, 236)(159, 223, 169, 233)(160, 224, 170, 234)(161, 225, 178, 242)(163, 227, 182, 246)(164, 228, 181, 245)(167, 231, 184, 248)(173, 237, 187, 251)(174, 238, 188, 252)(175, 239, 185, 249)(176, 240, 186, 250)(177, 241, 189, 253)(179, 243, 191, 255)(180, 244, 190, 254)(183, 247, 192, 256) L = (1, 132)(2, 137)(3, 140)(4, 143)(5, 142)(6, 129)(7, 148)(8, 150)(9, 152)(10, 130)(11, 154)(12, 156)(13, 131)(14, 158)(15, 134)(16, 157)(17, 133)(18, 163)(19, 165)(20, 167)(21, 135)(22, 168)(23, 136)(24, 138)(25, 170)(26, 172)(27, 139)(28, 141)(29, 174)(30, 145)(31, 173)(32, 144)(33, 179)(34, 181)(35, 183)(36, 146)(37, 184)(38, 147)(39, 149)(40, 151)(41, 186)(42, 188)(43, 153)(44, 155)(45, 177)(46, 160)(47, 180)(48, 159)(49, 176)(50, 190)(51, 175)(52, 161)(53, 192)(54, 162)(55, 164)(56, 166)(57, 191)(58, 189)(59, 169)(60, 171)(61, 187)(62, 185)(63, 178)(64, 182)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 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 E23.802 Graph:: simple bipartite v = 36 e = 128 f = 48 degree seq :: [ 4^32, 32^4 ] E23.811 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = (C16 x C2) : C2 (small group id <64, 189>) Aut = $<128, 2147>$ (small group id <128, 2147>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3^-1, Y1), (Y3 * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y1^-1 * Y2 * Y3 * Y1 * Y3 * Y2, (Y2 * Y1^-2)^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1, Y3^-4 * Y1^-4, Y3^5 * Y1^-1 * Y3 * Y1^-1 ] Map:: non-degenerate R = (1, 65, 2, 66, 7, 71, 21, 85, 44, 108, 38, 102, 15, 79, 29, 93, 51, 115, 34, 98, 20, 84, 30, 94, 52, 116, 41, 105, 18, 82, 5, 69)(3, 67, 11, 75, 31, 95, 57, 121, 63, 127, 45, 109, 27, 91, 8, 72, 25, 89, 17, 81, 36, 100, 59, 123, 61, 125, 49, 113, 22, 86, 13, 77)(4, 68, 9, 73, 23, 87, 46, 110, 43, 107, 56, 120, 37, 101, 55, 119, 42, 106, 19, 83, 6, 70, 10, 74, 24, 88, 47, 111, 40, 104, 16, 80)(12, 76, 28, 92, 53, 117, 39, 103, 60, 124, 62, 126, 54, 118, 26, 90, 50, 114, 35, 99, 14, 78, 32, 96, 58, 122, 64, 128, 48, 112, 33, 97)(129, 193, 131, 195)(130, 194, 136, 200)(132, 196, 142, 206)(133, 197, 145, 209)(134, 198, 140, 204)(135, 199, 150, 214)(137, 201, 156, 220)(138, 202, 154, 218)(139, 203, 157, 221)(141, 205, 162, 226)(143, 207, 164, 228)(144, 208, 167, 231)(146, 210, 159, 223)(147, 211, 163, 227)(148, 212, 155, 219)(149, 213, 173, 237)(151, 215, 178, 242)(152, 216, 176, 240)(153, 217, 179, 243)(158, 222, 177, 241)(160, 224, 183, 247)(161, 225, 174, 238)(165, 229, 188, 252)(166, 230, 185, 249)(168, 232, 186, 250)(169, 233, 187, 251)(170, 234, 181, 245)(171, 235, 182, 246)(172, 236, 189, 253)(175, 239, 190, 254)(180, 244, 191, 255)(184, 248, 192, 256) L = (1, 132)(2, 137)(3, 140)(4, 143)(5, 144)(6, 129)(7, 151)(8, 154)(9, 157)(10, 130)(11, 156)(12, 155)(13, 161)(14, 131)(15, 165)(16, 166)(17, 163)(18, 168)(19, 133)(20, 134)(21, 174)(22, 176)(23, 179)(24, 135)(25, 178)(26, 177)(27, 182)(28, 136)(29, 183)(30, 138)(31, 181)(32, 139)(33, 173)(34, 147)(35, 141)(36, 142)(37, 180)(38, 184)(39, 145)(40, 172)(41, 175)(42, 146)(43, 148)(44, 171)(45, 190)(46, 162)(47, 149)(48, 191)(49, 192)(50, 150)(51, 170)(52, 152)(53, 153)(54, 189)(55, 169)(56, 158)(57, 167)(58, 159)(59, 160)(60, 164)(61, 186)(62, 187)(63, 188)(64, 185)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 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 E23.800 Graph:: simple bipartite v = 36 e = 128 f = 48 degree seq :: [ 4^32, 32^4 ] E23.812 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = (C2 x D16) : C2 (small group id <64, 190>) Aut = $<128, 2147>$ (small group id <128, 2147>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3 * Y2)^2, (R * Y3)^2, Y3^-1 * Y1^-2 * Y3^-1, (R * Y1)^2, (Y2 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y1^-2 * Y3 * Y1^-1 * Y3 * Y1^-3, Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1^-1 * Y3 * Y1^-1, (Y3 * Y1)^4 ] Map:: non-degenerate R = (1, 65, 2, 66, 7, 71, 19, 83, 39, 103, 36, 100, 49, 113, 32, 96, 47, 111, 33, 97, 48, 112, 38, 102, 50, 114, 35, 99, 15, 79, 5, 69)(3, 67, 11, 75, 27, 91, 51, 115, 63, 127, 56, 120, 61, 125, 54, 118, 62, 126, 55, 119, 64, 128, 57, 121, 58, 122, 40, 104, 20, 84, 8, 72)(4, 68, 14, 78, 6, 70, 18, 82, 21, 85, 43, 107, 37, 101, 17, 81, 25, 89, 9, 73, 24, 88, 10, 74, 26, 90, 41, 105, 34, 98, 16, 80)(12, 76, 29, 93, 13, 77, 31, 95, 52, 116, 59, 123, 45, 109, 22, 86, 44, 108, 23, 87, 46, 110, 28, 92, 53, 117, 60, 124, 42, 106, 30, 94)(129, 193, 131, 195)(130, 194, 136, 200)(132, 196, 141, 205)(133, 197, 139, 203)(134, 198, 140, 204)(135, 199, 148, 212)(137, 201, 151, 215)(138, 202, 150, 214)(142, 206, 157, 221)(143, 207, 155, 219)(144, 208, 159, 223)(145, 209, 156, 220)(146, 210, 158, 222)(147, 211, 168, 232)(149, 213, 170, 234)(152, 216, 172, 236)(153, 217, 174, 238)(154, 218, 173, 237)(160, 224, 183, 247)(161, 225, 182, 246)(162, 226, 180, 244)(163, 227, 179, 243)(164, 228, 185, 249)(165, 229, 181, 245)(166, 230, 184, 248)(167, 231, 186, 250)(169, 233, 187, 251)(171, 235, 188, 252)(175, 239, 190, 254)(176, 240, 189, 253)(177, 241, 192, 256)(178, 242, 191, 255) L = (1, 132)(2, 137)(3, 140)(4, 143)(5, 145)(6, 129)(7, 134)(8, 150)(9, 133)(10, 130)(11, 151)(12, 148)(13, 131)(14, 160)(15, 162)(16, 164)(17, 163)(18, 161)(19, 138)(20, 170)(21, 135)(22, 168)(23, 136)(24, 175)(25, 177)(26, 176)(27, 141)(28, 139)(29, 182)(30, 184)(31, 183)(32, 144)(33, 142)(34, 178)(35, 171)(36, 169)(37, 167)(38, 146)(39, 149)(40, 187)(41, 147)(42, 186)(43, 166)(44, 189)(45, 191)(46, 190)(47, 153)(48, 152)(49, 165)(50, 154)(51, 156)(52, 155)(53, 192)(54, 158)(55, 157)(56, 188)(57, 159)(58, 181)(59, 185)(60, 179)(61, 173)(62, 172)(63, 180)(64, 174)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 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 E23.801 Graph:: simple bipartite v = 36 e = 128 f = 48 degree seq :: [ 4^32, 32^4 ] E23.813 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = C2 x QD32 (small group id <64, 187>) Aut = $<128, 2144>$ (small group id <128, 2144>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-2 * Y1^-1, Y1^4, (Y3 * Y2^-1)^2, (Y2 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, (Y2^-1 * Y1^-1)^2, (Y2^-1 * Y3^-1)^2, (Y3 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2 * Y1 * Y3 * Y2^-1 * Y1^-1, Y2^-1 * Y3^-1 * Y2^3 * Y3 * Y2^-4 ] Map:: polytopal non-degenerate R = (1, 65, 2, 66, 8, 72, 5, 69)(3, 67, 13, 77, 21, 85, 11, 75)(4, 68, 10, 74, 7, 71, 12, 76)(6, 70, 18, 82, 22, 86, 9, 73)(14, 78, 28, 92, 37, 101, 29, 93)(15, 79, 26, 90, 16, 80, 27, 91)(17, 81, 24, 88, 19, 83, 25, 89)(20, 84, 23, 87, 38, 102, 34, 98)(30, 94, 45, 109, 53, 117, 44, 108)(31, 95, 42, 106, 32, 96, 43, 107)(33, 97, 40, 104, 35, 99, 41, 105)(36, 100, 50, 114, 54, 118, 39, 103)(46, 110, 60, 124, 52, 116, 55, 119)(47, 111, 58, 122, 48, 112, 59, 123)(49, 113, 56, 120, 51, 115, 57, 121)(61, 125, 64, 128, 62, 126, 63, 127)(129, 193, 131, 195, 142, 206, 158, 222, 174, 238, 182, 246, 166, 230, 150, 214, 136, 200, 149, 213, 165, 229, 181, 245, 180, 244, 164, 228, 148, 212, 134, 198)(130, 194, 137, 201, 151, 215, 167, 231, 183, 247, 173, 237, 157, 221, 141, 205, 133, 197, 146, 210, 162, 226, 178, 242, 188, 252, 172, 236, 156, 220, 139, 203)(132, 196, 145, 209, 161, 225, 177, 241, 190, 254, 175, 239, 160, 224, 143, 207, 135, 199, 147, 211, 163, 227, 179, 243, 189, 253, 176, 240, 159, 223, 144, 208)(138, 202, 154, 218, 170, 234, 186, 250, 192, 256, 184, 248, 169, 233, 152, 216, 140, 204, 155, 219, 171, 235, 187, 251, 191, 255, 185, 249, 168, 232, 153, 217) L = (1, 132)(2, 138)(3, 143)(4, 136)(5, 140)(6, 147)(7, 129)(8, 135)(9, 152)(10, 133)(11, 155)(12, 130)(13, 154)(14, 159)(15, 149)(16, 131)(17, 134)(18, 153)(19, 150)(20, 161)(21, 144)(22, 145)(23, 168)(24, 146)(25, 137)(26, 139)(27, 141)(28, 170)(29, 171)(30, 175)(31, 165)(32, 142)(33, 166)(34, 169)(35, 148)(36, 179)(37, 160)(38, 163)(39, 184)(40, 162)(41, 151)(42, 157)(43, 156)(44, 187)(45, 186)(46, 189)(47, 181)(48, 158)(49, 164)(50, 185)(51, 182)(52, 190)(53, 176)(54, 177)(55, 191)(56, 178)(57, 167)(58, 172)(59, 173)(60, 192)(61, 180)(62, 174)(63, 188)(64, 183)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4^8 ), ( 4^32 ) } Outer automorphisms :: reflexible Dual of E23.789 Graph:: bipartite v = 20 e = 128 f = 64 degree seq :: [ 8^16, 32^4 ] E23.814 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = (C16 x C2) : C2 (small group id <64, 189>) Aut = $<128, 2147>$ (small group id <128, 2147>) |r| :: 2 Presentation :: [ R^2, Y3^2, R * Y2 * R * Y2^-1, (Y1^-1 * Y3)^2, (R * Y3)^2, Y2^-1 * Y1 * Y2^-1 * Y1^-1, (Y2^-1 * Y3)^2, Y1^4, (R * Y1)^2, Y1^-1 * Y2 * Y1^-2 * Y2^-1 * Y1^-1, Y2^3 * Y1^-1 * Y2^-5 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 65, 2, 66, 7, 71, 5, 69)(3, 67, 10, 74, 18, 82, 13, 77)(4, 68, 14, 78, 19, 83, 9, 73)(6, 70, 8, 72, 20, 84, 16, 80)(11, 75, 24, 88, 33, 97, 27, 91)(12, 76, 28, 92, 34, 98, 23, 87)(15, 79, 29, 93, 35, 99, 22, 86)(17, 81, 21, 85, 36, 100, 31, 95)(25, 89, 40, 104, 49, 113, 43, 107)(26, 90, 44, 108, 50, 114, 39, 103)(30, 94, 45, 109, 51, 115, 38, 102)(32, 96, 37, 101, 52, 116, 47, 111)(41, 105, 56, 120, 48, 112, 53, 117)(42, 106, 58, 122, 61, 125, 55, 119)(46, 110, 59, 123, 62, 126, 54, 118)(57, 121, 63, 127, 60, 124, 64, 128)(129, 193, 131, 195, 139, 203, 153, 217, 169, 233, 180, 244, 164, 228, 148, 212, 135, 199, 146, 210, 161, 225, 177, 241, 176, 240, 160, 224, 145, 209, 134, 198)(130, 194, 136, 200, 149, 213, 165, 229, 181, 245, 171, 235, 155, 219, 141, 205, 133, 197, 144, 208, 159, 223, 175, 239, 184, 248, 168, 232, 152, 216, 138, 202)(132, 196, 143, 207, 158, 222, 174, 238, 188, 252, 189, 253, 178, 242, 162, 226, 147, 211, 163, 227, 179, 243, 190, 254, 185, 249, 170, 234, 154, 218, 140, 204)(137, 201, 151, 215, 167, 231, 183, 247, 192, 256, 187, 251, 173, 237, 157, 221, 142, 206, 156, 220, 172, 236, 186, 250, 191, 255, 182, 246, 166, 230, 150, 214) L = (1, 132)(2, 137)(3, 140)(4, 129)(5, 142)(6, 143)(7, 147)(8, 150)(9, 130)(10, 151)(11, 154)(12, 131)(13, 156)(14, 133)(15, 134)(16, 157)(17, 158)(18, 162)(19, 135)(20, 163)(21, 166)(22, 136)(23, 138)(24, 167)(25, 170)(26, 139)(27, 172)(28, 141)(29, 144)(30, 145)(31, 173)(32, 174)(33, 178)(34, 146)(35, 148)(36, 179)(37, 182)(38, 149)(39, 152)(40, 183)(41, 185)(42, 153)(43, 186)(44, 155)(45, 159)(46, 160)(47, 187)(48, 188)(49, 189)(50, 161)(51, 164)(52, 190)(53, 191)(54, 165)(55, 168)(56, 192)(57, 169)(58, 171)(59, 175)(60, 176)(61, 177)(62, 180)(63, 181)(64, 184)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4^8 ), ( 4^32 ) } Outer automorphisms :: reflexible Dual of E23.791 Graph:: bipartite v = 20 e = 128 f = 64 degree seq :: [ 8^16, 32^4 ] E23.815 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = (C2 x D16) : C2 (small group id <64, 190>) Aut = $<128, 2147>$ (small group id <128, 2147>) |r| :: 2 Presentation :: [ R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y3)^2, (Y2^-1 * Y3)^2, (R * Y1)^2, Y2^-1 * Y1^-1 * Y2 * Y1^-1, Y1^4, (Y3 * Y1^-1)^2, Y1^-1 * Y2^8 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 65, 2, 66, 7, 71, 5, 69)(3, 67, 11, 75, 18, 82, 8, 72)(4, 68, 14, 78, 19, 83, 9, 73)(6, 70, 16, 80, 20, 84, 10, 74)(12, 76, 21, 85, 33, 97, 25, 89)(13, 77, 22, 86, 34, 98, 26, 90)(15, 79, 23, 87, 35, 99, 29, 93)(17, 81, 24, 88, 36, 100, 31, 95)(27, 91, 41, 105, 49, 113, 37, 101)(28, 92, 42, 106, 50, 114, 38, 102)(30, 94, 45, 109, 51, 115, 39, 103)(32, 96, 47, 111, 52, 116, 40, 104)(43, 107, 53, 117, 48, 112, 56, 120)(44, 108, 54, 118, 61, 125, 57, 121)(46, 110, 55, 119, 62, 126, 59, 123)(58, 122, 64, 128, 60, 124, 63, 127)(129, 193, 131, 195, 140, 204, 155, 219, 171, 235, 180, 244, 164, 228, 148, 212, 135, 199, 146, 210, 161, 225, 177, 241, 176, 240, 160, 224, 145, 209, 134, 198)(130, 194, 136, 200, 149, 213, 165, 229, 181, 245, 175, 239, 159, 223, 144, 208, 133, 197, 139, 203, 153, 217, 169, 233, 184, 248, 168, 232, 152, 216, 138, 202)(132, 196, 143, 207, 158, 222, 174, 238, 188, 252, 189, 253, 178, 242, 162, 226, 147, 211, 163, 227, 179, 243, 190, 254, 186, 250, 172, 236, 156, 220, 141, 205)(137, 201, 151, 215, 167, 231, 183, 247, 192, 256, 185, 249, 170, 234, 154, 218, 142, 206, 157, 221, 173, 237, 187, 251, 191, 255, 182, 246, 166, 230, 150, 214) L = (1, 132)(2, 137)(3, 141)(4, 129)(5, 142)(6, 143)(7, 147)(8, 150)(9, 130)(10, 151)(11, 154)(12, 156)(13, 131)(14, 133)(15, 134)(16, 157)(17, 158)(18, 162)(19, 135)(20, 163)(21, 166)(22, 136)(23, 138)(24, 167)(25, 170)(26, 139)(27, 172)(28, 140)(29, 144)(30, 145)(31, 173)(32, 174)(33, 178)(34, 146)(35, 148)(36, 179)(37, 182)(38, 149)(39, 152)(40, 183)(41, 185)(42, 153)(43, 186)(44, 155)(45, 159)(46, 160)(47, 187)(48, 188)(49, 189)(50, 161)(51, 164)(52, 190)(53, 191)(54, 165)(55, 168)(56, 192)(57, 169)(58, 171)(59, 175)(60, 176)(61, 177)(62, 180)(63, 181)(64, 184)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4^8 ), ( 4^32 ) } Outer automorphisms :: reflexible Dual of E23.792 Graph:: bipartite v = 20 e = 128 f = 64 degree seq :: [ 8^16, 32^4 ] E23.816 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = (C2 x D16) : C2 (small group id <64, 190>) Aut = $<128, 2147>$ (small group id <128, 2147>) |r| :: 2 Presentation :: [ R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y1)^2, (Y1^-1 * Y3)^2, (Y2^-1 * Y3)^2, (Y2^-1 * Y1)^2, (Y2^-1 * Y1^-1)^2, (R * Y3)^2, Y1^4, Y1^-1 * Y2^-8 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 65, 2, 66, 7, 71, 5, 69)(3, 67, 11, 75, 18, 82, 10, 74)(4, 68, 14, 78, 19, 83, 9, 73)(6, 70, 16, 80, 20, 84, 8, 72)(12, 76, 24, 88, 33, 97, 26, 90)(13, 77, 23, 87, 34, 98, 25, 89)(15, 79, 22, 86, 35, 99, 29, 93)(17, 81, 21, 85, 36, 100, 31, 95)(27, 91, 42, 106, 49, 113, 40, 104)(28, 92, 41, 105, 50, 114, 39, 103)(30, 94, 45, 109, 51, 115, 38, 102)(32, 96, 47, 111, 52, 116, 37, 101)(43, 107, 56, 120, 48, 112, 53, 117)(44, 108, 55, 119, 61, 125, 57, 121)(46, 110, 54, 118, 62, 126, 59, 123)(58, 122, 63, 127, 60, 124, 64, 128)(129, 193, 131, 195, 140, 204, 155, 219, 171, 235, 180, 244, 164, 228, 148, 212, 135, 199, 146, 210, 161, 225, 177, 241, 176, 240, 160, 224, 145, 209, 134, 198)(130, 194, 136, 200, 149, 213, 165, 229, 181, 245, 170, 234, 154, 218, 139, 203, 133, 197, 144, 208, 159, 223, 175, 239, 184, 248, 168, 232, 152, 216, 138, 202)(132, 196, 143, 207, 158, 222, 174, 238, 188, 252, 189, 253, 178, 242, 162, 226, 147, 211, 163, 227, 179, 243, 190, 254, 186, 250, 172, 236, 156, 220, 141, 205)(137, 201, 151, 215, 167, 231, 183, 247, 192, 256, 187, 251, 173, 237, 157, 221, 142, 206, 153, 217, 169, 233, 185, 249, 191, 255, 182, 246, 166, 230, 150, 214) L = (1, 132)(2, 137)(3, 141)(4, 129)(5, 142)(6, 143)(7, 147)(8, 150)(9, 130)(10, 151)(11, 153)(12, 156)(13, 131)(14, 133)(15, 134)(16, 157)(17, 158)(18, 162)(19, 135)(20, 163)(21, 166)(22, 136)(23, 138)(24, 167)(25, 139)(26, 169)(27, 172)(28, 140)(29, 144)(30, 145)(31, 173)(32, 174)(33, 178)(34, 146)(35, 148)(36, 179)(37, 182)(38, 149)(39, 152)(40, 183)(41, 154)(42, 185)(43, 186)(44, 155)(45, 159)(46, 160)(47, 187)(48, 188)(49, 189)(50, 161)(51, 164)(52, 190)(53, 191)(54, 165)(55, 168)(56, 192)(57, 170)(58, 171)(59, 175)(60, 176)(61, 177)(62, 180)(63, 181)(64, 184)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4^8 ), ( 4^32 ) } Outer automorphisms :: reflexible Dual of E23.790 Graph:: bipartite v = 20 e = 128 f = 64 degree seq :: [ 8^16, 32^4 ] E23.817 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = (C2 x Q16) : C2 (small group id <64, 191>) Aut = $<128, 2148>$ (small group id <128, 2148>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^4, Y3^-2 * Y2^2, Y3^-1 * Y2^-2 * Y3^-1, (Y3^-1 * Y1)^2, (R * Y1)^2, Y2 * Y1 * Y2^-1 * Y1, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2^-1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-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, 65, 2, 66)(3, 67, 7, 71)(4, 68, 10, 74)(5, 69, 9, 73)(6, 70, 8, 72)(11, 75, 16, 80)(12, 76, 18, 82)(13, 77, 17, 81)(14, 78, 20, 84)(15, 79, 19, 83)(21, 85, 26, 90)(22, 86, 25, 89)(23, 87, 27, 91)(24, 88, 28, 92)(29, 93, 33, 97)(30, 94, 34, 98)(31, 95, 35, 99)(32, 96, 36, 100)(37, 101, 41, 105)(38, 102, 42, 106)(39, 103, 44, 108)(40, 104, 43, 107)(45, 109, 50, 114)(46, 110, 49, 113)(47, 111, 52, 116)(48, 112, 51, 115)(53, 117, 58, 122)(54, 118, 57, 121)(55, 119, 59, 123)(56, 120, 60, 124)(61, 125, 63, 127)(62, 126, 64, 128)(129, 193, 131, 195, 139, 203, 133, 197)(130, 194, 135, 199, 144, 208, 137, 201)(132, 196, 142, 206, 134, 198, 143, 207)(136, 200, 147, 211, 138, 202, 148, 212)(140, 204, 149, 213, 141, 205, 150, 214)(145, 209, 153, 217, 146, 210, 154, 218)(151, 215, 159, 223, 152, 216, 160, 224)(155, 219, 163, 227, 156, 220, 164, 228)(157, 221, 165, 229, 158, 222, 166, 230)(161, 225, 169, 233, 162, 226, 170, 234)(167, 231, 175, 239, 168, 232, 176, 240)(171, 235, 179, 243, 172, 236, 180, 244)(173, 237, 181, 245, 174, 238, 182, 246)(177, 241, 185, 249, 178, 242, 186, 250)(183, 247, 190, 254, 184, 248, 189, 253)(187, 251, 192, 256, 188, 252, 191, 255) L = (1, 132)(2, 136)(3, 140)(4, 139)(5, 141)(6, 129)(7, 145)(8, 144)(9, 146)(10, 130)(11, 134)(12, 133)(13, 131)(14, 151)(15, 152)(16, 138)(17, 137)(18, 135)(19, 155)(20, 156)(21, 157)(22, 158)(23, 143)(24, 142)(25, 161)(26, 162)(27, 148)(28, 147)(29, 150)(30, 149)(31, 167)(32, 168)(33, 154)(34, 153)(35, 171)(36, 172)(37, 173)(38, 174)(39, 160)(40, 159)(41, 177)(42, 178)(43, 164)(44, 163)(45, 166)(46, 165)(47, 183)(48, 184)(49, 170)(50, 169)(51, 187)(52, 188)(53, 189)(54, 190)(55, 176)(56, 175)(57, 191)(58, 192)(59, 180)(60, 179)(61, 182)(62, 181)(63, 186)(64, 185)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32 ) } Outer automorphisms :: reflexible Dual of E23.818 Graph:: simple bipartite v = 48 e = 128 f = 36 degree seq :: [ 4^32, 8^16 ] E23.818 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = (C2 x Q16) : C2 (small group id <64, 191>) Aut = $<128, 2148>$ (small group id <128, 2148>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^4, Y1 * Y3 * Y1 * Y3^-1, (Y3 * Y2)^2, (R * Y1)^2, Y3^4, (R * Y3)^2, Y1 * Y3^2 * Y2 * Y1 * Y2, (Y2 * Y1^-2)^2, Y2 * Y1^-1 * Y3^2 * Y2 * Y1^-1, Y3 * Y2 * R * Y2 * R * Y3, (R * Y2 * Y3^-1)^2, Y1^-3 * Y2 * Y1 * Y2 * Y1^-4 ] Map:: non-degenerate R = (1, 65, 2, 66, 7, 71, 20, 84, 37, 101, 53, 117, 48, 112, 30, 94, 16, 80, 28, 92, 44, 108, 60, 124, 51, 115, 35, 99, 18, 82, 5, 69)(3, 67, 11, 75, 29, 93, 45, 109, 58, 122, 38, 102, 26, 90, 8, 72, 24, 88, 17, 81, 34, 98, 50, 114, 54, 118, 42, 106, 21, 85, 13, 77)(4, 68, 15, 79, 33, 97, 49, 113, 56, 120, 40, 104, 23, 87, 10, 74, 6, 70, 19, 83, 36, 100, 52, 116, 55, 119, 39, 103, 22, 86, 9, 73)(12, 76, 27, 91, 41, 105, 59, 123, 63, 127, 62, 126, 47, 111, 32, 96, 14, 78, 25, 89, 43, 107, 57, 121, 64, 128, 61, 125, 46, 110, 31, 95)(129, 193, 131, 195)(130, 194, 136, 200)(132, 196, 142, 206)(133, 197, 145, 209)(134, 198, 140, 204)(135, 199, 149, 213)(137, 201, 155, 219)(138, 202, 153, 217)(139, 203, 158, 222)(141, 205, 156, 220)(143, 207, 159, 223)(144, 208, 152, 216)(146, 210, 157, 221)(147, 211, 160, 224)(148, 212, 166, 230)(150, 214, 171, 235)(151, 215, 169, 233)(154, 218, 172, 236)(161, 225, 175, 239)(162, 226, 176, 240)(163, 227, 178, 242)(164, 228, 174, 238)(165, 229, 182, 246)(167, 231, 187, 251)(168, 232, 185, 249)(170, 234, 188, 252)(173, 237, 181, 245)(177, 241, 189, 253)(179, 243, 186, 250)(180, 244, 190, 254)(183, 247, 192, 256)(184, 248, 191, 255) L = (1, 132)(2, 137)(3, 140)(4, 144)(5, 143)(6, 129)(7, 150)(8, 153)(9, 156)(10, 130)(11, 159)(12, 152)(13, 155)(14, 131)(15, 158)(16, 134)(17, 160)(18, 161)(19, 133)(20, 167)(21, 169)(22, 172)(23, 135)(24, 142)(25, 141)(26, 171)(27, 136)(28, 138)(29, 174)(30, 147)(31, 145)(32, 139)(33, 176)(34, 175)(35, 177)(36, 146)(37, 183)(38, 185)(39, 188)(40, 148)(41, 154)(42, 187)(43, 149)(44, 151)(45, 189)(46, 162)(47, 157)(48, 164)(49, 181)(50, 190)(51, 184)(52, 163)(53, 180)(54, 191)(55, 179)(56, 165)(57, 170)(58, 192)(59, 166)(60, 168)(61, 178)(62, 173)(63, 186)(64, 182)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 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 E23.817 Graph:: simple bipartite v = 36 e = 128 f = 48 degree seq :: [ 4^32, 32^4 ] E23.819 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = (C2 x Q16) : C2 (small group id <64, 191>) Aut = $<128, 2146>$ (small group id <128, 2146>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y3^-1 * Y2 * Y3, (R * Y2)^2, Y3^4, (R * Y3)^2, (R * Y1)^2, Y3^-1 * Y1 * Y3^2 * Y1 * Y3^-1, Y1 * Y2 * Y1 * Y3^2 * Y2, Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 ] Map:: polytopal non-degenerate R = (1, 65, 2, 66)(3, 67, 9, 73)(4, 68, 12, 76)(5, 69, 14, 78)(6, 70, 15, 79)(7, 71, 18, 82)(8, 72, 20, 84)(10, 74, 21, 85)(11, 75, 22, 86)(13, 77, 19, 83)(16, 80, 25, 89)(17, 81, 26, 90)(23, 87, 31, 95)(24, 88, 32, 96)(27, 91, 35, 99)(28, 92, 36, 100)(29, 93, 37, 101)(30, 94, 38, 102)(33, 97, 41, 105)(34, 98, 42, 106)(39, 103, 47, 111)(40, 104, 48, 112)(43, 107, 51, 115)(44, 108, 52, 116)(45, 109, 53, 117)(46, 110, 54, 118)(49, 113, 57, 121)(50, 114, 58, 122)(55, 119, 60, 124)(56, 120, 59, 123)(61, 125, 63, 127)(62, 126, 64, 128)(129, 193, 131, 195)(130, 194, 134, 198)(132, 196, 138, 202)(133, 197, 139, 203)(135, 199, 144, 208)(136, 200, 145, 209)(137, 201, 147, 211)(140, 204, 150, 214)(141, 205, 143, 207)(142, 206, 149, 213)(146, 210, 154, 218)(148, 212, 153, 217)(151, 215, 158, 222)(152, 216, 157, 221)(155, 219, 162, 226)(156, 220, 161, 225)(159, 223, 165, 229)(160, 224, 166, 230)(163, 227, 169, 233)(164, 228, 170, 234)(167, 231, 173, 237)(168, 232, 174, 238)(171, 235, 177, 241)(172, 236, 178, 242)(175, 239, 182, 246)(176, 240, 181, 245)(179, 243, 186, 250)(180, 244, 185, 249)(183, 247, 190, 254)(184, 248, 189, 253)(187, 251, 192, 256)(188, 252, 191, 255) L = (1, 132)(2, 135)(3, 138)(4, 141)(5, 129)(6, 144)(7, 147)(8, 130)(9, 145)(10, 143)(11, 131)(12, 151)(13, 133)(14, 152)(15, 139)(16, 137)(17, 134)(18, 155)(19, 136)(20, 156)(21, 157)(22, 158)(23, 142)(24, 140)(25, 161)(26, 162)(27, 148)(28, 146)(29, 150)(30, 149)(31, 167)(32, 168)(33, 154)(34, 153)(35, 171)(36, 172)(37, 173)(38, 174)(39, 160)(40, 159)(41, 177)(42, 178)(43, 164)(44, 163)(45, 166)(46, 165)(47, 183)(48, 184)(49, 170)(50, 169)(51, 187)(52, 188)(53, 189)(54, 190)(55, 176)(56, 175)(57, 191)(58, 192)(59, 180)(60, 179)(61, 182)(62, 181)(63, 186)(64, 185)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 8, 32, 8, 32 ) } Outer automorphisms :: reflexible Dual of E23.822 Graph:: simple bipartite v = 64 e = 128 f = 20 degree seq :: [ 4^64 ] E23.820 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = (C2 x Q16) : C2 (small group id <64, 191>) Aut = $<128, 2146>$ (small group id <128, 2146>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^-1 * Y3^2 * Y2^-1, Y3^-1 * Y2^-2 * Y3^-1, Y3^4, (R * Y1)^2, (Y1 * Y3^-1)^2, (R * Y3)^2, Y2^-1 * R * Y3^-2 * R * Y2^-1, Y2^-1 * Y1 * Y3^-2 * Y1 * Y2^-1, Y3 * Y2^-1 * Y1 * Y3 * Y2 * Y1, (R * Y2 * Y3^-1)^2, Y2 * Y1 * Y2 * Y1 * Y2 * Y3 * Y2^-1 * Y1 * Y2 * Y3^-1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1, Y3^-1 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 65, 2, 66)(3, 67, 11, 75)(4, 68, 10, 74)(5, 69, 17, 81)(6, 70, 8, 72)(7, 71, 18, 82)(9, 73, 24, 88)(12, 76, 19, 83)(13, 77, 23, 87)(14, 78, 22, 86)(15, 79, 21, 85)(16, 80, 20, 84)(25, 89, 33, 97)(26, 90, 36, 100)(27, 91, 35, 99)(28, 92, 34, 98)(29, 93, 37, 101)(30, 94, 40, 104)(31, 95, 39, 103)(32, 96, 38, 102)(41, 105, 49, 113)(42, 106, 52, 116)(43, 107, 51, 115)(44, 108, 50, 114)(45, 109, 53, 117)(46, 110, 56, 120)(47, 111, 55, 119)(48, 112, 54, 118)(57, 121, 62, 126)(58, 122, 61, 125)(59, 123, 63, 127)(60, 124, 64, 128)(129, 193, 131, 195, 140, 204, 133, 197)(130, 194, 135, 199, 147, 211, 137, 201)(132, 196, 143, 207, 134, 198, 144, 208)(136, 200, 150, 214, 138, 202, 151, 215)(139, 203, 153, 217, 145, 209, 154, 218)(141, 205, 155, 219, 142, 206, 156, 220)(146, 210, 157, 221, 152, 216, 158, 222)(148, 212, 159, 223, 149, 213, 160, 224)(161, 225, 169, 233, 164, 228, 170, 234)(162, 226, 171, 235, 163, 227, 172, 236)(165, 229, 173, 237, 168, 232, 174, 238)(166, 230, 175, 239, 167, 231, 176, 240)(177, 241, 185, 249, 180, 244, 186, 250)(178, 242, 187, 251, 179, 243, 188, 252)(181, 245, 189, 253, 184, 248, 190, 254)(182, 246, 191, 255, 183, 247, 192, 256) L = (1, 132)(2, 136)(3, 141)(4, 140)(5, 142)(6, 129)(7, 148)(8, 147)(9, 149)(10, 130)(11, 150)(12, 134)(13, 133)(14, 131)(15, 152)(16, 146)(17, 151)(18, 143)(19, 138)(20, 137)(21, 135)(22, 145)(23, 139)(24, 144)(25, 162)(26, 163)(27, 164)(28, 161)(29, 166)(30, 167)(31, 168)(32, 165)(33, 155)(34, 154)(35, 153)(36, 156)(37, 159)(38, 158)(39, 157)(40, 160)(41, 178)(42, 179)(43, 180)(44, 177)(45, 182)(46, 183)(47, 184)(48, 181)(49, 171)(50, 170)(51, 169)(52, 172)(53, 175)(54, 174)(55, 173)(56, 176)(57, 192)(58, 191)(59, 189)(60, 190)(61, 188)(62, 187)(63, 185)(64, 186)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4, 32, 4, 32 ), ( 4, 32, 4, 32, 4, 32, 4, 32 ) } Outer automorphisms :: reflexible Dual of E23.821 Graph:: simple bipartite v = 48 e = 128 f = 36 degree seq :: [ 4^32, 8^16 ] E23.821 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = (C2 x Q16) : C2 (small group id <64, 191>) Aut = $<128, 2146>$ (small group id <128, 2146>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y2 * Y3^-1)^2, Y3^4, Y3^-1 * Y1 * Y3 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y3^-2 * Y1^-1 * Y2 * Y1 * Y2, Y2 * Y1^2 * Y2 * Y1^-2, Y1^-4 * Y3^2 * Y1^-4 ] Map:: non-degenerate R = (1, 65, 2, 66, 7, 71, 20, 84, 37, 101, 53, 117, 46, 110, 30, 94, 16, 80, 28, 92, 44, 108, 60, 124, 51, 115, 35, 99, 18, 82, 5, 69)(3, 67, 11, 75, 21, 85, 41, 105, 54, 118, 50, 114, 34, 98, 17, 81, 26, 90, 8, 72, 24, 88, 38, 102, 57, 121, 47, 111, 31, 95, 13, 77)(4, 68, 15, 79, 33, 97, 49, 113, 56, 120, 40, 104, 23, 87, 10, 74, 6, 70, 19, 83, 36, 100, 52, 116, 55, 119, 39, 103, 22, 86, 9, 73)(12, 76, 29, 93, 45, 109, 61, 125, 64, 128, 58, 122, 43, 107, 25, 89, 14, 78, 32, 96, 48, 112, 62, 126, 63, 127, 59, 123, 42, 106, 27, 91)(129, 193, 131, 195)(130, 194, 136, 200)(132, 196, 142, 206)(133, 197, 145, 209)(134, 198, 140, 204)(135, 199, 149, 213)(137, 201, 155, 219)(138, 202, 153, 217)(139, 203, 156, 220)(141, 205, 158, 222)(143, 207, 157, 221)(144, 208, 154, 218)(146, 210, 159, 223)(147, 211, 160, 224)(148, 212, 166, 230)(150, 214, 171, 235)(151, 215, 170, 234)(152, 216, 172, 236)(161, 225, 176, 240)(162, 226, 174, 238)(163, 227, 178, 242)(164, 228, 173, 237)(165, 229, 182, 246)(167, 231, 187, 251)(168, 232, 186, 250)(169, 233, 188, 252)(175, 239, 181, 245)(177, 241, 189, 253)(179, 243, 185, 249)(180, 244, 190, 254)(183, 247, 192, 256)(184, 248, 191, 255) L = (1, 132)(2, 137)(3, 140)(4, 144)(5, 143)(6, 129)(7, 150)(8, 153)(9, 156)(10, 130)(11, 155)(12, 154)(13, 157)(14, 131)(15, 158)(16, 134)(17, 160)(18, 161)(19, 133)(20, 167)(21, 170)(22, 172)(23, 135)(24, 171)(25, 139)(26, 142)(27, 136)(28, 138)(29, 145)(30, 147)(31, 173)(32, 141)(33, 174)(34, 176)(35, 177)(36, 146)(37, 183)(38, 186)(39, 188)(40, 148)(41, 187)(42, 152)(43, 149)(44, 151)(45, 162)(46, 164)(47, 189)(48, 159)(49, 181)(50, 190)(51, 184)(52, 163)(53, 180)(54, 191)(55, 179)(56, 165)(57, 192)(58, 169)(59, 166)(60, 168)(61, 178)(62, 175)(63, 185)(64, 182)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 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 E23.820 Graph:: simple bipartite v = 36 e = 128 f = 48 degree seq :: [ 4^32, 32^4 ] E23.822 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 16}) Quotient :: dipole Aut^+ = (C2 x Q16) : C2 (small group id <64, 191>) Aut = $<128, 2146>$ (small group id <128, 2146>) |r| :: 2 Presentation :: [ R^2, Y1^4, Y1^-1 * Y3^-2 * Y1^-1, (Y3^-1 * Y1^-1)^2, (R * Y3)^2, (Y2^-1 * Y3^-1)^2, Y2^-1 * Y1^-1 * Y2^-1 * Y1, (R * Y1)^2, (Y3 * Y1^-1)^2, (Y3 * Y2^-1)^2, Y1^-1 * Y2 * Y1^-2 * Y2^-1 * Y1^-1, Y2 * Y3^-1 * Y1 * Y2^-1 * Y3^-1 * Y1^-1, (R * Y2 * Y3^-1)^2, Y2^3 * Y1^-1 * Y2^-5 * Y1^-1, Y1 * Y3^-1 * Y2^3 * Y3 * Y1 * Y2^-3 ] Map:: polytopal non-degenerate R = (1, 65, 2, 66, 8, 72, 5, 69)(3, 67, 11, 75, 21, 85, 15, 79)(4, 68, 10, 74, 7, 71, 12, 76)(6, 70, 9, 73, 22, 86, 18, 82)(13, 77, 28, 92, 37, 101, 31, 95)(14, 78, 27, 91, 16, 80, 26, 90)(17, 81, 25, 89, 19, 83, 24, 88)(20, 84, 23, 87, 38, 102, 34, 98)(29, 93, 44, 108, 53, 117, 47, 111)(30, 94, 42, 106, 32, 96, 43, 107)(33, 97, 40, 104, 35, 99, 41, 105)(36, 100, 39, 103, 54, 118, 50, 114)(45, 109, 60, 124, 52, 116, 55, 119)(46, 110, 59, 123, 48, 112, 58, 122)(49, 113, 57, 121, 51, 115, 56, 120)(61, 125, 64, 128, 62, 126, 63, 127)(129, 193, 131, 195, 141, 205, 157, 221, 173, 237, 182, 246, 166, 230, 150, 214, 136, 200, 149, 213, 165, 229, 181, 245, 180, 244, 164, 228, 148, 212, 134, 198)(130, 194, 137, 201, 151, 215, 167, 231, 183, 247, 175, 239, 159, 223, 143, 207, 133, 197, 146, 210, 162, 226, 178, 242, 188, 252, 172, 236, 156, 220, 139, 203)(132, 196, 145, 209, 161, 225, 177, 241, 190, 254, 174, 238, 160, 224, 142, 206, 135, 199, 147, 211, 163, 227, 179, 243, 189, 253, 176, 240, 158, 222, 144, 208)(138, 202, 154, 218, 170, 234, 186, 250, 192, 256, 184, 248, 169, 233, 152, 216, 140, 204, 155, 219, 171, 235, 187, 251, 191, 255, 185, 249, 168, 232, 153, 217) L = (1, 132)(2, 138)(3, 142)(4, 136)(5, 140)(6, 147)(7, 129)(8, 135)(9, 152)(10, 133)(11, 155)(12, 130)(13, 158)(14, 149)(15, 154)(16, 131)(17, 134)(18, 153)(19, 150)(20, 161)(21, 144)(22, 145)(23, 168)(24, 146)(25, 137)(26, 139)(27, 143)(28, 170)(29, 174)(30, 165)(31, 171)(32, 141)(33, 166)(34, 169)(35, 148)(36, 179)(37, 160)(38, 163)(39, 184)(40, 162)(41, 151)(42, 159)(43, 156)(44, 187)(45, 189)(46, 181)(47, 186)(48, 157)(49, 164)(50, 185)(51, 182)(52, 190)(53, 176)(54, 177)(55, 191)(56, 178)(57, 167)(58, 172)(59, 175)(60, 192)(61, 180)(62, 173)(63, 188)(64, 183)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4^8 ), ( 4^32 ) } Outer automorphisms :: reflexible Dual of E23.819 Graph:: bipartite v = 20 e = 128 f = 64 degree seq :: [ 8^16, 32^4 ] E23.823 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {8, 8, 16}) Quotient :: edge Aut^+ = C4 . D16 = C8 . (C4 x C2) (small group id <64, 49>) Aut = $<128, 953>$ (small group id <128, 953>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^-1 * T2^-1 * T1 * T2^-1, T1^8, T2^4 * T1^-1 * T2^-4 * T1^-3, T2^2 * T1^-1 * T2^-1 * T1^-2 * T2^-5 * T1^-1, T2^16 ] Map:: non-degenerate R = (1, 3, 9, 19, 33, 49, 58, 42, 26, 41, 57, 56, 40, 25, 13, 5)(2, 7, 17, 31, 47, 63, 52, 36, 24, 39, 55, 64, 48, 32, 18, 8)(4, 11, 22, 37, 53, 60, 44, 28, 14, 27, 43, 59, 50, 34, 20, 10)(6, 15, 29, 45, 61, 54, 38, 23, 12, 21, 35, 51, 62, 46, 30, 16)(65, 66, 70, 78, 90, 88, 76, 68)(67, 72, 79, 92, 105, 100, 85, 74)(69, 71, 80, 91, 106, 103, 87, 75)(73, 82, 93, 108, 121, 116, 99, 84)(77, 81, 94, 107, 122, 119, 102, 86)(83, 96, 109, 124, 120, 127, 115, 98)(89, 95, 110, 123, 113, 128, 118, 101)(97, 112, 125, 117, 104, 111, 126, 114) L = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 81)(18, 82)(19, 83)(20, 84)(21, 85)(22, 86)(23, 87)(24, 88)(25, 89)(26, 90)(27, 91)(28, 92)(29, 93)(30, 94)(31, 95)(32, 96)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128) local type(s) :: { ( 16^8 ), ( 16^16 ) } Outer automorphisms :: reflexible Dual of E23.826 Transitivity :: ET+ Graph:: bipartite v = 12 e = 64 f = 8 degree seq :: [ 8^8, 16^4 ] E23.824 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {8, 8, 16}) Quotient :: edge Aut^+ = C4 . D16 = C8 . (C4 x C2) (small group id <64, 49>) Aut = $<128, 953>$ (small group id <128, 953>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1^2 * T2^-1 * T1^-1, T1^-3 * T2 * T1^-1 * T2, T2^-1 * T1^-1 * T2^-1 * T1^-3, T2^-2 * T1^-1 * T2^-2 * T1, (T2 * T1 * T2 * T1^-1)^2, T2^3 * T1 * T2^-5 * T1^-1 ] Map:: non-degenerate R = (1, 3, 10, 29, 46, 57, 41, 23, 36, 25, 43, 59, 52, 35, 17, 5)(2, 7, 22, 40, 56, 45, 28, 9, 27, 15, 33, 50, 60, 44, 26, 8)(4, 12, 32, 49, 62, 47, 31, 11, 18, 16, 34, 51, 61, 48, 30, 14)(6, 19, 37, 53, 63, 55, 39, 21, 13, 24, 42, 58, 64, 54, 38, 20)(65, 66, 70, 82, 100, 91, 77, 68)(67, 73, 83, 78, 89, 72, 88, 75)(69, 79, 84, 76, 87, 71, 85, 80)(74, 90, 101, 95, 107, 92, 106, 94)(81, 86, 102, 98, 105, 97, 103, 96)(93, 109, 117, 112, 123, 108, 122, 111)(99, 114, 118, 113, 121, 104, 119, 115)(110, 124, 127, 126, 116, 120, 128, 125) 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) :: { ( 16^8 ), ( 16^16 ) } Outer automorphisms :: reflexible Dual of E23.825 Transitivity :: ET+ Graph:: bipartite v = 12 e = 64 f = 8 degree seq :: [ 8^8, 16^4 ] E23.825 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {8, 8, 16}) Quotient :: loop Aut^+ = C4 . D16 = C8 . (C4 x C2) (small group id <64, 49>) Aut = $<128, 953>$ (small group id <128, 953>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, T2^-1 * T1^2 * T2^-1, (F * T1)^2, T1^-1 * T2^-1 * T1^-4 * T2^-1 * T1^-1, T1^8, T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, (T2^-1 * T1^-1)^16 ] Map:: non-degenerate R = (1, 65, 3, 67, 6, 70, 15, 79, 26, 90, 23, 87, 11, 75, 5, 69)(2, 66, 7, 71, 14, 78, 27, 91, 22, 86, 12, 76, 4, 68, 8, 72)(9, 73, 19, 83, 28, 92, 25, 89, 13, 77, 21, 85, 10, 74, 20, 84)(16, 80, 29, 93, 24, 88, 32, 96, 18, 82, 31, 95, 17, 81, 30, 94)(33, 97, 41, 105, 36, 100, 44, 108, 35, 99, 43, 107, 34, 98, 42, 106)(37, 101, 45, 109, 40, 104, 48, 112, 39, 103, 47, 111, 38, 102, 46, 110)(49, 113, 57, 121, 52, 116, 60, 124, 51, 115, 59, 123, 50, 114, 58, 122)(53, 117, 61, 125, 56, 120, 64, 128, 55, 119, 63, 127, 54, 118, 62, 126) L = (1, 66)(2, 70)(3, 73)(4, 65)(5, 74)(6, 78)(7, 80)(8, 81)(9, 79)(10, 67)(11, 68)(12, 82)(13, 69)(14, 90)(15, 92)(16, 91)(17, 71)(18, 72)(19, 97)(20, 98)(21, 99)(22, 75)(23, 77)(24, 76)(25, 100)(26, 86)(27, 88)(28, 87)(29, 101)(30, 102)(31, 103)(32, 104)(33, 89)(34, 83)(35, 84)(36, 85)(37, 96)(38, 93)(39, 94)(40, 95)(41, 113)(42, 114)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 108)(50, 105)(51, 106)(52, 107)(53, 112)(54, 109)(55, 110)(56, 111)(57, 127)(58, 128)(59, 125)(60, 126)(61, 122)(62, 123)(63, 124)(64, 121) local type(s) :: { ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E23.824 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 8 e = 64 f = 12 degree seq :: [ 16^8 ] E23.826 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {8, 8, 16}) Quotient :: loop Aut^+ = C4 . D16 = C8 . (C4 x C2) (small group id <64, 49>) Aut = $<128, 953>$ (small group id <128, 953>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T2 * T1^2 * T2, T1^8, T2^8, T1 * T2^-1 * T1 * T2^-1 * T1^2 * T2^-1 * T1^-1 * T2^-1 * T1, T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 65, 3, 67, 10, 74, 21, 85, 26, 90, 15, 79, 6, 70, 5, 69)(2, 66, 7, 71, 4, 68, 12, 76, 22, 86, 27, 91, 14, 78, 8, 72)(9, 73, 19, 83, 11, 75, 23, 87, 28, 92, 25, 89, 13, 77, 20, 84)(16, 80, 29, 93, 17, 81, 31, 95, 24, 88, 32, 96, 18, 82, 30, 94)(33, 97, 41, 105, 34, 98, 43, 107, 36, 100, 44, 108, 35, 99, 42, 106)(37, 101, 45, 109, 38, 102, 47, 111, 40, 104, 48, 112, 39, 103, 46, 110)(49, 113, 57, 121, 50, 114, 59, 123, 52, 116, 60, 124, 51, 115, 58, 122)(53, 117, 61, 125, 54, 118, 63, 127, 56, 120, 64, 128, 55, 119, 62, 126) L = (1, 66)(2, 70)(3, 73)(4, 65)(5, 77)(6, 78)(7, 80)(8, 82)(9, 69)(10, 68)(11, 67)(12, 81)(13, 79)(14, 90)(15, 92)(16, 72)(17, 71)(18, 91)(19, 97)(20, 99)(21, 75)(22, 74)(23, 98)(24, 76)(25, 100)(26, 86)(27, 88)(28, 85)(29, 101)(30, 103)(31, 102)(32, 104)(33, 84)(34, 83)(35, 89)(36, 87)(37, 94)(38, 93)(39, 96)(40, 95)(41, 113)(42, 115)(43, 114)(44, 116)(45, 117)(46, 119)(47, 118)(48, 120)(49, 106)(50, 105)(51, 108)(52, 107)(53, 110)(54, 109)(55, 112)(56, 111)(57, 128)(58, 127)(59, 126)(60, 125)(61, 123)(62, 121)(63, 124)(64, 122) local type(s) :: { ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E23.823 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 8 e = 64 f = 12 degree seq :: [ 16^8 ] E23.827 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 8, 16}) Quotient :: dipole Aut^+ = C4 . D16 = C8 . (C4 x C2) (small group id <64, 49>) Aut = $<128, 953>$ (small group id <128, 953>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-1, R * Y2 * R * Y3, (R * Y1)^2, Y1^-1 * Y2^-1 * Y1 * Y2^-1, Y1^8, Y2^2 * Y1^-1 * Y2^-1 * Y1^-2 * Y2^-5 * Y1^-1, Y2^3 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^4 * Y1^-2, (Y3^-1 * Y1^-1)^8, Y2^16 ] Map:: R = (1, 65, 2, 66, 6, 70, 14, 78, 26, 90, 24, 88, 12, 76, 4, 68)(3, 67, 8, 72, 15, 79, 28, 92, 41, 105, 36, 100, 21, 85, 10, 74)(5, 69, 7, 71, 16, 80, 27, 91, 42, 106, 39, 103, 23, 87, 11, 75)(9, 73, 18, 82, 29, 93, 44, 108, 57, 121, 52, 116, 35, 99, 20, 84)(13, 77, 17, 81, 30, 94, 43, 107, 58, 122, 55, 119, 38, 102, 22, 86)(19, 83, 32, 96, 45, 109, 60, 124, 56, 120, 63, 127, 51, 115, 34, 98)(25, 89, 31, 95, 46, 110, 59, 123, 49, 113, 64, 128, 54, 118, 37, 101)(33, 97, 48, 112, 61, 125, 53, 117, 40, 104, 47, 111, 62, 126, 50, 114)(129, 193, 131, 195, 137, 201, 147, 211, 161, 225, 177, 241, 186, 250, 170, 234, 154, 218, 169, 233, 185, 249, 184, 248, 168, 232, 153, 217, 141, 205, 133, 197)(130, 194, 135, 199, 145, 209, 159, 223, 175, 239, 191, 255, 180, 244, 164, 228, 152, 216, 167, 231, 183, 247, 192, 256, 176, 240, 160, 224, 146, 210, 136, 200)(132, 196, 139, 203, 150, 214, 165, 229, 181, 245, 188, 252, 172, 236, 156, 220, 142, 206, 155, 219, 171, 235, 187, 251, 178, 242, 162, 226, 148, 212, 138, 202)(134, 198, 143, 207, 157, 221, 173, 237, 189, 253, 182, 246, 166, 230, 151, 215, 140, 204, 149, 213, 163, 227, 179, 243, 190, 254, 174, 238, 158, 222, 144, 208) L = (1, 131)(2, 135)(3, 137)(4, 139)(5, 129)(6, 143)(7, 145)(8, 130)(9, 147)(10, 132)(11, 150)(12, 149)(13, 133)(14, 155)(15, 157)(16, 134)(17, 159)(18, 136)(19, 161)(20, 138)(21, 163)(22, 165)(23, 140)(24, 167)(25, 141)(26, 169)(27, 171)(28, 142)(29, 173)(30, 144)(31, 175)(32, 146)(33, 177)(34, 148)(35, 179)(36, 152)(37, 181)(38, 151)(39, 183)(40, 153)(41, 185)(42, 154)(43, 187)(44, 156)(45, 189)(46, 158)(47, 191)(48, 160)(49, 186)(50, 162)(51, 190)(52, 164)(53, 188)(54, 166)(55, 192)(56, 168)(57, 184)(58, 170)(59, 178)(60, 172)(61, 182)(62, 174)(63, 180)(64, 176)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ), ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ) } Outer automorphisms :: reflexible Dual of E23.829 Graph:: bipartite v = 12 e = 128 f = 72 degree seq :: [ 16^8, 32^4 ] E23.828 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 8, 16}) Quotient :: dipole Aut^+ = C4 . D16 = C8 . (C4 x C2) (small group id <64, 49>) Aut = $<128, 953>$ (small group id <128, 953>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y1^-1 * Y2 * Y1^2 * Y2^-1 * Y1^-1, Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-2, Y2^2 * Y1 * Y2^2 * Y1^-1, (Y2^-1 * Y1 * Y2^-1 * Y1^-1)^2, Y2 * Y1 * Y2^-7 * Y1^-1, (Y3^-1 * Y1^-1)^8 ] Map:: R = (1, 65, 2, 66, 6, 70, 18, 82, 36, 100, 27, 91, 13, 77, 4, 68)(3, 67, 9, 73, 19, 83, 14, 78, 25, 89, 8, 72, 24, 88, 11, 75)(5, 69, 15, 79, 20, 84, 12, 76, 23, 87, 7, 71, 21, 85, 16, 80)(10, 74, 26, 90, 37, 101, 31, 95, 43, 107, 28, 92, 42, 106, 30, 94)(17, 81, 22, 86, 38, 102, 34, 98, 41, 105, 33, 97, 39, 103, 32, 96)(29, 93, 45, 109, 53, 117, 48, 112, 59, 123, 44, 108, 58, 122, 47, 111)(35, 99, 50, 114, 54, 118, 49, 113, 57, 121, 40, 104, 55, 119, 51, 115)(46, 110, 60, 124, 63, 127, 62, 126, 52, 116, 56, 120, 64, 128, 61, 125)(129, 193, 131, 195, 138, 202, 157, 221, 174, 238, 185, 249, 169, 233, 151, 215, 164, 228, 153, 217, 171, 235, 187, 251, 180, 244, 163, 227, 145, 209, 133, 197)(130, 194, 135, 199, 150, 214, 168, 232, 184, 248, 173, 237, 156, 220, 137, 201, 155, 219, 143, 207, 161, 225, 178, 242, 188, 252, 172, 236, 154, 218, 136, 200)(132, 196, 140, 204, 160, 224, 177, 241, 190, 254, 175, 239, 159, 223, 139, 203, 146, 210, 144, 208, 162, 226, 179, 243, 189, 253, 176, 240, 158, 222, 142, 206)(134, 198, 147, 211, 165, 229, 181, 245, 191, 255, 183, 247, 167, 231, 149, 213, 141, 205, 152, 216, 170, 234, 186, 250, 192, 256, 182, 246, 166, 230, 148, 212) L = (1, 131)(2, 135)(3, 138)(4, 140)(5, 129)(6, 147)(7, 150)(8, 130)(9, 155)(10, 157)(11, 146)(12, 160)(13, 152)(14, 132)(15, 161)(16, 162)(17, 133)(18, 144)(19, 165)(20, 134)(21, 141)(22, 168)(23, 164)(24, 170)(25, 171)(26, 136)(27, 143)(28, 137)(29, 174)(30, 142)(31, 139)(32, 177)(33, 178)(34, 179)(35, 145)(36, 153)(37, 181)(38, 148)(39, 149)(40, 184)(41, 151)(42, 186)(43, 187)(44, 154)(45, 156)(46, 185)(47, 159)(48, 158)(49, 190)(50, 188)(51, 189)(52, 163)(53, 191)(54, 166)(55, 167)(56, 173)(57, 169)(58, 192)(59, 180)(60, 172)(61, 176)(62, 175)(63, 183)(64, 182)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ), ( 2, 16, 2, 16, 2, 16, 2, 16, 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 E23.830 Graph:: bipartite v = 12 e = 128 f = 72 degree seq :: [ 16^8, 32^4 ] E23.829 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 8, 16}) Quotient :: dipole Aut^+ = C4 . D16 = C8 . (C4 x C2) (small group id <64, 49>) Aut = $<128, 953>$ (small group id <128, 953>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y3^-1 * Y2 * Y3^-1, (R * Y2 * Y3^-1)^2, Y2^8, Y3^7 * Y2^-1 * Y3^-1 * Y2^-3, Y3^-4 * Y2^2 * Y3^4 * Y2^-2, (Y3^-1 * Y1^-1)^16 ] Map:: R = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 81)(18, 82)(19, 83)(20, 84)(21, 85)(22, 86)(23, 87)(24, 88)(25, 89)(26, 90)(27, 91)(28, 92)(29, 93)(30, 94)(31, 95)(32, 96)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)(129, 193, 130, 194, 134, 198, 142, 206, 154, 218, 152, 216, 140, 204, 132, 196)(131, 195, 136, 200, 143, 207, 156, 220, 169, 233, 164, 228, 149, 213, 138, 202)(133, 197, 135, 199, 144, 208, 155, 219, 170, 234, 167, 231, 151, 215, 139, 203)(137, 201, 146, 210, 157, 221, 172, 236, 185, 249, 180, 244, 163, 227, 148, 212)(141, 205, 145, 209, 158, 222, 171, 235, 186, 250, 183, 247, 166, 230, 150, 214)(147, 211, 160, 224, 173, 237, 188, 252, 184, 248, 191, 255, 179, 243, 162, 226)(153, 217, 159, 223, 174, 238, 187, 251, 177, 241, 192, 256, 182, 246, 165, 229)(161, 225, 176, 240, 189, 253, 181, 245, 168, 232, 175, 239, 190, 254, 178, 242) L = (1, 131)(2, 135)(3, 137)(4, 139)(5, 129)(6, 143)(7, 145)(8, 130)(9, 147)(10, 132)(11, 150)(12, 149)(13, 133)(14, 155)(15, 157)(16, 134)(17, 159)(18, 136)(19, 161)(20, 138)(21, 163)(22, 165)(23, 140)(24, 167)(25, 141)(26, 169)(27, 171)(28, 142)(29, 173)(30, 144)(31, 175)(32, 146)(33, 177)(34, 148)(35, 179)(36, 152)(37, 181)(38, 151)(39, 183)(40, 153)(41, 185)(42, 154)(43, 187)(44, 156)(45, 189)(46, 158)(47, 191)(48, 160)(49, 186)(50, 162)(51, 190)(52, 164)(53, 188)(54, 166)(55, 192)(56, 168)(57, 184)(58, 170)(59, 178)(60, 172)(61, 182)(62, 174)(63, 180)(64, 176)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) } Outer automorphisms :: reflexible Dual of E23.827 Graph:: simple bipartite v = 72 e = 128 f = 12 degree seq :: [ 2^64, 16^8 ] E23.830 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {8, 8, 16}) Quotient :: dipole Aut^+ = C4 . D16 = C8 . (C4 x C2) (small group id <64, 49>) Aut = $<128, 953>$ (small group id <128, 953>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y1)^2, (R * Y3)^2, Y3^-1 * Y2 * Y3^-1 * Y2^3, Y2^-1 * Y3 * Y2^2 * Y3^-1 * Y2^-1, (R * Y2 * Y3^-1)^2, Y2 * Y3^2 * Y2^-1 * Y3^2, Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-2, Y3^3 * Y2 * Y3^-5 * Y2^-1, (Y3^-1 * Y1^-1)^16 ] Map:: R = (1, 65)(2, 66)(3, 67)(4, 68)(5, 69)(6, 70)(7, 71)(8, 72)(9, 73)(10, 74)(11, 75)(12, 76)(13, 77)(14, 78)(15, 79)(16, 80)(17, 81)(18, 82)(19, 83)(20, 84)(21, 85)(22, 86)(23, 87)(24, 88)(25, 89)(26, 90)(27, 91)(28, 92)(29, 93)(30, 94)(31, 95)(32, 96)(33, 97)(34, 98)(35, 99)(36, 100)(37, 101)(38, 102)(39, 103)(40, 104)(41, 105)(42, 106)(43, 107)(44, 108)(45, 109)(46, 110)(47, 111)(48, 112)(49, 113)(50, 114)(51, 115)(52, 116)(53, 117)(54, 118)(55, 119)(56, 120)(57, 121)(58, 122)(59, 123)(60, 124)(61, 125)(62, 126)(63, 127)(64, 128)(129, 193, 130, 194, 134, 198, 146, 210, 164, 228, 155, 219, 141, 205, 132, 196)(131, 195, 137, 201, 147, 211, 142, 206, 153, 217, 136, 200, 152, 216, 139, 203)(133, 197, 143, 207, 148, 212, 140, 204, 151, 215, 135, 199, 149, 213, 144, 208)(138, 202, 154, 218, 165, 229, 159, 223, 171, 235, 156, 220, 170, 234, 158, 222)(145, 209, 150, 214, 166, 230, 162, 226, 169, 233, 161, 225, 167, 231, 160, 224)(157, 221, 173, 237, 181, 245, 176, 240, 187, 251, 172, 236, 186, 250, 175, 239)(163, 227, 178, 242, 182, 246, 177, 241, 185, 249, 168, 232, 183, 247, 179, 243)(174, 238, 188, 252, 191, 255, 190, 254, 180, 244, 184, 248, 192, 256, 189, 253) L = (1, 131)(2, 135)(3, 138)(4, 140)(5, 129)(6, 147)(7, 150)(8, 130)(9, 155)(10, 157)(11, 146)(12, 160)(13, 152)(14, 132)(15, 161)(16, 162)(17, 133)(18, 144)(19, 165)(20, 134)(21, 141)(22, 168)(23, 164)(24, 170)(25, 171)(26, 136)(27, 143)(28, 137)(29, 174)(30, 142)(31, 139)(32, 177)(33, 178)(34, 179)(35, 145)(36, 153)(37, 181)(38, 148)(39, 149)(40, 184)(41, 151)(42, 186)(43, 187)(44, 154)(45, 156)(46, 185)(47, 159)(48, 158)(49, 190)(50, 188)(51, 189)(52, 163)(53, 191)(54, 166)(55, 167)(56, 173)(57, 169)(58, 192)(59, 180)(60, 172)(61, 176)(62, 175)(63, 183)(64, 182)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 16, 32 ), ( 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32, 16, 32 ) } Outer automorphisms :: reflexible Dual of E23.828 Graph:: simple bipartite v = 72 e = 128 f = 12 degree seq :: [ 2^64, 16^8 ] E23.831 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 32, 32}) Quotient :: edge Aut^+ = C32 x C2 (small group id <64, 50>) Aut = $<128, 991>$ (small group id <128, 991>) |r| :: 2 Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, (T2^-1, T1), T2^16 * T1^2 ] Map:: non-degenerate R = (1, 3, 9, 17, 25, 33, 41, 49, 57, 62, 54, 46, 38, 30, 22, 14, 6, 13, 21, 29, 37, 45, 53, 61, 60, 52, 44, 36, 28, 20, 12, 5)(2, 7, 15, 23, 31, 39, 47, 55, 63, 59, 51, 43, 35, 27, 19, 11, 4, 10, 18, 26, 34, 42, 50, 58, 64, 56, 48, 40, 32, 24, 16, 8)(65, 66, 70, 68)(67, 71, 77, 74)(69, 72, 78, 75)(73, 79, 85, 82)(76, 80, 86, 83)(81, 87, 93, 90)(84, 88, 94, 91)(89, 95, 101, 98)(92, 96, 102, 99)(97, 103, 109, 106)(100, 104, 110, 107)(105, 111, 117, 114)(108, 112, 118, 115)(113, 119, 125, 122)(116, 120, 126, 123)(121, 127, 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) :: { ( 64^4 ), ( 64^32 ) } Outer automorphisms :: reflexible Dual of E23.832 Transitivity :: ET+ Graph:: bipartite v = 18 e = 64 f = 2 degree seq :: [ 4^16, 32^2 ] E23.832 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 32, 32}) Quotient :: loop Aut^+ = C32 x C2 (small group id <64, 50>) Aut = $<128, 991>$ (small group id <128, 991>) |r| :: 2 Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, (T2^-1, T1), T2^16 * T1^2 ] Map:: non-degenerate R = (1, 65, 3, 67, 9, 73, 17, 81, 25, 89, 33, 97, 41, 105, 49, 113, 57, 121, 62, 126, 54, 118, 46, 110, 38, 102, 30, 94, 22, 86, 14, 78, 6, 70, 13, 77, 21, 85, 29, 93, 37, 101, 45, 109, 53, 117, 61, 125, 60, 124, 52, 116, 44, 108, 36, 100, 28, 92, 20, 84, 12, 76, 5, 69)(2, 66, 7, 71, 15, 79, 23, 87, 31, 95, 39, 103, 47, 111, 55, 119, 63, 127, 59, 123, 51, 115, 43, 107, 35, 99, 27, 91, 19, 83, 11, 75, 4, 68, 10, 74, 18, 82, 26, 90, 34, 98, 42, 106, 50, 114, 58, 122, 64, 128, 56, 120, 48, 112, 40, 104, 32, 96, 24, 88, 16, 80, 8, 72) L = (1, 66)(2, 70)(3, 71)(4, 65)(5, 72)(6, 68)(7, 77)(8, 78)(9, 79)(10, 67)(11, 69)(12, 80)(13, 74)(14, 75)(15, 85)(16, 86)(17, 87)(18, 73)(19, 76)(20, 88)(21, 82)(22, 83)(23, 93)(24, 94)(25, 95)(26, 81)(27, 84)(28, 96)(29, 90)(30, 91)(31, 101)(32, 102)(33, 103)(34, 89)(35, 92)(36, 104)(37, 98)(38, 99)(39, 109)(40, 110)(41, 111)(42, 97)(43, 100)(44, 112)(45, 106)(46, 107)(47, 117)(48, 118)(49, 119)(50, 105)(51, 108)(52, 120)(53, 114)(54, 115)(55, 125)(56, 126)(57, 127)(58, 113)(59, 116)(60, 128)(61, 122)(62, 123)(63, 124)(64, 121) 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 E23.831 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 64 f = 18 degree seq :: [ 64^2 ] E23.833 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 32, 32}) Quotient :: dipole Aut^+ = C32 x C2 (small group id <64, 50>) Aut = $<128, 991>$ (small group id <128, 991>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, (R * Y3)^2, (R * Y2)^2, (R * Y1)^2, (Y2^-1, Y1^-1), (Y3^-1, Y2^-1), Y1^4, Y2^6 * Y3 * Y2^10 * Y1^-1, Y2^-4 * Y1 * Y3^-1 * Y2^-6 * Y1 * Y3^-1 * Y2^-6 * Y1 * Y3^-1, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 65, 2, 66, 6, 70, 4, 68)(3, 67, 7, 71, 13, 77, 10, 74)(5, 69, 8, 72, 14, 78, 11, 75)(9, 73, 15, 79, 21, 85, 18, 82)(12, 76, 16, 80, 22, 86, 19, 83)(17, 81, 23, 87, 29, 93, 26, 90)(20, 84, 24, 88, 30, 94, 27, 91)(25, 89, 31, 95, 37, 101, 34, 98)(28, 92, 32, 96, 38, 102, 35, 99)(33, 97, 39, 103, 45, 109, 42, 106)(36, 100, 40, 104, 46, 110, 43, 107)(41, 105, 47, 111, 53, 117, 50, 114)(44, 108, 48, 112, 54, 118, 51, 115)(49, 113, 55, 119, 61, 125, 58, 122)(52, 116, 56, 120, 62, 126, 59, 123)(57, 121, 63, 127, 60, 124, 64, 128)(129, 193, 131, 195, 137, 201, 145, 209, 153, 217, 161, 225, 169, 233, 177, 241, 185, 249, 190, 254, 182, 246, 174, 238, 166, 230, 158, 222, 150, 214, 142, 206, 134, 198, 141, 205, 149, 213, 157, 221, 165, 229, 173, 237, 181, 245, 189, 253, 188, 252, 180, 244, 172, 236, 164, 228, 156, 220, 148, 212, 140, 204, 133, 197)(130, 194, 135, 199, 143, 207, 151, 215, 159, 223, 167, 231, 175, 239, 183, 247, 191, 255, 187, 251, 179, 243, 171, 235, 163, 227, 155, 219, 147, 211, 139, 203, 132, 196, 138, 202, 146, 210, 154, 218, 162, 226, 170, 234, 178, 242, 186, 250, 192, 256, 184, 248, 176, 240, 168, 232, 160, 224, 152, 216, 144, 208, 136, 200) L = (1, 132)(2, 129)(3, 138)(4, 134)(5, 139)(6, 130)(7, 131)(8, 133)(9, 146)(10, 141)(11, 142)(12, 147)(13, 135)(14, 136)(15, 137)(16, 140)(17, 154)(18, 149)(19, 150)(20, 155)(21, 143)(22, 144)(23, 145)(24, 148)(25, 162)(26, 157)(27, 158)(28, 163)(29, 151)(30, 152)(31, 153)(32, 156)(33, 170)(34, 165)(35, 166)(36, 171)(37, 159)(38, 160)(39, 161)(40, 164)(41, 178)(42, 173)(43, 174)(44, 179)(45, 167)(46, 168)(47, 169)(48, 172)(49, 186)(50, 181)(51, 182)(52, 187)(53, 175)(54, 176)(55, 177)(56, 180)(57, 192)(58, 189)(59, 190)(60, 191)(61, 183)(62, 184)(63, 185)(64, 188)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 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 E23.834 Graph:: bipartite v = 18 e = 128 f = 66 degree seq :: [ 8^16, 64^2 ] E23.834 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 32, 32}) Quotient :: dipole Aut^+ = C32 x C2 (small group id <64, 50>) Aut = $<128, 991>$ (small group id <128, 991>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (Y3^-1, Y1^-1), (R * Y1)^2, Y1^-1 * Y3^2 * Y1 * Y3^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^4, Y1^-1 * Y3 * Y1^-6 * Y3 * Y1^-9, (Y1^-1 * Y3^-1)^32 ] Map:: R = (1, 65, 2, 66, 6, 70, 13, 77, 21, 85, 29, 93, 37, 101, 45, 109, 53, 117, 61, 125, 57, 121, 49, 113, 41, 105, 33, 97, 25, 89, 17, 81, 9, 73, 16, 80, 24, 88, 32, 96, 40, 104, 48, 112, 56, 120, 64, 128, 59, 123, 51, 115, 43, 107, 35, 99, 27, 91, 19, 83, 11, 75, 4, 68)(3, 67, 7, 71, 14, 78, 22, 86, 30, 94, 38, 102, 46, 110, 54, 118, 62, 126, 60, 124, 52, 116, 44, 108, 36, 100, 28, 92, 20, 84, 12, 76, 5, 69, 8, 72, 15, 79, 23, 87, 31, 95, 39, 103, 47, 111, 55, 119, 63, 127, 58, 122, 50, 114, 42, 106, 34, 98, 26, 90, 18, 82, 10, 74)(129, 193)(130, 194)(131, 195)(132, 196)(133, 197)(134, 198)(135, 199)(136, 200)(137, 201)(138, 202)(139, 203)(140, 204)(141, 205)(142, 206)(143, 207)(144, 208)(145, 209)(146, 210)(147, 211)(148, 212)(149, 213)(150, 214)(151, 215)(152, 216)(153, 217)(154, 218)(155, 219)(156, 220)(157, 221)(158, 222)(159, 223)(160, 224)(161, 225)(162, 226)(163, 227)(164, 228)(165, 229)(166, 230)(167, 231)(168, 232)(169, 233)(170, 234)(171, 235)(172, 236)(173, 237)(174, 238)(175, 239)(176, 240)(177, 241)(178, 242)(179, 243)(180, 244)(181, 245)(182, 246)(183, 247)(184, 248)(185, 249)(186, 250)(187, 251)(188, 252)(189, 253)(190, 254)(191, 255)(192, 256) L = (1, 131)(2, 135)(3, 137)(4, 138)(5, 129)(6, 142)(7, 144)(8, 130)(9, 133)(10, 145)(11, 146)(12, 132)(13, 150)(14, 152)(15, 134)(16, 136)(17, 140)(18, 153)(19, 154)(20, 139)(21, 158)(22, 160)(23, 141)(24, 143)(25, 148)(26, 161)(27, 162)(28, 147)(29, 166)(30, 168)(31, 149)(32, 151)(33, 156)(34, 169)(35, 170)(36, 155)(37, 174)(38, 176)(39, 157)(40, 159)(41, 164)(42, 177)(43, 178)(44, 163)(45, 182)(46, 184)(47, 165)(48, 167)(49, 172)(50, 185)(51, 186)(52, 171)(53, 190)(54, 192)(55, 173)(56, 175)(57, 180)(58, 189)(59, 191)(60, 179)(61, 188)(62, 187)(63, 181)(64, 183)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 8, 64 ), ( 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 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 E23.833 Graph:: simple bipartite v = 66 e = 128 f = 18 degree seq :: [ 2^64, 64^2 ] E23.835 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 32, 32}) Quotient :: edge Aut^+ = C32 : C2 (small group id <64, 51>) Aut = $<128, 995>$ (small group id <128, 995>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T2 * T1^-1 * T2^-1 * T1^-1, T1^-1 * T2^16 * T1^-1 ] Map:: non-degenerate R = (1, 3, 10, 18, 26, 34, 42, 50, 58, 62, 54, 46, 38, 30, 22, 14, 6, 13, 21, 29, 37, 45, 53, 61, 60, 52, 44, 36, 28, 20, 12, 5)(2, 7, 15, 23, 31, 39, 47, 55, 63, 59, 51, 43, 35, 27, 19, 11, 4, 9, 17, 25, 33, 41, 49, 57, 64, 56, 48, 40, 32, 24, 16, 8)(65, 66, 70, 68)(67, 73, 77, 71)(69, 75, 78, 72)(74, 79, 85, 81)(76, 80, 86, 83)(82, 89, 93, 87)(84, 91, 94, 88)(90, 95, 101, 97)(92, 96, 102, 99)(98, 105, 109, 103)(100, 107, 110, 104)(106, 111, 117, 113)(108, 112, 118, 115)(114, 121, 125, 119)(116, 123, 126, 120)(122, 127, 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) :: { ( 64^4 ), ( 64^32 ) } Outer automorphisms :: reflexible Dual of E23.836 Transitivity :: ET+ Graph:: bipartite v = 18 e = 64 f = 2 degree seq :: [ 4^16, 32^2 ] E23.836 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 32, 32}) Quotient :: loop Aut^+ = C32 : C2 (small group id <64, 51>) Aut = $<128, 995>$ (small group id <128, 995>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T2 * T1^-1 * T2^-1 * T1^-1, T1^-1 * T2^16 * T1^-1 ] Map:: non-degenerate R = (1, 65, 3, 67, 10, 74, 18, 82, 26, 90, 34, 98, 42, 106, 50, 114, 58, 122, 62, 126, 54, 118, 46, 110, 38, 102, 30, 94, 22, 86, 14, 78, 6, 70, 13, 77, 21, 85, 29, 93, 37, 101, 45, 109, 53, 117, 61, 125, 60, 124, 52, 116, 44, 108, 36, 100, 28, 92, 20, 84, 12, 76, 5, 69)(2, 66, 7, 71, 15, 79, 23, 87, 31, 95, 39, 103, 47, 111, 55, 119, 63, 127, 59, 123, 51, 115, 43, 107, 35, 99, 27, 91, 19, 83, 11, 75, 4, 68, 9, 73, 17, 81, 25, 89, 33, 97, 41, 105, 49, 113, 57, 121, 64, 128, 56, 120, 48, 112, 40, 104, 32, 96, 24, 88, 16, 80, 8, 72) L = (1, 66)(2, 70)(3, 73)(4, 65)(5, 75)(6, 68)(7, 67)(8, 69)(9, 77)(10, 79)(11, 78)(12, 80)(13, 71)(14, 72)(15, 85)(16, 86)(17, 74)(18, 89)(19, 76)(20, 91)(21, 81)(22, 83)(23, 82)(24, 84)(25, 93)(26, 95)(27, 94)(28, 96)(29, 87)(30, 88)(31, 101)(32, 102)(33, 90)(34, 105)(35, 92)(36, 107)(37, 97)(38, 99)(39, 98)(40, 100)(41, 109)(42, 111)(43, 110)(44, 112)(45, 103)(46, 104)(47, 117)(48, 118)(49, 106)(50, 121)(51, 108)(52, 123)(53, 113)(54, 115)(55, 114)(56, 116)(57, 125)(58, 127)(59, 126)(60, 128)(61, 119)(62, 120)(63, 124)(64, 122) 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 E23.835 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 64 f = 18 degree seq :: [ 64^2 ] E23.837 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 32, 32}) Quotient :: dipole Aut^+ = C32 : C2 (small group id <64, 51>) Aut = $<128, 995>$ (small group id <128, 995>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y1 * Y3^-3, (R * Y1)^2, (R * Y3)^2, Y1^4, Y2 * Y3 * Y2^-1 * Y1^-1, Y3 * Y2 * Y1^-1 * Y2^-1, (R * Y2 * Y3^-1)^2, Y2^7 * Y1 * Y2^9 * Y1^-1, (Y2^-1 * Y1)^32 ] Map:: R = (1, 65, 2, 66, 6, 70, 4, 68)(3, 67, 9, 73, 13, 77, 7, 71)(5, 69, 11, 75, 14, 78, 8, 72)(10, 74, 15, 79, 21, 85, 17, 81)(12, 76, 16, 80, 22, 86, 19, 83)(18, 82, 25, 89, 29, 93, 23, 87)(20, 84, 27, 91, 30, 94, 24, 88)(26, 90, 31, 95, 37, 101, 33, 97)(28, 92, 32, 96, 38, 102, 35, 99)(34, 98, 41, 105, 45, 109, 39, 103)(36, 100, 43, 107, 46, 110, 40, 104)(42, 106, 47, 111, 53, 117, 49, 113)(44, 108, 48, 112, 54, 118, 51, 115)(50, 114, 57, 121, 61, 125, 55, 119)(52, 116, 59, 123, 62, 126, 56, 120)(58, 122, 63, 127, 60, 124, 64, 128)(129, 193, 131, 195, 138, 202, 146, 210, 154, 218, 162, 226, 170, 234, 178, 242, 186, 250, 190, 254, 182, 246, 174, 238, 166, 230, 158, 222, 150, 214, 142, 206, 134, 198, 141, 205, 149, 213, 157, 221, 165, 229, 173, 237, 181, 245, 189, 253, 188, 252, 180, 244, 172, 236, 164, 228, 156, 220, 148, 212, 140, 204, 133, 197)(130, 194, 135, 199, 143, 207, 151, 215, 159, 223, 167, 231, 175, 239, 183, 247, 191, 255, 187, 251, 179, 243, 171, 235, 163, 227, 155, 219, 147, 211, 139, 203, 132, 196, 137, 201, 145, 209, 153, 217, 161, 225, 169, 233, 177, 241, 185, 249, 192, 256, 184, 248, 176, 240, 168, 232, 160, 224, 152, 216, 144, 208, 136, 200) L = (1, 132)(2, 129)(3, 135)(4, 134)(5, 136)(6, 130)(7, 141)(8, 142)(9, 131)(10, 145)(11, 133)(12, 147)(13, 137)(14, 139)(15, 138)(16, 140)(17, 149)(18, 151)(19, 150)(20, 152)(21, 143)(22, 144)(23, 157)(24, 158)(25, 146)(26, 161)(27, 148)(28, 163)(29, 153)(30, 155)(31, 154)(32, 156)(33, 165)(34, 167)(35, 166)(36, 168)(37, 159)(38, 160)(39, 173)(40, 174)(41, 162)(42, 177)(43, 164)(44, 179)(45, 169)(46, 171)(47, 170)(48, 172)(49, 181)(50, 183)(51, 182)(52, 184)(53, 175)(54, 176)(55, 189)(56, 190)(57, 178)(58, 192)(59, 180)(60, 191)(61, 185)(62, 187)(63, 186)(64, 188)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 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 E23.838 Graph:: bipartite v = 18 e = 128 f = 66 degree seq :: [ 8^16, 64^2 ] E23.838 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 32, 32}) Quotient :: dipole Aut^+ = C32 : C2 (small group id <64, 51>) Aut = $<128, 995>$ (small group id <128, 995>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^4, (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y3^-1 * Y1 * Y3^-1, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^4, Y1^-1 * Y3^2 * Y1^-15 ] Map:: R = (1, 65, 2, 66, 6, 70, 13, 77, 21, 85, 29, 93, 37, 101, 45, 109, 53, 117, 61, 125, 57, 121, 49, 113, 41, 105, 33, 97, 25, 89, 17, 81, 9, 73, 16, 80, 24, 88, 32, 96, 40, 104, 48, 112, 56, 120, 64, 128, 60, 124, 52, 116, 44, 108, 36, 100, 28, 92, 20, 84, 12, 76, 4, 68)(3, 67, 8, 72, 14, 78, 23, 87, 30, 94, 39, 103, 46, 110, 55, 119, 62, 126, 59, 123, 51, 115, 43, 107, 35, 99, 27, 91, 19, 83, 11, 75, 5, 69, 7, 71, 15, 79, 22, 86, 31, 95, 38, 102, 47, 111, 54, 118, 63, 127, 58, 122, 50, 114, 42, 106, 34, 98, 26, 90, 18, 82, 10, 74)(129, 193)(130, 194)(131, 195)(132, 196)(133, 197)(134, 198)(135, 199)(136, 200)(137, 201)(138, 202)(139, 203)(140, 204)(141, 205)(142, 206)(143, 207)(144, 208)(145, 209)(146, 210)(147, 211)(148, 212)(149, 213)(150, 214)(151, 215)(152, 216)(153, 217)(154, 218)(155, 219)(156, 220)(157, 221)(158, 222)(159, 223)(160, 224)(161, 225)(162, 226)(163, 227)(164, 228)(165, 229)(166, 230)(167, 231)(168, 232)(169, 233)(170, 234)(171, 235)(172, 236)(173, 237)(174, 238)(175, 239)(176, 240)(177, 241)(178, 242)(179, 243)(180, 244)(181, 245)(182, 246)(183, 247)(184, 248)(185, 249)(186, 250)(187, 251)(188, 252)(189, 253)(190, 254)(191, 255)(192, 256) L = (1, 131)(2, 135)(3, 137)(4, 139)(5, 129)(6, 142)(7, 144)(8, 130)(9, 133)(10, 132)(11, 145)(12, 146)(13, 150)(14, 152)(15, 134)(16, 136)(17, 138)(18, 153)(19, 140)(20, 155)(21, 158)(22, 160)(23, 141)(24, 143)(25, 147)(26, 148)(27, 161)(28, 162)(29, 166)(30, 168)(31, 149)(32, 151)(33, 154)(34, 169)(35, 156)(36, 171)(37, 174)(38, 176)(39, 157)(40, 159)(41, 163)(42, 164)(43, 177)(44, 178)(45, 182)(46, 184)(47, 165)(48, 167)(49, 170)(50, 185)(51, 172)(52, 187)(53, 190)(54, 192)(55, 173)(56, 175)(57, 179)(58, 180)(59, 189)(60, 191)(61, 186)(62, 188)(63, 181)(64, 183)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 8, 64 ), ( 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 8, 64, 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 E23.837 Graph:: simple bipartite v = 66 e = 128 f = 18 degree seq :: [ 2^64, 64^2 ] E23.839 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 6, 6}) Quotient :: halfedge^2 Aut^+ = C3 x D22 (small group id <66, 2>) Aut = S3 x D22 (small group id <132, 5>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y3 * Y2, R * Y2 * R * Y3, (R * Y1)^2, Y1^-1 * Y2 * Y1^2 * Y2 * Y1^-1, Y1^6, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1 ] Map:: R = (1, 68, 2, 71, 5, 77, 11, 76, 10, 70, 4, 67)(3, 73, 7, 78, 12, 86, 20, 83, 17, 74, 8, 69)(6, 79, 13, 85, 19, 84, 18, 75, 9, 80, 14, 72)(15, 89, 23, 93, 27, 91, 25, 82, 16, 90, 24, 81)(21, 94, 28, 92, 26, 96, 30, 88, 22, 95, 29, 87)(31, 103, 37, 99, 33, 105, 39, 98, 32, 104, 38, 97)(34, 106, 40, 102, 36, 108, 42, 101, 35, 107, 41, 100)(43, 115, 49, 111, 45, 117, 51, 110, 44, 116, 50, 109)(46, 118, 52, 114, 48, 120, 54, 113, 47, 119, 53, 112)(55, 127, 61, 123, 57, 129, 63, 122, 56, 128, 62, 121)(58, 130, 64, 126, 60, 132, 66, 125, 59, 131, 65, 124) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 15)(8, 16)(10, 17)(11, 19)(13, 21)(14, 22)(18, 26)(20, 27)(23, 31)(24, 32)(25, 33)(28, 34)(29, 35)(30, 36)(37, 43)(38, 44)(39, 45)(40, 46)(41, 47)(42, 48)(49, 55)(50, 56)(51, 57)(52, 58)(53, 59)(54, 60)(61, 66)(62, 64)(63, 65)(67, 69)(68, 72)(70, 75)(71, 78)(73, 81)(74, 82)(76, 83)(77, 85)(79, 87)(80, 88)(84, 92)(86, 93)(89, 97)(90, 98)(91, 99)(94, 100)(95, 101)(96, 102)(103, 109)(104, 110)(105, 111)(106, 112)(107, 113)(108, 114)(115, 121)(116, 122)(117, 123)(118, 124)(119, 125)(120, 126)(127, 132)(128, 130)(129, 131) local type(s) :: { ( 12^12 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: v = 11 e = 66 f = 11 degree seq :: [ 12^11 ] E23.840 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 6, 6}) Quotient :: edge^2 Aut^+ = C3 x D22 (small group id <66, 2>) Aut = S3 x D22 (small group id <132, 5>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y1, (R * Y3)^2, R * Y2 * R * Y1, Y3^-1 * Y1 * Y3^2 * Y1 * Y3^-1, Y3^6, Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 ] Map:: R = (1, 67, 3, 69, 8, 74, 17, 83, 10, 76, 4, 70)(2, 68, 5, 71, 12, 78, 21, 87, 14, 80, 6, 72)(7, 73, 15, 81, 24, 90, 18, 84, 9, 75, 16, 82)(11, 77, 19, 85, 28, 94, 22, 88, 13, 79, 20, 86)(23, 89, 31, 97, 26, 92, 33, 99, 25, 91, 32, 98)(27, 93, 34, 100, 30, 96, 36, 102, 29, 95, 35, 101)(37, 103, 43, 109, 39, 105, 45, 111, 38, 104, 44, 110)(40, 106, 46, 112, 42, 108, 48, 114, 41, 107, 47, 113)(49, 115, 55, 121, 51, 117, 57, 123, 50, 116, 56, 122)(52, 118, 58, 124, 54, 120, 60, 126, 53, 119, 59, 125)(61, 127, 65, 131, 63, 129, 64, 130, 62, 128, 66, 132)(133, 134)(135, 139)(136, 141)(137, 143)(138, 145)(140, 144)(142, 146)(147, 155)(148, 157)(149, 156)(150, 158)(151, 159)(152, 161)(153, 160)(154, 162)(163, 169)(164, 170)(165, 171)(166, 172)(167, 173)(168, 174)(175, 181)(176, 182)(177, 183)(178, 184)(179, 185)(180, 186)(187, 193)(188, 194)(189, 195)(190, 196)(191, 197)(192, 198)(199, 200)(201, 205)(202, 207)(203, 209)(204, 211)(206, 210)(208, 212)(213, 221)(214, 223)(215, 222)(216, 224)(217, 225)(218, 227)(219, 226)(220, 228)(229, 235)(230, 236)(231, 237)(232, 238)(233, 239)(234, 240)(241, 247)(242, 248)(243, 249)(244, 250)(245, 251)(246, 252)(253, 259)(254, 260)(255, 261)(256, 262)(257, 263)(258, 264) L = (1, 133)(2, 134)(3, 135)(4, 136)(5, 137)(6, 138)(7, 139)(8, 140)(9, 141)(10, 142)(11, 143)(12, 144)(13, 145)(14, 146)(15, 147)(16, 148)(17, 149)(18, 150)(19, 151)(20, 152)(21, 153)(22, 154)(23, 155)(24, 156)(25, 157)(26, 158)(27, 159)(28, 160)(29, 161)(30, 162)(31, 163)(32, 164)(33, 165)(34, 166)(35, 167)(36, 168)(37, 169)(38, 170)(39, 171)(40, 172)(41, 173)(42, 174)(43, 175)(44, 176)(45, 177)(46, 178)(47, 179)(48, 180)(49, 181)(50, 182)(51, 183)(52, 184)(53, 185)(54, 186)(55, 187)(56, 188)(57, 189)(58, 190)(59, 191)(60, 192)(61, 193)(62, 194)(63, 195)(64, 196)(65, 197)(66, 198)(67, 199)(68, 200)(69, 201)(70, 202)(71, 203)(72, 204)(73, 205)(74, 206)(75, 207)(76, 208)(77, 209)(78, 210)(79, 211)(80, 212)(81, 213)(82, 214)(83, 215)(84, 216)(85, 217)(86, 218)(87, 219)(88, 220)(89, 221)(90, 222)(91, 223)(92, 224)(93, 225)(94, 226)(95, 227)(96, 228)(97, 229)(98, 230)(99, 231)(100, 232)(101, 233)(102, 234)(103, 235)(104, 236)(105, 237)(106, 238)(107, 239)(108, 240)(109, 241)(110, 242)(111, 243)(112, 244)(113, 245)(114, 246)(115, 247)(116, 248)(117, 249)(118, 250)(119, 251)(120, 252)(121, 253)(122, 254)(123, 255)(124, 256)(125, 257)(126, 258)(127, 259)(128, 260)(129, 261)(130, 262)(131, 263)(132, 264) local type(s) :: { ( 24, 24 ), ( 24^12 ) } Outer automorphisms :: reflexible Dual of E23.842 Graph:: simple bipartite v = 77 e = 132 f = 11 degree seq :: [ 2^66, 12^11 ] E23.841 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 6, 6}) Quotient :: edge^2 Aut^+ = C3 x D22 (small group id <66, 2>) Aut = C6 x D22 (small group id <132, 7>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1^-1 * Y2^-1, (R * Y3)^2, R * Y1 * R * Y2, Y2^2 * Y1^-2 * Y2 * Y1^-1, Y3 * Y1^2 * Y3 * Y1^-2, Y2 * Y3 * Y1 * Y2^-1 * Y3 * Y1^-1, Y3 * Y2^2 * Y3 * Y2^-2, Y2^6, Y1^6, Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y2^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 67, 4, 70)(2, 68, 6, 72)(3, 69, 8, 74)(5, 71, 12, 78)(7, 73, 15, 81)(9, 75, 17, 83)(10, 76, 18, 84)(11, 77, 19, 85)(13, 79, 21, 87)(14, 80, 22, 88)(16, 82, 23, 89)(20, 86, 27, 93)(24, 90, 31, 97)(25, 91, 32, 98)(26, 92, 33, 99)(28, 94, 34, 100)(29, 95, 35, 101)(30, 96, 36, 102)(37, 103, 43, 109)(38, 104, 44, 110)(39, 105, 45, 111)(40, 106, 46, 112)(41, 107, 47, 113)(42, 108, 48, 114)(49, 115, 55, 121)(50, 116, 56, 122)(51, 117, 57, 123)(52, 118, 58, 124)(53, 119, 59, 125)(54, 120, 60, 126)(61, 127, 66, 132)(62, 128, 64, 130)(63, 129, 65, 131)(133, 134, 137, 143, 139, 135)(136, 141, 144, 152, 147, 142)(138, 145, 151, 148, 140, 146)(149, 156, 159, 158, 150, 157)(153, 160, 155, 162, 154, 161)(163, 169, 165, 171, 164, 170)(166, 172, 168, 174, 167, 173)(175, 181, 177, 183, 176, 182)(178, 184, 180, 186, 179, 185)(187, 193, 189, 195, 188, 194)(190, 196, 192, 198, 191, 197)(199, 201, 205, 209, 203, 200)(202, 208, 213, 218, 210, 207)(204, 212, 206, 214, 217, 211)(215, 223, 216, 224, 225, 222)(219, 227, 220, 228, 221, 226)(229, 236, 230, 237, 231, 235)(232, 239, 233, 240, 234, 238)(241, 248, 242, 249, 243, 247)(244, 251, 245, 252, 246, 250)(253, 260, 254, 261, 255, 259)(256, 263, 257, 264, 258, 262) L = (1, 133)(2, 134)(3, 135)(4, 136)(5, 137)(6, 138)(7, 139)(8, 140)(9, 141)(10, 142)(11, 143)(12, 144)(13, 145)(14, 146)(15, 147)(16, 148)(17, 149)(18, 150)(19, 151)(20, 152)(21, 153)(22, 154)(23, 155)(24, 156)(25, 157)(26, 158)(27, 159)(28, 160)(29, 161)(30, 162)(31, 163)(32, 164)(33, 165)(34, 166)(35, 167)(36, 168)(37, 169)(38, 170)(39, 171)(40, 172)(41, 173)(42, 174)(43, 175)(44, 176)(45, 177)(46, 178)(47, 179)(48, 180)(49, 181)(50, 182)(51, 183)(52, 184)(53, 185)(54, 186)(55, 187)(56, 188)(57, 189)(58, 190)(59, 191)(60, 192)(61, 193)(62, 194)(63, 195)(64, 196)(65, 197)(66, 198)(67, 199)(68, 200)(69, 201)(70, 202)(71, 203)(72, 204)(73, 205)(74, 206)(75, 207)(76, 208)(77, 209)(78, 210)(79, 211)(80, 212)(81, 213)(82, 214)(83, 215)(84, 216)(85, 217)(86, 218)(87, 219)(88, 220)(89, 221)(90, 222)(91, 223)(92, 224)(93, 225)(94, 226)(95, 227)(96, 228)(97, 229)(98, 230)(99, 231)(100, 232)(101, 233)(102, 234)(103, 235)(104, 236)(105, 237)(106, 238)(107, 239)(108, 240)(109, 241)(110, 242)(111, 243)(112, 244)(113, 245)(114, 246)(115, 247)(116, 248)(117, 249)(118, 250)(119, 251)(120, 252)(121, 253)(122, 254)(123, 255)(124, 256)(125, 257)(126, 258)(127, 259)(128, 260)(129, 261)(130, 262)(131, 263)(132, 264) local type(s) :: { ( 8^4 ), ( 8^6 ) } Outer automorphisms :: reflexible Dual of E23.843 Graph:: simple bipartite v = 55 e = 132 f = 33 degree seq :: [ 4^33, 6^22 ] E23.842 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 6, 6}) Quotient :: loop^2 Aut^+ = C3 x D22 (small group id <66, 2>) Aut = S3 x D22 (small group id <132, 5>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y1, (R * Y3)^2, R * Y2 * R * Y1, Y3^-1 * Y1 * Y3^2 * Y1 * Y3^-1, Y3^6, Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 ] Map:: R = (1, 67, 133, 199, 3, 69, 135, 201, 8, 74, 140, 206, 17, 83, 149, 215, 10, 76, 142, 208, 4, 70, 136, 202)(2, 68, 134, 200, 5, 71, 137, 203, 12, 78, 144, 210, 21, 87, 153, 219, 14, 80, 146, 212, 6, 72, 138, 204)(7, 73, 139, 205, 15, 81, 147, 213, 24, 90, 156, 222, 18, 84, 150, 216, 9, 75, 141, 207, 16, 82, 148, 214)(11, 77, 143, 209, 19, 85, 151, 217, 28, 94, 160, 226, 22, 88, 154, 220, 13, 79, 145, 211, 20, 86, 152, 218)(23, 89, 155, 221, 31, 97, 163, 229, 26, 92, 158, 224, 33, 99, 165, 231, 25, 91, 157, 223, 32, 98, 164, 230)(27, 93, 159, 225, 34, 100, 166, 232, 30, 96, 162, 228, 36, 102, 168, 234, 29, 95, 161, 227, 35, 101, 167, 233)(37, 103, 169, 235, 43, 109, 175, 241, 39, 105, 171, 237, 45, 111, 177, 243, 38, 104, 170, 236, 44, 110, 176, 242)(40, 106, 172, 238, 46, 112, 178, 244, 42, 108, 174, 240, 48, 114, 180, 246, 41, 107, 173, 239, 47, 113, 179, 245)(49, 115, 181, 247, 55, 121, 187, 253, 51, 117, 183, 249, 57, 123, 189, 255, 50, 116, 182, 248, 56, 122, 188, 254)(52, 118, 184, 250, 58, 124, 190, 256, 54, 120, 186, 252, 60, 126, 192, 258, 53, 119, 185, 251, 59, 125, 191, 257)(61, 127, 193, 259, 65, 131, 197, 263, 63, 129, 195, 261, 64, 130, 196, 262, 62, 128, 194, 260, 66, 132, 198, 264) L = (1, 68)(2, 67)(3, 73)(4, 75)(5, 77)(6, 79)(7, 69)(8, 78)(9, 70)(10, 80)(11, 71)(12, 74)(13, 72)(14, 76)(15, 89)(16, 91)(17, 90)(18, 92)(19, 93)(20, 95)(21, 94)(22, 96)(23, 81)(24, 83)(25, 82)(26, 84)(27, 85)(28, 87)(29, 86)(30, 88)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 97)(38, 98)(39, 99)(40, 100)(41, 101)(42, 102)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 109)(50, 110)(51, 111)(52, 112)(53, 113)(54, 114)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 121)(62, 122)(63, 123)(64, 124)(65, 125)(66, 126)(133, 200)(134, 199)(135, 205)(136, 207)(137, 209)(138, 211)(139, 201)(140, 210)(141, 202)(142, 212)(143, 203)(144, 206)(145, 204)(146, 208)(147, 221)(148, 223)(149, 222)(150, 224)(151, 225)(152, 227)(153, 226)(154, 228)(155, 213)(156, 215)(157, 214)(158, 216)(159, 217)(160, 219)(161, 218)(162, 220)(163, 235)(164, 236)(165, 237)(166, 238)(167, 239)(168, 240)(169, 229)(170, 230)(171, 231)(172, 232)(173, 233)(174, 234)(175, 247)(176, 248)(177, 249)(178, 250)(179, 251)(180, 252)(181, 241)(182, 242)(183, 243)(184, 244)(185, 245)(186, 246)(187, 259)(188, 260)(189, 261)(190, 262)(191, 263)(192, 264)(193, 253)(194, 254)(195, 255)(196, 256)(197, 257)(198, 258) 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 E23.840 Transitivity :: VT+ Graph:: v = 11 e = 132 f = 77 degree seq :: [ 24^11 ] E23.843 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 6, 6}) Quotient :: loop^2 Aut^+ = C3 x D22 (small group id <66, 2>) Aut = C6 x D22 (small group id <132, 7>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y1^-1 * Y2^-1, (R * Y3)^2, R * Y1 * R * Y2, Y2^2 * Y1^-2 * Y2 * Y1^-1, Y3 * Y1^2 * Y3 * Y1^-2, Y2 * Y3 * Y1 * Y2^-1 * Y3 * Y1^-1, Y3 * Y2^2 * Y3 * Y2^-2, Y2^6, Y1^6, Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y2^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y2^-1 ] Map:: non-degenerate R = (1, 67, 133, 199, 4, 70, 136, 202)(2, 68, 134, 200, 6, 72, 138, 204)(3, 69, 135, 201, 8, 74, 140, 206)(5, 71, 137, 203, 12, 78, 144, 210)(7, 73, 139, 205, 15, 81, 147, 213)(9, 75, 141, 207, 17, 83, 149, 215)(10, 76, 142, 208, 18, 84, 150, 216)(11, 77, 143, 209, 19, 85, 151, 217)(13, 79, 145, 211, 21, 87, 153, 219)(14, 80, 146, 212, 22, 88, 154, 220)(16, 82, 148, 214, 23, 89, 155, 221)(20, 86, 152, 218, 27, 93, 159, 225)(24, 90, 156, 222, 31, 97, 163, 229)(25, 91, 157, 223, 32, 98, 164, 230)(26, 92, 158, 224, 33, 99, 165, 231)(28, 94, 160, 226, 34, 100, 166, 232)(29, 95, 161, 227, 35, 101, 167, 233)(30, 96, 162, 228, 36, 102, 168, 234)(37, 103, 169, 235, 43, 109, 175, 241)(38, 104, 170, 236, 44, 110, 176, 242)(39, 105, 171, 237, 45, 111, 177, 243)(40, 106, 172, 238, 46, 112, 178, 244)(41, 107, 173, 239, 47, 113, 179, 245)(42, 108, 174, 240, 48, 114, 180, 246)(49, 115, 181, 247, 55, 121, 187, 253)(50, 116, 182, 248, 56, 122, 188, 254)(51, 117, 183, 249, 57, 123, 189, 255)(52, 118, 184, 250, 58, 124, 190, 256)(53, 119, 185, 251, 59, 125, 191, 257)(54, 120, 186, 252, 60, 126, 192, 258)(61, 127, 193, 259, 66, 132, 198, 264)(62, 128, 194, 260, 64, 130, 196, 262)(63, 129, 195, 261, 65, 131, 197, 263) L = (1, 68)(2, 71)(3, 67)(4, 75)(5, 77)(6, 79)(7, 69)(8, 80)(9, 78)(10, 70)(11, 73)(12, 86)(13, 85)(14, 72)(15, 76)(16, 74)(17, 90)(18, 91)(19, 82)(20, 81)(21, 94)(22, 95)(23, 96)(24, 93)(25, 83)(26, 84)(27, 92)(28, 89)(29, 87)(30, 88)(31, 103)(32, 104)(33, 105)(34, 106)(35, 107)(36, 108)(37, 99)(38, 97)(39, 98)(40, 102)(41, 100)(42, 101)(43, 115)(44, 116)(45, 117)(46, 118)(47, 119)(48, 120)(49, 111)(50, 109)(51, 110)(52, 114)(53, 112)(54, 113)(55, 127)(56, 128)(57, 129)(58, 130)(59, 131)(60, 132)(61, 123)(62, 121)(63, 122)(64, 126)(65, 124)(66, 125)(133, 201)(134, 199)(135, 205)(136, 208)(137, 200)(138, 212)(139, 209)(140, 214)(141, 202)(142, 213)(143, 203)(144, 207)(145, 204)(146, 206)(147, 218)(148, 217)(149, 223)(150, 224)(151, 211)(152, 210)(153, 227)(154, 228)(155, 226)(156, 215)(157, 216)(158, 225)(159, 222)(160, 219)(161, 220)(162, 221)(163, 236)(164, 237)(165, 235)(166, 239)(167, 240)(168, 238)(169, 229)(170, 230)(171, 231)(172, 232)(173, 233)(174, 234)(175, 248)(176, 249)(177, 247)(178, 251)(179, 252)(180, 250)(181, 241)(182, 242)(183, 243)(184, 244)(185, 245)(186, 246)(187, 260)(188, 261)(189, 259)(190, 263)(191, 264)(192, 262)(193, 253)(194, 254)(195, 255)(196, 256)(197, 257)(198, 258) local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E23.841 Transitivity :: VT+ Graph:: v = 33 e = 132 f = 55 degree seq :: [ 8^33 ] E23.844 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 6, 6}) Quotient :: dipole Aut^+ = C3 x D22 (small group id <66, 2>) Aut = S3 x D22 (small group id <132, 5>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, R^2, Y1^2, (R * Y3)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2^2 * Y1 * Y2^-2 * Y1, Y2^6, (Y3 * Y2^-1)^6, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 ] Map:: R = (1, 67, 2, 68)(3, 69, 7, 73)(4, 70, 9, 75)(5, 71, 11, 77)(6, 72, 13, 79)(8, 74, 12, 78)(10, 76, 14, 80)(15, 81, 23, 89)(16, 82, 25, 91)(17, 83, 24, 90)(18, 84, 26, 92)(19, 85, 27, 93)(20, 86, 29, 95)(21, 87, 28, 94)(22, 88, 30, 96)(31, 97, 37, 103)(32, 98, 38, 104)(33, 99, 39, 105)(34, 100, 40, 106)(35, 101, 41, 107)(36, 102, 42, 108)(43, 109, 49, 115)(44, 110, 50, 116)(45, 111, 51, 117)(46, 112, 52, 118)(47, 113, 53, 119)(48, 114, 54, 120)(55, 121, 61, 127)(56, 122, 62, 128)(57, 123, 63, 129)(58, 124, 64, 130)(59, 125, 65, 131)(60, 126, 66, 132)(133, 199, 135, 201, 140, 206, 149, 215, 142, 208, 136, 202)(134, 200, 137, 203, 144, 210, 153, 219, 146, 212, 138, 204)(139, 205, 147, 213, 156, 222, 150, 216, 141, 207, 148, 214)(143, 209, 151, 217, 160, 226, 154, 220, 145, 211, 152, 218)(155, 221, 163, 229, 158, 224, 165, 231, 157, 223, 164, 230)(159, 225, 166, 232, 162, 228, 168, 234, 161, 227, 167, 233)(169, 235, 175, 241, 171, 237, 177, 243, 170, 236, 176, 242)(172, 238, 178, 244, 174, 240, 180, 246, 173, 239, 179, 245)(181, 247, 187, 253, 183, 249, 189, 255, 182, 248, 188, 254)(184, 250, 190, 256, 186, 252, 192, 258, 185, 251, 191, 257)(193, 259, 197, 263, 195, 261, 196, 262, 194, 260, 198, 264) L = (1, 133)(2, 134)(3, 135)(4, 136)(5, 137)(6, 138)(7, 139)(8, 140)(9, 141)(10, 142)(11, 143)(12, 144)(13, 145)(14, 146)(15, 147)(16, 148)(17, 149)(18, 150)(19, 151)(20, 152)(21, 153)(22, 154)(23, 155)(24, 156)(25, 157)(26, 158)(27, 159)(28, 160)(29, 161)(30, 162)(31, 163)(32, 164)(33, 165)(34, 166)(35, 167)(36, 168)(37, 169)(38, 170)(39, 171)(40, 172)(41, 173)(42, 174)(43, 175)(44, 176)(45, 177)(46, 178)(47, 179)(48, 180)(49, 181)(50, 182)(51, 183)(52, 184)(53, 185)(54, 186)(55, 187)(56, 188)(57, 189)(58, 190)(59, 191)(60, 192)(61, 193)(62, 194)(63, 195)(64, 196)(65, 197)(66, 198)(67, 199)(68, 200)(69, 201)(70, 202)(71, 203)(72, 204)(73, 205)(74, 206)(75, 207)(76, 208)(77, 209)(78, 210)(79, 211)(80, 212)(81, 213)(82, 214)(83, 215)(84, 216)(85, 217)(86, 218)(87, 219)(88, 220)(89, 221)(90, 222)(91, 223)(92, 224)(93, 225)(94, 226)(95, 227)(96, 228)(97, 229)(98, 230)(99, 231)(100, 232)(101, 233)(102, 234)(103, 235)(104, 236)(105, 237)(106, 238)(107, 239)(108, 240)(109, 241)(110, 242)(111, 243)(112, 244)(113, 245)(114, 246)(115, 247)(116, 248)(117, 249)(118, 250)(119, 251)(120, 252)(121, 253)(122, 254)(123, 255)(124, 256)(125, 257)(126, 258)(127, 259)(128, 260)(129, 261)(130, 262)(131, 263)(132, 264) local type(s) :: { ( 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 44 e = 132 f = 44 degree seq :: [ 4^33, 12^11 ] E23.845 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 6, 6}) Quotient :: dipole Aut^+ = C3 x D22 (small group id <66, 2>) Aut = S3 x D22 (small group id <132, 5>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y1)^2, Y3^-1 * Y2^-1 * Y3^-1 * Y2, (Y3^-1 * Y1)^2, (R * Y3)^2, Y2^-1 * Y3^-1 * Y1 * Y2^-2, (R * Y2 * Y3^-1)^2, Y3^11, Y3^5 * Y1 * Y2 * Y3^4 * Y1 * Y2^-1 ] Map:: non-degenerate R = (1, 67, 2, 68)(3, 69, 11, 77)(4, 70, 10, 76)(5, 71, 17, 83)(6, 72, 8, 74)(7, 73, 21, 87)(9, 75, 24, 90)(12, 78, 16, 82)(13, 79, 27, 93)(14, 80, 19, 85)(15, 81, 26, 92)(18, 84, 30, 96)(20, 86, 23, 89)(22, 88, 33, 99)(25, 91, 36, 102)(28, 94, 39, 105)(29, 95, 38, 104)(31, 97, 42, 108)(32, 98, 35, 101)(34, 100, 45, 111)(37, 103, 48, 114)(40, 106, 51, 117)(41, 107, 50, 116)(43, 109, 54, 120)(44, 110, 47, 113)(46, 112, 57, 123)(49, 115, 60, 126)(52, 118, 63, 129)(53, 119, 62, 128)(55, 121, 65, 131)(56, 122, 59, 125)(58, 124, 64, 130)(61, 127, 66, 132)(133, 199, 135, 201, 144, 210, 140, 206, 151, 217, 137, 203)(134, 200, 139, 205, 148, 214, 136, 202, 146, 212, 141, 207)(138, 204, 145, 211, 149, 215, 155, 221, 143, 209, 150, 216)(142, 208, 154, 220, 156, 222, 147, 213, 153, 219, 157, 223)(152, 218, 160, 226, 162, 228, 167, 233, 159, 225, 163, 229)(158, 224, 166, 232, 168, 234, 161, 227, 165, 231, 169, 235)(164, 230, 172, 238, 174, 240, 179, 245, 171, 237, 175, 241)(170, 236, 178, 244, 180, 246, 173, 239, 177, 243, 181, 247)(176, 242, 184, 250, 186, 252, 191, 257, 183, 249, 187, 253)(182, 248, 190, 256, 192, 258, 185, 251, 189, 255, 193, 259)(188, 254, 196, 262, 197, 263, 194, 260, 195, 261, 198, 264) L = (1, 136)(2, 140)(3, 145)(4, 147)(5, 150)(6, 133)(7, 154)(8, 155)(9, 157)(10, 134)(11, 151)(12, 141)(13, 160)(14, 135)(15, 161)(16, 137)(17, 144)(18, 163)(19, 139)(20, 138)(21, 146)(22, 166)(23, 167)(24, 148)(25, 169)(26, 142)(27, 143)(28, 172)(29, 173)(30, 149)(31, 175)(32, 152)(33, 153)(34, 178)(35, 179)(36, 156)(37, 181)(38, 158)(39, 159)(40, 184)(41, 185)(42, 162)(43, 187)(44, 164)(45, 165)(46, 190)(47, 191)(48, 168)(49, 193)(50, 170)(51, 171)(52, 196)(53, 188)(54, 174)(55, 198)(56, 176)(57, 177)(58, 195)(59, 194)(60, 180)(61, 197)(62, 182)(63, 183)(64, 189)(65, 186)(66, 192)(67, 199)(68, 200)(69, 201)(70, 202)(71, 203)(72, 204)(73, 205)(74, 206)(75, 207)(76, 208)(77, 209)(78, 210)(79, 211)(80, 212)(81, 213)(82, 214)(83, 215)(84, 216)(85, 217)(86, 218)(87, 219)(88, 220)(89, 221)(90, 222)(91, 223)(92, 224)(93, 225)(94, 226)(95, 227)(96, 228)(97, 229)(98, 230)(99, 231)(100, 232)(101, 233)(102, 234)(103, 235)(104, 236)(105, 237)(106, 238)(107, 239)(108, 240)(109, 241)(110, 242)(111, 243)(112, 244)(113, 245)(114, 246)(115, 247)(116, 248)(117, 249)(118, 250)(119, 251)(120, 252)(121, 253)(122, 254)(123, 255)(124, 256)(125, 257)(126, 258)(127, 259)(128, 260)(129, 261)(130, 262)(131, 263)(132, 264) local type(s) :: { ( 4, 12, 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 44 e = 132 f = 44 degree seq :: [ 4^33, 12^11 ] E23.846 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 69, 69}) Quotient :: edge Aut^+ = C69 (small group id <69, 1>) Aut = D138 (small group id <138, 3>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T1)^2, (F * T2)^2, (T1, T2^-1), T1^-1 * T2^-23, (T1^-1 * T2^-1)^69 ] Map:: non-degenerate R = (1, 3, 8, 14, 20, 26, 32, 38, 44, 50, 56, 62, 68, 64, 58, 52, 46, 40, 34, 28, 22, 16, 10, 4, 9, 15, 21, 27, 33, 39, 45, 51, 57, 63, 69, 67, 61, 55, 49, 43, 37, 31, 25, 19, 13, 7, 2, 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 65, 59, 53, 47, 41, 35, 29, 23, 17, 11, 5)(70, 71, 73)(72, 75, 78)(74, 76, 79)(77, 81, 84)(80, 82, 85)(83, 87, 90)(86, 88, 91)(89, 93, 96)(92, 94, 97)(95, 99, 102)(98, 100, 103)(101, 105, 108)(104, 106, 109)(107, 111, 114)(110, 112, 115)(113, 117, 120)(116, 118, 121)(119, 123, 126)(122, 124, 127)(125, 129, 132)(128, 130, 133)(131, 135, 138)(134, 136, 137) L = (1, 70)(2, 71)(3, 72)(4, 73)(5, 74)(6, 75)(7, 76)(8, 77)(9, 78)(10, 79)(11, 80)(12, 81)(13, 82)(14, 83)(15, 84)(16, 85)(17, 86)(18, 87)(19, 88)(20, 89)(21, 90)(22, 91)(23, 92)(24, 93)(25, 94)(26, 95)(27, 96)(28, 97)(29, 98)(30, 99)(31, 100)(32, 101)(33, 102)(34, 103)(35, 104)(36, 105)(37, 106)(38, 107)(39, 108)(40, 109)(41, 110)(42, 111)(43, 112)(44, 113)(45, 114)(46, 115)(47, 116)(48, 117)(49, 118)(50, 119)(51, 120)(52, 121)(53, 122)(54, 123)(55, 124)(56, 125)(57, 126)(58, 127)(59, 128)(60, 129)(61, 130)(62, 131)(63, 132)(64, 133)(65, 134)(66, 135)(67, 136)(68, 137)(69, 138) local type(s) :: { ( 138^3 ), ( 138^69 ) } Outer automorphisms :: reflexible Dual of E23.847 Transitivity :: ET+ Graph:: bipartite v = 24 e = 69 f = 1 degree seq :: [ 3^23, 69 ] E23.847 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 69, 69}) Quotient :: loop Aut^+ = C69 (small group id <69, 1>) Aut = D138 (small group id <138, 3>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T1)^2, (F * T2)^2, (T1, T2^-1), T1^-1 * T2^-23, (T1^-1 * T2^-1)^69 ] Map:: non-degenerate R = (1, 70, 3, 72, 8, 77, 14, 83, 20, 89, 26, 95, 32, 101, 38, 107, 44, 113, 50, 119, 56, 125, 62, 131, 68, 137, 64, 133, 58, 127, 52, 121, 46, 115, 40, 109, 34, 103, 28, 97, 22, 91, 16, 85, 10, 79, 4, 73, 9, 78, 15, 84, 21, 90, 27, 96, 33, 102, 39, 108, 45, 114, 51, 120, 57, 126, 63, 132, 69, 138, 67, 136, 61, 130, 55, 124, 49, 118, 43, 112, 37, 106, 31, 100, 25, 94, 19, 88, 13, 82, 7, 76, 2, 71, 6, 75, 12, 81, 18, 87, 24, 93, 30, 99, 36, 105, 42, 111, 48, 117, 54, 123, 60, 129, 66, 135, 65, 134, 59, 128, 53, 122, 47, 116, 41, 110, 35, 104, 29, 98, 23, 92, 17, 86, 11, 80, 5, 74) L = (1, 71)(2, 73)(3, 75)(4, 70)(5, 76)(6, 78)(7, 79)(8, 81)(9, 72)(10, 74)(11, 82)(12, 84)(13, 85)(14, 87)(15, 77)(16, 80)(17, 88)(18, 90)(19, 91)(20, 93)(21, 83)(22, 86)(23, 94)(24, 96)(25, 97)(26, 99)(27, 89)(28, 92)(29, 100)(30, 102)(31, 103)(32, 105)(33, 95)(34, 98)(35, 106)(36, 108)(37, 109)(38, 111)(39, 101)(40, 104)(41, 112)(42, 114)(43, 115)(44, 117)(45, 107)(46, 110)(47, 118)(48, 120)(49, 121)(50, 123)(51, 113)(52, 116)(53, 124)(54, 126)(55, 127)(56, 129)(57, 119)(58, 122)(59, 130)(60, 132)(61, 133)(62, 135)(63, 125)(64, 128)(65, 136)(66, 138)(67, 137)(68, 134)(69, 131) local type(s) :: { ( 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69, 3, 69 ) } Outer automorphisms :: reflexible Dual of E23.846 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 69 f = 24 degree seq :: [ 138 ] E23.848 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 69, 69}) Quotient :: dipole Aut^+ = C69 (small group id <69, 1>) Aut = D138 (small group id <138, 3>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, Y1^3, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y2^-1, Y1^-1), (Y3^-1, Y2^-1), Y2^-23 * Y1^-1, Y2^-1 * Y3^2 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 70, 2, 71, 4, 73)(3, 72, 6, 75, 9, 78)(5, 74, 7, 76, 10, 79)(8, 77, 12, 81, 15, 84)(11, 80, 13, 82, 16, 85)(14, 83, 18, 87, 21, 90)(17, 86, 19, 88, 22, 91)(20, 89, 24, 93, 27, 96)(23, 92, 25, 94, 28, 97)(26, 95, 30, 99, 33, 102)(29, 98, 31, 100, 34, 103)(32, 101, 36, 105, 39, 108)(35, 104, 37, 106, 40, 109)(38, 107, 42, 111, 45, 114)(41, 110, 43, 112, 46, 115)(44, 113, 48, 117, 51, 120)(47, 116, 49, 118, 52, 121)(50, 119, 54, 123, 57, 126)(53, 122, 55, 124, 58, 127)(56, 125, 60, 129, 63, 132)(59, 128, 61, 130, 64, 133)(62, 131, 66, 135, 69, 138)(65, 134, 67, 136, 68, 137)(139, 208, 141, 210, 146, 215, 152, 221, 158, 227, 164, 233, 170, 239, 176, 245, 182, 251, 188, 257, 194, 263, 200, 269, 206, 275, 202, 271, 196, 265, 190, 259, 184, 253, 178, 247, 172, 241, 166, 235, 160, 229, 154, 223, 148, 217, 142, 211, 147, 216, 153, 222, 159, 228, 165, 234, 171, 240, 177, 246, 183, 252, 189, 258, 195, 264, 201, 270, 207, 276, 205, 274, 199, 268, 193, 262, 187, 256, 181, 250, 175, 244, 169, 238, 163, 232, 157, 226, 151, 220, 145, 214, 140, 209, 144, 213, 150, 219, 156, 225, 162, 231, 168, 237, 174, 243, 180, 249, 186, 255, 192, 261, 198, 267, 204, 273, 203, 272, 197, 266, 191, 260, 185, 254, 179, 248, 173, 242, 167, 236, 161, 230, 155, 224, 149, 218, 143, 212) L = (1, 142)(2, 139)(3, 147)(4, 140)(5, 148)(6, 141)(7, 143)(8, 153)(9, 144)(10, 145)(11, 154)(12, 146)(13, 149)(14, 159)(15, 150)(16, 151)(17, 160)(18, 152)(19, 155)(20, 165)(21, 156)(22, 157)(23, 166)(24, 158)(25, 161)(26, 171)(27, 162)(28, 163)(29, 172)(30, 164)(31, 167)(32, 177)(33, 168)(34, 169)(35, 178)(36, 170)(37, 173)(38, 183)(39, 174)(40, 175)(41, 184)(42, 176)(43, 179)(44, 189)(45, 180)(46, 181)(47, 190)(48, 182)(49, 185)(50, 195)(51, 186)(52, 187)(53, 196)(54, 188)(55, 191)(56, 201)(57, 192)(58, 193)(59, 202)(60, 194)(61, 197)(62, 207)(63, 198)(64, 199)(65, 206)(66, 200)(67, 203)(68, 205)(69, 204)(70, 208)(71, 209)(72, 210)(73, 211)(74, 212)(75, 213)(76, 214)(77, 215)(78, 216)(79, 217)(80, 218)(81, 219)(82, 220)(83, 221)(84, 222)(85, 223)(86, 224)(87, 225)(88, 226)(89, 227)(90, 228)(91, 229)(92, 230)(93, 231)(94, 232)(95, 233)(96, 234)(97, 235)(98, 236)(99, 237)(100, 238)(101, 239)(102, 240)(103, 241)(104, 242)(105, 243)(106, 244)(107, 245)(108, 246)(109, 247)(110, 248)(111, 249)(112, 250)(113, 251)(114, 252)(115, 253)(116, 254)(117, 255)(118, 256)(119, 257)(120, 258)(121, 259)(122, 260)(123, 261)(124, 262)(125, 263)(126, 264)(127, 265)(128, 266)(129, 267)(130, 268)(131, 269)(132, 270)(133, 271)(134, 272)(135, 273)(136, 274)(137, 275)(138, 276) local type(s) :: { ( 2, 138, 2, 138, 2, 138 ), ( 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138 ) } Outer automorphisms :: reflexible Dual of E23.849 Graph:: bipartite v = 24 e = 138 f = 70 degree seq :: [ 6^23, 138 ] E23.849 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 69, 69}) Quotient :: dipole Aut^+ = C69 (small group id <69, 1>) Aut = D138 (small group id <138, 3>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^3, (R * Y3)^2, (R * Y1)^2, (Y3, Y1), (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^3, Y3^-1 * Y1^-23, (Y1^-1 * Y3^-1)^69 ] Map:: R = (1, 70, 2, 71, 6, 75, 12, 81, 18, 87, 24, 93, 30, 99, 36, 105, 42, 111, 48, 117, 54, 123, 60, 129, 66, 135, 65, 134, 59, 128, 53, 122, 47, 116, 41, 110, 35, 104, 29, 98, 23, 92, 17, 86, 11, 80, 5, 74, 8, 77, 14, 83, 20, 89, 26, 95, 32, 101, 38, 107, 44, 113, 50, 119, 56, 125, 62, 131, 68, 137, 69, 138, 63, 132, 57, 126, 51, 120, 45, 114, 39, 108, 33, 102, 27, 96, 21, 90, 15, 84, 9, 78, 3, 72, 7, 76, 13, 82, 19, 88, 25, 94, 31, 100, 37, 106, 43, 112, 49, 118, 55, 124, 61, 130, 67, 136, 64, 133, 58, 127, 52, 121, 46, 115, 40, 109, 34, 103, 28, 97, 22, 91, 16, 85, 10, 79, 4, 73)(139, 208)(140, 209)(141, 210)(142, 211)(143, 212)(144, 213)(145, 214)(146, 215)(147, 216)(148, 217)(149, 218)(150, 219)(151, 220)(152, 221)(153, 222)(154, 223)(155, 224)(156, 225)(157, 226)(158, 227)(159, 228)(160, 229)(161, 230)(162, 231)(163, 232)(164, 233)(165, 234)(166, 235)(167, 236)(168, 237)(169, 238)(170, 239)(171, 240)(172, 241)(173, 242)(174, 243)(175, 244)(176, 245)(177, 246)(178, 247)(179, 248)(180, 249)(181, 250)(182, 251)(183, 252)(184, 253)(185, 254)(186, 255)(187, 256)(188, 257)(189, 258)(190, 259)(191, 260)(192, 261)(193, 262)(194, 263)(195, 264)(196, 265)(197, 266)(198, 267)(199, 268)(200, 269)(201, 270)(202, 271)(203, 272)(204, 273)(205, 274)(206, 275)(207, 276) L = (1, 141)(2, 145)(3, 143)(4, 147)(5, 139)(6, 151)(7, 146)(8, 140)(9, 149)(10, 153)(11, 142)(12, 157)(13, 152)(14, 144)(15, 155)(16, 159)(17, 148)(18, 163)(19, 158)(20, 150)(21, 161)(22, 165)(23, 154)(24, 169)(25, 164)(26, 156)(27, 167)(28, 171)(29, 160)(30, 175)(31, 170)(32, 162)(33, 173)(34, 177)(35, 166)(36, 181)(37, 176)(38, 168)(39, 179)(40, 183)(41, 172)(42, 187)(43, 182)(44, 174)(45, 185)(46, 189)(47, 178)(48, 193)(49, 188)(50, 180)(51, 191)(52, 195)(53, 184)(54, 199)(55, 194)(56, 186)(57, 197)(58, 201)(59, 190)(60, 205)(61, 200)(62, 192)(63, 203)(64, 207)(65, 196)(66, 202)(67, 206)(68, 198)(69, 204)(70, 208)(71, 209)(72, 210)(73, 211)(74, 212)(75, 213)(76, 214)(77, 215)(78, 216)(79, 217)(80, 218)(81, 219)(82, 220)(83, 221)(84, 222)(85, 223)(86, 224)(87, 225)(88, 226)(89, 227)(90, 228)(91, 229)(92, 230)(93, 231)(94, 232)(95, 233)(96, 234)(97, 235)(98, 236)(99, 237)(100, 238)(101, 239)(102, 240)(103, 241)(104, 242)(105, 243)(106, 244)(107, 245)(108, 246)(109, 247)(110, 248)(111, 249)(112, 250)(113, 251)(114, 252)(115, 253)(116, 254)(117, 255)(118, 256)(119, 257)(120, 258)(121, 259)(122, 260)(123, 261)(124, 262)(125, 263)(126, 264)(127, 265)(128, 266)(129, 267)(130, 268)(131, 269)(132, 270)(133, 271)(134, 272)(135, 273)(136, 274)(137, 275)(138, 276) local type(s) :: { ( 6, 138 ), ( 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138, 6, 138 ) } Outer automorphisms :: reflexible Dual of E23.848 Graph:: bipartite v = 70 e = 138 f = 24 degree seq :: [ 2^69, 138 ] E23.850 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 4, 4}) Quotient :: halfedge^2 Aut^+ = C4 x D22 (small group id <88, 4>) Aut = (C44 x C2) : C2 (small group id <176, 30>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y2 * Y3 * Y1^2, R * Y3 * R * Y2, Y1^-1 * Y2 * Y3 * Y1^-1, (R * Y1)^2, Y3 * Y1^-1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 ] Map:: non-degenerate R = (1, 90, 2, 94, 6, 93, 5, 89)(3, 97, 9, 92, 4, 98, 10, 91)(7, 99, 11, 96, 8, 100, 12, 95)(13, 105, 17, 102, 14, 106, 18, 101)(15, 107, 19, 104, 16, 108, 20, 103)(21, 113, 25, 110, 22, 114, 26, 109)(23, 115, 27, 112, 24, 116, 28, 111)(29, 121, 33, 118, 30, 122, 34, 117)(31, 143, 55, 120, 32, 144, 56, 119)(35, 147, 59, 128, 40, 150, 62, 123)(36, 151, 63, 127, 39, 154, 66, 124)(37, 152, 64, 126, 38, 153, 65, 125)(41, 149, 61, 130, 42, 148, 60, 129)(43, 155, 67, 132, 44, 156, 68, 131)(45, 157, 69, 134, 46, 158, 70, 133)(47, 159, 71, 136, 48, 160, 72, 135)(49, 161, 73, 138, 50, 162, 74, 137)(51, 163, 75, 140, 52, 164, 76, 139)(53, 165, 77, 142, 54, 166, 78, 141)(57, 169, 81, 146, 58, 170, 82, 145)(79, 171, 83, 168, 80, 172, 84, 167)(85, 175, 87, 174, 86, 176, 88, 173) L = (1, 3)(2, 7)(4, 6)(5, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19, 23)(20, 24)(25, 29)(26, 30)(27, 31)(28, 32)(33, 42)(34, 41)(35, 60)(36, 64)(37, 55)(38, 56)(39, 65)(40, 61)(43, 59)(44, 62)(45, 63)(46, 66)(47, 67)(48, 68)(49, 69)(50, 70)(51, 71)(52, 72)(53, 73)(54, 74)(57, 75)(58, 76)(77, 79)(78, 80)(81, 85)(82, 86)(83, 87)(84, 88)(89, 92)(90, 96)(91, 94)(93, 95)(97, 102)(98, 101)(99, 104)(100, 103)(105, 110)(106, 109)(107, 112)(108, 111)(113, 118)(114, 117)(115, 120)(116, 119)(121, 129)(122, 130)(123, 149)(124, 153)(125, 144)(126, 143)(127, 152)(128, 148)(131, 150)(132, 147)(133, 154)(134, 151)(135, 156)(136, 155)(137, 158)(138, 157)(139, 160)(140, 159)(141, 162)(142, 161)(145, 164)(146, 163)(165, 168)(166, 167)(169, 174)(170, 173)(171, 176)(172, 175) local type(s) :: { ( 8^8 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: bipartite v = 22 e = 88 f = 22 degree seq :: [ 8^22 ] E23.851 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 4, 4}) Quotient :: halfedge^2 Aut^+ = C4 x D22 (small group id <88, 4>) Aut = D8 x D22 (small group id <176, 31>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y3 * Y2, (R * Y1)^2, Y1^4, R * Y3 * R * Y2, (Y1^-1 * Y2 * Y1^-1)^2, Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 ] Map:: R = (1, 90, 2, 93, 5, 92, 4, 89)(3, 95, 7, 98, 10, 96, 8, 91)(6, 99, 11, 97, 9, 100, 12, 94)(13, 105, 17, 102, 14, 106, 18, 101)(15, 107, 19, 104, 16, 108, 20, 103)(21, 113, 25, 110, 22, 114, 26, 109)(23, 115, 27, 112, 24, 116, 28, 111)(29, 121, 33, 118, 30, 122, 34, 117)(31, 130, 42, 120, 32, 125, 37, 119)(35, 141, 53, 127, 39, 143, 55, 123)(36, 147, 59, 126, 38, 150, 62, 124)(40, 154, 66, 129, 41, 145, 57, 128)(43, 152, 64, 132, 44, 148, 60, 131)(45, 158, 70, 134, 46, 156, 68, 133)(47, 163, 75, 136, 48, 161, 73, 135)(49, 167, 79, 138, 50, 165, 77, 137)(51, 171, 83, 140, 52, 169, 81, 139)(54, 175, 87, 144, 56, 173, 85, 142)(58, 172, 84, 155, 67, 170, 82, 146)(61, 166, 78, 153, 65, 168, 80, 149)(63, 176, 88, 160, 72, 174, 86, 151)(69, 162, 74, 159, 71, 164, 76, 157) 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, 55)(35, 57)(36, 60)(37, 62)(38, 64)(39, 66)(40, 68)(41, 70)(42, 59)(43, 73)(44, 75)(45, 77)(46, 79)(47, 81)(48, 83)(49, 85)(50, 87)(51, 88)(52, 86)(54, 84)(56, 82)(58, 76)(61, 69)(63, 80)(65, 71)(67, 74)(72, 78)(89, 91)(90, 94)(92, 97)(93, 98)(95, 101)(96, 102)(99, 103)(100, 104)(105, 109)(106, 110)(107, 111)(108, 112)(113, 117)(114, 118)(115, 119)(116, 120)(121, 141)(122, 143)(123, 145)(124, 148)(125, 150)(126, 152)(127, 154)(128, 156)(129, 158)(130, 147)(131, 161)(132, 163)(133, 165)(134, 167)(135, 169)(136, 171)(137, 173)(138, 175)(139, 176)(140, 174)(142, 172)(144, 170)(146, 164)(149, 157)(151, 168)(153, 159)(155, 162)(160, 166) local type(s) :: { ( 8^8 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: bipartite v = 22 e = 88 f = 22 degree seq :: [ 8^22 ] E23.852 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 4, 4}) Quotient :: halfedge^2 Aut^+ = (C22 x C2) : C2 (small group id <88, 7>) Aut = D8 x D22 (small group id <176, 31>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y3 * Y2, Y1^4, R * Y3 * R * Y2, (R * Y1)^2, (Y1^-1 * Y2 * Y1^-1)^2, Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 ] Map:: R = (1, 90, 2, 93, 5, 92, 4, 89)(3, 95, 7, 98, 10, 96, 8, 91)(6, 99, 11, 97, 9, 100, 12, 94)(13, 105, 17, 102, 14, 106, 18, 101)(15, 107, 19, 104, 16, 108, 20, 103)(21, 113, 25, 110, 22, 114, 26, 109)(23, 115, 27, 112, 24, 116, 28, 111)(29, 121, 33, 118, 30, 122, 34, 117)(31, 130, 42, 120, 32, 125, 37, 119)(35, 141, 53, 127, 39, 143, 55, 123)(36, 147, 59, 126, 38, 150, 62, 124)(40, 154, 66, 129, 41, 145, 57, 128)(43, 152, 64, 132, 44, 148, 60, 131)(45, 158, 70, 134, 46, 156, 68, 133)(47, 163, 75, 136, 48, 161, 73, 135)(49, 167, 79, 138, 50, 165, 77, 137)(51, 171, 83, 140, 52, 169, 81, 139)(54, 175, 87, 144, 56, 173, 85, 142)(58, 170, 82, 155, 67, 172, 84, 146)(61, 168, 80, 153, 65, 166, 78, 149)(63, 174, 86, 160, 72, 176, 88, 151)(69, 164, 76, 159, 71, 162, 74, 157) 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, 55)(35, 57)(36, 60)(37, 62)(38, 64)(39, 66)(40, 68)(41, 70)(42, 59)(43, 73)(44, 75)(45, 77)(46, 79)(47, 81)(48, 83)(49, 85)(50, 87)(51, 86)(52, 88)(54, 82)(56, 84)(58, 74)(61, 71)(63, 78)(65, 69)(67, 76)(72, 80)(89, 91)(90, 94)(92, 97)(93, 98)(95, 101)(96, 102)(99, 103)(100, 104)(105, 109)(106, 110)(107, 111)(108, 112)(113, 117)(114, 118)(115, 119)(116, 120)(121, 141)(122, 143)(123, 145)(124, 148)(125, 150)(126, 152)(127, 154)(128, 156)(129, 158)(130, 147)(131, 161)(132, 163)(133, 165)(134, 167)(135, 169)(136, 171)(137, 173)(138, 175)(139, 174)(140, 176)(142, 170)(144, 172)(146, 162)(149, 159)(151, 166)(153, 157)(155, 164)(160, 168) local type(s) :: { ( 8^8 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: bipartite v = 22 e = 88 f = 22 degree seq :: [ 8^22 ] E23.853 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 4, 4}) Quotient :: edge^2 Aut^+ = C4 x D22 (small group id <88, 4>) Aut = (C44 x C2) : C2 (small group id <176, 30>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y1 * Y2 * Y3^2, Y3^-1 * Y1 * Y2 * Y3^-1, (R * Y3)^2, R * Y1 * R * Y2, Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ] Map:: R = (1, 89, 4, 92, 6, 94, 5, 93)(2, 90, 7, 95, 3, 91, 8, 96)(9, 97, 13, 101, 10, 98, 14, 102)(11, 99, 15, 103, 12, 100, 16, 104)(17, 105, 21, 109, 18, 106, 22, 110)(19, 107, 23, 111, 20, 108, 24, 112)(25, 113, 29, 117, 26, 114, 30, 118)(27, 115, 31, 119, 28, 116, 32, 120)(33, 121, 38, 126, 34, 122, 35, 123)(36, 124, 51, 139, 37, 125, 52, 140)(39, 127, 56, 144, 40, 128, 55, 143)(41, 129, 58, 146, 42, 130, 57, 145)(43, 131, 60, 148, 44, 132, 59, 147)(45, 133, 62, 150, 46, 134, 61, 149)(47, 135, 64, 152, 48, 136, 63, 151)(49, 137, 66, 154, 50, 138, 65, 153)(53, 141, 68, 156, 54, 142, 67, 155)(69, 157, 71, 159, 70, 158, 72, 160)(73, 161, 76, 164, 74, 162, 75, 163)(77, 165, 88, 176, 78, 166, 87, 175)(79, 167, 85, 173, 80, 168, 86, 174)(81, 169, 83, 171, 82, 170, 84, 172)(177, 178)(179, 182)(180, 185)(181, 186)(183, 187)(184, 188)(189, 193)(190, 194)(191, 195)(192, 196)(197, 201)(198, 202)(199, 203)(200, 204)(205, 209)(206, 210)(207, 227)(208, 228)(211, 231)(212, 233)(213, 234)(214, 232)(215, 235)(216, 236)(217, 237)(218, 238)(219, 239)(220, 240)(221, 241)(222, 242)(223, 243)(224, 244)(225, 245)(226, 246)(229, 249)(230, 250)(247, 264)(248, 263)(251, 262)(252, 261)(253, 260)(254, 259)(255, 257)(256, 258)(265, 267)(266, 270)(268, 274)(269, 273)(271, 276)(272, 275)(277, 282)(278, 281)(279, 284)(280, 283)(285, 290)(286, 289)(287, 292)(288, 291)(293, 298)(294, 297)(295, 316)(296, 315)(299, 320)(300, 322)(301, 321)(302, 319)(303, 324)(304, 323)(305, 326)(306, 325)(307, 328)(308, 327)(309, 330)(310, 329)(311, 332)(312, 331)(313, 334)(314, 333)(317, 338)(318, 337)(335, 351)(336, 352)(339, 349)(340, 350)(341, 347)(342, 348)(343, 346)(344, 345) L = (1, 177)(2, 178)(3, 179)(4, 180)(5, 181)(6, 182)(7, 183)(8, 184)(9, 185)(10, 186)(11, 187)(12, 188)(13, 189)(14, 190)(15, 191)(16, 192)(17, 193)(18, 194)(19, 195)(20, 196)(21, 197)(22, 198)(23, 199)(24, 200)(25, 201)(26, 202)(27, 203)(28, 204)(29, 205)(30, 206)(31, 207)(32, 208)(33, 209)(34, 210)(35, 211)(36, 212)(37, 213)(38, 214)(39, 215)(40, 216)(41, 217)(42, 218)(43, 219)(44, 220)(45, 221)(46, 222)(47, 223)(48, 224)(49, 225)(50, 226)(51, 227)(52, 228)(53, 229)(54, 230)(55, 231)(56, 232)(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, 245)(70, 246)(71, 247)(72, 248)(73, 249)(74, 250)(75, 251)(76, 252)(77, 253)(78, 254)(79, 255)(80, 256)(81, 257)(82, 258)(83, 259)(84, 260)(85, 261)(86, 262)(87, 263)(88, 264)(89, 265)(90, 266)(91, 267)(92, 268)(93, 269)(94, 270)(95, 271)(96, 272)(97, 273)(98, 274)(99, 275)(100, 276)(101, 277)(102, 278)(103, 279)(104, 280)(105, 281)(106, 282)(107, 283)(108, 284)(109, 285)(110, 286)(111, 287)(112, 288)(113, 289)(114, 290)(115, 291)(116, 292)(117, 293)(118, 294)(119, 295)(120, 296)(121, 297)(122, 298)(123, 299)(124, 300)(125, 301)(126, 302)(127, 303)(128, 304)(129, 305)(130, 306)(131, 307)(132, 308)(133, 309)(134, 310)(135, 311)(136, 312)(137, 313)(138, 314)(139, 315)(140, 316)(141, 317)(142, 318)(143, 319)(144, 320)(145, 321)(146, 322)(147, 323)(148, 324)(149, 325)(150, 326)(151, 327)(152, 328)(153, 329)(154, 330)(155, 331)(156, 332)(157, 333)(158, 334)(159, 335)(160, 336)(161, 337)(162, 338)(163, 339)(164, 340)(165, 341)(166, 342)(167, 343)(168, 344)(169, 345)(170, 346)(171, 347)(172, 348)(173, 349)(174, 350)(175, 351)(176, 352) local type(s) :: { ( 16, 16 ), ( 16^8 ) } Outer automorphisms :: reflexible Dual of E23.859 Graph:: simple bipartite v = 110 e = 176 f = 22 degree seq :: [ 2^88, 8^22 ] E23.854 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 4, 4}) Quotient :: edge^2 Aut^+ = C4 x D22 (small group id <88, 4>) Aut = D8 x D22 (small group id <176, 31>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y1, (R * Y3)^2, R * Y1 * R * Y2, Y3^4, (Y3^-1 * Y1 * Y3^-1)^2, Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ] Map:: R = (1, 89, 3, 91, 8, 96, 4, 92)(2, 90, 5, 93, 11, 99, 6, 94)(7, 95, 13, 101, 9, 97, 14, 102)(10, 98, 15, 103, 12, 100, 16, 104)(17, 105, 21, 109, 18, 106, 22, 110)(19, 107, 23, 111, 20, 108, 24, 112)(25, 113, 29, 117, 26, 114, 30, 118)(27, 115, 31, 119, 28, 116, 32, 120)(33, 121, 53, 141, 34, 122, 55, 143)(35, 123, 57, 145, 40, 128, 59, 147)(36, 124, 61, 149, 43, 131, 63, 151)(37, 125, 64, 152, 38, 126, 60, 148)(39, 127, 67, 155, 41, 129, 69, 157)(42, 130, 72, 160, 44, 132, 74, 162)(45, 133, 77, 165, 46, 134, 79, 167)(47, 135, 81, 169, 48, 136, 83, 171)(49, 137, 85, 173, 50, 138, 87, 175)(51, 139, 88, 176, 52, 140, 86, 174)(54, 142, 82, 170, 56, 144, 84, 172)(58, 146, 73, 161, 70, 158, 76, 164)(62, 150, 68, 156, 75, 163, 71, 159)(65, 153, 78, 166, 66, 154, 80, 168)(177, 178)(179, 183)(180, 185)(181, 186)(182, 188)(184, 187)(189, 193)(190, 194)(191, 195)(192, 196)(197, 201)(198, 202)(199, 203)(200, 204)(205, 209)(206, 210)(207, 213)(208, 214)(211, 231)(212, 236)(215, 233)(216, 229)(217, 235)(218, 237)(219, 240)(220, 239)(221, 243)(222, 245)(223, 248)(224, 250)(225, 253)(226, 255)(227, 257)(228, 259)(230, 261)(232, 263)(234, 260)(238, 256)(241, 264)(242, 262)(244, 249)(246, 258)(247, 252)(251, 254)(265, 266)(267, 271)(268, 273)(269, 274)(270, 276)(272, 275)(277, 281)(278, 282)(279, 283)(280, 284)(285, 289)(286, 290)(287, 291)(288, 292)(293, 297)(294, 298)(295, 301)(296, 302)(299, 319)(300, 324)(303, 321)(304, 317)(305, 323)(306, 325)(307, 328)(308, 327)(309, 331)(310, 333)(311, 336)(312, 338)(313, 341)(314, 343)(315, 345)(316, 347)(318, 349)(320, 351)(322, 348)(326, 344)(329, 352)(330, 350)(332, 337)(334, 346)(335, 340)(339, 342) L = (1, 177)(2, 178)(3, 179)(4, 180)(5, 181)(6, 182)(7, 183)(8, 184)(9, 185)(10, 186)(11, 187)(12, 188)(13, 189)(14, 190)(15, 191)(16, 192)(17, 193)(18, 194)(19, 195)(20, 196)(21, 197)(22, 198)(23, 199)(24, 200)(25, 201)(26, 202)(27, 203)(28, 204)(29, 205)(30, 206)(31, 207)(32, 208)(33, 209)(34, 210)(35, 211)(36, 212)(37, 213)(38, 214)(39, 215)(40, 216)(41, 217)(42, 218)(43, 219)(44, 220)(45, 221)(46, 222)(47, 223)(48, 224)(49, 225)(50, 226)(51, 227)(52, 228)(53, 229)(54, 230)(55, 231)(56, 232)(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, 245)(70, 246)(71, 247)(72, 248)(73, 249)(74, 250)(75, 251)(76, 252)(77, 253)(78, 254)(79, 255)(80, 256)(81, 257)(82, 258)(83, 259)(84, 260)(85, 261)(86, 262)(87, 263)(88, 264)(89, 265)(90, 266)(91, 267)(92, 268)(93, 269)(94, 270)(95, 271)(96, 272)(97, 273)(98, 274)(99, 275)(100, 276)(101, 277)(102, 278)(103, 279)(104, 280)(105, 281)(106, 282)(107, 283)(108, 284)(109, 285)(110, 286)(111, 287)(112, 288)(113, 289)(114, 290)(115, 291)(116, 292)(117, 293)(118, 294)(119, 295)(120, 296)(121, 297)(122, 298)(123, 299)(124, 300)(125, 301)(126, 302)(127, 303)(128, 304)(129, 305)(130, 306)(131, 307)(132, 308)(133, 309)(134, 310)(135, 311)(136, 312)(137, 313)(138, 314)(139, 315)(140, 316)(141, 317)(142, 318)(143, 319)(144, 320)(145, 321)(146, 322)(147, 323)(148, 324)(149, 325)(150, 326)(151, 327)(152, 328)(153, 329)(154, 330)(155, 331)(156, 332)(157, 333)(158, 334)(159, 335)(160, 336)(161, 337)(162, 338)(163, 339)(164, 340)(165, 341)(166, 342)(167, 343)(168, 344)(169, 345)(170, 346)(171, 347)(172, 348)(173, 349)(174, 350)(175, 351)(176, 352) local type(s) :: { ( 16, 16 ), ( 16^8 ) } Outer automorphisms :: reflexible Dual of E23.860 Graph:: simple bipartite v = 110 e = 176 f = 22 degree seq :: [ 2^88, 8^22 ] E23.855 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 4, 4}) Quotient :: edge^2 Aut^+ = (C22 x C2) : C2 (small group id <88, 7>) Aut = D8 x D22 (small group id <176, 31>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y1, Y3^4, (R * Y3)^2, R * Y1 * R * Y2, (Y3^-1 * Y1 * Y3^-1)^2, Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ] Map:: R = (1, 89, 3, 91, 8, 96, 4, 92)(2, 90, 5, 93, 11, 99, 6, 94)(7, 95, 13, 101, 9, 97, 14, 102)(10, 98, 15, 103, 12, 100, 16, 104)(17, 105, 21, 109, 18, 106, 22, 110)(19, 107, 23, 111, 20, 108, 24, 112)(25, 113, 29, 117, 26, 114, 30, 118)(27, 115, 31, 119, 28, 116, 32, 120)(33, 121, 53, 141, 34, 122, 55, 143)(35, 123, 57, 145, 40, 128, 59, 147)(36, 124, 61, 149, 43, 131, 63, 151)(37, 125, 64, 152, 38, 126, 60, 148)(39, 127, 67, 155, 41, 129, 69, 157)(42, 130, 72, 160, 44, 132, 74, 162)(45, 133, 77, 165, 46, 134, 79, 167)(47, 135, 81, 169, 48, 136, 83, 171)(49, 137, 85, 173, 50, 138, 87, 175)(51, 139, 88, 176, 52, 140, 86, 174)(54, 142, 82, 170, 56, 144, 84, 172)(58, 146, 76, 164, 70, 158, 73, 161)(62, 150, 71, 159, 75, 163, 68, 156)(65, 153, 80, 168, 66, 154, 78, 166)(177, 178)(179, 183)(180, 185)(181, 186)(182, 188)(184, 187)(189, 193)(190, 194)(191, 195)(192, 196)(197, 201)(198, 202)(199, 203)(200, 204)(205, 209)(206, 210)(207, 214)(208, 213)(211, 229)(212, 236)(215, 233)(216, 231)(217, 235)(218, 237)(219, 240)(220, 239)(221, 243)(222, 245)(223, 248)(224, 250)(225, 253)(226, 255)(227, 257)(228, 259)(230, 261)(232, 263)(234, 258)(238, 254)(241, 262)(242, 264)(244, 252)(246, 260)(247, 249)(251, 256)(265, 266)(267, 271)(268, 273)(269, 274)(270, 276)(272, 275)(277, 281)(278, 282)(279, 283)(280, 284)(285, 289)(286, 290)(287, 291)(288, 292)(293, 297)(294, 298)(295, 302)(296, 301)(299, 317)(300, 324)(303, 321)(304, 319)(305, 323)(306, 325)(307, 328)(308, 327)(309, 331)(310, 333)(311, 336)(312, 338)(313, 341)(314, 343)(315, 345)(316, 347)(318, 349)(320, 351)(322, 346)(326, 342)(329, 350)(330, 352)(332, 340)(334, 348)(335, 337)(339, 344) L = (1, 177)(2, 178)(3, 179)(4, 180)(5, 181)(6, 182)(7, 183)(8, 184)(9, 185)(10, 186)(11, 187)(12, 188)(13, 189)(14, 190)(15, 191)(16, 192)(17, 193)(18, 194)(19, 195)(20, 196)(21, 197)(22, 198)(23, 199)(24, 200)(25, 201)(26, 202)(27, 203)(28, 204)(29, 205)(30, 206)(31, 207)(32, 208)(33, 209)(34, 210)(35, 211)(36, 212)(37, 213)(38, 214)(39, 215)(40, 216)(41, 217)(42, 218)(43, 219)(44, 220)(45, 221)(46, 222)(47, 223)(48, 224)(49, 225)(50, 226)(51, 227)(52, 228)(53, 229)(54, 230)(55, 231)(56, 232)(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, 245)(70, 246)(71, 247)(72, 248)(73, 249)(74, 250)(75, 251)(76, 252)(77, 253)(78, 254)(79, 255)(80, 256)(81, 257)(82, 258)(83, 259)(84, 260)(85, 261)(86, 262)(87, 263)(88, 264)(89, 265)(90, 266)(91, 267)(92, 268)(93, 269)(94, 270)(95, 271)(96, 272)(97, 273)(98, 274)(99, 275)(100, 276)(101, 277)(102, 278)(103, 279)(104, 280)(105, 281)(106, 282)(107, 283)(108, 284)(109, 285)(110, 286)(111, 287)(112, 288)(113, 289)(114, 290)(115, 291)(116, 292)(117, 293)(118, 294)(119, 295)(120, 296)(121, 297)(122, 298)(123, 299)(124, 300)(125, 301)(126, 302)(127, 303)(128, 304)(129, 305)(130, 306)(131, 307)(132, 308)(133, 309)(134, 310)(135, 311)(136, 312)(137, 313)(138, 314)(139, 315)(140, 316)(141, 317)(142, 318)(143, 319)(144, 320)(145, 321)(146, 322)(147, 323)(148, 324)(149, 325)(150, 326)(151, 327)(152, 328)(153, 329)(154, 330)(155, 331)(156, 332)(157, 333)(158, 334)(159, 335)(160, 336)(161, 337)(162, 338)(163, 339)(164, 340)(165, 341)(166, 342)(167, 343)(168, 344)(169, 345)(170, 346)(171, 347)(172, 348)(173, 349)(174, 350)(175, 351)(176, 352) local type(s) :: { ( 16, 16 ), ( 16^8 ) } Outer automorphisms :: reflexible Dual of E23.861 Graph:: simple bipartite v = 110 e = 176 f = 22 degree seq :: [ 2^88, 8^22 ] E23.856 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 4, 4}) Quotient :: edge^2 Aut^+ = C4 x D22 (small group id <88, 4>) Aut = C2 x C4 x D22 (small group id <176, 28>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, (R * Y3)^2, Y1^4, Y2^4, R * Y2 * R * Y1, (Y3 * Y1^-2)^2, Y2 * Y3 * Y1 * Y2^-1 * Y3 * Y1^-1, Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 ] Map:: non-degenerate R = (1, 89, 4, 92)(2, 90, 6, 94)(3, 91, 7, 95)(5, 93, 10, 98)(8, 96, 13, 101)(9, 97, 14, 102)(11, 99, 15, 103)(12, 100, 16, 104)(17, 105, 21, 109)(18, 106, 22, 110)(19, 107, 23, 111)(20, 108, 24, 112)(25, 113, 29, 117)(26, 114, 30, 118)(27, 115, 31, 119)(28, 116, 32, 120)(33, 121, 53, 141)(34, 122, 54, 142)(35, 123, 55, 143)(36, 124, 56, 144)(37, 125, 57, 145)(38, 126, 58, 146)(39, 127, 59, 147)(40, 128, 60, 148)(41, 129, 61, 149)(42, 130, 62, 150)(43, 131, 63, 151)(44, 132, 64, 152)(45, 133, 65, 153)(46, 134, 66, 154)(47, 135, 67, 155)(48, 136, 68, 156)(49, 137, 69, 157)(50, 138, 70, 158)(51, 139, 71, 159)(52, 140, 72, 160)(73, 161, 88, 176)(74, 162, 87, 175)(75, 163, 86, 174)(76, 164, 85, 173)(77, 165, 84, 172)(78, 166, 83, 171)(79, 167, 81, 169)(80, 168, 82, 170)(177, 178, 181, 179)(180, 184, 186, 185)(182, 187, 183, 188)(189, 193, 190, 194)(191, 195, 192, 196)(197, 201, 198, 202)(199, 203, 200, 204)(205, 209, 206, 210)(207, 213, 208, 211)(212, 229, 216, 230)(214, 233, 215, 231)(217, 236, 218, 232)(219, 235, 220, 234)(221, 238, 222, 237)(223, 240, 224, 239)(225, 242, 226, 241)(227, 244, 228, 243)(245, 249, 246, 250)(247, 252, 248, 251)(253, 264, 254, 263)(255, 261, 256, 262)(257, 259, 258, 260)(265, 267, 269, 266)(268, 273, 274, 272)(270, 276, 271, 275)(277, 282, 278, 281)(279, 284, 280, 283)(285, 290, 286, 289)(287, 292, 288, 291)(293, 298, 294, 297)(295, 299, 296, 301)(300, 318, 304, 317)(302, 319, 303, 321)(305, 320, 306, 324)(307, 322, 308, 323)(309, 325, 310, 326)(311, 327, 312, 328)(313, 329, 314, 330)(315, 331, 316, 332)(333, 338, 334, 337)(335, 339, 336, 340)(341, 351, 342, 352)(343, 350, 344, 349)(345, 348, 346, 347) L = (1, 177)(2, 178)(3, 179)(4, 180)(5, 181)(6, 182)(7, 183)(8, 184)(9, 185)(10, 186)(11, 187)(12, 188)(13, 189)(14, 190)(15, 191)(16, 192)(17, 193)(18, 194)(19, 195)(20, 196)(21, 197)(22, 198)(23, 199)(24, 200)(25, 201)(26, 202)(27, 203)(28, 204)(29, 205)(30, 206)(31, 207)(32, 208)(33, 209)(34, 210)(35, 211)(36, 212)(37, 213)(38, 214)(39, 215)(40, 216)(41, 217)(42, 218)(43, 219)(44, 220)(45, 221)(46, 222)(47, 223)(48, 224)(49, 225)(50, 226)(51, 227)(52, 228)(53, 229)(54, 230)(55, 231)(56, 232)(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, 245)(70, 246)(71, 247)(72, 248)(73, 249)(74, 250)(75, 251)(76, 252)(77, 253)(78, 254)(79, 255)(80, 256)(81, 257)(82, 258)(83, 259)(84, 260)(85, 261)(86, 262)(87, 263)(88, 264)(89, 265)(90, 266)(91, 267)(92, 268)(93, 269)(94, 270)(95, 271)(96, 272)(97, 273)(98, 274)(99, 275)(100, 276)(101, 277)(102, 278)(103, 279)(104, 280)(105, 281)(106, 282)(107, 283)(108, 284)(109, 285)(110, 286)(111, 287)(112, 288)(113, 289)(114, 290)(115, 291)(116, 292)(117, 293)(118, 294)(119, 295)(120, 296)(121, 297)(122, 298)(123, 299)(124, 300)(125, 301)(126, 302)(127, 303)(128, 304)(129, 305)(130, 306)(131, 307)(132, 308)(133, 309)(134, 310)(135, 311)(136, 312)(137, 313)(138, 314)(139, 315)(140, 316)(141, 317)(142, 318)(143, 319)(144, 320)(145, 321)(146, 322)(147, 323)(148, 324)(149, 325)(150, 326)(151, 327)(152, 328)(153, 329)(154, 330)(155, 331)(156, 332)(157, 333)(158, 334)(159, 335)(160, 336)(161, 337)(162, 338)(163, 339)(164, 340)(165, 341)(166, 342)(167, 343)(168, 344)(169, 345)(170, 346)(171, 347)(172, 348)(173, 349)(174, 350)(175, 351)(176, 352) local type(s) :: { ( 8^4 ) } Outer automorphisms :: reflexible Dual of E23.862 Graph:: simple bipartite v = 88 e = 176 f = 44 degree seq :: [ 4^88 ] E23.857 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 4, 4}) Quotient :: edge^2 Aut^+ = C4 x D22 (small group id <88, 4>) Aut = D8 x D22 (small group id <176, 31>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2 * Y1^-1, R * Y2 * R * Y1, (R * Y3)^2, Y1^4, Y2^4, (Y1^-1 * Y3 * Y2^-1)^2, Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-2 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1, Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 89, 3, 91)(2, 90, 6, 94)(4, 92, 9, 97)(5, 93, 10, 98)(7, 95, 13, 101)(8, 96, 14, 102)(11, 99, 15, 103)(12, 100, 16, 104)(17, 105, 21, 109)(18, 106, 22, 110)(19, 107, 23, 111)(20, 108, 24, 112)(25, 113, 29, 117)(26, 114, 30, 118)(27, 115, 31, 119)(28, 116, 32, 120)(33, 121, 36, 124)(34, 122, 38, 126)(35, 123, 55, 143)(37, 125, 62, 150)(39, 127, 53, 141)(40, 128, 57, 145)(41, 129, 59, 147)(42, 130, 60, 148)(43, 131, 63, 151)(44, 132, 65, 153)(45, 133, 68, 156)(46, 134, 70, 158)(47, 135, 73, 161)(48, 136, 75, 163)(49, 137, 77, 165)(50, 138, 79, 167)(51, 139, 81, 169)(52, 140, 83, 171)(54, 142, 85, 173)(56, 144, 87, 175)(58, 146, 84, 172)(61, 149, 88, 176)(64, 152, 80, 168)(66, 154, 86, 174)(67, 155, 82, 170)(69, 157, 74, 162)(71, 159, 76, 164)(72, 160, 78, 166)(177, 178, 181, 180)(179, 183, 186, 184)(182, 187, 185, 188)(189, 193, 190, 194)(191, 195, 192, 196)(197, 201, 198, 202)(199, 203, 200, 204)(205, 209, 206, 210)(207, 229, 208, 231)(211, 233, 215, 235)(212, 236, 214, 238)(213, 239, 218, 241)(216, 244, 217, 246)(219, 249, 220, 251)(221, 253, 222, 255)(223, 257, 224, 259)(225, 261, 226, 263)(227, 264, 228, 262)(230, 258, 232, 260)(234, 250, 243, 252)(237, 254, 242, 256)(240, 245, 248, 247)(265, 266, 269, 268)(267, 271, 274, 272)(270, 275, 273, 276)(277, 281, 278, 282)(279, 283, 280, 284)(285, 289, 286, 290)(287, 291, 288, 292)(293, 297, 294, 298)(295, 317, 296, 319)(299, 321, 303, 323)(300, 324, 302, 326)(301, 327, 306, 329)(304, 332, 305, 334)(307, 337, 308, 339)(309, 341, 310, 343)(311, 345, 312, 347)(313, 349, 314, 351)(315, 352, 316, 350)(318, 346, 320, 348)(322, 338, 331, 340)(325, 342, 330, 344)(328, 333, 336, 335) L = (1, 177)(2, 178)(3, 179)(4, 180)(5, 181)(6, 182)(7, 183)(8, 184)(9, 185)(10, 186)(11, 187)(12, 188)(13, 189)(14, 190)(15, 191)(16, 192)(17, 193)(18, 194)(19, 195)(20, 196)(21, 197)(22, 198)(23, 199)(24, 200)(25, 201)(26, 202)(27, 203)(28, 204)(29, 205)(30, 206)(31, 207)(32, 208)(33, 209)(34, 210)(35, 211)(36, 212)(37, 213)(38, 214)(39, 215)(40, 216)(41, 217)(42, 218)(43, 219)(44, 220)(45, 221)(46, 222)(47, 223)(48, 224)(49, 225)(50, 226)(51, 227)(52, 228)(53, 229)(54, 230)(55, 231)(56, 232)(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, 245)(70, 246)(71, 247)(72, 248)(73, 249)(74, 250)(75, 251)(76, 252)(77, 253)(78, 254)(79, 255)(80, 256)(81, 257)(82, 258)(83, 259)(84, 260)(85, 261)(86, 262)(87, 263)(88, 264)(89, 265)(90, 266)(91, 267)(92, 268)(93, 269)(94, 270)(95, 271)(96, 272)(97, 273)(98, 274)(99, 275)(100, 276)(101, 277)(102, 278)(103, 279)(104, 280)(105, 281)(106, 282)(107, 283)(108, 284)(109, 285)(110, 286)(111, 287)(112, 288)(113, 289)(114, 290)(115, 291)(116, 292)(117, 293)(118, 294)(119, 295)(120, 296)(121, 297)(122, 298)(123, 299)(124, 300)(125, 301)(126, 302)(127, 303)(128, 304)(129, 305)(130, 306)(131, 307)(132, 308)(133, 309)(134, 310)(135, 311)(136, 312)(137, 313)(138, 314)(139, 315)(140, 316)(141, 317)(142, 318)(143, 319)(144, 320)(145, 321)(146, 322)(147, 323)(148, 324)(149, 325)(150, 326)(151, 327)(152, 328)(153, 329)(154, 330)(155, 331)(156, 332)(157, 333)(158, 334)(159, 335)(160, 336)(161, 337)(162, 338)(163, 339)(164, 340)(165, 341)(166, 342)(167, 343)(168, 344)(169, 345)(170, 346)(171, 347)(172, 348)(173, 349)(174, 350)(175, 351)(176, 352) local type(s) :: { ( 8^4 ) } Outer automorphisms :: reflexible Dual of E23.863 Graph:: simple bipartite v = 88 e = 176 f = 44 degree seq :: [ 4^88 ] E23.858 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 4, 4}) Quotient :: edge^2 Aut^+ = (C22 x C2) : C2 (small group id <88, 7>) Aut = D8 x D22 (small group id <176, 31>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2 * Y1^-1, R * Y2 * R * Y1, (R * Y3)^2, Y1^4, Y2^4, Y2^-1 * Y3 * Y1^2 * Y3 * Y1^-1, (Y1^-1 * Y3 * Y2^-1)^2, Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 89, 3, 91)(2, 90, 6, 94)(4, 92, 9, 97)(5, 93, 10, 98)(7, 95, 13, 101)(8, 96, 14, 102)(11, 99, 15, 103)(12, 100, 16, 104)(17, 105, 21, 109)(18, 106, 22, 110)(19, 107, 23, 111)(20, 108, 24, 112)(25, 113, 29, 117)(26, 114, 30, 118)(27, 115, 31, 119)(28, 116, 32, 120)(33, 121, 38, 126)(34, 122, 35, 123)(36, 124, 52, 140)(37, 125, 51, 139)(39, 127, 55, 143)(40, 128, 56, 144)(41, 129, 57, 145)(42, 130, 58, 146)(43, 131, 59, 147)(44, 132, 60, 148)(45, 133, 61, 149)(46, 134, 62, 150)(47, 135, 63, 151)(48, 136, 64, 152)(49, 137, 65, 153)(50, 138, 66, 154)(53, 141, 67, 155)(54, 142, 68, 156)(69, 157, 71, 159)(70, 158, 72, 160)(73, 161, 76, 164)(74, 162, 75, 163)(77, 165, 87, 175)(78, 166, 88, 176)(79, 167, 85, 173)(80, 168, 86, 174)(81, 169, 84, 172)(82, 170, 83, 171)(177, 178, 181, 180)(179, 183, 186, 184)(182, 187, 185, 188)(189, 193, 190, 194)(191, 195, 192, 196)(197, 201, 198, 202)(199, 203, 200, 204)(205, 209, 206, 210)(207, 227, 208, 228)(211, 231, 214, 232)(212, 233, 213, 234)(215, 235, 216, 236)(217, 237, 218, 238)(219, 239, 220, 240)(221, 241, 222, 242)(223, 243, 224, 244)(225, 245, 226, 246)(229, 249, 230, 250)(247, 264, 248, 263)(251, 261, 252, 262)(253, 260, 254, 259)(255, 258, 256, 257)(265, 266, 269, 268)(267, 271, 274, 272)(270, 275, 273, 276)(277, 281, 278, 282)(279, 283, 280, 284)(285, 289, 286, 290)(287, 291, 288, 292)(293, 297, 294, 298)(295, 315, 296, 316)(299, 319, 302, 320)(300, 321, 301, 322)(303, 323, 304, 324)(305, 325, 306, 326)(307, 327, 308, 328)(309, 329, 310, 330)(311, 331, 312, 332)(313, 333, 314, 334)(317, 337, 318, 338)(335, 352, 336, 351)(339, 349, 340, 350)(341, 348, 342, 347)(343, 346, 344, 345) L = (1, 177)(2, 178)(3, 179)(4, 180)(5, 181)(6, 182)(7, 183)(8, 184)(9, 185)(10, 186)(11, 187)(12, 188)(13, 189)(14, 190)(15, 191)(16, 192)(17, 193)(18, 194)(19, 195)(20, 196)(21, 197)(22, 198)(23, 199)(24, 200)(25, 201)(26, 202)(27, 203)(28, 204)(29, 205)(30, 206)(31, 207)(32, 208)(33, 209)(34, 210)(35, 211)(36, 212)(37, 213)(38, 214)(39, 215)(40, 216)(41, 217)(42, 218)(43, 219)(44, 220)(45, 221)(46, 222)(47, 223)(48, 224)(49, 225)(50, 226)(51, 227)(52, 228)(53, 229)(54, 230)(55, 231)(56, 232)(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, 245)(70, 246)(71, 247)(72, 248)(73, 249)(74, 250)(75, 251)(76, 252)(77, 253)(78, 254)(79, 255)(80, 256)(81, 257)(82, 258)(83, 259)(84, 260)(85, 261)(86, 262)(87, 263)(88, 264)(89, 265)(90, 266)(91, 267)(92, 268)(93, 269)(94, 270)(95, 271)(96, 272)(97, 273)(98, 274)(99, 275)(100, 276)(101, 277)(102, 278)(103, 279)(104, 280)(105, 281)(106, 282)(107, 283)(108, 284)(109, 285)(110, 286)(111, 287)(112, 288)(113, 289)(114, 290)(115, 291)(116, 292)(117, 293)(118, 294)(119, 295)(120, 296)(121, 297)(122, 298)(123, 299)(124, 300)(125, 301)(126, 302)(127, 303)(128, 304)(129, 305)(130, 306)(131, 307)(132, 308)(133, 309)(134, 310)(135, 311)(136, 312)(137, 313)(138, 314)(139, 315)(140, 316)(141, 317)(142, 318)(143, 319)(144, 320)(145, 321)(146, 322)(147, 323)(148, 324)(149, 325)(150, 326)(151, 327)(152, 328)(153, 329)(154, 330)(155, 331)(156, 332)(157, 333)(158, 334)(159, 335)(160, 336)(161, 337)(162, 338)(163, 339)(164, 340)(165, 341)(166, 342)(167, 343)(168, 344)(169, 345)(170, 346)(171, 347)(172, 348)(173, 349)(174, 350)(175, 351)(176, 352) local type(s) :: { ( 8^4 ) } Outer automorphisms :: reflexible Dual of E23.864 Graph:: simple bipartite v = 88 e = 176 f = 44 degree seq :: [ 4^88 ] E23.859 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 4, 4}) Quotient :: loop^2 Aut^+ = C4 x D22 (small group id <88, 4>) Aut = (C44 x C2) : C2 (small group id <176, 30>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y1 * Y2 * Y3^2, Y3^-1 * Y1 * Y2 * Y3^-1, (R * Y3)^2, R * Y1 * R * Y2, Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ] Map:: R = (1, 89, 177, 265, 4, 92, 180, 268, 6, 94, 182, 270, 5, 93, 181, 269)(2, 90, 178, 266, 7, 95, 183, 271, 3, 91, 179, 267, 8, 96, 184, 272)(9, 97, 185, 273, 13, 101, 189, 277, 10, 98, 186, 274, 14, 102, 190, 278)(11, 99, 187, 275, 15, 103, 191, 279, 12, 100, 188, 276, 16, 104, 192, 280)(17, 105, 193, 281, 21, 109, 197, 285, 18, 106, 194, 282, 22, 110, 198, 286)(19, 107, 195, 283, 23, 111, 199, 287, 20, 108, 196, 284, 24, 112, 200, 288)(25, 113, 201, 289, 29, 117, 205, 293, 26, 114, 202, 290, 30, 118, 206, 294)(27, 115, 203, 291, 31, 119, 207, 295, 28, 116, 204, 292, 32, 120, 208, 296)(33, 121, 209, 297, 57, 145, 233, 321, 34, 122, 210, 298, 58, 146, 234, 322)(35, 123, 211, 299, 61, 149, 237, 325, 40, 128, 216, 304, 62, 150, 238, 326)(36, 124, 212, 300, 63, 151, 239, 327, 37, 125, 213, 301, 64, 152, 240, 328)(38, 126, 214, 302, 65, 153, 241, 329, 39, 127, 215, 303, 66, 154, 242, 330)(41, 129, 217, 305, 67, 155, 243, 331, 42, 130, 218, 306, 68, 156, 244, 332)(43, 131, 219, 307, 60, 148, 236, 324, 44, 132, 220, 308, 59, 147, 235, 323)(45, 133, 221, 309, 69, 157, 245, 333, 46, 134, 222, 310, 70, 158, 246, 334)(47, 135, 223, 311, 71, 159, 247, 335, 48, 136, 224, 312, 72, 160, 248, 336)(49, 137, 225, 313, 73, 161, 249, 337, 50, 138, 226, 314, 74, 162, 250, 338)(51, 139, 227, 315, 75, 163, 251, 339, 52, 140, 228, 316, 76, 164, 252, 340)(53, 141, 229, 317, 77, 165, 253, 341, 54, 142, 230, 318, 78, 166, 254, 342)(55, 143, 231, 319, 79, 167, 255, 343, 56, 144, 232, 320, 80, 168, 256, 344)(81, 169, 257, 345, 85, 173, 261, 349, 82, 170, 258, 346, 86, 174, 262, 350)(83, 171, 259, 347, 87, 175, 263, 351, 84, 172, 260, 348, 88, 176, 264, 352) L = (1, 90)(2, 89)(3, 94)(4, 97)(5, 98)(6, 91)(7, 99)(8, 100)(9, 92)(10, 93)(11, 95)(12, 96)(13, 105)(14, 106)(15, 107)(16, 108)(17, 101)(18, 102)(19, 103)(20, 104)(21, 113)(22, 114)(23, 115)(24, 116)(25, 109)(26, 110)(27, 111)(28, 112)(29, 121)(30, 122)(31, 132)(32, 131)(33, 117)(34, 118)(35, 147)(36, 145)(37, 146)(38, 151)(39, 152)(40, 148)(41, 149)(42, 150)(43, 120)(44, 119)(45, 153)(46, 154)(47, 155)(48, 156)(49, 157)(50, 158)(51, 159)(52, 160)(53, 161)(54, 162)(55, 163)(56, 164)(57, 124)(58, 125)(59, 123)(60, 128)(61, 129)(62, 130)(63, 126)(64, 127)(65, 133)(66, 134)(67, 135)(68, 136)(69, 137)(70, 138)(71, 139)(72, 140)(73, 141)(74, 142)(75, 143)(76, 144)(77, 169)(78, 170)(79, 171)(80, 172)(81, 165)(82, 166)(83, 167)(84, 168)(85, 175)(86, 176)(87, 173)(88, 174)(177, 267)(178, 270)(179, 265)(180, 274)(181, 273)(182, 266)(183, 276)(184, 275)(185, 269)(186, 268)(187, 272)(188, 271)(189, 282)(190, 281)(191, 284)(192, 283)(193, 278)(194, 277)(195, 280)(196, 279)(197, 290)(198, 289)(199, 292)(200, 291)(201, 286)(202, 285)(203, 288)(204, 287)(205, 298)(206, 297)(207, 307)(208, 308)(209, 294)(210, 293)(211, 324)(212, 322)(213, 321)(214, 328)(215, 327)(216, 323)(217, 326)(218, 325)(219, 295)(220, 296)(221, 330)(222, 329)(223, 332)(224, 331)(225, 334)(226, 333)(227, 336)(228, 335)(229, 338)(230, 337)(231, 340)(232, 339)(233, 301)(234, 300)(235, 304)(236, 299)(237, 306)(238, 305)(239, 303)(240, 302)(241, 310)(242, 309)(243, 312)(244, 311)(245, 314)(246, 313)(247, 316)(248, 315)(249, 318)(250, 317)(251, 320)(252, 319)(253, 346)(254, 345)(255, 348)(256, 347)(257, 342)(258, 341)(259, 344)(260, 343)(261, 352)(262, 351)(263, 350)(264, 349) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) } Outer automorphisms :: reflexible Dual of E23.853 Transitivity :: VT+ Graph:: bipartite v = 22 e = 176 f = 110 degree seq :: [ 16^22 ] E23.860 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 4, 4}) Quotient :: loop^2 Aut^+ = C4 x D22 (small group id <88, 4>) Aut = D8 x D22 (small group id <176, 31>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y1, (R * Y3)^2, R * Y1 * R * Y2, Y3^4, (Y3^-1 * Y1 * Y3^-1)^2, Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ] Map:: R = (1, 89, 177, 265, 3, 91, 179, 267, 8, 96, 184, 272, 4, 92, 180, 268)(2, 90, 178, 266, 5, 93, 181, 269, 11, 99, 187, 275, 6, 94, 182, 270)(7, 95, 183, 271, 13, 101, 189, 277, 9, 97, 185, 273, 14, 102, 190, 278)(10, 98, 186, 274, 15, 103, 191, 279, 12, 100, 188, 276, 16, 104, 192, 280)(17, 105, 193, 281, 21, 109, 197, 285, 18, 106, 194, 282, 22, 110, 198, 286)(19, 107, 195, 283, 23, 111, 199, 287, 20, 108, 196, 284, 24, 112, 200, 288)(25, 113, 201, 289, 29, 117, 205, 293, 26, 114, 202, 290, 30, 118, 206, 294)(27, 115, 203, 291, 31, 119, 207, 295, 28, 116, 204, 292, 32, 120, 208, 296)(33, 121, 209, 297, 53, 141, 229, 317, 34, 122, 210, 298, 55, 143, 231, 319)(35, 123, 211, 299, 57, 145, 233, 321, 40, 128, 216, 304, 59, 147, 235, 323)(36, 124, 212, 300, 61, 149, 237, 325, 43, 131, 219, 307, 63, 151, 239, 327)(37, 125, 213, 301, 64, 152, 240, 328, 38, 126, 214, 302, 60, 148, 236, 324)(39, 127, 215, 303, 67, 155, 243, 331, 41, 129, 217, 305, 69, 157, 245, 333)(42, 130, 218, 306, 72, 160, 248, 336, 44, 132, 220, 308, 74, 162, 250, 338)(45, 133, 221, 309, 77, 165, 253, 341, 46, 134, 222, 310, 79, 167, 255, 343)(47, 135, 223, 311, 81, 169, 257, 345, 48, 136, 224, 312, 83, 171, 259, 347)(49, 137, 225, 313, 85, 173, 261, 349, 50, 138, 226, 314, 87, 175, 263, 351)(51, 139, 227, 315, 86, 174, 262, 350, 52, 140, 228, 316, 88, 176, 264, 352)(54, 142, 230, 318, 84, 172, 260, 348, 56, 144, 232, 320, 82, 170, 258, 346)(58, 146, 234, 322, 73, 161, 249, 337, 70, 158, 246, 334, 76, 164, 252, 340)(62, 150, 238, 326, 68, 156, 244, 332, 75, 163, 251, 339, 71, 159, 247, 335)(65, 153, 241, 329, 78, 166, 254, 342, 66, 154, 242, 330, 80, 168, 256, 344) L = (1, 90)(2, 89)(3, 95)(4, 97)(5, 98)(6, 100)(7, 91)(8, 99)(9, 92)(10, 93)(11, 96)(12, 94)(13, 105)(14, 106)(15, 107)(16, 108)(17, 101)(18, 102)(19, 103)(20, 104)(21, 113)(22, 114)(23, 115)(24, 116)(25, 109)(26, 110)(27, 111)(28, 112)(29, 121)(30, 122)(31, 126)(32, 125)(33, 117)(34, 118)(35, 141)(36, 148)(37, 120)(38, 119)(39, 145)(40, 143)(41, 147)(42, 149)(43, 152)(44, 151)(45, 155)(46, 157)(47, 160)(48, 162)(49, 165)(50, 167)(51, 169)(52, 171)(53, 123)(54, 173)(55, 128)(56, 175)(57, 127)(58, 172)(59, 129)(60, 124)(61, 130)(62, 168)(63, 132)(64, 131)(65, 176)(66, 174)(67, 133)(68, 161)(69, 134)(70, 170)(71, 164)(72, 135)(73, 156)(74, 136)(75, 166)(76, 159)(77, 137)(78, 163)(79, 138)(80, 150)(81, 139)(82, 158)(83, 140)(84, 146)(85, 142)(86, 154)(87, 144)(88, 153)(177, 266)(178, 265)(179, 271)(180, 273)(181, 274)(182, 276)(183, 267)(184, 275)(185, 268)(186, 269)(187, 272)(188, 270)(189, 281)(190, 282)(191, 283)(192, 284)(193, 277)(194, 278)(195, 279)(196, 280)(197, 289)(198, 290)(199, 291)(200, 292)(201, 285)(202, 286)(203, 287)(204, 288)(205, 297)(206, 298)(207, 302)(208, 301)(209, 293)(210, 294)(211, 317)(212, 324)(213, 296)(214, 295)(215, 321)(216, 319)(217, 323)(218, 325)(219, 328)(220, 327)(221, 331)(222, 333)(223, 336)(224, 338)(225, 341)(226, 343)(227, 345)(228, 347)(229, 299)(230, 349)(231, 304)(232, 351)(233, 303)(234, 348)(235, 305)(236, 300)(237, 306)(238, 344)(239, 308)(240, 307)(241, 352)(242, 350)(243, 309)(244, 337)(245, 310)(246, 346)(247, 340)(248, 311)(249, 332)(250, 312)(251, 342)(252, 335)(253, 313)(254, 339)(255, 314)(256, 326)(257, 315)(258, 334)(259, 316)(260, 322)(261, 318)(262, 330)(263, 320)(264, 329) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) } Outer automorphisms :: reflexible Dual of E23.854 Transitivity :: VT+ Graph:: bipartite v = 22 e = 176 f = 110 degree seq :: [ 16^22 ] E23.861 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 4, 4}) Quotient :: loop^2 Aut^+ = (C22 x C2) : C2 (small group id <88, 7>) Aut = D8 x D22 (small group id <176, 31>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y1, Y3^4, (R * Y3)^2, R * Y1 * R * Y2, (Y3^-1 * Y1 * Y3^-1)^2, Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ] Map:: R = (1, 89, 177, 265, 3, 91, 179, 267, 8, 96, 184, 272, 4, 92, 180, 268)(2, 90, 178, 266, 5, 93, 181, 269, 11, 99, 187, 275, 6, 94, 182, 270)(7, 95, 183, 271, 13, 101, 189, 277, 9, 97, 185, 273, 14, 102, 190, 278)(10, 98, 186, 274, 15, 103, 191, 279, 12, 100, 188, 276, 16, 104, 192, 280)(17, 105, 193, 281, 21, 109, 197, 285, 18, 106, 194, 282, 22, 110, 198, 286)(19, 107, 195, 283, 23, 111, 199, 287, 20, 108, 196, 284, 24, 112, 200, 288)(25, 113, 201, 289, 29, 117, 205, 293, 26, 114, 202, 290, 30, 118, 206, 294)(27, 115, 203, 291, 31, 119, 207, 295, 28, 116, 204, 292, 32, 120, 208, 296)(33, 121, 209, 297, 35, 123, 211, 299, 34, 122, 210, 298, 38, 126, 214, 302)(36, 124, 212, 300, 52, 140, 228, 316, 41, 129, 217, 305, 51, 139, 227, 315)(37, 125, 213, 301, 58, 146, 234, 322, 39, 127, 215, 303, 55, 143, 231, 319)(40, 128, 216, 304, 61, 149, 237, 325, 42, 130, 218, 306, 56, 144, 232, 320)(43, 131, 219, 307, 59, 147, 235, 323, 44, 132, 220, 308, 57, 145, 233, 321)(45, 133, 221, 309, 62, 150, 238, 326, 46, 134, 222, 310, 60, 148, 236, 324)(47, 135, 223, 311, 64, 152, 240, 328, 48, 136, 224, 312, 63, 151, 239, 327)(49, 137, 225, 313, 66, 154, 242, 330, 50, 138, 226, 314, 65, 153, 241, 329)(53, 141, 229, 317, 68, 156, 244, 332, 54, 142, 230, 318, 67, 155, 243, 331)(69, 157, 245, 333, 71, 159, 247, 335, 70, 158, 246, 334, 72, 160, 248, 336)(73, 161, 249, 337, 75, 163, 251, 339, 74, 162, 250, 338, 76, 164, 252, 340)(77, 165, 253, 341, 87, 175, 263, 351, 78, 166, 254, 342, 88, 176, 264, 352)(79, 167, 255, 343, 86, 174, 262, 350, 80, 168, 256, 344, 85, 173, 261, 349)(81, 169, 257, 345, 84, 172, 260, 348, 82, 170, 258, 346, 83, 171, 259, 347) L = (1, 90)(2, 89)(3, 95)(4, 97)(5, 98)(6, 100)(7, 91)(8, 99)(9, 92)(10, 93)(11, 96)(12, 94)(13, 105)(14, 106)(15, 107)(16, 108)(17, 101)(18, 102)(19, 103)(20, 104)(21, 113)(22, 114)(23, 115)(24, 116)(25, 109)(26, 110)(27, 111)(28, 112)(29, 121)(30, 122)(31, 139)(32, 140)(33, 117)(34, 118)(35, 143)(36, 144)(37, 145)(38, 146)(39, 147)(40, 148)(41, 149)(42, 150)(43, 151)(44, 152)(45, 153)(46, 154)(47, 155)(48, 156)(49, 157)(50, 158)(51, 119)(52, 120)(53, 161)(54, 162)(55, 123)(56, 124)(57, 125)(58, 126)(59, 127)(60, 128)(61, 129)(62, 130)(63, 131)(64, 132)(65, 133)(66, 134)(67, 135)(68, 136)(69, 137)(70, 138)(71, 176)(72, 175)(73, 141)(74, 142)(75, 173)(76, 174)(77, 171)(78, 172)(79, 170)(80, 169)(81, 168)(82, 167)(83, 165)(84, 166)(85, 163)(86, 164)(87, 160)(88, 159)(177, 266)(178, 265)(179, 271)(180, 273)(181, 274)(182, 276)(183, 267)(184, 275)(185, 268)(186, 269)(187, 272)(188, 270)(189, 281)(190, 282)(191, 283)(192, 284)(193, 277)(194, 278)(195, 279)(196, 280)(197, 289)(198, 290)(199, 291)(200, 292)(201, 285)(202, 286)(203, 287)(204, 288)(205, 297)(206, 298)(207, 315)(208, 316)(209, 293)(210, 294)(211, 319)(212, 320)(213, 321)(214, 322)(215, 323)(216, 324)(217, 325)(218, 326)(219, 327)(220, 328)(221, 329)(222, 330)(223, 331)(224, 332)(225, 333)(226, 334)(227, 295)(228, 296)(229, 337)(230, 338)(231, 299)(232, 300)(233, 301)(234, 302)(235, 303)(236, 304)(237, 305)(238, 306)(239, 307)(240, 308)(241, 309)(242, 310)(243, 311)(244, 312)(245, 313)(246, 314)(247, 352)(248, 351)(249, 317)(250, 318)(251, 349)(252, 350)(253, 347)(254, 348)(255, 346)(256, 345)(257, 344)(258, 343)(259, 341)(260, 342)(261, 339)(262, 340)(263, 336)(264, 335) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) } Outer automorphisms :: reflexible Dual of E23.855 Transitivity :: VT+ Graph:: bipartite v = 22 e = 176 f = 110 degree seq :: [ 16^22 ] E23.862 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 4, 4}) Quotient :: loop^2 Aut^+ = C4 x D22 (small group id <88, 4>) Aut = C2 x C4 x D22 (small group id <176, 28>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, (R * Y3)^2, Y1^4, Y2^4, R * Y2 * R * Y1, (Y3 * Y1^-2)^2, Y2 * Y3 * Y1 * Y2^-1 * Y3 * Y1^-1, Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 ] Map:: non-degenerate R = (1, 89, 177, 265, 4, 92, 180, 268)(2, 90, 178, 266, 6, 94, 182, 270)(3, 91, 179, 267, 7, 95, 183, 271)(5, 93, 181, 269, 10, 98, 186, 274)(8, 96, 184, 272, 13, 101, 189, 277)(9, 97, 185, 273, 14, 102, 190, 278)(11, 99, 187, 275, 15, 103, 191, 279)(12, 100, 188, 276, 16, 104, 192, 280)(17, 105, 193, 281, 21, 109, 197, 285)(18, 106, 194, 282, 22, 110, 198, 286)(19, 107, 195, 283, 23, 111, 199, 287)(20, 108, 196, 284, 24, 112, 200, 288)(25, 113, 201, 289, 29, 117, 205, 293)(26, 114, 202, 290, 30, 118, 206, 294)(27, 115, 203, 291, 31, 119, 207, 295)(28, 116, 204, 292, 32, 120, 208, 296)(33, 121, 209, 297, 38, 126, 214, 302)(34, 122, 210, 298, 35, 123, 211, 299)(36, 124, 212, 300, 52, 140, 228, 316)(37, 125, 213, 301, 51, 139, 227, 315)(39, 127, 215, 303, 55, 143, 231, 319)(40, 128, 216, 304, 56, 144, 232, 320)(41, 129, 217, 305, 57, 145, 233, 321)(42, 130, 218, 306, 58, 146, 234, 322)(43, 131, 219, 307, 59, 147, 235, 323)(44, 132, 220, 308, 60, 148, 236, 324)(45, 133, 221, 309, 61, 149, 237, 325)(46, 134, 222, 310, 62, 150, 238, 326)(47, 135, 223, 311, 63, 151, 239, 327)(48, 136, 224, 312, 64, 152, 240, 328)(49, 137, 225, 313, 65, 153, 241, 329)(50, 138, 226, 314, 66, 154, 242, 330)(53, 141, 229, 317, 67, 155, 243, 331)(54, 142, 230, 318, 68, 156, 244, 332)(69, 157, 245, 333, 71, 159, 247, 335)(70, 158, 246, 334, 72, 160, 248, 336)(73, 161, 249, 337, 76, 164, 252, 340)(74, 162, 250, 338, 75, 163, 251, 339)(77, 165, 253, 341, 88, 176, 264, 352)(78, 166, 254, 342, 87, 175, 263, 351)(79, 167, 255, 343, 86, 174, 262, 350)(80, 168, 256, 344, 85, 173, 261, 349)(81, 169, 257, 345, 83, 171, 259, 347)(82, 170, 258, 346, 84, 172, 260, 348) L = (1, 90)(2, 93)(3, 89)(4, 96)(5, 91)(6, 99)(7, 100)(8, 98)(9, 92)(10, 97)(11, 95)(12, 94)(13, 105)(14, 106)(15, 107)(16, 108)(17, 102)(18, 101)(19, 104)(20, 103)(21, 113)(22, 114)(23, 115)(24, 116)(25, 110)(26, 109)(27, 112)(28, 111)(29, 121)(30, 122)(31, 139)(32, 140)(33, 118)(34, 117)(35, 143)(36, 145)(37, 146)(38, 144)(39, 147)(40, 148)(41, 149)(42, 150)(43, 151)(44, 152)(45, 153)(46, 154)(47, 155)(48, 156)(49, 157)(50, 158)(51, 120)(52, 119)(53, 161)(54, 162)(55, 126)(56, 123)(57, 125)(58, 124)(59, 128)(60, 127)(61, 130)(62, 129)(63, 132)(64, 131)(65, 134)(66, 133)(67, 136)(68, 135)(69, 138)(70, 137)(71, 175)(72, 176)(73, 142)(74, 141)(75, 174)(76, 173)(77, 171)(78, 172)(79, 169)(80, 170)(81, 168)(82, 167)(83, 166)(84, 165)(85, 163)(86, 164)(87, 160)(88, 159)(177, 267)(178, 265)(179, 269)(180, 273)(181, 266)(182, 276)(183, 275)(184, 268)(185, 274)(186, 272)(187, 270)(188, 271)(189, 282)(190, 281)(191, 284)(192, 283)(193, 277)(194, 278)(195, 279)(196, 280)(197, 290)(198, 289)(199, 292)(200, 291)(201, 285)(202, 286)(203, 287)(204, 288)(205, 298)(206, 297)(207, 316)(208, 315)(209, 293)(210, 294)(211, 320)(212, 322)(213, 321)(214, 319)(215, 324)(216, 323)(217, 326)(218, 325)(219, 328)(220, 327)(221, 330)(222, 329)(223, 332)(224, 331)(225, 334)(226, 333)(227, 295)(228, 296)(229, 338)(230, 337)(231, 299)(232, 302)(233, 300)(234, 301)(235, 303)(236, 304)(237, 305)(238, 306)(239, 307)(240, 308)(241, 309)(242, 310)(243, 311)(244, 312)(245, 313)(246, 314)(247, 352)(248, 351)(249, 317)(250, 318)(251, 349)(252, 350)(253, 348)(254, 347)(255, 346)(256, 345)(257, 343)(258, 344)(259, 341)(260, 342)(261, 340)(262, 339)(263, 335)(264, 336) local type(s) :: { ( 4^8 ) } Outer automorphisms :: reflexible Dual of E23.856 Transitivity :: VT+ Graph:: bipartite v = 44 e = 176 f = 88 degree seq :: [ 8^44 ] E23.863 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 4, 4}) Quotient :: loop^2 Aut^+ = C4 x D22 (small group id <88, 4>) Aut = D8 x D22 (small group id <176, 31>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2 * Y1^-1, R * Y2 * R * Y1, (R * Y3)^2, Y1^4, Y2^4, (Y1^-1 * Y3 * Y2^-1)^2, Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-2 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1, Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 89, 177, 265, 3, 91, 179, 267)(2, 90, 178, 266, 6, 94, 182, 270)(4, 92, 180, 268, 9, 97, 185, 273)(5, 93, 181, 269, 10, 98, 186, 274)(7, 95, 183, 271, 13, 101, 189, 277)(8, 96, 184, 272, 14, 102, 190, 278)(11, 99, 187, 275, 15, 103, 191, 279)(12, 100, 188, 276, 16, 104, 192, 280)(17, 105, 193, 281, 21, 109, 197, 285)(18, 106, 194, 282, 22, 110, 198, 286)(19, 107, 195, 283, 23, 111, 199, 287)(20, 108, 196, 284, 24, 112, 200, 288)(25, 113, 201, 289, 29, 117, 205, 293)(26, 114, 202, 290, 30, 118, 206, 294)(27, 115, 203, 291, 31, 119, 207, 295)(28, 116, 204, 292, 32, 120, 208, 296)(33, 121, 209, 297, 57, 145, 233, 321)(34, 122, 210, 298, 59, 147, 235, 323)(35, 123, 211, 299, 62, 150, 238, 326)(36, 124, 212, 300, 66, 154, 242, 330)(37, 125, 213, 301, 68, 156, 244, 332)(38, 126, 214, 302, 72, 160, 248, 336)(39, 127, 215, 303, 74, 162, 250, 338)(40, 128, 216, 304, 61, 149, 237, 325)(41, 129, 217, 305, 77, 165, 253, 341)(42, 130, 218, 306, 79, 167, 255, 343)(43, 131, 219, 307, 64, 152, 240, 328)(44, 132, 220, 308, 65, 153, 241, 329)(45, 133, 221, 309, 83, 171, 259, 347)(46, 134, 222, 310, 85, 173, 261, 349)(47, 135, 223, 311, 69, 157, 245, 333)(48, 136, 224, 312, 71, 159, 247, 335)(49, 137, 225, 313, 86, 174, 262, 350)(50, 138, 226, 314, 84, 172, 260, 348)(51, 139, 227, 315, 78, 166, 254, 342)(52, 140, 228, 316, 80, 168, 256, 344)(53, 141, 229, 317, 67, 155, 243, 331)(54, 142, 230, 318, 73, 161, 249, 337)(55, 143, 231, 319, 75, 163, 251, 339)(56, 144, 232, 320, 63, 151, 239, 327)(58, 146, 234, 322, 82, 170, 258, 346)(60, 148, 236, 324, 70, 158, 246, 334)(76, 164, 252, 340, 87, 175, 263, 351)(81, 169, 257, 345, 88, 176, 264, 352) L = (1, 90)(2, 93)(3, 95)(4, 89)(5, 92)(6, 99)(7, 98)(8, 91)(9, 100)(10, 96)(11, 97)(12, 94)(13, 105)(14, 106)(15, 107)(16, 108)(17, 102)(18, 101)(19, 104)(20, 103)(21, 113)(22, 114)(23, 115)(24, 116)(25, 110)(26, 109)(27, 112)(28, 111)(29, 121)(30, 122)(31, 136)(32, 135)(33, 118)(34, 117)(35, 149)(36, 153)(37, 157)(38, 156)(39, 152)(40, 145)(41, 162)(42, 150)(43, 147)(44, 159)(45, 160)(46, 154)(47, 119)(48, 120)(49, 167)(50, 165)(51, 173)(52, 171)(53, 172)(54, 174)(55, 168)(56, 166)(57, 131)(58, 161)(59, 128)(60, 155)(61, 127)(62, 129)(63, 175)(64, 123)(65, 126)(66, 133)(67, 146)(68, 124)(69, 132)(70, 164)(71, 125)(72, 134)(73, 148)(74, 130)(75, 176)(76, 170)(77, 137)(78, 143)(79, 138)(80, 144)(81, 158)(82, 169)(83, 139)(84, 142)(85, 140)(86, 141)(87, 163)(88, 151)(177, 266)(178, 269)(179, 271)(180, 265)(181, 268)(182, 275)(183, 274)(184, 267)(185, 276)(186, 272)(187, 273)(188, 270)(189, 281)(190, 282)(191, 283)(192, 284)(193, 278)(194, 277)(195, 280)(196, 279)(197, 289)(198, 290)(199, 291)(200, 292)(201, 286)(202, 285)(203, 288)(204, 287)(205, 297)(206, 298)(207, 312)(208, 311)(209, 294)(210, 293)(211, 325)(212, 329)(213, 333)(214, 332)(215, 328)(216, 321)(217, 338)(218, 326)(219, 323)(220, 335)(221, 336)(222, 330)(223, 295)(224, 296)(225, 343)(226, 341)(227, 349)(228, 347)(229, 348)(230, 350)(231, 344)(232, 342)(233, 307)(234, 337)(235, 304)(236, 331)(237, 303)(238, 305)(239, 351)(240, 299)(241, 302)(242, 309)(243, 322)(244, 300)(245, 308)(246, 340)(247, 301)(248, 310)(249, 324)(250, 306)(251, 352)(252, 346)(253, 313)(254, 319)(255, 314)(256, 320)(257, 334)(258, 345)(259, 315)(260, 318)(261, 316)(262, 317)(263, 339)(264, 327) local type(s) :: { ( 4^8 ) } Outer automorphisms :: reflexible Dual of E23.857 Transitivity :: VT+ Graph:: bipartite v = 44 e = 176 f = 88 degree seq :: [ 8^44 ] E23.864 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 4, 4}) Quotient :: loop^2 Aut^+ = (C22 x C2) : C2 (small group id <88, 7>) Aut = D8 x D22 (small group id <176, 31>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2 * Y1^-1, R * Y2 * R * Y1, (R * Y3)^2, Y1^4, Y2^4, Y2^-1 * Y3 * Y1^2 * Y3 * Y1^-1, (Y1^-1 * Y3 * Y2^-1)^2, Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 89, 177, 265, 3, 91, 179, 267)(2, 90, 178, 266, 6, 94, 182, 270)(4, 92, 180, 268, 9, 97, 185, 273)(5, 93, 181, 269, 10, 98, 186, 274)(7, 95, 183, 271, 13, 101, 189, 277)(8, 96, 184, 272, 14, 102, 190, 278)(11, 99, 187, 275, 15, 103, 191, 279)(12, 100, 188, 276, 16, 104, 192, 280)(17, 105, 193, 281, 21, 109, 197, 285)(18, 106, 194, 282, 22, 110, 198, 286)(19, 107, 195, 283, 23, 111, 199, 287)(20, 108, 196, 284, 24, 112, 200, 288)(25, 113, 201, 289, 29, 117, 205, 293)(26, 114, 202, 290, 30, 118, 206, 294)(27, 115, 203, 291, 31, 119, 207, 295)(28, 116, 204, 292, 32, 120, 208, 296)(33, 121, 209, 297, 53, 141, 229, 317)(34, 122, 210, 298, 54, 142, 230, 318)(35, 123, 211, 299, 55, 143, 231, 319)(36, 124, 212, 300, 56, 144, 232, 320)(37, 125, 213, 301, 57, 145, 233, 321)(38, 126, 214, 302, 58, 146, 234, 322)(39, 127, 215, 303, 59, 147, 235, 323)(40, 128, 216, 304, 60, 148, 236, 324)(41, 129, 217, 305, 61, 149, 237, 325)(42, 130, 218, 306, 62, 150, 238, 326)(43, 131, 219, 307, 63, 151, 239, 327)(44, 132, 220, 308, 64, 152, 240, 328)(45, 133, 221, 309, 65, 153, 241, 329)(46, 134, 222, 310, 66, 154, 242, 330)(47, 135, 223, 311, 67, 155, 243, 331)(48, 136, 224, 312, 68, 156, 244, 332)(49, 137, 225, 313, 69, 157, 245, 333)(50, 138, 226, 314, 70, 158, 246, 334)(51, 139, 227, 315, 71, 159, 247, 335)(52, 140, 228, 316, 72, 160, 248, 336)(73, 161, 249, 337, 87, 175, 263, 351)(74, 162, 250, 338, 88, 176, 264, 352)(75, 163, 251, 339, 85, 173, 261, 349)(76, 164, 252, 340, 86, 174, 262, 350)(77, 165, 253, 341, 83, 171, 259, 347)(78, 166, 254, 342, 84, 172, 260, 348)(79, 167, 255, 343, 82, 170, 258, 346)(80, 168, 256, 344, 81, 169, 257, 345) L = (1, 90)(2, 93)(3, 95)(4, 89)(5, 92)(6, 99)(7, 98)(8, 91)(9, 100)(10, 96)(11, 97)(12, 94)(13, 105)(14, 106)(15, 107)(16, 108)(17, 102)(18, 101)(19, 104)(20, 103)(21, 113)(22, 114)(23, 115)(24, 116)(25, 110)(26, 109)(27, 112)(28, 111)(29, 121)(30, 122)(31, 125)(32, 123)(33, 118)(34, 117)(35, 119)(36, 141)(37, 120)(38, 145)(39, 143)(40, 142)(41, 148)(42, 144)(43, 147)(44, 146)(45, 150)(46, 149)(47, 152)(48, 151)(49, 154)(50, 153)(51, 156)(52, 155)(53, 128)(54, 124)(55, 126)(56, 129)(57, 127)(58, 131)(59, 132)(60, 130)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 161)(70, 162)(71, 164)(72, 163)(73, 158)(74, 157)(75, 159)(76, 160)(77, 175)(78, 176)(79, 174)(80, 173)(81, 172)(82, 171)(83, 169)(84, 170)(85, 167)(86, 168)(87, 166)(88, 165)(177, 266)(178, 269)(179, 271)(180, 265)(181, 268)(182, 275)(183, 274)(184, 267)(185, 276)(186, 272)(187, 273)(188, 270)(189, 281)(190, 282)(191, 283)(192, 284)(193, 278)(194, 277)(195, 280)(196, 279)(197, 289)(198, 290)(199, 291)(200, 292)(201, 286)(202, 285)(203, 288)(204, 287)(205, 297)(206, 298)(207, 301)(208, 299)(209, 294)(210, 293)(211, 295)(212, 317)(213, 296)(214, 321)(215, 319)(216, 318)(217, 324)(218, 320)(219, 323)(220, 322)(221, 326)(222, 325)(223, 328)(224, 327)(225, 330)(226, 329)(227, 332)(228, 331)(229, 304)(230, 300)(231, 302)(232, 305)(233, 303)(234, 307)(235, 308)(236, 306)(237, 309)(238, 310)(239, 311)(240, 312)(241, 313)(242, 314)(243, 315)(244, 316)(245, 337)(246, 338)(247, 340)(248, 339)(249, 334)(250, 333)(251, 335)(252, 336)(253, 351)(254, 352)(255, 350)(256, 349)(257, 348)(258, 347)(259, 345)(260, 346)(261, 343)(262, 344)(263, 342)(264, 341) local type(s) :: { ( 4^8 ) } Outer automorphisms :: reflexible Dual of E23.858 Transitivity :: VT+ Graph:: bipartite v = 44 e = 176 f = 88 degree seq :: [ 8^44 ] E23.865 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 4}) Quotient :: dipole Aut^+ = C4 x D22 (small group id <88, 4>) Aut = D8 x D22 (small group id <176, 31>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y1^2, R^2, (Y3^-1 * Y1)^2, (R * Y3)^2, (R * Y1)^2, Y2^4, (Y2^-1 * Y1 * Y2^-1)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^4, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 ] Map:: R = (1, 89, 2, 90)(3, 91, 7, 95)(4, 92, 9, 97)(5, 93, 10, 98)(6, 94, 12, 100)(8, 96, 11, 99)(13, 101, 17, 105)(14, 102, 18, 106)(15, 103, 19, 107)(16, 104, 20, 108)(21, 109, 25, 113)(22, 110, 26, 114)(23, 111, 27, 115)(24, 112, 28, 116)(29, 117, 33, 121)(30, 118, 34, 122)(31, 119, 40, 128)(32, 120, 35, 123)(36, 124, 54, 142)(37, 125, 53, 141)(38, 126, 55, 143)(39, 127, 56, 144)(41, 129, 57, 145)(42, 130, 58, 146)(43, 131, 59, 147)(44, 132, 60, 148)(45, 133, 61, 149)(46, 134, 62, 150)(47, 135, 63, 151)(48, 136, 64, 152)(49, 137, 65, 153)(50, 138, 66, 154)(51, 139, 67, 155)(52, 140, 68, 156)(69, 157, 73, 161)(70, 158, 74, 162)(71, 159, 76, 164)(72, 160, 75, 163)(77, 165, 88, 176)(78, 166, 87, 175)(79, 167, 86, 174)(80, 168, 85, 173)(81, 169, 83, 171)(82, 170, 84, 172)(177, 265, 179, 267, 184, 272, 180, 268)(178, 266, 181, 269, 187, 275, 182, 270)(183, 271, 189, 277, 185, 273, 190, 278)(186, 274, 191, 279, 188, 276, 192, 280)(193, 281, 197, 285, 194, 282, 198, 286)(195, 283, 199, 287, 196, 284, 200, 288)(201, 289, 205, 293, 202, 290, 206, 294)(203, 291, 207, 295, 204, 292, 208, 296)(209, 297, 229, 317, 210, 298, 230, 318)(211, 299, 231, 319, 216, 304, 232, 320)(212, 300, 233, 321, 213, 301, 234, 322)(214, 302, 235, 323, 215, 303, 236, 324)(217, 305, 237, 325, 218, 306, 238, 326)(219, 307, 239, 327, 220, 308, 240, 328)(221, 309, 241, 329, 222, 310, 242, 330)(223, 311, 243, 331, 224, 312, 244, 332)(225, 313, 245, 333, 226, 314, 246, 334)(227, 315, 247, 335, 228, 316, 248, 336)(249, 337, 263, 351, 250, 338, 264, 352)(251, 339, 262, 350, 252, 340, 261, 349)(253, 341, 259, 347, 254, 342, 260, 348)(255, 343, 257, 345, 256, 344, 258, 346) L = (1, 177)(2, 178)(3, 179)(4, 180)(5, 181)(6, 182)(7, 183)(8, 184)(9, 185)(10, 186)(11, 187)(12, 188)(13, 189)(14, 190)(15, 191)(16, 192)(17, 193)(18, 194)(19, 195)(20, 196)(21, 197)(22, 198)(23, 199)(24, 200)(25, 201)(26, 202)(27, 203)(28, 204)(29, 205)(30, 206)(31, 207)(32, 208)(33, 209)(34, 210)(35, 211)(36, 212)(37, 213)(38, 214)(39, 215)(40, 216)(41, 217)(42, 218)(43, 219)(44, 220)(45, 221)(46, 222)(47, 223)(48, 224)(49, 225)(50, 226)(51, 227)(52, 228)(53, 229)(54, 230)(55, 231)(56, 232)(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, 245)(70, 246)(71, 247)(72, 248)(73, 249)(74, 250)(75, 251)(76, 252)(77, 253)(78, 254)(79, 255)(80, 256)(81, 257)(82, 258)(83, 259)(84, 260)(85, 261)(86, 262)(87, 263)(88, 264)(89, 265)(90, 266)(91, 267)(92, 268)(93, 269)(94, 270)(95, 271)(96, 272)(97, 273)(98, 274)(99, 275)(100, 276)(101, 277)(102, 278)(103, 279)(104, 280)(105, 281)(106, 282)(107, 283)(108, 284)(109, 285)(110, 286)(111, 287)(112, 288)(113, 289)(114, 290)(115, 291)(116, 292)(117, 293)(118, 294)(119, 295)(120, 296)(121, 297)(122, 298)(123, 299)(124, 300)(125, 301)(126, 302)(127, 303)(128, 304)(129, 305)(130, 306)(131, 307)(132, 308)(133, 309)(134, 310)(135, 311)(136, 312)(137, 313)(138, 314)(139, 315)(140, 316)(141, 317)(142, 318)(143, 319)(144, 320)(145, 321)(146, 322)(147, 323)(148, 324)(149, 325)(150, 326)(151, 327)(152, 328)(153, 329)(154, 330)(155, 331)(156, 332)(157, 333)(158, 334)(159, 335)(160, 336)(161, 337)(162, 338)(163, 339)(164, 340)(165, 341)(166, 342)(167, 343)(168, 344)(169, 345)(170, 346)(171, 347)(172, 348)(173, 349)(174, 350)(175, 351)(176, 352) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 66 e = 176 f = 66 degree seq :: [ 4^44, 8^22 ] E23.866 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 4}) Quotient :: dipole Aut^+ = (C22 x C2) : C2 (small group id <88, 7>) Aut = D8 x D22 (small group id <176, 31>) |r| :: 2 Presentation :: [ Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y3, Y1^2, R^2, Y2^4, (Y3^-1 * Y1)^2, (R * Y3)^2, (R * Y1)^2, (Y2^-1 * Y1 * Y2^-1)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^4, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 ] Map:: R = (1, 89, 2, 90)(3, 91, 7, 95)(4, 92, 9, 97)(5, 93, 10, 98)(6, 94, 12, 100)(8, 96, 11, 99)(13, 101, 17, 105)(14, 102, 18, 106)(15, 103, 19, 107)(16, 104, 20, 108)(21, 109, 25, 113)(22, 110, 26, 114)(23, 111, 27, 115)(24, 112, 28, 116)(29, 117, 33, 121)(30, 118, 34, 122)(31, 119, 38, 126)(32, 120, 37, 125)(35, 123, 53, 141)(36, 124, 60, 148)(39, 127, 57, 145)(40, 128, 55, 143)(41, 129, 59, 147)(42, 130, 61, 149)(43, 131, 64, 152)(44, 132, 63, 151)(45, 133, 67, 155)(46, 134, 69, 157)(47, 135, 72, 160)(48, 136, 74, 162)(49, 137, 77, 165)(50, 138, 79, 167)(51, 139, 81, 169)(52, 140, 83, 171)(54, 142, 85, 173)(56, 144, 87, 175)(58, 146, 82, 170)(62, 150, 78, 166)(65, 153, 86, 174)(66, 154, 88, 176)(68, 156, 76, 164)(70, 158, 84, 172)(71, 159, 73, 161)(75, 163, 80, 168)(177, 265, 179, 267, 184, 272, 180, 268)(178, 266, 181, 269, 187, 275, 182, 270)(183, 271, 189, 277, 185, 273, 190, 278)(186, 274, 191, 279, 188, 276, 192, 280)(193, 281, 197, 285, 194, 282, 198, 286)(195, 283, 199, 287, 196, 284, 200, 288)(201, 289, 205, 293, 202, 290, 206, 294)(203, 291, 207, 295, 204, 292, 208, 296)(209, 297, 229, 317, 210, 298, 231, 319)(211, 299, 233, 321, 216, 304, 235, 323)(212, 300, 237, 325, 219, 307, 239, 327)(213, 301, 240, 328, 214, 302, 236, 324)(215, 303, 243, 331, 217, 305, 245, 333)(218, 306, 248, 336, 220, 308, 250, 338)(221, 309, 253, 341, 222, 310, 255, 343)(223, 311, 257, 345, 224, 312, 259, 347)(225, 313, 261, 349, 226, 314, 263, 351)(227, 315, 264, 352, 228, 316, 262, 350)(230, 318, 258, 346, 232, 320, 260, 348)(234, 322, 252, 340, 246, 334, 249, 337)(238, 326, 247, 335, 251, 339, 244, 332)(241, 329, 256, 344, 242, 330, 254, 342) L = (1, 177)(2, 178)(3, 179)(4, 180)(5, 181)(6, 182)(7, 183)(8, 184)(9, 185)(10, 186)(11, 187)(12, 188)(13, 189)(14, 190)(15, 191)(16, 192)(17, 193)(18, 194)(19, 195)(20, 196)(21, 197)(22, 198)(23, 199)(24, 200)(25, 201)(26, 202)(27, 203)(28, 204)(29, 205)(30, 206)(31, 207)(32, 208)(33, 209)(34, 210)(35, 211)(36, 212)(37, 213)(38, 214)(39, 215)(40, 216)(41, 217)(42, 218)(43, 219)(44, 220)(45, 221)(46, 222)(47, 223)(48, 224)(49, 225)(50, 226)(51, 227)(52, 228)(53, 229)(54, 230)(55, 231)(56, 232)(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, 245)(70, 246)(71, 247)(72, 248)(73, 249)(74, 250)(75, 251)(76, 252)(77, 253)(78, 254)(79, 255)(80, 256)(81, 257)(82, 258)(83, 259)(84, 260)(85, 261)(86, 262)(87, 263)(88, 264)(89, 265)(90, 266)(91, 267)(92, 268)(93, 269)(94, 270)(95, 271)(96, 272)(97, 273)(98, 274)(99, 275)(100, 276)(101, 277)(102, 278)(103, 279)(104, 280)(105, 281)(106, 282)(107, 283)(108, 284)(109, 285)(110, 286)(111, 287)(112, 288)(113, 289)(114, 290)(115, 291)(116, 292)(117, 293)(118, 294)(119, 295)(120, 296)(121, 297)(122, 298)(123, 299)(124, 300)(125, 301)(126, 302)(127, 303)(128, 304)(129, 305)(130, 306)(131, 307)(132, 308)(133, 309)(134, 310)(135, 311)(136, 312)(137, 313)(138, 314)(139, 315)(140, 316)(141, 317)(142, 318)(143, 319)(144, 320)(145, 321)(146, 322)(147, 323)(148, 324)(149, 325)(150, 326)(151, 327)(152, 328)(153, 329)(154, 330)(155, 331)(156, 332)(157, 333)(158, 334)(159, 335)(160, 336)(161, 337)(162, 338)(163, 339)(164, 340)(165, 341)(166, 342)(167, 343)(168, 344)(169, 345)(170, 346)(171, 347)(172, 348)(173, 349)(174, 350)(175, 351)(176, 352) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 66 e = 176 f = 66 degree seq :: [ 4^44, 8^22 ] E23.867 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 4}) Quotient :: dipole Aut^+ = C4 x D22 (small group id <88, 4>) Aut = D8 x D22 (small group id <176, 31>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^2, Y2^2 * Y3, (Y1 * Y3)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y3 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y3, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 ] Map:: non-degenerate R = (1, 89, 2, 90)(3, 91, 9, 97)(4, 92, 7, 95)(5, 93, 10, 98)(6, 94, 11, 99)(8, 96, 12, 100)(13, 101, 17, 105)(14, 102, 18, 106)(15, 103, 19, 107)(16, 104, 20, 108)(21, 109, 25, 113)(22, 110, 26, 114)(23, 111, 27, 115)(24, 112, 28, 116)(29, 117, 33, 121)(30, 118, 34, 122)(31, 119, 51, 139)(32, 120, 52, 140)(35, 123, 55, 143)(36, 124, 56, 144)(37, 125, 57, 145)(38, 126, 58, 146)(39, 127, 59, 147)(40, 128, 60, 148)(41, 129, 61, 149)(42, 130, 62, 150)(43, 131, 63, 151)(44, 132, 64, 152)(45, 133, 65, 153)(46, 134, 66, 154)(47, 135, 67, 155)(48, 136, 68, 156)(49, 137, 69, 157)(50, 138, 70, 158)(53, 141, 73, 161)(54, 142, 74, 162)(71, 159, 88, 176)(72, 160, 87, 175)(75, 163, 86, 174)(76, 164, 85, 173)(77, 165, 84, 172)(78, 166, 83, 171)(79, 167, 81, 169)(80, 168, 82, 170)(177, 265, 179, 267, 180, 268, 181, 269)(178, 266, 182, 270, 183, 271, 184, 272)(185, 273, 189, 277, 186, 274, 190, 278)(187, 275, 191, 279, 188, 276, 192, 280)(193, 281, 197, 285, 194, 282, 198, 286)(195, 283, 199, 287, 196, 284, 200, 288)(201, 289, 205, 293, 202, 290, 206, 294)(203, 291, 207, 295, 204, 292, 208, 296)(209, 297, 213, 301, 210, 298, 211, 299)(212, 300, 227, 315, 214, 302, 228, 316)(215, 303, 233, 321, 216, 304, 231, 319)(217, 305, 234, 322, 218, 306, 232, 320)(219, 307, 236, 324, 220, 308, 235, 323)(221, 309, 238, 326, 222, 310, 237, 325)(223, 311, 240, 328, 224, 312, 239, 327)(225, 313, 242, 330, 226, 314, 241, 329)(229, 317, 244, 332, 230, 318, 243, 331)(245, 333, 247, 335, 246, 334, 248, 336)(249, 337, 252, 340, 250, 338, 251, 339)(253, 341, 264, 352, 254, 342, 263, 351)(255, 343, 261, 349, 256, 344, 262, 350)(257, 345, 259, 347, 258, 346, 260, 348) L = (1, 180)(2, 183)(3, 181)(4, 177)(5, 179)(6, 184)(7, 178)(8, 182)(9, 186)(10, 185)(11, 188)(12, 187)(13, 190)(14, 189)(15, 192)(16, 191)(17, 194)(18, 193)(19, 196)(20, 195)(21, 198)(22, 197)(23, 200)(24, 199)(25, 202)(26, 201)(27, 204)(28, 203)(29, 206)(30, 205)(31, 208)(32, 207)(33, 210)(34, 209)(35, 213)(36, 214)(37, 211)(38, 212)(39, 216)(40, 215)(41, 218)(42, 217)(43, 220)(44, 219)(45, 222)(46, 221)(47, 224)(48, 223)(49, 226)(50, 225)(51, 228)(52, 227)(53, 230)(54, 229)(55, 233)(56, 234)(57, 231)(58, 232)(59, 236)(60, 235)(61, 238)(62, 237)(63, 240)(64, 239)(65, 242)(66, 241)(67, 244)(68, 243)(69, 246)(70, 245)(71, 248)(72, 247)(73, 250)(74, 249)(75, 252)(76, 251)(77, 254)(78, 253)(79, 256)(80, 255)(81, 258)(82, 257)(83, 260)(84, 259)(85, 262)(86, 261)(87, 264)(88, 263)(89, 265)(90, 266)(91, 267)(92, 268)(93, 269)(94, 270)(95, 271)(96, 272)(97, 273)(98, 274)(99, 275)(100, 276)(101, 277)(102, 278)(103, 279)(104, 280)(105, 281)(106, 282)(107, 283)(108, 284)(109, 285)(110, 286)(111, 287)(112, 288)(113, 289)(114, 290)(115, 291)(116, 292)(117, 293)(118, 294)(119, 295)(120, 296)(121, 297)(122, 298)(123, 299)(124, 300)(125, 301)(126, 302)(127, 303)(128, 304)(129, 305)(130, 306)(131, 307)(132, 308)(133, 309)(134, 310)(135, 311)(136, 312)(137, 313)(138, 314)(139, 315)(140, 316)(141, 317)(142, 318)(143, 319)(144, 320)(145, 321)(146, 322)(147, 323)(148, 324)(149, 325)(150, 326)(151, 327)(152, 328)(153, 329)(154, 330)(155, 331)(156, 332)(157, 333)(158, 334)(159, 335)(160, 336)(161, 337)(162, 338)(163, 339)(164, 340)(165, 341)(166, 342)(167, 343)(168, 344)(169, 345)(170, 346)(171, 347)(172, 348)(173, 349)(174, 350)(175, 351)(176, 352) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 66 e = 176 f = 66 degree seq :: [ 4^44, 8^22 ] E23.868 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 4}) Quotient :: dipole Aut^+ = (C22 x C2) : C2 (small group id <88, 7>) Aut = D8 x D22 (small group id <176, 31>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^2, Y2^2 * Y3, (Y1 * Y3)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 ] Map:: non-degenerate R = (1, 89, 2, 90)(3, 91, 9, 97)(4, 92, 7, 95)(5, 93, 10, 98)(6, 94, 11, 99)(8, 96, 12, 100)(13, 101, 17, 105)(14, 102, 18, 106)(15, 103, 19, 107)(16, 104, 20, 108)(21, 109, 25, 113)(22, 110, 26, 114)(23, 111, 27, 115)(24, 112, 28, 116)(29, 117, 33, 121)(30, 118, 34, 122)(31, 119, 51, 139)(32, 120, 52, 140)(35, 123, 55, 143)(36, 124, 56, 144)(37, 125, 57, 145)(38, 126, 58, 146)(39, 127, 59, 147)(40, 128, 60, 148)(41, 129, 61, 149)(42, 130, 62, 150)(43, 131, 63, 151)(44, 132, 64, 152)(45, 133, 65, 153)(46, 134, 66, 154)(47, 135, 67, 155)(48, 136, 68, 156)(49, 137, 69, 157)(50, 138, 70, 158)(53, 141, 73, 161)(54, 142, 74, 162)(71, 159, 88, 176)(72, 160, 87, 175)(75, 163, 85, 173)(76, 164, 86, 174)(77, 165, 83, 171)(78, 166, 84, 172)(79, 167, 82, 170)(80, 168, 81, 169)(177, 265, 179, 267, 180, 268, 181, 269)(178, 266, 182, 270, 183, 271, 184, 272)(185, 273, 189, 277, 186, 274, 190, 278)(187, 275, 191, 279, 188, 276, 192, 280)(193, 281, 197, 285, 194, 282, 198, 286)(195, 283, 199, 287, 196, 284, 200, 288)(201, 289, 205, 293, 202, 290, 206, 294)(203, 291, 207, 295, 204, 292, 208, 296)(209, 297, 211, 299, 210, 298, 213, 301)(212, 300, 228, 316, 214, 302, 227, 315)(215, 303, 233, 321, 216, 304, 231, 319)(217, 305, 234, 322, 218, 306, 232, 320)(219, 307, 236, 324, 220, 308, 235, 323)(221, 309, 238, 326, 222, 310, 237, 325)(223, 311, 240, 328, 224, 312, 239, 327)(225, 313, 242, 330, 226, 314, 241, 329)(229, 317, 244, 332, 230, 318, 243, 331)(245, 333, 247, 335, 246, 334, 248, 336)(249, 337, 251, 339, 250, 338, 252, 340)(253, 341, 263, 351, 254, 342, 264, 352)(255, 343, 262, 350, 256, 344, 261, 349)(257, 345, 260, 348, 258, 346, 259, 347) L = (1, 180)(2, 183)(3, 181)(4, 177)(5, 179)(6, 184)(7, 178)(8, 182)(9, 186)(10, 185)(11, 188)(12, 187)(13, 190)(14, 189)(15, 192)(16, 191)(17, 194)(18, 193)(19, 196)(20, 195)(21, 198)(22, 197)(23, 200)(24, 199)(25, 202)(26, 201)(27, 204)(28, 203)(29, 206)(30, 205)(31, 208)(32, 207)(33, 210)(34, 209)(35, 213)(36, 214)(37, 211)(38, 212)(39, 216)(40, 215)(41, 218)(42, 217)(43, 220)(44, 219)(45, 222)(46, 221)(47, 224)(48, 223)(49, 226)(50, 225)(51, 228)(52, 227)(53, 230)(54, 229)(55, 233)(56, 234)(57, 231)(58, 232)(59, 236)(60, 235)(61, 238)(62, 237)(63, 240)(64, 239)(65, 242)(66, 241)(67, 244)(68, 243)(69, 246)(70, 245)(71, 248)(72, 247)(73, 250)(74, 249)(75, 252)(76, 251)(77, 254)(78, 253)(79, 256)(80, 255)(81, 258)(82, 257)(83, 260)(84, 259)(85, 262)(86, 261)(87, 264)(88, 263)(89, 265)(90, 266)(91, 267)(92, 268)(93, 269)(94, 270)(95, 271)(96, 272)(97, 273)(98, 274)(99, 275)(100, 276)(101, 277)(102, 278)(103, 279)(104, 280)(105, 281)(106, 282)(107, 283)(108, 284)(109, 285)(110, 286)(111, 287)(112, 288)(113, 289)(114, 290)(115, 291)(116, 292)(117, 293)(118, 294)(119, 295)(120, 296)(121, 297)(122, 298)(123, 299)(124, 300)(125, 301)(126, 302)(127, 303)(128, 304)(129, 305)(130, 306)(131, 307)(132, 308)(133, 309)(134, 310)(135, 311)(136, 312)(137, 313)(138, 314)(139, 315)(140, 316)(141, 317)(142, 318)(143, 319)(144, 320)(145, 321)(146, 322)(147, 323)(148, 324)(149, 325)(150, 326)(151, 327)(152, 328)(153, 329)(154, 330)(155, 331)(156, 332)(157, 333)(158, 334)(159, 335)(160, 336)(161, 337)(162, 338)(163, 339)(164, 340)(165, 341)(166, 342)(167, 343)(168, 344)(169, 345)(170, 346)(171, 347)(172, 348)(173, 349)(174, 350)(175, 351)(176, 352) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible selfdual Graph:: bipartite v = 66 e = 176 f = 66 degree seq :: [ 4^44, 8^22 ] E23.869 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 4}) Quotient :: dipole Aut^+ = C4 x D22 (small group id <88, 4>) Aut = D8 x D22 (small group id <176, 31>) |r| :: 2 Presentation :: [ Y1^2, R^2, (R * Y3)^2, Y3^-1 * Y2 * Y3^-1 * Y2^-1, (Y3^-1 * Y1)^2, (R * Y1)^2, Y2^4, Y3 * Y2^-1 * Y3^-1 * Y1 * Y2 * Y1, (R * Y2 * Y3^-1)^2, (Y2^-2 * Y1)^2, Y3^11, Y3^5 * Y1 * Y2 * Y3^4 * Y1 * Y2^-1 ] Map:: non-degenerate R = (1, 89, 2, 90)(3, 91, 11, 99)(4, 92, 10, 98)(5, 93, 17, 105)(6, 94, 8, 96)(7, 95, 20, 108)(9, 97, 26, 114)(12, 100, 21, 109)(13, 101, 30, 118)(14, 102, 23, 111)(15, 103, 28, 116)(16, 104, 25, 113)(18, 106, 35, 123)(19, 107, 24, 112)(22, 110, 39, 127)(27, 115, 44, 132)(29, 117, 47, 135)(31, 119, 41, 129)(32, 120, 40, 128)(33, 121, 49, 137)(34, 122, 46, 134)(36, 124, 52, 140)(37, 125, 43, 131)(38, 126, 55, 143)(42, 130, 57, 145)(45, 133, 60, 148)(48, 136, 63, 151)(50, 138, 65, 153)(51, 139, 62, 150)(53, 141, 68, 156)(54, 142, 59, 147)(56, 144, 71, 159)(58, 146, 73, 161)(61, 149, 76, 164)(64, 152, 79, 167)(66, 154, 81, 169)(67, 155, 78, 166)(69, 157, 83, 171)(70, 158, 75, 163)(72, 160, 85, 173)(74, 162, 82, 170)(77, 165, 84, 172)(80, 168, 87, 175)(86, 174, 88, 176)(177, 265, 179, 267, 188, 276, 181, 269)(178, 266, 183, 271, 197, 285, 185, 273)(180, 268, 190, 278, 207, 295, 192, 280)(182, 270, 189, 277, 208, 296, 194, 282)(184, 272, 199, 287, 216, 304, 201, 289)(186, 274, 198, 286, 217, 305, 203, 291)(187, 275, 205, 293, 193, 281, 200, 288)(191, 279, 196, 284, 214, 302, 202, 290)(195, 283, 209, 297, 223, 311, 212, 300)(204, 292, 218, 306, 231, 319, 221, 309)(206, 294, 224, 312, 211, 299, 219, 307)(210, 298, 215, 303, 232, 320, 220, 308)(213, 301, 226, 314, 239, 327, 229, 317)(222, 310, 234, 322, 247, 335, 237, 325)(225, 313, 240, 328, 228, 316, 235, 323)(227, 315, 233, 321, 248, 336, 236, 324)(230, 318, 242, 330, 255, 343, 245, 333)(238, 326, 250, 338, 261, 349, 253, 341)(241, 329, 256, 344, 244, 332, 251, 339)(243, 331, 249, 337, 262, 350, 252, 340)(246, 334, 258, 346, 263, 351, 260, 348)(254, 342, 257, 345, 264, 352, 259, 347) L = (1, 180)(2, 184)(3, 189)(4, 191)(5, 194)(6, 177)(7, 198)(8, 200)(9, 203)(10, 178)(11, 199)(12, 207)(13, 209)(14, 179)(15, 210)(16, 181)(17, 201)(18, 212)(19, 182)(20, 190)(21, 216)(22, 218)(23, 183)(24, 219)(25, 185)(26, 192)(27, 221)(28, 186)(29, 224)(30, 187)(31, 214)(32, 188)(33, 226)(34, 227)(35, 193)(36, 229)(37, 195)(38, 232)(39, 196)(40, 205)(41, 197)(42, 234)(43, 235)(44, 202)(45, 237)(46, 204)(47, 208)(48, 240)(49, 206)(50, 242)(51, 243)(52, 211)(53, 245)(54, 213)(55, 217)(56, 248)(57, 215)(58, 250)(59, 251)(60, 220)(61, 253)(62, 222)(63, 223)(64, 256)(65, 225)(66, 258)(67, 246)(68, 228)(69, 260)(70, 230)(71, 231)(72, 262)(73, 233)(74, 257)(75, 254)(76, 236)(77, 259)(78, 238)(79, 239)(80, 264)(81, 241)(82, 249)(83, 244)(84, 252)(85, 247)(86, 263)(87, 255)(88, 261)(89, 265)(90, 266)(91, 267)(92, 268)(93, 269)(94, 270)(95, 271)(96, 272)(97, 273)(98, 274)(99, 275)(100, 276)(101, 277)(102, 278)(103, 279)(104, 280)(105, 281)(106, 282)(107, 283)(108, 284)(109, 285)(110, 286)(111, 287)(112, 288)(113, 289)(114, 290)(115, 291)(116, 292)(117, 293)(118, 294)(119, 295)(120, 296)(121, 297)(122, 298)(123, 299)(124, 300)(125, 301)(126, 302)(127, 303)(128, 304)(129, 305)(130, 306)(131, 307)(132, 308)(133, 309)(134, 310)(135, 311)(136, 312)(137, 313)(138, 314)(139, 315)(140, 316)(141, 317)(142, 318)(143, 319)(144, 320)(145, 321)(146, 322)(147, 323)(148, 324)(149, 325)(150, 326)(151, 327)(152, 328)(153, 329)(154, 330)(155, 331)(156, 332)(157, 333)(158, 334)(159, 335)(160, 336)(161, 337)(162, 338)(163, 339)(164, 340)(165, 341)(166, 342)(167, 343)(168, 344)(169, 345)(170, 346)(171, 347)(172, 348)(173, 349)(174, 350)(175, 351)(176, 352) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible selfdual Graph:: simple bipartite v = 66 e = 176 f = 66 degree seq :: [ 4^44, 8^22 ] E23.870 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 4}) Quotient :: dipole Aut^+ = C4 x D22 (small group id <88, 4>) Aut = D8 x D22 (small group id <176, 31>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y2^4, (R * Y3)^2, Y3^-1 * Y2 * Y3^-1 * Y2^-1, (R * Y1)^2, (Y3^-1 * Y1)^2, Y3 * Y2 * Y3^-1 * Y1 * Y2^-1 * Y1, (R * Y2 * Y3^-1)^2, (Y1 * Y2^-2)^2, Y3^5 * Y1 * Y2^-1 * Y3^4 * Y1 * Y2^-1, Y3 * Y2 * Y3^-2 * Y2 * Y3^8 ] Map:: non-degenerate R = (1, 89, 2, 90)(3, 91, 11, 99)(4, 92, 10, 98)(5, 93, 17, 105)(6, 94, 8, 96)(7, 95, 20, 108)(9, 97, 26, 114)(12, 100, 21, 109)(13, 101, 30, 118)(14, 102, 23, 111)(15, 103, 28, 116)(16, 104, 25, 113)(18, 106, 35, 123)(19, 107, 24, 112)(22, 110, 39, 127)(27, 115, 44, 132)(29, 117, 47, 135)(31, 119, 41, 129)(32, 120, 40, 128)(33, 121, 49, 137)(34, 122, 46, 134)(36, 124, 52, 140)(37, 125, 43, 131)(38, 126, 55, 143)(42, 130, 57, 145)(45, 133, 60, 148)(48, 136, 63, 151)(50, 138, 65, 153)(51, 139, 62, 150)(53, 141, 68, 156)(54, 142, 59, 147)(56, 144, 71, 159)(58, 146, 73, 161)(61, 149, 76, 164)(64, 152, 79, 167)(66, 154, 81, 169)(67, 155, 78, 166)(69, 157, 84, 172)(70, 158, 75, 163)(72, 160, 87, 175)(74, 162, 85, 173)(77, 165, 82, 170)(80, 168, 83, 171)(86, 174, 88, 176)(177, 265, 179, 267, 188, 276, 181, 269)(178, 266, 183, 271, 197, 285, 185, 273)(180, 268, 190, 278, 207, 295, 192, 280)(182, 270, 189, 277, 208, 296, 194, 282)(184, 272, 199, 287, 216, 304, 201, 289)(186, 274, 198, 286, 217, 305, 203, 291)(187, 275, 205, 293, 193, 281, 200, 288)(191, 279, 196, 284, 214, 302, 202, 290)(195, 283, 209, 297, 223, 311, 212, 300)(204, 292, 218, 306, 231, 319, 221, 309)(206, 294, 224, 312, 211, 299, 219, 307)(210, 298, 215, 303, 232, 320, 220, 308)(213, 301, 226, 314, 239, 327, 229, 317)(222, 310, 234, 322, 247, 335, 237, 325)(225, 313, 240, 328, 228, 316, 235, 323)(227, 315, 233, 321, 248, 336, 236, 324)(230, 318, 242, 330, 255, 343, 245, 333)(238, 326, 250, 338, 263, 351, 253, 341)(241, 329, 256, 344, 244, 332, 251, 339)(243, 331, 249, 337, 262, 350, 252, 340)(246, 334, 258, 346, 259, 347, 261, 349)(254, 342, 260, 348, 264, 352, 257, 345) L = (1, 180)(2, 184)(3, 189)(4, 191)(5, 194)(6, 177)(7, 198)(8, 200)(9, 203)(10, 178)(11, 199)(12, 207)(13, 209)(14, 179)(15, 210)(16, 181)(17, 201)(18, 212)(19, 182)(20, 190)(21, 216)(22, 218)(23, 183)(24, 219)(25, 185)(26, 192)(27, 221)(28, 186)(29, 224)(30, 187)(31, 214)(32, 188)(33, 226)(34, 227)(35, 193)(36, 229)(37, 195)(38, 232)(39, 196)(40, 205)(41, 197)(42, 234)(43, 235)(44, 202)(45, 237)(46, 204)(47, 208)(48, 240)(49, 206)(50, 242)(51, 243)(52, 211)(53, 245)(54, 213)(55, 217)(56, 248)(57, 215)(58, 250)(59, 251)(60, 220)(61, 253)(62, 222)(63, 223)(64, 256)(65, 225)(66, 258)(67, 259)(68, 228)(69, 261)(70, 230)(71, 231)(72, 262)(73, 233)(74, 260)(75, 264)(76, 236)(77, 257)(78, 238)(79, 239)(80, 254)(81, 241)(82, 252)(83, 255)(84, 244)(85, 249)(86, 246)(87, 247)(88, 263)(89, 265)(90, 266)(91, 267)(92, 268)(93, 269)(94, 270)(95, 271)(96, 272)(97, 273)(98, 274)(99, 275)(100, 276)(101, 277)(102, 278)(103, 279)(104, 280)(105, 281)(106, 282)(107, 283)(108, 284)(109, 285)(110, 286)(111, 287)(112, 288)(113, 289)(114, 290)(115, 291)(116, 292)(117, 293)(118, 294)(119, 295)(120, 296)(121, 297)(122, 298)(123, 299)(124, 300)(125, 301)(126, 302)(127, 303)(128, 304)(129, 305)(130, 306)(131, 307)(132, 308)(133, 309)(134, 310)(135, 311)(136, 312)(137, 313)(138, 314)(139, 315)(140, 316)(141, 317)(142, 318)(143, 319)(144, 320)(145, 321)(146, 322)(147, 323)(148, 324)(149, 325)(150, 326)(151, 327)(152, 328)(153, 329)(154, 330)(155, 331)(156, 332)(157, 333)(158, 334)(159, 335)(160, 336)(161, 337)(162, 338)(163, 339)(164, 340)(165, 341)(166, 342)(167, 343)(168, 344)(169, 345)(170, 346)(171, 347)(172, 348)(173, 349)(174, 350)(175, 351)(176, 352) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible selfdual Graph:: simple bipartite v = 66 e = 176 f = 66 degree seq :: [ 4^44, 8^22 ] E23.871 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 4, 4}) Quotient :: halfedge^2 Aut^+ = (C22 x C2) : C2 (small group id <88, 7>) Aut = C2 x ((C22 x C2) : C2) (small group id <176, 36>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y2 * Y3 * Y1^2, R * Y3 * R * Y2, Y1^-1 * Y2 * Y3 * Y1^-1, (R * Y1)^2, Y3 * Y1^-1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y3 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 ] Map:: non-degenerate R = (1, 90, 2, 94, 6, 93, 5, 89)(3, 97, 9, 92, 4, 98, 10, 91)(7, 99, 11, 96, 8, 100, 12, 95)(13, 105, 17, 102, 14, 106, 18, 101)(15, 107, 19, 104, 16, 108, 20, 103)(21, 113, 25, 110, 22, 114, 26, 109)(23, 115, 27, 112, 24, 116, 28, 111)(29, 121, 33, 118, 30, 122, 34, 117)(31, 131, 43, 120, 32, 132, 44, 119)(35, 147, 59, 128, 40, 150, 62, 123)(36, 146, 58, 127, 39, 145, 57, 124)(37, 151, 63, 126, 38, 152, 64, 125)(41, 149, 61, 130, 42, 148, 60, 129)(45, 154, 66, 134, 46, 153, 65, 133)(47, 156, 68, 136, 48, 155, 67, 135)(49, 158, 70, 138, 50, 157, 69, 137)(51, 160, 72, 140, 52, 159, 71, 139)(53, 162, 74, 142, 54, 161, 73, 141)(55, 164, 76, 144, 56, 163, 75, 143)(77, 169, 81, 166, 78, 170, 82, 165)(79, 171, 83, 168, 80, 174, 86, 167)(84, 176, 88, 173, 85, 175, 87, 172) L = (1, 3)(2, 7)(4, 6)(5, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19, 23)(20, 24)(25, 29)(26, 30)(27, 31)(28, 32)(33, 57)(34, 58)(35, 60)(36, 63)(37, 65)(38, 66)(39, 64)(40, 61)(41, 67)(42, 68)(43, 59)(44, 62)(45, 69)(46, 70)(47, 71)(48, 72)(49, 73)(50, 74)(51, 75)(52, 76)(53, 77)(54, 78)(55, 79)(56, 80)(81, 85)(82, 84)(83, 88)(86, 87)(89, 92)(90, 96)(91, 94)(93, 95)(97, 102)(98, 101)(99, 104)(100, 103)(105, 110)(106, 109)(107, 112)(108, 111)(113, 118)(114, 117)(115, 120)(116, 119)(121, 146)(122, 145)(123, 149)(124, 152)(125, 154)(126, 153)(127, 151)(128, 148)(129, 156)(130, 155)(131, 150)(132, 147)(133, 158)(134, 157)(135, 160)(136, 159)(137, 162)(138, 161)(139, 164)(140, 163)(141, 166)(142, 165)(143, 168)(144, 167)(169, 172)(170, 173)(171, 175)(174, 176) local type(s) :: { ( 8^8 ) } Outer automorphisms :: reflexible selfdual Transitivity :: VT+ AT Graph:: bipartite v = 22 e = 88 f = 22 degree seq :: [ 8^22 ] E23.872 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 4, 4}) Quotient :: edge^2 Aut^+ = (C22 x C2) : C2 (small group id <88, 7>) Aut = C2 x ((C22 x C2) : C2) (small group id <176, 36>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y1 * Y2 * Y3^2, Y3^-1 * Y1 * Y2 * Y3^-1, (R * Y3)^2, R * Y1 * R * Y2, Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ] Map:: R = (1, 89, 4, 92, 6, 94, 5, 93)(2, 90, 7, 95, 3, 91, 8, 96)(9, 97, 13, 101, 10, 98, 14, 102)(11, 99, 15, 103, 12, 100, 16, 104)(17, 105, 21, 109, 18, 106, 22, 110)(19, 107, 23, 111, 20, 108, 24, 112)(25, 113, 29, 117, 26, 114, 30, 118)(27, 115, 31, 119, 28, 116, 32, 120)(33, 121, 61, 149, 34, 122, 62, 150)(35, 123, 65, 153, 40, 128, 66, 154)(36, 124, 69, 157, 37, 125, 70, 158)(38, 126, 71, 159, 39, 127, 72, 160)(41, 129, 73, 161, 42, 130, 74, 162)(43, 131, 64, 152, 44, 132, 63, 151)(45, 133, 68, 156, 46, 134, 67, 155)(47, 135, 77, 165, 48, 136, 78, 166)(49, 137, 79, 167, 50, 138, 80, 168)(51, 139, 76, 164, 52, 140, 75, 163)(53, 141, 81, 169, 54, 142, 82, 170)(55, 143, 83, 171, 56, 144, 84, 172)(57, 145, 85, 173, 58, 146, 86, 174)(59, 147, 87, 175, 60, 148, 88, 176)(177, 178)(179, 182)(180, 185)(181, 186)(183, 187)(184, 188)(189, 193)(190, 194)(191, 195)(192, 196)(197, 201)(198, 202)(199, 203)(200, 204)(205, 209)(206, 210)(207, 227)(208, 228)(211, 239)(212, 243)(213, 244)(214, 245)(215, 246)(216, 240)(217, 241)(218, 242)(219, 251)(220, 252)(221, 238)(222, 237)(223, 247)(224, 248)(225, 249)(226, 250)(229, 253)(230, 254)(231, 255)(232, 256)(233, 257)(234, 258)(235, 259)(236, 260)(261, 264)(262, 263)(265, 267)(266, 270)(268, 274)(269, 273)(271, 276)(272, 275)(277, 282)(278, 281)(279, 284)(280, 283)(285, 290)(286, 289)(287, 292)(288, 291)(293, 298)(294, 297)(295, 316)(296, 315)(299, 328)(300, 332)(301, 331)(302, 334)(303, 333)(304, 327)(305, 330)(306, 329)(307, 340)(308, 339)(309, 325)(310, 326)(311, 336)(312, 335)(313, 338)(314, 337)(317, 342)(318, 341)(319, 344)(320, 343)(321, 346)(322, 345)(323, 348)(324, 347)(349, 351)(350, 352) L = (1, 177)(2, 178)(3, 179)(4, 180)(5, 181)(6, 182)(7, 183)(8, 184)(9, 185)(10, 186)(11, 187)(12, 188)(13, 189)(14, 190)(15, 191)(16, 192)(17, 193)(18, 194)(19, 195)(20, 196)(21, 197)(22, 198)(23, 199)(24, 200)(25, 201)(26, 202)(27, 203)(28, 204)(29, 205)(30, 206)(31, 207)(32, 208)(33, 209)(34, 210)(35, 211)(36, 212)(37, 213)(38, 214)(39, 215)(40, 216)(41, 217)(42, 218)(43, 219)(44, 220)(45, 221)(46, 222)(47, 223)(48, 224)(49, 225)(50, 226)(51, 227)(52, 228)(53, 229)(54, 230)(55, 231)(56, 232)(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, 245)(70, 246)(71, 247)(72, 248)(73, 249)(74, 250)(75, 251)(76, 252)(77, 253)(78, 254)(79, 255)(80, 256)(81, 257)(82, 258)(83, 259)(84, 260)(85, 261)(86, 262)(87, 263)(88, 264)(89, 265)(90, 266)(91, 267)(92, 268)(93, 269)(94, 270)(95, 271)(96, 272)(97, 273)(98, 274)(99, 275)(100, 276)(101, 277)(102, 278)(103, 279)(104, 280)(105, 281)(106, 282)(107, 283)(108, 284)(109, 285)(110, 286)(111, 287)(112, 288)(113, 289)(114, 290)(115, 291)(116, 292)(117, 293)(118, 294)(119, 295)(120, 296)(121, 297)(122, 298)(123, 299)(124, 300)(125, 301)(126, 302)(127, 303)(128, 304)(129, 305)(130, 306)(131, 307)(132, 308)(133, 309)(134, 310)(135, 311)(136, 312)(137, 313)(138, 314)(139, 315)(140, 316)(141, 317)(142, 318)(143, 319)(144, 320)(145, 321)(146, 322)(147, 323)(148, 324)(149, 325)(150, 326)(151, 327)(152, 328)(153, 329)(154, 330)(155, 331)(156, 332)(157, 333)(158, 334)(159, 335)(160, 336)(161, 337)(162, 338)(163, 339)(164, 340)(165, 341)(166, 342)(167, 343)(168, 344)(169, 345)(170, 346)(171, 347)(172, 348)(173, 349)(174, 350)(175, 351)(176, 352) local type(s) :: { ( 16, 16 ), ( 16^8 ) } Outer automorphisms :: reflexible Dual of E23.874 Graph:: simple bipartite v = 110 e = 176 f = 22 degree seq :: [ 2^88, 8^22 ] E23.873 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 4, 4}) Quotient :: edge^2 Aut^+ = (C22 x C2) : C2 (small group id <88, 7>) Aut = C2 x ((C22 x C2) : C2) (small group id <176, 36>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, Y1^4, Y2^2 * Y1^-2, (R * Y3)^2, R * Y2 * R * Y1, Y3 * Y2^2 * Y3 * Y1^-2, (Y2^-1 * Y3 * Y1)^2, Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y2 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 ] Map:: non-degenerate R = (1, 89, 4, 92)(2, 90, 6, 94)(3, 91, 7, 95)(5, 93, 10, 98)(8, 96, 13, 101)(9, 97, 14, 102)(11, 99, 15, 103)(12, 100, 16, 104)(17, 105, 21, 109)(18, 106, 22, 110)(19, 107, 23, 111)(20, 108, 24, 112)(25, 113, 29, 117)(26, 114, 30, 118)(27, 115, 31, 119)(28, 116, 32, 120)(33, 121, 65, 153)(34, 122, 66, 154)(35, 123, 69, 157)(36, 124, 72, 160)(37, 125, 73, 161)(38, 126, 74, 162)(39, 127, 75, 163)(40, 128, 76, 164)(41, 129, 77, 165)(42, 130, 67, 155)(43, 131, 68, 156)(44, 132, 80, 168)(45, 133, 70, 158)(46, 134, 71, 159)(47, 135, 83, 171)(48, 136, 84, 172)(49, 137, 85, 173)(50, 138, 86, 174)(51, 139, 78, 166)(52, 140, 79, 167)(53, 141, 81, 169)(54, 142, 82, 170)(55, 143, 63, 151)(56, 144, 64, 152)(57, 145, 62, 150)(58, 146, 61, 149)(59, 147, 87, 175)(60, 148, 88, 176)(177, 178, 181, 179)(180, 184, 186, 185)(182, 187, 183, 188)(189, 193, 190, 194)(191, 195, 192, 196)(197, 201, 198, 202)(199, 203, 200, 204)(205, 209, 206, 210)(207, 235, 208, 236)(211, 243, 215, 244)(212, 246, 213, 247)(214, 248, 220, 249)(216, 251, 217, 245)(218, 254, 219, 255)(221, 257, 222, 258)(223, 256, 224, 250)(225, 253, 226, 252)(227, 263, 228, 264)(229, 242, 230, 241)(231, 260, 232, 259)(233, 262, 234, 261)(237, 240, 238, 239)(265, 267, 269, 266)(268, 273, 274, 272)(270, 276, 271, 275)(277, 282, 278, 281)(279, 284, 280, 283)(285, 290, 286, 289)(287, 292, 288, 291)(293, 298, 294, 297)(295, 324, 296, 323)(299, 332, 303, 331)(300, 335, 301, 334)(302, 337, 308, 336)(304, 333, 305, 339)(306, 343, 307, 342)(309, 346, 310, 345)(311, 338, 312, 344)(313, 340, 314, 341)(315, 352, 316, 351)(317, 329, 318, 330)(319, 347, 320, 348)(321, 349, 322, 350)(325, 327, 326, 328) L = (1, 177)(2, 178)(3, 179)(4, 180)(5, 181)(6, 182)(7, 183)(8, 184)(9, 185)(10, 186)(11, 187)(12, 188)(13, 189)(14, 190)(15, 191)(16, 192)(17, 193)(18, 194)(19, 195)(20, 196)(21, 197)(22, 198)(23, 199)(24, 200)(25, 201)(26, 202)(27, 203)(28, 204)(29, 205)(30, 206)(31, 207)(32, 208)(33, 209)(34, 210)(35, 211)(36, 212)(37, 213)(38, 214)(39, 215)(40, 216)(41, 217)(42, 218)(43, 219)(44, 220)(45, 221)(46, 222)(47, 223)(48, 224)(49, 225)(50, 226)(51, 227)(52, 228)(53, 229)(54, 230)(55, 231)(56, 232)(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, 245)(70, 246)(71, 247)(72, 248)(73, 249)(74, 250)(75, 251)(76, 252)(77, 253)(78, 254)(79, 255)(80, 256)(81, 257)(82, 258)(83, 259)(84, 260)(85, 261)(86, 262)(87, 263)(88, 264)(89, 265)(90, 266)(91, 267)(92, 268)(93, 269)(94, 270)(95, 271)(96, 272)(97, 273)(98, 274)(99, 275)(100, 276)(101, 277)(102, 278)(103, 279)(104, 280)(105, 281)(106, 282)(107, 283)(108, 284)(109, 285)(110, 286)(111, 287)(112, 288)(113, 289)(114, 290)(115, 291)(116, 292)(117, 293)(118, 294)(119, 295)(120, 296)(121, 297)(122, 298)(123, 299)(124, 300)(125, 301)(126, 302)(127, 303)(128, 304)(129, 305)(130, 306)(131, 307)(132, 308)(133, 309)(134, 310)(135, 311)(136, 312)(137, 313)(138, 314)(139, 315)(140, 316)(141, 317)(142, 318)(143, 319)(144, 320)(145, 321)(146, 322)(147, 323)(148, 324)(149, 325)(150, 326)(151, 327)(152, 328)(153, 329)(154, 330)(155, 331)(156, 332)(157, 333)(158, 334)(159, 335)(160, 336)(161, 337)(162, 338)(163, 339)(164, 340)(165, 341)(166, 342)(167, 343)(168, 344)(169, 345)(170, 346)(171, 347)(172, 348)(173, 349)(174, 350)(175, 351)(176, 352) local type(s) :: { ( 8^4 ) } Outer automorphisms :: reflexible Dual of E23.875 Graph:: simple bipartite v = 88 e = 176 f = 44 degree seq :: [ 4^88 ] E23.874 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 4, 4}) Quotient :: loop^2 Aut^+ = (C22 x C2) : C2 (small group id <88, 7>) Aut = C2 x ((C22 x C2) : C2) (small group id <176, 36>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y1 * Y2 * Y3^2, Y3^-1 * Y1 * Y2 * Y3^-1, (R * Y3)^2, R * Y1 * R * Y2, Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ] Map:: R = (1, 89, 177, 265, 4, 92, 180, 268, 6, 94, 182, 270, 5, 93, 181, 269)(2, 90, 178, 266, 7, 95, 183, 271, 3, 91, 179, 267, 8, 96, 184, 272)(9, 97, 185, 273, 13, 101, 189, 277, 10, 98, 186, 274, 14, 102, 190, 278)(11, 99, 187, 275, 15, 103, 191, 279, 12, 100, 188, 276, 16, 104, 192, 280)(17, 105, 193, 281, 21, 109, 197, 285, 18, 106, 194, 282, 22, 110, 198, 286)(19, 107, 195, 283, 23, 111, 199, 287, 20, 108, 196, 284, 24, 112, 200, 288)(25, 113, 201, 289, 29, 117, 205, 293, 26, 114, 202, 290, 30, 118, 206, 294)(27, 115, 203, 291, 31, 119, 207, 295, 28, 116, 204, 292, 32, 120, 208, 296)(33, 121, 209, 297, 53, 141, 229, 317, 34, 122, 210, 298, 54, 142, 230, 318)(35, 123, 211, 299, 55, 143, 231, 319, 38, 126, 214, 302, 56, 144, 232, 320)(36, 124, 212, 300, 57, 145, 233, 321, 37, 125, 213, 301, 58, 146, 234, 322)(39, 127, 215, 303, 59, 147, 235, 323, 40, 128, 216, 304, 60, 148, 236, 324)(41, 129, 217, 305, 61, 149, 237, 325, 42, 130, 218, 306, 62, 150, 238, 326)(43, 131, 219, 307, 63, 151, 239, 327, 44, 132, 220, 308, 64, 152, 240, 328)(45, 133, 221, 309, 65, 153, 241, 329, 46, 134, 222, 310, 66, 154, 242, 330)(47, 135, 223, 311, 67, 155, 243, 331, 48, 136, 224, 312, 68, 156, 244, 332)(49, 137, 225, 313, 69, 157, 245, 333, 50, 138, 226, 314, 70, 158, 246, 334)(51, 139, 227, 315, 71, 159, 247, 335, 52, 140, 228, 316, 72, 160, 248, 336)(73, 161, 249, 337, 88, 176, 264, 352, 74, 162, 250, 338, 87, 175, 263, 351)(75, 163, 251, 339, 85, 173, 261, 349, 76, 164, 252, 340, 86, 174, 262, 350)(77, 165, 253, 341, 84, 172, 260, 348, 78, 166, 254, 342, 83, 171, 259, 347)(79, 167, 255, 343, 82, 170, 258, 346, 80, 168, 256, 344, 81, 169, 257, 345) L = (1, 90)(2, 89)(3, 94)(4, 97)(5, 98)(6, 91)(7, 99)(8, 100)(9, 92)(10, 93)(11, 95)(12, 96)(13, 105)(14, 106)(15, 107)(16, 108)(17, 101)(18, 102)(19, 103)(20, 104)(21, 113)(22, 114)(23, 115)(24, 116)(25, 109)(26, 110)(27, 111)(28, 112)(29, 121)(30, 122)(31, 126)(32, 123)(33, 117)(34, 118)(35, 120)(36, 142)(37, 141)(38, 119)(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, 125)(54, 124)(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, 161)(70, 162)(71, 164)(72, 163)(73, 157)(74, 158)(75, 160)(76, 159)(77, 175)(78, 176)(79, 173)(80, 174)(81, 172)(82, 171)(83, 170)(84, 169)(85, 167)(86, 168)(87, 165)(88, 166)(177, 267)(178, 270)(179, 265)(180, 274)(181, 273)(182, 266)(183, 276)(184, 275)(185, 269)(186, 268)(187, 272)(188, 271)(189, 282)(190, 281)(191, 284)(192, 283)(193, 278)(194, 277)(195, 280)(196, 279)(197, 290)(198, 289)(199, 292)(200, 291)(201, 286)(202, 285)(203, 288)(204, 287)(205, 298)(206, 297)(207, 299)(208, 302)(209, 294)(210, 293)(211, 295)(212, 317)(213, 318)(214, 296)(215, 320)(216, 319)(217, 322)(218, 321)(219, 324)(220, 323)(221, 326)(222, 325)(223, 328)(224, 327)(225, 330)(226, 329)(227, 332)(228, 331)(229, 300)(230, 301)(231, 304)(232, 303)(233, 306)(234, 305)(235, 308)(236, 307)(237, 310)(238, 309)(239, 312)(240, 311)(241, 314)(242, 313)(243, 316)(244, 315)(245, 338)(246, 337)(247, 339)(248, 340)(249, 334)(250, 333)(251, 335)(252, 336)(253, 352)(254, 351)(255, 350)(256, 349)(257, 347)(258, 348)(259, 345)(260, 346)(261, 344)(262, 343)(263, 342)(264, 341) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) } Outer automorphisms :: reflexible Dual of E23.872 Transitivity :: VT+ Graph:: bipartite v = 22 e = 176 f = 110 degree seq :: [ 16^22 ] E23.875 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 4, 4}) Quotient :: loop^2 Aut^+ = (C22 x C2) : C2 (small group id <88, 7>) Aut = C2 x ((C22 x C2) : C2) (small group id <176, 36>) |r| :: 2 Presentation :: [ R^2, Y3^2, Y2^-1 * Y1^-1, Y1^4, Y2^2 * Y1^-2, (R * Y3)^2, R * Y2 * R * Y1, Y3 * Y2^2 * Y3 * Y1^-2, (Y2^-1 * Y3 * Y1)^2, Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y2 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 ] Map:: non-degenerate R = (1, 89, 177, 265, 4, 92, 180, 268)(2, 90, 178, 266, 6, 94, 182, 270)(3, 91, 179, 267, 7, 95, 183, 271)(5, 93, 181, 269, 10, 98, 186, 274)(8, 96, 184, 272, 13, 101, 189, 277)(9, 97, 185, 273, 14, 102, 190, 278)(11, 99, 187, 275, 15, 103, 191, 279)(12, 100, 188, 276, 16, 104, 192, 280)(17, 105, 193, 281, 21, 109, 197, 285)(18, 106, 194, 282, 22, 110, 198, 286)(19, 107, 195, 283, 23, 111, 199, 287)(20, 108, 196, 284, 24, 112, 200, 288)(25, 113, 201, 289, 29, 117, 205, 293)(26, 114, 202, 290, 30, 118, 206, 294)(27, 115, 203, 291, 31, 119, 207, 295)(28, 116, 204, 292, 32, 120, 208, 296)(33, 121, 209, 297, 53, 141, 229, 317)(34, 122, 210, 298, 54, 142, 230, 318)(35, 123, 211, 299, 55, 143, 231, 319)(36, 124, 212, 300, 56, 144, 232, 320)(37, 125, 213, 301, 57, 145, 233, 321)(38, 126, 214, 302, 58, 146, 234, 322)(39, 127, 215, 303, 59, 147, 235, 323)(40, 128, 216, 304, 60, 148, 236, 324)(41, 129, 217, 305, 61, 149, 237, 325)(42, 130, 218, 306, 62, 150, 238, 326)(43, 131, 219, 307, 63, 151, 239, 327)(44, 132, 220, 308, 64, 152, 240, 328)(45, 133, 221, 309, 65, 153, 241, 329)(46, 134, 222, 310, 66, 154, 242, 330)(47, 135, 223, 311, 67, 155, 243, 331)(48, 136, 224, 312, 68, 156, 244, 332)(49, 137, 225, 313, 69, 157, 245, 333)(50, 138, 226, 314, 70, 158, 246, 334)(51, 139, 227, 315, 71, 159, 247, 335)(52, 140, 228, 316, 72, 160, 248, 336)(73, 161, 249, 337, 87, 175, 263, 351)(74, 162, 250, 338, 88, 176, 264, 352)(75, 163, 251, 339, 85, 173, 261, 349)(76, 164, 252, 340, 86, 174, 262, 350)(77, 165, 253, 341, 83, 171, 259, 347)(78, 166, 254, 342, 84, 172, 260, 348)(79, 167, 255, 343, 82, 170, 258, 346)(80, 168, 256, 344, 81, 169, 257, 345) L = (1, 90)(2, 93)(3, 89)(4, 96)(5, 91)(6, 99)(7, 100)(8, 98)(9, 92)(10, 97)(11, 95)(12, 94)(13, 105)(14, 106)(15, 107)(16, 108)(17, 102)(18, 101)(19, 104)(20, 103)(21, 113)(22, 114)(23, 115)(24, 116)(25, 110)(26, 109)(27, 112)(28, 111)(29, 121)(30, 122)(31, 125)(32, 123)(33, 118)(34, 117)(35, 119)(36, 141)(37, 120)(38, 145)(39, 143)(40, 142)(41, 148)(42, 144)(43, 147)(44, 146)(45, 150)(46, 149)(47, 152)(48, 151)(49, 154)(50, 153)(51, 156)(52, 155)(53, 128)(54, 124)(55, 126)(56, 129)(57, 127)(58, 131)(59, 132)(60, 130)(61, 133)(62, 134)(63, 135)(64, 136)(65, 137)(66, 138)(67, 139)(68, 140)(69, 161)(70, 162)(71, 164)(72, 163)(73, 158)(74, 157)(75, 159)(76, 160)(77, 175)(78, 176)(79, 174)(80, 173)(81, 172)(82, 171)(83, 169)(84, 170)(85, 167)(86, 168)(87, 166)(88, 165)(177, 267)(178, 265)(179, 269)(180, 273)(181, 266)(182, 276)(183, 275)(184, 268)(185, 274)(186, 272)(187, 270)(188, 271)(189, 282)(190, 281)(191, 284)(192, 283)(193, 277)(194, 278)(195, 279)(196, 280)(197, 290)(198, 289)(199, 292)(200, 291)(201, 285)(202, 286)(203, 287)(204, 288)(205, 298)(206, 297)(207, 299)(208, 301)(209, 293)(210, 294)(211, 296)(212, 318)(213, 295)(214, 319)(215, 321)(216, 317)(217, 320)(218, 324)(219, 322)(220, 323)(221, 325)(222, 326)(223, 327)(224, 328)(225, 329)(226, 330)(227, 331)(228, 332)(229, 300)(230, 304)(231, 303)(232, 306)(233, 302)(234, 308)(235, 307)(236, 305)(237, 310)(238, 309)(239, 312)(240, 311)(241, 314)(242, 313)(243, 316)(244, 315)(245, 338)(246, 337)(247, 339)(248, 340)(249, 333)(250, 334)(251, 336)(252, 335)(253, 352)(254, 351)(255, 349)(256, 350)(257, 347)(258, 348)(259, 346)(260, 345)(261, 344)(262, 343)(263, 341)(264, 342) local type(s) :: { ( 4^8 ) } Outer automorphisms :: reflexible Dual of E23.873 Transitivity :: VT+ Graph:: bipartite v = 44 e = 176 f = 88 degree seq :: [ 8^44 ] E23.876 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 4}) Quotient :: dipole Aut^+ = (C22 x C2) : C2 (small group id <88, 7>) Aut = C2 x ((C22 x C2) : C2) (small group id <176, 36>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y2^-1 * Y3^-1 * Y2, (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y3)^2, Y2^4, Y3 * Y2^-1 * Y3^-1 * Y1 * Y2^-1 * Y1, (R * Y2 * Y3^-1)^2, (Y2^-2 * Y1)^2, Y3^11, Y3^4 * Y1 * Y2 * Y3^5 * Y1 * Y2 ] Map:: non-degenerate R = (1, 89, 2, 90)(3, 91, 11, 99)(4, 92, 10, 98)(5, 93, 17, 105)(6, 94, 8, 96)(7, 95, 20, 108)(9, 97, 26, 114)(12, 100, 21, 109)(13, 101, 30, 118)(14, 102, 25, 113)(15, 103, 28, 116)(16, 104, 23, 111)(18, 106, 35, 123)(19, 107, 24, 112)(22, 110, 39, 127)(27, 115, 44, 132)(29, 117, 47, 135)(31, 119, 41, 129)(32, 120, 40, 128)(33, 121, 49, 137)(34, 122, 46, 134)(36, 124, 52, 140)(37, 125, 43, 131)(38, 126, 55, 143)(42, 130, 57, 145)(45, 133, 60, 148)(48, 136, 63, 151)(50, 138, 65, 153)(51, 139, 62, 150)(53, 141, 68, 156)(54, 142, 59, 147)(56, 144, 71, 159)(58, 146, 73, 161)(61, 149, 76, 164)(64, 152, 79, 167)(66, 154, 81, 169)(67, 155, 78, 166)(69, 157, 83, 171)(70, 158, 75, 163)(72, 160, 85, 173)(74, 162, 84, 172)(77, 165, 82, 170)(80, 168, 87, 175)(86, 174, 88, 176)(177, 265, 179, 267, 188, 276, 181, 269)(178, 266, 183, 271, 197, 285, 185, 273)(180, 268, 190, 278, 207, 295, 192, 280)(182, 270, 189, 277, 208, 296, 194, 282)(184, 272, 199, 287, 216, 304, 201, 289)(186, 274, 198, 286, 217, 305, 203, 291)(187, 275, 200, 288, 193, 281, 205, 293)(191, 279, 202, 290, 214, 302, 196, 284)(195, 283, 209, 297, 223, 311, 212, 300)(204, 292, 218, 306, 231, 319, 221, 309)(206, 294, 219, 307, 211, 299, 224, 312)(210, 298, 220, 308, 232, 320, 215, 303)(213, 301, 226, 314, 239, 327, 229, 317)(222, 310, 234, 322, 247, 335, 237, 325)(225, 313, 235, 323, 228, 316, 240, 328)(227, 315, 236, 324, 248, 336, 233, 321)(230, 318, 242, 330, 255, 343, 245, 333)(238, 326, 250, 338, 261, 349, 253, 341)(241, 329, 251, 339, 244, 332, 256, 344)(243, 331, 252, 340, 262, 350, 249, 337)(246, 334, 258, 346, 263, 351, 260, 348)(254, 342, 259, 347, 264, 352, 257, 345) L = (1, 180)(2, 184)(3, 189)(4, 191)(5, 194)(6, 177)(7, 198)(8, 200)(9, 203)(10, 178)(11, 201)(12, 207)(13, 209)(14, 179)(15, 210)(16, 181)(17, 199)(18, 212)(19, 182)(20, 192)(21, 216)(22, 218)(23, 183)(24, 219)(25, 185)(26, 190)(27, 221)(28, 186)(29, 224)(30, 187)(31, 214)(32, 188)(33, 226)(34, 227)(35, 193)(36, 229)(37, 195)(38, 232)(39, 196)(40, 205)(41, 197)(42, 234)(43, 235)(44, 202)(45, 237)(46, 204)(47, 208)(48, 240)(49, 206)(50, 242)(51, 243)(52, 211)(53, 245)(54, 213)(55, 217)(56, 248)(57, 215)(58, 250)(59, 251)(60, 220)(61, 253)(62, 222)(63, 223)(64, 256)(65, 225)(66, 258)(67, 246)(68, 228)(69, 260)(70, 230)(71, 231)(72, 262)(73, 233)(74, 259)(75, 254)(76, 236)(77, 257)(78, 238)(79, 239)(80, 264)(81, 241)(82, 252)(83, 244)(84, 249)(85, 247)(86, 263)(87, 255)(88, 261)(89, 265)(90, 266)(91, 267)(92, 268)(93, 269)(94, 270)(95, 271)(96, 272)(97, 273)(98, 274)(99, 275)(100, 276)(101, 277)(102, 278)(103, 279)(104, 280)(105, 281)(106, 282)(107, 283)(108, 284)(109, 285)(110, 286)(111, 287)(112, 288)(113, 289)(114, 290)(115, 291)(116, 292)(117, 293)(118, 294)(119, 295)(120, 296)(121, 297)(122, 298)(123, 299)(124, 300)(125, 301)(126, 302)(127, 303)(128, 304)(129, 305)(130, 306)(131, 307)(132, 308)(133, 309)(134, 310)(135, 311)(136, 312)(137, 313)(138, 314)(139, 315)(140, 316)(141, 317)(142, 318)(143, 319)(144, 320)(145, 321)(146, 322)(147, 323)(148, 324)(149, 325)(150, 326)(151, 327)(152, 328)(153, 329)(154, 330)(155, 331)(156, 332)(157, 333)(158, 334)(159, 335)(160, 336)(161, 337)(162, 338)(163, 339)(164, 340)(165, 341)(166, 342)(167, 343)(168, 344)(169, 345)(170, 346)(171, 347)(172, 348)(173, 349)(174, 350)(175, 351)(176, 352) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible selfdual Graph:: simple bipartite v = 66 e = 176 f = 66 degree seq :: [ 4^44, 8^22 ] E23.877 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 4, 4}) Quotient :: dipole Aut^+ = (C22 x C2) : C2 (small group id <88, 7>) Aut = C2 x ((C22 x C2) : C2) (small group id <176, 36>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y2^-1 * Y3^-1 * Y2, (Y3^-1 * Y1)^2, (R * Y1)^2, (R * Y3)^2, Y2^4, Y3 * Y2 * Y3^-1 * Y1 * Y2 * Y1, (R * Y2 * Y3^-1)^2, (Y1 * Y2^-2)^2, Y3^4 * Y1 * Y2 * Y3^5 * Y1 * Y2^-1, Y3 * Y2^-1 * Y3^-2 * Y2^-1 * Y3^8 ] Map:: non-degenerate R = (1, 89, 2, 90)(3, 91, 11, 99)(4, 92, 10, 98)(5, 93, 17, 105)(6, 94, 8, 96)(7, 95, 20, 108)(9, 97, 26, 114)(12, 100, 21, 109)(13, 101, 30, 118)(14, 102, 25, 113)(15, 103, 28, 116)(16, 104, 23, 111)(18, 106, 35, 123)(19, 107, 24, 112)(22, 110, 39, 127)(27, 115, 44, 132)(29, 117, 47, 135)(31, 119, 41, 129)(32, 120, 40, 128)(33, 121, 49, 137)(34, 122, 46, 134)(36, 124, 52, 140)(37, 125, 43, 131)(38, 126, 55, 143)(42, 130, 57, 145)(45, 133, 60, 148)(48, 136, 63, 151)(50, 138, 65, 153)(51, 139, 62, 150)(53, 141, 68, 156)(54, 142, 59, 147)(56, 144, 71, 159)(58, 146, 73, 161)(61, 149, 76, 164)(64, 152, 79, 167)(66, 154, 81, 169)(67, 155, 78, 166)(69, 157, 84, 172)(70, 158, 75, 163)(72, 160, 87, 175)(74, 162, 82, 170)(77, 165, 85, 173)(80, 168, 83, 171)(86, 174, 88, 176)(177, 265, 179, 267, 188, 276, 181, 269)(178, 266, 183, 271, 197, 285, 185, 273)(180, 268, 190, 278, 207, 295, 192, 280)(182, 270, 189, 277, 208, 296, 194, 282)(184, 272, 199, 287, 216, 304, 201, 289)(186, 274, 198, 286, 217, 305, 203, 291)(187, 275, 200, 288, 193, 281, 205, 293)(191, 279, 202, 290, 214, 302, 196, 284)(195, 283, 209, 297, 223, 311, 212, 300)(204, 292, 218, 306, 231, 319, 221, 309)(206, 294, 219, 307, 211, 299, 224, 312)(210, 298, 220, 308, 232, 320, 215, 303)(213, 301, 226, 314, 239, 327, 229, 317)(222, 310, 234, 322, 247, 335, 237, 325)(225, 313, 235, 323, 228, 316, 240, 328)(227, 315, 236, 324, 248, 336, 233, 321)(230, 318, 242, 330, 255, 343, 245, 333)(238, 326, 250, 338, 263, 351, 253, 341)(241, 329, 251, 339, 244, 332, 256, 344)(243, 331, 252, 340, 262, 350, 249, 337)(246, 334, 258, 346, 259, 347, 261, 349)(254, 342, 257, 345, 264, 352, 260, 348) L = (1, 180)(2, 184)(3, 189)(4, 191)(5, 194)(6, 177)(7, 198)(8, 200)(9, 203)(10, 178)(11, 201)(12, 207)(13, 209)(14, 179)(15, 210)(16, 181)(17, 199)(18, 212)(19, 182)(20, 192)(21, 216)(22, 218)(23, 183)(24, 219)(25, 185)(26, 190)(27, 221)(28, 186)(29, 224)(30, 187)(31, 214)(32, 188)(33, 226)(34, 227)(35, 193)(36, 229)(37, 195)(38, 232)(39, 196)(40, 205)(41, 197)(42, 234)(43, 235)(44, 202)(45, 237)(46, 204)(47, 208)(48, 240)(49, 206)(50, 242)(51, 243)(52, 211)(53, 245)(54, 213)(55, 217)(56, 248)(57, 215)(58, 250)(59, 251)(60, 220)(61, 253)(62, 222)(63, 223)(64, 256)(65, 225)(66, 258)(67, 259)(68, 228)(69, 261)(70, 230)(71, 231)(72, 262)(73, 233)(74, 257)(75, 264)(76, 236)(77, 260)(78, 238)(79, 239)(80, 254)(81, 241)(82, 249)(83, 255)(84, 244)(85, 252)(86, 246)(87, 247)(88, 263)(89, 265)(90, 266)(91, 267)(92, 268)(93, 269)(94, 270)(95, 271)(96, 272)(97, 273)(98, 274)(99, 275)(100, 276)(101, 277)(102, 278)(103, 279)(104, 280)(105, 281)(106, 282)(107, 283)(108, 284)(109, 285)(110, 286)(111, 287)(112, 288)(113, 289)(114, 290)(115, 291)(116, 292)(117, 293)(118, 294)(119, 295)(120, 296)(121, 297)(122, 298)(123, 299)(124, 300)(125, 301)(126, 302)(127, 303)(128, 304)(129, 305)(130, 306)(131, 307)(132, 308)(133, 309)(134, 310)(135, 311)(136, 312)(137, 313)(138, 314)(139, 315)(140, 316)(141, 317)(142, 318)(143, 319)(144, 320)(145, 321)(146, 322)(147, 323)(148, 324)(149, 325)(150, 326)(151, 327)(152, 328)(153, 329)(154, 330)(155, 331)(156, 332)(157, 333)(158, 334)(159, 335)(160, 336)(161, 337)(162, 338)(163, 339)(164, 340)(165, 341)(166, 342)(167, 343)(168, 344)(169, 345)(170, 346)(171, 347)(172, 348)(173, 349)(174, 350)(175, 351)(176, 352) local type(s) :: { ( 4, 8, 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible selfdual Graph:: simple bipartite v = 66 e = 176 f = 66 degree seq :: [ 4^44, 8^22 ] E23.878 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 46}) Quotient :: dipole Aut^+ = D92 (small group id <92, 3>) Aut = C2 x C2 x D46 (small group id <184, 11>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y3)^2, (Y2 * Y1)^2, (R * Y1)^2, Y2 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 ] Map:: non-degenerate R = (1, 93, 2, 94)(3, 95, 5, 97)(4, 96, 8, 100)(6, 98, 10, 102)(7, 99, 11, 103)(9, 101, 13, 105)(12, 104, 16, 108)(14, 106, 18, 110)(15, 107, 19, 111)(17, 109, 21, 113)(20, 112, 24, 116)(22, 114, 26, 118)(23, 115, 27, 119)(25, 117, 29, 121)(28, 120, 32, 124)(30, 122, 58, 150)(31, 123, 59, 151)(33, 125, 61, 153)(34, 126, 63, 155)(35, 127, 65, 157)(36, 128, 64, 156)(37, 129, 68, 160)(38, 130, 62, 154)(39, 131, 69, 161)(40, 132, 72, 164)(41, 133, 66, 158)(42, 134, 74, 166)(43, 135, 75, 167)(44, 136, 67, 159)(45, 137, 76, 168)(46, 138, 70, 162)(47, 139, 71, 163)(48, 140, 78, 170)(49, 141, 73, 165)(50, 142, 79, 171)(51, 143, 80, 172)(52, 144, 81, 173)(53, 145, 77, 169)(54, 146, 82, 174)(55, 147, 83, 175)(56, 148, 84, 176)(57, 149, 85, 177)(60, 152, 88, 180)(86, 178, 91, 183)(87, 179, 89, 181)(90, 182, 92, 184)(185, 277, 187, 279)(186, 278, 189, 281)(188, 280, 191, 283)(190, 282, 193, 285)(192, 284, 195, 287)(194, 286, 197, 289)(196, 288, 199, 291)(198, 290, 201, 293)(200, 292, 203, 295)(202, 294, 205, 297)(204, 296, 207, 299)(206, 298, 209, 301)(208, 300, 211, 303)(210, 302, 213, 305)(212, 304, 215, 307)(214, 306, 237, 329)(216, 308, 243, 335)(217, 309, 219, 311)(218, 310, 221, 313)(220, 312, 223, 315)(222, 314, 225, 317)(224, 316, 227, 319)(226, 318, 229, 321)(228, 320, 231, 323)(230, 322, 233, 325)(232, 324, 235, 327)(234, 326, 236, 328)(238, 330, 240, 332)(239, 331, 241, 333)(242, 334, 261, 353)(244, 336, 271, 363)(245, 337, 249, 341)(246, 338, 250, 342)(247, 339, 252, 344)(248, 340, 253, 345)(251, 343, 255, 347)(254, 346, 257, 349)(256, 348, 259, 351)(258, 350, 260, 352)(262, 354, 264, 356)(263, 355, 265, 357)(266, 358, 268, 360)(267, 359, 269, 361)(270, 362, 276, 368)(272, 364, 273, 365)(274, 366, 275, 367) L = (1, 188)(2, 190)(3, 191)(4, 185)(5, 193)(6, 186)(7, 187)(8, 196)(9, 189)(10, 198)(11, 199)(12, 192)(13, 201)(14, 194)(15, 195)(16, 204)(17, 197)(18, 206)(19, 207)(20, 200)(21, 209)(22, 202)(23, 203)(24, 212)(25, 205)(26, 214)(27, 215)(28, 208)(29, 237)(30, 210)(31, 211)(32, 230)(33, 246)(34, 248)(35, 250)(36, 251)(37, 253)(38, 254)(39, 255)(40, 245)(41, 257)(42, 247)(43, 249)(44, 242)(45, 252)(46, 216)(47, 261)(48, 256)(49, 243)(50, 258)(51, 259)(52, 260)(53, 213)(54, 262)(55, 263)(56, 264)(57, 265)(58, 228)(59, 233)(60, 266)(61, 224)(62, 217)(63, 226)(64, 218)(65, 227)(66, 219)(67, 220)(68, 229)(69, 221)(70, 222)(71, 223)(72, 232)(73, 225)(74, 234)(75, 235)(76, 236)(77, 231)(78, 238)(79, 239)(80, 240)(81, 241)(82, 244)(83, 270)(84, 271)(85, 276)(86, 267)(87, 268)(88, 274)(89, 275)(90, 272)(91, 273)(92, 269)(93, 277)(94, 278)(95, 279)(96, 280)(97, 281)(98, 282)(99, 283)(100, 284)(101, 285)(102, 286)(103, 287)(104, 288)(105, 289)(106, 290)(107, 291)(108, 292)(109, 293)(110, 294)(111, 295)(112, 296)(113, 297)(114, 298)(115, 299)(116, 300)(117, 301)(118, 302)(119, 303)(120, 304)(121, 305)(122, 306)(123, 307)(124, 308)(125, 309)(126, 310)(127, 311)(128, 312)(129, 313)(130, 314)(131, 315)(132, 316)(133, 317)(134, 318)(135, 319)(136, 320)(137, 321)(138, 322)(139, 323)(140, 324)(141, 325)(142, 326)(143, 327)(144, 328)(145, 329)(146, 330)(147, 331)(148, 332)(149, 333)(150, 334)(151, 335)(152, 336)(153, 337)(154, 338)(155, 339)(156, 340)(157, 341)(158, 342)(159, 343)(160, 344)(161, 345)(162, 346)(163, 347)(164, 348)(165, 349)(166, 350)(167, 351)(168, 352)(169, 353)(170, 354)(171, 355)(172, 356)(173, 357)(174, 358)(175, 359)(176, 360)(177, 361)(178, 362)(179, 363)(180, 364)(181, 365)(182, 366)(183, 367)(184, 368) local type(s) :: { ( 4, 92, 4, 92 ) } Outer automorphisms :: reflexible Dual of E23.879 Graph:: simple bipartite v = 92 e = 184 f = 48 degree seq :: [ 4^92 ] E23.879 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 46}) Quotient :: dipole Aut^+ = D92 (small group id <92, 3>) Aut = C2 x C2 x D46 (small group id <184, 11>) |r| :: 2 Presentation :: [ Y3^2, Y2^2, R^2, (R * Y2)^2, (Y3 * Y2)^2, (Y3 * Y1^-1)^2, (R * Y1)^2, (Y1^-1 * Y2)^2, (R * Y3)^2, Y1^12 * Y3 * Y1^-11 * Y2, Y1^2 * Y3 * Y1^-1 * Y2 * Y1^10 * Y3 * Y2 * Y1^10 * Y3 * Y2 ] Map:: non-degenerate R = (1, 93, 2, 94, 6, 98, 13, 105, 21, 113, 29, 121, 37, 129, 45, 137, 53, 145, 61, 153, 69, 161, 77, 169, 85, 177, 90, 182, 82, 174, 74, 166, 66, 158, 58, 150, 50, 142, 42, 134, 34, 126, 26, 118, 18, 110, 10, 102, 16, 108, 24, 116, 32, 124, 40, 132, 48, 140, 56, 148, 64, 156, 72, 164, 80, 172, 88, 180, 92, 184, 84, 176, 76, 168, 68, 160, 60, 152, 52, 144, 44, 136, 36, 128, 28, 120, 20, 112, 12, 104, 5, 97)(3, 95, 9, 101, 17, 109, 25, 117, 33, 125, 41, 133, 49, 141, 57, 149, 65, 157, 73, 165, 81, 173, 89, 181, 87, 179, 79, 171, 71, 163, 63, 155, 55, 147, 47, 139, 39, 131, 31, 123, 23, 115, 15, 107, 8, 100, 4, 96, 11, 103, 19, 111, 27, 119, 35, 127, 43, 135, 51, 143, 59, 151, 67, 159, 75, 167, 83, 175, 91, 183, 86, 178, 78, 170, 70, 162, 62, 154, 54, 146, 46, 138, 38, 130, 30, 122, 22, 114, 14, 106, 7, 99)(185, 277, 187, 279)(186, 278, 191, 283)(188, 280, 194, 286)(189, 281, 193, 285)(190, 282, 198, 290)(192, 284, 200, 292)(195, 287, 202, 294)(196, 288, 201, 293)(197, 289, 206, 298)(199, 291, 208, 300)(203, 295, 210, 302)(204, 296, 209, 301)(205, 297, 214, 306)(207, 299, 216, 308)(211, 303, 218, 310)(212, 304, 217, 309)(213, 305, 222, 314)(215, 307, 224, 316)(219, 311, 226, 318)(220, 312, 225, 317)(221, 313, 230, 322)(223, 315, 232, 324)(227, 319, 234, 326)(228, 320, 233, 325)(229, 321, 238, 330)(231, 323, 240, 332)(235, 327, 242, 334)(236, 328, 241, 333)(237, 329, 246, 338)(239, 331, 248, 340)(243, 335, 250, 342)(244, 336, 249, 341)(245, 337, 254, 346)(247, 339, 256, 348)(251, 343, 258, 350)(252, 344, 257, 349)(253, 345, 262, 354)(255, 347, 264, 356)(259, 351, 266, 358)(260, 352, 265, 357)(261, 353, 270, 362)(263, 355, 272, 364)(267, 359, 274, 366)(268, 360, 273, 365)(269, 361, 275, 367)(271, 363, 276, 368) L = (1, 188)(2, 192)(3, 194)(4, 185)(5, 195)(6, 199)(7, 200)(8, 186)(9, 202)(10, 187)(11, 189)(12, 203)(13, 207)(14, 208)(15, 190)(16, 191)(17, 210)(18, 193)(19, 196)(20, 211)(21, 215)(22, 216)(23, 197)(24, 198)(25, 218)(26, 201)(27, 204)(28, 219)(29, 223)(30, 224)(31, 205)(32, 206)(33, 226)(34, 209)(35, 212)(36, 227)(37, 231)(38, 232)(39, 213)(40, 214)(41, 234)(42, 217)(43, 220)(44, 235)(45, 239)(46, 240)(47, 221)(48, 222)(49, 242)(50, 225)(51, 228)(52, 243)(53, 247)(54, 248)(55, 229)(56, 230)(57, 250)(58, 233)(59, 236)(60, 251)(61, 255)(62, 256)(63, 237)(64, 238)(65, 258)(66, 241)(67, 244)(68, 259)(69, 263)(70, 264)(71, 245)(72, 246)(73, 266)(74, 249)(75, 252)(76, 267)(77, 271)(78, 272)(79, 253)(80, 254)(81, 274)(82, 257)(83, 260)(84, 275)(85, 273)(86, 276)(87, 261)(88, 262)(89, 269)(90, 265)(91, 268)(92, 270)(93, 277)(94, 278)(95, 279)(96, 280)(97, 281)(98, 282)(99, 283)(100, 284)(101, 285)(102, 286)(103, 287)(104, 288)(105, 289)(106, 290)(107, 291)(108, 292)(109, 293)(110, 294)(111, 295)(112, 296)(113, 297)(114, 298)(115, 299)(116, 300)(117, 301)(118, 302)(119, 303)(120, 304)(121, 305)(122, 306)(123, 307)(124, 308)(125, 309)(126, 310)(127, 311)(128, 312)(129, 313)(130, 314)(131, 315)(132, 316)(133, 317)(134, 318)(135, 319)(136, 320)(137, 321)(138, 322)(139, 323)(140, 324)(141, 325)(142, 326)(143, 327)(144, 328)(145, 329)(146, 330)(147, 331)(148, 332)(149, 333)(150, 334)(151, 335)(152, 336)(153, 337)(154, 338)(155, 339)(156, 340)(157, 341)(158, 342)(159, 343)(160, 344)(161, 345)(162, 346)(163, 347)(164, 348)(165, 349)(166, 350)(167, 351)(168, 352)(169, 353)(170, 354)(171, 355)(172, 356)(173, 357)(174, 358)(175, 359)(176, 360)(177, 361)(178, 362)(179, 363)(180, 364)(181, 365)(182, 366)(183, 367)(184, 368) local type(s) :: { ( 4^4 ), ( 4^92 ) } Outer automorphisms :: reflexible Dual of E23.878 Graph:: bipartite v = 48 e = 184 f = 92 degree seq :: [ 4^46, 92^2 ] E23.880 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 4, 46}) Quotient :: edge Aut^+ = C23 : C4 (small group id <92, 1>) Aut = (C46 x C2) : C2 (small group id <184, 7>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T1^-1 * T2^-1 * T1 * T2^-1, T1^-2 * T2^23 ] Map:: non-degenerate R = (1, 3, 9, 17, 25, 33, 41, 49, 57, 65, 73, 81, 89, 86, 78, 70, 62, 54, 46, 38, 30, 22, 14, 6, 13, 21, 29, 37, 45, 53, 61, 69, 77, 85, 92, 84, 76, 68, 60, 52, 44, 36, 28, 20, 12, 5)(2, 7, 15, 23, 31, 39, 47, 55, 63, 71, 79, 87, 90, 82, 74, 66, 58, 50, 42, 34, 26, 18, 10, 4, 11, 19, 27, 35, 43, 51, 59, 67, 75, 83, 91, 88, 80, 72, 64, 56, 48, 40, 32, 24, 16, 8)(93, 94, 98, 96)(95, 100, 105, 102)(97, 99, 106, 103)(101, 108, 113, 110)(104, 107, 114, 111)(109, 116, 121, 118)(112, 115, 122, 119)(117, 124, 129, 126)(120, 123, 130, 127)(125, 132, 137, 134)(128, 131, 138, 135)(133, 140, 145, 142)(136, 139, 146, 143)(141, 148, 153, 150)(144, 147, 154, 151)(149, 156, 161, 158)(152, 155, 162, 159)(157, 164, 169, 166)(160, 163, 170, 167)(165, 172, 177, 174)(168, 171, 178, 175)(173, 180, 184, 182)(176, 179, 181, 183) L = (1, 93)(2, 94)(3, 95)(4, 96)(5, 97)(6, 98)(7, 99)(8, 100)(9, 101)(10, 102)(11, 103)(12, 104)(13, 105)(14, 106)(15, 107)(16, 108)(17, 109)(18, 110)(19, 111)(20, 112)(21, 113)(22, 114)(23, 115)(24, 116)(25, 117)(26, 118)(27, 119)(28, 120)(29, 121)(30, 122)(31, 123)(32, 124)(33, 125)(34, 126)(35, 127)(36, 128)(37, 129)(38, 130)(39, 131)(40, 132)(41, 133)(42, 134)(43, 135)(44, 136)(45, 137)(46, 138)(47, 139)(48, 140)(49, 141)(50, 142)(51, 143)(52, 144)(53, 145)(54, 146)(55, 147)(56, 148)(57, 149)(58, 150)(59, 151)(60, 152)(61, 153)(62, 154)(63, 155)(64, 156)(65, 157)(66, 158)(67, 159)(68, 160)(69, 161)(70, 162)(71, 163)(72, 164)(73, 165)(74, 166)(75, 167)(76, 168)(77, 169)(78, 170)(79, 171)(80, 172)(81, 173)(82, 174)(83, 175)(84, 176)(85, 177)(86, 178)(87, 179)(88, 180)(89, 181)(90, 182)(91, 183)(92, 184) local type(s) :: { ( 8^4 ), ( 8^46 ) } Outer automorphisms :: reflexible Dual of E23.881 Transitivity :: ET+ Graph:: bipartite v = 25 e = 92 f = 23 degree seq :: [ 4^23, 46^2 ] E23.881 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 4, 46}) Quotient :: loop Aut^+ = C23 : C4 (small group id <92, 1>) Aut = (C46 x C2) : C2 (small group id <184, 7>) |r| :: 2 Presentation :: [ F^2, T1^2 * T2^2, T2^4, (F * T2)^2, T2^-1 * T1^2 * T2^-1, (F * T1)^2, T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * 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, 93, 3, 95, 6, 98, 5, 97)(2, 94, 7, 99, 4, 96, 8, 100)(9, 101, 13, 105, 10, 102, 14, 106)(11, 103, 15, 107, 12, 104, 16, 108)(17, 109, 21, 113, 18, 110, 22, 114)(19, 111, 23, 115, 20, 112, 24, 116)(25, 117, 29, 121, 26, 118, 30, 122)(27, 119, 31, 123, 28, 120, 32, 124)(33, 125, 53, 145, 34, 126, 54, 146)(35, 127, 55, 147, 38, 130, 56, 148)(36, 128, 57, 149, 37, 129, 58, 150)(39, 131, 59, 151, 40, 132, 60, 152)(41, 133, 61, 153, 42, 134, 62, 154)(43, 135, 63, 155, 44, 136, 64, 156)(45, 137, 65, 157, 46, 138, 66, 158)(47, 139, 67, 159, 48, 140, 68, 160)(49, 141, 69, 161, 50, 142, 70, 162)(51, 143, 71, 163, 52, 144, 72, 164)(73, 165, 92, 184, 74, 166, 91, 183)(75, 167, 90, 182, 76, 168, 89, 181)(77, 169, 87, 179, 78, 170, 88, 180)(79, 171, 86, 178, 80, 172, 85, 177)(81, 173, 83, 175, 82, 174, 84, 176) L = (1, 94)(2, 98)(3, 101)(4, 93)(5, 102)(6, 96)(7, 103)(8, 104)(9, 97)(10, 95)(11, 100)(12, 99)(13, 109)(14, 110)(15, 111)(16, 112)(17, 106)(18, 105)(19, 108)(20, 107)(21, 117)(22, 118)(23, 119)(24, 120)(25, 114)(26, 113)(27, 116)(28, 115)(29, 125)(30, 126)(31, 130)(32, 127)(33, 122)(34, 121)(35, 123)(36, 145)(37, 146)(38, 124)(39, 148)(40, 147)(41, 150)(42, 149)(43, 152)(44, 151)(45, 154)(46, 153)(47, 156)(48, 155)(49, 158)(50, 157)(51, 160)(52, 159)(53, 129)(54, 128)(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, 165)(70, 166)(71, 168)(72, 167)(73, 162)(74, 161)(75, 163)(76, 164)(77, 184)(78, 183)(79, 181)(80, 182)(81, 180)(82, 179)(83, 177)(84, 178)(85, 176)(86, 175)(87, 173)(88, 174)(89, 172)(90, 171)(91, 169)(92, 170) local type(s) :: { ( 4, 46, 4, 46, 4, 46, 4, 46 ) } Outer automorphisms :: reflexible Dual of E23.880 Transitivity :: ET+ VT+ AT Graph:: v = 23 e = 92 f = 25 degree seq :: [ 8^23 ] E23.882 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 46}) Quotient :: dipole Aut^+ = C23 : C4 (small group id <92, 1>) Aut = (C46 x C2) : C2 (small group id <184, 7>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y1^-1 * Y2^-1 * Y1 * Y2^-1, Y1^4, (Y3^-1 * Y1^-1)^4, Y2^-1 * Y1 * Y2^11 * Y1 * Y2^-11, Y2^46 ] Map:: R = (1, 93, 2, 94, 6, 98, 4, 96)(3, 95, 8, 100, 13, 105, 10, 102)(5, 97, 7, 99, 14, 106, 11, 103)(9, 101, 16, 108, 21, 113, 18, 110)(12, 104, 15, 107, 22, 114, 19, 111)(17, 109, 24, 116, 29, 121, 26, 118)(20, 112, 23, 115, 30, 122, 27, 119)(25, 117, 32, 124, 37, 129, 34, 126)(28, 120, 31, 123, 38, 130, 35, 127)(33, 125, 40, 132, 45, 137, 42, 134)(36, 128, 39, 131, 46, 138, 43, 135)(41, 133, 48, 140, 53, 145, 50, 142)(44, 136, 47, 139, 54, 146, 51, 143)(49, 141, 56, 148, 61, 153, 58, 150)(52, 144, 55, 147, 62, 154, 59, 151)(57, 149, 64, 156, 69, 161, 66, 158)(60, 152, 63, 155, 70, 162, 67, 159)(65, 157, 72, 164, 77, 169, 74, 166)(68, 160, 71, 163, 78, 170, 75, 167)(73, 165, 80, 172, 85, 177, 82, 174)(76, 168, 79, 171, 86, 178, 83, 175)(81, 173, 88, 180, 92, 184, 90, 182)(84, 176, 87, 179, 89, 181, 91, 183)(185, 277, 187, 279, 193, 285, 201, 293, 209, 301, 217, 309, 225, 317, 233, 325, 241, 333, 249, 341, 257, 349, 265, 357, 273, 365, 270, 362, 262, 354, 254, 346, 246, 338, 238, 330, 230, 322, 222, 314, 214, 306, 206, 298, 198, 290, 190, 282, 197, 289, 205, 297, 213, 305, 221, 313, 229, 321, 237, 329, 245, 337, 253, 345, 261, 353, 269, 361, 276, 368, 268, 360, 260, 352, 252, 344, 244, 336, 236, 328, 228, 320, 220, 312, 212, 304, 204, 296, 196, 288, 189, 281)(186, 278, 191, 283, 199, 291, 207, 299, 215, 307, 223, 315, 231, 323, 239, 331, 247, 339, 255, 347, 263, 355, 271, 363, 274, 366, 266, 358, 258, 350, 250, 342, 242, 334, 234, 326, 226, 318, 218, 310, 210, 302, 202, 294, 194, 286, 188, 280, 195, 287, 203, 295, 211, 303, 219, 311, 227, 319, 235, 327, 243, 335, 251, 343, 259, 351, 267, 359, 275, 367, 272, 364, 264, 356, 256, 348, 248, 340, 240, 332, 232, 324, 224, 316, 216, 308, 208, 300, 200, 292, 192, 284) L = (1, 187)(2, 191)(3, 193)(4, 195)(5, 185)(6, 197)(7, 199)(8, 186)(9, 201)(10, 188)(11, 203)(12, 189)(13, 205)(14, 190)(15, 207)(16, 192)(17, 209)(18, 194)(19, 211)(20, 196)(21, 213)(22, 198)(23, 215)(24, 200)(25, 217)(26, 202)(27, 219)(28, 204)(29, 221)(30, 206)(31, 223)(32, 208)(33, 225)(34, 210)(35, 227)(36, 212)(37, 229)(38, 214)(39, 231)(40, 216)(41, 233)(42, 218)(43, 235)(44, 220)(45, 237)(46, 222)(47, 239)(48, 224)(49, 241)(50, 226)(51, 243)(52, 228)(53, 245)(54, 230)(55, 247)(56, 232)(57, 249)(58, 234)(59, 251)(60, 236)(61, 253)(62, 238)(63, 255)(64, 240)(65, 257)(66, 242)(67, 259)(68, 244)(69, 261)(70, 246)(71, 263)(72, 248)(73, 265)(74, 250)(75, 267)(76, 252)(77, 269)(78, 254)(79, 271)(80, 256)(81, 273)(82, 258)(83, 275)(84, 260)(85, 276)(86, 262)(87, 274)(88, 264)(89, 270)(90, 266)(91, 272)(92, 268)(93, 277)(94, 278)(95, 279)(96, 280)(97, 281)(98, 282)(99, 283)(100, 284)(101, 285)(102, 286)(103, 287)(104, 288)(105, 289)(106, 290)(107, 291)(108, 292)(109, 293)(110, 294)(111, 295)(112, 296)(113, 297)(114, 298)(115, 299)(116, 300)(117, 301)(118, 302)(119, 303)(120, 304)(121, 305)(122, 306)(123, 307)(124, 308)(125, 309)(126, 310)(127, 311)(128, 312)(129, 313)(130, 314)(131, 315)(132, 316)(133, 317)(134, 318)(135, 319)(136, 320)(137, 321)(138, 322)(139, 323)(140, 324)(141, 325)(142, 326)(143, 327)(144, 328)(145, 329)(146, 330)(147, 331)(148, 332)(149, 333)(150, 334)(151, 335)(152, 336)(153, 337)(154, 338)(155, 339)(156, 340)(157, 341)(158, 342)(159, 343)(160, 344)(161, 345)(162, 346)(163, 347)(164, 348)(165, 349)(166, 350)(167, 351)(168, 352)(169, 353)(170, 354)(171, 355)(172, 356)(173, 357)(174, 358)(175, 359)(176, 360)(177, 361)(178, 362)(179, 363)(180, 364)(181, 365)(182, 366)(183, 367)(184, 368) 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 E23.883 Graph:: bipartite v = 25 e = 184 f = 115 degree seq :: [ 8^23, 92^2 ] E23.883 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 46}) Quotient :: dipole Aut^+ = C23 : C4 (small group id <92, 1>) Aut = (C46 x C2) : C2 (small group id <184, 7>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, Y2^4, Y2^-1 * Y3^-1 * Y2 * Y3^-1, (R * Y2 * Y3^-1)^2, Y2^-2 * Y3^23, (Y3^-1 * Y1^-1)^46 ] Map:: R = (1, 93)(2, 94)(3, 95)(4, 96)(5, 97)(6, 98)(7, 99)(8, 100)(9, 101)(10, 102)(11, 103)(12, 104)(13, 105)(14, 106)(15, 107)(16, 108)(17, 109)(18, 110)(19, 111)(20, 112)(21, 113)(22, 114)(23, 115)(24, 116)(25, 117)(26, 118)(27, 119)(28, 120)(29, 121)(30, 122)(31, 123)(32, 124)(33, 125)(34, 126)(35, 127)(36, 128)(37, 129)(38, 130)(39, 131)(40, 132)(41, 133)(42, 134)(43, 135)(44, 136)(45, 137)(46, 138)(47, 139)(48, 140)(49, 141)(50, 142)(51, 143)(52, 144)(53, 145)(54, 146)(55, 147)(56, 148)(57, 149)(58, 150)(59, 151)(60, 152)(61, 153)(62, 154)(63, 155)(64, 156)(65, 157)(66, 158)(67, 159)(68, 160)(69, 161)(70, 162)(71, 163)(72, 164)(73, 165)(74, 166)(75, 167)(76, 168)(77, 169)(78, 170)(79, 171)(80, 172)(81, 173)(82, 174)(83, 175)(84, 176)(85, 177)(86, 178)(87, 179)(88, 180)(89, 181)(90, 182)(91, 183)(92, 184)(185, 277, 186, 278, 190, 282, 188, 280)(187, 279, 192, 284, 197, 289, 194, 286)(189, 281, 191, 283, 198, 290, 195, 287)(193, 285, 200, 292, 205, 297, 202, 294)(196, 288, 199, 291, 206, 298, 203, 295)(201, 293, 208, 300, 213, 305, 210, 302)(204, 296, 207, 299, 214, 306, 211, 303)(209, 301, 216, 308, 221, 313, 218, 310)(212, 304, 215, 307, 222, 314, 219, 311)(217, 309, 224, 316, 229, 321, 226, 318)(220, 312, 223, 315, 230, 322, 227, 319)(225, 317, 232, 324, 237, 329, 234, 326)(228, 320, 231, 323, 238, 330, 235, 327)(233, 325, 240, 332, 245, 337, 242, 334)(236, 328, 239, 331, 246, 338, 243, 335)(241, 333, 248, 340, 253, 345, 250, 342)(244, 336, 247, 339, 254, 346, 251, 343)(249, 341, 256, 348, 261, 353, 258, 350)(252, 344, 255, 347, 262, 354, 259, 351)(257, 349, 264, 356, 269, 361, 266, 358)(260, 352, 263, 355, 270, 362, 267, 359)(265, 357, 272, 364, 276, 368, 274, 366)(268, 360, 271, 363, 273, 365, 275, 367) L = (1, 187)(2, 191)(3, 193)(4, 195)(5, 185)(6, 197)(7, 199)(8, 186)(9, 201)(10, 188)(11, 203)(12, 189)(13, 205)(14, 190)(15, 207)(16, 192)(17, 209)(18, 194)(19, 211)(20, 196)(21, 213)(22, 198)(23, 215)(24, 200)(25, 217)(26, 202)(27, 219)(28, 204)(29, 221)(30, 206)(31, 223)(32, 208)(33, 225)(34, 210)(35, 227)(36, 212)(37, 229)(38, 214)(39, 231)(40, 216)(41, 233)(42, 218)(43, 235)(44, 220)(45, 237)(46, 222)(47, 239)(48, 224)(49, 241)(50, 226)(51, 243)(52, 228)(53, 245)(54, 230)(55, 247)(56, 232)(57, 249)(58, 234)(59, 251)(60, 236)(61, 253)(62, 238)(63, 255)(64, 240)(65, 257)(66, 242)(67, 259)(68, 244)(69, 261)(70, 246)(71, 263)(72, 248)(73, 265)(74, 250)(75, 267)(76, 252)(77, 269)(78, 254)(79, 271)(80, 256)(81, 273)(82, 258)(83, 275)(84, 260)(85, 276)(86, 262)(87, 274)(88, 264)(89, 270)(90, 266)(91, 272)(92, 268)(93, 277)(94, 278)(95, 279)(96, 280)(97, 281)(98, 282)(99, 283)(100, 284)(101, 285)(102, 286)(103, 287)(104, 288)(105, 289)(106, 290)(107, 291)(108, 292)(109, 293)(110, 294)(111, 295)(112, 296)(113, 297)(114, 298)(115, 299)(116, 300)(117, 301)(118, 302)(119, 303)(120, 304)(121, 305)(122, 306)(123, 307)(124, 308)(125, 309)(126, 310)(127, 311)(128, 312)(129, 313)(130, 314)(131, 315)(132, 316)(133, 317)(134, 318)(135, 319)(136, 320)(137, 321)(138, 322)(139, 323)(140, 324)(141, 325)(142, 326)(143, 327)(144, 328)(145, 329)(146, 330)(147, 331)(148, 332)(149, 333)(150, 334)(151, 335)(152, 336)(153, 337)(154, 338)(155, 339)(156, 340)(157, 341)(158, 342)(159, 343)(160, 344)(161, 345)(162, 346)(163, 347)(164, 348)(165, 349)(166, 350)(167, 351)(168, 352)(169, 353)(170, 354)(171, 355)(172, 356)(173, 357)(174, 358)(175, 359)(176, 360)(177, 361)(178, 362)(179, 363)(180, 364)(181, 365)(182, 366)(183, 367)(184, 368) local type(s) :: { ( 8, 92 ), ( 8, 92, 8, 92, 8, 92, 8, 92 ) } Outer automorphisms :: reflexible Dual of E23.882 Graph:: simple bipartite v = 115 e = 184 f = 25 degree seq :: [ 2^92, 8^23 ] E23.884 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 92, 92}) Quotient :: regular Aut^+ = C92 (small group id <92, 2>) Aut = D184 (small group id <184, 5>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T2 * T1^46 ] Map:: R = (1, 2, 5, 9, 13, 17, 21, 25, 29, 36, 38, 40, 42, 44, 46, 48, 50, 51, 52, 54, 56, 58, 60, 62, 64, 71, 73, 75, 77, 78, 80, 82, 85, 86, 87, 89, 84, 66, 49, 31, 27, 23, 19, 15, 11, 7, 3, 6, 10, 14, 18, 22, 26, 30, 33, 34, 35, 37, 39, 41, 43, 45, 47, 53, 55, 57, 59, 61, 63, 65, 68, 69, 70, 72, 74, 76, 67, 79, 81, 88, 90, 91, 92, 83, 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, 33)(32, 49)(34, 36)(35, 38)(37, 40)(39, 42)(41, 44)(43, 46)(45, 48)(47, 50)(51, 53)(52, 55)(54, 57)(56, 59)(58, 61)(60, 63)(62, 65)(64, 68)(66, 83)(67, 80)(69, 71)(70, 73)(72, 75)(74, 77)(76, 78)(79, 82)(81, 85)(84, 92)(86, 88)(87, 90)(89, 91) local type(s) :: { ( 92^92 ) } Outer automorphisms :: reflexible selfdual Transitivity :: ET+ VT+ AT+ REG+ Graph:: v = 1 e = 46 f = 1 degree seq :: [ 92 ] E23.885 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 92, 92}) Quotient :: edge Aut^+ = C92 (small group id <92, 2>) Aut = D184 (small group id <184, 5>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^46 * T1 ] Map:: R = (1, 3, 7, 11, 15, 19, 23, 27, 31, 36, 33, 35, 39, 42, 44, 46, 48, 50, 52, 57, 54, 56, 60, 63, 65, 67, 69, 71, 73, 78, 75, 77, 81, 84, 86, 88, 90, 74, 53, 30, 26, 22, 18, 14, 10, 6, 2, 5, 9, 13, 17, 21, 25, 29, 41, 38, 34, 37, 40, 43, 45, 47, 49, 51, 62, 59, 55, 58, 61, 64, 66, 68, 70, 72, 83, 80, 76, 79, 82, 85, 87, 89, 91, 92, 32, 28, 24, 20, 16, 12, 8, 4)(93, 94)(95, 97)(96, 98)(99, 101)(100, 102)(103, 105)(104, 106)(107, 109)(108, 110)(111, 113)(112, 114)(115, 117)(116, 118)(119, 121)(120, 122)(123, 133)(124, 145)(125, 126)(127, 129)(128, 130)(131, 132)(134, 135)(136, 137)(138, 139)(140, 141)(142, 143)(144, 154)(146, 147)(148, 150)(149, 151)(152, 153)(155, 156)(157, 158)(159, 160)(161, 162)(163, 164)(165, 175)(166, 184)(167, 168)(169, 171)(170, 172)(173, 174)(176, 177)(178, 179)(180, 181)(182, 183) L = (1, 93)(2, 94)(3, 95)(4, 96)(5, 97)(6, 98)(7, 99)(8, 100)(9, 101)(10, 102)(11, 103)(12, 104)(13, 105)(14, 106)(15, 107)(16, 108)(17, 109)(18, 110)(19, 111)(20, 112)(21, 113)(22, 114)(23, 115)(24, 116)(25, 117)(26, 118)(27, 119)(28, 120)(29, 121)(30, 122)(31, 123)(32, 124)(33, 125)(34, 126)(35, 127)(36, 128)(37, 129)(38, 130)(39, 131)(40, 132)(41, 133)(42, 134)(43, 135)(44, 136)(45, 137)(46, 138)(47, 139)(48, 140)(49, 141)(50, 142)(51, 143)(52, 144)(53, 145)(54, 146)(55, 147)(56, 148)(57, 149)(58, 150)(59, 151)(60, 152)(61, 153)(62, 154)(63, 155)(64, 156)(65, 157)(66, 158)(67, 159)(68, 160)(69, 161)(70, 162)(71, 163)(72, 164)(73, 165)(74, 166)(75, 167)(76, 168)(77, 169)(78, 170)(79, 171)(80, 172)(81, 173)(82, 174)(83, 175)(84, 176)(85, 177)(86, 178)(87, 179)(88, 180)(89, 181)(90, 182)(91, 183)(92, 184) local type(s) :: { ( 184, 184 ), ( 184^92 ) } Outer automorphisms :: reflexible Dual of E23.886 Transitivity :: ET+ Graph:: bipartite v = 47 e = 92 f = 1 degree seq :: [ 2^46, 92 ] E23.886 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 92, 92}) Quotient :: loop Aut^+ = C92 (small group id <92, 2>) Aut = D184 (small group id <184, 5>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^46 * T1 ] Map:: R = (1, 93, 3, 95, 7, 99, 11, 103, 15, 107, 19, 111, 23, 115, 27, 119, 31, 123, 34, 126, 37, 129, 39, 131, 41, 133, 43, 135, 45, 137, 47, 139, 49, 141, 55, 147, 52, 144, 54, 146, 57, 149, 59, 151, 61, 153, 63, 155, 65, 157, 67, 159, 69, 161, 73, 165, 76, 168, 77, 169, 79, 171, 81, 173, 83, 175, 85, 177, 87, 179, 92, 184, 90, 182, 70, 162, 51, 143, 30, 122, 26, 118, 22, 114, 18, 110, 14, 106, 10, 102, 6, 98, 2, 94, 5, 97, 9, 101, 13, 105, 17, 109, 21, 113, 25, 117, 29, 121, 36, 128, 33, 125, 35, 127, 38, 130, 40, 132, 42, 134, 44, 136, 46, 138, 48, 140, 50, 142, 53, 145, 56, 148, 58, 150, 60, 152, 62, 154, 64, 156, 66, 158, 68, 160, 75, 167, 72, 164, 74, 166, 71, 163, 78, 170, 80, 172, 82, 174, 84, 176, 86, 178, 88, 180, 91, 183, 89, 181, 32, 124, 28, 120, 24, 116, 20, 112, 16, 108, 12, 104, 8, 100, 4, 96) L = (1, 94)(2, 93)(3, 97)(4, 98)(5, 95)(6, 96)(7, 101)(8, 102)(9, 99)(10, 100)(11, 105)(12, 106)(13, 103)(14, 104)(15, 109)(16, 110)(17, 107)(18, 108)(19, 113)(20, 114)(21, 111)(22, 112)(23, 117)(24, 118)(25, 115)(26, 116)(27, 121)(28, 122)(29, 119)(30, 120)(31, 128)(32, 143)(33, 126)(34, 125)(35, 129)(36, 123)(37, 127)(38, 131)(39, 130)(40, 133)(41, 132)(42, 135)(43, 134)(44, 137)(45, 136)(46, 139)(47, 138)(48, 141)(49, 140)(50, 147)(51, 124)(52, 145)(53, 144)(54, 148)(55, 142)(56, 146)(57, 150)(58, 149)(59, 152)(60, 151)(61, 154)(62, 153)(63, 156)(64, 155)(65, 158)(66, 157)(67, 160)(68, 159)(69, 167)(70, 181)(71, 169)(72, 165)(73, 164)(74, 168)(75, 161)(76, 166)(77, 163)(78, 171)(79, 170)(80, 173)(81, 172)(82, 175)(83, 174)(84, 177)(85, 176)(86, 179)(87, 178)(88, 184)(89, 162)(90, 183)(91, 182)(92, 180) local type(s) :: { ( 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92, 2, 92 ) } Outer automorphisms :: reflexible Dual of E23.885 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 92 f = 47 degree seq :: [ 184 ] E23.887 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 92, 92}) Quotient :: dipole Aut^+ = C92 (small group id <92, 2>) Aut = D184 (small group id <184, 5>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y1 * Y2 * Y1, (R * Y2 * Y3^-1)^2, Y2^46 * Y1, (Y3 * Y2^-1)^92 ] Map:: R = (1, 93, 2, 94)(3, 95, 5, 97)(4, 96, 6, 98)(7, 99, 9, 101)(8, 100, 10, 102)(11, 103, 13, 105)(12, 104, 14, 106)(15, 107, 17, 109)(16, 108, 18, 110)(19, 111, 21, 113)(20, 112, 22, 114)(23, 115, 25, 117)(24, 116, 26, 118)(27, 119, 29, 121)(28, 120, 30, 122)(31, 123, 33, 125)(32, 124, 49, 141)(34, 126, 35, 127)(36, 128, 37, 129)(38, 130, 39, 131)(40, 132, 41, 133)(42, 134, 43, 135)(44, 136, 45, 137)(46, 138, 47, 139)(48, 140, 50, 142)(51, 143, 52, 144)(53, 145, 54, 146)(55, 147, 56, 148)(57, 149, 58, 150)(59, 151, 60, 152)(61, 153, 62, 154)(63, 155, 64, 156)(65, 157, 68, 160)(66, 158, 83, 175)(67, 159, 79, 171)(69, 161, 70, 162)(71, 163, 72, 164)(73, 165, 74, 166)(75, 167, 76, 168)(77, 169, 78, 170)(80, 172, 81, 173)(82, 174, 85, 177)(84, 176, 92, 184)(86, 178, 87, 179)(88, 180, 89, 181)(90, 182, 91, 183)(185, 277, 187, 279, 191, 283, 195, 287, 199, 291, 203, 295, 207, 299, 211, 303, 215, 307, 219, 311, 221, 313, 223, 315, 225, 317, 227, 319, 229, 321, 231, 323, 234, 326, 235, 327, 237, 329, 239, 331, 241, 333, 243, 335, 245, 337, 247, 339, 249, 341, 254, 346, 256, 348, 258, 350, 260, 352, 262, 354, 263, 355, 265, 357, 269, 361, 270, 362, 272, 364, 274, 366, 268, 360, 250, 342, 233, 325, 214, 306, 210, 302, 206, 298, 202, 294, 198, 290, 194, 286, 190, 282, 186, 278, 189, 281, 193, 285, 197, 289, 201, 293, 205, 297, 209, 301, 213, 305, 217, 309, 218, 310, 220, 312, 222, 314, 224, 316, 226, 318, 228, 320, 230, 322, 232, 324, 236, 328, 238, 330, 240, 332, 242, 334, 244, 336, 246, 338, 248, 340, 252, 344, 253, 345, 255, 347, 257, 349, 259, 351, 261, 353, 251, 343, 264, 356, 266, 358, 271, 363, 273, 365, 275, 367, 276, 368, 267, 359, 216, 308, 212, 304, 208, 300, 204, 296, 200, 292, 196, 288, 192, 284, 188, 280) L = (1, 186)(2, 185)(3, 189)(4, 190)(5, 187)(6, 188)(7, 193)(8, 194)(9, 191)(10, 192)(11, 197)(12, 198)(13, 195)(14, 196)(15, 201)(16, 202)(17, 199)(18, 200)(19, 205)(20, 206)(21, 203)(22, 204)(23, 209)(24, 210)(25, 207)(26, 208)(27, 213)(28, 214)(29, 211)(30, 212)(31, 217)(32, 233)(33, 215)(34, 219)(35, 218)(36, 221)(37, 220)(38, 223)(39, 222)(40, 225)(41, 224)(42, 227)(43, 226)(44, 229)(45, 228)(46, 231)(47, 230)(48, 234)(49, 216)(50, 232)(51, 236)(52, 235)(53, 238)(54, 237)(55, 240)(56, 239)(57, 242)(58, 241)(59, 244)(60, 243)(61, 246)(62, 245)(63, 248)(64, 247)(65, 252)(66, 267)(67, 263)(68, 249)(69, 254)(70, 253)(71, 256)(72, 255)(73, 258)(74, 257)(75, 260)(76, 259)(77, 262)(78, 261)(79, 251)(80, 265)(81, 264)(82, 269)(83, 250)(84, 276)(85, 266)(86, 271)(87, 270)(88, 273)(89, 272)(90, 275)(91, 274)(92, 268)(93, 277)(94, 278)(95, 279)(96, 280)(97, 281)(98, 282)(99, 283)(100, 284)(101, 285)(102, 286)(103, 287)(104, 288)(105, 289)(106, 290)(107, 291)(108, 292)(109, 293)(110, 294)(111, 295)(112, 296)(113, 297)(114, 298)(115, 299)(116, 300)(117, 301)(118, 302)(119, 303)(120, 304)(121, 305)(122, 306)(123, 307)(124, 308)(125, 309)(126, 310)(127, 311)(128, 312)(129, 313)(130, 314)(131, 315)(132, 316)(133, 317)(134, 318)(135, 319)(136, 320)(137, 321)(138, 322)(139, 323)(140, 324)(141, 325)(142, 326)(143, 327)(144, 328)(145, 329)(146, 330)(147, 331)(148, 332)(149, 333)(150, 334)(151, 335)(152, 336)(153, 337)(154, 338)(155, 339)(156, 340)(157, 341)(158, 342)(159, 343)(160, 344)(161, 345)(162, 346)(163, 347)(164, 348)(165, 349)(166, 350)(167, 351)(168, 352)(169, 353)(170, 354)(171, 355)(172, 356)(173, 357)(174, 358)(175, 359)(176, 360)(177, 361)(178, 362)(179, 363)(180, 364)(181, 365)(182, 366)(183, 367)(184, 368) local type(s) :: { ( 2, 184, 2, 184 ), ( 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184, 2, 184 ) } Outer automorphisms :: reflexible Dual of E23.888 Graph:: bipartite v = 47 e = 184 f = 93 degree seq :: [ 4^46, 184 ] E23.888 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 92, 92}) Quotient :: dipole Aut^+ = C92 (small group id <92, 2>) Aut = D184 (small group id <184, 5>) |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 * Y1^46 ] Map:: R = (1, 93, 2, 94, 5, 97, 9, 101, 13, 105, 17, 109, 21, 113, 25, 117, 29, 121, 35, 127, 38, 130, 40, 132, 42, 134, 44, 136, 46, 138, 48, 140, 50, 142, 55, 147, 52, 144, 53, 145, 56, 148, 58, 150, 60, 152, 62, 154, 64, 156, 66, 158, 68, 160, 74, 166, 76, 168, 78, 170, 80, 172, 82, 174, 84, 176, 86, 178, 88, 180, 92, 184, 90, 182, 70, 162, 51, 143, 31, 123, 27, 119, 23, 115, 19, 111, 15, 107, 11, 103, 7, 99, 3, 95, 6, 98, 10, 102, 14, 106, 18, 110, 22, 114, 26, 118, 30, 122, 36, 128, 33, 125, 34, 126, 37, 129, 39, 131, 41, 133, 43, 135, 45, 137, 47, 139, 49, 141, 54, 146, 57, 149, 59, 151, 61, 153, 63, 155, 65, 157, 67, 159, 69, 161, 75, 167, 72, 164, 73, 165, 71, 163, 77, 169, 79, 171, 81, 173, 83, 175, 85, 177, 87, 179, 91, 183, 89, 181, 32, 124, 28, 120, 24, 116, 20, 112, 16, 108, 12, 104, 8, 100, 4, 96)(185, 277)(186, 278)(187, 279)(188, 280)(189, 281)(190, 282)(191, 283)(192, 284)(193, 285)(194, 286)(195, 287)(196, 288)(197, 289)(198, 290)(199, 291)(200, 292)(201, 293)(202, 294)(203, 295)(204, 296)(205, 297)(206, 298)(207, 299)(208, 300)(209, 301)(210, 302)(211, 303)(212, 304)(213, 305)(214, 306)(215, 307)(216, 308)(217, 309)(218, 310)(219, 311)(220, 312)(221, 313)(222, 314)(223, 315)(224, 316)(225, 317)(226, 318)(227, 319)(228, 320)(229, 321)(230, 322)(231, 323)(232, 324)(233, 325)(234, 326)(235, 327)(236, 328)(237, 329)(238, 330)(239, 331)(240, 332)(241, 333)(242, 334)(243, 335)(244, 336)(245, 337)(246, 338)(247, 339)(248, 340)(249, 341)(250, 342)(251, 343)(252, 344)(253, 345)(254, 346)(255, 347)(256, 348)(257, 349)(258, 350)(259, 351)(260, 352)(261, 353)(262, 354)(263, 355)(264, 356)(265, 357)(266, 358)(267, 359)(268, 360)(269, 361)(270, 362)(271, 363)(272, 364)(273, 365)(274, 366)(275, 367)(276, 368) L = (1, 187)(2, 190)(3, 185)(4, 191)(5, 194)(6, 186)(7, 188)(8, 195)(9, 198)(10, 189)(11, 192)(12, 199)(13, 202)(14, 193)(15, 196)(16, 203)(17, 206)(18, 197)(19, 200)(20, 207)(21, 210)(22, 201)(23, 204)(24, 211)(25, 214)(26, 205)(27, 208)(28, 215)(29, 220)(30, 209)(31, 212)(32, 235)(33, 219)(34, 222)(35, 217)(36, 213)(37, 224)(38, 218)(39, 226)(40, 221)(41, 228)(42, 223)(43, 230)(44, 225)(45, 232)(46, 227)(47, 234)(48, 229)(49, 239)(50, 231)(51, 216)(52, 238)(53, 241)(54, 236)(55, 233)(56, 243)(57, 237)(58, 245)(59, 240)(60, 247)(61, 242)(62, 249)(63, 244)(64, 251)(65, 246)(66, 253)(67, 248)(68, 259)(69, 250)(70, 273)(71, 262)(72, 258)(73, 260)(74, 256)(75, 252)(76, 257)(77, 264)(78, 255)(79, 266)(80, 261)(81, 268)(82, 263)(83, 270)(84, 265)(85, 272)(86, 267)(87, 276)(88, 269)(89, 254)(90, 275)(91, 274)(92, 271)(93, 277)(94, 278)(95, 279)(96, 280)(97, 281)(98, 282)(99, 283)(100, 284)(101, 285)(102, 286)(103, 287)(104, 288)(105, 289)(106, 290)(107, 291)(108, 292)(109, 293)(110, 294)(111, 295)(112, 296)(113, 297)(114, 298)(115, 299)(116, 300)(117, 301)(118, 302)(119, 303)(120, 304)(121, 305)(122, 306)(123, 307)(124, 308)(125, 309)(126, 310)(127, 311)(128, 312)(129, 313)(130, 314)(131, 315)(132, 316)(133, 317)(134, 318)(135, 319)(136, 320)(137, 321)(138, 322)(139, 323)(140, 324)(141, 325)(142, 326)(143, 327)(144, 328)(145, 329)(146, 330)(147, 331)(148, 332)(149, 333)(150, 334)(151, 335)(152, 336)(153, 337)(154, 338)(155, 339)(156, 340)(157, 341)(158, 342)(159, 343)(160, 344)(161, 345)(162, 346)(163, 347)(164, 348)(165, 349)(166, 350)(167, 351)(168, 352)(169, 353)(170, 354)(171, 355)(172, 356)(173, 357)(174, 358)(175, 359)(176, 360)(177, 361)(178, 362)(179, 363)(180, 364)(181, 365)(182, 366)(183, 367)(184, 368) local type(s) :: { ( 4, 184 ), ( 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184, 4, 184 ) } Outer automorphisms :: reflexible Dual of E23.887 Graph:: bipartite v = 93 e = 184 f = 47 degree seq :: [ 2^92, 184 ] E23.889 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 47, 94}) Quotient :: regular Aut^+ = C94 (small group id <94, 2>) Aut = D188 (small group id <188, 3>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T2 * T1^-47 ] Map:: R = (1, 2, 5, 9, 13, 17, 21, 25, 29, 44, 40, 36, 33, 34, 37, 41, 45, 48, 51, 53, 55, 69, 65, 61, 58, 59, 62, 66, 70, 73, 76, 78, 80, 92, 89, 86, 83, 84, 82, 57, 31, 27, 23, 19, 15, 11, 7, 3, 6, 10, 14, 18, 22, 26, 30, 50, 47, 43, 39, 35, 38, 42, 46, 49, 52, 54, 56, 75, 72, 68, 64, 60, 63, 67, 71, 74, 77, 79, 81, 94, 93, 91, 88, 85, 87, 90, 32, 28, 24, 20, 16, 12, 8, 4) L = (1, 3)(2, 6)(4, 7)(5, 10)(8, 11)(9, 14)(12, 15)(13, 18)(16, 19)(17, 22)(20, 23)(21, 26)(24, 27)(25, 30)(28, 31)(29, 50)(32, 57)(33, 35)(34, 38)(36, 39)(37, 42)(40, 43)(41, 46)(44, 47)(45, 49)(48, 52)(51, 54)(53, 56)(55, 75)(58, 60)(59, 63)(61, 64)(62, 67)(65, 68)(66, 71)(69, 72)(70, 74)(73, 77)(76, 79)(78, 81)(80, 94)(82, 90)(83, 85)(84, 87)(86, 88)(89, 91)(92, 93) local type(s) :: { ( 47^94 ) } Outer automorphisms :: reflexible Dual of E23.890 Transitivity :: ET+ VT+ AT+ REG+ Graph:: v = 1 e = 47 f = 2 degree seq :: [ 94 ] E23.890 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 47, 94}) Quotient :: regular Aut^+ = C94 (small group id <94, 2>) Aut = D188 (small group id <188, 3>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T1^47 ] Map:: R = (1, 2, 5, 9, 13, 17, 21, 25, 29, 33, 34, 36, 39, 41, 43, 45, 47, 49, 52, 53, 55, 58, 60, 62, 64, 66, 68, 72, 73, 75, 78, 80, 81, 83, 85, 87, 91, 92, 89, 32, 28, 24, 20, 16, 12, 8, 4)(3, 6, 10, 14, 18, 22, 26, 30, 38, 35, 37, 40, 42, 44, 46, 48, 50, 57, 54, 56, 59, 61, 63, 65, 67, 69, 77, 74, 76, 79, 71, 82, 84, 86, 88, 94, 93, 90, 70, 51, 31, 27, 23, 19, 15, 11, 7) L = (1, 3)(2, 6)(4, 7)(5, 10)(8, 11)(9, 14)(12, 15)(13, 18)(16, 19)(17, 22)(20, 23)(21, 26)(24, 27)(25, 30)(28, 31)(29, 38)(32, 51)(33, 35)(34, 37)(36, 40)(39, 42)(41, 44)(43, 46)(45, 48)(47, 50)(49, 57)(52, 54)(53, 56)(55, 59)(58, 61)(60, 63)(62, 65)(64, 67)(66, 69)(68, 77)(70, 89)(71, 78)(72, 74)(73, 76)(75, 79)(80, 82)(81, 84)(83, 86)(85, 88)(87, 94)(90, 92)(91, 93) local type(s) :: { ( 94^47 ) } Outer automorphisms :: reflexible Dual of E23.889 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 2 e = 47 f = 1 degree seq :: [ 47^2 ] E23.891 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 47, 94}) Quotient :: edge Aut^+ = C94 (small group id <94, 2>) Aut = D188 (small group id <188, 3>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^47 ] Map:: R = (1, 3, 7, 11, 15, 19, 23, 27, 31, 44, 40, 36, 33, 35, 39, 43, 47, 50, 52, 54, 56, 69, 65, 61, 58, 60, 64, 68, 72, 75, 77, 79, 81, 92, 90, 86, 83, 85, 89, 32, 28, 24, 20, 16, 12, 8, 4)(2, 5, 9, 13, 17, 21, 25, 29, 49, 46, 42, 38, 34, 37, 41, 45, 48, 51, 53, 55, 74, 71, 67, 63, 59, 62, 66, 70, 73, 76, 78, 80, 94, 93, 91, 88, 84, 87, 82, 57, 30, 26, 22, 18, 14, 10, 6)(95, 96)(97, 99)(98, 100)(101, 103)(102, 104)(105, 107)(106, 108)(109, 111)(110, 112)(113, 115)(114, 116)(117, 119)(118, 120)(121, 123)(122, 124)(125, 143)(126, 151)(127, 128)(129, 131)(130, 132)(133, 135)(134, 136)(137, 139)(138, 140)(141, 142)(144, 145)(146, 147)(148, 149)(150, 168)(152, 153)(154, 156)(155, 157)(158, 160)(159, 161)(162, 164)(163, 165)(166, 167)(169, 170)(171, 172)(173, 174)(175, 188)(176, 183)(177, 178)(179, 181)(180, 182)(184, 185)(186, 187) L = (1, 95)(2, 96)(3, 97)(4, 98)(5, 99)(6, 100)(7, 101)(8, 102)(9, 103)(10, 104)(11, 105)(12, 106)(13, 107)(14, 108)(15, 109)(16, 110)(17, 111)(18, 112)(19, 113)(20, 114)(21, 115)(22, 116)(23, 117)(24, 118)(25, 119)(26, 120)(27, 121)(28, 122)(29, 123)(30, 124)(31, 125)(32, 126)(33, 127)(34, 128)(35, 129)(36, 130)(37, 131)(38, 132)(39, 133)(40, 134)(41, 135)(42, 136)(43, 137)(44, 138)(45, 139)(46, 140)(47, 141)(48, 142)(49, 143)(50, 144)(51, 145)(52, 146)(53, 147)(54, 148)(55, 149)(56, 150)(57, 151)(58, 152)(59, 153)(60, 154)(61, 155)(62, 156)(63, 157)(64, 158)(65, 159)(66, 160)(67, 161)(68, 162)(69, 163)(70, 164)(71, 165)(72, 166)(73, 167)(74, 168)(75, 169)(76, 170)(77, 171)(78, 172)(79, 173)(80, 174)(81, 175)(82, 176)(83, 177)(84, 178)(85, 179)(86, 180)(87, 181)(88, 182)(89, 183)(90, 184)(91, 185)(92, 186)(93, 187)(94, 188) local type(s) :: { ( 188, 188 ), ( 188^47 ) } Outer automorphisms :: reflexible Dual of E23.895 Transitivity :: ET+ Graph:: simple bipartite v = 49 e = 94 f = 1 degree seq :: [ 2^47, 47^2 ] E23.892 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 47, 94}) Quotient :: edge Aut^+ = C94 (small group id <94, 2>) Aut = D188 (small group id <188, 3>) |r| :: 2 Presentation :: [ F^2, T2^-2 * T1^-2, (F * T2)^2, (F * T1)^2, (T2^-1 * T1^-1)^2, T2^-2 * T1^45, T2^-2 * T1^21 * T2^-24 ] Map:: non-degenerate R = (1, 3, 9, 13, 17, 21, 25, 29, 33, 55, 77, 93, 92, 89, 88, 84, 83, 79, 81, 76, 73, 72, 69, 68, 65, 64, 58, 63, 60, 53, 52, 49, 48, 45, 44, 40, 39, 35, 37, 32, 27, 24, 19, 16, 11, 8, 2, 7, 4, 10, 14, 18, 22, 26, 30, 34, 56, 78, 94, 91, 90, 87, 86, 80, 85, 82, 75, 74, 71, 70, 67, 66, 62, 61, 57, 59, 54, 51, 50, 47, 46, 43, 42, 36, 41, 38, 31, 28, 23, 20, 15, 12, 6, 5)(95, 96, 100, 105, 109, 113, 117, 121, 125, 131, 135, 133, 136, 138, 140, 142, 144, 146, 148, 154, 151, 152, 156, 159, 161, 163, 165, 167, 169, 175, 179, 177, 180, 182, 184, 186, 188, 171, 150, 127, 124, 119, 116, 111, 108, 103, 98)(97, 101, 99, 102, 106, 110, 114, 118, 122, 126, 132, 129, 130, 134, 137, 139, 141, 143, 145, 147, 153, 157, 155, 158, 160, 162, 164, 166, 168, 170, 176, 173, 174, 178, 181, 183, 185, 187, 172, 149, 128, 123, 120, 115, 112, 107, 104) L = (1, 95)(2, 96)(3, 97)(4, 98)(5, 99)(6, 100)(7, 101)(8, 102)(9, 103)(10, 104)(11, 105)(12, 106)(13, 107)(14, 108)(15, 109)(16, 110)(17, 111)(18, 112)(19, 113)(20, 114)(21, 115)(22, 116)(23, 117)(24, 118)(25, 119)(26, 120)(27, 121)(28, 122)(29, 123)(30, 124)(31, 125)(32, 126)(33, 127)(34, 128)(35, 129)(36, 130)(37, 131)(38, 132)(39, 133)(40, 134)(41, 135)(42, 136)(43, 137)(44, 138)(45, 139)(46, 140)(47, 141)(48, 142)(49, 143)(50, 144)(51, 145)(52, 146)(53, 147)(54, 148)(55, 149)(56, 150)(57, 151)(58, 152)(59, 153)(60, 154)(61, 155)(62, 156)(63, 157)(64, 158)(65, 159)(66, 160)(67, 161)(68, 162)(69, 163)(70, 164)(71, 165)(72, 166)(73, 167)(74, 168)(75, 169)(76, 170)(77, 171)(78, 172)(79, 173)(80, 174)(81, 175)(82, 176)(83, 177)(84, 178)(85, 179)(86, 180)(87, 181)(88, 182)(89, 183)(90, 184)(91, 185)(92, 186)(93, 187)(94, 188) local type(s) :: { ( 4^47 ), ( 4^94 ) } Outer automorphisms :: reflexible Dual of E23.896 Transitivity :: ET+ Graph:: bipartite v = 3 e = 94 f = 47 degree seq :: [ 47^2, 94 ] E23.893 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 47, 94}) Quotient :: edge Aut^+ = C94 (small group id <94, 2>) Aut = D188 (small group id <188, 3>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T2 * T1^-47 ] 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, 38)(32, 51)(33, 35)(34, 37)(36, 40)(39, 42)(41, 44)(43, 46)(45, 48)(47, 50)(49, 57)(52, 54)(53, 56)(55, 59)(58, 61)(60, 63)(62, 65)(64, 67)(66, 69)(68, 77)(70, 89)(71, 80)(72, 74)(73, 76)(75, 78)(79, 82)(81, 84)(83, 86)(85, 88)(87, 94)(90, 93)(91, 92)(95, 96, 99, 103, 107, 111, 115, 119, 123, 127, 128, 130, 133, 135, 137, 139, 141, 143, 146, 147, 149, 152, 154, 156, 158, 160, 162, 166, 167, 169, 165, 173, 175, 177, 179, 181, 185, 184, 164, 145, 125, 121, 117, 113, 109, 105, 101, 97, 100, 104, 108, 112, 116, 120, 124, 132, 129, 131, 134, 136, 138, 140, 142, 144, 151, 148, 150, 153, 155, 157, 159, 161, 163, 171, 168, 170, 172, 174, 176, 178, 180, 182, 188, 186, 187, 183, 126, 122, 118, 114, 110, 106, 102, 98) L = (1, 95)(2, 96)(3, 97)(4, 98)(5, 99)(6, 100)(7, 101)(8, 102)(9, 103)(10, 104)(11, 105)(12, 106)(13, 107)(14, 108)(15, 109)(16, 110)(17, 111)(18, 112)(19, 113)(20, 114)(21, 115)(22, 116)(23, 117)(24, 118)(25, 119)(26, 120)(27, 121)(28, 122)(29, 123)(30, 124)(31, 125)(32, 126)(33, 127)(34, 128)(35, 129)(36, 130)(37, 131)(38, 132)(39, 133)(40, 134)(41, 135)(42, 136)(43, 137)(44, 138)(45, 139)(46, 140)(47, 141)(48, 142)(49, 143)(50, 144)(51, 145)(52, 146)(53, 147)(54, 148)(55, 149)(56, 150)(57, 151)(58, 152)(59, 153)(60, 154)(61, 155)(62, 156)(63, 157)(64, 158)(65, 159)(66, 160)(67, 161)(68, 162)(69, 163)(70, 164)(71, 165)(72, 166)(73, 167)(74, 168)(75, 169)(76, 170)(77, 171)(78, 172)(79, 173)(80, 174)(81, 175)(82, 176)(83, 177)(84, 178)(85, 179)(86, 180)(87, 181)(88, 182)(89, 183)(90, 184)(91, 185)(92, 186)(93, 187)(94, 188) local type(s) :: { ( 94, 94 ), ( 94^94 ) } Outer automorphisms :: reflexible Dual of E23.894 Transitivity :: ET+ Graph:: bipartite v = 48 e = 94 f = 2 degree seq :: [ 2^47, 94 ] E23.894 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 47, 94}) Quotient :: loop Aut^+ = C94 (small group id <94, 2>) Aut = D188 (small group id <188, 3>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^47 ] Map:: R = (1, 95, 3, 97, 7, 101, 11, 105, 15, 109, 19, 113, 23, 117, 27, 121, 31, 125, 38, 132, 34, 128, 37, 131, 41, 135, 43, 137, 45, 139, 47, 141, 49, 143, 51, 145, 61, 155, 57, 151, 54, 148, 56, 150, 60, 154, 63, 157, 65, 159, 67, 161, 69, 163, 71, 165, 73, 167, 75, 169, 77, 171, 80, 174, 83, 177, 85, 179, 87, 181, 89, 183, 91, 185, 93, 187, 94, 188, 32, 126, 28, 122, 24, 118, 20, 114, 16, 110, 12, 106, 8, 102, 4, 98)(2, 96, 5, 99, 9, 103, 13, 107, 17, 111, 21, 115, 25, 119, 29, 123, 40, 134, 36, 130, 33, 127, 35, 129, 39, 133, 42, 136, 44, 138, 46, 140, 48, 142, 50, 144, 52, 146, 59, 153, 55, 149, 58, 152, 62, 156, 64, 158, 66, 160, 68, 162, 70, 164, 72, 166, 82, 176, 79, 173, 76, 170, 78, 172, 81, 175, 84, 178, 86, 180, 88, 182, 90, 184, 92, 186, 74, 168, 53, 147, 30, 124, 26, 120, 22, 116, 18, 112, 14, 108, 10, 104, 6, 100) L = (1, 96)(2, 95)(3, 99)(4, 100)(5, 97)(6, 98)(7, 103)(8, 104)(9, 101)(10, 102)(11, 107)(12, 108)(13, 105)(14, 106)(15, 111)(16, 112)(17, 109)(18, 110)(19, 115)(20, 116)(21, 113)(22, 114)(23, 119)(24, 120)(25, 117)(26, 118)(27, 123)(28, 124)(29, 121)(30, 122)(31, 134)(32, 147)(33, 128)(34, 127)(35, 131)(36, 132)(37, 129)(38, 130)(39, 135)(40, 125)(41, 133)(42, 137)(43, 136)(44, 139)(45, 138)(46, 141)(47, 140)(48, 143)(49, 142)(50, 145)(51, 144)(52, 155)(53, 126)(54, 149)(55, 148)(56, 152)(57, 153)(58, 150)(59, 151)(60, 156)(61, 146)(62, 154)(63, 158)(64, 157)(65, 160)(66, 159)(67, 162)(68, 161)(69, 164)(70, 163)(71, 166)(72, 165)(73, 176)(74, 188)(75, 173)(76, 171)(77, 170)(78, 174)(79, 169)(80, 172)(81, 177)(82, 167)(83, 175)(84, 179)(85, 178)(86, 181)(87, 180)(88, 183)(89, 182)(90, 185)(91, 184)(92, 187)(93, 186)(94, 168) local type(s) :: { ( 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94 ) } Outer automorphisms :: reflexible Dual of E23.893 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 94 f = 48 degree seq :: [ 94^2 ] E23.895 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 47, 94}) Quotient :: loop Aut^+ = C94 (small group id <94, 2>) Aut = D188 (small group id <188, 3>) |r| :: 2 Presentation :: [ F^2, T2^-2 * T1^-2, (F * T2)^2, (F * T1)^2, (T2^-1 * T1^-1)^2, T2^-2 * T1^45, T2^-2 * T1^21 * T2^-24 ] Map:: R = (1, 95, 3, 97, 9, 103, 13, 107, 17, 111, 21, 115, 25, 119, 29, 123, 33, 127, 59, 153, 85, 179, 87, 181, 88, 182, 91, 185, 93, 187, 84, 178, 81, 175, 80, 174, 77, 171, 76, 170, 71, 165, 68, 162, 62, 156, 67, 161, 64, 158, 70, 164, 74, 168, 57, 151, 56, 150, 53, 147, 52, 146, 49, 143, 46, 140, 40, 134, 39, 133, 35, 129, 37, 131, 43, 137, 47, 141, 32, 126, 27, 121, 24, 118, 19, 113, 16, 110, 11, 105, 8, 102, 2, 96, 7, 101, 4, 98, 10, 104, 14, 108, 18, 112, 22, 116, 26, 120, 30, 124, 34, 128, 60, 154, 86, 180, 90, 184, 89, 183, 92, 186, 94, 188, 83, 177, 82, 176, 79, 173, 78, 172, 75, 169, 72, 166, 66, 160, 65, 159, 61, 155, 63, 157, 69, 163, 73, 167, 58, 152, 55, 149, 54, 148, 51, 145, 50, 144, 45, 139, 42, 136, 36, 130, 41, 135, 38, 132, 44, 138, 48, 142, 31, 125, 28, 122, 23, 117, 20, 114, 15, 109, 12, 106, 6, 100, 5, 99) L = (1, 96)(2, 100)(3, 101)(4, 95)(5, 102)(6, 105)(7, 99)(8, 106)(9, 98)(10, 97)(11, 109)(12, 110)(13, 104)(14, 103)(15, 113)(16, 114)(17, 108)(18, 107)(19, 117)(20, 118)(21, 112)(22, 111)(23, 121)(24, 122)(25, 116)(26, 115)(27, 125)(28, 126)(29, 120)(30, 119)(31, 141)(32, 142)(33, 124)(34, 123)(35, 130)(36, 134)(37, 135)(38, 129)(39, 136)(40, 139)(41, 133)(42, 140)(43, 132)(44, 131)(45, 143)(46, 144)(47, 138)(48, 137)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 167)(58, 168)(59, 128)(60, 127)(61, 156)(62, 160)(63, 161)(64, 155)(65, 162)(66, 165)(67, 159)(68, 166)(69, 158)(70, 157)(71, 169)(72, 170)(73, 164)(74, 163)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 187)(84, 188)(85, 154)(86, 153)(87, 180)(88, 184)(89, 181)(90, 179)(91, 183)(92, 182)(93, 186)(94, 185) local type(s) :: { ( 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47, 2, 47 ) } Outer automorphisms :: reflexible Dual of E23.891 Transitivity :: ET+ VT+ AT Graph:: v = 1 e = 94 f = 49 degree seq :: [ 188 ] E23.896 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 47, 94}) Quotient :: loop Aut^+ = C94 (small group id <94, 2>) Aut = D188 (small group id <188, 3>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T2 * T1^-47 ] Map:: non-degenerate R = (1, 95, 3, 97)(2, 96, 6, 100)(4, 98, 7, 101)(5, 99, 10, 104)(8, 102, 11, 105)(9, 103, 14, 108)(12, 106, 15, 109)(13, 107, 18, 112)(16, 110, 19, 113)(17, 111, 22, 116)(20, 114, 23, 117)(21, 115, 26, 120)(24, 118, 27, 121)(25, 119, 30, 124)(28, 122, 31, 125)(29, 123, 38, 132)(32, 126, 51, 145)(33, 127, 35, 129)(34, 128, 37, 131)(36, 130, 40, 134)(39, 133, 42, 136)(41, 135, 44, 138)(43, 137, 46, 140)(45, 139, 48, 142)(47, 141, 50, 144)(49, 143, 57, 151)(52, 146, 54, 148)(53, 147, 56, 150)(55, 149, 59, 153)(58, 152, 61, 155)(60, 154, 63, 157)(62, 156, 65, 159)(64, 158, 67, 161)(66, 160, 69, 163)(68, 162, 77, 171)(70, 164, 89, 183)(71, 165, 80, 174)(72, 166, 74, 168)(73, 167, 76, 170)(75, 169, 78, 172)(79, 173, 82, 176)(81, 175, 84, 178)(83, 177, 86, 180)(85, 179, 88, 182)(87, 181, 94, 188)(90, 184, 93, 187)(91, 185, 92, 186) L = (1, 96)(2, 99)(3, 100)(4, 95)(5, 103)(6, 104)(7, 97)(8, 98)(9, 107)(10, 108)(11, 101)(12, 102)(13, 111)(14, 112)(15, 105)(16, 106)(17, 115)(18, 116)(19, 109)(20, 110)(21, 119)(22, 120)(23, 113)(24, 114)(25, 123)(26, 124)(27, 117)(28, 118)(29, 127)(30, 132)(31, 121)(32, 122)(33, 128)(34, 130)(35, 131)(36, 133)(37, 134)(38, 129)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 146)(50, 151)(51, 125)(52, 147)(53, 149)(54, 150)(55, 152)(56, 153)(57, 148)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 166)(69, 171)(70, 145)(71, 173)(72, 167)(73, 169)(74, 170)(75, 165)(76, 172)(77, 168)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 185)(88, 188)(89, 126)(90, 164)(91, 184)(92, 187)(93, 183)(94, 186) local type(s) :: { ( 47, 94, 47, 94 ) } Outer automorphisms :: reflexible Dual of E23.892 Transitivity :: ET+ VT+ AT Graph:: v = 47 e = 94 f = 3 degree seq :: [ 4^47 ] E23.897 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 47, 94}) Quotient :: dipole Aut^+ = C94 (small group id <94, 2>) Aut = D188 (small group id <188, 3>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y1 * Y2 * Y1, (R * Y2 * Y3^-1)^2, Y2^47, (Y3 * Y2^-1)^94 ] Map:: R = (1, 95, 2, 96)(3, 97, 5, 99)(4, 98, 6, 100)(7, 101, 9, 103)(8, 102, 10, 104)(11, 105, 13, 107)(12, 106, 14, 108)(15, 109, 17, 111)(16, 110, 18, 112)(19, 113, 21, 115)(20, 114, 22, 116)(23, 117, 25, 119)(24, 118, 26, 120)(27, 121, 29, 123)(28, 122, 30, 124)(31, 125, 44, 138)(32, 126, 55, 149)(33, 127, 34, 128)(35, 129, 37, 131)(36, 130, 38, 132)(39, 133, 41, 135)(40, 134, 42, 136)(43, 137, 45, 139)(46, 140, 47, 141)(48, 142, 49, 143)(50, 144, 51, 145)(52, 146, 53, 147)(54, 148, 67, 161)(56, 150, 57, 151)(58, 152, 60, 154)(59, 153, 61, 155)(62, 156, 64, 158)(63, 157, 65, 159)(66, 160, 68, 162)(69, 163, 70, 164)(71, 165, 72, 166)(73, 167, 74, 168)(75, 169, 76, 170)(77, 171, 90, 184)(78, 172, 94, 188)(79, 173, 80, 174)(81, 175, 83, 177)(82, 176, 84, 178)(85, 179, 87, 181)(86, 180, 88, 182)(89, 183, 91, 185)(92, 186, 93, 187)(189, 283, 191, 285, 195, 289, 199, 293, 203, 297, 207, 301, 211, 305, 215, 309, 219, 313, 230, 324, 226, 320, 222, 316, 225, 319, 229, 323, 233, 327, 235, 329, 237, 331, 239, 333, 241, 335, 255, 349, 251, 345, 247, 341, 244, 338, 246, 340, 250, 344, 254, 348, 257, 351, 259, 353, 261, 355, 263, 357, 265, 359, 276, 370, 272, 366, 268, 362, 271, 365, 275, 369, 279, 373, 281, 375, 282, 376, 220, 314, 216, 310, 212, 306, 208, 302, 204, 298, 200, 294, 196, 290, 192, 286)(190, 284, 193, 287, 197, 291, 201, 295, 205, 299, 209, 303, 213, 307, 217, 311, 232, 326, 228, 322, 224, 318, 221, 315, 223, 317, 227, 321, 231, 325, 234, 328, 236, 330, 238, 332, 240, 334, 242, 336, 253, 347, 249, 343, 245, 339, 248, 342, 252, 346, 256, 350, 258, 352, 260, 354, 262, 356, 264, 358, 278, 372, 274, 368, 270, 364, 267, 361, 269, 363, 273, 367, 277, 371, 280, 374, 266, 360, 243, 337, 218, 312, 214, 308, 210, 304, 206, 300, 202, 296, 198, 292, 194, 288) L = (1, 190)(2, 189)(3, 193)(4, 194)(5, 191)(6, 192)(7, 197)(8, 198)(9, 195)(10, 196)(11, 201)(12, 202)(13, 199)(14, 200)(15, 205)(16, 206)(17, 203)(18, 204)(19, 209)(20, 210)(21, 207)(22, 208)(23, 213)(24, 214)(25, 211)(26, 212)(27, 217)(28, 218)(29, 215)(30, 216)(31, 232)(32, 243)(33, 222)(34, 221)(35, 225)(36, 226)(37, 223)(38, 224)(39, 229)(40, 230)(41, 227)(42, 228)(43, 233)(44, 219)(45, 231)(46, 235)(47, 234)(48, 237)(49, 236)(50, 239)(51, 238)(52, 241)(53, 240)(54, 255)(55, 220)(56, 245)(57, 244)(58, 248)(59, 249)(60, 246)(61, 247)(62, 252)(63, 253)(64, 250)(65, 251)(66, 256)(67, 242)(68, 254)(69, 258)(70, 257)(71, 260)(72, 259)(73, 262)(74, 261)(75, 264)(76, 263)(77, 278)(78, 282)(79, 268)(80, 267)(81, 271)(82, 272)(83, 269)(84, 270)(85, 275)(86, 276)(87, 273)(88, 274)(89, 279)(90, 265)(91, 277)(92, 281)(93, 280)(94, 266)(95, 283)(96, 284)(97, 285)(98, 286)(99, 287)(100, 288)(101, 289)(102, 290)(103, 291)(104, 292)(105, 293)(106, 294)(107, 295)(108, 296)(109, 297)(110, 298)(111, 299)(112, 300)(113, 301)(114, 302)(115, 303)(116, 304)(117, 305)(118, 306)(119, 307)(120, 308)(121, 309)(122, 310)(123, 311)(124, 312)(125, 313)(126, 314)(127, 315)(128, 316)(129, 317)(130, 318)(131, 319)(132, 320)(133, 321)(134, 322)(135, 323)(136, 324)(137, 325)(138, 326)(139, 327)(140, 328)(141, 329)(142, 330)(143, 331)(144, 332)(145, 333)(146, 334)(147, 335)(148, 336)(149, 337)(150, 338)(151, 339)(152, 340)(153, 341)(154, 342)(155, 343)(156, 344)(157, 345)(158, 346)(159, 347)(160, 348)(161, 349)(162, 350)(163, 351)(164, 352)(165, 353)(166, 354)(167, 355)(168, 356)(169, 357)(170, 358)(171, 359)(172, 360)(173, 361)(174, 362)(175, 363)(176, 364)(177, 365)(178, 366)(179, 367)(180, 368)(181, 369)(182, 370)(183, 371)(184, 372)(185, 373)(186, 374)(187, 375)(188, 376) local type(s) :: { ( 2, 188, 2, 188 ), ( 2, 188, 2, 188, 2, 188, 2, 188, 2, 188, 2, 188, 2, 188, 2, 188, 2, 188, 2, 188, 2, 188, 2, 188, 2, 188, 2, 188, 2, 188, 2, 188, 2, 188, 2, 188, 2, 188, 2, 188, 2, 188, 2, 188, 2, 188, 2, 188, 2, 188, 2, 188, 2, 188, 2, 188, 2, 188, 2, 188, 2, 188, 2, 188, 2, 188, 2, 188, 2, 188, 2, 188, 2, 188, 2, 188, 2, 188, 2, 188, 2, 188, 2, 188, 2, 188, 2, 188, 2, 188, 2, 188, 2, 188 ) } Outer automorphisms :: reflexible Dual of E23.900 Graph:: bipartite v = 49 e = 188 f = 95 degree seq :: [ 4^47, 94^2 ] E23.898 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 47, 94}) Quotient :: dipole Aut^+ = C94 (small group id <94, 2>) Aut = D188 (small group id <188, 3>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y3)^2, (R * Y1)^2, (Y1, Y2^-1), (Y3^-1 * Y1^-1)^2, Y1^22 * Y2^22, Y1^21 * Y2^-1 * Y1 * Y2^-23 * Y1, Y1^47, Y2^308 * Y1^-21 ] Map:: R = (1, 95, 2, 96, 6, 100, 11, 105, 15, 109, 19, 113, 23, 117, 27, 121, 31, 125, 39, 133, 37, 131, 40, 134, 42, 136, 44, 138, 46, 140, 48, 142, 50, 144, 52, 146, 55, 149, 56, 150, 58, 152, 61, 155, 63, 157, 65, 159, 67, 161, 69, 163, 71, 165, 80, 174, 79, 173, 75, 169, 82, 176, 84, 178, 86, 180, 88, 182, 90, 184, 92, 186, 94, 188, 73, 167, 54, 148, 33, 127, 30, 124, 25, 119, 22, 116, 17, 111, 14, 108, 9, 103, 4, 98)(3, 97, 7, 101, 5, 99, 8, 102, 12, 106, 16, 110, 20, 114, 24, 118, 28, 122, 32, 126, 35, 129, 36, 130, 38, 132, 41, 135, 43, 137, 45, 139, 47, 141, 49, 143, 51, 145, 59, 153, 57, 151, 60, 154, 62, 156, 64, 158, 66, 160, 68, 162, 70, 164, 72, 166, 77, 171, 78, 172, 76, 170, 81, 175, 83, 177, 85, 179, 87, 181, 89, 183, 91, 185, 93, 187, 74, 168, 53, 147, 34, 128, 29, 123, 26, 120, 21, 115, 18, 112, 13, 107, 10, 104)(189, 283, 191, 285, 197, 291, 201, 295, 205, 299, 209, 303, 213, 307, 217, 311, 221, 315, 241, 335, 261, 355, 281, 375, 280, 374, 277, 371, 276, 370, 273, 367, 272, 366, 269, 363, 263, 357, 266, 360, 268, 362, 260, 354, 257, 351, 256, 350, 253, 347, 252, 346, 249, 343, 248, 342, 244, 338, 247, 341, 240, 334, 237, 331, 236, 330, 233, 327, 232, 326, 229, 323, 228, 322, 224, 318, 227, 321, 220, 314, 215, 309, 212, 306, 207, 301, 204, 298, 199, 293, 196, 290, 190, 284, 195, 289, 192, 286, 198, 292, 202, 296, 206, 300, 210, 304, 214, 308, 218, 312, 222, 316, 242, 336, 262, 356, 282, 376, 279, 373, 278, 372, 275, 369, 274, 368, 271, 365, 270, 364, 264, 358, 267, 361, 265, 359, 259, 353, 258, 352, 255, 349, 254, 348, 251, 345, 250, 344, 246, 340, 245, 339, 243, 337, 239, 333, 238, 332, 235, 329, 234, 328, 231, 325, 230, 324, 226, 320, 225, 319, 223, 317, 219, 313, 216, 310, 211, 305, 208, 302, 203, 297, 200, 294, 194, 288, 193, 287) L = (1, 191)(2, 195)(3, 197)(4, 198)(5, 189)(6, 193)(7, 192)(8, 190)(9, 201)(10, 202)(11, 196)(12, 194)(13, 205)(14, 206)(15, 200)(16, 199)(17, 209)(18, 210)(19, 204)(20, 203)(21, 213)(22, 214)(23, 208)(24, 207)(25, 217)(26, 218)(27, 212)(28, 211)(29, 221)(30, 222)(31, 216)(32, 215)(33, 241)(34, 242)(35, 219)(36, 227)(37, 223)(38, 225)(39, 220)(40, 224)(41, 228)(42, 226)(43, 230)(44, 229)(45, 232)(46, 231)(47, 234)(48, 233)(49, 236)(50, 235)(51, 238)(52, 237)(53, 261)(54, 262)(55, 239)(56, 247)(57, 243)(58, 245)(59, 240)(60, 244)(61, 248)(62, 246)(63, 250)(64, 249)(65, 252)(66, 251)(67, 254)(68, 253)(69, 256)(70, 255)(71, 258)(72, 257)(73, 281)(74, 282)(75, 266)(76, 267)(77, 259)(78, 268)(79, 265)(80, 260)(81, 263)(82, 264)(83, 270)(84, 269)(85, 272)(86, 271)(87, 274)(88, 273)(89, 276)(90, 275)(91, 278)(92, 277)(93, 280)(94, 279)(95, 283)(96, 284)(97, 285)(98, 286)(99, 287)(100, 288)(101, 289)(102, 290)(103, 291)(104, 292)(105, 293)(106, 294)(107, 295)(108, 296)(109, 297)(110, 298)(111, 299)(112, 300)(113, 301)(114, 302)(115, 303)(116, 304)(117, 305)(118, 306)(119, 307)(120, 308)(121, 309)(122, 310)(123, 311)(124, 312)(125, 313)(126, 314)(127, 315)(128, 316)(129, 317)(130, 318)(131, 319)(132, 320)(133, 321)(134, 322)(135, 323)(136, 324)(137, 325)(138, 326)(139, 327)(140, 328)(141, 329)(142, 330)(143, 331)(144, 332)(145, 333)(146, 334)(147, 335)(148, 336)(149, 337)(150, 338)(151, 339)(152, 340)(153, 341)(154, 342)(155, 343)(156, 344)(157, 345)(158, 346)(159, 347)(160, 348)(161, 349)(162, 350)(163, 351)(164, 352)(165, 353)(166, 354)(167, 355)(168, 356)(169, 357)(170, 358)(171, 359)(172, 360)(173, 361)(174, 362)(175, 363)(176, 364)(177, 365)(178, 366)(179, 367)(180, 368)(181, 369)(182, 370)(183, 371)(184, 372)(185, 373)(186, 374)(187, 375)(188, 376) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) } Outer automorphisms :: reflexible Dual of E23.899 Graph:: bipartite v = 3 e = 188 f = 141 degree seq :: [ 94^2, 188 ] E23.899 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 47, 94}) Quotient :: dipole Aut^+ = C94 (small group id <94, 2>) Aut = D188 (small group id <188, 3>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, Y3 * Y2 * Y3^-1 * Y2, Y3^47 * Y2, (Y3^-1 * Y1^-1)^94 ] Map:: R = (1, 95)(2, 96)(3, 97)(4, 98)(5, 99)(6, 100)(7, 101)(8, 102)(9, 103)(10, 104)(11, 105)(12, 106)(13, 107)(14, 108)(15, 109)(16, 110)(17, 111)(18, 112)(19, 113)(20, 114)(21, 115)(22, 116)(23, 117)(24, 118)(25, 119)(26, 120)(27, 121)(28, 122)(29, 123)(30, 124)(31, 125)(32, 126)(33, 127)(34, 128)(35, 129)(36, 130)(37, 131)(38, 132)(39, 133)(40, 134)(41, 135)(42, 136)(43, 137)(44, 138)(45, 139)(46, 140)(47, 141)(48, 142)(49, 143)(50, 144)(51, 145)(52, 146)(53, 147)(54, 148)(55, 149)(56, 150)(57, 151)(58, 152)(59, 153)(60, 154)(61, 155)(62, 156)(63, 157)(64, 158)(65, 159)(66, 160)(67, 161)(68, 162)(69, 163)(70, 164)(71, 165)(72, 166)(73, 167)(74, 168)(75, 169)(76, 170)(77, 171)(78, 172)(79, 173)(80, 174)(81, 175)(82, 176)(83, 177)(84, 178)(85, 179)(86, 180)(87, 181)(88, 182)(89, 183)(90, 184)(91, 185)(92, 186)(93, 187)(94, 188)(189, 283, 190, 284)(191, 285, 193, 287)(192, 286, 194, 288)(195, 289, 197, 291)(196, 290, 198, 292)(199, 293, 201, 295)(200, 294, 202, 296)(203, 297, 205, 299)(204, 298, 206, 300)(207, 301, 209, 303)(208, 302, 210, 304)(211, 305, 213, 307)(212, 306, 214, 308)(215, 309, 217, 311)(216, 310, 218, 312)(219, 313, 224, 318)(220, 314, 239, 333)(221, 315, 222, 316)(223, 317, 225, 319)(226, 320, 227, 321)(228, 322, 229, 323)(230, 324, 231, 325)(232, 326, 233, 327)(234, 328, 235, 329)(236, 330, 237, 331)(238, 332, 243, 337)(240, 334, 241, 335)(242, 336, 244, 338)(245, 339, 246, 340)(247, 341, 248, 342)(249, 343, 250, 344)(251, 345, 252, 346)(253, 347, 254, 348)(255, 349, 256, 350)(257, 351, 263, 357)(258, 352, 277, 371)(259, 353, 267, 361)(260, 354, 261, 355)(262, 356, 264, 358)(265, 359, 266, 360)(268, 362, 269, 363)(270, 364, 271, 365)(272, 366, 273, 367)(274, 368, 275, 369)(276, 370, 281, 375)(278, 372, 282, 376)(279, 373, 280, 374) L = (1, 191)(2, 193)(3, 195)(4, 189)(5, 197)(6, 190)(7, 199)(8, 192)(9, 201)(10, 194)(11, 203)(12, 196)(13, 205)(14, 198)(15, 207)(16, 200)(17, 209)(18, 202)(19, 211)(20, 204)(21, 213)(22, 206)(23, 215)(24, 208)(25, 217)(26, 210)(27, 219)(28, 212)(29, 224)(30, 214)(31, 222)(32, 216)(33, 223)(34, 225)(35, 226)(36, 221)(37, 227)(38, 228)(39, 229)(40, 230)(41, 231)(42, 232)(43, 233)(44, 234)(45, 235)(46, 236)(47, 237)(48, 238)(49, 243)(50, 241)(51, 218)(52, 242)(53, 244)(54, 245)(55, 240)(56, 246)(57, 247)(58, 248)(59, 249)(60, 250)(61, 251)(62, 252)(63, 253)(64, 254)(65, 255)(66, 256)(67, 257)(68, 263)(69, 261)(70, 239)(71, 268)(72, 262)(73, 264)(74, 265)(75, 260)(76, 266)(77, 259)(78, 267)(79, 269)(80, 270)(81, 271)(82, 272)(83, 273)(84, 274)(85, 275)(86, 276)(87, 281)(88, 280)(89, 220)(90, 258)(91, 278)(92, 282)(93, 279)(94, 277)(95, 283)(96, 284)(97, 285)(98, 286)(99, 287)(100, 288)(101, 289)(102, 290)(103, 291)(104, 292)(105, 293)(106, 294)(107, 295)(108, 296)(109, 297)(110, 298)(111, 299)(112, 300)(113, 301)(114, 302)(115, 303)(116, 304)(117, 305)(118, 306)(119, 307)(120, 308)(121, 309)(122, 310)(123, 311)(124, 312)(125, 313)(126, 314)(127, 315)(128, 316)(129, 317)(130, 318)(131, 319)(132, 320)(133, 321)(134, 322)(135, 323)(136, 324)(137, 325)(138, 326)(139, 327)(140, 328)(141, 329)(142, 330)(143, 331)(144, 332)(145, 333)(146, 334)(147, 335)(148, 336)(149, 337)(150, 338)(151, 339)(152, 340)(153, 341)(154, 342)(155, 343)(156, 344)(157, 345)(158, 346)(159, 347)(160, 348)(161, 349)(162, 350)(163, 351)(164, 352)(165, 353)(166, 354)(167, 355)(168, 356)(169, 357)(170, 358)(171, 359)(172, 360)(173, 361)(174, 362)(175, 363)(176, 364)(177, 365)(178, 366)(179, 367)(180, 368)(181, 369)(182, 370)(183, 371)(184, 372)(185, 373)(186, 374)(187, 375)(188, 376) local type(s) :: { ( 94, 188 ), ( 94, 188, 94, 188 ) } Outer automorphisms :: reflexible Dual of E23.898 Graph:: simple bipartite v = 141 e = 188 f = 3 degree seq :: [ 2^94, 4^47 ] E23.900 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 47, 94}) Quotient :: dipole Aut^+ = C94 (small group id <94, 2>) Aut = D188 (small group id <188, 3>) |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^-47 ] Map:: R = (1, 95, 2, 96, 5, 99, 9, 103, 13, 107, 17, 111, 21, 115, 25, 119, 29, 123, 35, 129, 38, 132, 40, 134, 42, 136, 44, 138, 46, 140, 48, 142, 50, 144, 55, 149, 52, 146, 53, 147, 56, 150, 58, 152, 60, 154, 62, 156, 64, 158, 66, 160, 68, 162, 74, 168, 77, 171, 78, 172, 80, 174, 82, 176, 84, 178, 86, 180, 88, 182, 93, 187, 91, 185, 90, 184, 70, 164, 51, 145, 31, 125, 27, 121, 23, 117, 19, 113, 15, 109, 11, 105, 7, 101, 3, 97, 6, 100, 10, 104, 14, 108, 18, 112, 22, 116, 26, 120, 30, 124, 36, 130, 33, 127, 34, 128, 37, 131, 39, 133, 41, 135, 43, 137, 45, 139, 47, 141, 49, 143, 54, 148, 57, 151, 59, 153, 61, 155, 63, 157, 65, 159, 67, 161, 69, 163, 75, 169, 72, 166, 73, 167, 76, 170, 71, 165, 79, 173, 81, 175, 83, 177, 85, 179, 87, 181, 92, 186, 94, 188, 89, 183, 32, 126, 28, 122, 24, 118, 20, 114, 16, 110, 12, 106, 8, 102, 4, 98)(189, 283)(190, 284)(191, 285)(192, 286)(193, 287)(194, 288)(195, 289)(196, 290)(197, 291)(198, 292)(199, 293)(200, 294)(201, 295)(202, 296)(203, 297)(204, 298)(205, 299)(206, 300)(207, 301)(208, 302)(209, 303)(210, 304)(211, 305)(212, 306)(213, 307)(214, 308)(215, 309)(216, 310)(217, 311)(218, 312)(219, 313)(220, 314)(221, 315)(222, 316)(223, 317)(224, 318)(225, 319)(226, 320)(227, 321)(228, 322)(229, 323)(230, 324)(231, 325)(232, 326)(233, 327)(234, 328)(235, 329)(236, 330)(237, 331)(238, 332)(239, 333)(240, 334)(241, 335)(242, 336)(243, 337)(244, 338)(245, 339)(246, 340)(247, 341)(248, 342)(249, 343)(250, 344)(251, 345)(252, 346)(253, 347)(254, 348)(255, 349)(256, 350)(257, 351)(258, 352)(259, 353)(260, 354)(261, 355)(262, 356)(263, 357)(264, 358)(265, 359)(266, 360)(267, 361)(268, 362)(269, 363)(270, 364)(271, 365)(272, 366)(273, 367)(274, 368)(275, 369)(276, 370)(277, 371)(278, 372)(279, 373)(280, 374)(281, 375)(282, 376) L = (1, 191)(2, 194)(3, 189)(4, 195)(5, 198)(6, 190)(7, 192)(8, 199)(9, 202)(10, 193)(11, 196)(12, 203)(13, 206)(14, 197)(15, 200)(16, 207)(17, 210)(18, 201)(19, 204)(20, 211)(21, 214)(22, 205)(23, 208)(24, 215)(25, 218)(26, 209)(27, 212)(28, 219)(29, 224)(30, 213)(31, 216)(32, 239)(33, 223)(34, 226)(35, 221)(36, 217)(37, 228)(38, 222)(39, 230)(40, 225)(41, 232)(42, 227)(43, 234)(44, 229)(45, 236)(46, 231)(47, 238)(48, 233)(49, 243)(50, 235)(51, 220)(52, 242)(53, 245)(54, 240)(55, 237)(56, 247)(57, 241)(58, 249)(59, 244)(60, 251)(61, 246)(62, 253)(63, 248)(64, 255)(65, 250)(66, 257)(67, 252)(68, 263)(69, 254)(70, 277)(71, 268)(72, 262)(73, 265)(74, 260)(75, 256)(76, 266)(77, 261)(78, 264)(79, 270)(80, 259)(81, 272)(82, 267)(83, 274)(84, 269)(85, 276)(86, 271)(87, 281)(88, 273)(89, 258)(90, 282)(91, 280)(92, 279)(93, 275)(94, 278)(95, 283)(96, 284)(97, 285)(98, 286)(99, 287)(100, 288)(101, 289)(102, 290)(103, 291)(104, 292)(105, 293)(106, 294)(107, 295)(108, 296)(109, 297)(110, 298)(111, 299)(112, 300)(113, 301)(114, 302)(115, 303)(116, 304)(117, 305)(118, 306)(119, 307)(120, 308)(121, 309)(122, 310)(123, 311)(124, 312)(125, 313)(126, 314)(127, 315)(128, 316)(129, 317)(130, 318)(131, 319)(132, 320)(133, 321)(134, 322)(135, 323)(136, 324)(137, 325)(138, 326)(139, 327)(140, 328)(141, 329)(142, 330)(143, 331)(144, 332)(145, 333)(146, 334)(147, 335)(148, 336)(149, 337)(150, 338)(151, 339)(152, 340)(153, 341)(154, 342)(155, 343)(156, 344)(157, 345)(158, 346)(159, 347)(160, 348)(161, 349)(162, 350)(163, 351)(164, 352)(165, 353)(166, 354)(167, 355)(168, 356)(169, 357)(170, 358)(171, 359)(172, 360)(173, 361)(174, 362)(175, 363)(176, 364)(177, 365)(178, 366)(179, 367)(180, 368)(181, 369)(182, 370)(183, 371)(184, 372)(185, 373)(186, 374)(187, 375)(188, 376) local type(s) :: { ( 4, 94 ), ( 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94, 4, 94 ) } Outer automorphisms :: reflexible Dual of E23.897 Graph:: bipartite v = 95 e = 188 f = 49 degree seq :: [ 2^94, 188 ] E23.901 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 47, 94}) Quotient :: dipole Aut^+ = C94 (small group id <94, 2>) Aut = D188 (small group id <188, 3>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y1 * Y2 * Y1, (R * Y2 * Y3^-1)^2, Y2^47 * Y1, (Y3 * Y2^-1)^47 ] Map:: R = (1, 95, 2, 96)(3, 97, 5, 99)(4, 98, 6, 100)(7, 101, 9, 103)(8, 102, 10, 104)(11, 105, 13, 107)(12, 106, 14, 108)(15, 109, 17, 111)(16, 110, 18, 112)(19, 113, 21, 115)(20, 114, 22, 116)(23, 117, 25, 119)(24, 118, 26, 120)(27, 121, 29, 123)(28, 122, 30, 124)(31, 125, 33, 127)(32, 126, 49, 143)(34, 128, 35, 129)(36, 130, 37, 131)(38, 132, 39, 133)(40, 134, 41, 135)(42, 136, 43, 137)(44, 138, 45, 139)(46, 140, 47, 141)(48, 142, 50, 144)(51, 145, 52, 146)(53, 147, 54, 148)(55, 149, 56, 150)(57, 151, 58, 152)(59, 153, 60, 154)(61, 155, 62, 156)(63, 157, 64, 158)(65, 159, 68, 162)(66, 160, 83, 177)(67, 161, 81, 175)(69, 163, 70, 164)(71, 165, 72, 166)(73, 167, 74, 168)(75, 169, 76, 170)(77, 171, 78, 172)(79, 173, 80, 174)(82, 176, 85, 179)(84, 178, 94, 188)(86, 180, 87, 181)(88, 182, 89, 183)(90, 184, 91, 185)(92, 186, 93, 187)(189, 283, 191, 285, 195, 289, 199, 293, 203, 297, 207, 301, 211, 305, 215, 309, 219, 313, 223, 317, 225, 319, 227, 321, 229, 323, 231, 325, 233, 327, 235, 329, 238, 332, 239, 333, 241, 335, 243, 337, 245, 339, 247, 341, 249, 343, 251, 345, 253, 347, 258, 352, 260, 354, 262, 356, 264, 358, 266, 360, 268, 362, 269, 363, 273, 367, 274, 368, 276, 370, 278, 372, 280, 374, 272, 366, 254, 348, 237, 331, 218, 312, 214, 308, 210, 304, 206, 300, 202, 296, 198, 292, 194, 288, 190, 284, 193, 287, 197, 291, 201, 295, 205, 299, 209, 303, 213, 307, 217, 311, 221, 315, 222, 316, 224, 318, 226, 320, 228, 322, 230, 324, 232, 326, 234, 328, 236, 330, 240, 334, 242, 336, 244, 338, 246, 340, 248, 342, 250, 344, 252, 346, 256, 350, 257, 351, 259, 353, 261, 355, 263, 357, 265, 359, 267, 361, 255, 349, 270, 364, 275, 369, 277, 371, 279, 373, 281, 375, 282, 376, 271, 365, 220, 314, 216, 310, 212, 306, 208, 302, 204, 298, 200, 294, 196, 290, 192, 286) L = (1, 190)(2, 189)(3, 193)(4, 194)(5, 191)(6, 192)(7, 197)(8, 198)(9, 195)(10, 196)(11, 201)(12, 202)(13, 199)(14, 200)(15, 205)(16, 206)(17, 203)(18, 204)(19, 209)(20, 210)(21, 207)(22, 208)(23, 213)(24, 214)(25, 211)(26, 212)(27, 217)(28, 218)(29, 215)(30, 216)(31, 221)(32, 237)(33, 219)(34, 223)(35, 222)(36, 225)(37, 224)(38, 227)(39, 226)(40, 229)(41, 228)(42, 231)(43, 230)(44, 233)(45, 232)(46, 235)(47, 234)(48, 238)(49, 220)(50, 236)(51, 240)(52, 239)(53, 242)(54, 241)(55, 244)(56, 243)(57, 246)(58, 245)(59, 248)(60, 247)(61, 250)(62, 249)(63, 252)(64, 251)(65, 256)(66, 271)(67, 269)(68, 253)(69, 258)(70, 257)(71, 260)(72, 259)(73, 262)(74, 261)(75, 264)(76, 263)(77, 266)(78, 265)(79, 268)(80, 267)(81, 255)(82, 273)(83, 254)(84, 282)(85, 270)(86, 275)(87, 274)(88, 277)(89, 276)(90, 279)(91, 278)(92, 281)(93, 280)(94, 272)(95, 283)(96, 284)(97, 285)(98, 286)(99, 287)(100, 288)(101, 289)(102, 290)(103, 291)(104, 292)(105, 293)(106, 294)(107, 295)(108, 296)(109, 297)(110, 298)(111, 299)(112, 300)(113, 301)(114, 302)(115, 303)(116, 304)(117, 305)(118, 306)(119, 307)(120, 308)(121, 309)(122, 310)(123, 311)(124, 312)(125, 313)(126, 314)(127, 315)(128, 316)(129, 317)(130, 318)(131, 319)(132, 320)(133, 321)(134, 322)(135, 323)(136, 324)(137, 325)(138, 326)(139, 327)(140, 328)(141, 329)(142, 330)(143, 331)(144, 332)(145, 333)(146, 334)(147, 335)(148, 336)(149, 337)(150, 338)(151, 339)(152, 340)(153, 341)(154, 342)(155, 343)(156, 344)(157, 345)(158, 346)(159, 347)(160, 348)(161, 349)(162, 350)(163, 351)(164, 352)(165, 353)(166, 354)(167, 355)(168, 356)(169, 357)(170, 358)(171, 359)(172, 360)(173, 361)(174, 362)(175, 363)(176, 364)(177, 365)(178, 366)(179, 367)(180, 368)(181, 369)(182, 370)(183, 371)(184, 372)(185, 373)(186, 374)(187, 375)(188, 376) local type(s) :: { ( 2, 94, 2, 94 ), ( 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94, 2, 94 ) } Outer automorphisms :: reflexible Dual of E23.902 Graph:: bipartite v = 48 e = 188 f = 96 degree seq :: [ 4^47, 188 ] E23.902 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 47, 94}) Quotient :: dipole Aut^+ = C94 (small group id <94, 2>) Aut = D188 (small group id <188, 3>) |r| :: 2 Presentation :: [ Y2, R^2, Y1^-1 * Y3^-2 * Y1^-1, (R * Y3)^2, (R * Y1)^2, (Y3, Y1^-1), (R * Y2 * Y3^-1)^2, Y3^-2 * Y1^21 * Y3^-24, Y3^-2 * Y1^45, (Y3 * Y2^-1)^94 ] Map:: R = (1, 95, 2, 96, 6, 100, 11, 105, 15, 109, 19, 113, 23, 117, 27, 121, 31, 125, 38, 132, 35, 129, 36, 130, 40, 134, 43, 137, 45, 139, 47, 141, 49, 143, 51, 145, 53, 147, 60, 154, 57, 151, 58, 152, 62, 156, 65, 159, 67, 161, 69, 163, 71, 165, 73, 167, 75, 169, 82, 176, 79, 173, 80, 174, 84, 178, 87, 181, 89, 183, 91, 185, 93, 187, 77, 171, 56, 150, 33, 127, 30, 124, 25, 119, 22, 116, 17, 111, 14, 108, 9, 103, 4, 98)(3, 97, 7, 101, 5, 99, 8, 102, 12, 106, 16, 110, 20, 114, 24, 118, 28, 122, 32, 126, 37, 131, 41, 135, 39, 133, 42, 136, 44, 138, 46, 140, 48, 142, 50, 144, 52, 146, 54, 148, 59, 153, 63, 157, 61, 155, 64, 158, 66, 160, 68, 162, 70, 164, 72, 166, 74, 168, 76, 170, 81, 175, 85, 179, 83, 177, 86, 180, 88, 182, 90, 184, 92, 186, 94, 188, 78, 172, 55, 149, 34, 128, 29, 123, 26, 120, 21, 115, 18, 112, 13, 107, 10, 104)(189, 283)(190, 284)(191, 285)(192, 286)(193, 287)(194, 288)(195, 289)(196, 290)(197, 291)(198, 292)(199, 293)(200, 294)(201, 295)(202, 296)(203, 297)(204, 298)(205, 299)(206, 300)(207, 301)(208, 302)(209, 303)(210, 304)(211, 305)(212, 306)(213, 307)(214, 308)(215, 309)(216, 310)(217, 311)(218, 312)(219, 313)(220, 314)(221, 315)(222, 316)(223, 317)(224, 318)(225, 319)(226, 320)(227, 321)(228, 322)(229, 323)(230, 324)(231, 325)(232, 326)(233, 327)(234, 328)(235, 329)(236, 330)(237, 331)(238, 332)(239, 333)(240, 334)(241, 335)(242, 336)(243, 337)(244, 338)(245, 339)(246, 340)(247, 341)(248, 342)(249, 343)(250, 344)(251, 345)(252, 346)(253, 347)(254, 348)(255, 349)(256, 350)(257, 351)(258, 352)(259, 353)(260, 354)(261, 355)(262, 356)(263, 357)(264, 358)(265, 359)(266, 360)(267, 361)(268, 362)(269, 363)(270, 364)(271, 365)(272, 366)(273, 367)(274, 368)(275, 369)(276, 370)(277, 371)(278, 372)(279, 373)(280, 374)(281, 375)(282, 376) L = (1, 191)(2, 195)(3, 197)(4, 198)(5, 189)(6, 193)(7, 192)(8, 190)(9, 201)(10, 202)(11, 196)(12, 194)(13, 205)(14, 206)(15, 200)(16, 199)(17, 209)(18, 210)(19, 204)(20, 203)(21, 213)(22, 214)(23, 208)(24, 207)(25, 217)(26, 218)(27, 212)(28, 211)(29, 221)(30, 222)(31, 216)(32, 215)(33, 243)(34, 244)(35, 225)(36, 229)(37, 219)(38, 220)(39, 223)(40, 227)(41, 226)(42, 224)(43, 230)(44, 228)(45, 232)(46, 231)(47, 234)(48, 233)(49, 236)(50, 235)(51, 238)(52, 237)(53, 240)(54, 239)(55, 265)(56, 266)(57, 247)(58, 251)(59, 241)(60, 242)(61, 245)(62, 249)(63, 248)(64, 246)(65, 252)(66, 250)(67, 254)(68, 253)(69, 256)(70, 255)(71, 258)(72, 257)(73, 260)(74, 259)(75, 262)(76, 261)(77, 282)(78, 281)(79, 269)(80, 273)(81, 263)(82, 264)(83, 267)(84, 271)(85, 270)(86, 268)(87, 274)(88, 272)(89, 276)(90, 275)(91, 278)(92, 277)(93, 280)(94, 279)(95, 283)(96, 284)(97, 285)(98, 286)(99, 287)(100, 288)(101, 289)(102, 290)(103, 291)(104, 292)(105, 293)(106, 294)(107, 295)(108, 296)(109, 297)(110, 298)(111, 299)(112, 300)(113, 301)(114, 302)(115, 303)(116, 304)(117, 305)(118, 306)(119, 307)(120, 308)(121, 309)(122, 310)(123, 311)(124, 312)(125, 313)(126, 314)(127, 315)(128, 316)(129, 317)(130, 318)(131, 319)(132, 320)(133, 321)(134, 322)(135, 323)(136, 324)(137, 325)(138, 326)(139, 327)(140, 328)(141, 329)(142, 330)(143, 331)(144, 332)(145, 333)(146, 334)(147, 335)(148, 336)(149, 337)(150, 338)(151, 339)(152, 340)(153, 341)(154, 342)(155, 343)(156, 344)(157, 345)(158, 346)(159, 347)(160, 348)(161, 349)(162, 350)(163, 351)(164, 352)(165, 353)(166, 354)(167, 355)(168, 356)(169, 357)(170, 358)(171, 359)(172, 360)(173, 361)(174, 362)(175, 363)(176, 364)(177, 365)(178, 366)(179, 367)(180, 368)(181, 369)(182, 370)(183, 371)(184, 372)(185, 373)(186, 374)(187, 375)(188, 376) local type(s) :: { ( 4, 188 ), ( 4, 188, 4, 188, 4, 188, 4, 188, 4, 188, 4, 188, 4, 188, 4, 188, 4, 188, 4, 188, 4, 188, 4, 188, 4, 188, 4, 188, 4, 188, 4, 188, 4, 188, 4, 188, 4, 188, 4, 188, 4, 188, 4, 188, 4, 188, 4, 188, 4, 188, 4, 188, 4, 188, 4, 188, 4, 188, 4, 188, 4, 188, 4, 188, 4, 188, 4, 188, 4, 188, 4, 188, 4, 188, 4, 188, 4, 188, 4, 188, 4, 188, 4, 188, 4, 188, 4, 188, 4, 188, 4, 188, 4, 188 ) } Outer automorphisms :: reflexible Dual of E23.901 Graph:: simple bipartite v = 96 e = 188 f = 48 degree seq :: [ 2^94, 94^2 ] E23.903 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 6, 8}) Quotient :: edge Aut^+ = (C2 x (C3 : C8)) : C2 (small group id <96, 39>) Aut = $<192, 715>$ (small group id <192, 715>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T2 * T1^-2 * T2^-1 * T1^-2, T2^-2 * T1^-1 * T2^-2 * T1, T2^6, (T2 * T1^-1)^8 ] Map:: polytopal non-degenerate R = (1, 3, 10, 27, 16, 5)(2, 7, 20, 38, 24, 8)(4, 12, 31, 49, 28, 13)(6, 17, 34, 52, 35, 18)(9, 25, 14, 32, 47, 26)(11, 29, 15, 33, 48, 30)(19, 36, 22, 41, 57, 37)(21, 39, 23, 42, 58, 40)(43, 61, 45, 65, 50, 62)(44, 63, 46, 66, 51, 64)(53, 67, 55, 71, 59, 68)(54, 69, 56, 72, 60, 70)(73, 85, 75, 89, 77, 86)(74, 87, 76, 90, 78, 88)(79, 91, 81, 95, 83, 92)(80, 93, 82, 96, 84, 94)(97, 98, 102, 100)(99, 105, 113, 107)(101, 110, 114, 111)(103, 115, 108, 117)(104, 118, 109, 119)(106, 120, 130, 124)(112, 116, 131, 127)(121, 139, 125, 140)(122, 141, 126, 142)(123, 143, 148, 144)(128, 146, 129, 147)(132, 149, 135, 150)(133, 151, 136, 152)(134, 153, 145, 154)(137, 155, 138, 156)(157, 169, 159, 170)(158, 171, 160, 172)(161, 173, 162, 174)(163, 175, 165, 176)(164, 177, 166, 178)(167, 179, 168, 180)(181, 187, 183, 189)(182, 191, 184, 192)(185, 188, 186, 190) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 16^4 ), ( 16^6 ) } Outer automorphisms :: reflexible Dual of E23.907 Transitivity :: ET+ Graph:: simple bipartite v = 40 e = 96 f = 12 degree seq :: [ 4^24, 6^16 ] E23.904 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 6, 8}) Quotient :: edge Aut^+ = (C2 x (C3 : C8)) : C2 (small group id <96, 39>) Aut = $<192, 715>$ (small group id <192, 715>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1^-2 * T2^-1 * T1^-1, T2^2 * T1 * T2^2 * T1^-1, T1^6, T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1, T2^8 ] Map:: polytopal non-degenerate R = (1, 3, 10, 30, 59, 40, 17, 5)(2, 7, 22, 49, 75, 54, 26, 8)(4, 12, 35, 63, 82, 61, 31, 14)(6, 19, 43, 69, 88, 73, 46, 20)(9, 28, 15, 38, 65, 81, 58, 29)(11, 32, 16, 39, 66, 83, 60, 33)(13, 27, 55, 79, 93, 85, 64, 36)(18, 41, 67, 86, 95, 87, 68, 42)(21, 47, 24, 52, 77, 91, 74, 48)(23, 50, 25, 53, 78, 92, 76, 51)(34, 56, 37, 57, 80, 94, 84, 62)(44, 70, 45, 72, 90, 96, 89, 71)(97, 98, 102, 114, 109, 100)(99, 105, 123, 140, 115, 107)(101, 111, 132, 141, 116, 112)(103, 117, 108, 130, 137, 119)(104, 120, 110, 133, 138, 121)(106, 122, 139, 164, 151, 127)(113, 118, 142, 163, 160, 131)(124, 143, 128, 146, 166, 152)(125, 148, 129, 149, 167, 153)(126, 154, 175, 185, 165, 156)(134, 144, 135, 147, 168, 158)(136, 161, 181, 186, 169, 162)(145, 170, 159, 180, 182, 172)(150, 173, 157, 176, 183, 174)(155, 171, 184, 191, 189, 178)(177, 187, 179, 188, 192, 190) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8^6 ), ( 8^8 ) } Outer automorphisms :: reflexible Dual of E23.908 Transitivity :: ET+ Graph:: simple bipartite v = 28 e = 96 f = 24 degree seq :: [ 6^16, 8^12 ] E23.905 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 6, 8}) Quotient :: edge Aut^+ = (C2 x (C3 : C8)) : C2 (small group id <96, 39>) Aut = $<192, 715>$ (small group id <192, 715>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^4, T2^-1 * T1 * T2^-2 * T1^-1 * T2^-1, T2^-1 * T1^-2 * T2 * T1^-2, T1^8, T1^-1 * T2^-1 * T1 * T2^-1 * T1^-1 * T2 * T1^-1 * T2 * T1 * T2^-1 * T1^-1 * T2^-1, (T2 * T1^-1)^6 ] Map:: polytopal non-degenerate R = (1, 3, 10, 5)(2, 7, 21, 8)(4, 12, 28, 14)(6, 18, 38, 19)(9, 26, 15, 27)(11, 29, 16, 30)(13, 25, 46, 33)(17, 36, 60, 37)(20, 41, 23, 42)(22, 43, 24, 44)(31, 54, 34, 55)(32, 53, 73, 56)(35, 58, 82, 59)(39, 63, 40, 64)(45, 71, 57, 72)(47, 74, 49, 75)(48, 76, 50, 77)(51, 78, 52, 79)(61, 83, 62, 84)(65, 87, 67, 88)(66, 89, 68, 90)(69, 91, 70, 92)(80, 94, 81, 93)(85, 95, 86, 96)(97, 98, 102, 113, 131, 128, 109, 100)(99, 105, 121, 141, 154, 135, 114, 107)(101, 111, 129, 153, 155, 136, 115, 112)(103, 116, 108, 127, 149, 157, 132, 118)(104, 119, 110, 130, 152, 158, 133, 120)(106, 117, 134, 156, 178, 169, 142, 124)(122, 143, 125, 147, 159, 181, 167, 144)(123, 145, 126, 148, 160, 182, 168, 146)(137, 161, 139, 165, 179, 176, 150, 162)(138, 163, 140, 166, 180, 177, 151, 164)(170, 186, 172, 189, 191, 188, 174, 184)(171, 185, 173, 190, 192, 187, 175, 183) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 12^4 ), ( 12^8 ) } Outer automorphisms :: reflexible Dual of E23.906 Transitivity :: ET+ Graph:: simple bipartite v = 36 e = 96 f = 16 degree seq :: [ 4^24, 8^12 ] E23.906 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 6, 8}) Quotient :: loop Aut^+ = (C2 x (C3 : C8)) : C2 (small group id <96, 39>) Aut = $<192, 715>$ (small group id <192, 715>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T2 * T1^-2 * T2^-1 * T1^-2, T2^-2 * T1^-1 * T2^-2 * T1, T2^6, (T2 * T1^-1)^8 ] Map:: polytopal non-degenerate R = (1, 97, 3, 99, 10, 106, 27, 123, 16, 112, 5, 101)(2, 98, 7, 103, 20, 116, 38, 134, 24, 120, 8, 104)(4, 100, 12, 108, 31, 127, 49, 145, 28, 124, 13, 109)(6, 102, 17, 113, 34, 130, 52, 148, 35, 131, 18, 114)(9, 105, 25, 121, 14, 110, 32, 128, 47, 143, 26, 122)(11, 107, 29, 125, 15, 111, 33, 129, 48, 144, 30, 126)(19, 115, 36, 132, 22, 118, 41, 137, 57, 153, 37, 133)(21, 117, 39, 135, 23, 119, 42, 138, 58, 154, 40, 136)(43, 139, 61, 157, 45, 141, 65, 161, 50, 146, 62, 158)(44, 140, 63, 159, 46, 142, 66, 162, 51, 147, 64, 160)(53, 149, 67, 163, 55, 151, 71, 167, 59, 155, 68, 164)(54, 150, 69, 165, 56, 152, 72, 168, 60, 156, 70, 166)(73, 169, 85, 181, 75, 171, 89, 185, 77, 173, 86, 182)(74, 170, 87, 183, 76, 172, 90, 186, 78, 174, 88, 184)(79, 175, 91, 187, 81, 177, 95, 191, 83, 179, 92, 188)(80, 176, 93, 189, 82, 178, 96, 192, 84, 180, 94, 190) L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 110)(6, 100)(7, 115)(8, 118)(9, 113)(10, 120)(11, 99)(12, 117)(13, 119)(14, 114)(15, 101)(16, 116)(17, 107)(18, 111)(19, 108)(20, 131)(21, 103)(22, 109)(23, 104)(24, 130)(25, 139)(26, 141)(27, 143)(28, 106)(29, 140)(30, 142)(31, 112)(32, 146)(33, 147)(34, 124)(35, 127)(36, 149)(37, 151)(38, 153)(39, 150)(40, 152)(41, 155)(42, 156)(43, 125)(44, 121)(45, 126)(46, 122)(47, 148)(48, 123)(49, 154)(50, 129)(51, 128)(52, 144)(53, 135)(54, 132)(55, 136)(56, 133)(57, 145)(58, 134)(59, 138)(60, 137)(61, 169)(62, 171)(63, 170)(64, 172)(65, 173)(66, 174)(67, 175)(68, 177)(69, 176)(70, 178)(71, 179)(72, 180)(73, 159)(74, 157)(75, 160)(76, 158)(77, 162)(78, 161)(79, 165)(80, 163)(81, 166)(82, 164)(83, 168)(84, 167)(85, 187)(86, 191)(87, 189)(88, 192)(89, 188)(90, 190)(91, 183)(92, 186)(93, 181)(94, 185)(95, 184)(96, 182) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E23.905 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 16 e = 96 f = 36 degree seq :: [ 12^16 ] E23.907 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 6, 8}) Quotient :: loop Aut^+ = (C2 x (C3 : C8)) : C2 (small group id <96, 39>) Aut = $<192, 715>$ (small group id <192, 715>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1^-2 * T2^-1 * T1^-1, T2^2 * T1 * T2^2 * T1^-1, T1^6, T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1, T2^8 ] Map:: polytopal non-degenerate R = (1, 97, 3, 99, 10, 106, 30, 126, 59, 155, 40, 136, 17, 113, 5, 101)(2, 98, 7, 103, 22, 118, 49, 145, 75, 171, 54, 150, 26, 122, 8, 104)(4, 100, 12, 108, 35, 131, 63, 159, 82, 178, 61, 157, 31, 127, 14, 110)(6, 102, 19, 115, 43, 139, 69, 165, 88, 184, 73, 169, 46, 142, 20, 116)(9, 105, 28, 124, 15, 111, 38, 134, 65, 161, 81, 177, 58, 154, 29, 125)(11, 107, 32, 128, 16, 112, 39, 135, 66, 162, 83, 179, 60, 156, 33, 129)(13, 109, 27, 123, 55, 151, 79, 175, 93, 189, 85, 181, 64, 160, 36, 132)(18, 114, 41, 137, 67, 163, 86, 182, 95, 191, 87, 183, 68, 164, 42, 138)(21, 117, 47, 143, 24, 120, 52, 148, 77, 173, 91, 187, 74, 170, 48, 144)(23, 119, 50, 146, 25, 121, 53, 149, 78, 174, 92, 188, 76, 172, 51, 147)(34, 130, 56, 152, 37, 133, 57, 153, 80, 176, 94, 190, 84, 180, 62, 158)(44, 140, 70, 166, 45, 141, 72, 168, 90, 186, 96, 192, 89, 185, 71, 167) L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 111)(6, 114)(7, 117)(8, 120)(9, 123)(10, 122)(11, 99)(12, 130)(13, 100)(14, 133)(15, 132)(16, 101)(17, 118)(18, 109)(19, 107)(20, 112)(21, 108)(22, 142)(23, 103)(24, 110)(25, 104)(26, 139)(27, 140)(28, 143)(29, 148)(30, 154)(31, 106)(32, 146)(33, 149)(34, 137)(35, 113)(36, 141)(37, 138)(38, 144)(39, 147)(40, 161)(41, 119)(42, 121)(43, 164)(44, 115)(45, 116)(46, 163)(47, 128)(48, 135)(49, 170)(50, 166)(51, 168)(52, 129)(53, 167)(54, 173)(55, 127)(56, 124)(57, 125)(58, 175)(59, 171)(60, 126)(61, 176)(62, 134)(63, 180)(64, 131)(65, 181)(66, 136)(67, 160)(68, 151)(69, 156)(70, 152)(71, 153)(72, 158)(73, 162)(74, 159)(75, 184)(76, 145)(77, 157)(78, 150)(79, 185)(80, 183)(81, 187)(82, 155)(83, 188)(84, 182)(85, 186)(86, 172)(87, 174)(88, 191)(89, 165)(90, 169)(91, 179)(92, 192)(93, 178)(94, 177)(95, 189)(96, 190) local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E23.903 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 12 e = 96 f = 40 degree seq :: [ 16^12 ] E23.908 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 6, 8}) Quotient :: loop Aut^+ = (C2 x (C3 : C8)) : C2 (small group id <96, 39>) Aut = $<192, 715>$ (small group id <192, 715>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^4, T2^-1 * T1 * T2^-2 * T1^-1 * T2^-1, T2^-1 * T1^-2 * T2 * T1^-2, T1^8, T1^-1 * T2^-1 * T1 * T2^-1 * T1^-1 * T2 * T1^-1 * T2 * T1 * T2^-1 * T1^-1 * T2^-1, (T2 * T1^-1)^6 ] Map:: polytopal non-degenerate R = (1, 97, 3, 99, 10, 106, 5, 101)(2, 98, 7, 103, 21, 117, 8, 104)(4, 100, 12, 108, 28, 124, 14, 110)(6, 102, 18, 114, 38, 134, 19, 115)(9, 105, 26, 122, 15, 111, 27, 123)(11, 107, 29, 125, 16, 112, 30, 126)(13, 109, 25, 121, 46, 142, 33, 129)(17, 113, 36, 132, 60, 156, 37, 133)(20, 116, 41, 137, 23, 119, 42, 138)(22, 118, 43, 139, 24, 120, 44, 140)(31, 127, 54, 150, 34, 130, 55, 151)(32, 128, 53, 149, 73, 169, 56, 152)(35, 131, 58, 154, 82, 178, 59, 155)(39, 135, 63, 159, 40, 136, 64, 160)(45, 141, 71, 167, 57, 153, 72, 168)(47, 143, 74, 170, 49, 145, 75, 171)(48, 144, 76, 172, 50, 146, 77, 173)(51, 147, 78, 174, 52, 148, 79, 175)(61, 157, 83, 179, 62, 158, 84, 180)(65, 161, 87, 183, 67, 163, 88, 184)(66, 162, 89, 185, 68, 164, 90, 186)(69, 165, 91, 187, 70, 166, 92, 188)(80, 176, 94, 190, 81, 177, 93, 189)(85, 181, 95, 191, 86, 182, 96, 192) L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 111)(6, 113)(7, 116)(8, 119)(9, 121)(10, 117)(11, 99)(12, 127)(13, 100)(14, 130)(15, 129)(16, 101)(17, 131)(18, 107)(19, 112)(20, 108)(21, 134)(22, 103)(23, 110)(24, 104)(25, 141)(26, 143)(27, 145)(28, 106)(29, 147)(30, 148)(31, 149)(32, 109)(33, 153)(34, 152)(35, 128)(36, 118)(37, 120)(38, 156)(39, 114)(40, 115)(41, 161)(42, 163)(43, 165)(44, 166)(45, 154)(46, 124)(47, 125)(48, 122)(49, 126)(50, 123)(51, 159)(52, 160)(53, 157)(54, 162)(55, 164)(56, 158)(57, 155)(58, 135)(59, 136)(60, 178)(61, 132)(62, 133)(63, 181)(64, 182)(65, 139)(66, 137)(67, 140)(68, 138)(69, 179)(70, 180)(71, 144)(72, 146)(73, 142)(74, 186)(75, 185)(76, 189)(77, 190)(78, 184)(79, 183)(80, 150)(81, 151)(82, 169)(83, 176)(84, 177)(85, 167)(86, 168)(87, 171)(88, 170)(89, 173)(90, 172)(91, 175)(92, 174)(93, 191)(94, 192)(95, 188)(96, 187) local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E23.904 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 24 e = 96 f = 28 degree seq :: [ 8^24 ] E23.909 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 8}) Quotient :: dipole Aut^+ = (C2 x (C3 : C8)) : C2 (small group id <96, 39>) Aut = $<192, 715>$ (small group id <192, 715>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y1)^2, (R * Y3)^2, Y1^4, (R * Y2 * Y3^-1)^2, Y2 * Y1^-2 * Y2^-1 * Y1^-2, Y2^-1 * Y3 * Y2^-2 * Y3^-1 * Y2^-1, Y2^6, Y2^2 * Y1 * Y2^2 * Y1^-1, Y3 * Y2 * Y1 * Y3^-1 * Y2^-1 * Y1^-1, Y3 * Y2^-1 * Y1 * Y3^-1 * Y2 * Y1^-1, (Y3 * Y2)^8 ] Map:: R = (1, 97, 2, 98, 6, 102, 4, 100)(3, 99, 9, 105, 17, 113, 11, 107)(5, 101, 14, 110, 18, 114, 15, 111)(7, 103, 19, 115, 12, 108, 21, 117)(8, 104, 22, 118, 13, 109, 23, 119)(10, 106, 24, 120, 34, 130, 28, 124)(16, 112, 20, 116, 35, 131, 31, 127)(25, 121, 43, 139, 29, 125, 44, 140)(26, 122, 45, 141, 30, 126, 46, 142)(27, 123, 47, 143, 52, 148, 48, 144)(32, 128, 50, 146, 33, 129, 51, 147)(36, 132, 53, 149, 39, 135, 54, 150)(37, 133, 55, 151, 40, 136, 56, 152)(38, 134, 57, 153, 49, 145, 58, 154)(41, 137, 59, 155, 42, 138, 60, 156)(61, 157, 73, 169, 63, 159, 74, 170)(62, 158, 75, 171, 64, 160, 76, 172)(65, 161, 77, 173, 66, 162, 78, 174)(67, 163, 79, 175, 69, 165, 80, 176)(68, 164, 81, 177, 70, 166, 82, 178)(71, 167, 83, 179, 72, 168, 84, 180)(85, 181, 91, 187, 87, 183, 93, 189)(86, 182, 95, 191, 88, 184, 96, 192)(89, 185, 92, 188, 90, 186, 94, 190)(193, 289, 195, 291, 202, 298, 219, 315, 208, 304, 197, 293)(194, 290, 199, 295, 212, 308, 230, 326, 216, 312, 200, 296)(196, 292, 204, 300, 223, 319, 241, 337, 220, 316, 205, 301)(198, 294, 209, 305, 226, 322, 244, 340, 227, 323, 210, 306)(201, 297, 217, 313, 206, 302, 224, 320, 239, 335, 218, 314)(203, 299, 221, 317, 207, 303, 225, 321, 240, 336, 222, 318)(211, 307, 228, 324, 214, 310, 233, 329, 249, 345, 229, 325)(213, 309, 231, 327, 215, 311, 234, 330, 250, 346, 232, 328)(235, 331, 253, 349, 237, 333, 257, 353, 242, 338, 254, 350)(236, 332, 255, 351, 238, 334, 258, 354, 243, 339, 256, 352)(245, 341, 259, 355, 247, 343, 263, 359, 251, 347, 260, 356)(246, 342, 261, 357, 248, 344, 264, 360, 252, 348, 262, 358)(265, 361, 277, 373, 267, 363, 281, 377, 269, 365, 278, 374)(266, 362, 279, 375, 268, 364, 282, 378, 270, 366, 280, 376)(271, 367, 283, 379, 273, 369, 287, 383, 275, 371, 284, 380)(272, 368, 285, 381, 274, 370, 288, 384, 276, 372, 286, 382) L = (1, 196)(2, 193)(3, 203)(4, 198)(5, 207)(6, 194)(7, 213)(8, 215)(9, 195)(10, 220)(11, 209)(12, 211)(13, 214)(14, 197)(15, 210)(16, 223)(17, 201)(18, 206)(19, 199)(20, 208)(21, 204)(22, 200)(23, 205)(24, 202)(25, 236)(26, 238)(27, 240)(28, 226)(29, 235)(30, 237)(31, 227)(32, 243)(33, 242)(34, 216)(35, 212)(36, 246)(37, 248)(38, 250)(39, 245)(40, 247)(41, 252)(42, 251)(43, 217)(44, 221)(45, 218)(46, 222)(47, 219)(48, 244)(49, 249)(50, 224)(51, 225)(52, 239)(53, 228)(54, 231)(55, 229)(56, 232)(57, 230)(58, 241)(59, 233)(60, 234)(61, 266)(62, 268)(63, 265)(64, 267)(65, 270)(66, 269)(67, 272)(68, 274)(69, 271)(70, 273)(71, 276)(72, 275)(73, 253)(74, 255)(75, 254)(76, 256)(77, 257)(78, 258)(79, 259)(80, 261)(81, 260)(82, 262)(83, 263)(84, 264)(85, 285)(86, 288)(87, 283)(88, 287)(89, 286)(90, 284)(91, 277)(92, 281)(93, 279)(94, 282)(95, 278)(96, 280)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 2, 16, 2, 16, 2, 16, 2, 16 ), ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ) } Outer automorphisms :: reflexible Dual of E23.912 Graph:: bipartite v = 40 e = 192 f = 108 degree seq :: [ 8^24, 12^16 ] E23.910 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 8}) Quotient :: dipole Aut^+ = (C2 x (C3 : C8)) : C2 (small group id <96, 39>) Aut = $<192, 715>$ (small group id <192, 715>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y2^2 * Y1 * Y2^2 * Y1^-1, Y2 * Y1^-2 * Y2^-1 * Y1^-2, Y1^6, Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2^-1 * Y1^-1, (Y3^-1 * Y1^-1)^4, Y2^8 ] Map:: R = (1, 97, 2, 98, 6, 102, 18, 114, 13, 109, 4, 100)(3, 99, 9, 105, 27, 123, 44, 140, 19, 115, 11, 107)(5, 101, 15, 111, 36, 132, 45, 141, 20, 116, 16, 112)(7, 103, 21, 117, 12, 108, 34, 130, 41, 137, 23, 119)(8, 104, 24, 120, 14, 110, 37, 133, 42, 138, 25, 121)(10, 106, 26, 122, 43, 139, 68, 164, 55, 151, 31, 127)(17, 113, 22, 118, 46, 142, 67, 163, 64, 160, 35, 131)(28, 124, 47, 143, 32, 128, 50, 146, 70, 166, 56, 152)(29, 125, 52, 148, 33, 129, 53, 149, 71, 167, 57, 153)(30, 126, 58, 154, 79, 175, 89, 185, 69, 165, 60, 156)(38, 134, 48, 144, 39, 135, 51, 147, 72, 168, 62, 158)(40, 136, 65, 161, 85, 181, 90, 186, 73, 169, 66, 162)(49, 145, 74, 170, 63, 159, 84, 180, 86, 182, 76, 172)(54, 150, 77, 173, 61, 157, 80, 176, 87, 183, 78, 174)(59, 155, 75, 171, 88, 184, 95, 191, 93, 189, 82, 178)(81, 177, 91, 187, 83, 179, 92, 188, 96, 192, 94, 190)(193, 289, 195, 291, 202, 298, 222, 318, 251, 347, 232, 328, 209, 305, 197, 293)(194, 290, 199, 295, 214, 310, 241, 337, 267, 363, 246, 342, 218, 314, 200, 296)(196, 292, 204, 300, 227, 323, 255, 351, 274, 370, 253, 349, 223, 319, 206, 302)(198, 294, 211, 307, 235, 331, 261, 357, 280, 376, 265, 361, 238, 334, 212, 308)(201, 297, 220, 316, 207, 303, 230, 326, 257, 353, 273, 369, 250, 346, 221, 317)(203, 299, 224, 320, 208, 304, 231, 327, 258, 354, 275, 371, 252, 348, 225, 321)(205, 301, 219, 315, 247, 343, 271, 367, 285, 381, 277, 373, 256, 352, 228, 324)(210, 306, 233, 329, 259, 355, 278, 374, 287, 383, 279, 375, 260, 356, 234, 330)(213, 309, 239, 335, 216, 312, 244, 340, 269, 365, 283, 379, 266, 362, 240, 336)(215, 311, 242, 338, 217, 313, 245, 341, 270, 366, 284, 380, 268, 364, 243, 339)(226, 322, 248, 344, 229, 325, 249, 345, 272, 368, 286, 382, 276, 372, 254, 350)(236, 332, 262, 358, 237, 333, 264, 360, 282, 378, 288, 384, 281, 377, 263, 359) L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 211)(7, 214)(8, 194)(9, 220)(10, 222)(11, 224)(12, 227)(13, 219)(14, 196)(15, 230)(16, 231)(17, 197)(18, 233)(19, 235)(20, 198)(21, 239)(22, 241)(23, 242)(24, 244)(25, 245)(26, 200)(27, 247)(28, 207)(29, 201)(30, 251)(31, 206)(32, 208)(33, 203)(34, 248)(35, 255)(36, 205)(37, 249)(38, 257)(39, 258)(40, 209)(41, 259)(42, 210)(43, 261)(44, 262)(45, 264)(46, 212)(47, 216)(48, 213)(49, 267)(50, 217)(51, 215)(52, 269)(53, 270)(54, 218)(55, 271)(56, 229)(57, 272)(58, 221)(59, 232)(60, 225)(61, 223)(62, 226)(63, 274)(64, 228)(65, 273)(66, 275)(67, 278)(68, 234)(69, 280)(70, 237)(71, 236)(72, 282)(73, 238)(74, 240)(75, 246)(76, 243)(77, 283)(78, 284)(79, 285)(80, 286)(81, 250)(82, 253)(83, 252)(84, 254)(85, 256)(86, 287)(87, 260)(88, 265)(89, 263)(90, 288)(91, 266)(92, 268)(93, 277)(94, 276)(95, 279)(96, 281)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 2, 8, 2, 8, 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 E23.911 Graph:: bipartite v = 28 e = 192 f = 120 degree seq :: [ 12^16, 16^12 ] E23.911 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 8}) Quotient :: dipole Aut^+ = (C2 x (C3 : C8)) : C2 (small group id <96, 39>) Aut = $<192, 715>$ (small group id <192, 715>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, Y2^4, (R * Y2 * Y3^-1)^2, Y3 * Y2^-2 * Y3^-1 * Y2^-2, Y3^-1 * Y2^-1 * Y3^-2 * Y2 * Y3^-1, Y3^8, Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1, (Y3^-1 * Y1^-1)^8 ] Map:: polytopal R = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)(193, 289, 194, 290, 198, 294, 196, 292)(195, 291, 201, 297, 209, 305, 203, 299)(197, 293, 206, 302, 210, 306, 207, 303)(199, 295, 211, 307, 204, 300, 213, 309)(200, 296, 214, 310, 205, 301, 215, 311)(202, 298, 216, 312, 227, 323, 220, 316)(208, 304, 212, 308, 228, 324, 223, 319)(217, 313, 237, 333, 221, 317, 238, 334)(218, 314, 239, 335, 222, 318, 240, 336)(219, 315, 241, 337, 250, 346, 243, 339)(224, 320, 246, 342, 225, 321, 248, 344)(226, 322, 247, 343, 251, 347, 249, 345)(229, 325, 252, 348, 232, 328, 253, 349)(230, 326, 254, 350, 233, 329, 255, 351)(231, 327, 256, 352, 245, 341, 258, 354)(234, 330, 259, 355, 235, 331, 261, 357)(236, 332, 260, 356, 244, 340, 262, 358)(242, 338, 257, 353, 274, 370, 270, 366)(263, 359, 278, 374, 265, 361, 276, 372)(264, 360, 277, 373, 266, 362, 275, 371)(267, 363, 284, 380, 268, 364, 283, 379)(269, 365, 285, 381, 271, 367, 286, 382)(272, 368, 280, 376, 273, 369, 279, 375)(281, 377, 287, 383, 282, 378, 288, 384) L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 209)(7, 212)(8, 194)(9, 217)(10, 219)(11, 221)(12, 223)(13, 196)(14, 224)(15, 225)(16, 197)(17, 227)(18, 198)(19, 229)(20, 231)(21, 232)(22, 234)(23, 235)(24, 200)(25, 206)(26, 201)(27, 242)(28, 205)(29, 207)(30, 203)(31, 245)(32, 247)(33, 249)(34, 208)(35, 250)(36, 210)(37, 214)(38, 211)(39, 257)(40, 215)(41, 213)(42, 260)(43, 262)(44, 216)(45, 263)(46, 265)(47, 267)(48, 268)(49, 218)(50, 226)(51, 222)(52, 220)(53, 270)(54, 264)(55, 269)(56, 266)(57, 271)(58, 274)(59, 228)(60, 275)(61, 277)(62, 279)(63, 280)(64, 230)(65, 236)(66, 233)(67, 276)(68, 281)(69, 278)(70, 282)(71, 239)(72, 237)(73, 240)(74, 238)(75, 285)(76, 286)(77, 241)(78, 244)(79, 243)(80, 246)(81, 248)(82, 251)(83, 254)(84, 252)(85, 255)(86, 253)(87, 287)(88, 288)(89, 256)(90, 258)(91, 259)(92, 261)(93, 272)(94, 273)(95, 283)(96, 284)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 12, 16 ), ( 12, 16, 12, 16, 12, 16, 12, 16 ) } Outer automorphisms :: reflexible Dual of E23.910 Graph:: simple bipartite v = 120 e = 192 f = 28 degree seq :: [ 2^96, 8^24 ] E23.912 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 8}) Quotient :: dipole Aut^+ = (C2 x (C3 : C8)) : C2 (small group id <96, 39>) Aut = $<192, 715>$ (small group id <192, 715>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y1 * Y3^2 * Y1^-1 * Y3^-1, Y1^-1 * Y3^-1 * Y1^-2 * Y3 * Y1^-1, (Y3 * Y2^-1)^4, Y1^8, Y1^-1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1^-1 * Y3^-1, (Y3^-1 * Y1)^6 ] Map:: polytopal R = (1, 97, 2, 98, 6, 102, 17, 113, 35, 131, 32, 128, 13, 109, 4, 100)(3, 99, 9, 105, 25, 121, 45, 141, 58, 154, 39, 135, 18, 114, 11, 107)(5, 101, 15, 111, 33, 129, 57, 153, 59, 155, 40, 136, 19, 115, 16, 112)(7, 103, 20, 116, 12, 108, 31, 127, 53, 149, 61, 157, 36, 132, 22, 118)(8, 104, 23, 119, 14, 110, 34, 130, 56, 152, 62, 158, 37, 133, 24, 120)(10, 106, 21, 117, 38, 134, 60, 156, 82, 178, 73, 169, 46, 142, 28, 124)(26, 122, 47, 143, 29, 125, 51, 147, 63, 159, 85, 181, 71, 167, 48, 144)(27, 123, 49, 145, 30, 126, 52, 148, 64, 160, 86, 182, 72, 168, 50, 146)(41, 137, 65, 161, 43, 139, 69, 165, 83, 179, 80, 176, 54, 150, 66, 162)(42, 138, 67, 163, 44, 140, 70, 166, 84, 180, 81, 177, 55, 151, 68, 164)(74, 170, 90, 186, 76, 172, 93, 189, 95, 191, 92, 188, 78, 174, 88, 184)(75, 171, 89, 185, 77, 173, 94, 190, 96, 192, 91, 187, 79, 175, 87, 183)(193, 289)(194, 290)(195, 291)(196, 292)(197, 293)(198, 294)(199, 295)(200, 296)(201, 297)(202, 298)(203, 299)(204, 300)(205, 301)(206, 302)(207, 303)(208, 304)(209, 305)(210, 306)(211, 307)(212, 308)(213, 309)(214, 310)(215, 311)(216, 312)(217, 313)(218, 314)(219, 315)(220, 316)(221, 317)(222, 318)(223, 319)(224, 320)(225, 321)(226, 322)(227, 323)(228, 324)(229, 325)(230, 326)(231, 327)(232, 328)(233, 329)(234, 330)(235, 331)(236, 332)(237, 333)(238, 334)(239, 335)(240, 336)(241, 337)(242, 338)(243, 339)(244, 340)(245, 341)(246, 342)(247, 343)(248, 344)(249, 345)(250, 346)(251, 347)(252, 348)(253, 349)(254, 350)(255, 351)(256, 352)(257, 353)(258, 354)(259, 355)(260, 356)(261, 357)(262, 358)(263, 359)(264, 360)(265, 361)(266, 362)(267, 363)(268, 364)(269, 365)(270, 366)(271, 367)(272, 368)(273, 369)(274, 370)(275, 371)(276, 372)(277, 373)(278, 374)(279, 375)(280, 376)(281, 377)(282, 378)(283, 379)(284, 380)(285, 381)(286, 382)(287, 383)(288, 384) L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 210)(7, 213)(8, 194)(9, 218)(10, 197)(11, 221)(12, 220)(13, 217)(14, 196)(15, 219)(16, 222)(17, 228)(18, 230)(19, 198)(20, 233)(21, 200)(22, 235)(23, 234)(24, 236)(25, 238)(26, 207)(27, 201)(28, 206)(29, 208)(30, 203)(31, 246)(32, 245)(33, 205)(34, 247)(35, 250)(36, 252)(37, 209)(38, 211)(39, 255)(40, 256)(41, 215)(42, 212)(43, 216)(44, 214)(45, 263)(46, 225)(47, 266)(48, 268)(49, 267)(50, 269)(51, 270)(52, 271)(53, 265)(54, 226)(55, 223)(56, 224)(57, 264)(58, 274)(59, 227)(60, 229)(61, 275)(62, 276)(63, 232)(64, 231)(65, 279)(66, 281)(67, 280)(68, 282)(69, 283)(70, 284)(71, 249)(72, 237)(73, 248)(74, 241)(75, 239)(76, 242)(77, 240)(78, 244)(79, 243)(80, 286)(81, 285)(82, 251)(83, 254)(84, 253)(85, 287)(86, 288)(87, 259)(88, 257)(89, 260)(90, 258)(91, 262)(92, 261)(93, 272)(94, 273)(95, 278)(96, 277)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E23.909 Graph:: simple bipartite v = 108 e = 192 f = 40 degree seq :: [ 2^96, 16^12 ] E23.913 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 8}) Quotient :: dipole Aut^+ = (C2 x (C3 : C8)) : C2 (small group id <96, 39>) Aut = $<192, 715>$ (small group id <192, 715>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y3^-2 * Y1^-2, (R * Y1)^2, Y1^4, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2 * Y1^-2 * Y2^-1 * Y1^-2, Y2^-1 * Y3 * Y2^-2 * Y3^-1 * Y2^-1, Y3 * Y2 * Y1 * Y3^-1 * Y2^-1 * Y1^-1, Y2^2 * Y1 * Y2^2 * Y1^-1, Y3 * Y2^-1 * Y1 * Y3^-1 * Y2 * Y1^-1, Y2^8, Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2 * Y3 * Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, (Y3 * Y2)^6 ] Map:: R = (1, 97, 2, 98, 6, 102, 4, 100)(3, 99, 9, 105, 17, 113, 11, 107)(5, 101, 14, 110, 18, 114, 15, 111)(7, 103, 19, 115, 12, 108, 21, 117)(8, 104, 22, 118, 13, 109, 23, 119)(10, 106, 24, 120, 35, 131, 28, 124)(16, 112, 20, 116, 36, 132, 31, 127)(25, 121, 45, 141, 29, 125, 46, 142)(26, 122, 47, 143, 30, 126, 48, 144)(27, 123, 49, 145, 58, 154, 51, 147)(32, 128, 54, 150, 33, 129, 56, 152)(34, 130, 55, 151, 59, 155, 57, 153)(37, 133, 60, 156, 40, 136, 61, 157)(38, 134, 62, 158, 41, 137, 63, 159)(39, 135, 64, 160, 53, 149, 66, 162)(42, 138, 67, 163, 43, 139, 69, 165)(44, 140, 68, 164, 52, 148, 70, 166)(50, 146, 65, 161, 82, 178, 78, 174)(71, 167, 86, 182, 73, 169, 84, 180)(72, 168, 85, 181, 74, 170, 83, 179)(75, 171, 92, 188, 76, 172, 91, 187)(77, 173, 93, 189, 79, 175, 94, 190)(80, 176, 88, 184, 81, 177, 87, 183)(89, 185, 95, 191, 90, 186, 96, 192)(193, 289, 195, 291, 202, 298, 219, 315, 242, 338, 226, 322, 208, 304, 197, 293)(194, 290, 199, 295, 212, 308, 231, 327, 257, 353, 236, 332, 216, 312, 200, 296)(196, 292, 204, 300, 223, 319, 245, 341, 270, 366, 244, 340, 220, 316, 205, 301)(198, 294, 209, 305, 227, 323, 250, 346, 274, 370, 251, 347, 228, 324, 210, 306)(201, 297, 217, 313, 206, 302, 224, 320, 247, 343, 269, 365, 241, 337, 218, 314)(203, 299, 221, 317, 207, 303, 225, 321, 249, 345, 271, 367, 243, 339, 222, 318)(211, 307, 229, 325, 214, 310, 234, 330, 260, 356, 281, 377, 256, 352, 230, 326)(213, 309, 232, 328, 215, 311, 235, 331, 262, 358, 282, 378, 258, 354, 233, 329)(237, 333, 263, 359, 239, 335, 267, 363, 285, 381, 272, 368, 246, 342, 264, 360)(238, 334, 265, 361, 240, 336, 268, 364, 286, 382, 273, 369, 248, 344, 266, 362)(252, 348, 275, 371, 254, 350, 279, 375, 287, 383, 283, 379, 259, 355, 276, 372)(253, 349, 277, 373, 255, 351, 280, 376, 288, 384, 284, 380, 261, 357, 278, 374) L = (1, 196)(2, 193)(3, 203)(4, 198)(5, 207)(6, 194)(7, 213)(8, 215)(9, 195)(10, 220)(11, 209)(12, 211)(13, 214)(14, 197)(15, 210)(16, 223)(17, 201)(18, 206)(19, 199)(20, 208)(21, 204)(22, 200)(23, 205)(24, 202)(25, 238)(26, 240)(27, 243)(28, 227)(29, 237)(30, 239)(31, 228)(32, 248)(33, 246)(34, 249)(35, 216)(36, 212)(37, 253)(38, 255)(39, 258)(40, 252)(41, 254)(42, 261)(43, 259)(44, 262)(45, 217)(46, 221)(47, 218)(48, 222)(49, 219)(50, 270)(51, 250)(52, 260)(53, 256)(54, 224)(55, 226)(56, 225)(57, 251)(58, 241)(59, 247)(60, 229)(61, 232)(62, 230)(63, 233)(64, 231)(65, 242)(66, 245)(67, 234)(68, 236)(69, 235)(70, 244)(71, 276)(72, 275)(73, 278)(74, 277)(75, 283)(76, 284)(77, 286)(78, 274)(79, 285)(80, 279)(81, 280)(82, 257)(83, 266)(84, 265)(85, 264)(86, 263)(87, 273)(88, 272)(89, 288)(90, 287)(91, 268)(92, 267)(93, 269)(94, 271)(95, 281)(96, 282)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 2, 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 E23.914 Graph:: bipartite v = 36 e = 192 f = 112 degree seq :: [ 8^24, 16^12 ] E23.914 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 8}) Quotient :: dipole Aut^+ = (C2 x (C3 : C8)) : C2 (small group id <96, 39>) Aut = $<192, 715>$ (small group id <192, 715>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3 * Y1^-1 * Y3^2 * Y1 * Y3, Y1^6, Y3^-1 * Y1^-2 * Y3 * Y1^-2, Y3^8, Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1, (Y3 * Y2^-1)^8 ] Map:: polytopal R = (1, 97, 2, 98, 6, 102, 18, 114, 13, 109, 4, 100)(3, 99, 9, 105, 27, 123, 44, 140, 19, 115, 11, 107)(5, 101, 15, 111, 36, 132, 45, 141, 20, 116, 16, 112)(7, 103, 21, 117, 12, 108, 34, 130, 41, 137, 23, 119)(8, 104, 24, 120, 14, 110, 37, 133, 42, 138, 25, 121)(10, 106, 26, 122, 43, 139, 68, 164, 55, 151, 31, 127)(17, 113, 22, 118, 46, 142, 67, 163, 64, 160, 35, 131)(28, 124, 47, 143, 32, 128, 50, 146, 70, 166, 56, 152)(29, 125, 52, 148, 33, 129, 53, 149, 71, 167, 57, 153)(30, 126, 58, 154, 79, 175, 89, 185, 69, 165, 60, 156)(38, 134, 48, 144, 39, 135, 51, 147, 72, 168, 62, 158)(40, 136, 65, 161, 85, 181, 90, 186, 73, 169, 66, 162)(49, 145, 74, 170, 63, 159, 84, 180, 86, 182, 76, 172)(54, 150, 77, 173, 61, 157, 80, 176, 87, 183, 78, 174)(59, 155, 75, 171, 88, 184, 95, 191, 93, 189, 82, 178)(81, 177, 91, 187, 83, 179, 92, 188, 96, 192, 94, 190)(193, 289)(194, 290)(195, 291)(196, 292)(197, 293)(198, 294)(199, 295)(200, 296)(201, 297)(202, 298)(203, 299)(204, 300)(205, 301)(206, 302)(207, 303)(208, 304)(209, 305)(210, 306)(211, 307)(212, 308)(213, 309)(214, 310)(215, 311)(216, 312)(217, 313)(218, 314)(219, 315)(220, 316)(221, 317)(222, 318)(223, 319)(224, 320)(225, 321)(226, 322)(227, 323)(228, 324)(229, 325)(230, 326)(231, 327)(232, 328)(233, 329)(234, 330)(235, 331)(236, 332)(237, 333)(238, 334)(239, 335)(240, 336)(241, 337)(242, 338)(243, 339)(244, 340)(245, 341)(246, 342)(247, 343)(248, 344)(249, 345)(250, 346)(251, 347)(252, 348)(253, 349)(254, 350)(255, 351)(256, 352)(257, 353)(258, 354)(259, 355)(260, 356)(261, 357)(262, 358)(263, 359)(264, 360)(265, 361)(266, 362)(267, 363)(268, 364)(269, 365)(270, 366)(271, 367)(272, 368)(273, 369)(274, 370)(275, 371)(276, 372)(277, 373)(278, 374)(279, 375)(280, 376)(281, 377)(282, 378)(283, 379)(284, 380)(285, 381)(286, 382)(287, 383)(288, 384) L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 211)(7, 214)(8, 194)(9, 220)(10, 222)(11, 224)(12, 227)(13, 219)(14, 196)(15, 230)(16, 231)(17, 197)(18, 233)(19, 235)(20, 198)(21, 239)(22, 241)(23, 242)(24, 244)(25, 245)(26, 200)(27, 247)(28, 207)(29, 201)(30, 251)(31, 206)(32, 208)(33, 203)(34, 248)(35, 255)(36, 205)(37, 249)(38, 257)(39, 258)(40, 209)(41, 259)(42, 210)(43, 261)(44, 262)(45, 264)(46, 212)(47, 216)(48, 213)(49, 267)(50, 217)(51, 215)(52, 269)(53, 270)(54, 218)(55, 271)(56, 229)(57, 272)(58, 221)(59, 232)(60, 225)(61, 223)(62, 226)(63, 274)(64, 228)(65, 273)(66, 275)(67, 278)(68, 234)(69, 280)(70, 237)(71, 236)(72, 282)(73, 238)(74, 240)(75, 246)(76, 243)(77, 283)(78, 284)(79, 285)(80, 286)(81, 250)(82, 253)(83, 252)(84, 254)(85, 256)(86, 287)(87, 260)(88, 265)(89, 263)(90, 288)(91, 266)(92, 268)(93, 277)(94, 276)(95, 279)(96, 281)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E23.913 Graph:: simple bipartite v = 112 e = 192 f = 36 degree seq :: [ 2^96, 12^16 ] E23.915 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 6, 8}) Quotient :: edge Aut^+ = (C4 x (C3 : C4)) : C2 (small group id <96, 44>) Aut = $<192, 757>$ (small group id <192, 757>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T2^-1 * T1^-1 * T2^-2 * T1 * T2^-1, T2^6, T2^-1 * T1^-1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1^-1, T1^-3 * T2^-1 * T1^-4 * T2 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 3, 10, 28, 16, 5)(2, 7, 20, 49, 24, 8)(4, 12, 33, 61, 29, 13)(6, 17, 41, 72, 45, 18)(9, 26, 14, 38, 59, 27)(11, 30, 15, 39, 60, 31)(19, 47, 22, 53, 80, 48)(21, 50, 23, 54, 81, 51)(25, 55, 83, 68, 37, 56)(32, 57, 35, 58, 86, 65)(34, 62, 36, 63, 87, 66)(40, 70, 43, 76, 91, 71)(42, 73, 44, 77, 92, 74)(46, 78, 94, 82, 52, 79)(64, 88, 95, 84, 67, 85)(69, 89, 96, 93, 75, 90)(97, 98, 102, 100)(99, 105, 121, 107)(101, 110, 133, 111)(103, 115, 142, 117)(104, 118, 148, 119)(106, 120, 137, 125)(108, 128, 160, 130)(109, 131, 163, 132)(112, 116, 141, 129)(113, 136, 165, 138)(114, 139, 171, 140)(122, 143, 166, 153)(123, 149, 167, 154)(124, 155, 179, 156)(126, 146, 169, 158)(127, 150, 170, 159)(134, 144, 172, 161)(135, 147, 173, 162)(145, 176, 190, 177)(151, 178, 185, 180)(152, 175, 186, 181)(157, 182, 191, 183)(164, 174, 189, 184)(168, 187, 192, 188) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 16^4 ), ( 16^6 ) } Outer automorphisms :: reflexible Dual of E23.919 Transitivity :: ET+ Graph:: simple bipartite v = 40 e = 96 f = 12 degree seq :: [ 4^24, 6^16 ] E23.916 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 6, 8}) Quotient :: edge Aut^+ = (C4 x (C3 : C4)) : C2 (small group id <96, 44>) Aut = $<192, 757>$ (small group id <192, 757>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^-1 * T2^-1 * T1^-2 * T2 * T1^-1, T2^-1 * T1^-1 * T2^2 * T1 * T2^-1, T1^6, (T1^-1 * T2^-1)^4, T2^8 ] Map:: polytopal non-degenerate R = (1, 3, 10, 30, 60, 40, 17, 5)(2, 7, 22, 49, 80, 54, 26, 8)(4, 12, 31, 62, 88, 67, 37, 14)(6, 19, 43, 72, 92, 76, 46, 20)(9, 28, 56, 79, 68, 38, 15, 29)(11, 32, 61, 78, 69, 39, 16, 33)(13, 27, 55, 85, 95, 89, 66, 35)(18, 41, 70, 90, 96, 91, 71, 42)(21, 47, 77, 58, 83, 52, 24, 48)(23, 50, 81, 63, 84, 53, 25, 51)(34, 64, 87, 59, 86, 57, 36, 65)(44, 73, 93, 82, 94, 75, 45, 74)(97, 98, 102, 114, 109, 100)(99, 105, 123, 140, 115, 107)(101, 111, 131, 141, 116, 112)(103, 117, 108, 130, 137, 119)(104, 120, 110, 132, 138, 121)(106, 118, 139, 166, 151, 127)(113, 122, 142, 167, 162, 133)(124, 148, 128, 149, 169, 153)(125, 154, 129, 159, 170, 155)(126, 152, 181, 189, 168, 157)(134, 143, 135, 146, 171, 160)(136, 164, 185, 190, 172, 165)(144, 174, 147, 178, 161, 175)(145, 173, 158, 183, 186, 177)(150, 179, 163, 182, 187, 180)(156, 176, 188, 192, 191, 184) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8^6 ), ( 8^8 ) } Outer automorphisms :: reflexible Dual of E23.920 Transitivity :: ET+ Graph:: simple bipartite v = 28 e = 96 f = 24 degree seq :: [ 6^16, 8^12 ] E23.917 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 6, 8}) Quotient :: edge Aut^+ = (C4 x (C3 : C4)) : C2 (small group id <96, 44>) Aut = $<192, 757>$ (small group id <192, 757>) |r| :: 2 Presentation :: [ F^2, T2^4, (F * T1)^2, (F * T2)^2, T1^2 * T2 * T1^-2 * T2^-1, T1^-1 * T2^-1 * T1^2 * T2 * T1^-1, T1^-2 * T2^2 * T1^-1 * T2^2 * T1^-1, T2 * T1^3 * T2^2 * T1 * T2, T1^8, (T2^-1 * T1^-1)^6 ] Map:: polytopal non-degenerate R = (1, 3, 10, 5)(2, 7, 21, 8)(4, 12, 32, 14)(6, 18, 45, 19)(9, 25, 58, 26)(11, 29, 46, 31)(13, 30, 49, 35)(15, 37, 65, 38)(16, 39, 44, 40)(17, 42, 28, 43)(20, 47, 36, 48)(22, 51, 72, 52)(23, 53, 33, 54)(24, 55, 71, 56)(27, 62, 34, 63)(41, 69, 50, 70)(57, 81, 66, 82)(59, 83, 67, 84)(60, 85, 64, 86)(61, 87, 68, 88)(73, 89, 78, 90)(74, 91, 79, 92)(75, 93, 77, 94)(76, 95, 80, 96)(97, 98, 102, 113, 137, 130, 109, 100)(99, 105, 114, 140, 165, 161, 126, 107)(101, 111, 115, 142, 166, 154, 131, 112)(103, 116, 138, 167, 159, 129, 108, 118)(104, 119, 139, 168, 158, 132, 110, 120)(106, 123, 141, 128, 146, 117, 145, 124)(121, 153, 136, 164, 134, 160, 125, 155)(122, 156, 135, 163, 133, 162, 127, 157)(143, 169, 152, 176, 150, 173, 147, 170)(144, 171, 151, 175, 149, 174, 148, 172)(177, 188, 184, 186, 182, 191, 179, 189)(178, 192, 183, 190, 181, 187, 180, 185) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 12^4 ), ( 12^8 ) } Outer automorphisms :: reflexible Dual of E23.918 Transitivity :: ET+ Graph:: simple bipartite v = 36 e = 96 f = 16 degree seq :: [ 4^24, 8^12 ] E23.918 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 6, 8}) Quotient :: loop Aut^+ = (C4 x (C3 : C4)) : C2 (small group id <96, 44>) Aut = $<192, 757>$ (small group id <192, 757>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T2^-1 * T1^-1 * T2^-2 * T1 * T2^-1, T2^6, T2^-1 * T1^-1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1^-1, T1^-3 * T2^-1 * T1^-4 * T2 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 97, 3, 99, 10, 106, 28, 124, 16, 112, 5, 101)(2, 98, 7, 103, 20, 116, 49, 145, 24, 120, 8, 104)(4, 100, 12, 108, 33, 129, 61, 157, 29, 125, 13, 109)(6, 102, 17, 113, 41, 137, 72, 168, 45, 141, 18, 114)(9, 105, 26, 122, 14, 110, 38, 134, 59, 155, 27, 123)(11, 107, 30, 126, 15, 111, 39, 135, 60, 156, 31, 127)(19, 115, 47, 143, 22, 118, 53, 149, 80, 176, 48, 144)(21, 117, 50, 146, 23, 119, 54, 150, 81, 177, 51, 147)(25, 121, 55, 151, 83, 179, 68, 164, 37, 133, 56, 152)(32, 128, 57, 153, 35, 131, 58, 154, 86, 182, 65, 161)(34, 130, 62, 158, 36, 132, 63, 159, 87, 183, 66, 162)(40, 136, 70, 166, 43, 139, 76, 172, 91, 187, 71, 167)(42, 138, 73, 169, 44, 140, 77, 173, 92, 188, 74, 170)(46, 142, 78, 174, 94, 190, 82, 178, 52, 148, 79, 175)(64, 160, 88, 184, 95, 191, 84, 180, 67, 163, 85, 181)(69, 165, 89, 185, 96, 192, 93, 189, 75, 171, 90, 186) L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 110)(6, 100)(7, 115)(8, 118)(9, 121)(10, 120)(11, 99)(12, 128)(13, 131)(14, 133)(15, 101)(16, 116)(17, 136)(18, 139)(19, 142)(20, 141)(21, 103)(22, 148)(23, 104)(24, 137)(25, 107)(26, 143)(27, 149)(28, 155)(29, 106)(30, 146)(31, 150)(32, 160)(33, 112)(34, 108)(35, 163)(36, 109)(37, 111)(38, 144)(39, 147)(40, 165)(41, 125)(42, 113)(43, 171)(44, 114)(45, 129)(46, 117)(47, 166)(48, 172)(49, 176)(50, 169)(51, 173)(52, 119)(53, 167)(54, 170)(55, 178)(56, 175)(57, 122)(58, 123)(59, 179)(60, 124)(61, 182)(62, 126)(63, 127)(64, 130)(65, 134)(66, 135)(67, 132)(68, 174)(69, 138)(70, 153)(71, 154)(72, 187)(73, 158)(74, 159)(75, 140)(76, 161)(77, 162)(78, 189)(79, 186)(80, 190)(81, 145)(82, 185)(83, 156)(84, 151)(85, 152)(86, 191)(87, 157)(88, 164)(89, 180)(90, 181)(91, 192)(92, 168)(93, 184)(94, 177)(95, 183)(96, 188) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E23.917 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 16 e = 96 f = 36 degree seq :: [ 12^16 ] E23.919 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 6, 8}) Quotient :: loop Aut^+ = (C4 x (C3 : C4)) : C2 (small group id <96, 44>) Aut = $<192, 757>$ (small group id <192, 757>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^-1 * T2^-1 * T1^-2 * T2 * T1^-1, T2^-1 * T1^-1 * T2^2 * T1 * T2^-1, T1^6, (T1^-1 * T2^-1)^4, T2^8 ] Map:: polytopal non-degenerate R = (1, 97, 3, 99, 10, 106, 30, 126, 60, 156, 40, 136, 17, 113, 5, 101)(2, 98, 7, 103, 22, 118, 49, 145, 80, 176, 54, 150, 26, 122, 8, 104)(4, 100, 12, 108, 31, 127, 62, 158, 88, 184, 67, 163, 37, 133, 14, 110)(6, 102, 19, 115, 43, 139, 72, 168, 92, 188, 76, 172, 46, 142, 20, 116)(9, 105, 28, 124, 56, 152, 79, 175, 68, 164, 38, 134, 15, 111, 29, 125)(11, 107, 32, 128, 61, 157, 78, 174, 69, 165, 39, 135, 16, 112, 33, 129)(13, 109, 27, 123, 55, 151, 85, 181, 95, 191, 89, 185, 66, 162, 35, 131)(18, 114, 41, 137, 70, 166, 90, 186, 96, 192, 91, 187, 71, 167, 42, 138)(21, 117, 47, 143, 77, 173, 58, 154, 83, 179, 52, 148, 24, 120, 48, 144)(23, 119, 50, 146, 81, 177, 63, 159, 84, 180, 53, 149, 25, 121, 51, 147)(34, 130, 64, 160, 87, 183, 59, 155, 86, 182, 57, 153, 36, 132, 65, 161)(44, 140, 73, 169, 93, 189, 82, 178, 94, 190, 75, 171, 45, 141, 74, 170) L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 111)(6, 114)(7, 117)(8, 120)(9, 123)(10, 118)(11, 99)(12, 130)(13, 100)(14, 132)(15, 131)(16, 101)(17, 122)(18, 109)(19, 107)(20, 112)(21, 108)(22, 139)(23, 103)(24, 110)(25, 104)(26, 142)(27, 140)(28, 148)(29, 154)(30, 152)(31, 106)(32, 149)(33, 159)(34, 137)(35, 141)(36, 138)(37, 113)(38, 143)(39, 146)(40, 164)(41, 119)(42, 121)(43, 166)(44, 115)(45, 116)(46, 167)(47, 135)(48, 174)(49, 173)(50, 171)(51, 178)(52, 128)(53, 169)(54, 179)(55, 127)(56, 181)(57, 124)(58, 129)(59, 125)(60, 176)(61, 126)(62, 183)(63, 170)(64, 134)(65, 175)(66, 133)(67, 182)(68, 185)(69, 136)(70, 151)(71, 162)(72, 157)(73, 153)(74, 155)(75, 160)(76, 165)(77, 158)(78, 147)(79, 144)(80, 188)(81, 145)(82, 161)(83, 163)(84, 150)(85, 189)(86, 187)(87, 186)(88, 156)(89, 190)(90, 177)(91, 180)(92, 192)(93, 168)(94, 172)(95, 184)(96, 191) local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E23.915 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 12 e = 96 f = 40 degree seq :: [ 16^12 ] E23.920 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 6, 8}) Quotient :: loop Aut^+ = (C4 x (C3 : C4)) : C2 (small group id <96, 44>) Aut = $<192, 757>$ (small group id <192, 757>) |r| :: 2 Presentation :: [ F^2, T2^4, (F * T1)^2, (F * T2)^2, T1^2 * T2 * T1^-2 * T2^-1, T1^-1 * T2^-1 * T1^2 * T2 * T1^-1, T1^-2 * T2^2 * T1^-1 * T2^2 * T1^-1, T2 * T1^3 * T2^2 * T1 * T2, T1^8, (T2^-1 * T1^-1)^6 ] Map:: polytopal non-degenerate R = (1, 97, 3, 99, 10, 106, 5, 101)(2, 98, 7, 103, 21, 117, 8, 104)(4, 100, 12, 108, 32, 128, 14, 110)(6, 102, 18, 114, 45, 141, 19, 115)(9, 105, 25, 121, 58, 154, 26, 122)(11, 107, 29, 125, 46, 142, 31, 127)(13, 109, 30, 126, 49, 145, 35, 131)(15, 111, 37, 133, 65, 161, 38, 134)(16, 112, 39, 135, 44, 140, 40, 136)(17, 113, 42, 138, 28, 124, 43, 139)(20, 116, 47, 143, 36, 132, 48, 144)(22, 118, 51, 147, 72, 168, 52, 148)(23, 119, 53, 149, 33, 129, 54, 150)(24, 120, 55, 151, 71, 167, 56, 152)(27, 123, 62, 158, 34, 130, 63, 159)(41, 137, 69, 165, 50, 146, 70, 166)(57, 153, 81, 177, 66, 162, 82, 178)(59, 155, 83, 179, 67, 163, 84, 180)(60, 156, 85, 181, 64, 160, 86, 182)(61, 157, 87, 183, 68, 164, 88, 184)(73, 169, 89, 185, 78, 174, 90, 186)(74, 170, 91, 187, 79, 175, 92, 188)(75, 171, 93, 189, 77, 173, 94, 190)(76, 172, 95, 191, 80, 176, 96, 192) L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 111)(6, 113)(7, 116)(8, 119)(9, 114)(10, 123)(11, 99)(12, 118)(13, 100)(14, 120)(15, 115)(16, 101)(17, 137)(18, 140)(19, 142)(20, 138)(21, 145)(22, 103)(23, 139)(24, 104)(25, 153)(26, 156)(27, 141)(28, 106)(29, 155)(30, 107)(31, 157)(32, 146)(33, 108)(34, 109)(35, 112)(36, 110)(37, 162)(38, 160)(39, 163)(40, 164)(41, 130)(42, 167)(43, 168)(44, 165)(45, 128)(46, 166)(47, 169)(48, 171)(49, 124)(50, 117)(51, 170)(52, 172)(53, 174)(54, 173)(55, 175)(56, 176)(57, 136)(58, 131)(59, 121)(60, 135)(61, 122)(62, 132)(63, 129)(64, 125)(65, 126)(66, 127)(67, 133)(68, 134)(69, 161)(70, 154)(71, 159)(72, 158)(73, 152)(74, 143)(75, 151)(76, 144)(77, 147)(78, 148)(79, 149)(80, 150)(81, 188)(82, 192)(83, 189)(84, 185)(85, 187)(86, 191)(87, 190)(88, 186)(89, 178)(90, 182)(91, 180)(92, 184)(93, 177)(94, 181)(95, 179)(96, 183) local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E23.916 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 24 e = 96 f = 28 degree seq :: [ 8^24 ] E23.921 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 8}) Quotient :: dipole Aut^+ = (C4 x (C3 : C4)) : C2 (small group id <96, 44>) Aut = $<192, 757>$ (small group id <192, 757>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, (R * Y1)^2, (R * Y3)^2, Y1^4, (R * Y2 * Y3^-1)^2, Y3 * Y2^-2 * Y3^-1 * Y2^-2, Y2^-2 * Y1 * Y2^-2 * Y1^-1, Y2^-1 * R * Y2^2 * R * Y2^-1, Y2^6, Y3 * Y2^-1 * Y1 * Y2^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y2^-1, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, Y3 * Y2^-1 * Y3 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1, Y2 * Y3 * Y2 * Y1 * Y2 * Y3^-1 * Y2 * Y1^-1, Y3^3 * Y2^-1 * Y3^4 * Y2 * Y3 ] Map:: R = (1, 97, 2, 98, 6, 102, 4, 100)(3, 99, 9, 105, 25, 121, 11, 107)(5, 101, 14, 110, 37, 133, 15, 111)(7, 103, 19, 115, 46, 142, 21, 117)(8, 104, 22, 118, 52, 148, 23, 119)(10, 106, 24, 120, 41, 137, 29, 125)(12, 108, 32, 128, 64, 160, 34, 130)(13, 109, 35, 131, 67, 163, 36, 132)(16, 112, 20, 116, 45, 141, 33, 129)(17, 113, 40, 136, 69, 165, 42, 138)(18, 114, 43, 139, 75, 171, 44, 140)(26, 122, 47, 143, 70, 166, 57, 153)(27, 123, 53, 149, 71, 167, 58, 154)(28, 124, 59, 155, 83, 179, 60, 156)(30, 126, 50, 146, 73, 169, 62, 158)(31, 127, 54, 150, 74, 170, 63, 159)(38, 134, 48, 144, 76, 172, 65, 161)(39, 135, 51, 147, 77, 173, 66, 162)(49, 145, 80, 176, 94, 190, 81, 177)(55, 151, 82, 178, 89, 185, 84, 180)(56, 152, 79, 175, 90, 186, 85, 181)(61, 157, 86, 182, 95, 191, 87, 183)(68, 164, 78, 174, 93, 189, 88, 184)(72, 168, 91, 187, 96, 192, 92, 188)(193, 289, 195, 291, 202, 298, 220, 316, 208, 304, 197, 293)(194, 290, 199, 295, 212, 308, 241, 337, 216, 312, 200, 296)(196, 292, 204, 300, 225, 321, 253, 349, 221, 317, 205, 301)(198, 294, 209, 305, 233, 329, 264, 360, 237, 333, 210, 306)(201, 297, 218, 314, 206, 302, 230, 326, 251, 347, 219, 315)(203, 299, 222, 318, 207, 303, 231, 327, 252, 348, 223, 319)(211, 307, 239, 335, 214, 310, 245, 341, 272, 368, 240, 336)(213, 309, 242, 338, 215, 311, 246, 342, 273, 369, 243, 339)(217, 313, 247, 343, 275, 371, 260, 356, 229, 325, 248, 344)(224, 320, 249, 345, 227, 323, 250, 346, 278, 374, 257, 353)(226, 322, 254, 350, 228, 324, 255, 351, 279, 375, 258, 354)(232, 328, 262, 358, 235, 331, 268, 364, 283, 379, 263, 359)(234, 330, 265, 361, 236, 332, 269, 365, 284, 380, 266, 362)(238, 334, 270, 366, 286, 382, 274, 370, 244, 340, 271, 367)(256, 352, 280, 376, 287, 383, 276, 372, 259, 355, 277, 373)(261, 357, 281, 377, 288, 384, 285, 381, 267, 363, 282, 378) L = (1, 196)(2, 193)(3, 203)(4, 198)(5, 207)(6, 194)(7, 213)(8, 215)(9, 195)(10, 221)(11, 217)(12, 226)(13, 228)(14, 197)(15, 229)(16, 225)(17, 234)(18, 236)(19, 199)(20, 208)(21, 238)(22, 200)(23, 244)(24, 202)(25, 201)(26, 249)(27, 250)(28, 252)(29, 233)(30, 254)(31, 255)(32, 204)(33, 237)(34, 256)(35, 205)(36, 259)(37, 206)(38, 257)(39, 258)(40, 209)(41, 216)(42, 261)(43, 210)(44, 267)(45, 212)(46, 211)(47, 218)(48, 230)(49, 273)(50, 222)(51, 231)(52, 214)(53, 219)(54, 223)(55, 276)(56, 277)(57, 262)(58, 263)(59, 220)(60, 275)(61, 279)(62, 265)(63, 266)(64, 224)(65, 268)(66, 269)(67, 227)(68, 280)(69, 232)(70, 239)(71, 245)(72, 284)(73, 242)(74, 246)(75, 235)(76, 240)(77, 243)(78, 260)(79, 248)(80, 241)(81, 286)(82, 247)(83, 251)(84, 281)(85, 282)(86, 253)(87, 287)(88, 285)(89, 274)(90, 271)(91, 264)(92, 288)(93, 270)(94, 272)(95, 278)(96, 283)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 2, 16, 2, 16, 2, 16, 2, 16 ), ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ) } Outer automorphisms :: reflexible Dual of E23.924 Graph:: bipartite v = 40 e = 192 f = 108 degree seq :: [ 8^24, 12^16 ] E23.922 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 8}) Quotient :: dipole Aut^+ = (C4 x (C3 : C4)) : C2 (small group id <96, 44>) Aut = $<192, 757>$ (small group id <192, 757>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y1^-1 * Y2 * Y1^-2 * Y2^-1 * Y1^-1, Y1^6, Y2^-1 * Y1^-1 * Y2^2 * Y1 * Y2^-1, (Y1^-1 * Y2^-1)^4, Y2^8, (Y3^-1 * Y1^-1)^4 ] Map:: R = (1, 97, 2, 98, 6, 102, 18, 114, 13, 109, 4, 100)(3, 99, 9, 105, 27, 123, 44, 140, 19, 115, 11, 107)(5, 101, 15, 111, 35, 131, 45, 141, 20, 116, 16, 112)(7, 103, 21, 117, 12, 108, 34, 130, 41, 137, 23, 119)(8, 104, 24, 120, 14, 110, 36, 132, 42, 138, 25, 121)(10, 106, 22, 118, 43, 139, 70, 166, 55, 151, 31, 127)(17, 113, 26, 122, 46, 142, 71, 167, 66, 162, 37, 133)(28, 124, 52, 148, 32, 128, 53, 149, 73, 169, 57, 153)(29, 125, 58, 154, 33, 129, 63, 159, 74, 170, 59, 155)(30, 126, 56, 152, 85, 181, 93, 189, 72, 168, 61, 157)(38, 134, 47, 143, 39, 135, 50, 146, 75, 171, 64, 160)(40, 136, 68, 164, 89, 185, 94, 190, 76, 172, 69, 165)(48, 144, 78, 174, 51, 147, 82, 178, 65, 161, 79, 175)(49, 145, 77, 173, 62, 158, 87, 183, 90, 186, 81, 177)(54, 150, 83, 179, 67, 163, 86, 182, 91, 187, 84, 180)(60, 156, 80, 176, 92, 188, 96, 192, 95, 191, 88, 184)(193, 289, 195, 291, 202, 298, 222, 318, 252, 348, 232, 328, 209, 305, 197, 293)(194, 290, 199, 295, 214, 310, 241, 337, 272, 368, 246, 342, 218, 314, 200, 296)(196, 292, 204, 300, 223, 319, 254, 350, 280, 376, 259, 355, 229, 325, 206, 302)(198, 294, 211, 307, 235, 331, 264, 360, 284, 380, 268, 364, 238, 334, 212, 308)(201, 297, 220, 316, 248, 344, 271, 367, 260, 356, 230, 326, 207, 303, 221, 317)(203, 299, 224, 320, 253, 349, 270, 366, 261, 357, 231, 327, 208, 304, 225, 321)(205, 301, 219, 315, 247, 343, 277, 373, 287, 383, 281, 377, 258, 354, 227, 323)(210, 306, 233, 329, 262, 358, 282, 378, 288, 384, 283, 379, 263, 359, 234, 330)(213, 309, 239, 335, 269, 365, 250, 346, 275, 371, 244, 340, 216, 312, 240, 336)(215, 311, 242, 338, 273, 369, 255, 351, 276, 372, 245, 341, 217, 313, 243, 339)(226, 322, 256, 352, 279, 375, 251, 347, 278, 374, 249, 345, 228, 324, 257, 353)(236, 332, 265, 361, 285, 381, 274, 370, 286, 382, 267, 363, 237, 333, 266, 362) L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 211)(7, 214)(8, 194)(9, 220)(10, 222)(11, 224)(12, 223)(13, 219)(14, 196)(15, 221)(16, 225)(17, 197)(18, 233)(19, 235)(20, 198)(21, 239)(22, 241)(23, 242)(24, 240)(25, 243)(26, 200)(27, 247)(28, 248)(29, 201)(30, 252)(31, 254)(32, 253)(33, 203)(34, 256)(35, 205)(36, 257)(37, 206)(38, 207)(39, 208)(40, 209)(41, 262)(42, 210)(43, 264)(44, 265)(45, 266)(46, 212)(47, 269)(48, 213)(49, 272)(50, 273)(51, 215)(52, 216)(53, 217)(54, 218)(55, 277)(56, 271)(57, 228)(58, 275)(59, 278)(60, 232)(61, 270)(62, 280)(63, 276)(64, 279)(65, 226)(66, 227)(67, 229)(68, 230)(69, 231)(70, 282)(71, 234)(72, 284)(73, 285)(74, 236)(75, 237)(76, 238)(77, 250)(78, 261)(79, 260)(80, 246)(81, 255)(82, 286)(83, 244)(84, 245)(85, 287)(86, 249)(87, 251)(88, 259)(89, 258)(90, 288)(91, 263)(92, 268)(93, 274)(94, 267)(95, 281)(96, 283)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 2, 8, 2, 8, 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 E23.923 Graph:: bipartite v = 28 e = 192 f = 120 degree seq :: [ 12^16, 16^12 ] E23.923 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 8}) Quotient :: dipole Aut^+ = (C4 x (C3 : C4)) : C2 (small group id <96, 44>) Aut = $<192, 757>$ (small group id <192, 757>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y3^-1)^2, Y2^4, (R * Y3)^2, (R * Y1)^2, R * Y3 * Y2 * Y3^-1 * R * Y2, Y2 * Y3^2 * Y2^-1 * Y3^-2, Y3^-1 * Y2^-2 * Y3^-1 * Y2^-2 * Y3^-2, Y3^-2 * Y2^-1 * Y3^-1 * Y2^2 * Y3^-1 * Y2^-1, (Y3 * Y2^-1)^6, (Y3^-1 * Y1^-1)^8 ] Map:: polytopal R = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)(193, 289, 194, 290, 198, 294, 196, 292)(195, 291, 201, 297, 217, 313, 203, 299)(197, 293, 206, 302, 229, 325, 207, 303)(199, 295, 211, 307, 239, 335, 213, 309)(200, 296, 214, 310, 245, 341, 215, 311)(202, 298, 212, 308, 234, 330, 221, 317)(204, 300, 224, 320, 248, 344, 225, 321)(205, 301, 226, 322, 242, 338, 227, 323)(208, 304, 216, 312, 238, 334, 228, 324)(209, 305, 233, 329, 232, 328, 235, 331)(210, 306, 236, 332, 220, 316, 237, 333)(218, 314, 250, 346, 231, 327, 251, 347)(219, 315, 252, 348, 261, 357, 253, 349)(222, 318, 255, 351, 230, 326, 256, 352)(223, 319, 257, 353, 262, 358, 258, 354)(240, 336, 264, 360, 247, 343, 265, 361)(241, 337, 266, 362, 259, 355, 267, 363)(243, 339, 269, 365, 246, 342, 270, 366)(244, 340, 271, 367, 260, 356, 272, 368)(249, 345, 263, 359, 254, 350, 268, 364)(273, 369, 287, 383, 278, 374, 282, 378)(274, 370, 283, 379, 279, 375, 285, 381)(275, 371, 288, 384, 277, 373, 284, 380)(276, 372, 281, 377, 280, 376, 286, 382) L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 209)(7, 212)(8, 194)(9, 218)(10, 220)(11, 222)(12, 221)(13, 196)(14, 219)(15, 223)(16, 197)(17, 234)(18, 198)(19, 240)(20, 242)(21, 243)(22, 241)(23, 244)(24, 200)(25, 238)(26, 237)(27, 201)(28, 254)(29, 245)(30, 236)(31, 203)(32, 247)(33, 246)(34, 259)(35, 260)(36, 205)(37, 249)(38, 206)(39, 207)(40, 208)(41, 231)(42, 229)(43, 230)(44, 261)(45, 262)(46, 210)(47, 228)(48, 227)(49, 211)(50, 268)(51, 226)(52, 213)(53, 263)(54, 214)(55, 215)(56, 216)(57, 217)(58, 273)(59, 275)(60, 274)(61, 276)(62, 232)(63, 278)(64, 277)(65, 279)(66, 280)(67, 224)(68, 225)(69, 233)(70, 235)(71, 239)(72, 281)(73, 283)(74, 282)(75, 284)(76, 248)(77, 286)(78, 285)(79, 287)(80, 288)(81, 258)(82, 250)(83, 257)(84, 251)(85, 252)(86, 253)(87, 255)(88, 256)(89, 272)(90, 264)(91, 271)(92, 265)(93, 266)(94, 267)(95, 269)(96, 270)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 12, 16 ), ( 12, 16, 12, 16, 12, 16, 12, 16 ) } Outer automorphisms :: reflexible Dual of E23.922 Graph:: simple bipartite v = 120 e = 192 f = 28 degree seq :: [ 2^96, 8^24 ] E23.924 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 8}) Quotient :: dipole Aut^+ = (C4 x (C3 : C4)) : C2 (small group id <96, 44>) Aut = $<192, 757>$ (small group id <192, 757>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^4, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y1^-2 * Y3 * Y1^2 * Y3^-1, Y1^8, (Y3 * Y2^-1)^4, Y3^2 * Y1^-1 * Y3^2 * Y1^-3, (Y3^-1 * Y1^-1)^6 ] Map:: polytopal R = (1, 97, 2, 98, 6, 102, 17, 113, 41, 137, 34, 130, 13, 109, 4, 100)(3, 99, 9, 105, 18, 114, 44, 140, 69, 165, 65, 161, 30, 126, 11, 107)(5, 101, 15, 111, 19, 115, 46, 142, 70, 166, 58, 154, 35, 131, 16, 112)(7, 103, 20, 116, 42, 138, 71, 167, 63, 159, 33, 129, 12, 108, 22, 118)(8, 104, 23, 119, 43, 139, 72, 168, 62, 158, 36, 132, 14, 110, 24, 120)(10, 106, 27, 123, 45, 141, 32, 128, 50, 146, 21, 117, 49, 145, 28, 124)(25, 121, 57, 153, 40, 136, 68, 164, 38, 134, 64, 160, 29, 125, 59, 155)(26, 122, 60, 156, 39, 135, 67, 163, 37, 133, 66, 162, 31, 127, 61, 157)(47, 143, 73, 169, 56, 152, 80, 176, 54, 150, 77, 173, 51, 147, 74, 170)(48, 144, 75, 171, 55, 151, 79, 175, 53, 149, 78, 174, 52, 148, 76, 172)(81, 177, 92, 188, 88, 184, 90, 186, 86, 182, 95, 191, 83, 179, 93, 189)(82, 178, 96, 192, 87, 183, 94, 190, 85, 181, 91, 187, 84, 180, 89, 185)(193, 289)(194, 290)(195, 291)(196, 292)(197, 293)(198, 294)(199, 295)(200, 296)(201, 297)(202, 298)(203, 299)(204, 300)(205, 301)(206, 302)(207, 303)(208, 304)(209, 305)(210, 306)(211, 307)(212, 308)(213, 309)(214, 310)(215, 311)(216, 312)(217, 313)(218, 314)(219, 315)(220, 316)(221, 317)(222, 318)(223, 319)(224, 320)(225, 321)(226, 322)(227, 323)(228, 324)(229, 325)(230, 326)(231, 327)(232, 328)(233, 329)(234, 330)(235, 331)(236, 332)(237, 333)(238, 334)(239, 335)(240, 336)(241, 337)(242, 338)(243, 339)(244, 340)(245, 341)(246, 342)(247, 343)(248, 344)(249, 345)(250, 346)(251, 347)(252, 348)(253, 349)(254, 350)(255, 351)(256, 352)(257, 353)(258, 354)(259, 355)(260, 356)(261, 357)(262, 358)(263, 359)(264, 360)(265, 361)(266, 362)(267, 363)(268, 364)(269, 365)(270, 366)(271, 367)(272, 368)(273, 369)(274, 370)(275, 371)(276, 372)(277, 373)(278, 374)(279, 375)(280, 376)(281, 377)(282, 378)(283, 379)(284, 380)(285, 381)(286, 382)(287, 383)(288, 384) L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 210)(7, 213)(8, 194)(9, 217)(10, 197)(11, 221)(12, 224)(13, 222)(14, 196)(15, 229)(16, 231)(17, 234)(18, 237)(19, 198)(20, 239)(21, 200)(22, 243)(23, 245)(24, 247)(25, 250)(26, 201)(27, 254)(28, 235)(29, 238)(30, 241)(31, 203)(32, 206)(33, 246)(34, 255)(35, 205)(36, 240)(37, 257)(38, 207)(39, 236)(40, 208)(41, 261)(42, 220)(43, 209)(44, 232)(45, 211)(46, 223)(47, 228)(48, 212)(49, 227)(50, 262)(51, 264)(52, 214)(53, 225)(54, 215)(55, 263)(56, 216)(57, 273)(58, 218)(59, 275)(60, 277)(61, 279)(62, 226)(63, 219)(64, 278)(65, 230)(66, 274)(67, 276)(68, 280)(69, 242)(70, 233)(71, 248)(72, 244)(73, 281)(74, 283)(75, 285)(76, 287)(77, 286)(78, 282)(79, 284)(80, 288)(81, 258)(82, 249)(83, 259)(84, 251)(85, 256)(86, 252)(87, 260)(88, 253)(89, 270)(90, 265)(91, 271)(92, 266)(93, 269)(94, 267)(95, 272)(96, 268)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E23.921 Graph:: simple bipartite v = 108 e = 192 f = 40 degree seq :: [ 2^96, 16^12 ] E23.925 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 8}) Quotient :: dipole Aut^+ = (C4 x (C3 : C4)) : C2 (small group id <96, 44>) Aut = $<192, 757>$ (small group id <192, 757>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, (R * Y1)^2, Y1^-2 * Y3 * Y1^-1, (R * Y3)^2, (Y2^-1 * R * Y2^-1)^2, Y1 * Y2^2 * Y3 * Y2^-2, (R * Y2 * Y3^-1)^2, Y2^-2 * Y3^-1 * Y2^2 * Y1^-1, Y2 * Y3 * Y1^-1 * Y2 * Y3^-1 * Y2^2 * Y1, Y3 * Y2^-1 * Y3 * Y2^-2 * Y1^-1 * Y2^-1 * Y1^-1, Y3 * Y2^-1 * Y1 * Y2^-2 * Y3^-1 * Y2^-1 * Y1^-1, Y3 * Y1^-1 * Y2^-3 * Y1^-2 * Y2^-1, Y2^8, Y1^-1 * Y2^3 * Y3^-1 * Y1 * Y2 * Y1^-1, Y3^2 * Y2^-1 * Y1^-1 * Y2^-2 * Y3 * Y2^-1, Y3^-2 * Y2 * Y3 * Y1^-1 * Y2 * Y1^-1 * Y2^2 * Y1, Y3 * Y2 * Y1 * Y2 * Y3^-1 * Y2 * Y1 * Y2 * Y3^-1 * Y2^-1 * Y3 * Y2^-1 ] Map:: R = (1, 97, 2, 98, 6, 102, 4, 100)(3, 99, 9, 105, 25, 121, 11, 107)(5, 101, 14, 110, 37, 133, 15, 111)(7, 103, 19, 115, 47, 143, 21, 117)(8, 104, 22, 118, 53, 149, 23, 119)(10, 106, 20, 116, 42, 138, 29, 125)(12, 108, 32, 128, 56, 152, 33, 129)(13, 109, 34, 130, 50, 146, 35, 131)(16, 112, 24, 120, 46, 142, 36, 132)(17, 113, 41, 137, 40, 136, 43, 139)(18, 114, 44, 140, 28, 124, 45, 141)(26, 122, 58, 154, 39, 135, 59, 155)(27, 123, 60, 156, 69, 165, 61, 157)(30, 126, 63, 159, 38, 134, 64, 160)(31, 127, 65, 161, 70, 166, 66, 162)(48, 144, 72, 168, 55, 151, 73, 169)(49, 145, 74, 170, 67, 163, 75, 171)(51, 147, 77, 173, 54, 150, 78, 174)(52, 148, 79, 175, 68, 164, 80, 176)(57, 153, 71, 167, 62, 158, 76, 172)(81, 177, 92, 188, 86, 182, 96, 192)(82, 178, 94, 190, 87, 183, 89, 185)(83, 179, 90, 186, 85, 181, 95, 191)(84, 180, 93, 189, 88, 184, 91, 187)(193, 289, 195, 291, 202, 298, 220, 316, 254, 350, 232, 328, 208, 304, 197, 293)(194, 290, 199, 295, 212, 308, 242, 338, 268, 364, 248, 344, 216, 312, 200, 296)(196, 292, 204, 300, 221, 317, 245, 341, 263, 359, 239, 335, 228, 324, 205, 301)(198, 294, 209, 305, 234, 330, 229, 325, 249, 345, 217, 313, 238, 334, 210, 306)(201, 297, 218, 314, 237, 333, 262, 358, 235, 331, 230, 326, 206, 302, 219, 315)(203, 299, 222, 318, 236, 332, 261, 357, 233, 329, 231, 327, 207, 303, 223, 319)(211, 307, 240, 336, 227, 323, 260, 356, 225, 321, 246, 342, 214, 310, 241, 337)(213, 309, 243, 339, 226, 322, 259, 355, 224, 320, 247, 343, 215, 311, 244, 340)(250, 346, 273, 369, 258, 354, 280, 376, 256, 352, 277, 373, 252, 348, 274, 370)(251, 347, 275, 371, 257, 353, 279, 375, 255, 351, 278, 374, 253, 349, 276, 372)(264, 360, 281, 377, 272, 368, 288, 384, 270, 366, 285, 381, 266, 362, 282, 378)(265, 361, 283, 379, 271, 367, 287, 383, 269, 365, 286, 382, 267, 363, 284, 380) L = (1, 196)(2, 193)(3, 203)(4, 198)(5, 207)(6, 194)(7, 213)(8, 215)(9, 195)(10, 221)(11, 217)(12, 225)(13, 227)(14, 197)(15, 229)(16, 228)(17, 235)(18, 237)(19, 199)(20, 202)(21, 239)(22, 200)(23, 245)(24, 208)(25, 201)(26, 251)(27, 253)(28, 236)(29, 234)(30, 256)(31, 258)(32, 204)(33, 248)(34, 205)(35, 242)(36, 238)(37, 206)(38, 255)(39, 250)(40, 233)(41, 209)(42, 212)(43, 232)(44, 210)(45, 220)(46, 216)(47, 211)(48, 265)(49, 267)(50, 226)(51, 270)(52, 272)(53, 214)(54, 269)(55, 264)(56, 224)(57, 268)(58, 218)(59, 231)(60, 219)(61, 261)(62, 263)(63, 222)(64, 230)(65, 223)(66, 262)(67, 266)(68, 271)(69, 252)(70, 257)(71, 249)(72, 240)(73, 247)(74, 241)(75, 259)(76, 254)(77, 243)(78, 246)(79, 244)(80, 260)(81, 288)(82, 281)(83, 287)(84, 283)(85, 282)(86, 284)(87, 286)(88, 285)(89, 279)(90, 275)(91, 280)(92, 273)(93, 276)(94, 274)(95, 277)(96, 278)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 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 E23.926 Graph:: bipartite v = 36 e = 192 f = 112 degree seq :: [ 8^24, 16^12 ] E23.926 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 8}) Quotient :: dipole Aut^+ = (C4 x (C3 : C4)) : C2 (small group id <96, 44>) Aut = $<192, 757>$ (small group id <192, 757>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3 * Y1^-2 * Y3^-1 * Y1^-1, Y3^-1 * Y1 * Y3^2 * Y1^-1 * Y3^-1, Y1^6, (Y1^-1 * Y3^-1)^4, (Y3 * Y2^-1)^8 ] Map:: polytopal R = (1, 97, 2, 98, 6, 102, 18, 114, 13, 109, 4, 100)(3, 99, 9, 105, 27, 123, 44, 140, 19, 115, 11, 107)(5, 101, 15, 111, 35, 131, 45, 141, 20, 116, 16, 112)(7, 103, 21, 117, 12, 108, 34, 130, 41, 137, 23, 119)(8, 104, 24, 120, 14, 110, 36, 132, 42, 138, 25, 121)(10, 106, 22, 118, 43, 139, 70, 166, 55, 151, 31, 127)(17, 113, 26, 122, 46, 142, 71, 167, 66, 162, 37, 133)(28, 124, 52, 148, 32, 128, 53, 149, 73, 169, 57, 153)(29, 125, 58, 154, 33, 129, 63, 159, 74, 170, 59, 155)(30, 126, 56, 152, 85, 181, 93, 189, 72, 168, 61, 157)(38, 134, 47, 143, 39, 135, 50, 146, 75, 171, 64, 160)(40, 136, 68, 164, 89, 185, 94, 190, 76, 172, 69, 165)(48, 144, 78, 174, 51, 147, 82, 178, 65, 161, 79, 175)(49, 145, 77, 173, 62, 158, 87, 183, 90, 186, 81, 177)(54, 150, 83, 179, 67, 163, 86, 182, 91, 187, 84, 180)(60, 156, 80, 176, 92, 188, 96, 192, 95, 191, 88, 184)(193, 289)(194, 290)(195, 291)(196, 292)(197, 293)(198, 294)(199, 295)(200, 296)(201, 297)(202, 298)(203, 299)(204, 300)(205, 301)(206, 302)(207, 303)(208, 304)(209, 305)(210, 306)(211, 307)(212, 308)(213, 309)(214, 310)(215, 311)(216, 312)(217, 313)(218, 314)(219, 315)(220, 316)(221, 317)(222, 318)(223, 319)(224, 320)(225, 321)(226, 322)(227, 323)(228, 324)(229, 325)(230, 326)(231, 327)(232, 328)(233, 329)(234, 330)(235, 331)(236, 332)(237, 333)(238, 334)(239, 335)(240, 336)(241, 337)(242, 338)(243, 339)(244, 340)(245, 341)(246, 342)(247, 343)(248, 344)(249, 345)(250, 346)(251, 347)(252, 348)(253, 349)(254, 350)(255, 351)(256, 352)(257, 353)(258, 354)(259, 355)(260, 356)(261, 357)(262, 358)(263, 359)(264, 360)(265, 361)(266, 362)(267, 363)(268, 364)(269, 365)(270, 366)(271, 367)(272, 368)(273, 369)(274, 370)(275, 371)(276, 372)(277, 373)(278, 374)(279, 375)(280, 376)(281, 377)(282, 378)(283, 379)(284, 380)(285, 381)(286, 382)(287, 383)(288, 384) L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 211)(7, 214)(8, 194)(9, 220)(10, 222)(11, 224)(12, 223)(13, 219)(14, 196)(15, 221)(16, 225)(17, 197)(18, 233)(19, 235)(20, 198)(21, 239)(22, 241)(23, 242)(24, 240)(25, 243)(26, 200)(27, 247)(28, 248)(29, 201)(30, 252)(31, 254)(32, 253)(33, 203)(34, 256)(35, 205)(36, 257)(37, 206)(38, 207)(39, 208)(40, 209)(41, 262)(42, 210)(43, 264)(44, 265)(45, 266)(46, 212)(47, 269)(48, 213)(49, 272)(50, 273)(51, 215)(52, 216)(53, 217)(54, 218)(55, 277)(56, 271)(57, 228)(58, 275)(59, 278)(60, 232)(61, 270)(62, 280)(63, 276)(64, 279)(65, 226)(66, 227)(67, 229)(68, 230)(69, 231)(70, 282)(71, 234)(72, 284)(73, 285)(74, 236)(75, 237)(76, 238)(77, 250)(78, 261)(79, 260)(80, 246)(81, 255)(82, 286)(83, 244)(84, 245)(85, 287)(86, 249)(87, 251)(88, 259)(89, 258)(90, 288)(91, 263)(92, 268)(93, 274)(94, 267)(95, 281)(96, 283)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E23.925 Graph:: simple bipartite v = 112 e = 192 f = 36 degree seq :: [ 2^96, 12^16 ] E23.927 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 6, 8}) Quotient :: edge Aut^+ = SL(2,3) : C4 (small group id <96, 66>) Aut = $<192, 986>$ (small group id <192, 986>) |r| :: 2 Presentation :: [ F^2, T1^4, T1^4, (F * T2)^2, (F * T1)^2, T2^6, T1 * T2 * T1^-2 * T2^-1 * T1, T2^6, T2^-3 * T1 * T2^-3 * T1^-1, T1 * T2^-1 * T1^-1 * T2^2 * T1 * T2^-1 * T1^-1 * T2^-1, (T2^-1 * T1^-1)^8 ] Map:: non-degenerate R = (1, 3, 10, 28, 16, 5)(2, 7, 20, 45, 24, 8)(4, 12, 32, 63, 33, 13)(6, 17, 40, 72, 41, 18)(9, 25, 56, 38, 60, 26)(11, 30, 66, 39, 67, 31)(14, 34, 62, 27, 61, 35)(15, 36, 65, 29, 64, 37)(19, 42, 73, 53, 70, 43)(21, 47, 78, 54, 71, 48)(22, 49, 55, 44, 76, 50)(23, 51, 57, 46, 77, 52)(58, 83, 85, 81, 87, 68)(59, 84, 86, 82, 88, 69)(74, 91, 93, 89, 95, 79)(75, 92, 94, 90, 96, 80)(97, 98, 102, 100)(99, 105, 113, 107)(101, 110, 114, 111)(103, 115, 108, 117)(104, 118, 109, 119)(106, 123, 136, 125)(112, 134, 137, 135)(116, 140, 128, 142)(120, 149, 129, 150)(121, 151, 126, 153)(122, 154, 127, 155)(124, 141, 168, 159)(130, 164, 132, 165)(131, 166, 133, 167)(138, 161, 143, 158)(139, 170, 144, 171)(145, 175, 147, 176)(146, 163, 148, 156)(152, 177, 162, 178)(157, 181, 160, 182)(169, 185, 174, 186)(172, 189, 173, 190)(179, 191, 180, 192)(183, 187, 184, 188) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 16^4 ), ( 16^6 ) } Outer automorphisms :: reflexible Dual of E23.939 Transitivity :: ET+ Graph:: simple bipartite v = 40 e = 96 f = 12 degree seq :: [ 4^24, 6^16 ] E23.928 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 6, 8}) Quotient :: edge Aut^+ = SL(2,3) : C4 (small group id <96, 66>) Aut = $<192, 986>$ (small group id <192, 986>) |r| :: 2 Presentation :: [ F^2, T1^4, (F * T1)^2, (F * T2)^2, T1 * T2^-1 * T1^2 * T2 * T1, T2^6, T2 * T1 * T2^-3 * T1^-1 * T2^2, T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2^-2 * T1 * T2, T1^-1 * T2^2 * T1^-1 * T2^-1 * T1 * T2^-1 * T1^-1 * T2^-1, T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1 * T2^2 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 3, 10, 28, 16, 5)(2, 7, 20, 45, 24, 8)(4, 12, 32, 63, 33, 13)(6, 17, 40, 72, 41, 18)(9, 25, 56, 38, 60, 26)(11, 30, 66, 39, 67, 31)(14, 34, 62, 27, 61, 35)(15, 36, 65, 29, 64, 37)(19, 42, 73, 53, 71, 43)(21, 47, 78, 54, 70, 48)(22, 49, 57, 44, 76, 50)(23, 51, 55, 46, 77, 52)(58, 83, 86, 81, 88, 69)(59, 84, 85, 82, 87, 68)(74, 91, 94, 89, 96, 80)(75, 92, 93, 90, 95, 79)(97, 98, 102, 100)(99, 105, 113, 107)(101, 110, 114, 111)(103, 115, 108, 117)(104, 118, 109, 119)(106, 123, 136, 125)(112, 134, 137, 135)(116, 140, 128, 142)(120, 149, 129, 150)(121, 151, 126, 153)(122, 154, 127, 155)(124, 141, 168, 159)(130, 164, 132, 165)(131, 166, 133, 167)(138, 158, 143, 161)(139, 170, 144, 171)(145, 175, 147, 176)(146, 156, 148, 163)(152, 177, 162, 178)(157, 181, 160, 182)(169, 185, 174, 186)(172, 189, 173, 190)(179, 191, 180, 192)(183, 187, 184, 188) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 16^4 ), ( 16^6 ) } Outer automorphisms :: reflexible Dual of E23.940 Transitivity :: ET+ Graph:: simple bipartite v = 40 e = 96 f = 12 degree seq :: [ 4^24, 6^16 ] E23.929 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 6, 8}) Quotient :: edge Aut^+ = SL(2,3) : C4 (small group id <96, 66>) Aut = $<192, 986>$ (small group id <192, 986>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T1^-1 * T2^3 * T1^-1, T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1^-1 * T2^-1 * T1 * T2, (T2^-1 * T1^-1)^8 ] Map:: polytopal 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, 53, 56, 38, 55, 54)(39, 57, 60, 40, 59, 58)(41, 61, 64, 42, 63, 62)(43, 65, 68, 44, 67, 66)(45, 69, 72, 46, 71, 70)(47, 73, 76, 48, 75, 74)(49, 77, 80, 50, 79, 78)(51, 81, 84, 52, 83, 82)(85, 93, 87, 86, 94, 88)(89, 95, 91, 90, 96, 92)(97, 98, 102, 100)(99, 105, 112, 107)(101, 110, 106, 111)(103, 113, 108, 114)(104, 115, 109, 116)(117, 133, 119, 134)(118, 135, 120, 136)(121, 137, 123, 138)(122, 139, 124, 140)(125, 141, 127, 142)(126, 143, 128, 144)(129, 145, 131, 146)(130, 147, 132, 148)(149, 181, 151, 182)(150, 170, 152, 172)(153, 174, 155, 176)(154, 166, 156, 168)(157, 177, 159, 179)(158, 169, 160, 171)(161, 173, 163, 175)(162, 183, 164, 184)(165, 185, 167, 186)(178, 187, 180, 188)(189, 191, 190, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 16^4 ), ( 16^6 ) } Outer automorphisms :: reflexible Dual of E23.941 Transitivity :: ET+ Graph:: bipartite v = 40 e = 96 f = 12 degree seq :: [ 4^24, 6^16 ] E23.930 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 6, 8}) Quotient :: edge Aut^+ = SL(2,3) : C4 (small group id <96, 66>) Aut = $<192, 986>$ (small group id <192, 986>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^6, T2^2 * T1^-3 * T2^2, T2 * T1^-1 * T2^-1 * T1 * T2^-1 * T1^-1 * T2, (T1 * T2)^4, T2 * T1 * T2 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, T1 * T2 * T1^2 * T2 * T1 * T2^2, T2^2 * T1 * T2^-1 * T1 * T2^2 * T1^-1 * T2 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 3, 10, 31, 18, 52, 17, 5)(2, 7, 22, 40, 13, 39, 26, 8)(4, 12, 37, 20, 6, 19, 43, 14)(9, 28, 64, 79, 34, 68, 25, 29)(11, 33, 77, 71, 27, 70, 81, 35)(15, 45, 84, 60, 48, 87, 85, 46)(16, 47, 36, 72, 44, 83, 53, 49)(21, 58, 42, 80, 62, 91, 56, 59)(23, 32, 76, 92, 57, 51, 89, 63)(24, 65, 94, 78, 67, 86, 95, 66)(30, 55, 90, 88, 50, 41, 74, 75)(38, 69, 96, 73, 54, 61, 93, 82)(97, 98, 102, 114, 109, 100)(99, 105, 123, 148, 130, 107)(101, 111, 140, 127, 144, 112)(103, 117, 153, 135, 158, 119)(104, 120, 160, 136, 163, 121)(106, 126, 147, 113, 146, 128)(108, 132, 150, 115, 149, 134)(110, 137, 152, 116, 151, 138)(118, 156, 165, 122, 142, 157)(124, 154, 145, 164, 187, 168)(125, 169, 186, 175, 178, 170)(129, 133, 162, 166, 139, 174)(131, 141, 155, 167, 183, 176)(143, 159, 161, 179, 188, 182)(171, 191, 181, 184, 190, 180)(172, 173, 192, 185, 177, 189) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8^6 ), ( 8^8 ) } Outer automorphisms :: reflexible Dual of E23.943 Transitivity :: ET+ Graph:: bipartite v = 28 e = 96 f = 24 degree seq :: [ 6^16, 8^12 ] E23.931 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 6, 8}) Quotient :: edge Aut^+ = SL(2,3) : C4 (small group id <96, 66>) Aut = $<192, 986>$ (small group id <192, 986>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^6, T1^-1 * T2^-1 * T1^2 * T2^3, T1^-2 * T2^-3 * T1 * T2, (T2 * T1)^4, T1^-2 * T2^-1 * T1^-3 * T2 * T1^-1, T2 * T1 * T2 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, T1^2 * T2 * T1 * T2^2 * T1 * T2, T2^8, T2^2 * T1 * T2^-1 * T1 * T2^2 * T1^-1 * T2 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 3, 10, 31, 78, 52, 17, 5)(2, 7, 22, 36, 74, 44, 26, 8)(4, 12, 37, 34, 70, 25, 43, 14)(6, 19, 29, 9, 28, 66, 58, 20)(11, 33, 81, 80, 41, 76, 84, 35)(13, 39, 87, 55, 49, 16, 47, 40)(15, 45, 88, 65, 23, 64, 89, 46)(18, 53, 61, 21, 60, 42, 83, 54)(24, 67, 94, 82, 56, 90, 95, 68)(27, 73, 77, 30, 57, 85, 91, 50)(32, 79, 71, 59, 51, 92, 62, 48)(38, 72, 96, 75, 69, 63, 93, 86)(97, 98, 102, 114, 109, 100)(99, 105, 123, 149, 130, 107)(101, 111, 140, 150, 144, 112)(103, 117, 155, 135, 127, 119)(104, 120, 162, 136, 165, 121)(106, 126, 141, 157, 176, 128)(108, 132, 152, 115, 151, 134)(110, 137, 148, 116, 153, 138)(113, 146, 160, 179, 131, 147)(118, 158, 163, 183, 142, 159)(122, 167, 186, 143, 161, 168)(124, 156, 145, 166, 174, 170)(125, 171, 181, 133, 164, 172)(129, 154, 182, 169, 139, 178)(173, 191, 185, 177, 192, 188)(175, 187, 190, 184, 180, 189) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8^6 ), ( 8^8 ) } Outer automorphisms :: reflexible Dual of E23.944 Transitivity :: ET+ Graph:: simple bipartite v = 28 e = 96 f = 24 degree seq :: [ 6^16, 8^12 ] E23.932 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 6, 8}) Quotient :: edge Aut^+ = SL(2,3) : C4 (small group id <96, 66>) Aut = $<192, 986>$ (small group id <192, 986>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^2 * T2^-1 * T1^-1 * T2^-1, T1^6, T1^6, T2^8, T2^2 * T1^-1 * T2^-2 * T1^-1 * T2^2 * T1^-1, T2^2 * T1 * T2^-1 * T1 * T2^2 * T1^-1 * T2 * T1^-1 ] Map:: non-degenerate R = (1, 3, 10, 27, 59, 42, 17, 5)(2, 7, 21, 46, 85, 52, 23, 8)(4, 12, 31, 67, 94, 71, 35, 14)(6, 19, 43, 80, 93, 55, 25, 9)(11, 29, 63, 79, 81, 82, 66, 30)(13, 16, 38, 74, 95, 60, 70, 33)(15, 36, 72, 91, 58, 56, 73, 37)(18, 34, 65, 92, 96, 83, 44, 20)(22, 48, 88, 64, 84, 75, 89, 49)(24, 53, 77, 40, 76, 68, 57, 26)(28, 61, 45, 39, 41, 78, 50, 62)(32, 51, 90, 54, 87, 47, 86, 69)(97, 98, 102, 114, 109, 100)(99, 105, 120, 130, 110, 107)(101, 111, 103, 116, 135, 112)(104, 118, 115, 129, 128, 108)(106, 122, 152, 161, 126, 124)(113, 136, 132, 140, 175, 137)(117, 141, 171, 134, 133, 143)(119, 146, 144, 166, 187, 147)(121, 150, 149, 131, 160, 125)(123, 154, 148, 188, 158, 156)(127, 145, 178, 139, 165, 164)(138, 176, 172, 179, 163, 177)(142, 180, 151, 170, 183, 167)(153, 185, 169, 162, 182, 157)(155, 181, 189, 192, 191, 190)(159, 186, 174, 173, 184, 168) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8^6 ), ( 8^8 ) } Outer automorphisms :: reflexible Dual of E23.942 Transitivity :: ET+ Graph:: simple bipartite v = 28 e = 96 f = 24 degree seq :: [ 6^16, 8^12 ] E23.933 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 6, 8}) Quotient :: edge Aut^+ = SL(2,3) : C4 (small group id <96, 66>) Aut = $<192, 986>$ (small group id <192, 986>) |r| :: 2 Presentation :: [ F^2, T2^4, (F * T1)^2, (F * T2)^2, T2^-1 * T1^-1 * T2^2 * T1 * T2^-1, T1 * T2^-1 * T1 * T2 * T1 * T2, T1^8, T1 * T2 * T1^-1 * T2^-1 * T1^2 * T2 * T1^-1 * T2 * T1, T2 * T1^-4 * T2^-1 * T1^-4, T2 * T1^2 * T2^-1 * T1^-1 * T2^-1 * T1^2 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 3, 10, 5)(2, 7, 21, 8)(4, 12, 28, 14)(6, 18, 41, 19)(9, 26, 15, 27)(11, 23, 16, 20)(13, 31, 54, 33)(17, 38, 71, 39)(22, 43, 24, 40)(25, 50, 35, 51)(29, 55, 36, 57)(30, 59, 34, 60)(32, 62, 89, 63)(37, 68, 92, 69)(42, 73, 44, 70)(45, 80, 47, 81)(46, 82, 48, 84)(49, 86, 66, 83)(52, 88, 53, 87)(56, 72, 67, 74)(58, 91, 65, 90)(61, 79, 64, 85)(75, 93, 77, 94)(76, 95, 78, 96)(97, 98, 102, 113, 133, 128, 109, 100)(99, 105, 121, 145, 164, 152, 125, 107)(101, 111, 131, 162, 165, 163, 132, 112)(103, 116, 141, 175, 158, 179, 142, 118)(104, 119, 143, 181, 159, 182, 144, 120)(106, 117, 137, 167, 188, 185, 150, 124)(108, 126, 154, 168, 134, 166, 148, 122)(110, 130, 161, 170, 135, 169, 149, 123)(114, 136, 171, 155, 127, 157, 172, 138)(115, 139, 173, 156, 129, 160, 174, 140)(146, 183, 191, 177, 151, 186, 189, 180)(147, 184, 192, 176, 153, 187, 190, 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) :: { ( 12^4 ), ( 12^8 ) } Outer automorphisms :: reflexible Dual of E23.938 Transitivity :: ET+ Graph:: simple bipartite v = 36 e = 96 f = 16 degree seq :: [ 4^24, 8^12 ] E23.934 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 6, 8}) Quotient :: edge Aut^+ = SL(2,3) : C4 (small group id <96, 66>) Aut = $<192, 986>$ (small group id <192, 986>) |r| :: 2 Presentation :: [ F^2, T2^4, (F * T1)^2, (F * T2)^2, T1^-1 * T2^-2 * T1 * T2^2, T2 * T1 * T2^-2 * T1^-1 * T2, T2 * T1^-1 * T2^-1 * T1^3 * T2 * T1^-1, T2^-1 * T1 * T2^-1 * T1 * T2 * T1^-3, T1^8, T2 * T1^2 * T2^-1 * T1^2 * T2 * T1^-1 * T2^-1 * T1 * T2^-1 * T1^-1, (T2^-1 * T1^-1)^6 ] Map:: non-degenerate R = (1, 3, 10, 5)(2, 7, 21, 8)(4, 12, 28, 14)(6, 18, 45, 19)(9, 26, 15, 27)(11, 29, 16, 31)(13, 34, 61, 36)(17, 42, 75, 43)(20, 50, 23, 51)(22, 52, 24, 54)(25, 57, 39, 58)(30, 63, 40, 65)(32, 48, 37, 46)(33, 64, 38, 68)(35, 62, 91, 66)(41, 72, 92, 73)(44, 78, 47, 79)(49, 83, 55, 84)(53, 85, 56, 86)(59, 89, 60, 90)(67, 88, 71, 87)(69, 74, 70, 76)(77, 93, 81, 94)(80, 95, 82, 96)(97, 98, 102, 113, 137, 131, 109, 100)(99, 105, 121, 147, 168, 160, 126, 107)(101, 111, 135, 146, 169, 164, 136, 112)(103, 116, 145, 175, 158, 125, 149, 118)(104, 119, 151, 174, 162, 127, 152, 120)(106, 117, 141, 171, 188, 187, 157, 124)(108, 128, 156, 123, 138, 170, 163, 129)(110, 133, 155, 122, 139, 172, 167, 134)(114, 140, 173, 165, 130, 148, 176, 142)(115, 143, 177, 166, 132, 150, 178, 144)(153, 183, 191, 180, 159, 185, 189, 182)(154, 184, 192, 179, 161, 186, 190, 181) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 12^4 ), ( 12^8 ) } Outer automorphisms :: reflexible Dual of E23.936 Transitivity :: ET+ Graph:: simple bipartite v = 36 e = 96 f = 16 degree seq :: [ 4^24, 8^12 ] E23.935 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 6, 8}) Quotient :: edge Aut^+ = SL(2,3) : C4 (small group id <96, 66>) Aut = $<192, 986>$ (small group id <192, 986>) |r| :: 2 Presentation :: [ F^2, T2^4, T2^4, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-2 * T1^-1 * T2, T2^-1 * T1 * T2 * T1 * T2 * T1^-3, T1^8, T1^-1 * T2^-1 * T1^-2 * T2 * T1^-1 * T2 * T1^-2 * T2, T1^-3 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 3, 10, 5)(2, 7, 21, 8)(4, 12, 28, 14)(6, 18, 45, 19)(9, 26, 15, 27)(11, 29, 16, 31)(13, 34, 61, 36)(17, 42, 75, 43)(20, 50, 23, 51)(22, 52, 24, 54)(25, 57, 39, 58)(30, 63, 40, 65)(32, 46, 37, 48)(33, 67, 38, 64)(35, 66, 91, 62)(41, 72, 92, 73)(44, 78, 47, 79)(49, 83, 55, 84)(53, 85, 56, 86)(59, 89, 60, 90)(68, 88, 71, 87)(69, 76, 70, 74)(77, 93, 81, 94)(80, 95, 82, 96)(97, 98, 102, 113, 137, 131, 109, 100)(99, 105, 121, 146, 168, 160, 126, 107)(101, 111, 135, 147, 169, 163, 136, 112)(103, 116, 145, 174, 162, 127, 149, 118)(104, 119, 151, 175, 158, 125, 152, 120)(106, 117, 141, 171, 188, 187, 157, 124)(108, 128, 155, 122, 138, 170, 164, 129)(110, 133, 156, 123, 139, 172, 167, 134)(114, 140, 173, 165, 130, 150, 176, 142)(115, 143, 177, 166, 132, 148, 178, 144)(153, 183, 191, 180, 159, 186, 189, 182)(154, 184, 192, 179, 161, 185, 190, 181) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 12^4 ), ( 12^8 ) } Outer automorphisms :: reflexible Dual of E23.937 Transitivity :: ET+ Graph:: simple bipartite v = 36 e = 96 f = 16 degree seq :: [ 4^24, 8^12 ] E23.936 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 6, 8}) Quotient :: loop Aut^+ = SL(2,3) : C4 (small group id <96, 66>) Aut = $<192, 986>$ (small group id <192, 986>) |r| :: 2 Presentation :: [ F^2, T1^4, T1^4, (F * T2)^2, (F * T1)^2, T2^6, T1 * T2 * T1^-2 * T2^-1 * T1, T2^6, T2^-3 * T1 * T2^-3 * T1^-1, T1 * T2^-1 * T1^-1 * T2^2 * T1 * T2^-1 * T1^-1 * T2^-1, (T2^-1 * T1^-1)^8 ] Map:: non-degenerate R = (1, 97, 3, 99, 10, 106, 28, 124, 16, 112, 5, 101)(2, 98, 7, 103, 20, 116, 45, 141, 24, 120, 8, 104)(4, 100, 12, 108, 32, 128, 63, 159, 33, 129, 13, 109)(6, 102, 17, 113, 40, 136, 72, 168, 41, 137, 18, 114)(9, 105, 25, 121, 56, 152, 38, 134, 60, 156, 26, 122)(11, 107, 30, 126, 66, 162, 39, 135, 67, 163, 31, 127)(14, 110, 34, 130, 62, 158, 27, 123, 61, 157, 35, 131)(15, 111, 36, 132, 65, 161, 29, 125, 64, 160, 37, 133)(19, 115, 42, 138, 73, 169, 53, 149, 70, 166, 43, 139)(21, 117, 47, 143, 78, 174, 54, 150, 71, 167, 48, 144)(22, 118, 49, 145, 55, 151, 44, 140, 76, 172, 50, 146)(23, 119, 51, 147, 57, 153, 46, 142, 77, 173, 52, 148)(58, 154, 83, 179, 85, 181, 81, 177, 87, 183, 68, 164)(59, 155, 84, 180, 86, 182, 82, 178, 88, 184, 69, 165)(74, 170, 91, 187, 93, 189, 89, 185, 95, 191, 79, 175)(75, 171, 92, 188, 94, 190, 90, 186, 96, 192, 80, 176) L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 110)(6, 100)(7, 115)(8, 118)(9, 113)(10, 123)(11, 99)(12, 117)(13, 119)(14, 114)(15, 101)(16, 134)(17, 107)(18, 111)(19, 108)(20, 140)(21, 103)(22, 109)(23, 104)(24, 149)(25, 151)(26, 154)(27, 136)(28, 141)(29, 106)(30, 153)(31, 155)(32, 142)(33, 150)(34, 164)(35, 166)(36, 165)(37, 167)(38, 137)(39, 112)(40, 125)(41, 135)(42, 161)(43, 170)(44, 128)(45, 168)(46, 116)(47, 158)(48, 171)(49, 175)(50, 163)(51, 176)(52, 156)(53, 129)(54, 120)(55, 126)(56, 177)(57, 121)(58, 127)(59, 122)(60, 146)(61, 181)(62, 138)(63, 124)(64, 182)(65, 143)(66, 178)(67, 148)(68, 132)(69, 130)(70, 133)(71, 131)(72, 159)(73, 185)(74, 144)(75, 139)(76, 189)(77, 190)(78, 186)(79, 147)(80, 145)(81, 162)(82, 152)(83, 191)(84, 192)(85, 160)(86, 157)(87, 187)(88, 188)(89, 174)(90, 169)(91, 184)(92, 183)(93, 173)(94, 172)(95, 180)(96, 179) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E23.934 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 16 e = 96 f = 36 degree seq :: [ 12^16 ] E23.937 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 6, 8}) Quotient :: loop Aut^+ = SL(2,3) : C4 (small group id <96, 66>) Aut = $<192, 986>$ (small group id <192, 986>) |r| :: 2 Presentation :: [ F^2, T1^4, (F * T1)^2, (F * T2)^2, T1 * T2^-1 * T1^2 * T2 * T1, T2^6, T2 * T1 * T2^-3 * T1^-1 * T2^2, T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2^-2 * T1 * T2, T1^-1 * T2^2 * T1^-1 * T2^-1 * T1 * T2^-1 * T1^-1 * T2^-1, T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1 * T2^2 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 97, 3, 99, 10, 106, 28, 124, 16, 112, 5, 101)(2, 98, 7, 103, 20, 116, 45, 141, 24, 120, 8, 104)(4, 100, 12, 108, 32, 128, 63, 159, 33, 129, 13, 109)(6, 102, 17, 113, 40, 136, 72, 168, 41, 137, 18, 114)(9, 105, 25, 121, 56, 152, 38, 134, 60, 156, 26, 122)(11, 107, 30, 126, 66, 162, 39, 135, 67, 163, 31, 127)(14, 110, 34, 130, 62, 158, 27, 123, 61, 157, 35, 131)(15, 111, 36, 132, 65, 161, 29, 125, 64, 160, 37, 133)(19, 115, 42, 138, 73, 169, 53, 149, 71, 167, 43, 139)(21, 117, 47, 143, 78, 174, 54, 150, 70, 166, 48, 144)(22, 118, 49, 145, 57, 153, 44, 140, 76, 172, 50, 146)(23, 119, 51, 147, 55, 151, 46, 142, 77, 173, 52, 148)(58, 154, 83, 179, 86, 182, 81, 177, 88, 184, 69, 165)(59, 155, 84, 180, 85, 181, 82, 178, 87, 183, 68, 164)(74, 170, 91, 187, 94, 190, 89, 185, 96, 192, 80, 176)(75, 171, 92, 188, 93, 189, 90, 186, 95, 191, 79, 175) L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 110)(6, 100)(7, 115)(8, 118)(9, 113)(10, 123)(11, 99)(12, 117)(13, 119)(14, 114)(15, 101)(16, 134)(17, 107)(18, 111)(19, 108)(20, 140)(21, 103)(22, 109)(23, 104)(24, 149)(25, 151)(26, 154)(27, 136)(28, 141)(29, 106)(30, 153)(31, 155)(32, 142)(33, 150)(34, 164)(35, 166)(36, 165)(37, 167)(38, 137)(39, 112)(40, 125)(41, 135)(42, 158)(43, 170)(44, 128)(45, 168)(46, 116)(47, 161)(48, 171)(49, 175)(50, 156)(51, 176)(52, 163)(53, 129)(54, 120)(55, 126)(56, 177)(57, 121)(58, 127)(59, 122)(60, 148)(61, 181)(62, 143)(63, 124)(64, 182)(65, 138)(66, 178)(67, 146)(68, 132)(69, 130)(70, 133)(71, 131)(72, 159)(73, 185)(74, 144)(75, 139)(76, 189)(77, 190)(78, 186)(79, 147)(80, 145)(81, 162)(82, 152)(83, 191)(84, 192)(85, 160)(86, 157)(87, 187)(88, 188)(89, 174)(90, 169)(91, 184)(92, 183)(93, 173)(94, 172)(95, 180)(96, 179) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E23.935 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 16 e = 96 f = 36 degree seq :: [ 12^16 ] E23.938 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 6, 8}) Quotient :: loop Aut^+ = SL(2,3) : C4 (small group id <96, 66>) Aut = $<192, 986>$ (small group id <192, 986>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T1^-1 * T2^3 * T1^-1, T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1^-1 * T2^-1 * T1 * T2, (T2^-1 * T1^-1)^8 ] Map:: non-degenerate R = (1, 97, 3, 99, 10, 106, 6, 102, 16, 112, 5, 101)(2, 98, 7, 103, 13, 109, 4, 100, 12, 108, 8, 104)(9, 105, 21, 117, 24, 120, 11, 107, 23, 119, 22, 118)(14, 110, 25, 121, 28, 124, 15, 111, 27, 123, 26, 122)(17, 113, 29, 125, 32, 128, 18, 114, 31, 127, 30, 126)(19, 115, 33, 129, 36, 132, 20, 116, 35, 131, 34, 130)(37, 133, 53, 149, 56, 152, 38, 134, 55, 151, 54, 150)(39, 135, 57, 153, 60, 156, 40, 136, 59, 155, 58, 154)(41, 137, 61, 157, 64, 160, 42, 138, 63, 159, 62, 158)(43, 139, 65, 161, 68, 164, 44, 140, 67, 163, 66, 162)(45, 141, 69, 165, 72, 168, 46, 142, 71, 167, 70, 166)(47, 143, 73, 169, 76, 172, 48, 144, 75, 171, 74, 170)(49, 145, 77, 173, 80, 176, 50, 146, 79, 175, 78, 174)(51, 147, 81, 177, 84, 180, 52, 148, 83, 179, 82, 178)(85, 181, 93, 189, 87, 183, 86, 182, 94, 190, 88, 184)(89, 185, 95, 191, 91, 187, 90, 186, 96, 192, 92, 188) L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 110)(6, 100)(7, 113)(8, 115)(9, 112)(10, 111)(11, 99)(12, 114)(13, 116)(14, 106)(15, 101)(16, 107)(17, 108)(18, 103)(19, 109)(20, 104)(21, 133)(22, 135)(23, 134)(24, 136)(25, 137)(26, 139)(27, 138)(28, 140)(29, 141)(30, 143)(31, 142)(32, 144)(33, 145)(34, 147)(35, 146)(36, 148)(37, 119)(38, 117)(39, 120)(40, 118)(41, 123)(42, 121)(43, 124)(44, 122)(45, 127)(46, 125)(47, 128)(48, 126)(49, 131)(50, 129)(51, 132)(52, 130)(53, 181)(54, 170)(55, 182)(56, 172)(57, 174)(58, 166)(59, 176)(60, 168)(61, 177)(62, 169)(63, 179)(64, 171)(65, 173)(66, 183)(67, 175)(68, 184)(69, 185)(70, 156)(71, 186)(72, 154)(73, 160)(74, 152)(75, 158)(76, 150)(77, 163)(78, 155)(79, 161)(80, 153)(81, 159)(82, 187)(83, 157)(84, 188)(85, 151)(86, 149)(87, 164)(88, 162)(89, 167)(90, 165)(91, 180)(92, 178)(93, 191)(94, 192)(95, 190)(96, 189) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E23.933 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 16 e = 96 f = 36 degree seq :: [ 12^16 ] E23.939 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 6, 8}) Quotient :: loop Aut^+ = SL(2,3) : C4 (small group id <96, 66>) Aut = $<192, 986>$ (small group id <192, 986>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^6, T2^2 * T1^-3 * T2^2, T2 * T1^-1 * T2^-1 * T1 * T2^-1 * T1^-1 * T2, (T1 * T2)^4, T2 * T1 * T2 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, T1 * T2 * T1^2 * T2 * T1 * T2^2, T2^2 * T1 * T2^-1 * T1 * T2^2 * T1^-1 * T2 * T1^-1 ] Map:: non-degenerate R = (1, 97, 3, 99, 10, 106, 31, 127, 18, 114, 52, 148, 17, 113, 5, 101)(2, 98, 7, 103, 22, 118, 40, 136, 13, 109, 39, 135, 26, 122, 8, 104)(4, 100, 12, 108, 37, 133, 20, 116, 6, 102, 19, 115, 43, 139, 14, 110)(9, 105, 28, 124, 64, 160, 79, 175, 34, 130, 68, 164, 25, 121, 29, 125)(11, 107, 33, 129, 77, 173, 71, 167, 27, 123, 70, 166, 81, 177, 35, 131)(15, 111, 45, 141, 84, 180, 60, 156, 48, 144, 87, 183, 85, 181, 46, 142)(16, 112, 47, 143, 36, 132, 72, 168, 44, 140, 83, 179, 53, 149, 49, 145)(21, 117, 58, 154, 42, 138, 80, 176, 62, 158, 91, 187, 56, 152, 59, 155)(23, 119, 32, 128, 76, 172, 92, 188, 57, 153, 51, 147, 89, 185, 63, 159)(24, 120, 65, 161, 94, 190, 78, 174, 67, 163, 86, 182, 95, 191, 66, 162)(30, 126, 55, 151, 90, 186, 88, 184, 50, 146, 41, 137, 74, 170, 75, 171)(38, 134, 69, 165, 96, 192, 73, 169, 54, 150, 61, 157, 93, 189, 82, 178) L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 111)(6, 114)(7, 117)(8, 120)(9, 123)(10, 126)(11, 99)(12, 132)(13, 100)(14, 137)(15, 140)(16, 101)(17, 146)(18, 109)(19, 149)(20, 151)(21, 153)(22, 156)(23, 103)(24, 160)(25, 104)(26, 142)(27, 148)(28, 154)(29, 169)(30, 147)(31, 144)(32, 106)(33, 133)(34, 107)(35, 141)(36, 150)(37, 162)(38, 108)(39, 158)(40, 163)(41, 152)(42, 110)(43, 174)(44, 127)(45, 155)(46, 157)(47, 159)(48, 112)(49, 164)(50, 128)(51, 113)(52, 130)(53, 134)(54, 115)(55, 138)(56, 116)(57, 135)(58, 145)(59, 167)(60, 165)(61, 118)(62, 119)(63, 161)(64, 136)(65, 179)(66, 166)(67, 121)(68, 187)(69, 122)(70, 139)(71, 183)(72, 124)(73, 186)(74, 125)(75, 191)(76, 173)(77, 192)(78, 129)(79, 178)(80, 131)(81, 189)(82, 170)(83, 188)(84, 171)(85, 184)(86, 143)(87, 176)(88, 190)(89, 177)(90, 175)(91, 168)(92, 182)(93, 172)(94, 180)(95, 181)(96, 185) local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E23.927 Transitivity :: ET+ VT+ AT Graph:: v = 12 e = 96 f = 40 degree seq :: [ 16^12 ] E23.940 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 6, 8}) Quotient :: loop Aut^+ = SL(2,3) : C4 (small group id <96, 66>) Aut = $<192, 986>$ (small group id <192, 986>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^6, T1^-1 * T2^-1 * T1^2 * T2^3, T1^-2 * T2^-3 * T1 * T2, (T2 * T1)^4, T1^-2 * T2^-1 * T1^-3 * T2 * T1^-1, T2 * T1 * T2 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, T1^2 * T2 * T1 * T2^2 * T1 * T2, T2^8, T2^2 * T1 * T2^-1 * T1 * T2^2 * T1^-1 * T2 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 97, 3, 99, 10, 106, 31, 127, 78, 174, 52, 148, 17, 113, 5, 101)(2, 98, 7, 103, 22, 118, 36, 132, 74, 170, 44, 140, 26, 122, 8, 104)(4, 100, 12, 108, 37, 133, 34, 130, 70, 166, 25, 121, 43, 139, 14, 110)(6, 102, 19, 115, 29, 125, 9, 105, 28, 124, 66, 162, 58, 154, 20, 116)(11, 107, 33, 129, 81, 177, 80, 176, 41, 137, 76, 172, 84, 180, 35, 131)(13, 109, 39, 135, 87, 183, 55, 151, 49, 145, 16, 112, 47, 143, 40, 136)(15, 111, 45, 141, 88, 184, 65, 161, 23, 119, 64, 160, 89, 185, 46, 142)(18, 114, 53, 149, 61, 157, 21, 117, 60, 156, 42, 138, 83, 179, 54, 150)(24, 120, 67, 163, 94, 190, 82, 178, 56, 152, 90, 186, 95, 191, 68, 164)(27, 123, 73, 169, 77, 173, 30, 126, 57, 153, 85, 181, 91, 187, 50, 146)(32, 128, 79, 175, 71, 167, 59, 155, 51, 147, 92, 188, 62, 158, 48, 144)(38, 134, 72, 168, 96, 192, 75, 171, 69, 165, 63, 159, 93, 189, 86, 182) L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 111)(6, 114)(7, 117)(8, 120)(9, 123)(10, 126)(11, 99)(12, 132)(13, 100)(14, 137)(15, 140)(16, 101)(17, 146)(18, 109)(19, 151)(20, 153)(21, 155)(22, 158)(23, 103)(24, 162)(25, 104)(26, 167)(27, 149)(28, 156)(29, 171)(30, 141)(31, 119)(32, 106)(33, 154)(34, 107)(35, 147)(36, 152)(37, 164)(38, 108)(39, 127)(40, 165)(41, 148)(42, 110)(43, 178)(44, 150)(45, 157)(46, 159)(47, 161)(48, 112)(49, 166)(50, 160)(51, 113)(52, 116)(53, 130)(54, 144)(55, 134)(56, 115)(57, 138)(58, 182)(59, 135)(60, 145)(61, 176)(62, 163)(63, 118)(64, 179)(65, 168)(66, 136)(67, 183)(68, 172)(69, 121)(70, 174)(71, 186)(72, 122)(73, 139)(74, 124)(75, 181)(76, 125)(77, 191)(78, 170)(79, 187)(80, 128)(81, 192)(82, 129)(83, 131)(84, 189)(85, 133)(86, 169)(87, 142)(88, 180)(89, 177)(90, 143)(91, 190)(92, 173)(93, 175)(94, 184)(95, 185)(96, 188) local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E23.928 Transitivity :: ET+ VT+ AT Graph:: v = 12 e = 96 f = 40 degree seq :: [ 16^12 ] E23.941 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 6, 8}) Quotient :: loop Aut^+ = SL(2,3) : C4 (small group id <96, 66>) Aut = $<192, 986>$ (small group id <192, 986>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^2 * T2^-1 * T1^-1 * T2^-1, T1^6, T1^6, T2^8, T2^2 * T1^-1 * T2^-2 * T1^-1 * T2^2 * T1^-1, T2^2 * T1 * T2^-1 * T1 * T2^2 * T1^-1 * T2 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 97, 3, 99, 10, 106, 27, 123, 59, 155, 42, 138, 17, 113, 5, 101)(2, 98, 7, 103, 21, 117, 46, 142, 85, 181, 52, 148, 23, 119, 8, 104)(4, 100, 12, 108, 31, 127, 67, 163, 94, 190, 71, 167, 35, 131, 14, 110)(6, 102, 19, 115, 43, 139, 80, 176, 93, 189, 55, 151, 25, 121, 9, 105)(11, 107, 29, 125, 63, 159, 79, 175, 81, 177, 82, 178, 66, 162, 30, 126)(13, 109, 16, 112, 38, 134, 74, 170, 95, 191, 60, 156, 70, 166, 33, 129)(15, 111, 36, 132, 72, 168, 91, 187, 58, 154, 56, 152, 73, 169, 37, 133)(18, 114, 34, 130, 65, 161, 92, 188, 96, 192, 83, 179, 44, 140, 20, 116)(22, 118, 48, 144, 88, 184, 64, 160, 84, 180, 75, 171, 89, 185, 49, 145)(24, 120, 53, 149, 77, 173, 40, 136, 76, 172, 68, 164, 57, 153, 26, 122)(28, 124, 61, 157, 45, 141, 39, 135, 41, 137, 78, 174, 50, 146, 62, 158)(32, 128, 51, 147, 90, 186, 54, 150, 87, 183, 47, 143, 86, 182, 69, 165) L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 111)(6, 114)(7, 116)(8, 118)(9, 120)(10, 122)(11, 99)(12, 104)(13, 100)(14, 107)(15, 103)(16, 101)(17, 136)(18, 109)(19, 129)(20, 135)(21, 141)(22, 115)(23, 146)(24, 130)(25, 150)(26, 152)(27, 154)(28, 106)(29, 121)(30, 124)(31, 145)(32, 108)(33, 128)(34, 110)(35, 160)(36, 140)(37, 143)(38, 133)(39, 112)(40, 132)(41, 113)(42, 176)(43, 165)(44, 175)(45, 171)(46, 180)(47, 117)(48, 166)(49, 178)(50, 144)(51, 119)(52, 188)(53, 131)(54, 149)(55, 170)(56, 161)(57, 185)(58, 148)(59, 181)(60, 123)(61, 153)(62, 156)(63, 186)(64, 125)(65, 126)(66, 182)(67, 177)(68, 127)(69, 164)(70, 187)(71, 142)(72, 159)(73, 162)(74, 183)(75, 134)(76, 179)(77, 184)(78, 173)(79, 137)(80, 172)(81, 138)(82, 139)(83, 163)(84, 151)(85, 189)(86, 157)(87, 167)(88, 168)(89, 169)(90, 174)(91, 147)(92, 158)(93, 192)(94, 155)(95, 190)(96, 191) local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E23.929 Transitivity :: ET+ VT+ AT Graph:: v = 12 e = 96 f = 40 degree seq :: [ 16^12 ] E23.942 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 6, 8}) Quotient :: loop Aut^+ = SL(2,3) : C4 (small group id <96, 66>) Aut = $<192, 986>$ (small group id <192, 986>) |r| :: 2 Presentation :: [ F^2, T2^4, (F * T1)^2, (F * T2)^2, T2^-1 * T1^-1 * T2^2 * T1 * T2^-1, T1 * T2^-1 * T1 * T2 * T1 * T2, T1^8, T1 * T2 * T1^-1 * T2^-1 * T1^2 * T2 * T1^-1 * T2 * T1, T2 * T1^-4 * T2^-1 * T1^-4, T2 * T1^2 * T2^-1 * T1^-1 * T2^-1 * T1^2 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 97, 3, 99, 10, 106, 5, 101)(2, 98, 7, 103, 21, 117, 8, 104)(4, 100, 12, 108, 28, 124, 14, 110)(6, 102, 18, 114, 41, 137, 19, 115)(9, 105, 26, 122, 15, 111, 27, 123)(11, 107, 23, 119, 16, 112, 20, 116)(13, 109, 31, 127, 54, 150, 33, 129)(17, 113, 38, 134, 71, 167, 39, 135)(22, 118, 43, 139, 24, 120, 40, 136)(25, 121, 50, 146, 35, 131, 51, 147)(29, 125, 55, 151, 36, 132, 57, 153)(30, 126, 59, 155, 34, 130, 60, 156)(32, 128, 62, 158, 89, 185, 63, 159)(37, 133, 68, 164, 92, 188, 69, 165)(42, 138, 73, 169, 44, 140, 70, 166)(45, 141, 80, 176, 47, 143, 81, 177)(46, 142, 82, 178, 48, 144, 84, 180)(49, 145, 86, 182, 66, 162, 83, 179)(52, 148, 88, 184, 53, 149, 87, 183)(56, 152, 72, 168, 67, 163, 74, 170)(58, 154, 91, 187, 65, 161, 90, 186)(61, 157, 79, 175, 64, 160, 85, 181)(75, 171, 93, 189, 77, 173, 94, 190)(76, 172, 95, 191, 78, 174, 96, 192) L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 111)(6, 113)(7, 116)(8, 119)(9, 121)(10, 117)(11, 99)(12, 126)(13, 100)(14, 130)(15, 131)(16, 101)(17, 133)(18, 136)(19, 139)(20, 141)(21, 137)(22, 103)(23, 143)(24, 104)(25, 145)(26, 108)(27, 110)(28, 106)(29, 107)(30, 154)(31, 157)(32, 109)(33, 160)(34, 161)(35, 162)(36, 112)(37, 128)(38, 166)(39, 169)(40, 171)(41, 167)(42, 114)(43, 173)(44, 115)(45, 175)(46, 118)(47, 181)(48, 120)(49, 164)(50, 183)(51, 184)(52, 122)(53, 123)(54, 124)(55, 186)(56, 125)(57, 187)(58, 168)(59, 127)(60, 129)(61, 172)(62, 179)(63, 182)(64, 174)(65, 170)(66, 165)(67, 132)(68, 152)(69, 163)(70, 148)(71, 188)(72, 134)(73, 149)(74, 135)(75, 155)(76, 138)(77, 156)(78, 140)(79, 158)(80, 153)(81, 151)(82, 147)(83, 142)(84, 146)(85, 159)(86, 144)(87, 191)(88, 192)(89, 150)(90, 189)(91, 190)(92, 185)(93, 180)(94, 178)(95, 177)(96, 176) local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E23.932 Transitivity :: ET+ VT+ AT Graph:: v = 24 e = 96 f = 28 degree seq :: [ 8^24 ] E23.943 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 6, 8}) Quotient :: loop Aut^+ = SL(2,3) : C4 (small group id <96, 66>) Aut = $<192, 986>$ (small group id <192, 986>) |r| :: 2 Presentation :: [ F^2, T2^4, (F * T1)^2, (F * T2)^2, T1^-1 * T2^-2 * T1 * T2^2, T2 * T1 * T2^-2 * T1^-1 * T2, T2 * T1^-1 * T2^-1 * T1^3 * T2 * T1^-1, T2^-1 * T1 * T2^-1 * T1 * T2 * T1^-3, T1^8, T2 * T1^2 * T2^-1 * T1^2 * T2 * T1^-1 * T2^-1 * T1 * T2^-1 * T1^-1, (T2^-1 * T1^-1)^6 ] Map:: polytopal non-degenerate R = (1, 97, 3, 99, 10, 106, 5, 101)(2, 98, 7, 103, 21, 117, 8, 104)(4, 100, 12, 108, 28, 124, 14, 110)(6, 102, 18, 114, 45, 141, 19, 115)(9, 105, 26, 122, 15, 111, 27, 123)(11, 107, 29, 125, 16, 112, 31, 127)(13, 109, 34, 130, 61, 157, 36, 132)(17, 113, 42, 138, 75, 171, 43, 139)(20, 116, 50, 146, 23, 119, 51, 147)(22, 118, 52, 148, 24, 120, 54, 150)(25, 121, 57, 153, 39, 135, 58, 154)(30, 126, 63, 159, 40, 136, 65, 161)(32, 128, 48, 144, 37, 133, 46, 142)(33, 129, 64, 160, 38, 134, 68, 164)(35, 131, 62, 158, 91, 187, 66, 162)(41, 137, 72, 168, 92, 188, 73, 169)(44, 140, 78, 174, 47, 143, 79, 175)(49, 145, 83, 179, 55, 151, 84, 180)(53, 149, 85, 181, 56, 152, 86, 182)(59, 155, 89, 185, 60, 156, 90, 186)(67, 163, 88, 184, 71, 167, 87, 183)(69, 165, 74, 170, 70, 166, 76, 172)(77, 173, 93, 189, 81, 177, 94, 190)(80, 176, 95, 191, 82, 178, 96, 192) L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 111)(6, 113)(7, 116)(8, 119)(9, 121)(10, 117)(11, 99)(12, 128)(13, 100)(14, 133)(15, 135)(16, 101)(17, 137)(18, 140)(19, 143)(20, 145)(21, 141)(22, 103)(23, 151)(24, 104)(25, 147)(26, 139)(27, 138)(28, 106)(29, 149)(30, 107)(31, 152)(32, 156)(33, 108)(34, 148)(35, 109)(36, 150)(37, 155)(38, 110)(39, 146)(40, 112)(41, 131)(42, 170)(43, 172)(44, 173)(45, 171)(46, 114)(47, 177)(48, 115)(49, 175)(50, 169)(51, 168)(52, 176)(53, 118)(54, 178)(55, 174)(56, 120)(57, 183)(58, 184)(59, 122)(60, 123)(61, 124)(62, 125)(63, 185)(64, 126)(65, 186)(66, 127)(67, 129)(68, 136)(69, 130)(70, 132)(71, 134)(72, 160)(73, 164)(74, 163)(75, 188)(76, 167)(77, 165)(78, 162)(79, 158)(80, 142)(81, 166)(82, 144)(83, 161)(84, 159)(85, 154)(86, 153)(87, 191)(88, 192)(89, 189)(90, 190)(91, 157)(92, 187)(93, 182)(94, 181)(95, 180)(96, 179) local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E23.930 Transitivity :: ET+ VT+ AT Graph:: v = 24 e = 96 f = 28 degree seq :: [ 8^24 ] E23.944 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 6, 8}) Quotient :: loop Aut^+ = SL(2,3) : C4 (small group id <96, 66>) Aut = $<192, 986>$ (small group id <192, 986>) |r| :: 2 Presentation :: [ F^2, T2^4, T2^4, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-2 * T1^-1 * T2, T2^-1 * T1 * T2 * T1 * T2 * T1^-3, T1^8, T1^-1 * T2^-1 * T1^-2 * T2 * T1^-1 * T2 * T1^-2 * T2, T1^-3 * T2^-2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 97, 3, 99, 10, 106, 5, 101)(2, 98, 7, 103, 21, 117, 8, 104)(4, 100, 12, 108, 28, 124, 14, 110)(6, 102, 18, 114, 45, 141, 19, 115)(9, 105, 26, 122, 15, 111, 27, 123)(11, 107, 29, 125, 16, 112, 31, 127)(13, 109, 34, 130, 61, 157, 36, 132)(17, 113, 42, 138, 75, 171, 43, 139)(20, 116, 50, 146, 23, 119, 51, 147)(22, 118, 52, 148, 24, 120, 54, 150)(25, 121, 57, 153, 39, 135, 58, 154)(30, 126, 63, 159, 40, 136, 65, 161)(32, 128, 46, 142, 37, 133, 48, 144)(33, 129, 67, 163, 38, 134, 64, 160)(35, 131, 66, 162, 91, 187, 62, 158)(41, 137, 72, 168, 92, 188, 73, 169)(44, 140, 78, 174, 47, 143, 79, 175)(49, 145, 83, 179, 55, 151, 84, 180)(53, 149, 85, 181, 56, 152, 86, 182)(59, 155, 89, 185, 60, 156, 90, 186)(68, 164, 88, 184, 71, 167, 87, 183)(69, 165, 76, 172, 70, 166, 74, 170)(77, 173, 93, 189, 81, 177, 94, 190)(80, 176, 95, 191, 82, 178, 96, 192) L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 111)(6, 113)(7, 116)(8, 119)(9, 121)(10, 117)(11, 99)(12, 128)(13, 100)(14, 133)(15, 135)(16, 101)(17, 137)(18, 140)(19, 143)(20, 145)(21, 141)(22, 103)(23, 151)(24, 104)(25, 146)(26, 138)(27, 139)(28, 106)(29, 152)(30, 107)(31, 149)(32, 155)(33, 108)(34, 150)(35, 109)(36, 148)(37, 156)(38, 110)(39, 147)(40, 112)(41, 131)(42, 170)(43, 172)(44, 173)(45, 171)(46, 114)(47, 177)(48, 115)(49, 174)(50, 168)(51, 169)(52, 178)(53, 118)(54, 176)(55, 175)(56, 120)(57, 183)(58, 184)(59, 122)(60, 123)(61, 124)(62, 125)(63, 186)(64, 126)(65, 185)(66, 127)(67, 136)(68, 129)(69, 130)(70, 132)(71, 134)(72, 160)(73, 163)(74, 164)(75, 188)(76, 167)(77, 165)(78, 162)(79, 158)(80, 142)(81, 166)(82, 144)(83, 161)(84, 159)(85, 154)(86, 153)(87, 191)(88, 192)(89, 190)(90, 189)(91, 157)(92, 187)(93, 182)(94, 181)(95, 180)(96, 179) local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E23.931 Transitivity :: ET+ VT+ AT Graph:: v = 24 e = 96 f = 28 degree seq :: [ 8^24 ] E23.945 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 8}) Quotient :: dipole Aut^+ = SL(2,3) : C4 (small group id <96, 66>) Aut = $<192, 986>$ (small group id <192, 986>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, Y1^3 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y3 * Y2^-1 * Y1^-2 * Y2 * Y1^-1, Y2^6, (R * Y2 * Y3^-1)^2, Y3 * Y1^-1 * Y2 * Y1 * Y3^-1 * Y2^-1, R * Y2^-2 * Y1^-1 * R * Y2^-2 * Y3, Y2^-3 * Y1 * Y2^-3 * Y1^-1, Y2^2 * Y3 * Y2^-3 * Y3^-1 * Y2, Y1 * Y2 * Y1 * Y2^-2 * Y1 * Y2 * Y3^-1 * Y2, Y3 * Y2^-2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2, Y1 * Y2 * Y1 * Y2 * Y3 * Y2 * Y1^-1 * Y2^-2, (Y3 * Y2^-1)^8 ] Map:: R = (1, 97, 2, 98, 6, 102, 4, 100)(3, 99, 9, 105, 17, 113, 11, 107)(5, 101, 14, 110, 18, 114, 15, 111)(7, 103, 19, 115, 12, 108, 21, 117)(8, 104, 22, 118, 13, 109, 23, 119)(10, 106, 27, 123, 40, 136, 29, 125)(16, 112, 38, 134, 41, 137, 39, 135)(20, 116, 44, 140, 32, 128, 46, 142)(24, 120, 53, 149, 33, 129, 54, 150)(25, 121, 55, 151, 30, 126, 57, 153)(26, 122, 58, 154, 31, 127, 59, 155)(28, 124, 45, 141, 72, 168, 63, 159)(34, 130, 68, 164, 36, 132, 69, 165)(35, 131, 70, 166, 37, 133, 71, 167)(42, 138, 65, 161, 47, 143, 62, 158)(43, 139, 74, 170, 48, 144, 75, 171)(49, 145, 79, 175, 51, 147, 80, 176)(50, 146, 67, 163, 52, 148, 60, 156)(56, 152, 81, 177, 66, 162, 82, 178)(61, 157, 85, 181, 64, 160, 86, 182)(73, 169, 89, 185, 78, 174, 90, 186)(76, 172, 93, 189, 77, 173, 94, 190)(83, 179, 95, 191, 84, 180, 96, 192)(87, 183, 91, 187, 88, 184, 92, 188)(193, 289, 195, 291, 202, 298, 220, 316, 208, 304, 197, 293)(194, 290, 199, 295, 212, 308, 237, 333, 216, 312, 200, 296)(196, 292, 204, 300, 224, 320, 255, 351, 225, 321, 205, 301)(198, 294, 209, 305, 232, 328, 264, 360, 233, 329, 210, 306)(201, 297, 217, 313, 248, 344, 230, 326, 252, 348, 218, 314)(203, 299, 222, 318, 258, 354, 231, 327, 259, 355, 223, 319)(206, 302, 226, 322, 254, 350, 219, 315, 253, 349, 227, 323)(207, 303, 228, 324, 257, 353, 221, 317, 256, 352, 229, 325)(211, 307, 234, 330, 265, 361, 245, 341, 262, 358, 235, 331)(213, 309, 239, 335, 270, 366, 246, 342, 263, 359, 240, 336)(214, 310, 241, 337, 247, 343, 236, 332, 268, 364, 242, 338)(215, 311, 243, 339, 249, 345, 238, 334, 269, 365, 244, 340)(250, 346, 275, 371, 277, 373, 273, 369, 279, 375, 260, 356)(251, 347, 276, 372, 278, 374, 274, 370, 280, 376, 261, 357)(266, 362, 283, 379, 285, 381, 281, 377, 287, 383, 271, 367)(267, 363, 284, 380, 286, 382, 282, 378, 288, 384, 272, 368) L = (1, 196)(2, 193)(3, 203)(4, 198)(5, 207)(6, 194)(7, 213)(8, 215)(9, 195)(10, 221)(11, 209)(12, 211)(13, 214)(14, 197)(15, 210)(16, 231)(17, 201)(18, 206)(19, 199)(20, 238)(21, 204)(22, 200)(23, 205)(24, 246)(25, 249)(26, 251)(27, 202)(28, 255)(29, 232)(30, 247)(31, 250)(32, 236)(33, 245)(34, 261)(35, 263)(36, 260)(37, 262)(38, 208)(39, 233)(40, 219)(41, 230)(42, 254)(43, 267)(44, 212)(45, 220)(46, 224)(47, 257)(48, 266)(49, 272)(50, 252)(51, 271)(52, 259)(53, 216)(54, 225)(55, 217)(56, 274)(57, 222)(58, 218)(59, 223)(60, 244)(61, 278)(62, 239)(63, 264)(64, 277)(65, 234)(66, 273)(67, 242)(68, 226)(69, 228)(70, 227)(71, 229)(72, 237)(73, 282)(74, 235)(75, 240)(76, 286)(77, 285)(78, 281)(79, 241)(80, 243)(81, 248)(82, 258)(83, 288)(84, 287)(85, 253)(86, 256)(87, 284)(88, 283)(89, 265)(90, 270)(91, 279)(92, 280)(93, 268)(94, 269)(95, 275)(96, 276)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 2, 16, 2, 16, 2, 16, 2, 16 ), ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ) } Outer automorphisms :: reflexible Dual of E23.955 Graph:: bipartite v = 40 e = 192 f = 108 degree seq :: [ 8^24, 12^16 ] E23.946 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 8}) Quotient :: dipole Aut^+ = SL(2,3) : C4 (small group id <96, 66>) Aut = $<192, 986>$ (small group id <192, 986>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, Y3 * Y1, Y3^3 * Y1^-1, (R * Y1)^2, Y1^4, (Y3 * Y1^-1)^2, (R * Y3)^2, Y3^-1 * Y2^-1 * Y1^-1 * Y3 * Y2 * Y3^-1, Y1 * Y3^-1 * Y2 * Y1^-1 * Y3 * Y2^-1, Y2^6, (R * Y2 * Y3^-1)^2, Y1^-2 * Y2 * Y3 * Y1^-1 * Y2^-1, R * Y2^-2 * R * Y3^-1 * Y2^-2 * Y1^-1, Y2^-3 * Y1 * Y2^-3 * Y1^-1, Y3 * Y2^-3 * Y3^-1 * Y2^-3, Y1 * Y2^-1 * Y3 * Y2^-1 * Y3^-1 * Y2^2 * Y3^-1 * Y2^-1, Y1 * Y2^2 * Y3 * Y2^-1 * Y3^-1 * Y2^-1 * Y1 * Y2^-1, Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y3^-1 * Y2^-1 * Y1^-1 * Y2, Y2^-1 * Y3 * Y2 * Y1 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2^-1, (Y3 * Y2^-1)^8 ] Map:: R = (1, 97, 2, 98, 6, 102, 4, 100)(3, 99, 9, 105, 17, 113, 11, 107)(5, 101, 14, 110, 18, 114, 15, 111)(7, 103, 19, 115, 12, 108, 21, 117)(8, 104, 22, 118, 13, 109, 23, 119)(10, 106, 27, 123, 40, 136, 29, 125)(16, 112, 38, 134, 41, 137, 39, 135)(20, 116, 44, 140, 32, 128, 46, 142)(24, 120, 53, 149, 33, 129, 54, 150)(25, 121, 55, 151, 30, 126, 57, 153)(26, 122, 58, 154, 31, 127, 59, 155)(28, 124, 45, 141, 72, 168, 63, 159)(34, 130, 68, 164, 36, 132, 69, 165)(35, 131, 70, 166, 37, 133, 71, 167)(42, 138, 62, 158, 47, 143, 65, 161)(43, 139, 74, 170, 48, 144, 75, 171)(49, 145, 79, 175, 51, 147, 80, 176)(50, 146, 60, 156, 52, 148, 67, 163)(56, 152, 81, 177, 66, 162, 82, 178)(61, 157, 85, 181, 64, 160, 86, 182)(73, 169, 89, 185, 78, 174, 90, 186)(76, 172, 93, 189, 77, 173, 94, 190)(83, 179, 95, 191, 84, 180, 96, 192)(87, 183, 91, 187, 88, 184, 92, 188)(193, 289, 195, 291, 202, 298, 220, 316, 208, 304, 197, 293)(194, 290, 199, 295, 212, 308, 237, 333, 216, 312, 200, 296)(196, 292, 204, 300, 224, 320, 255, 351, 225, 321, 205, 301)(198, 294, 209, 305, 232, 328, 264, 360, 233, 329, 210, 306)(201, 297, 217, 313, 248, 344, 230, 326, 252, 348, 218, 314)(203, 299, 222, 318, 258, 354, 231, 327, 259, 355, 223, 319)(206, 302, 226, 322, 254, 350, 219, 315, 253, 349, 227, 323)(207, 303, 228, 324, 257, 353, 221, 317, 256, 352, 229, 325)(211, 307, 234, 330, 265, 361, 245, 341, 263, 359, 235, 331)(213, 309, 239, 335, 270, 366, 246, 342, 262, 358, 240, 336)(214, 310, 241, 337, 249, 345, 236, 332, 268, 364, 242, 338)(215, 311, 243, 339, 247, 343, 238, 334, 269, 365, 244, 340)(250, 346, 275, 371, 278, 374, 273, 369, 280, 376, 261, 357)(251, 347, 276, 372, 277, 373, 274, 370, 279, 375, 260, 356)(266, 362, 283, 379, 286, 382, 281, 377, 288, 384, 272, 368)(267, 363, 284, 380, 285, 381, 282, 378, 287, 383, 271, 367) L = (1, 196)(2, 193)(3, 203)(4, 198)(5, 207)(6, 194)(7, 213)(8, 215)(9, 195)(10, 221)(11, 209)(12, 211)(13, 214)(14, 197)(15, 210)(16, 231)(17, 201)(18, 206)(19, 199)(20, 238)(21, 204)(22, 200)(23, 205)(24, 246)(25, 249)(26, 251)(27, 202)(28, 255)(29, 232)(30, 247)(31, 250)(32, 236)(33, 245)(34, 261)(35, 263)(36, 260)(37, 262)(38, 208)(39, 233)(40, 219)(41, 230)(42, 257)(43, 267)(44, 212)(45, 220)(46, 224)(47, 254)(48, 266)(49, 272)(50, 259)(51, 271)(52, 252)(53, 216)(54, 225)(55, 217)(56, 274)(57, 222)(58, 218)(59, 223)(60, 242)(61, 278)(62, 234)(63, 264)(64, 277)(65, 239)(66, 273)(67, 244)(68, 226)(69, 228)(70, 227)(71, 229)(72, 237)(73, 282)(74, 235)(75, 240)(76, 286)(77, 285)(78, 281)(79, 241)(80, 243)(81, 248)(82, 258)(83, 288)(84, 287)(85, 253)(86, 256)(87, 284)(88, 283)(89, 265)(90, 270)(91, 279)(92, 280)(93, 268)(94, 269)(95, 275)(96, 276)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 2, 16, 2, 16, 2, 16, 2, 16 ), ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ) } Outer automorphisms :: reflexible Dual of E23.954 Graph:: bipartite v = 40 e = 192 f = 108 degree seq :: [ 8^24, 12^16 ] E23.947 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 8}) Quotient :: dipole Aut^+ = SL(2,3) : C4 (small group id <96, 66>) Aut = $<192, 986>$ (small group id <192, 986>) |r| :: 2 Presentation :: [ R^2, Y1 * Y3, Y1^4, (R * Y1)^2, (Y1^-1 * Y3)^2, (R * Y3)^2, Y3 * Y2^3 * Y1^-1, (R * Y2 * Y3^-1)^2, Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y3^-1 * Y2 * Y1^-1 * Y2 * Y1^-2 * Y3, Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y3 * Y2 * Y3^-1 * Y2 * Y1^-1 * Y2^-1 * Y1^-1, Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2 * Y1^-1, Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y3 * Y2^-1 * Y3^-1 * Y2 * Y1^-1 * Y2 * Y1^-1, (Y3 * Y2^-1)^8 ] Map:: R = (1, 97, 2, 98, 6, 102, 4, 100)(3, 99, 9, 105, 16, 112, 11, 107)(5, 101, 14, 110, 10, 106, 15, 111)(7, 103, 17, 113, 12, 108, 18, 114)(8, 104, 19, 115, 13, 109, 20, 116)(21, 117, 37, 133, 23, 119, 38, 134)(22, 118, 39, 135, 24, 120, 40, 136)(25, 121, 41, 137, 27, 123, 42, 138)(26, 122, 43, 139, 28, 124, 44, 140)(29, 125, 45, 141, 31, 127, 46, 142)(30, 126, 47, 143, 32, 128, 48, 144)(33, 129, 49, 145, 35, 131, 50, 146)(34, 130, 51, 147, 36, 132, 52, 148)(53, 149, 85, 181, 55, 151, 86, 182)(54, 150, 74, 170, 56, 152, 76, 172)(57, 153, 78, 174, 59, 155, 80, 176)(58, 154, 70, 166, 60, 156, 72, 168)(61, 157, 81, 177, 63, 159, 83, 179)(62, 158, 73, 169, 64, 160, 75, 171)(65, 161, 77, 173, 67, 163, 79, 175)(66, 162, 87, 183, 68, 164, 88, 184)(69, 165, 89, 185, 71, 167, 90, 186)(82, 178, 91, 187, 84, 180, 92, 188)(93, 189, 95, 191, 94, 190, 96, 192)(193, 289, 195, 291, 202, 298, 198, 294, 208, 304, 197, 293)(194, 290, 199, 295, 205, 301, 196, 292, 204, 300, 200, 296)(201, 297, 213, 309, 216, 312, 203, 299, 215, 311, 214, 310)(206, 302, 217, 313, 220, 316, 207, 303, 219, 315, 218, 314)(209, 305, 221, 317, 224, 320, 210, 306, 223, 319, 222, 318)(211, 307, 225, 321, 228, 324, 212, 308, 227, 323, 226, 322)(229, 325, 245, 341, 248, 344, 230, 326, 247, 343, 246, 342)(231, 327, 249, 345, 252, 348, 232, 328, 251, 347, 250, 346)(233, 329, 253, 349, 256, 352, 234, 330, 255, 351, 254, 350)(235, 331, 257, 353, 260, 356, 236, 332, 259, 355, 258, 354)(237, 333, 261, 357, 264, 360, 238, 334, 263, 359, 262, 358)(239, 335, 265, 361, 268, 364, 240, 336, 267, 363, 266, 362)(241, 337, 269, 365, 272, 368, 242, 338, 271, 367, 270, 366)(243, 339, 273, 369, 276, 372, 244, 340, 275, 371, 274, 370)(277, 373, 285, 381, 279, 375, 278, 374, 286, 382, 280, 376)(281, 377, 287, 383, 283, 379, 282, 378, 288, 384, 284, 380) L = (1, 196)(2, 193)(3, 203)(4, 198)(5, 207)(6, 194)(7, 210)(8, 212)(9, 195)(10, 206)(11, 208)(12, 209)(13, 211)(14, 197)(15, 202)(16, 201)(17, 199)(18, 204)(19, 200)(20, 205)(21, 230)(22, 232)(23, 229)(24, 231)(25, 234)(26, 236)(27, 233)(28, 235)(29, 238)(30, 240)(31, 237)(32, 239)(33, 242)(34, 244)(35, 241)(36, 243)(37, 213)(38, 215)(39, 214)(40, 216)(41, 217)(42, 219)(43, 218)(44, 220)(45, 221)(46, 223)(47, 222)(48, 224)(49, 225)(50, 227)(51, 226)(52, 228)(53, 278)(54, 268)(55, 277)(56, 266)(57, 272)(58, 264)(59, 270)(60, 262)(61, 275)(62, 267)(63, 273)(64, 265)(65, 271)(66, 280)(67, 269)(68, 279)(69, 282)(70, 250)(71, 281)(72, 252)(73, 254)(74, 246)(75, 256)(76, 248)(77, 257)(78, 249)(79, 259)(80, 251)(81, 253)(82, 284)(83, 255)(84, 283)(85, 245)(86, 247)(87, 258)(88, 260)(89, 261)(90, 263)(91, 274)(92, 276)(93, 288)(94, 287)(95, 285)(96, 286)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 2, 16, 2, 16, 2, 16, 2, 16 ), ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ) } Outer automorphisms :: reflexible Dual of E23.956 Graph:: bipartite v = 40 e = 192 f = 108 degree seq :: [ 8^24, 12^16 ] E23.948 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 8}) Quotient :: dipole Aut^+ = SL(2,3) : C4 (small group id <96, 66>) Aut = $<192, 986>$ (small group id <192, 986>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y1^6, Y2 * Y1^-3 * Y2^3, Y2 * Y1^-1 * Y2^-1 * Y1 * Y2^-1 * Y1^-1 * Y2, (Y1 * Y2)^4, Y1 * Y2 * Y1^2 * Y2 * Y1 * Y2^2, (Y3^-1 * Y1^-1)^4, Y2^2 * Y1 * Y2^-1 * Y1 * Y2^2 * Y1^-1 * Y2 * Y1^-1 ] Map:: R = (1, 97, 2, 98, 6, 102, 18, 114, 13, 109, 4, 100)(3, 99, 9, 105, 27, 123, 52, 148, 34, 130, 11, 107)(5, 101, 15, 111, 44, 140, 31, 127, 48, 144, 16, 112)(7, 103, 21, 117, 57, 153, 39, 135, 62, 158, 23, 119)(8, 104, 24, 120, 64, 160, 40, 136, 67, 163, 25, 121)(10, 106, 30, 126, 51, 147, 17, 113, 50, 146, 32, 128)(12, 108, 36, 132, 54, 150, 19, 115, 53, 149, 38, 134)(14, 110, 41, 137, 56, 152, 20, 116, 55, 151, 42, 138)(22, 118, 60, 156, 69, 165, 26, 122, 46, 142, 61, 157)(28, 124, 58, 154, 49, 145, 68, 164, 91, 187, 72, 168)(29, 125, 73, 169, 90, 186, 79, 175, 82, 178, 74, 170)(33, 129, 37, 133, 66, 162, 70, 166, 43, 139, 78, 174)(35, 131, 45, 141, 59, 155, 71, 167, 87, 183, 80, 176)(47, 143, 63, 159, 65, 161, 83, 179, 92, 188, 86, 182)(75, 171, 95, 191, 85, 181, 88, 184, 94, 190, 84, 180)(76, 172, 77, 173, 96, 192, 89, 185, 81, 177, 93, 189)(193, 289, 195, 291, 202, 298, 223, 319, 210, 306, 244, 340, 209, 305, 197, 293)(194, 290, 199, 295, 214, 310, 232, 328, 205, 301, 231, 327, 218, 314, 200, 296)(196, 292, 204, 300, 229, 325, 212, 308, 198, 294, 211, 307, 235, 331, 206, 302)(201, 297, 220, 316, 256, 352, 271, 367, 226, 322, 260, 356, 217, 313, 221, 317)(203, 299, 225, 321, 269, 365, 263, 359, 219, 315, 262, 358, 273, 369, 227, 323)(207, 303, 237, 333, 276, 372, 252, 348, 240, 336, 279, 375, 277, 373, 238, 334)(208, 304, 239, 335, 228, 324, 264, 360, 236, 332, 275, 371, 245, 341, 241, 337)(213, 309, 250, 346, 234, 330, 272, 368, 254, 350, 283, 379, 248, 344, 251, 347)(215, 311, 224, 320, 268, 364, 284, 380, 249, 345, 243, 339, 281, 377, 255, 351)(216, 312, 257, 353, 286, 382, 270, 366, 259, 355, 278, 374, 287, 383, 258, 354)(222, 318, 247, 343, 282, 378, 280, 376, 242, 338, 233, 329, 266, 362, 267, 363)(230, 326, 261, 357, 288, 384, 265, 361, 246, 342, 253, 349, 285, 381, 274, 370) L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 211)(7, 214)(8, 194)(9, 220)(10, 223)(11, 225)(12, 229)(13, 231)(14, 196)(15, 237)(16, 239)(17, 197)(18, 244)(19, 235)(20, 198)(21, 250)(22, 232)(23, 224)(24, 257)(25, 221)(26, 200)(27, 262)(28, 256)(29, 201)(30, 247)(31, 210)(32, 268)(33, 269)(34, 260)(35, 203)(36, 264)(37, 212)(38, 261)(39, 218)(40, 205)(41, 266)(42, 272)(43, 206)(44, 275)(45, 276)(46, 207)(47, 228)(48, 279)(49, 208)(50, 233)(51, 281)(52, 209)(53, 241)(54, 253)(55, 282)(56, 251)(57, 243)(58, 234)(59, 213)(60, 240)(61, 285)(62, 283)(63, 215)(64, 271)(65, 286)(66, 216)(67, 278)(68, 217)(69, 288)(70, 273)(71, 219)(72, 236)(73, 246)(74, 267)(75, 222)(76, 284)(77, 263)(78, 259)(79, 226)(80, 254)(81, 227)(82, 230)(83, 245)(84, 252)(85, 238)(86, 287)(87, 277)(88, 242)(89, 255)(90, 280)(91, 248)(92, 249)(93, 274)(94, 270)(95, 258)(96, 265)(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 ) } Outer automorphisms :: reflexible Dual of E23.951 Graph:: bipartite v = 28 e = 192 f = 120 degree seq :: [ 12^16, 16^12 ] E23.949 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 8}) Quotient :: dipole Aut^+ = SL(2,3) : C4 (small group id <96, 66>) Aut = $<192, 986>$ (small group id <192, 986>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y1^6, Y1^2 * Y2^-1 * Y1^-1 * Y2^3, Y1^2 * Y2^3 * Y1^-1 * Y2^-1, Y2^2 * Y1 * Y2 * Y1^2 * Y2 * Y1, Y2^-1 * Y1^-1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1^-1, (Y1 * Y2)^4, Y2 * Y1^-2 * Y2^2 * Y1 * Y2 * Y1^-1, (Y3^-1 * Y1^-1)^4, Y2^8 ] Map:: R = (1, 97, 2, 98, 6, 102, 18, 114, 13, 109, 4, 100)(3, 99, 9, 105, 27, 123, 53, 149, 34, 130, 11, 107)(5, 101, 15, 111, 44, 140, 54, 150, 48, 144, 16, 112)(7, 103, 21, 117, 59, 155, 39, 135, 31, 127, 23, 119)(8, 104, 24, 120, 66, 162, 40, 136, 69, 165, 25, 121)(10, 106, 30, 126, 45, 141, 61, 157, 80, 176, 32, 128)(12, 108, 36, 132, 56, 152, 19, 115, 55, 151, 38, 134)(14, 110, 41, 137, 52, 148, 20, 116, 57, 153, 42, 138)(17, 113, 50, 146, 64, 160, 83, 179, 35, 131, 51, 147)(22, 118, 62, 158, 67, 163, 87, 183, 46, 142, 63, 159)(26, 122, 71, 167, 90, 186, 47, 143, 65, 161, 72, 168)(28, 124, 60, 156, 49, 145, 70, 166, 78, 174, 74, 170)(29, 125, 75, 171, 85, 181, 37, 133, 68, 164, 76, 172)(33, 129, 58, 154, 86, 182, 73, 169, 43, 139, 82, 178)(77, 173, 95, 191, 89, 185, 81, 177, 96, 192, 92, 188)(79, 175, 91, 187, 94, 190, 88, 184, 84, 180, 93, 189)(193, 289, 195, 291, 202, 298, 223, 319, 270, 366, 244, 340, 209, 305, 197, 293)(194, 290, 199, 295, 214, 310, 228, 324, 266, 362, 236, 332, 218, 314, 200, 296)(196, 292, 204, 300, 229, 325, 226, 322, 262, 358, 217, 313, 235, 331, 206, 302)(198, 294, 211, 307, 221, 317, 201, 297, 220, 316, 258, 354, 250, 346, 212, 308)(203, 299, 225, 321, 273, 369, 272, 368, 233, 329, 268, 364, 276, 372, 227, 323)(205, 301, 231, 327, 279, 375, 247, 343, 241, 337, 208, 304, 239, 335, 232, 328)(207, 303, 237, 333, 280, 376, 257, 353, 215, 311, 256, 352, 281, 377, 238, 334)(210, 306, 245, 341, 253, 349, 213, 309, 252, 348, 234, 330, 275, 371, 246, 342)(216, 312, 259, 355, 286, 382, 274, 370, 248, 344, 282, 378, 287, 383, 260, 356)(219, 315, 265, 361, 269, 365, 222, 318, 249, 345, 277, 373, 283, 379, 242, 338)(224, 320, 271, 367, 263, 359, 251, 347, 243, 339, 284, 380, 254, 350, 240, 336)(230, 326, 264, 360, 288, 384, 267, 363, 261, 357, 255, 351, 285, 381, 278, 374) L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 211)(7, 214)(8, 194)(9, 220)(10, 223)(11, 225)(12, 229)(13, 231)(14, 196)(15, 237)(16, 239)(17, 197)(18, 245)(19, 221)(20, 198)(21, 252)(22, 228)(23, 256)(24, 259)(25, 235)(26, 200)(27, 265)(28, 258)(29, 201)(30, 249)(31, 270)(32, 271)(33, 273)(34, 262)(35, 203)(36, 266)(37, 226)(38, 264)(39, 279)(40, 205)(41, 268)(42, 275)(43, 206)(44, 218)(45, 280)(46, 207)(47, 232)(48, 224)(49, 208)(50, 219)(51, 284)(52, 209)(53, 253)(54, 210)(55, 241)(56, 282)(57, 277)(58, 212)(59, 243)(60, 234)(61, 213)(62, 240)(63, 285)(64, 281)(65, 215)(66, 250)(67, 286)(68, 216)(69, 255)(70, 217)(71, 251)(72, 288)(73, 269)(74, 236)(75, 261)(76, 276)(77, 222)(78, 244)(79, 263)(80, 233)(81, 272)(82, 248)(83, 246)(84, 227)(85, 283)(86, 230)(87, 247)(88, 257)(89, 238)(90, 287)(91, 242)(92, 254)(93, 278)(94, 274)(95, 260)(96, 267)(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 ) } Outer automorphisms :: reflexible Dual of E23.952 Graph:: bipartite v = 28 e = 192 f = 120 degree seq :: [ 12^16, 16^12 ] E23.950 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 8}) Quotient :: dipole Aut^+ = SL(2,3) : C4 (small group id <96, 66>) Aut = $<192, 986>$ (small group id <192, 986>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y1 * Y2 * Y1^-2 * Y2, Y1^6, (Y3^-1 * Y1^-1)^4, Y2^8, Y2^-1 * Y1^-1 * Y2^-2 * Y1^-3 * Y2 * Y1^-1, Y2^-2 * Y1^-2 * Y2^-3 * Y1 * Y2^-1, Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2^-3 * Y1^-1 ] Map:: R = (1, 97, 2, 98, 6, 102, 18, 114, 13, 109, 4, 100)(3, 99, 9, 105, 24, 120, 34, 130, 14, 110, 11, 107)(5, 101, 15, 111, 7, 103, 20, 116, 39, 135, 16, 112)(8, 104, 22, 118, 19, 115, 33, 129, 32, 128, 12, 108)(10, 106, 26, 122, 56, 152, 65, 161, 30, 126, 28, 124)(17, 113, 40, 136, 36, 132, 44, 140, 79, 175, 41, 137)(21, 117, 45, 141, 75, 171, 38, 134, 37, 133, 47, 143)(23, 119, 50, 146, 48, 144, 70, 166, 91, 187, 51, 147)(25, 121, 54, 150, 53, 149, 35, 131, 64, 160, 29, 125)(27, 123, 58, 154, 52, 148, 92, 188, 62, 158, 60, 156)(31, 127, 49, 145, 82, 178, 43, 139, 69, 165, 68, 164)(42, 138, 80, 176, 76, 172, 83, 179, 67, 163, 81, 177)(46, 142, 84, 180, 55, 151, 74, 170, 87, 183, 71, 167)(57, 153, 89, 185, 73, 169, 66, 162, 86, 182, 61, 157)(59, 155, 85, 181, 93, 189, 96, 192, 95, 191, 94, 190)(63, 159, 90, 186, 78, 174, 77, 173, 88, 184, 72, 168)(193, 289, 195, 291, 202, 298, 219, 315, 251, 347, 234, 330, 209, 305, 197, 293)(194, 290, 199, 295, 213, 309, 238, 334, 277, 373, 244, 340, 215, 311, 200, 296)(196, 292, 204, 300, 223, 319, 259, 355, 286, 382, 263, 359, 227, 323, 206, 302)(198, 294, 211, 307, 235, 331, 272, 368, 285, 381, 247, 343, 217, 313, 201, 297)(203, 299, 221, 317, 255, 351, 271, 367, 273, 369, 274, 370, 258, 354, 222, 318)(205, 301, 208, 304, 230, 326, 266, 362, 287, 383, 252, 348, 262, 358, 225, 321)(207, 303, 228, 324, 264, 360, 283, 379, 250, 346, 248, 344, 265, 361, 229, 325)(210, 306, 226, 322, 257, 353, 284, 380, 288, 384, 275, 371, 236, 332, 212, 308)(214, 310, 240, 336, 280, 376, 256, 352, 276, 372, 267, 363, 281, 377, 241, 337)(216, 312, 245, 341, 269, 365, 232, 328, 268, 364, 260, 356, 249, 345, 218, 314)(220, 316, 253, 349, 237, 333, 231, 327, 233, 329, 270, 366, 242, 338, 254, 350)(224, 320, 243, 339, 282, 378, 246, 342, 279, 375, 239, 335, 278, 374, 261, 357) L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 211)(7, 213)(8, 194)(9, 198)(10, 219)(11, 221)(12, 223)(13, 208)(14, 196)(15, 228)(16, 230)(17, 197)(18, 226)(19, 235)(20, 210)(21, 238)(22, 240)(23, 200)(24, 245)(25, 201)(26, 216)(27, 251)(28, 253)(29, 255)(30, 203)(31, 259)(32, 243)(33, 205)(34, 257)(35, 206)(36, 264)(37, 207)(38, 266)(39, 233)(40, 268)(41, 270)(42, 209)(43, 272)(44, 212)(45, 231)(46, 277)(47, 278)(48, 280)(49, 214)(50, 254)(51, 282)(52, 215)(53, 269)(54, 279)(55, 217)(56, 265)(57, 218)(58, 248)(59, 234)(60, 262)(61, 237)(62, 220)(63, 271)(64, 276)(65, 284)(66, 222)(67, 286)(68, 249)(69, 224)(70, 225)(71, 227)(72, 283)(73, 229)(74, 287)(75, 281)(76, 260)(77, 232)(78, 242)(79, 273)(80, 285)(81, 274)(82, 258)(83, 236)(84, 267)(85, 244)(86, 261)(87, 239)(88, 256)(89, 241)(90, 246)(91, 250)(92, 288)(93, 247)(94, 263)(95, 252)(96, 275)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) } Outer automorphisms :: reflexible Dual of E23.953 Graph:: bipartite v = 28 e = 192 f = 120 degree seq :: [ 12^16, 16^12 ] E23.951 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 8}) Quotient :: dipole Aut^+ = SL(2,3) : C4 (small group id <96, 66>) Aut = $<192, 986>$ (small group id <192, 986>) |r| :: 2 Presentation :: [ Y1, R^2, Y2^4, Y2^4, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2 * Y3 * Y2^-2 * Y3^-1 * Y2, Y3 * Y2^-1 * Y3^-3 * Y2^-1 * Y3 * Y2^-1, Y3^8, Y3 * Y2^-1 * Y3^2 * Y2 * Y3 * Y2 * Y3^2 * Y2, Y3 * Y2^-1 * Y3^-1 * Y2 * Y3 * Y2 * Y3^-2 * Y2 * Y3^-2 * Y2, (Y3^-1 * Y1^-1)^8 ] Map:: polytopal R = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)(193, 289, 194, 290, 198, 294, 196, 292)(195, 291, 201, 297, 209, 305, 203, 299)(197, 293, 206, 302, 210, 306, 207, 303)(199, 295, 211, 307, 204, 300, 213, 309)(200, 296, 214, 310, 205, 301, 215, 311)(202, 298, 219, 315, 233, 329, 221, 317)(208, 304, 230, 326, 234, 330, 231, 327)(212, 308, 237, 333, 224, 320, 239, 335)(216, 312, 246, 342, 225, 321, 247, 343)(217, 313, 238, 334, 222, 318, 250, 346)(218, 314, 251, 347, 223, 319, 252, 348)(220, 316, 235, 331, 264, 360, 240, 336)(226, 322, 254, 350, 228, 324, 257, 353)(227, 323, 259, 355, 229, 325, 248, 344)(232, 328, 245, 341, 265, 361, 243, 339)(236, 332, 267, 363, 241, 337, 268, 364)(242, 338, 270, 366, 244, 340, 273, 369)(249, 345, 278, 374, 258, 354, 277, 373)(253, 349, 276, 372, 256, 352, 275, 371)(255, 351, 271, 367, 284, 380, 279, 375)(260, 356, 272, 368, 261, 357, 269, 365)(262, 358, 274, 370, 263, 359, 266, 362)(280, 376, 288, 384, 281, 377, 287, 383)(282, 378, 286, 382, 283, 379, 285, 381) L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 209)(7, 212)(8, 194)(9, 217)(10, 220)(11, 222)(12, 224)(13, 196)(14, 226)(15, 228)(16, 197)(17, 233)(18, 198)(19, 235)(20, 238)(21, 240)(22, 242)(23, 244)(24, 200)(25, 249)(26, 201)(27, 253)(28, 255)(29, 256)(30, 258)(31, 203)(32, 250)(33, 205)(34, 236)(35, 206)(36, 241)(37, 207)(38, 252)(39, 251)(40, 208)(41, 264)(42, 210)(43, 266)(44, 211)(45, 269)(46, 271)(47, 272)(48, 274)(49, 213)(50, 223)(51, 214)(52, 218)(53, 215)(54, 268)(55, 267)(56, 216)(57, 276)(58, 279)(59, 280)(60, 281)(61, 282)(62, 219)(63, 232)(64, 283)(65, 221)(66, 275)(67, 225)(68, 227)(69, 229)(70, 230)(71, 231)(72, 284)(73, 234)(74, 260)(75, 285)(76, 286)(77, 287)(78, 237)(79, 248)(80, 288)(81, 239)(82, 261)(83, 243)(84, 245)(85, 246)(86, 247)(87, 259)(88, 257)(89, 254)(90, 262)(91, 263)(92, 265)(93, 273)(94, 270)(95, 277)(96, 278)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 12, 16 ), ( 12, 16, 12, 16, 12, 16, 12, 16 ) } Outer automorphisms :: reflexible Dual of E23.948 Graph:: simple bipartite v = 120 e = 192 f = 28 degree seq :: [ 2^96, 8^24 ] E23.952 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 8}) Quotient :: dipole Aut^+ = SL(2,3) : C4 (small group id <96, 66>) Aut = $<192, 986>$ (small group id <192, 986>) |r| :: 2 Presentation :: [ Y1, R^2, Y2^4, Y2^4, (R * Y1)^2, (R * Y3)^2, Y2 * Y3 * Y2^2 * Y3^-1 * Y2, (R * Y2 * Y3^-1)^2, Y3^3 * Y2 * Y3^-1 * Y2 * Y3^-1 * Y2^-1, Y3 * Y2 * Y3 * Y2^-1 * Y3^5 * Y2^-1, (Y3^-1 * Y1^-1)^8 ] Map:: polytopal R = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)(193, 289, 194, 290, 198, 294, 196, 292)(195, 291, 201, 297, 209, 305, 203, 299)(197, 293, 206, 302, 210, 306, 207, 303)(199, 295, 211, 307, 204, 300, 213, 309)(200, 296, 214, 310, 205, 301, 215, 311)(202, 298, 219, 315, 233, 329, 221, 317)(208, 304, 230, 326, 234, 330, 231, 327)(212, 308, 237, 333, 224, 320, 239, 335)(216, 312, 246, 342, 225, 321, 247, 343)(217, 313, 249, 345, 222, 318, 238, 334)(218, 314, 251, 347, 223, 319, 252, 348)(220, 316, 240, 336, 264, 360, 235, 331)(226, 322, 257, 353, 228, 324, 254, 350)(227, 323, 248, 344, 229, 325, 259, 355)(232, 328, 243, 339, 265, 361, 245, 341)(236, 332, 267, 363, 241, 337, 268, 364)(242, 338, 273, 369, 244, 340, 270, 366)(250, 346, 278, 374, 258, 354, 277, 373)(253, 349, 276, 372, 256, 352, 275, 371)(255, 351, 271, 367, 284, 380, 279, 375)(260, 356, 272, 368, 261, 357, 269, 365)(262, 358, 274, 370, 263, 359, 266, 362)(280, 376, 287, 383, 281, 377, 288, 384)(282, 378, 285, 381, 283, 379, 286, 382) L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 209)(7, 212)(8, 194)(9, 217)(10, 220)(11, 222)(12, 224)(13, 196)(14, 226)(15, 228)(16, 197)(17, 233)(18, 198)(19, 235)(20, 238)(21, 240)(22, 242)(23, 244)(24, 200)(25, 250)(26, 201)(27, 253)(28, 255)(29, 256)(30, 258)(31, 203)(32, 249)(33, 205)(34, 241)(35, 206)(36, 236)(37, 207)(38, 251)(39, 252)(40, 208)(41, 264)(42, 210)(43, 266)(44, 211)(45, 269)(46, 271)(47, 272)(48, 274)(49, 213)(50, 218)(51, 214)(52, 223)(53, 215)(54, 267)(55, 268)(56, 216)(57, 279)(58, 275)(59, 280)(60, 281)(61, 282)(62, 219)(63, 232)(64, 283)(65, 221)(66, 276)(67, 225)(68, 227)(69, 229)(70, 230)(71, 231)(72, 284)(73, 234)(74, 261)(75, 285)(76, 286)(77, 287)(78, 237)(79, 248)(80, 288)(81, 239)(82, 260)(83, 243)(84, 245)(85, 246)(86, 247)(87, 259)(88, 254)(89, 257)(90, 262)(91, 263)(92, 265)(93, 270)(94, 273)(95, 277)(96, 278)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 12, 16 ), ( 12, 16, 12, 16, 12, 16, 12, 16 ) } Outer automorphisms :: reflexible Dual of E23.949 Graph:: simple bipartite v = 120 e = 192 f = 28 degree seq :: [ 2^96, 8^24 ] E23.953 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 8}) Quotient :: dipole Aut^+ = SL(2,3) : C4 (small group id <96, 66>) Aut = $<192, 986>$ (small group id <192, 986>) |r| :: 2 Presentation :: [ Y1, R^2, Y2^4, (R * Y1)^2, (R * Y3)^2, Y3 * Y2^-2 * Y3^-1 * Y2^-2, (Y2^-1 * R * Y2^-1)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2)^3, Y3^-3 * Y2 * Y3 * Y2^-1 * Y3^-3 * Y2^-1, Y2^-1 * Y3^4 * Y2 * Y3^-4, (Y3^-1 * Y1^-1)^8 ] Map:: R = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)(193, 289, 194, 290, 198, 294, 196, 292)(195, 291, 201, 297, 209, 305, 203, 299)(197, 293, 206, 302, 210, 306, 207, 303)(199, 295, 211, 307, 204, 300, 213, 309)(200, 296, 214, 310, 205, 301, 215, 311)(202, 298, 218, 314, 229, 325, 220, 316)(208, 304, 226, 322, 230, 326, 227, 323)(212, 308, 232, 328, 222, 318, 234, 330)(216, 312, 238, 334, 223, 319, 239, 335)(217, 313, 241, 337, 221, 317, 242, 338)(219, 315, 245, 341, 260, 356, 247, 343)(224, 320, 252, 348, 225, 321, 254, 350)(228, 324, 258, 354, 261, 357, 259, 355)(231, 327, 262, 358, 235, 331, 263, 359)(233, 329, 266, 362, 250, 346, 268, 364)(236, 332, 271, 367, 237, 333, 273, 369)(240, 336, 277, 373, 251, 347, 278, 374)(243, 339, 269, 365, 249, 345, 265, 361)(244, 340, 270, 366, 248, 344, 264, 360)(246, 342, 267, 363, 284, 380, 282, 378)(253, 349, 276, 372, 255, 351, 275, 371)(256, 352, 274, 370, 257, 353, 272, 368)(279, 375, 287, 383, 280, 376, 288, 384)(281, 377, 285, 381, 283, 379, 286, 382) L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 209)(7, 212)(8, 194)(9, 214)(10, 219)(11, 215)(12, 222)(13, 196)(14, 224)(15, 225)(16, 197)(17, 229)(18, 198)(19, 207)(20, 233)(21, 206)(22, 236)(23, 237)(24, 200)(25, 201)(26, 241)(27, 246)(28, 242)(29, 203)(30, 250)(31, 205)(32, 253)(33, 255)(34, 256)(35, 257)(36, 208)(37, 260)(38, 210)(39, 211)(40, 262)(41, 267)(42, 263)(43, 213)(44, 272)(45, 274)(46, 275)(47, 276)(48, 216)(49, 279)(50, 280)(51, 217)(52, 218)(53, 270)(54, 228)(55, 264)(56, 220)(57, 221)(58, 282)(59, 223)(60, 227)(61, 278)(62, 226)(63, 277)(64, 281)(65, 283)(66, 266)(67, 268)(68, 284)(69, 230)(70, 285)(71, 286)(72, 231)(73, 232)(74, 243)(75, 240)(76, 249)(77, 234)(78, 235)(79, 239)(80, 258)(81, 238)(82, 259)(83, 287)(84, 288)(85, 247)(86, 245)(87, 254)(88, 252)(89, 244)(90, 251)(91, 248)(92, 261)(93, 273)(94, 271)(95, 265)(96, 269)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 12, 16 ), ( 12, 16, 12, 16, 12, 16, 12, 16 ) } Outer automorphisms :: reflexible Dual of E23.950 Graph:: simple bipartite v = 120 e = 192 f = 28 degree seq :: [ 2^96, 8^24 ] E23.954 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 8}) Quotient :: dipole Aut^+ = SL(2,3) : C4 (small group id <96, 66>) Aut = $<192, 986>$ (small group id <192, 986>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^4, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y3^-2 * Y1 * Y3^-2 * Y1^-1, Y3 * Y1^3 * Y3 * Y1^-1 * Y3 * Y1^-1, Y1^8, (Y3 * Y2^-1)^4, Y1^-1 * Y3 * Y1^-2 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-2 * Y3^-1, Y3^-1 * Y1^-4 * Y3 * Y1^-4 ] Map:: polytopal R = (1, 97, 2, 98, 6, 102, 17, 113, 41, 137, 35, 131, 13, 109, 4, 100)(3, 99, 9, 105, 25, 121, 50, 146, 72, 168, 64, 160, 30, 126, 11, 107)(5, 101, 15, 111, 39, 135, 51, 147, 73, 169, 67, 163, 40, 136, 16, 112)(7, 103, 20, 116, 49, 145, 78, 174, 66, 162, 31, 127, 53, 149, 22, 118)(8, 104, 23, 119, 55, 151, 79, 175, 62, 158, 29, 125, 56, 152, 24, 120)(10, 106, 21, 117, 45, 141, 75, 171, 92, 188, 91, 187, 61, 157, 28, 124)(12, 108, 32, 128, 59, 155, 26, 122, 42, 138, 74, 170, 68, 164, 33, 129)(14, 110, 37, 133, 60, 156, 27, 123, 43, 139, 76, 172, 71, 167, 38, 134)(18, 114, 44, 140, 77, 173, 69, 165, 34, 130, 54, 150, 80, 176, 46, 142)(19, 115, 47, 143, 81, 177, 70, 166, 36, 132, 52, 148, 82, 178, 48, 144)(57, 153, 87, 183, 95, 191, 84, 180, 63, 159, 90, 186, 93, 189, 86, 182)(58, 154, 88, 184, 96, 192, 83, 179, 65, 161, 89, 185, 94, 190, 85, 181)(193, 289)(194, 290)(195, 291)(196, 292)(197, 293)(198, 294)(199, 295)(200, 296)(201, 297)(202, 298)(203, 299)(204, 300)(205, 301)(206, 302)(207, 303)(208, 304)(209, 305)(210, 306)(211, 307)(212, 308)(213, 309)(214, 310)(215, 311)(216, 312)(217, 313)(218, 314)(219, 315)(220, 316)(221, 317)(222, 318)(223, 319)(224, 320)(225, 321)(226, 322)(227, 323)(228, 324)(229, 325)(230, 326)(231, 327)(232, 328)(233, 329)(234, 330)(235, 331)(236, 332)(237, 333)(238, 334)(239, 335)(240, 336)(241, 337)(242, 338)(243, 339)(244, 340)(245, 341)(246, 342)(247, 343)(248, 344)(249, 345)(250, 346)(251, 347)(252, 348)(253, 349)(254, 350)(255, 351)(256, 352)(257, 353)(258, 354)(259, 355)(260, 356)(261, 357)(262, 358)(263, 359)(264, 360)(265, 361)(266, 362)(267, 363)(268, 364)(269, 365)(270, 366)(271, 367)(272, 368)(273, 369)(274, 370)(275, 371)(276, 372)(277, 373)(278, 374)(279, 375)(280, 376)(281, 377)(282, 378)(283, 379)(284, 380)(285, 381)(286, 382)(287, 383)(288, 384) L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 210)(7, 213)(8, 194)(9, 218)(10, 197)(11, 221)(12, 220)(13, 226)(14, 196)(15, 219)(16, 223)(17, 234)(18, 237)(19, 198)(20, 242)(21, 200)(22, 244)(23, 243)(24, 246)(25, 249)(26, 207)(27, 201)(28, 206)(29, 208)(30, 255)(31, 203)(32, 238)(33, 259)(34, 253)(35, 258)(36, 205)(37, 240)(38, 256)(39, 250)(40, 257)(41, 264)(42, 267)(43, 209)(44, 270)(45, 211)(46, 229)(47, 271)(48, 224)(49, 275)(50, 215)(51, 212)(52, 216)(53, 277)(54, 214)(55, 276)(56, 278)(57, 231)(58, 217)(59, 281)(60, 282)(61, 228)(62, 227)(63, 232)(64, 225)(65, 222)(66, 283)(67, 230)(68, 280)(69, 268)(70, 266)(71, 279)(72, 284)(73, 233)(74, 261)(75, 235)(76, 262)(77, 285)(78, 239)(79, 236)(80, 287)(81, 286)(82, 288)(83, 247)(84, 241)(85, 248)(86, 245)(87, 260)(88, 263)(89, 252)(90, 251)(91, 254)(92, 265)(93, 273)(94, 269)(95, 274)(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) :: { ( 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E23.946 Graph:: simple bipartite v = 108 e = 192 f = 40 degree seq :: [ 2^96, 16^12 ] E23.955 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 8}) Quotient :: dipole Aut^+ = SL(2,3) : C4 (small group id <96, 66>) Aut = $<192, 986>$ (small group id <192, 986>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^4, (R * Y3)^2, (R * Y1)^2, Y1^-1 * Y3^-2 * Y1 * Y3^2, (R * Y2 * Y3^-1)^2, Y3 * Y1 * Y3^-2 * Y1^-1 * Y3, Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1^-3, (Y3 * Y2^-1)^4, Y1^8, Y1^-1 * Y3 * Y1^-1 * Y3^-1 * Y1^3 * Y3, Y3 * Y1^2 * Y3^-1 * Y1^2 * Y3 * Y1^-1 * Y3^-1 * Y1 * Y3^-1 * Y1^-1, (Y3^-1 * Y1^-1)^6 ] Map:: R = (1, 97, 2, 98, 6, 102, 17, 113, 41, 137, 35, 131, 13, 109, 4, 100)(3, 99, 9, 105, 25, 121, 51, 147, 72, 168, 64, 160, 30, 126, 11, 107)(5, 101, 15, 111, 39, 135, 50, 146, 73, 169, 68, 164, 40, 136, 16, 112)(7, 103, 20, 116, 49, 145, 79, 175, 62, 158, 29, 125, 53, 149, 22, 118)(8, 104, 23, 119, 55, 151, 78, 174, 66, 162, 31, 127, 56, 152, 24, 120)(10, 106, 21, 117, 45, 141, 75, 171, 92, 188, 91, 187, 61, 157, 28, 124)(12, 108, 32, 128, 60, 156, 27, 123, 42, 138, 74, 170, 67, 163, 33, 129)(14, 110, 37, 133, 59, 155, 26, 122, 43, 139, 76, 172, 71, 167, 38, 134)(18, 114, 44, 140, 77, 173, 69, 165, 34, 130, 52, 148, 80, 176, 46, 142)(19, 115, 47, 143, 81, 177, 70, 166, 36, 132, 54, 150, 82, 178, 48, 144)(57, 153, 87, 183, 95, 191, 84, 180, 63, 159, 89, 185, 93, 189, 86, 182)(58, 154, 88, 184, 96, 192, 83, 179, 65, 161, 90, 186, 94, 190, 85, 181)(193, 289)(194, 290)(195, 291)(196, 292)(197, 293)(198, 294)(199, 295)(200, 296)(201, 297)(202, 298)(203, 299)(204, 300)(205, 301)(206, 302)(207, 303)(208, 304)(209, 305)(210, 306)(211, 307)(212, 308)(213, 309)(214, 310)(215, 311)(216, 312)(217, 313)(218, 314)(219, 315)(220, 316)(221, 317)(222, 318)(223, 319)(224, 320)(225, 321)(226, 322)(227, 323)(228, 324)(229, 325)(230, 326)(231, 327)(232, 328)(233, 329)(234, 330)(235, 331)(236, 332)(237, 333)(238, 334)(239, 335)(240, 336)(241, 337)(242, 338)(243, 339)(244, 340)(245, 341)(246, 342)(247, 343)(248, 344)(249, 345)(250, 346)(251, 347)(252, 348)(253, 349)(254, 350)(255, 351)(256, 352)(257, 353)(258, 354)(259, 355)(260, 356)(261, 357)(262, 358)(263, 359)(264, 360)(265, 361)(266, 362)(267, 363)(268, 364)(269, 365)(270, 366)(271, 367)(272, 368)(273, 369)(274, 370)(275, 371)(276, 372)(277, 373)(278, 374)(279, 375)(280, 376)(281, 377)(282, 378)(283, 379)(284, 380)(285, 381)(286, 382)(287, 383)(288, 384) L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 210)(7, 213)(8, 194)(9, 218)(10, 197)(11, 221)(12, 220)(13, 226)(14, 196)(15, 219)(16, 223)(17, 234)(18, 237)(19, 198)(20, 242)(21, 200)(22, 244)(23, 243)(24, 246)(25, 249)(26, 207)(27, 201)(28, 206)(29, 208)(30, 255)(31, 203)(32, 240)(33, 256)(34, 253)(35, 254)(36, 205)(37, 238)(38, 260)(39, 250)(40, 257)(41, 264)(42, 267)(43, 209)(44, 270)(45, 211)(46, 224)(47, 271)(48, 229)(49, 275)(50, 215)(51, 212)(52, 216)(53, 277)(54, 214)(55, 276)(56, 278)(57, 231)(58, 217)(59, 281)(60, 282)(61, 228)(62, 283)(63, 232)(64, 230)(65, 222)(66, 227)(67, 280)(68, 225)(69, 266)(70, 268)(71, 279)(72, 284)(73, 233)(74, 262)(75, 235)(76, 261)(77, 285)(78, 239)(79, 236)(80, 287)(81, 286)(82, 288)(83, 247)(84, 241)(85, 248)(86, 245)(87, 259)(88, 263)(89, 252)(90, 251)(91, 258)(92, 265)(93, 273)(94, 269)(95, 274)(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) :: { ( 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E23.945 Graph:: simple bipartite v = 108 e = 192 f = 40 degree seq :: [ 2^96, 16^12 ] E23.956 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 8}) Quotient :: dipole Aut^+ = SL(2,3) : C4 (small group id <96, 66>) Aut = $<192, 986>$ (small group id <192, 986>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^4, (R * Y3)^2, (R * Y1)^2, Y3 * Y1^-1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1, (R * Y2 * Y3^-1)^2, Y3^2 * Y1 * Y3^2 * Y1^-1, Y1^8, (Y3 * Y2^-1)^4, Y3 * Y1^2 * Y3 * Y1^-1 * Y3^-1 * Y1^2 * Y3 * Y1^-1, Y1^-1 * Y3^-1 * Y1^3 * Y3 * Y1^3 * Y3^-1 ] Map:: polytopal R = (1, 97, 2, 98, 6, 102, 17, 113, 37, 133, 32, 128, 13, 109, 4, 100)(3, 99, 9, 105, 25, 121, 49, 145, 68, 164, 56, 152, 29, 125, 11, 107)(5, 101, 15, 111, 35, 131, 66, 162, 69, 165, 67, 163, 36, 132, 16, 112)(7, 103, 20, 116, 45, 141, 79, 175, 62, 158, 83, 179, 46, 142, 22, 118)(8, 104, 23, 119, 47, 143, 85, 181, 63, 159, 86, 182, 48, 144, 24, 120)(10, 106, 21, 117, 41, 137, 71, 167, 92, 188, 89, 185, 54, 150, 28, 124)(12, 108, 30, 126, 58, 154, 72, 168, 38, 134, 70, 166, 52, 148, 26, 122)(14, 110, 34, 130, 65, 161, 74, 170, 39, 135, 73, 169, 53, 149, 27, 123)(18, 114, 40, 136, 75, 171, 59, 155, 31, 127, 61, 157, 76, 172, 42, 138)(19, 115, 43, 139, 77, 173, 60, 156, 33, 129, 64, 160, 78, 174, 44, 140)(50, 146, 87, 183, 95, 191, 81, 177, 55, 151, 90, 186, 93, 189, 84, 180)(51, 147, 88, 184, 96, 192, 80, 176, 57, 153, 91, 187, 94, 190, 82, 178)(193, 289)(194, 290)(195, 291)(196, 292)(197, 293)(198, 294)(199, 295)(200, 296)(201, 297)(202, 298)(203, 299)(204, 300)(205, 301)(206, 302)(207, 303)(208, 304)(209, 305)(210, 306)(211, 307)(212, 308)(213, 309)(214, 310)(215, 311)(216, 312)(217, 313)(218, 314)(219, 315)(220, 316)(221, 317)(222, 318)(223, 319)(224, 320)(225, 321)(226, 322)(227, 323)(228, 324)(229, 325)(230, 326)(231, 327)(232, 328)(233, 329)(234, 330)(235, 331)(236, 332)(237, 333)(238, 334)(239, 335)(240, 336)(241, 337)(242, 338)(243, 339)(244, 340)(245, 341)(246, 342)(247, 343)(248, 344)(249, 345)(250, 346)(251, 347)(252, 348)(253, 349)(254, 350)(255, 351)(256, 352)(257, 353)(258, 354)(259, 355)(260, 356)(261, 357)(262, 358)(263, 359)(264, 360)(265, 361)(266, 362)(267, 363)(268, 364)(269, 365)(270, 366)(271, 367)(272, 368)(273, 369)(274, 370)(275, 371)(276, 372)(277, 373)(278, 374)(279, 375)(280, 376)(281, 377)(282, 378)(283, 379)(284, 380)(285, 381)(286, 382)(287, 383)(288, 384) L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 210)(7, 213)(8, 194)(9, 218)(10, 197)(11, 215)(12, 220)(13, 223)(14, 196)(15, 219)(16, 212)(17, 230)(18, 233)(19, 198)(20, 203)(21, 200)(22, 235)(23, 208)(24, 232)(25, 242)(26, 207)(27, 201)(28, 206)(29, 247)(30, 251)(31, 246)(32, 254)(33, 205)(34, 252)(35, 243)(36, 249)(37, 260)(38, 263)(39, 209)(40, 214)(41, 211)(42, 265)(43, 216)(44, 262)(45, 272)(46, 274)(47, 273)(48, 276)(49, 278)(50, 227)(51, 217)(52, 280)(53, 279)(54, 225)(55, 228)(56, 264)(57, 221)(58, 283)(59, 226)(60, 222)(61, 271)(62, 281)(63, 224)(64, 277)(65, 282)(66, 275)(67, 266)(68, 284)(69, 229)(70, 234)(71, 231)(72, 259)(73, 236)(74, 248)(75, 285)(76, 287)(77, 286)(78, 288)(79, 256)(80, 239)(81, 237)(82, 240)(83, 241)(84, 238)(85, 253)(86, 258)(87, 244)(88, 245)(89, 255)(90, 250)(91, 257)(92, 261)(93, 269)(94, 267)(95, 270)(96, 268)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E23.947 Graph:: simple bipartite v = 108 e = 192 f = 40 degree seq :: [ 2^96, 16^12 ] E23.957 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 8}) Quotient :: dipole Aut^+ = SL(2,3) : C4 (small group id <96, 66>) Aut = $<192, 986>$ (small group id <192, 986>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, Y1 * Y3, (R * Y3)^2, Y3^-1 * Y1^2 * Y3^-1, (R * Y1)^2, Y3 * Y2 * Y1 * R * Y2 * R, (R * Y2 * Y3^-1)^2, Y1 * Y2 * Y1^2 * Y2^-1 * Y3^-1, Y2 * Y3 * Y1^-1 * Y2^-1 * Y3 * Y1^-1, Y2^8, Y2^3 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y3^-1, Y1 * Y2 * Y1 * Y2 * Y3 * Y2^-3, R * Y2 * Y3^-1 * Y2^-3 * R * Y2^-1, Y2^-1 * Y1 * Y2^-1 * Y3 * Y2^3 * Y1^-1, Y2^-1 * Y3 * R * Y2 * Y3^-1 * Y2^-1 * R * Y2 * Y1^-1 * Y2^-1, Y2^-2 * Y3^-1 * Y2^2 * Y1^-1 * Y2^-2 * Y3^-1 * Y2^-2 * Y1^-1, (Y3 * Y2^-1)^6 ] Map:: R = (1, 97, 2, 98, 6, 102, 4, 100)(3, 99, 9, 105, 17, 113, 11, 107)(5, 101, 14, 110, 18, 114, 15, 111)(7, 103, 19, 115, 12, 108, 21, 117)(8, 104, 22, 118, 13, 109, 23, 119)(10, 106, 27, 123, 41, 137, 29, 125)(16, 112, 38, 134, 42, 138, 39, 135)(20, 116, 45, 141, 32, 128, 47, 143)(24, 120, 54, 150, 33, 129, 55, 151)(25, 121, 46, 142, 30, 126, 58, 154)(26, 122, 59, 155, 31, 127, 60, 156)(28, 124, 43, 139, 72, 168, 48, 144)(34, 130, 62, 158, 36, 132, 65, 161)(35, 131, 67, 163, 37, 133, 56, 152)(40, 136, 53, 149, 73, 169, 51, 147)(44, 140, 75, 171, 49, 145, 76, 172)(50, 146, 78, 174, 52, 148, 81, 177)(57, 153, 86, 182, 66, 162, 85, 181)(61, 157, 84, 180, 64, 160, 83, 179)(63, 159, 79, 175, 92, 188, 87, 183)(68, 164, 80, 176, 69, 165, 77, 173)(70, 166, 82, 178, 71, 167, 74, 170)(88, 184, 96, 192, 89, 185, 95, 191)(90, 186, 94, 190, 91, 187, 93, 189)(193, 289, 195, 291, 202, 298, 220, 316, 255, 351, 232, 328, 208, 304, 197, 293)(194, 290, 199, 295, 212, 308, 238, 334, 271, 367, 248, 344, 216, 312, 200, 296)(196, 292, 204, 300, 224, 320, 250, 346, 279, 375, 259, 355, 225, 321, 205, 301)(198, 294, 209, 305, 233, 329, 264, 360, 284, 380, 265, 361, 234, 330, 210, 306)(201, 297, 217, 313, 249, 345, 276, 372, 245, 341, 215, 311, 244, 340, 218, 314)(203, 299, 222, 318, 258, 354, 275, 371, 243, 339, 214, 310, 242, 338, 223, 319)(206, 302, 226, 322, 236, 332, 211, 307, 235, 331, 266, 362, 260, 356, 227, 323)(207, 303, 228, 324, 241, 337, 213, 309, 240, 336, 274, 370, 261, 357, 229, 325)(219, 315, 253, 349, 282, 378, 262, 358, 230, 326, 252, 348, 281, 377, 254, 350)(221, 317, 256, 352, 283, 379, 263, 359, 231, 327, 251, 347, 280, 376, 257, 353)(237, 333, 269, 365, 287, 383, 277, 373, 246, 342, 268, 364, 286, 382, 270, 366)(239, 335, 272, 368, 288, 384, 278, 374, 247, 343, 267, 363, 285, 381, 273, 369) L = (1, 196)(2, 193)(3, 203)(4, 198)(5, 207)(6, 194)(7, 213)(8, 215)(9, 195)(10, 221)(11, 209)(12, 211)(13, 214)(14, 197)(15, 210)(16, 231)(17, 201)(18, 206)(19, 199)(20, 239)(21, 204)(22, 200)(23, 205)(24, 247)(25, 250)(26, 252)(27, 202)(28, 240)(29, 233)(30, 238)(31, 251)(32, 237)(33, 246)(34, 257)(35, 248)(36, 254)(37, 259)(38, 208)(39, 234)(40, 243)(41, 219)(42, 230)(43, 220)(44, 268)(45, 212)(46, 217)(47, 224)(48, 264)(49, 267)(50, 273)(51, 265)(52, 270)(53, 232)(54, 216)(55, 225)(56, 229)(57, 277)(58, 222)(59, 218)(60, 223)(61, 275)(62, 226)(63, 279)(64, 276)(65, 228)(66, 278)(67, 227)(68, 269)(69, 272)(70, 266)(71, 274)(72, 235)(73, 245)(74, 263)(75, 236)(76, 241)(77, 261)(78, 242)(79, 255)(80, 260)(81, 244)(82, 262)(83, 256)(84, 253)(85, 258)(86, 249)(87, 284)(88, 287)(89, 288)(90, 285)(91, 286)(92, 271)(93, 283)(94, 282)(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, 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 E23.961 Graph:: bipartite v = 36 e = 192 f = 112 degree seq :: [ 8^24, 16^12 ] E23.958 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 8}) Quotient :: dipole Aut^+ = SL(2,3) : C4 (small group id <96, 66>) Aut = $<192, 986>$ (small group id <192, 986>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y3^-1 * Y1^2 * Y3^-1, (Y3 * Y1^-1)^2, Y1^4, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1 * Y2^-1, Y2 * Y1 * Y3^-1 * Y2^-1 * Y3^-1 * Y1, (Y2^-1 * Y1)^3, Y2^8, (Y1 * Y2^-2 * R)^2, Y2^-1 * Y1 * Y2 * R * Y2^3 * R * Y2^-2, Y2^-4 * Y1 * Y2^-4 * Y1^-1, Y2 * Y3 * Y2^-2 * Y1^-1 * Y2 * Y1 * Y2^-2 * Y1^-1, Y2^-1 * Y3 * Y2 * R * Y2^2 * R * Y2 * Y1^-1 * Y2^-1, Y3 * Y2^-4 * Y3^-1 * Y2^-4, (Y3 * Y2^-1)^6 ] Map:: R = (1, 97, 2, 98, 6, 102, 4, 100)(3, 99, 9, 105, 17, 113, 11, 107)(5, 101, 14, 110, 18, 114, 15, 111)(7, 103, 19, 115, 12, 108, 21, 117)(8, 104, 22, 118, 13, 109, 23, 119)(10, 106, 26, 122, 37, 133, 28, 124)(16, 112, 34, 130, 38, 134, 35, 131)(20, 116, 40, 136, 30, 126, 42, 138)(24, 120, 46, 142, 31, 127, 47, 143)(25, 121, 49, 145, 29, 125, 50, 146)(27, 123, 53, 149, 68, 164, 55, 151)(32, 128, 60, 156, 33, 129, 62, 158)(36, 132, 66, 162, 69, 165, 67, 163)(39, 135, 70, 166, 43, 139, 71, 167)(41, 137, 74, 170, 58, 154, 76, 172)(44, 140, 79, 175, 45, 141, 81, 177)(48, 144, 85, 181, 59, 155, 86, 182)(51, 147, 77, 173, 57, 153, 73, 169)(52, 148, 78, 174, 56, 152, 72, 168)(54, 150, 75, 171, 92, 188, 90, 186)(61, 157, 84, 180, 63, 159, 83, 179)(64, 160, 82, 178, 65, 161, 80, 176)(87, 183, 96, 192, 88, 184, 95, 191)(89, 185, 94, 190, 91, 187, 93, 189)(193, 289, 195, 291, 202, 298, 219, 315, 246, 342, 228, 324, 208, 304, 197, 293)(194, 290, 199, 295, 212, 308, 233, 329, 267, 363, 240, 336, 216, 312, 200, 296)(196, 292, 204, 300, 222, 318, 250, 346, 282, 378, 251, 347, 223, 319, 205, 301)(198, 294, 209, 305, 229, 325, 260, 356, 284, 380, 261, 357, 230, 326, 210, 306)(201, 297, 215, 311, 237, 333, 274, 370, 258, 354, 268, 364, 243, 339, 217, 313)(203, 299, 214, 310, 236, 332, 272, 368, 259, 355, 266, 362, 249, 345, 221, 317)(206, 302, 224, 320, 253, 349, 277, 373, 245, 341, 264, 360, 231, 327, 211, 307)(207, 303, 225, 321, 255, 351, 278, 374, 247, 343, 270, 366, 235, 331, 213, 309)(218, 314, 242, 338, 280, 376, 252, 348, 226, 322, 256, 352, 281, 377, 244, 340)(220, 316, 241, 337, 279, 375, 254, 350, 227, 323, 257, 353, 283, 379, 248, 344)(232, 328, 263, 359, 286, 382, 271, 367, 238, 334, 275, 371, 287, 383, 265, 361)(234, 330, 262, 358, 285, 381, 273, 369, 239, 335, 276, 372, 288, 384, 269, 365) L = (1, 196)(2, 193)(3, 203)(4, 198)(5, 207)(6, 194)(7, 213)(8, 215)(9, 195)(10, 220)(11, 209)(12, 211)(13, 214)(14, 197)(15, 210)(16, 227)(17, 201)(18, 206)(19, 199)(20, 234)(21, 204)(22, 200)(23, 205)(24, 239)(25, 242)(26, 202)(27, 247)(28, 229)(29, 241)(30, 232)(31, 238)(32, 254)(33, 252)(34, 208)(35, 230)(36, 259)(37, 218)(38, 226)(39, 263)(40, 212)(41, 268)(42, 222)(43, 262)(44, 273)(45, 271)(46, 216)(47, 223)(48, 278)(49, 217)(50, 221)(51, 265)(52, 264)(53, 219)(54, 282)(55, 260)(56, 270)(57, 269)(58, 266)(59, 277)(60, 224)(61, 275)(62, 225)(63, 276)(64, 272)(65, 274)(66, 228)(67, 261)(68, 245)(69, 258)(70, 231)(71, 235)(72, 248)(73, 249)(74, 233)(75, 246)(76, 250)(77, 243)(78, 244)(79, 236)(80, 257)(81, 237)(82, 256)(83, 255)(84, 253)(85, 240)(86, 251)(87, 287)(88, 288)(89, 285)(90, 284)(91, 286)(92, 267)(93, 283)(94, 281)(95, 280)(96, 279)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 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 E23.962 Graph:: bipartite v = 36 e = 192 f = 112 degree seq :: [ 8^24, 16^12 ] E23.959 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 8}) Quotient :: dipole Aut^+ = SL(2,3) : C4 (small group id <96, 66>) Aut = $<192, 986>$ (small group id <192, 986>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, (R * Y3)^2, (R * Y1)^2, Y3^-3 * Y1, Y1 * Y2 * Y1^-1 * Y3 * Y2^-1 * Y3^-1, (R * Y2 * Y3^-1)^2, Y1 * Y2 * Y3^2 * Y2^-1 * Y3^-1, Y2^-1 * Y3^-2 * Y2 * Y1 * Y3^-1, Y2 * Y1^-2 * Y2^-1 * Y1 * Y3^-2 * Y1^-1, Y2^3 * Y1 * Y2^-1 * Y3 * Y2^-1 * Y3^-1, Y2 * Y1 * Y2^-3 * Y1^-1 * Y2 * Y1^-1, Y2^8, Y2^-1 * Y1 * Y2^-1 * Y3 * Y2^3 * Y3^-1, Y2 * R * Y2^3 * R * Y2 * Y1^-1, Y2^-1 * Y1^2 * Y2^-1 * R * Y2^-1 * Y3 * Y2^-1 * R * Y2^-1, Y2^-2 * Y3 * Y2^2 * Y1 * Y2^-2 * Y3^-1 * Y2^-2 * Y1^-1, Y2^2 * Y1 * Y2^-2 * Y1 * Y2^-2 * Y1^-1 * Y2^-2 * Y1^-1, (Y3 * Y2^-1)^6 ] Map:: R = (1, 97, 2, 98, 6, 102, 4, 100)(3, 99, 9, 105, 17, 113, 11, 107)(5, 101, 14, 110, 18, 114, 15, 111)(7, 103, 19, 115, 12, 108, 21, 117)(8, 104, 22, 118, 13, 109, 23, 119)(10, 106, 27, 123, 41, 137, 29, 125)(16, 112, 38, 134, 42, 138, 39, 135)(20, 116, 45, 141, 32, 128, 47, 143)(24, 120, 54, 150, 33, 129, 55, 151)(25, 121, 57, 153, 30, 126, 46, 142)(26, 122, 59, 155, 31, 127, 60, 156)(28, 124, 48, 144, 72, 168, 43, 139)(34, 130, 65, 161, 36, 132, 62, 158)(35, 131, 56, 152, 37, 133, 67, 163)(40, 136, 51, 147, 73, 169, 53, 149)(44, 140, 75, 171, 49, 145, 76, 172)(50, 146, 81, 177, 52, 148, 78, 174)(58, 154, 86, 182, 66, 162, 85, 181)(61, 157, 84, 180, 64, 160, 83, 179)(63, 159, 79, 175, 92, 188, 87, 183)(68, 164, 80, 176, 69, 165, 77, 173)(70, 166, 82, 178, 71, 167, 74, 170)(88, 184, 95, 191, 89, 185, 96, 192)(90, 186, 93, 189, 91, 187, 94, 190)(193, 289, 195, 291, 202, 298, 220, 316, 255, 351, 232, 328, 208, 304, 197, 293)(194, 290, 199, 295, 212, 308, 238, 334, 271, 367, 248, 344, 216, 312, 200, 296)(196, 292, 204, 300, 224, 320, 249, 345, 279, 375, 259, 355, 225, 321, 205, 301)(198, 294, 209, 305, 233, 329, 264, 360, 284, 380, 265, 361, 234, 330, 210, 306)(201, 297, 217, 313, 250, 346, 275, 371, 243, 339, 214, 310, 242, 338, 218, 314)(203, 299, 222, 318, 258, 354, 276, 372, 245, 341, 215, 311, 244, 340, 223, 319)(206, 302, 226, 322, 241, 337, 213, 309, 240, 336, 274, 370, 260, 356, 227, 323)(207, 303, 228, 324, 236, 332, 211, 307, 235, 331, 266, 362, 261, 357, 229, 325)(219, 315, 253, 349, 282, 378, 262, 358, 230, 326, 251, 347, 280, 376, 254, 350)(221, 317, 256, 352, 283, 379, 263, 359, 231, 327, 252, 348, 281, 377, 257, 353)(237, 333, 269, 365, 287, 383, 277, 373, 246, 342, 267, 363, 285, 381, 270, 366)(239, 335, 272, 368, 288, 384, 278, 374, 247, 343, 268, 364, 286, 382, 273, 369) L = (1, 196)(2, 193)(3, 203)(4, 198)(5, 207)(6, 194)(7, 213)(8, 215)(9, 195)(10, 221)(11, 209)(12, 211)(13, 214)(14, 197)(15, 210)(16, 231)(17, 201)(18, 206)(19, 199)(20, 239)(21, 204)(22, 200)(23, 205)(24, 247)(25, 238)(26, 252)(27, 202)(28, 235)(29, 233)(30, 249)(31, 251)(32, 237)(33, 246)(34, 254)(35, 259)(36, 257)(37, 248)(38, 208)(39, 234)(40, 245)(41, 219)(42, 230)(43, 264)(44, 268)(45, 212)(46, 222)(47, 224)(48, 220)(49, 267)(50, 270)(51, 232)(52, 273)(53, 265)(54, 216)(55, 225)(56, 227)(57, 217)(58, 277)(59, 218)(60, 223)(61, 275)(62, 228)(63, 279)(64, 276)(65, 226)(66, 278)(67, 229)(68, 269)(69, 272)(70, 266)(71, 274)(72, 240)(73, 243)(74, 263)(75, 236)(76, 241)(77, 261)(78, 244)(79, 255)(80, 260)(81, 242)(82, 262)(83, 256)(84, 253)(85, 258)(86, 250)(87, 284)(88, 288)(89, 287)(90, 286)(91, 285)(92, 271)(93, 282)(94, 283)(95, 280)(96, 281)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 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 E23.960 Graph:: bipartite v = 36 e = 192 f = 112 degree seq :: [ 8^24, 16^12 ] E23.960 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 8}) Quotient :: dipole Aut^+ = SL(2,3) : C4 (small group id <96, 66>) Aut = $<192, 986>$ (small group id <192, 986>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1^6, Y1^-1 * Y3^4 * Y1^-2, Y3 * Y1^-1 * Y3^-1 * Y1 * Y3^-1 * Y1^-1 * Y3, (Y1^-1 * Y3^-1)^4, Y1 * Y3 * Y1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 * Y3, Y3^2 * Y1 * Y3^-1 * Y1 * Y3^2 * Y1^-1 * Y3 * Y1^-1, (Y3 * Y2^-1)^8 ] Map:: R = (1, 97, 2, 98, 6, 102, 18, 114, 13, 109, 4, 100)(3, 99, 9, 105, 27, 123, 52, 148, 34, 130, 11, 107)(5, 101, 15, 111, 44, 140, 31, 127, 48, 144, 16, 112)(7, 103, 21, 117, 57, 153, 39, 135, 62, 158, 23, 119)(8, 104, 24, 120, 64, 160, 40, 136, 67, 163, 25, 121)(10, 106, 30, 126, 51, 147, 17, 113, 50, 146, 32, 128)(12, 108, 36, 132, 54, 150, 19, 115, 53, 149, 38, 134)(14, 110, 41, 137, 56, 152, 20, 116, 55, 151, 42, 138)(22, 118, 60, 156, 69, 165, 26, 122, 46, 142, 61, 157)(28, 124, 58, 154, 49, 145, 68, 164, 91, 187, 72, 168)(29, 125, 73, 169, 90, 186, 79, 175, 82, 178, 74, 170)(33, 129, 37, 133, 66, 162, 70, 166, 43, 139, 78, 174)(35, 131, 45, 141, 59, 155, 71, 167, 87, 183, 80, 176)(47, 143, 63, 159, 65, 161, 83, 179, 92, 188, 86, 182)(75, 171, 95, 191, 85, 181, 88, 184, 94, 190, 84, 180)(76, 172, 77, 173, 96, 192, 89, 185, 81, 177, 93, 189)(193, 289)(194, 290)(195, 291)(196, 292)(197, 293)(198, 294)(199, 295)(200, 296)(201, 297)(202, 298)(203, 299)(204, 300)(205, 301)(206, 302)(207, 303)(208, 304)(209, 305)(210, 306)(211, 307)(212, 308)(213, 309)(214, 310)(215, 311)(216, 312)(217, 313)(218, 314)(219, 315)(220, 316)(221, 317)(222, 318)(223, 319)(224, 320)(225, 321)(226, 322)(227, 323)(228, 324)(229, 325)(230, 326)(231, 327)(232, 328)(233, 329)(234, 330)(235, 331)(236, 332)(237, 333)(238, 334)(239, 335)(240, 336)(241, 337)(242, 338)(243, 339)(244, 340)(245, 341)(246, 342)(247, 343)(248, 344)(249, 345)(250, 346)(251, 347)(252, 348)(253, 349)(254, 350)(255, 351)(256, 352)(257, 353)(258, 354)(259, 355)(260, 356)(261, 357)(262, 358)(263, 359)(264, 360)(265, 361)(266, 362)(267, 363)(268, 364)(269, 365)(270, 366)(271, 367)(272, 368)(273, 369)(274, 370)(275, 371)(276, 372)(277, 373)(278, 374)(279, 375)(280, 376)(281, 377)(282, 378)(283, 379)(284, 380)(285, 381)(286, 382)(287, 383)(288, 384) L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 211)(7, 214)(8, 194)(9, 220)(10, 223)(11, 225)(12, 229)(13, 231)(14, 196)(15, 237)(16, 239)(17, 197)(18, 244)(19, 235)(20, 198)(21, 250)(22, 232)(23, 224)(24, 257)(25, 221)(26, 200)(27, 262)(28, 256)(29, 201)(30, 247)(31, 210)(32, 268)(33, 269)(34, 260)(35, 203)(36, 264)(37, 212)(38, 261)(39, 218)(40, 205)(41, 266)(42, 272)(43, 206)(44, 275)(45, 276)(46, 207)(47, 228)(48, 279)(49, 208)(50, 233)(51, 281)(52, 209)(53, 241)(54, 253)(55, 282)(56, 251)(57, 243)(58, 234)(59, 213)(60, 240)(61, 285)(62, 283)(63, 215)(64, 271)(65, 286)(66, 216)(67, 278)(68, 217)(69, 288)(70, 273)(71, 219)(72, 236)(73, 246)(74, 267)(75, 222)(76, 284)(77, 263)(78, 259)(79, 226)(80, 254)(81, 227)(82, 230)(83, 245)(84, 252)(85, 238)(86, 287)(87, 277)(88, 242)(89, 255)(90, 280)(91, 248)(92, 249)(93, 274)(94, 270)(95, 258)(96, 265)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E23.959 Graph:: simple bipartite v = 112 e = 192 f = 36 degree seq :: [ 2^96, 12^16 ] E23.961 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 8}) Quotient :: dipole Aut^+ = SL(2,3) : C4 (small group id <96, 66>) Aut = $<192, 986>$ (small group id <192, 986>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1^6, Y3 * Y1^2 * Y3^-1 * Y1^-1 * Y3^2, Y1^2 * Y3^3 * Y1^-1 * Y3^-1, Y3 * Y1^2 * Y3 * Y1 * Y3^2 * Y1, Y1^-1 * Y3^-1 * Y1^-1 * Y3^-2 * Y1^-1 * Y3^-1 * Y1^-1, Y1 * Y3 * Y1^3 * Y3^-1 * Y1^2, Y3^-1 * Y1^-1 * Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1^-1, Y3 * Y1^-1 * Y3 * Y1 * Y3^2 * Y1^-2, Y3^-1 * Y1 * Y3^-1 * Y1^-1 * Y3^-2 * Y1^2, (Y3 * Y2^-1)^8 ] Map:: polytopal R = (1, 97, 2, 98, 6, 102, 18, 114, 13, 109, 4, 100)(3, 99, 9, 105, 27, 123, 53, 149, 34, 130, 11, 107)(5, 101, 15, 111, 44, 140, 54, 150, 48, 144, 16, 112)(7, 103, 21, 117, 59, 155, 39, 135, 31, 127, 23, 119)(8, 104, 24, 120, 66, 162, 40, 136, 69, 165, 25, 121)(10, 106, 30, 126, 45, 141, 61, 157, 80, 176, 32, 128)(12, 108, 36, 132, 56, 152, 19, 115, 55, 151, 38, 134)(14, 110, 41, 137, 52, 148, 20, 116, 57, 153, 42, 138)(17, 113, 50, 146, 64, 160, 83, 179, 35, 131, 51, 147)(22, 118, 62, 158, 67, 163, 87, 183, 46, 142, 63, 159)(26, 122, 71, 167, 90, 186, 47, 143, 65, 161, 72, 168)(28, 124, 60, 156, 49, 145, 70, 166, 78, 174, 74, 170)(29, 125, 75, 171, 85, 181, 37, 133, 68, 164, 76, 172)(33, 129, 58, 154, 86, 182, 73, 169, 43, 139, 82, 178)(77, 173, 95, 191, 89, 185, 81, 177, 96, 192, 92, 188)(79, 175, 91, 187, 94, 190, 88, 184, 84, 180, 93, 189)(193, 289)(194, 290)(195, 291)(196, 292)(197, 293)(198, 294)(199, 295)(200, 296)(201, 297)(202, 298)(203, 299)(204, 300)(205, 301)(206, 302)(207, 303)(208, 304)(209, 305)(210, 306)(211, 307)(212, 308)(213, 309)(214, 310)(215, 311)(216, 312)(217, 313)(218, 314)(219, 315)(220, 316)(221, 317)(222, 318)(223, 319)(224, 320)(225, 321)(226, 322)(227, 323)(228, 324)(229, 325)(230, 326)(231, 327)(232, 328)(233, 329)(234, 330)(235, 331)(236, 332)(237, 333)(238, 334)(239, 335)(240, 336)(241, 337)(242, 338)(243, 339)(244, 340)(245, 341)(246, 342)(247, 343)(248, 344)(249, 345)(250, 346)(251, 347)(252, 348)(253, 349)(254, 350)(255, 351)(256, 352)(257, 353)(258, 354)(259, 355)(260, 356)(261, 357)(262, 358)(263, 359)(264, 360)(265, 361)(266, 362)(267, 363)(268, 364)(269, 365)(270, 366)(271, 367)(272, 368)(273, 369)(274, 370)(275, 371)(276, 372)(277, 373)(278, 374)(279, 375)(280, 376)(281, 377)(282, 378)(283, 379)(284, 380)(285, 381)(286, 382)(287, 383)(288, 384) L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 211)(7, 214)(8, 194)(9, 220)(10, 223)(11, 225)(12, 229)(13, 231)(14, 196)(15, 237)(16, 239)(17, 197)(18, 245)(19, 221)(20, 198)(21, 252)(22, 228)(23, 256)(24, 259)(25, 235)(26, 200)(27, 265)(28, 258)(29, 201)(30, 249)(31, 270)(32, 271)(33, 273)(34, 262)(35, 203)(36, 266)(37, 226)(38, 264)(39, 279)(40, 205)(41, 268)(42, 275)(43, 206)(44, 218)(45, 280)(46, 207)(47, 232)(48, 224)(49, 208)(50, 219)(51, 284)(52, 209)(53, 253)(54, 210)(55, 241)(56, 282)(57, 277)(58, 212)(59, 243)(60, 234)(61, 213)(62, 240)(63, 285)(64, 281)(65, 215)(66, 250)(67, 286)(68, 216)(69, 255)(70, 217)(71, 251)(72, 288)(73, 269)(74, 236)(75, 261)(76, 276)(77, 222)(78, 244)(79, 263)(80, 233)(81, 272)(82, 248)(83, 246)(84, 227)(85, 283)(86, 230)(87, 247)(88, 257)(89, 238)(90, 287)(91, 242)(92, 254)(93, 278)(94, 274)(95, 260)(96, 267)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E23.957 Graph:: simple bipartite v = 112 e = 192 f = 36 degree seq :: [ 2^96, 12^16 ] E23.962 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 8}) Quotient :: dipole Aut^+ = SL(2,3) : C4 (small group id <96, 66>) Aut = $<192, 986>$ (small group id <192, 986>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, Y1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1, (R * Y2 * Y3^-1)^2, Y1^6, Y3^-1 * Y1^-1 * Y3^-2 * Y1^-3 * Y3 * Y1^-1, Y3^-2 * Y1^-2 * Y3^-3 * Y1 * Y3^-1, Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3^-3 * Y1^-1, (Y3 * Y2^-1)^8 ] Map:: R = (1, 97, 2, 98, 6, 102, 18, 114, 13, 109, 4, 100)(3, 99, 9, 105, 24, 120, 34, 130, 14, 110, 11, 107)(5, 101, 15, 111, 7, 103, 20, 116, 39, 135, 16, 112)(8, 104, 22, 118, 19, 115, 33, 129, 32, 128, 12, 108)(10, 106, 26, 122, 56, 152, 65, 161, 30, 126, 28, 124)(17, 113, 40, 136, 36, 132, 44, 140, 79, 175, 41, 137)(21, 117, 45, 141, 75, 171, 38, 134, 37, 133, 47, 143)(23, 119, 50, 146, 48, 144, 70, 166, 91, 187, 51, 147)(25, 121, 54, 150, 53, 149, 35, 131, 64, 160, 29, 125)(27, 123, 58, 154, 52, 148, 92, 188, 62, 158, 60, 156)(31, 127, 49, 145, 82, 178, 43, 139, 69, 165, 68, 164)(42, 138, 80, 176, 76, 172, 83, 179, 67, 163, 81, 177)(46, 142, 84, 180, 55, 151, 74, 170, 87, 183, 71, 167)(57, 153, 89, 185, 73, 169, 66, 162, 86, 182, 61, 157)(59, 155, 85, 181, 93, 189, 96, 192, 95, 191, 94, 190)(63, 159, 90, 186, 78, 174, 77, 173, 88, 184, 72, 168)(193, 289)(194, 290)(195, 291)(196, 292)(197, 293)(198, 294)(199, 295)(200, 296)(201, 297)(202, 298)(203, 299)(204, 300)(205, 301)(206, 302)(207, 303)(208, 304)(209, 305)(210, 306)(211, 307)(212, 308)(213, 309)(214, 310)(215, 311)(216, 312)(217, 313)(218, 314)(219, 315)(220, 316)(221, 317)(222, 318)(223, 319)(224, 320)(225, 321)(226, 322)(227, 323)(228, 324)(229, 325)(230, 326)(231, 327)(232, 328)(233, 329)(234, 330)(235, 331)(236, 332)(237, 333)(238, 334)(239, 335)(240, 336)(241, 337)(242, 338)(243, 339)(244, 340)(245, 341)(246, 342)(247, 343)(248, 344)(249, 345)(250, 346)(251, 347)(252, 348)(253, 349)(254, 350)(255, 351)(256, 352)(257, 353)(258, 354)(259, 355)(260, 356)(261, 357)(262, 358)(263, 359)(264, 360)(265, 361)(266, 362)(267, 363)(268, 364)(269, 365)(270, 366)(271, 367)(272, 368)(273, 369)(274, 370)(275, 371)(276, 372)(277, 373)(278, 374)(279, 375)(280, 376)(281, 377)(282, 378)(283, 379)(284, 380)(285, 381)(286, 382)(287, 383)(288, 384) L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 211)(7, 213)(8, 194)(9, 198)(10, 219)(11, 221)(12, 223)(13, 208)(14, 196)(15, 228)(16, 230)(17, 197)(18, 226)(19, 235)(20, 210)(21, 238)(22, 240)(23, 200)(24, 245)(25, 201)(26, 216)(27, 251)(28, 253)(29, 255)(30, 203)(31, 259)(32, 243)(33, 205)(34, 257)(35, 206)(36, 264)(37, 207)(38, 266)(39, 233)(40, 268)(41, 270)(42, 209)(43, 272)(44, 212)(45, 231)(46, 277)(47, 278)(48, 280)(49, 214)(50, 254)(51, 282)(52, 215)(53, 269)(54, 279)(55, 217)(56, 265)(57, 218)(58, 248)(59, 234)(60, 262)(61, 237)(62, 220)(63, 271)(64, 276)(65, 284)(66, 222)(67, 286)(68, 249)(69, 224)(70, 225)(71, 227)(72, 283)(73, 229)(74, 287)(75, 281)(76, 260)(77, 232)(78, 242)(79, 273)(80, 285)(81, 274)(82, 258)(83, 236)(84, 267)(85, 244)(86, 261)(87, 239)(88, 256)(89, 241)(90, 246)(91, 250)(92, 288)(93, 247)(94, 263)(95, 252)(96, 275)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E23.958 Graph:: simple bipartite v = 112 e = 192 f = 36 degree seq :: [ 2^96, 12^16 ] E23.963 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 6, 8}) Quotient :: edge Aut^+ = SL(2,3) : C4 (small group id <96, 67>) Aut = (SL(2,3) : C4) : C2 (small group id <192, 988>) |r| :: 2 Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, T2^6, T2^-1 * T1 * T2 * T1^2 * T2 * T1, T2^-2 * T1 * T2^-3 * T1^-1 * T2^-1, (T2^-1 * T1)^4, (T1^-1 * T2^-1)^8 ] Map:: non-degenerate R = (1, 3, 10, 29, 16, 5)(2, 7, 20, 52, 24, 8)(4, 12, 34, 69, 38, 13)(6, 17, 46, 87, 49, 18)(9, 26, 62, 44, 65, 27)(11, 31, 73, 45, 74, 32)(14, 40, 68, 28, 67, 41)(15, 42, 71, 30, 70, 43)(19, 50, 77, 59, 80, 37)(21, 54, 92, 60, 84, 55)(22, 39, 83, 51, 66, 57)(23, 33, 63, 53, 81, 58)(25, 35, 78, 85, 82, 61)(36, 64, 72, 76, 95, 79)(47, 88, 96, 90, 94, 75)(48, 56, 93, 86, 91, 89)(97, 98, 102, 100)(99, 105, 121, 107)(101, 110, 135, 111)(103, 115, 128, 117)(104, 118, 152, 119)(106, 124, 162, 126)(108, 129, 171, 131)(109, 132, 136, 133)(112, 140, 181, 141)(113, 138, 151, 143)(114, 144, 160, 123)(116, 147, 187, 149)(120, 155, 169, 156)(122, 146, 167, 159)(125, 148, 183, 165)(127, 168, 190, 153)(130, 172, 163, 173)(134, 177, 192, 178)(137, 174, 189, 180)(139, 154, 161, 176)(142, 182, 191, 158)(145, 166, 188, 186)(150, 164, 157, 185)(170, 175, 184, 179) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 16^4 ), ( 16^6 ) } Outer automorphisms :: reflexible Dual of E23.967 Transitivity :: ET+ Graph:: simple bipartite v = 40 e = 96 f = 12 degree seq :: [ 4^24, 6^16 ] E23.964 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 6, 8}) Quotient :: edge Aut^+ = SL(2,3) : C4 (small group id <96, 67>) Aut = (SL(2,3) : C4) : C2 (small group id <192, 988>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1 * T2^2 * T1^-1 * T2^-2, T1^6, T1^-3 * T2^4, T1^3 * T2^-1 * T1^-3 * T2, (T2^-1 * T1^-1)^4, (T1 * T2^-1)^4, T1 * T2 * T1 * T2^-1 * T1^-2 * T2 * T1 * T2^-1 ] Map:: polytopal non-degenerate R = (1, 3, 10, 30, 18, 46, 17, 5)(2, 7, 22, 38, 13, 37, 26, 8)(4, 12, 31, 20, 6, 19, 41, 14)(9, 28, 44, 67, 33, 43, 15, 29)(11, 32, 42, 61, 27, 45, 16, 34)(21, 52, 59, 69, 55, 58, 24, 53)(23, 54, 57, 78, 51, 60, 25, 56)(35, 70, 49, 77, 47, 74, 39, 71)(36, 72, 50, 64, 48, 62, 40, 73)(63, 83, 85, 91, 75, 86, 65, 84)(66, 87, 82, 92, 76, 89, 68, 88)(79, 93, 90, 96, 81, 95, 80, 94)(97, 98, 102, 114, 109, 100)(99, 105, 123, 142, 129, 107)(101, 111, 138, 126, 140, 112)(103, 117, 147, 133, 151, 119)(104, 120, 153, 134, 155, 121)(106, 118, 137, 113, 122, 127)(108, 131, 144, 115, 143, 132)(110, 135, 146, 116, 145, 136)(124, 158, 171, 139, 168, 159)(125, 160, 181, 163, 169, 161)(128, 162, 148, 141, 172, 154)(130, 164, 149, 157, 178, 165)(150, 175, 170, 156, 177, 166)(152, 176, 173, 174, 186, 167)(179, 191, 185, 182, 189, 183)(180, 192, 188, 187, 190, 184) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8^6 ), ( 8^8 ) } Outer automorphisms :: reflexible Dual of E23.968 Transitivity :: ET+ Graph:: bipartite v = 28 e = 96 f = 24 degree seq :: [ 6^16, 8^12 ] E23.965 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 6, 8}) Quotient :: edge Aut^+ = SL(2,3) : C4 (small group id <96, 67>) Aut = (SL(2,3) : C4) : C2 (small group id <192, 988>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, T2^4, (F * T2)^2, T1^-2 * T2 * T1^2 * T2^-1, T1 * T2 * T1^-1 * T2 * T1^-1 * T2, T2 * T1^2 * T2^-1 * T1^-2, T1^8, T1^-4 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, T2^2 * T1 * T2^2 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1^-1 ] Map:: non-degenerate R = (1, 3, 10, 5)(2, 7, 21, 8)(4, 12, 30, 14)(6, 18, 41, 19)(9, 23, 47, 25)(11, 24, 48, 29)(13, 28, 52, 33)(15, 35, 46, 22)(16, 36, 58, 31)(17, 38, 66, 39)(20, 42, 70, 43)(26, 49, 77, 51)(27, 50, 78, 53)(32, 57, 83, 59)(34, 61, 81, 54)(37, 63, 87, 64)(40, 67, 90, 68)(44, 71, 93, 73)(45, 72, 94, 74)(55, 82, 92, 79)(56, 75, 95, 84)(60, 80, 88, 65)(62, 69, 91, 86)(76, 89, 85, 96)(97, 98, 102, 113, 133, 128, 109, 100)(99, 105, 114, 136, 159, 150, 124, 107)(101, 111, 115, 138, 160, 156, 129, 112)(103, 116, 134, 161, 153, 127, 108, 118)(104, 119, 135, 163, 155, 130, 110, 120)(106, 122, 137, 165, 183, 175, 148, 123)(117, 140, 162, 185, 179, 152, 126, 141)(121, 145, 164, 187, 177, 151, 125, 146)(131, 158, 166, 188, 176, 149, 132, 147)(139, 167, 184, 181, 154, 171, 142, 168)(143, 172, 186, 180, 157, 170, 144, 169)(173, 191, 182, 190, 178, 189, 174, 192) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 12^4 ), ( 12^8 ) } Outer automorphisms :: reflexible Dual of E23.966 Transitivity :: ET+ Graph:: simple bipartite v = 36 e = 96 f = 16 degree seq :: [ 4^24, 8^12 ] E23.966 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 6, 8}) Quotient :: loop Aut^+ = SL(2,3) : C4 (small group id <96, 67>) Aut = (SL(2,3) : C4) : C2 (small group id <192, 988>) |r| :: 2 Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, T2^6, T2^-1 * T1 * T2 * T1^2 * T2 * T1, T2^-2 * T1 * T2^-3 * T1^-1 * T2^-1, (T2^-1 * T1)^4, (T1^-1 * T2^-1)^8 ] Map:: non-degenerate R = (1, 97, 3, 99, 10, 106, 29, 125, 16, 112, 5, 101)(2, 98, 7, 103, 20, 116, 52, 148, 24, 120, 8, 104)(4, 100, 12, 108, 34, 130, 69, 165, 38, 134, 13, 109)(6, 102, 17, 113, 46, 142, 87, 183, 49, 145, 18, 114)(9, 105, 26, 122, 62, 158, 44, 140, 65, 161, 27, 123)(11, 107, 31, 127, 73, 169, 45, 141, 74, 170, 32, 128)(14, 110, 40, 136, 68, 164, 28, 124, 67, 163, 41, 137)(15, 111, 42, 138, 71, 167, 30, 126, 70, 166, 43, 139)(19, 115, 50, 146, 77, 173, 59, 155, 80, 176, 37, 133)(21, 117, 54, 150, 92, 188, 60, 156, 84, 180, 55, 151)(22, 118, 39, 135, 83, 179, 51, 147, 66, 162, 57, 153)(23, 119, 33, 129, 63, 159, 53, 149, 81, 177, 58, 154)(25, 121, 35, 131, 78, 174, 85, 181, 82, 178, 61, 157)(36, 132, 64, 160, 72, 168, 76, 172, 95, 191, 79, 175)(47, 143, 88, 184, 96, 192, 90, 186, 94, 190, 75, 171)(48, 144, 56, 152, 93, 189, 86, 182, 91, 187, 89, 185) L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 110)(6, 100)(7, 115)(8, 118)(9, 121)(10, 124)(11, 99)(12, 129)(13, 132)(14, 135)(15, 101)(16, 140)(17, 138)(18, 144)(19, 128)(20, 147)(21, 103)(22, 152)(23, 104)(24, 155)(25, 107)(26, 146)(27, 114)(28, 162)(29, 148)(30, 106)(31, 168)(32, 117)(33, 171)(34, 172)(35, 108)(36, 136)(37, 109)(38, 177)(39, 111)(40, 133)(41, 174)(42, 151)(43, 154)(44, 181)(45, 112)(46, 182)(47, 113)(48, 160)(49, 166)(50, 167)(51, 187)(52, 183)(53, 116)(54, 164)(55, 143)(56, 119)(57, 127)(58, 161)(59, 169)(60, 120)(61, 185)(62, 142)(63, 122)(64, 123)(65, 176)(66, 126)(67, 173)(68, 157)(69, 125)(70, 188)(71, 159)(72, 190)(73, 156)(74, 175)(75, 131)(76, 163)(77, 130)(78, 189)(79, 184)(80, 139)(81, 192)(82, 134)(83, 170)(84, 137)(85, 141)(86, 191)(87, 165)(88, 179)(89, 150)(90, 145)(91, 149)(92, 186)(93, 180)(94, 153)(95, 158)(96, 178) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E23.965 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 16 e = 96 f = 36 degree seq :: [ 12^16 ] E23.967 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 6, 8}) Quotient :: loop Aut^+ = SL(2,3) : C4 (small group id <96, 67>) Aut = (SL(2,3) : C4) : C2 (small group id <192, 988>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1 * T2^2 * T1^-1 * T2^-2, T1^6, T1^-3 * T2^4, T1^3 * T2^-1 * T1^-3 * T2, (T2^-1 * T1^-1)^4, (T1 * T2^-1)^4, T1 * T2 * T1 * T2^-1 * T1^-2 * T2 * T1 * T2^-1 ] Map:: non-degenerate R = (1, 97, 3, 99, 10, 106, 30, 126, 18, 114, 46, 142, 17, 113, 5, 101)(2, 98, 7, 103, 22, 118, 38, 134, 13, 109, 37, 133, 26, 122, 8, 104)(4, 100, 12, 108, 31, 127, 20, 116, 6, 102, 19, 115, 41, 137, 14, 110)(9, 105, 28, 124, 44, 140, 67, 163, 33, 129, 43, 139, 15, 111, 29, 125)(11, 107, 32, 128, 42, 138, 61, 157, 27, 123, 45, 141, 16, 112, 34, 130)(21, 117, 52, 148, 59, 155, 69, 165, 55, 151, 58, 154, 24, 120, 53, 149)(23, 119, 54, 150, 57, 153, 78, 174, 51, 147, 60, 156, 25, 121, 56, 152)(35, 131, 70, 166, 49, 145, 77, 173, 47, 143, 74, 170, 39, 135, 71, 167)(36, 132, 72, 168, 50, 146, 64, 160, 48, 144, 62, 158, 40, 136, 73, 169)(63, 159, 83, 179, 85, 181, 91, 187, 75, 171, 86, 182, 65, 161, 84, 180)(66, 162, 87, 183, 82, 178, 92, 188, 76, 172, 89, 185, 68, 164, 88, 184)(79, 175, 93, 189, 90, 186, 96, 192, 81, 177, 95, 191, 80, 176, 94, 190) L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 111)(6, 114)(7, 117)(8, 120)(9, 123)(10, 118)(11, 99)(12, 131)(13, 100)(14, 135)(15, 138)(16, 101)(17, 122)(18, 109)(19, 143)(20, 145)(21, 147)(22, 137)(23, 103)(24, 153)(25, 104)(26, 127)(27, 142)(28, 158)(29, 160)(30, 140)(31, 106)(32, 162)(33, 107)(34, 164)(35, 144)(36, 108)(37, 151)(38, 155)(39, 146)(40, 110)(41, 113)(42, 126)(43, 168)(44, 112)(45, 172)(46, 129)(47, 132)(48, 115)(49, 136)(50, 116)(51, 133)(52, 141)(53, 157)(54, 175)(55, 119)(56, 176)(57, 134)(58, 128)(59, 121)(60, 177)(61, 178)(62, 171)(63, 124)(64, 181)(65, 125)(66, 148)(67, 169)(68, 149)(69, 130)(70, 150)(71, 152)(72, 159)(73, 161)(74, 156)(75, 139)(76, 154)(77, 174)(78, 186)(79, 170)(80, 173)(81, 166)(82, 165)(83, 191)(84, 192)(85, 163)(86, 189)(87, 179)(88, 180)(89, 182)(90, 167)(91, 190)(92, 187)(93, 183)(94, 184)(95, 185)(96, 188) local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E23.963 Transitivity :: ET+ VT+ AT Graph:: v = 12 e = 96 f = 40 degree seq :: [ 16^12 ] E23.968 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 6, 8}) Quotient :: loop Aut^+ = SL(2,3) : C4 (small group id <96, 67>) Aut = (SL(2,3) : C4) : C2 (small group id <192, 988>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, T2^4, (F * T2)^2, T1^-2 * T2 * T1^2 * T2^-1, T1 * T2 * T1^-1 * T2 * T1^-1 * T2, T2 * T1^2 * T2^-1 * T1^-2, T1^8, T1^-4 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, T2^2 * T1 * T2^2 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 97, 3, 99, 10, 106, 5, 101)(2, 98, 7, 103, 21, 117, 8, 104)(4, 100, 12, 108, 30, 126, 14, 110)(6, 102, 18, 114, 41, 137, 19, 115)(9, 105, 23, 119, 47, 143, 25, 121)(11, 107, 24, 120, 48, 144, 29, 125)(13, 109, 28, 124, 52, 148, 33, 129)(15, 111, 35, 131, 46, 142, 22, 118)(16, 112, 36, 132, 58, 154, 31, 127)(17, 113, 38, 134, 66, 162, 39, 135)(20, 116, 42, 138, 70, 166, 43, 139)(26, 122, 49, 145, 77, 173, 51, 147)(27, 123, 50, 146, 78, 174, 53, 149)(32, 128, 57, 153, 83, 179, 59, 155)(34, 130, 61, 157, 81, 177, 54, 150)(37, 133, 63, 159, 87, 183, 64, 160)(40, 136, 67, 163, 90, 186, 68, 164)(44, 140, 71, 167, 93, 189, 73, 169)(45, 141, 72, 168, 94, 190, 74, 170)(55, 151, 82, 178, 92, 188, 79, 175)(56, 152, 75, 171, 95, 191, 84, 180)(60, 156, 80, 176, 88, 184, 65, 161)(62, 158, 69, 165, 91, 187, 86, 182)(76, 172, 89, 185, 85, 181, 96, 192) L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 111)(6, 113)(7, 116)(8, 119)(9, 114)(10, 122)(11, 99)(12, 118)(13, 100)(14, 120)(15, 115)(16, 101)(17, 133)(18, 136)(19, 138)(20, 134)(21, 140)(22, 103)(23, 135)(24, 104)(25, 145)(26, 137)(27, 106)(28, 107)(29, 146)(30, 141)(31, 108)(32, 109)(33, 112)(34, 110)(35, 158)(36, 147)(37, 128)(38, 161)(39, 163)(40, 159)(41, 165)(42, 160)(43, 167)(44, 162)(45, 117)(46, 168)(47, 172)(48, 169)(49, 164)(50, 121)(51, 131)(52, 123)(53, 132)(54, 124)(55, 125)(56, 126)(57, 127)(58, 171)(59, 130)(60, 129)(61, 170)(62, 166)(63, 150)(64, 156)(65, 153)(66, 185)(67, 155)(68, 187)(69, 183)(70, 188)(71, 184)(72, 139)(73, 143)(74, 144)(75, 142)(76, 186)(77, 191)(78, 192)(79, 148)(80, 149)(81, 151)(82, 189)(83, 152)(84, 157)(85, 154)(86, 190)(87, 175)(88, 181)(89, 179)(90, 180)(91, 177)(92, 176)(93, 174)(94, 178)(95, 182)(96, 173) local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E23.964 Transitivity :: ET+ VT+ AT Graph:: simple v = 24 e = 96 f = 28 degree seq :: [ 8^24 ] E23.969 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 8}) Quotient :: dipole Aut^+ = SL(2,3) : C4 (small group id <96, 67>) Aut = (SL(2,3) : C4) : C2 (small group id <192, 988>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y1^2 * Y3^-1 * Y1, Y3 * Y2 * Y3^-1 * Y1^-1 * Y2^-1 * Y1, Y2^-1 * Y1 * Y3 * Y2 * Y1^-1 * Y3^-1, (R * Y2 * Y3^-1)^2, Y2^6, Y1^-1 * Y2 * Y1 * Y2^-1 * Y3^-1 * Y2 * Y1^-1, Y1 * Y2^-1 * Y1 * Y2 * Y1^2 * Y2, Y2^2 * Y1 * Y2^3 * Y3 * Y2, Y3 * Y2^-1 * Y1 * Y2 * Y3^-1 * Y2 * Y1^-1 * Y2^-1, Y1 * Y2^-1 * Y1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1, Y1 * Y2 * Y3 * Y2 * Y1 * Y2 * Y1^-1 * Y2^-2, (Y3 * Y2^-1)^8 ] Map:: R = (1, 97, 2, 98, 6, 102, 4, 100)(3, 99, 9, 105, 25, 121, 11, 107)(5, 101, 14, 110, 39, 135, 15, 111)(7, 103, 19, 115, 32, 128, 21, 117)(8, 104, 22, 118, 56, 152, 23, 119)(10, 106, 28, 124, 66, 162, 30, 126)(12, 108, 33, 129, 75, 171, 35, 131)(13, 109, 36, 132, 40, 136, 37, 133)(16, 112, 44, 140, 85, 181, 45, 141)(17, 113, 42, 138, 55, 151, 47, 143)(18, 114, 48, 144, 64, 160, 27, 123)(20, 116, 51, 147, 91, 187, 53, 149)(24, 120, 59, 155, 73, 169, 60, 156)(26, 122, 50, 146, 71, 167, 63, 159)(29, 125, 52, 148, 87, 183, 69, 165)(31, 127, 72, 168, 94, 190, 57, 153)(34, 130, 76, 172, 67, 163, 77, 173)(38, 134, 81, 177, 96, 192, 82, 178)(41, 137, 78, 174, 93, 189, 84, 180)(43, 139, 58, 154, 65, 161, 80, 176)(46, 142, 86, 182, 95, 191, 62, 158)(49, 145, 70, 166, 92, 188, 90, 186)(54, 150, 68, 164, 61, 157, 89, 185)(74, 170, 79, 175, 88, 184, 83, 179)(193, 289, 195, 291, 202, 298, 221, 317, 208, 304, 197, 293)(194, 290, 199, 295, 212, 308, 244, 340, 216, 312, 200, 296)(196, 292, 204, 300, 226, 322, 261, 357, 230, 326, 205, 301)(198, 294, 209, 305, 238, 334, 279, 375, 241, 337, 210, 306)(201, 297, 218, 314, 254, 350, 236, 332, 257, 353, 219, 315)(203, 299, 223, 319, 265, 361, 237, 333, 266, 362, 224, 320)(206, 302, 232, 328, 260, 356, 220, 316, 259, 355, 233, 329)(207, 303, 234, 330, 263, 359, 222, 318, 262, 358, 235, 331)(211, 307, 242, 338, 269, 365, 251, 347, 272, 368, 229, 325)(213, 309, 246, 342, 284, 380, 252, 348, 276, 372, 247, 343)(214, 310, 231, 327, 275, 371, 243, 339, 258, 354, 249, 345)(215, 311, 225, 321, 255, 351, 245, 341, 273, 369, 250, 346)(217, 313, 227, 323, 270, 366, 277, 373, 274, 370, 253, 349)(228, 324, 256, 352, 264, 360, 268, 364, 287, 383, 271, 367)(239, 335, 280, 376, 288, 384, 282, 378, 286, 382, 267, 363)(240, 336, 248, 344, 285, 381, 278, 374, 283, 379, 281, 377) L = (1, 196)(2, 193)(3, 203)(4, 198)(5, 207)(6, 194)(7, 213)(8, 215)(9, 195)(10, 222)(11, 217)(12, 227)(13, 229)(14, 197)(15, 231)(16, 237)(17, 239)(18, 219)(19, 199)(20, 245)(21, 224)(22, 200)(23, 248)(24, 252)(25, 201)(26, 255)(27, 256)(28, 202)(29, 261)(30, 258)(31, 249)(32, 211)(33, 204)(34, 269)(35, 267)(36, 205)(37, 232)(38, 274)(39, 206)(40, 228)(41, 276)(42, 209)(43, 272)(44, 208)(45, 277)(46, 254)(47, 247)(48, 210)(49, 282)(50, 218)(51, 212)(52, 221)(53, 283)(54, 281)(55, 234)(56, 214)(57, 286)(58, 235)(59, 216)(60, 265)(61, 260)(62, 287)(63, 263)(64, 240)(65, 250)(66, 220)(67, 268)(68, 246)(69, 279)(70, 241)(71, 242)(72, 223)(73, 251)(74, 275)(75, 225)(76, 226)(77, 259)(78, 233)(79, 266)(80, 257)(81, 230)(82, 288)(83, 280)(84, 285)(85, 236)(86, 238)(87, 244)(88, 271)(89, 253)(90, 284)(91, 243)(92, 262)(93, 270)(94, 264)(95, 278)(96, 273)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 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 E23.972 Graph:: bipartite v = 40 e = 192 f = 108 degree seq :: [ 8^24, 12^16 ] E23.970 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 8}) Quotient :: dipole Aut^+ = SL(2,3) : C4 (small group id <96, 67>) Aut = (SL(2,3) : C4) : C2 (small group id <192, 988>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y1 * Y2^2 * Y1^-1 * Y2^-2, Y1^6, Y2^3 * Y1^-3 * Y2, Y1^3 * Y2^-1 * Y1^-3 * Y2, (Y3^-1 * Y1^-1)^4, (Y1 * Y2^-1)^4, Y1 * Y2 * Y1 * Y2^-1 * Y1^-2 * Y2 * Y1 * Y2^-1 ] Map:: R = (1, 97, 2, 98, 6, 102, 18, 114, 13, 109, 4, 100)(3, 99, 9, 105, 27, 123, 46, 142, 33, 129, 11, 107)(5, 101, 15, 111, 42, 138, 30, 126, 44, 140, 16, 112)(7, 103, 21, 117, 51, 147, 37, 133, 55, 151, 23, 119)(8, 104, 24, 120, 57, 153, 38, 134, 59, 155, 25, 121)(10, 106, 22, 118, 41, 137, 17, 113, 26, 122, 31, 127)(12, 108, 35, 131, 48, 144, 19, 115, 47, 143, 36, 132)(14, 110, 39, 135, 50, 146, 20, 116, 49, 145, 40, 136)(28, 124, 62, 158, 75, 171, 43, 139, 72, 168, 63, 159)(29, 125, 64, 160, 85, 181, 67, 163, 73, 169, 65, 161)(32, 128, 66, 162, 52, 148, 45, 141, 76, 172, 58, 154)(34, 130, 68, 164, 53, 149, 61, 157, 82, 178, 69, 165)(54, 150, 79, 175, 74, 170, 60, 156, 81, 177, 70, 166)(56, 152, 80, 176, 77, 173, 78, 174, 90, 186, 71, 167)(83, 179, 95, 191, 89, 185, 86, 182, 93, 189, 87, 183)(84, 180, 96, 192, 92, 188, 91, 187, 94, 190, 88, 184)(193, 289, 195, 291, 202, 298, 222, 318, 210, 306, 238, 334, 209, 305, 197, 293)(194, 290, 199, 295, 214, 310, 230, 326, 205, 301, 229, 325, 218, 314, 200, 296)(196, 292, 204, 300, 223, 319, 212, 308, 198, 294, 211, 307, 233, 329, 206, 302)(201, 297, 220, 316, 236, 332, 259, 355, 225, 321, 235, 331, 207, 303, 221, 317)(203, 299, 224, 320, 234, 330, 253, 349, 219, 315, 237, 333, 208, 304, 226, 322)(213, 309, 244, 340, 251, 347, 261, 357, 247, 343, 250, 346, 216, 312, 245, 341)(215, 311, 246, 342, 249, 345, 270, 366, 243, 339, 252, 348, 217, 313, 248, 344)(227, 323, 262, 358, 241, 337, 269, 365, 239, 335, 266, 362, 231, 327, 263, 359)(228, 324, 264, 360, 242, 338, 256, 352, 240, 336, 254, 350, 232, 328, 265, 361)(255, 351, 275, 371, 277, 373, 283, 379, 267, 363, 278, 374, 257, 353, 276, 372)(258, 354, 279, 375, 274, 370, 284, 380, 268, 364, 281, 377, 260, 356, 280, 376)(271, 367, 285, 381, 282, 378, 288, 384, 273, 369, 287, 383, 272, 368, 286, 382) L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 211)(7, 214)(8, 194)(9, 220)(10, 222)(11, 224)(12, 223)(13, 229)(14, 196)(15, 221)(16, 226)(17, 197)(18, 238)(19, 233)(20, 198)(21, 244)(22, 230)(23, 246)(24, 245)(25, 248)(26, 200)(27, 237)(28, 236)(29, 201)(30, 210)(31, 212)(32, 234)(33, 235)(34, 203)(35, 262)(36, 264)(37, 218)(38, 205)(39, 263)(40, 265)(41, 206)(42, 253)(43, 207)(44, 259)(45, 208)(46, 209)(47, 266)(48, 254)(49, 269)(50, 256)(51, 252)(52, 251)(53, 213)(54, 249)(55, 250)(56, 215)(57, 270)(58, 216)(59, 261)(60, 217)(61, 219)(62, 232)(63, 275)(64, 240)(65, 276)(66, 279)(67, 225)(68, 280)(69, 247)(70, 241)(71, 227)(72, 242)(73, 228)(74, 231)(75, 278)(76, 281)(77, 239)(78, 243)(79, 285)(80, 286)(81, 287)(82, 284)(83, 277)(84, 255)(85, 283)(86, 257)(87, 274)(88, 258)(89, 260)(90, 288)(91, 267)(92, 268)(93, 282)(94, 271)(95, 272)(96, 273)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 2, 8, 2, 8, 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 E23.971 Graph:: bipartite v = 28 e = 192 f = 120 degree seq :: [ 12^16, 16^12 ] E23.971 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 8}) Quotient :: dipole Aut^+ = SL(2,3) : C4 (small group id <96, 67>) Aut = (SL(2,3) : C4) : C2 (small group id <192, 988>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, Y2^4, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3 * Y2^-1, Y3^2 * Y2^2 * Y3^-2 * Y2^-2, Y3^2 * Y2^-1 * Y3^2 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1, (Y3^-1 * Y1^-1)^8 ] Map:: polytopal R = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)(193, 289, 194, 290, 198, 294, 196, 292)(195, 291, 201, 297, 217, 313, 203, 299)(197, 293, 206, 302, 226, 322, 207, 303)(199, 295, 211, 307, 235, 331, 213, 309)(200, 296, 214, 310, 238, 334, 215, 311)(202, 298, 212, 308, 230, 326, 221, 317)(204, 300, 223, 319, 244, 340, 218, 314)(205, 301, 224, 320, 245, 341, 219, 315)(208, 304, 216, 312, 234, 330, 225, 321)(209, 305, 229, 325, 255, 351, 231, 327)(210, 306, 232, 328, 258, 354, 233, 329)(220, 316, 243, 339, 270, 366, 247, 343)(222, 318, 249, 345, 264, 360, 236, 332)(227, 323, 251, 347, 277, 373, 253, 349)(228, 324, 254, 350, 267, 363, 239, 335)(237, 333, 265, 361, 282, 378, 256, 352)(240, 336, 268, 364, 285, 381, 259, 355)(241, 337, 269, 365, 284, 380, 271, 367)(242, 338, 272, 368, 287, 383, 261, 357)(246, 342, 263, 359, 281, 377, 275, 371)(248, 344, 257, 353, 283, 379, 273, 369)(250, 346, 260, 356, 286, 382, 276, 372)(252, 348, 278, 374, 279, 375, 262, 358)(266, 362, 288, 384, 274, 370, 280, 376) L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 209)(7, 212)(8, 194)(9, 218)(10, 220)(11, 222)(12, 221)(13, 196)(14, 219)(15, 211)(16, 197)(17, 230)(18, 198)(19, 203)(20, 236)(21, 237)(22, 207)(23, 229)(24, 200)(25, 241)(26, 243)(27, 201)(28, 246)(29, 248)(30, 247)(31, 231)(32, 233)(33, 205)(34, 242)(35, 206)(36, 208)(37, 213)(38, 256)(39, 257)(40, 215)(41, 223)(42, 210)(43, 261)(44, 263)(45, 264)(46, 262)(47, 214)(48, 216)(49, 270)(50, 217)(51, 273)(52, 274)(53, 269)(54, 228)(55, 268)(56, 275)(57, 271)(58, 224)(59, 225)(60, 226)(61, 272)(62, 227)(63, 279)(64, 281)(65, 282)(66, 280)(67, 232)(68, 234)(69, 249)(70, 235)(71, 240)(72, 286)(73, 287)(74, 238)(75, 252)(76, 239)(77, 244)(78, 288)(79, 285)(80, 245)(81, 254)(82, 283)(83, 251)(84, 284)(85, 250)(86, 253)(87, 265)(88, 255)(89, 260)(90, 277)(91, 278)(92, 258)(93, 266)(94, 259)(95, 276)(96, 267)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 12, 16 ), ( 12, 16, 12, 16, 12, 16, 12, 16 ) } Outer automorphisms :: reflexible Dual of E23.970 Graph:: simple bipartite v = 120 e = 192 f = 28 degree seq :: [ 2^96, 8^24 ] E23.972 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 8}) Quotient :: dipole Aut^+ = SL(2,3) : C4 (small group id <96, 67>) Aut = (SL(2,3) : C4) : C2 (small group id <192, 988>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, Y3^4, Y1^-2 * Y3 * Y1^2 * Y3^-1, (R * Y2 * Y3^-1)^2, Y3^-1 * Y1^-1 * Y3^-1 * Y1 * Y3^-1 * Y1, Y3 * Y1^2 * Y3^-1 * Y1^-2, (Y3 * Y2^-1)^4, Y1^8, Y3^2 * Y1 * Y3^-1 * Y1 * Y3^2 * Y1 * Y3^-1 * Y1^-1, (Y1^-1 * Y3 * Y1^-2)^3 ] Map:: R = (1, 97, 2, 98, 6, 102, 17, 113, 37, 133, 32, 128, 13, 109, 4, 100)(3, 99, 9, 105, 18, 114, 40, 136, 63, 159, 54, 150, 28, 124, 11, 107)(5, 101, 15, 111, 19, 115, 42, 138, 64, 160, 60, 156, 33, 129, 16, 112)(7, 103, 20, 116, 38, 134, 65, 161, 57, 153, 31, 127, 12, 108, 22, 118)(8, 104, 23, 119, 39, 135, 67, 163, 59, 155, 34, 130, 14, 110, 24, 120)(10, 106, 26, 122, 41, 137, 69, 165, 87, 183, 79, 175, 52, 148, 27, 123)(21, 117, 44, 140, 66, 162, 89, 185, 83, 179, 56, 152, 30, 126, 45, 141)(25, 121, 49, 145, 68, 164, 91, 187, 81, 177, 55, 151, 29, 125, 50, 146)(35, 131, 62, 158, 70, 166, 92, 188, 80, 176, 53, 149, 36, 132, 51, 147)(43, 139, 71, 167, 88, 184, 85, 181, 58, 154, 75, 171, 46, 142, 72, 168)(47, 143, 76, 172, 90, 186, 84, 180, 61, 157, 74, 170, 48, 144, 73, 169)(77, 173, 95, 191, 86, 182, 94, 190, 82, 178, 93, 189, 78, 174, 96, 192)(193, 289)(194, 290)(195, 291)(196, 292)(197, 293)(198, 294)(199, 295)(200, 296)(201, 297)(202, 298)(203, 299)(204, 300)(205, 301)(206, 302)(207, 303)(208, 304)(209, 305)(210, 306)(211, 307)(212, 308)(213, 309)(214, 310)(215, 311)(216, 312)(217, 313)(218, 314)(219, 315)(220, 316)(221, 317)(222, 318)(223, 319)(224, 320)(225, 321)(226, 322)(227, 323)(228, 324)(229, 325)(230, 326)(231, 327)(232, 328)(233, 329)(234, 330)(235, 331)(236, 332)(237, 333)(238, 334)(239, 335)(240, 336)(241, 337)(242, 338)(243, 339)(244, 340)(245, 341)(246, 342)(247, 343)(248, 344)(249, 345)(250, 346)(251, 347)(252, 348)(253, 349)(254, 350)(255, 351)(256, 352)(257, 353)(258, 354)(259, 355)(260, 356)(261, 357)(262, 358)(263, 359)(264, 360)(265, 361)(266, 362)(267, 363)(268, 364)(269, 365)(270, 366)(271, 367)(272, 368)(273, 369)(274, 370)(275, 371)(276, 372)(277, 373)(278, 374)(279, 375)(280, 376)(281, 377)(282, 378)(283, 379)(284, 380)(285, 381)(286, 382)(287, 383)(288, 384) L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 210)(7, 213)(8, 194)(9, 215)(10, 197)(11, 216)(12, 222)(13, 220)(14, 196)(15, 227)(16, 228)(17, 230)(18, 233)(19, 198)(20, 234)(21, 200)(22, 207)(23, 239)(24, 240)(25, 201)(26, 241)(27, 242)(28, 244)(29, 203)(30, 206)(31, 208)(32, 249)(33, 205)(34, 253)(35, 238)(36, 250)(37, 255)(38, 258)(39, 209)(40, 259)(41, 211)(42, 262)(43, 212)(44, 263)(45, 264)(46, 214)(47, 217)(48, 221)(49, 269)(50, 270)(51, 218)(52, 225)(53, 219)(54, 226)(55, 274)(56, 267)(57, 275)(58, 223)(59, 224)(60, 272)(61, 273)(62, 261)(63, 279)(64, 229)(65, 252)(66, 231)(67, 282)(68, 232)(69, 283)(70, 235)(71, 285)(72, 286)(73, 236)(74, 237)(75, 287)(76, 281)(77, 243)(78, 245)(79, 247)(80, 280)(81, 246)(82, 284)(83, 251)(84, 248)(85, 288)(86, 254)(87, 256)(88, 257)(89, 277)(90, 260)(91, 278)(92, 271)(93, 265)(94, 266)(95, 276)(96, 268)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E23.969 Graph:: simple bipartite v = 108 e = 192 f = 40 degree seq :: [ 2^96, 16^12 ] E23.973 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 8}) Quotient :: dipole Aut^+ = SL(2,3) : C4 (small group id <96, 67>) Aut = (SL(2,3) : C4) : C2 (small group id <192, 988>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, (R * Y1)^2, (R * Y3)^2, Y1^3 * Y3^-1, Y3 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2^-1, Y2 * Y1^-1 * Y2 * Y3 * Y2^-1 * Y1^-1, (R * Y2 * Y3^-1)^2, (R * Y2^-2)^2, Y2 * Y3 * Y2 * Y1^-1 * Y2^-1 * Y1^-1, Y2^-1 * Y3 * Y1^-1 * Y2^2 * Y3^-1 * Y1 * Y2^-1, Y2^8, (Y3 * Y2^-1)^6 ] Map:: R = (1, 97, 2, 98, 6, 102, 4, 100)(3, 99, 9, 105, 25, 121, 11, 107)(5, 101, 14, 110, 34, 130, 15, 111)(7, 103, 19, 115, 43, 139, 21, 117)(8, 104, 22, 118, 46, 142, 23, 119)(10, 106, 20, 116, 38, 134, 29, 125)(12, 108, 30, 126, 54, 150, 27, 123)(13, 109, 31, 127, 57, 153, 32, 128)(16, 112, 24, 120, 42, 138, 33, 129)(17, 113, 37, 133, 63, 159, 39, 135)(18, 114, 40, 136, 66, 162, 41, 137)(26, 122, 51, 147, 79, 175, 53, 149)(28, 124, 52, 148, 72, 168, 44, 140)(35, 131, 61, 157, 76, 172, 48, 144)(36, 132, 58, 154, 85, 181, 62, 158)(45, 141, 71, 167, 90, 186, 64, 160)(47, 143, 75, 171, 94, 190, 68, 164)(49, 145, 77, 173, 92, 188, 70, 166)(50, 146, 78, 174, 96, 192, 74, 170)(55, 151, 73, 169, 91, 187, 80, 176)(56, 152, 65, 161, 89, 185, 83, 179)(59, 155, 67, 163, 93, 189, 81, 177)(60, 156, 82, 178, 87, 183, 86, 182)(69, 165, 95, 191, 84, 180, 88, 184)(193, 289, 195, 291, 202, 298, 220, 316, 247, 343, 228, 324, 208, 304, 197, 293)(194, 290, 199, 295, 212, 308, 237, 333, 265, 361, 240, 336, 216, 312, 200, 296)(196, 292, 204, 300, 221, 317, 243, 339, 272, 368, 251, 347, 225, 321, 205, 301)(198, 294, 209, 305, 230, 326, 257, 353, 283, 379, 260, 356, 234, 330, 210, 306)(201, 297, 218, 314, 244, 340, 273, 369, 250, 346, 224, 320, 206, 302, 219, 315)(203, 299, 211, 307, 236, 332, 263, 359, 254, 350, 227, 323, 207, 303, 214, 310)(213, 309, 229, 325, 256, 352, 281, 377, 268, 364, 239, 335, 215, 311, 232, 328)(217, 313, 241, 337, 264, 360, 287, 383, 277, 373, 252, 348, 226, 322, 242, 338)(222, 318, 248, 344, 271, 367, 286, 382, 259, 355, 233, 329, 223, 319, 231, 327)(235, 331, 261, 357, 282, 378, 278, 374, 253, 349, 266, 362, 238, 334, 262, 358)(245, 341, 269, 365, 285, 381, 276, 372, 249, 345, 274, 370, 246, 342, 270, 366)(255, 351, 279, 375, 275, 371, 288, 384, 267, 363, 284, 380, 258, 354, 280, 376) L = (1, 196)(2, 193)(3, 203)(4, 198)(5, 207)(6, 194)(7, 213)(8, 215)(9, 195)(10, 221)(11, 217)(12, 219)(13, 224)(14, 197)(15, 226)(16, 225)(17, 231)(18, 233)(19, 199)(20, 202)(21, 235)(22, 200)(23, 238)(24, 208)(25, 201)(26, 245)(27, 246)(28, 236)(29, 230)(30, 204)(31, 205)(32, 249)(33, 234)(34, 206)(35, 240)(36, 254)(37, 209)(38, 212)(39, 255)(40, 210)(41, 258)(42, 216)(43, 211)(44, 264)(45, 256)(46, 214)(47, 260)(48, 268)(49, 262)(50, 266)(51, 218)(52, 220)(53, 271)(54, 222)(55, 272)(56, 275)(57, 223)(58, 228)(59, 273)(60, 278)(61, 227)(62, 277)(63, 229)(64, 282)(65, 248)(66, 232)(67, 251)(68, 286)(69, 280)(70, 284)(71, 237)(72, 244)(73, 247)(74, 288)(75, 239)(76, 253)(77, 241)(78, 242)(79, 243)(80, 283)(81, 285)(82, 252)(83, 281)(84, 287)(85, 250)(86, 279)(87, 274)(88, 276)(89, 257)(90, 263)(91, 265)(92, 269)(93, 259)(94, 267)(95, 261)(96, 270)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 2, 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 E23.974 Graph:: bipartite v = 36 e = 192 f = 112 degree seq :: [ 8^24, 16^12 ] E23.974 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 8}) Quotient :: dipole Aut^+ = SL(2,3) : C4 (small group id <96, 67>) Aut = (SL(2,3) : C4) : C2 (small group id <192, 988>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^2 * Y1^-1 * Y3^-2 * Y1, Y1^6, Y3 * Y1^-1 * Y3^2 * Y1^-2 * Y3, Y3^2 * Y1 * Y3^2 * Y1^2, Y1^3 * Y3^-1 * Y1^-3 * Y3, (Y1 * Y3^-1)^4, (Y3^-1 * Y1^-1)^4, Y1 * Y3 * Y1 * Y3^-1 * Y1^-2 * Y3 * Y1 * Y3^-1, (Y3 * Y2^-1)^8 ] Map:: R = (1, 97, 2, 98, 6, 102, 18, 114, 13, 109, 4, 100)(3, 99, 9, 105, 27, 123, 46, 142, 33, 129, 11, 107)(5, 101, 15, 111, 42, 138, 30, 126, 44, 140, 16, 112)(7, 103, 21, 117, 51, 147, 37, 133, 55, 151, 23, 119)(8, 104, 24, 120, 57, 153, 38, 134, 59, 155, 25, 121)(10, 106, 22, 118, 41, 137, 17, 113, 26, 122, 31, 127)(12, 108, 35, 131, 48, 144, 19, 115, 47, 143, 36, 132)(14, 110, 39, 135, 50, 146, 20, 116, 49, 145, 40, 136)(28, 124, 62, 158, 75, 171, 43, 139, 72, 168, 63, 159)(29, 125, 64, 160, 85, 181, 67, 163, 73, 169, 65, 161)(32, 128, 66, 162, 52, 148, 45, 141, 76, 172, 58, 154)(34, 130, 68, 164, 53, 149, 61, 157, 82, 178, 69, 165)(54, 150, 79, 175, 74, 170, 60, 156, 81, 177, 70, 166)(56, 152, 80, 176, 77, 173, 78, 174, 90, 186, 71, 167)(83, 179, 95, 191, 89, 185, 86, 182, 93, 189, 87, 183)(84, 180, 96, 192, 92, 188, 91, 187, 94, 190, 88, 184)(193, 289)(194, 290)(195, 291)(196, 292)(197, 293)(198, 294)(199, 295)(200, 296)(201, 297)(202, 298)(203, 299)(204, 300)(205, 301)(206, 302)(207, 303)(208, 304)(209, 305)(210, 306)(211, 307)(212, 308)(213, 309)(214, 310)(215, 311)(216, 312)(217, 313)(218, 314)(219, 315)(220, 316)(221, 317)(222, 318)(223, 319)(224, 320)(225, 321)(226, 322)(227, 323)(228, 324)(229, 325)(230, 326)(231, 327)(232, 328)(233, 329)(234, 330)(235, 331)(236, 332)(237, 333)(238, 334)(239, 335)(240, 336)(241, 337)(242, 338)(243, 339)(244, 340)(245, 341)(246, 342)(247, 343)(248, 344)(249, 345)(250, 346)(251, 347)(252, 348)(253, 349)(254, 350)(255, 351)(256, 352)(257, 353)(258, 354)(259, 355)(260, 356)(261, 357)(262, 358)(263, 359)(264, 360)(265, 361)(266, 362)(267, 363)(268, 364)(269, 365)(270, 366)(271, 367)(272, 368)(273, 369)(274, 370)(275, 371)(276, 372)(277, 373)(278, 374)(279, 375)(280, 376)(281, 377)(282, 378)(283, 379)(284, 380)(285, 381)(286, 382)(287, 383)(288, 384) L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 211)(7, 214)(8, 194)(9, 220)(10, 222)(11, 224)(12, 223)(13, 229)(14, 196)(15, 221)(16, 226)(17, 197)(18, 238)(19, 233)(20, 198)(21, 244)(22, 230)(23, 246)(24, 245)(25, 248)(26, 200)(27, 237)(28, 236)(29, 201)(30, 210)(31, 212)(32, 234)(33, 235)(34, 203)(35, 262)(36, 264)(37, 218)(38, 205)(39, 263)(40, 265)(41, 206)(42, 253)(43, 207)(44, 259)(45, 208)(46, 209)(47, 266)(48, 254)(49, 269)(50, 256)(51, 252)(52, 251)(53, 213)(54, 249)(55, 250)(56, 215)(57, 270)(58, 216)(59, 261)(60, 217)(61, 219)(62, 232)(63, 275)(64, 240)(65, 276)(66, 279)(67, 225)(68, 280)(69, 247)(70, 241)(71, 227)(72, 242)(73, 228)(74, 231)(75, 278)(76, 281)(77, 239)(78, 243)(79, 285)(80, 286)(81, 287)(82, 284)(83, 277)(84, 255)(85, 283)(86, 257)(87, 274)(88, 258)(89, 260)(90, 288)(91, 267)(92, 268)(93, 282)(94, 271)(95, 272)(96, 273)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E23.973 Graph:: simple bipartite v = 112 e = 192 f = 36 degree seq :: [ 2^96, 12^16 ] E23.975 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 6, 8}) Quotient :: edge Aut^+ = C2 x (C2 . S4 = SL(2,3) . C2) (small group id <96, 188>) Aut = $<192, 1480>$ (small group id <192, 1480>) |r| :: 2 Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, T1 * T2^-1 * T1^2 * T2 * T1, T1^-1 * T2 * T1^2 * T2^-1 * T1^-1, T2^6, T2^-3 * T1 * T2^-3 * T1^-1, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1, T2^2 * T1^-1 * T2^-1 * T1 * T2^2 * T1^-1 * T2^-1 * T1^-1, T2 * T1^-1 * T2^-2 * T1^-1 * T2 * T1^-1 * T2^-2 * T1, T2^-1 * T1^-1 * T2 * T1^-1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 ] Map:: non-degenerate R = (1, 3, 10, 28, 16, 5)(2, 7, 20, 45, 24, 8)(4, 12, 32, 61, 33, 13)(6, 17, 40, 68, 41, 18)(9, 25, 55, 38, 58, 26)(11, 30, 64, 39, 65, 31)(14, 34, 60, 27, 59, 35)(15, 36, 63, 29, 62, 37)(19, 42, 69, 53, 72, 43)(21, 47, 77, 54, 78, 48)(22, 49, 74, 44, 73, 50)(23, 51, 76, 46, 75, 52)(56, 83, 67, 81, 93, 84)(57, 85, 66, 82, 94, 86)(70, 89, 80, 87, 95, 90)(71, 91, 79, 88, 96, 92)(97, 98, 102, 100)(99, 105, 113, 107)(101, 110, 114, 111)(103, 115, 108, 117)(104, 118, 109, 119)(106, 123, 136, 125)(112, 134, 137, 135)(116, 140, 128, 142)(120, 149, 129, 150)(121, 148, 126, 146)(122, 152, 127, 153)(124, 141, 164, 157)(130, 162, 132, 163)(131, 143, 133, 138)(139, 166, 144, 167)(145, 175, 147, 176)(151, 177, 160, 178)(154, 172, 161, 170)(155, 182, 158, 180)(156, 174, 159, 168)(165, 183, 173, 184)(169, 188, 171, 186)(179, 187, 181, 185)(189, 192, 190, 191) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 16^4 ), ( 16^6 ) } Outer automorphisms :: reflexible Dual of E23.979 Transitivity :: ET+ Graph:: simple bipartite v = 40 e = 96 f = 12 degree seq :: [ 4^24, 6^16 ] E23.976 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 6, 8}) Quotient :: edge Aut^+ = C2 x (C2 . S4 = SL(2,3) . C2) (small group id <96, 188>) Aut = $<192, 1480>$ (small group id <192, 1480>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^2 * T1^-1 * T2^-1 * T1^-1 * T2, T1^6, T1^-3 * T2 * T1^-3 * T2^-1, T2^8, T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-2 * T2^-1, T1^-2 * T2 * T1^-1 * T2 * T1 * T2^2 ] Map:: non-degenerate R = (1, 3, 10, 21, 56, 40, 17, 5)(2, 7, 22, 49, 45, 16, 26, 8)(4, 12, 29, 9, 28, 62, 41, 14)(6, 19, 50, 33, 65, 25, 54, 20)(11, 32, 72, 30, 52, 83, 76, 34)(13, 37, 77, 35, 69, 42, 78, 38)(15, 31, 73, 87, 55, 46, 79, 43)(18, 47, 80, 60, 86, 53, 81, 48)(23, 59, 89, 57, 44, 71, 91, 61)(24, 58, 90, 75, 36, 66, 92, 63)(27, 67, 93, 74, 39, 70, 94, 68)(51, 84, 95, 82, 64, 88, 96, 85)(97, 98, 102, 114, 109, 100)(99, 105, 123, 143, 129, 107)(101, 111, 138, 144, 140, 112)(103, 117, 151, 133, 156, 119)(104, 120, 158, 134, 160, 121)(106, 126, 167, 176, 170, 127)(108, 131, 147, 115, 145, 132)(110, 135, 149, 116, 148, 136)(113, 130, 155, 177, 164, 142)(118, 153, 184, 173, 139, 154)(122, 157, 180, 174, 183, 162)(124, 152, 141, 161, 182, 165)(125, 159, 179, 146, 178, 166)(128, 150, 181, 163, 137, 171)(168, 188, 175, 189, 191, 185)(169, 190, 192, 187, 172, 186) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8^6 ), ( 8^8 ) } Outer automorphisms :: reflexible Dual of E23.980 Transitivity :: ET+ Graph:: simple bipartite v = 28 e = 96 f = 24 degree seq :: [ 6^16, 8^12 ] E23.977 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 6, 8}) Quotient :: edge Aut^+ = C2 x (C2 . S4 = SL(2,3) . C2) (small group id <96, 188>) Aut = $<192, 1480>$ (small group id <192, 1480>) |r| :: 2 Presentation :: [ F^2, T2^4, (F * T1)^2, (F * T2)^2, T2^4, T1^-2 * T2^-2 * T1^-2, T2^-1 * T1^2 * T2^-1 * T1 * T2 * T1^-2 * T2 * T1, T2^-1 * T1^-2 * T2^-1 * T1^-1 * T2 * T1^-2 * T2^-1 * T1^-1, T2 * T1 * T2 * T1^-2 * T2 * T1 * T2^-1 * T1^-2, (T2^-1 * T1 * T2^-1 * T1 * T2 * T1)^2 ] Map:: polytopal non-degenerate R = (1, 3, 10, 5)(2, 7, 21, 8)(4, 12, 17, 14)(6, 18, 13, 19)(9, 26, 15, 27)(11, 28, 16, 30)(20, 40, 23, 41)(22, 42, 24, 44)(25, 45, 29, 46)(31, 56, 33, 57)(32, 58, 34, 60)(35, 62, 37, 63)(36, 64, 38, 66)(39, 67, 43, 68)(47, 79, 49, 80)(48, 81, 50, 82)(51, 83, 53, 84)(52, 85, 54, 86)(55, 77, 59, 78)(61, 87, 65, 88)(69, 89, 71, 90)(70, 91, 72, 92)(73, 93, 75, 94)(74, 95, 76, 96)(97, 98, 102, 113, 106, 117, 109, 100)(99, 105, 121, 112, 101, 111, 125, 107)(103, 116, 135, 120, 104, 119, 139, 118)(108, 127, 151, 130, 110, 129, 155, 128)(114, 131, 157, 134, 115, 133, 161, 132)(122, 143, 160, 146, 123, 145, 162, 144)(124, 147, 158, 150, 126, 149, 159, 148)(136, 165, 156, 168, 137, 167, 154, 166)(138, 169, 153, 172, 140, 171, 152, 170)(141, 173, 184, 164, 142, 174, 183, 163)(175, 185, 182, 192, 176, 186, 181, 191)(177, 190, 180, 188, 178, 189, 179, 187) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 12^4 ), ( 12^8 ) } Outer automorphisms :: reflexible Dual of E23.978 Transitivity :: ET+ Graph:: bipartite v = 36 e = 96 f = 16 degree seq :: [ 4^24, 8^12 ] E23.978 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 6, 8}) Quotient :: loop Aut^+ = C2 x (C2 . S4 = SL(2,3) . C2) (small group id <96, 188>) Aut = $<192, 1480>$ (small group id <192, 1480>) |r| :: 2 Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, T1 * T2^-1 * T1^2 * T2 * T1, T1^-1 * T2 * T1^2 * T2^-1 * T1^-1, T2^6, T2^-3 * T1 * T2^-3 * T1^-1, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1, T2^2 * T1^-1 * T2^-1 * T1 * T2^2 * T1^-1 * T2^-1 * T1^-1, T2 * T1^-1 * T2^-2 * T1^-1 * T2 * T1^-1 * T2^-2 * T1, T2^-1 * T1^-1 * T2 * T1^-1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 ] Map:: polytopal non-degenerate R = (1, 97, 3, 99, 10, 106, 28, 124, 16, 112, 5, 101)(2, 98, 7, 103, 20, 116, 45, 141, 24, 120, 8, 104)(4, 100, 12, 108, 32, 128, 61, 157, 33, 129, 13, 109)(6, 102, 17, 113, 40, 136, 68, 164, 41, 137, 18, 114)(9, 105, 25, 121, 55, 151, 38, 134, 58, 154, 26, 122)(11, 107, 30, 126, 64, 160, 39, 135, 65, 161, 31, 127)(14, 110, 34, 130, 60, 156, 27, 123, 59, 155, 35, 131)(15, 111, 36, 132, 63, 159, 29, 125, 62, 158, 37, 133)(19, 115, 42, 138, 69, 165, 53, 149, 72, 168, 43, 139)(21, 117, 47, 143, 77, 173, 54, 150, 78, 174, 48, 144)(22, 118, 49, 145, 74, 170, 44, 140, 73, 169, 50, 146)(23, 119, 51, 147, 76, 172, 46, 142, 75, 171, 52, 148)(56, 152, 83, 179, 67, 163, 81, 177, 93, 189, 84, 180)(57, 153, 85, 181, 66, 162, 82, 178, 94, 190, 86, 182)(70, 166, 89, 185, 80, 176, 87, 183, 95, 191, 90, 186)(71, 167, 91, 187, 79, 175, 88, 184, 96, 192, 92, 188) L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 110)(6, 100)(7, 115)(8, 118)(9, 113)(10, 123)(11, 99)(12, 117)(13, 119)(14, 114)(15, 101)(16, 134)(17, 107)(18, 111)(19, 108)(20, 140)(21, 103)(22, 109)(23, 104)(24, 149)(25, 148)(26, 152)(27, 136)(28, 141)(29, 106)(30, 146)(31, 153)(32, 142)(33, 150)(34, 162)(35, 143)(36, 163)(37, 138)(38, 137)(39, 112)(40, 125)(41, 135)(42, 131)(43, 166)(44, 128)(45, 164)(46, 116)(47, 133)(48, 167)(49, 175)(50, 121)(51, 176)(52, 126)(53, 129)(54, 120)(55, 177)(56, 127)(57, 122)(58, 172)(59, 182)(60, 174)(61, 124)(62, 180)(63, 168)(64, 178)(65, 170)(66, 132)(67, 130)(68, 157)(69, 183)(70, 144)(71, 139)(72, 156)(73, 188)(74, 154)(75, 186)(76, 161)(77, 184)(78, 159)(79, 147)(80, 145)(81, 160)(82, 151)(83, 187)(84, 155)(85, 185)(86, 158)(87, 173)(88, 165)(89, 179)(90, 169)(91, 181)(92, 171)(93, 192)(94, 191)(95, 189)(96, 190) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E23.977 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 16 e = 96 f = 36 degree seq :: [ 12^16 ] E23.979 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 6, 8}) Quotient :: loop Aut^+ = C2 x (C2 . S4 = SL(2,3) . C2) (small group id <96, 188>) Aut = $<192, 1480>$ (small group id <192, 1480>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T2^2 * T1^-1 * T2^-1 * T1^-1 * T2, T1^6, T1^-3 * T2 * T1^-3 * T2^-1, T2^8, T1^-1 * T2^-2 * T1^-1 * T2^-1 * T1^-2 * T2^-1, T1^-2 * T2 * T1^-1 * T2 * T1 * T2^2 ] Map:: non-degenerate R = (1, 97, 3, 99, 10, 106, 21, 117, 56, 152, 40, 136, 17, 113, 5, 101)(2, 98, 7, 103, 22, 118, 49, 145, 45, 141, 16, 112, 26, 122, 8, 104)(4, 100, 12, 108, 29, 125, 9, 105, 28, 124, 62, 158, 41, 137, 14, 110)(6, 102, 19, 115, 50, 146, 33, 129, 65, 161, 25, 121, 54, 150, 20, 116)(11, 107, 32, 128, 72, 168, 30, 126, 52, 148, 83, 179, 76, 172, 34, 130)(13, 109, 37, 133, 77, 173, 35, 131, 69, 165, 42, 138, 78, 174, 38, 134)(15, 111, 31, 127, 73, 169, 87, 183, 55, 151, 46, 142, 79, 175, 43, 139)(18, 114, 47, 143, 80, 176, 60, 156, 86, 182, 53, 149, 81, 177, 48, 144)(23, 119, 59, 155, 89, 185, 57, 153, 44, 140, 71, 167, 91, 187, 61, 157)(24, 120, 58, 154, 90, 186, 75, 171, 36, 132, 66, 162, 92, 188, 63, 159)(27, 123, 67, 163, 93, 189, 74, 170, 39, 135, 70, 166, 94, 190, 68, 164)(51, 147, 84, 180, 95, 191, 82, 178, 64, 160, 88, 184, 96, 192, 85, 181) L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 111)(6, 114)(7, 117)(8, 120)(9, 123)(10, 126)(11, 99)(12, 131)(13, 100)(14, 135)(15, 138)(16, 101)(17, 130)(18, 109)(19, 145)(20, 148)(21, 151)(22, 153)(23, 103)(24, 158)(25, 104)(26, 157)(27, 143)(28, 152)(29, 159)(30, 167)(31, 106)(32, 150)(33, 107)(34, 155)(35, 147)(36, 108)(37, 156)(38, 160)(39, 149)(40, 110)(41, 171)(42, 144)(43, 154)(44, 112)(45, 161)(46, 113)(47, 129)(48, 140)(49, 132)(50, 178)(51, 115)(52, 136)(53, 116)(54, 181)(55, 133)(56, 141)(57, 184)(58, 118)(59, 177)(60, 119)(61, 180)(62, 134)(63, 179)(64, 121)(65, 182)(66, 122)(67, 137)(68, 142)(69, 124)(70, 125)(71, 176)(72, 188)(73, 190)(74, 127)(75, 128)(76, 186)(77, 139)(78, 183)(79, 189)(80, 170)(81, 164)(82, 166)(83, 146)(84, 174)(85, 163)(86, 165)(87, 162)(88, 173)(89, 168)(90, 169)(91, 172)(92, 175)(93, 191)(94, 192)(95, 185)(96, 187) local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E23.975 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 12 e = 96 f = 40 degree seq :: [ 16^12 ] E23.980 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 6, 8}) Quotient :: loop Aut^+ = C2 x (C2 . S4 = SL(2,3) . C2) (small group id <96, 188>) Aut = $<192, 1480>$ (small group id <192, 1480>) |r| :: 2 Presentation :: [ F^2, T2^4, (F * T1)^2, (F * T2)^2, T2^4, T1^-2 * T2^-2 * T1^-2, T2^-1 * T1^2 * T2^-1 * T1 * T2 * T1^-2 * T2 * T1, T2^-1 * T1^-2 * T2^-1 * T1^-1 * T2 * T1^-2 * T2^-1 * T1^-1, T2 * T1 * T2 * T1^-2 * T2 * T1 * T2^-1 * T1^-2, (T2^-1 * T1 * T2^-1 * T1 * T2 * T1)^2 ] Map:: non-degenerate R = (1, 97, 3, 99, 10, 106, 5, 101)(2, 98, 7, 103, 21, 117, 8, 104)(4, 100, 12, 108, 17, 113, 14, 110)(6, 102, 18, 114, 13, 109, 19, 115)(9, 105, 26, 122, 15, 111, 27, 123)(11, 107, 28, 124, 16, 112, 30, 126)(20, 116, 40, 136, 23, 119, 41, 137)(22, 118, 42, 138, 24, 120, 44, 140)(25, 121, 45, 141, 29, 125, 46, 142)(31, 127, 56, 152, 33, 129, 57, 153)(32, 128, 58, 154, 34, 130, 60, 156)(35, 131, 62, 158, 37, 133, 63, 159)(36, 132, 64, 160, 38, 134, 66, 162)(39, 135, 67, 163, 43, 139, 68, 164)(47, 143, 79, 175, 49, 145, 80, 176)(48, 144, 81, 177, 50, 146, 82, 178)(51, 147, 83, 179, 53, 149, 84, 180)(52, 148, 85, 181, 54, 150, 86, 182)(55, 151, 77, 173, 59, 155, 78, 174)(61, 157, 87, 183, 65, 161, 88, 184)(69, 165, 89, 185, 71, 167, 90, 186)(70, 166, 91, 187, 72, 168, 92, 188)(73, 169, 93, 189, 75, 171, 94, 190)(74, 170, 95, 191, 76, 172, 96, 192) L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 111)(6, 113)(7, 116)(8, 119)(9, 121)(10, 117)(11, 99)(12, 127)(13, 100)(14, 129)(15, 125)(16, 101)(17, 106)(18, 131)(19, 133)(20, 135)(21, 109)(22, 103)(23, 139)(24, 104)(25, 112)(26, 143)(27, 145)(28, 147)(29, 107)(30, 149)(31, 151)(32, 108)(33, 155)(34, 110)(35, 157)(36, 114)(37, 161)(38, 115)(39, 120)(40, 165)(41, 167)(42, 169)(43, 118)(44, 171)(45, 173)(46, 174)(47, 160)(48, 122)(49, 162)(50, 123)(51, 158)(52, 124)(53, 159)(54, 126)(55, 130)(56, 170)(57, 172)(58, 166)(59, 128)(60, 168)(61, 134)(62, 150)(63, 148)(64, 146)(65, 132)(66, 144)(67, 141)(68, 142)(69, 156)(70, 136)(71, 154)(72, 137)(73, 153)(74, 138)(75, 152)(76, 140)(77, 184)(78, 183)(79, 185)(80, 186)(81, 190)(82, 189)(83, 187)(84, 188)(85, 191)(86, 192)(87, 163)(88, 164)(89, 182)(90, 181)(91, 177)(92, 178)(93, 179)(94, 180)(95, 175)(96, 176) local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E23.976 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 24 e = 96 f = 28 degree seq :: [ 8^24 ] E23.981 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 8}) Quotient :: dipole Aut^+ = C2 x (C2 . S4 = SL(2,3) . C2) (small group id <96, 188>) Aut = $<192, 1480>$ (small group id <192, 1480>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y3^-1 * Y1^-2 * Y3^-1, (R * Y3)^2, (Y3 * Y1^-1)^2, Y1^4, (R * Y1)^2, Y2^6, (R * Y2 * Y3^-1)^2, Y2 * Y1^-2 * Y2^-1 * Y1^-2, Y3 * Y2 * Y3^-1 * Y1 * Y2^-1 * Y1^-1, R * Y2^-1 * Y3 * Y2^-1 * R * Y2 * Y1 * Y2, Y2^-3 * Y1 * Y2^-3 * Y1^-1, Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y3^-1 * Y2 * Y1^-1, (Y2^-1 * R * Y2^-2)^2, Y2^-1 * Y1 * Y3^-1 * Y2^2 * Y1 * Y3^-1 * Y2^-1, Y3 * Y2^-3 * Y3^-1 * Y2^-3, Y2^2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^2 * Y3^-1 * Y2^-1 * Y1^-1, Y2^-1 * Y1 * Y2 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y1^-1 * Y2 * Y1^-1 * Y2^-1 * Y1^-1, Y2^-2 * Y1 * Y2^-1 * Y1^-1 * Y2 * Y1^-1 * Y2^-1 * Y3^-1 * Y2^-2 * Y1^-1 * Y2^-1 * Y1^-1, (Y3 * Y2^-1)^8 ] Map:: R = (1, 97, 2, 98, 6, 102, 4, 100)(3, 99, 9, 105, 17, 113, 11, 107)(5, 101, 14, 110, 18, 114, 15, 111)(7, 103, 19, 115, 12, 108, 21, 117)(8, 104, 22, 118, 13, 109, 23, 119)(10, 106, 27, 123, 40, 136, 29, 125)(16, 112, 38, 134, 41, 137, 39, 135)(20, 116, 44, 140, 32, 128, 46, 142)(24, 120, 53, 149, 33, 129, 54, 150)(25, 121, 52, 148, 30, 126, 50, 146)(26, 122, 56, 152, 31, 127, 57, 153)(28, 124, 45, 141, 68, 164, 61, 157)(34, 130, 66, 162, 36, 132, 67, 163)(35, 131, 47, 143, 37, 133, 42, 138)(43, 139, 70, 166, 48, 144, 71, 167)(49, 145, 79, 175, 51, 147, 80, 176)(55, 151, 81, 177, 64, 160, 82, 178)(58, 154, 76, 172, 65, 161, 74, 170)(59, 155, 86, 182, 62, 158, 84, 180)(60, 156, 78, 174, 63, 159, 72, 168)(69, 165, 87, 183, 77, 173, 88, 184)(73, 169, 92, 188, 75, 171, 90, 186)(83, 179, 91, 187, 85, 181, 89, 185)(93, 189, 96, 192, 94, 190, 95, 191)(193, 289, 195, 291, 202, 298, 220, 316, 208, 304, 197, 293)(194, 290, 199, 295, 212, 308, 237, 333, 216, 312, 200, 296)(196, 292, 204, 300, 224, 320, 253, 349, 225, 321, 205, 301)(198, 294, 209, 305, 232, 328, 260, 356, 233, 329, 210, 306)(201, 297, 217, 313, 247, 343, 230, 326, 250, 346, 218, 314)(203, 299, 222, 318, 256, 352, 231, 327, 257, 353, 223, 319)(206, 302, 226, 322, 252, 348, 219, 315, 251, 347, 227, 323)(207, 303, 228, 324, 255, 351, 221, 317, 254, 350, 229, 325)(211, 307, 234, 330, 261, 357, 245, 341, 264, 360, 235, 331)(213, 309, 239, 335, 269, 365, 246, 342, 270, 366, 240, 336)(214, 310, 241, 337, 266, 362, 236, 332, 265, 361, 242, 338)(215, 311, 243, 339, 268, 364, 238, 334, 267, 363, 244, 340)(248, 344, 275, 371, 259, 355, 273, 369, 285, 381, 276, 372)(249, 345, 277, 373, 258, 354, 274, 370, 286, 382, 278, 374)(262, 358, 281, 377, 272, 368, 279, 375, 287, 383, 282, 378)(263, 359, 283, 379, 271, 367, 280, 376, 288, 384, 284, 380) L = (1, 196)(2, 193)(3, 203)(4, 198)(5, 207)(6, 194)(7, 213)(8, 215)(9, 195)(10, 221)(11, 209)(12, 211)(13, 214)(14, 197)(15, 210)(16, 231)(17, 201)(18, 206)(19, 199)(20, 238)(21, 204)(22, 200)(23, 205)(24, 246)(25, 242)(26, 249)(27, 202)(28, 253)(29, 232)(30, 244)(31, 248)(32, 236)(33, 245)(34, 259)(35, 234)(36, 258)(37, 239)(38, 208)(39, 233)(40, 219)(41, 230)(42, 229)(43, 263)(44, 212)(45, 220)(46, 224)(47, 227)(48, 262)(49, 272)(50, 222)(51, 271)(52, 217)(53, 216)(54, 225)(55, 274)(56, 218)(57, 223)(58, 266)(59, 276)(60, 264)(61, 260)(62, 278)(63, 270)(64, 273)(65, 268)(66, 226)(67, 228)(68, 237)(69, 280)(70, 235)(71, 240)(72, 255)(73, 282)(74, 257)(75, 284)(76, 250)(77, 279)(78, 252)(79, 241)(80, 243)(81, 247)(82, 256)(83, 281)(84, 254)(85, 283)(86, 251)(87, 261)(88, 269)(89, 277)(90, 267)(91, 275)(92, 265)(93, 287)(94, 288)(95, 286)(96, 285)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 2, 16, 2, 16, 2, 16, 2, 16 ), ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ) } Outer automorphisms :: reflexible Dual of E23.984 Graph:: bipartite v = 40 e = 192 f = 108 degree seq :: [ 8^24, 12^16 ] E23.982 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 8}) Quotient :: dipole Aut^+ = C2 x (C2 . S4 = SL(2,3) . C2) (small group id <96, 188>) Aut = $<192, 1480>$ (small group id <192, 1480>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y2^3 * Y1^-1 * Y2^-1 * Y1^-1, Y1^6, Y1^-1 * Y2^-2 * Y1^2 * Y2^-1 * Y1 * Y2^-1, Y2^-1 * Y1^3 * Y2 * Y1^3, (Y3^-1 * Y1^-1)^4 ] Map:: R = (1, 97, 2, 98, 6, 102, 18, 114, 13, 109, 4, 100)(3, 99, 9, 105, 27, 123, 47, 143, 33, 129, 11, 107)(5, 101, 15, 111, 42, 138, 48, 144, 44, 140, 16, 112)(7, 103, 21, 117, 55, 151, 37, 133, 60, 156, 23, 119)(8, 104, 24, 120, 62, 158, 38, 134, 64, 160, 25, 121)(10, 106, 30, 126, 71, 167, 80, 176, 74, 170, 31, 127)(12, 108, 35, 131, 51, 147, 19, 115, 49, 145, 36, 132)(14, 110, 39, 135, 53, 149, 20, 116, 52, 148, 40, 136)(17, 113, 34, 130, 59, 155, 81, 177, 68, 164, 46, 142)(22, 118, 57, 153, 88, 184, 77, 173, 43, 139, 58, 154)(26, 122, 61, 157, 84, 180, 78, 174, 87, 183, 66, 162)(28, 124, 56, 152, 45, 141, 65, 161, 86, 182, 69, 165)(29, 125, 63, 159, 83, 179, 50, 146, 82, 178, 70, 166)(32, 128, 54, 150, 85, 181, 67, 163, 41, 137, 75, 171)(72, 168, 92, 188, 79, 175, 93, 189, 95, 191, 89, 185)(73, 169, 94, 190, 96, 192, 91, 187, 76, 172, 90, 186)(193, 289, 195, 291, 202, 298, 213, 309, 248, 344, 232, 328, 209, 305, 197, 293)(194, 290, 199, 295, 214, 310, 241, 337, 237, 333, 208, 304, 218, 314, 200, 296)(196, 292, 204, 300, 221, 317, 201, 297, 220, 316, 254, 350, 233, 329, 206, 302)(198, 294, 211, 307, 242, 338, 225, 321, 257, 353, 217, 313, 246, 342, 212, 308)(203, 299, 224, 320, 264, 360, 222, 318, 244, 340, 275, 371, 268, 364, 226, 322)(205, 301, 229, 325, 269, 365, 227, 323, 261, 357, 234, 330, 270, 366, 230, 326)(207, 303, 223, 319, 265, 361, 279, 375, 247, 343, 238, 334, 271, 367, 235, 331)(210, 306, 239, 335, 272, 368, 252, 348, 278, 374, 245, 341, 273, 369, 240, 336)(215, 311, 251, 347, 281, 377, 249, 345, 236, 332, 263, 359, 283, 379, 253, 349)(216, 312, 250, 346, 282, 378, 267, 363, 228, 324, 258, 354, 284, 380, 255, 351)(219, 315, 259, 355, 285, 381, 266, 362, 231, 327, 262, 358, 286, 382, 260, 356)(243, 339, 276, 372, 287, 383, 274, 370, 256, 352, 280, 376, 288, 384, 277, 373) L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 211)(7, 214)(8, 194)(9, 220)(10, 213)(11, 224)(12, 221)(13, 229)(14, 196)(15, 223)(16, 218)(17, 197)(18, 239)(19, 242)(20, 198)(21, 248)(22, 241)(23, 251)(24, 250)(25, 246)(26, 200)(27, 259)(28, 254)(29, 201)(30, 244)(31, 265)(32, 264)(33, 257)(34, 203)(35, 261)(36, 258)(37, 269)(38, 205)(39, 262)(40, 209)(41, 206)(42, 270)(43, 207)(44, 263)(45, 208)(46, 271)(47, 272)(48, 210)(49, 237)(50, 225)(51, 276)(52, 275)(53, 273)(54, 212)(55, 238)(56, 232)(57, 236)(58, 282)(59, 281)(60, 278)(61, 215)(62, 233)(63, 216)(64, 280)(65, 217)(66, 284)(67, 285)(68, 219)(69, 234)(70, 286)(71, 283)(72, 222)(73, 279)(74, 231)(75, 228)(76, 226)(77, 227)(78, 230)(79, 235)(80, 252)(81, 240)(82, 256)(83, 268)(84, 287)(85, 243)(86, 245)(87, 247)(88, 288)(89, 249)(90, 267)(91, 253)(92, 255)(93, 266)(94, 260)(95, 274)(96, 277)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) } Outer automorphisms :: reflexible Dual of E23.983 Graph:: bipartite v = 28 e = 192 f = 120 degree seq :: [ 12^16, 16^12 ] E23.983 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 8}) Quotient :: dipole Aut^+ = C2 x (C2 . S4 = SL(2,3) . C2) (small group id <96, 188>) Aut = $<192, 1480>$ (small group id <192, 1480>) |r| :: 2 Presentation :: [ Y1, R^2, Y2^4, Y2^4, (R * Y3)^2, (R * Y1)^2, Y2 * Y3 * Y2^2 * Y3^-1 * Y2, (Y2^-1 * R * Y2^-1)^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2^-2 * Y3^-3, Y3^-1 * Y2 * Y3 * Y2^-1 * Y3^2 * Y2 * Y3 * Y2^-1 * Y3^-1, Y3^-2 * Y2^-1 * Y3 * Y2 * Y3^-2 * Y2^-1 * Y3 * Y2^-1, Y3^-1 * Y2^-1 * Y3 * Y2 * Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3 * Y2^-1 * Y3^-1 * Y2^-1, (Y3 * Y2^-1)^6, (Y3^-1 * Y1^-1)^8 ] Map:: R = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)(193, 289, 194, 290, 198, 294, 196, 292)(195, 291, 201, 297, 209, 305, 203, 299)(197, 293, 206, 302, 210, 306, 207, 303)(199, 295, 211, 307, 204, 300, 213, 309)(200, 296, 214, 310, 205, 301, 215, 311)(202, 298, 219, 315, 208, 304, 220, 316)(212, 308, 229, 325, 216, 312, 230, 326)(217, 313, 237, 333, 221, 317, 239, 335)(218, 314, 240, 336, 222, 318, 241, 337)(223, 319, 247, 343, 225, 321, 249, 345)(224, 320, 250, 346, 226, 322, 251, 347)(227, 323, 253, 349, 231, 327, 255, 351)(228, 324, 256, 352, 232, 328, 257, 353)(233, 329, 263, 359, 235, 331, 265, 361)(234, 330, 266, 362, 236, 332, 267, 363)(238, 334, 260, 356, 242, 338, 262, 358)(243, 339, 264, 360, 245, 341, 268, 364)(244, 340, 254, 350, 246, 342, 258, 354)(248, 344, 259, 355, 252, 348, 261, 357)(269, 365, 279, 375, 271, 367, 281, 377)(270, 366, 284, 380, 272, 368, 286, 382)(273, 369, 285, 381, 275, 371, 283, 379)(274, 370, 280, 376, 276, 372, 282, 378)(277, 373, 288, 384, 278, 374, 287, 383) L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 209)(7, 212)(8, 194)(9, 217)(10, 210)(11, 221)(12, 216)(13, 196)(14, 223)(15, 225)(16, 197)(17, 208)(18, 198)(19, 227)(20, 205)(21, 231)(22, 233)(23, 235)(24, 200)(25, 238)(26, 201)(27, 243)(28, 245)(29, 242)(30, 203)(31, 248)(32, 206)(33, 252)(34, 207)(35, 254)(36, 211)(37, 259)(38, 261)(39, 258)(40, 213)(41, 264)(42, 214)(43, 268)(44, 215)(45, 269)(46, 222)(47, 271)(48, 273)(49, 275)(50, 218)(51, 277)(52, 219)(53, 278)(54, 220)(55, 274)(56, 226)(57, 276)(58, 270)(59, 272)(60, 224)(61, 279)(62, 232)(63, 281)(64, 283)(65, 285)(66, 228)(67, 287)(68, 229)(69, 288)(70, 230)(71, 284)(72, 236)(73, 286)(74, 280)(75, 282)(76, 234)(77, 251)(78, 237)(79, 250)(80, 239)(81, 249)(82, 240)(83, 247)(84, 241)(85, 246)(86, 244)(87, 267)(88, 253)(89, 266)(90, 255)(91, 265)(92, 256)(93, 263)(94, 257)(95, 262)(96, 260)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 12, 16 ), ( 12, 16, 12, 16, 12, 16, 12, 16 ) } Outer automorphisms :: reflexible Dual of E23.982 Graph:: simple bipartite v = 120 e = 192 f = 28 degree seq :: [ 2^96, 8^24 ] E23.984 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 8}) Quotient :: dipole Aut^+ = C2 x (C2 . S4 = SL(2,3) . C2) (small group id <96, 188>) Aut = $<192, 1480>$ (small group id <192, 1480>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^4, (R * Y3)^2, Y3^4, (R * Y1)^2, Y1^-1 * Y3^2 * Y1 * Y3^-2, Y1^2 * Y3^2 * Y1^2, Y1^-1 * Y3^-2 * Y1^-3, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^4, Y3^-1 * Y1^-2 * Y3 * Y1^-1 * Y3^-1 * Y1^-2 * Y3^-1 * Y1^-1, (Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y1)^2 ] Map:: R = (1, 97, 2, 98, 6, 102, 17, 113, 10, 106, 21, 117, 13, 109, 4, 100)(3, 99, 9, 105, 25, 121, 16, 112, 5, 101, 15, 111, 29, 125, 11, 107)(7, 103, 20, 116, 39, 135, 24, 120, 8, 104, 23, 119, 43, 139, 22, 118)(12, 108, 31, 127, 55, 151, 34, 130, 14, 110, 33, 129, 59, 155, 32, 128)(18, 114, 35, 131, 61, 157, 38, 134, 19, 115, 37, 133, 65, 161, 36, 132)(26, 122, 47, 143, 64, 160, 50, 146, 27, 123, 49, 145, 66, 162, 48, 144)(28, 124, 51, 147, 62, 158, 54, 150, 30, 126, 53, 149, 63, 159, 52, 148)(40, 136, 69, 165, 60, 156, 72, 168, 41, 137, 71, 167, 58, 154, 70, 166)(42, 138, 73, 169, 57, 153, 76, 172, 44, 140, 75, 171, 56, 152, 74, 170)(45, 141, 77, 173, 88, 184, 68, 164, 46, 142, 78, 174, 87, 183, 67, 163)(79, 175, 89, 185, 86, 182, 96, 192, 80, 176, 90, 186, 85, 181, 95, 191)(81, 177, 94, 190, 84, 180, 92, 188, 82, 178, 93, 189, 83, 179, 91, 187)(193, 289)(194, 290)(195, 291)(196, 292)(197, 293)(198, 294)(199, 295)(200, 296)(201, 297)(202, 298)(203, 299)(204, 300)(205, 301)(206, 302)(207, 303)(208, 304)(209, 305)(210, 306)(211, 307)(212, 308)(213, 309)(214, 310)(215, 311)(216, 312)(217, 313)(218, 314)(219, 315)(220, 316)(221, 317)(222, 318)(223, 319)(224, 320)(225, 321)(226, 322)(227, 323)(228, 324)(229, 325)(230, 326)(231, 327)(232, 328)(233, 329)(234, 330)(235, 331)(236, 332)(237, 333)(238, 334)(239, 335)(240, 336)(241, 337)(242, 338)(243, 339)(244, 340)(245, 341)(246, 342)(247, 343)(248, 344)(249, 345)(250, 346)(251, 347)(252, 348)(253, 349)(254, 350)(255, 351)(256, 352)(257, 353)(258, 354)(259, 355)(260, 356)(261, 357)(262, 358)(263, 359)(264, 360)(265, 361)(266, 362)(267, 363)(268, 364)(269, 365)(270, 366)(271, 367)(272, 368)(273, 369)(274, 370)(275, 371)(276, 372)(277, 373)(278, 374)(279, 375)(280, 376)(281, 377)(282, 378)(283, 379)(284, 380)(285, 381)(286, 382)(287, 383)(288, 384) L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 210)(7, 213)(8, 194)(9, 218)(10, 197)(11, 220)(12, 209)(13, 211)(14, 196)(15, 219)(16, 222)(17, 206)(18, 205)(19, 198)(20, 232)(21, 200)(22, 234)(23, 233)(24, 236)(25, 237)(26, 207)(27, 201)(28, 208)(29, 238)(30, 203)(31, 248)(32, 250)(33, 249)(34, 252)(35, 254)(36, 256)(37, 255)(38, 258)(39, 259)(40, 215)(41, 212)(42, 216)(43, 260)(44, 214)(45, 221)(46, 217)(47, 271)(48, 273)(49, 272)(50, 274)(51, 275)(52, 277)(53, 276)(54, 278)(55, 269)(56, 225)(57, 223)(58, 226)(59, 270)(60, 224)(61, 279)(62, 229)(63, 227)(64, 230)(65, 280)(66, 228)(67, 235)(68, 231)(69, 281)(70, 283)(71, 282)(72, 284)(73, 285)(74, 287)(75, 286)(76, 288)(77, 251)(78, 247)(79, 241)(80, 239)(81, 242)(82, 240)(83, 245)(84, 243)(85, 246)(86, 244)(87, 257)(88, 253)(89, 263)(90, 261)(91, 264)(92, 262)(93, 267)(94, 265)(95, 268)(96, 266)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E23.981 Graph:: simple bipartite v = 108 e = 192 f = 40 degree seq :: [ 2^96, 16^12 ] E23.985 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 8}) Quotient :: dipole Aut^+ = C2 x (C2 . S4 = SL(2,3) . C2) (small group id <96, 188>) Aut = $<192, 1480>$ (small group id <192, 1480>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, Y1 * Y3^-3, Y1^-2 * Y3^-2, (R * Y1)^2, Y1^4, Y1^-1 * Y3^2 * Y1^-1, (Y1 * Y3^-1)^2, (R * Y3)^2, Y1 * Y2^-1 * Y3^-1 * Y1 * Y2 * Y1, Y3 * Y2^4 * Y3, (R * Y2 * Y3^-1)^2, Y2 * Y1^-2 * Y2^-1 * Y1^-2, Y2 * Y1 * Y2^-2 * Y1 * Y2 * Y3^-1 * Y2^2 * Y3^-1, Y2^2 * Y3 * Y2 * Y3 * Y2^-2 * Y1^-1 * Y2 * Y1^-1, Y2^-1 * Y1 * Y2 * R * Y2^2 * Y3 * Y2^-1 * R * Y2^-1, Y2 * Y3 * Y2^-2 * Y1 * Y2 * Y1^-1 * Y2^-2 * Y1^-1, (Y1^-1 * Y2^-1)^6, Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2 * Y1 * Y2^-1 * Y3^-1 * Y2 * Y1^-1 * Y2^-1 * Y1^-1 ] Map:: R = (1, 97, 2, 98, 6, 102, 4, 100)(3, 99, 9, 105, 17, 113, 11, 107)(5, 101, 14, 110, 18, 114, 15, 111)(7, 103, 19, 115, 12, 108, 21, 117)(8, 104, 22, 118, 13, 109, 23, 119)(10, 106, 27, 123, 16, 112, 28, 124)(20, 116, 37, 133, 24, 120, 38, 134)(25, 121, 45, 141, 29, 125, 47, 143)(26, 122, 48, 144, 30, 126, 49, 145)(31, 127, 55, 151, 33, 129, 57, 153)(32, 128, 58, 154, 34, 130, 59, 155)(35, 131, 61, 157, 39, 135, 63, 159)(36, 132, 64, 160, 40, 136, 65, 161)(41, 137, 71, 167, 43, 139, 73, 169)(42, 138, 74, 170, 44, 140, 75, 171)(46, 142, 68, 164, 50, 146, 70, 166)(51, 147, 72, 168, 53, 149, 76, 172)(52, 148, 62, 158, 54, 150, 66, 162)(56, 152, 67, 163, 60, 156, 69, 165)(77, 173, 87, 183, 79, 175, 89, 185)(78, 174, 92, 188, 80, 176, 94, 190)(81, 177, 93, 189, 83, 179, 91, 187)(82, 178, 88, 184, 84, 180, 90, 186)(85, 181, 96, 192, 86, 182, 95, 191)(193, 289, 195, 291, 202, 298, 210, 306, 198, 294, 209, 305, 208, 304, 197, 293)(194, 290, 199, 295, 212, 308, 205, 301, 196, 292, 204, 300, 216, 312, 200, 296)(201, 297, 217, 313, 238, 334, 222, 318, 203, 299, 221, 317, 242, 338, 218, 314)(206, 302, 223, 319, 248, 344, 226, 322, 207, 303, 225, 321, 252, 348, 224, 320)(211, 307, 227, 323, 254, 350, 232, 328, 213, 309, 231, 327, 258, 354, 228, 324)(214, 310, 233, 329, 264, 360, 236, 332, 215, 311, 235, 331, 268, 364, 234, 330)(219, 315, 243, 339, 277, 373, 246, 342, 220, 316, 245, 341, 278, 374, 244, 340)(229, 325, 259, 355, 287, 383, 262, 358, 230, 326, 261, 357, 288, 384, 260, 356)(237, 333, 269, 365, 251, 347, 272, 368, 239, 335, 271, 367, 250, 346, 270, 366)(240, 336, 273, 369, 249, 345, 276, 372, 241, 337, 275, 371, 247, 343, 274, 370)(253, 349, 279, 375, 267, 363, 282, 378, 255, 351, 281, 377, 266, 362, 280, 376)(256, 352, 283, 379, 265, 361, 286, 382, 257, 353, 285, 381, 263, 359, 284, 380) L = (1, 196)(2, 193)(3, 203)(4, 198)(5, 207)(6, 194)(7, 213)(8, 215)(9, 195)(10, 220)(11, 209)(12, 211)(13, 214)(14, 197)(15, 210)(16, 219)(17, 201)(18, 206)(19, 199)(20, 230)(21, 204)(22, 200)(23, 205)(24, 229)(25, 239)(26, 241)(27, 202)(28, 208)(29, 237)(30, 240)(31, 249)(32, 251)(33, 247)(34, 250)(35, 255)(36, 257)(37, 212)(38, 216)(39, 253)(40, 256)(41, 265)(42, 267)(43, 263)(44, 266)(45, 217)(46, 262)(47, 221)(48, 218)(49, 222)(50, 260)(51, 268)(52, 258)(53, 264)(54, 254)(55, 223)(56, 261)(57, 225)(58, 224)(59, 226)(60, 259)(61, 227)(62, 244)(63, 231)(64, 228)(65, 232)(66, 246)(67, 248)(68, 238)(69, 252)(70, 242)(71, 233)(72, 243)(73, 235)(74, 234)(75, 236)(76, 245)(77, 281)(78, 286)(79, 279)(80, 284)(81, 283)(82, 282)(83, 285)(84, 280)(85, 287)(86, 288)(87, 269)(88, 274)(89, 271)(90, 276)(91, 275)(92, 270)(93, 273)(94, 272)(95, 278)(96, 277)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 2, 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 E23.986 Graph:: bipartite v = 36 e = 192 f = 112 degree seq :: [ 8^24, 16^12 ] E23.986 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 8}) Quotient :: dipole Aut^+ = C2 x (C2 . S4 = SL(2,3) . C2) (small group id <96, 188>) Aut = $<192, 1480>$ (small group id <192, 1480>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^3 * Y1^-1 * Y3^-1 * Y1^-1, Y1^6, Y3 * Y1^-3 * Y3^-1 * Y1^-3, Y3^8, Y3^-1 * Y1^-1 * Y3^-2 * Y1^-1 * Y3^-1 * Y1^-2, (Y3 * Y2^-1)^8 ] Map:: polytopal R = (1, 97, 2, 98, 6, 102, 18, 114, 13, 109, 4, 100)(3, 99, 9, 105, 27, 123, 47, 143, 33, 129, 11, 107)(5, 101, 15, 111, 42, 138, 48, 144, 44, 140, 16, 112)(7, 103, 21, 117, 55, 151, 37, 133, 60, 156, 23, 119)(8, 104, 24, 120, 62, 158, 38, 134, 64, 160, 25, 121)(10, 106, 30, 126, 71, 167, 80, 176, 74, 170, 31, 127)(12, 108, 35, 131, 51, 147, 19, 115, 49, 145, 36, 132)(14, 110, 39, 135, 53, 149, 20, 116, 52, 148, 40, 136)(17, 113, 34, 130, 59, 155, 81, 177, 68, 164, 46, 142)(22, 118, 57, 153, 88, 184, 77, 173, 43, 139, 58, 154)(26, 122, 61, 157, 84, 180, 78, 174, 87, 183, 66, 162)(28, 124, 56, 152, 45, 141, 65, 161, 86, 182, 69, 165)(29, 125, 63, 159, 83, 179, 50, 146, 82, 178, 70, 166)(32, 128, 54, 150, 85, 181, 67, 163, 41, 137, 75, 171)(72, 168, 92, 188, 79, 175, 93, 189, 95, 191, 89, 185)(73, 169, 94, 190, 96, 192, 91, 187, 76, 172, 90, 186)(193, 289)(194, 290)(195, 291)(196, 292)(197, 293)(198, 294)(199, 295)(200, 296)(201, 297)(202, 298)(203, 299)(204, 300)(205, 301)(206, 302)(207, 303)(208, 304)(209, 305)(210, 306)(211, 307)(212, 308)(213, 309)(214, 310)(215, 311)(216, 312)(217, 313)(218, 314)(219, 315)(220, 316)(221, 317)(222, 318)(223, 319)(224, 320)(225, 321)(226, 322)(227, 323)(228, 324)(229, 325)(230, 326)(231, 327)(232, 328)(233, 329)(234, 330)(235, 331)(236, 332)(237, 333)(238, 334)(239, 335)(240, 336)(241, 337)(242, 338)(243, 339)(244, 340)(245, 341)(246, 342)(247, 343)(248, 344)(249, 345)(250, 346)(251, 347)(252, 348)(253, 349)(254, 350)(255, 351)(256, 352)(257, 353)(258, 354)(259, 355)(260, 356)(261, 357)(262, 358)(263, 359)(264, 360)(265, 361)(266, 362)(267, 363)(268, 364)(269, 365)(270, 366)(271, 367)(272, 368)(273, 369)(274, 370)(275, 371)(276, 372)(277, 373)(278, 374)(279, 375)(280, 376)(281, 377)(282, 378)(283, 379)(284, 380)(285, 381)(286, 382)(287, 383)(288, 384) L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 211)(7, 214)(8, 194)(9, 220)(10, 213)(11, 224)(12, 221)(13, 229)(14, 196)(15, 223)(16, 218)(17, 197)(18, 239)(19, 242)(20, 198)(21, 248)(22, 241)(23, 251)(24, 250)(25, 246)(26, 200)(27, 259)(28, 254)(29, 201)(30, 244)(31, 265)(32, 264)(33, 257)(34, 203)(35, 261)(36, 258)(37, 269)(38, 205)(39, 262)(40, 209)(41, 206)(42, 270)(43, 207)(44, 263)(45, 208)(46, 271)(47, 272)(48, 210)(49, 237)(50, 225)(51, 276)(52, 275)(53, 273)(54, 212)(55, 238)(56, 232)(57, 236)(58, 282)(59, 281)(60, 278)(61, 215)(62, 233)(63, 216)(64, 280)(65, 217)(66, 284)(67, 285)(68, 219)(69, 234)(70, 286)(71, 283)(72, 222)(73, 279)(74, 231)(75, 228)(76, 226)(77, 227)(78, 230)(79, 235)(80, 252)(81, 240)(82, 256)(83, 268)(84, 287)(85, 243)(86, 245)(87, 247)(88, 288)(89, 249)(90, 267)(91, 253)(92, 255)(93, 266)(94, 260)(95, 274)(96, 277)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E23.985 Graph:: simple bipartite v = 112 e = 192 f = 36 degree seq :: [ 2^96, 12^16 ] E23.987 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 6, 8}) Quotient :: edge Aut^+ = (C2 x SL(2,3)) : C2 (small group id <96, 190>) Aut = $<192, 1485>$ (small group id <192, 1485>) |r| :: 2 Presentation :: [ F^2, T1^4, (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1^2 * T2^-1 * T1^-1, T2^6, (T2^-3 * T1^-1)^2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1, T1 * T2^-2 * T1^-1 * T2^3 * T1 * T2^-1 * T1, T2^2 * T1^-1 * T2^-1 * T1 * T2^2 * T1^-1 * T2^-1 * T1^-1, T2 * T1^-1 * T2^-2 * T1^-1 * T2 * T1^-1 * T2^-2 * T1 ] Map:: non-degenerate R = (1, 3, 10, 28, 16, 5)(2, 7, 20, 45, 24, 8)(4, 12, 32, 61, 33, 13)(6, 17, 40, 68, 41, 18)(9, 25, 55, 39, 58, 26)(11, 30, 64, 38, 65, 31)(14, 34, 63, 29, 62, 35)(15, 36, 60, 27, 59, 37)(19, 42, 69, 54, 72, 43)(21, 47, 77, 53, 78, 48)(22, 49, 76, 46, 75, 50)(23, 51, 74, 44, 73, 52)(56, 83, 67, 82, 94, 84)(57, 85, 66, 81, 93, 86)(70, 89, 80, 88, 96, 90)(71, 91, 79, 87, 95, 92)(97, 98, 102, 100)(99, 105, 113, 107)(101, 110, 114, 111)(103, 115, 108, 117)(104, 118, 109, 119)(106, 123, 136, 125)(112, 134, 137, 135)(116, 140, 128, 142)(120, 149, 129, 150)(121, 148, 126, 146)(122, 152, 127, 153)(124, 157, 164, 141)(130, 162, 132, 163)(131, 143, 133, 138)(139, 166, 144, 167)(145, 175, 147, 176)(151, 177, 160, 178)(154, 172, 161, 170)(155, 182, 158, 180)(156, 174, 159, 168)(165, 183, 173, 184)(169, 188, 171, 186)(179, 185, 181, 187)(189, 192, 190, 191) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 16^4 ), ( 16^6 ) } Outer automorphisms :: reflexible Dual of E23.991 Transitivity :: ET+ Graph:: simple bipartite v = 40 e = 96 f = 12 degree seq :: [ 4^24, 6^16 ] E23.988 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 6, 8}) Quotient :: edge Aut^+ = (C2 x SL(2,3)) : C2 (small group id <96, 190>) Aut = $<192, 1485>$ (small group id <192, 1485>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T1 * T2^-1 * T1)^2, T1^6, T2^3 * T1^-1 * T2^-1 * T1^-1, T2^8, T1 * T2 * T1^2 * T2 * T1 * T2^2 ] Map:: non-degenerate R = (1, 3, 10, 21, 52, 38, 17, 5)(2, 7, 22, 46, 42, 16, 26, 8)(4, 12, 29, 9, 28, 63, 39, 14)(6, 19, 47, 77, 59, 25, 50, 20)(11, 32, 68, 30, 67, 86, 71, 33)(13, 35, 72, 34, 64, 79, 74, 36)(15, 31, 69, 87, 51, 43, 76, 40)(18, 44, 78, 73, 85, 49, 80, 45)(23, 55, 88, 53, 41, 70, 91, 56)(24, 54, 89, 65, 81, 60, 92, 57)(27, 61, 93, 75, 37, 66, 94, 62)(48, 83, 95, 82, 58, 90, 96, 84)(97, 98, 102, 114, 109, 100)(99, 105, 123, 145, 116, 107)(101, 111, 131, 169, 137, 112)(103, 117, 147, 175, 141, 119)(104, 120, 108, 130, 154, 121)(106, 126, 151, 174, 158, 127)(110, 133, 140, 173, 163, 134)(113, 129, 166, 176, 171, 139)(115, 142, 177, 159, 132, 144)(118, 149, 179, 168, 183, 150)(122, 152, 186, 170, 136, 156)(124, 148, 138, 155, 181, 160)(125, 161, 128, 143, 178, 162)(135, 153, 182, 146, 180, 157)(164, 188, 165, 189, 191, 187)(167, 185, 172, 190, 192, 184) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8^6 ), ( 8^8 ) } Outer automorphisms :: reflexible Dual of E23.992 Transitivity :: ET+ Graph:: simple bipartite v = 28 e = 96 f = 24 degree seq :: [ 6^16, 8^12 ] E23.989 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 6, 8}) Quotient :: edge Aut^+ = (C2 x SL(2,3)) : C2 (small group id <96, 190>) Aut = $<192, 1485>$ (small group id <192, 1485>) |r| :: 2 Presentation :: [ F^2, T2^4, T2^4, T2^4, (F * T2)^2, (F * T1)^2, T2^-1 * T1^-1 * T2^2 * T1 * T2^-1, T2^2 * T1^-4, T1^-2 * T2 * T1 * T2^-1 * T1^2 * T2^-1 * T1 * T2^-1, T2 * T1^-2 * T2 * T1^-1 * T2^-1 * T1^-2 * T2^-1 * T1^-1, (T2^-1 * T1^-1)^6 ] Map:: polytopal non-degenerate R = (1, 3, 10, 5)(2, 7, 21, 8)(4, 12, 17, 14)(6, 18, 13, 19)(9, 26, 15, 27)(11, 28, 16, 30)(20, 40, 23, 41)(22, 42, 24, 44)(25, 45, 29, 46)(31, 56, 33, 57)(32, 58, 34, 60)(35, 62, 37, 63)(36, 64, 38, 66)(39, 67, 43, 68)(47, 79, 49, 80)(48, 81, 50, 82)(51, 83, 53, 84)(52, 85, 54, 86)(55, 78, 59, 77)(61, 87, 65, 88)(69, 89, 71, 90)(70, 91, 72, 92)(73, 93, 75, 94)(74, 95, 76, 96)(97, 98, 102, 113, 106, 117, 109, 100)(99, 105, 121, 112, 101, 111, 125, 107)(103, 116, 135, 120, 104, 119, 139, 118)(108, 127, 151, 130, 110, 129, 155, 128)(114, 131, 157, 134, 115, 133, 161, 132)(122, 143, 162, 146, 123, 145, 160, 144)(124, 147, 159, 150, 126, 149, 158, 148)(136, 165, 154, 168, 137, 167, 156, 166)(138, 169, 152, 172, 140, 171, 153, 170)(141, 173, 184, 163, 142, 174, 183, 164)(175, 186, 181, 192, 176, 185, 182, 191)(177, 189, 179, 188, 178, 190, 180, 187) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 12^4 ), ( 12^8 ) } Outer automorphisms :: reflexible Dual of E23.990 Transitivity :: ET+ Graph:: bipartite v = 36 e = 96 f = 16 degree seq :: [ 4^24, 8^12 ] E23.990 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 6, 8}) Quotient :: loop Aut^+ = (C2 x SL(2,3)) : C2 (small group id <96, 190>) Aut = $<192, 1485>$ (small group id <192, 1485>) |r| :: 2 Presentation :: [ F^2, T1^4, (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1^2 * T2^-1 * T1^-1, T2^6, (T2^-3 * T1^-1)^2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1, T1 * T2^-2 * T1^-1 * T2^3 * T1 * T2^-1 * T1, T2^2 * T1^-1 * T2^-1 * T1 * T2^2 * T1^-1 * T2^-1 * T1^-1, T2 * T1^-1 * T2^-2 * T1^-1 * T2 * T1^-1 * T2^-2 * T1 ] Map:: polytopal non-degenerate R = (1, 97, 3, 99, 10, 106, 28, 124, 16, 112, 5, 101)(2, 98, 7, 103, 20, 116, 45, 141, 24, 120, 8, 104)(4, 100, 12, 108, 32, 128, 61, 157, 33, 129, 13, 109)(6, 102, 17, 113, 40, 136, 68, 164, 41, 137, 18, 114)(9, 105, 25, 121, 55, 151, 39, 135, 58, 154, 26, 122)(11, 107, 30, 126, 64, 160, 38, 134, 65, 161, 31, 127)(14, 110, 34, 130, 63, 159, 29, 125, 62, 158, 35, 131)(15, 111, 36, 132, 60, 156, 27, 123, 59, 155, 37, 133)(19, 115, 42, 138, 69, 165, 54, 150, 72, 168, 43, 139)(21, 117, 47, 143, 77, 173, 53, 149, 78, 174, 48, 144)(22, 118, 49, 145, 76, 172, 46, 142, 75, 171, 50, 146)(23, 119, 51, 147, 74, 170, 44, 140, 73, 169, 52, 148)(56, 152, 83, 179, 67, 163, 82, 178, 94, 190, 84, 180)(57, 153, 85, 181, 66, 162, 81, 177, 93, 189, 86, 182)(70, 166, 89, 185, 80, 176, 88, 184, 96, 192, 90, 186)(71, 167, 91, 187, 79, 175, 87, 183, 95, 191, 92, 188) L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 110)(6, 100)(7, 115)(8, 118)(9, 113)(10, 123)(11, 99)(12, 117)(13, 119)(14, 114)(15, 101)(16, 134)(17, 107)(18, 111)(19, 108)(20, 140)(21, 103)(22, 109)(23, 104)(24, 149)(25, 148)(26, 152)(27, 136)(28, 157)(29, 106)(30, 146)(31, 153)(32, 142)(33, 150)(34, 162)(35, 143)(36, 163)(37, 138)(38, 137)(39, 112)(40, 125)(41, 135)(42, 131)(43, 166)(44, 128)(45, 124)(46, 116)(47, 133)(48, 167)(49, 175)(50, 121)(51, 176)(52, 126)(53, 129)(54, 120)(55, 177)(56, 127)(57, 122)(58, 172)(59, 182)(60, 174)(61, 164)(62, 180)(63, 168)(64, 178)(65, 170)(66, 132)(67, 130)(68, 141)(69, 183)(70, 144)(71, 139)(72, 156)(73, 188)(74, 154)(75, 186)(76, 161)(77, 184)(78, 159)(79, 147)(80, 145)(81, 160)(82, 151)(83, 185)(84, 155)(85, 187)(86, 158)(87, 173)(88, 165)(89, 181)(90, 169)(91, 179)(92, 171)(93, 192)(94, 191)(95, 189)(96, 190) local type(s) :: { ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E23.989 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 16 e = 96 f = 36 degree seq :: [ 12^16 ] E23.991 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 6, 8}) Quotient :: loop Aut^+ = (C2 x SL(2,3)) : C2 (small group id <96, 190>) Aut = $<192, 1485>$ (small group id <192, 1485>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T1 * T2^-1 * T1)^2, T1^6, T2^3 * T1^-1 * T2^-1 * T1^-1, T2^8, T1 * T2 * T1^2 * T2 * T1 * T2^2 ] Map:: non-degenerate R = (1, 97, 3, 99, 10, 106, 21, 117, 52, 148, 38, 134, 17, 113, 5, 101)(2, 98, 7, 103, 22, 118, 46, 142, 42, 138, 16, 112, 26, 122, 8, 104)(4, 100, 12, 108, 29, 125, 9, 105, 28, 124, 63, 159, 39, 135, 14, 110)(6, 102, 19, 115, 47, 143, 77, 173, 59, 155, 25, 121, 50, 146, 20, 116)(11, 107, 32, 128, 68, 164, 30, 126, 67, 163, 86, 182, 71, 167, 33, 129)(13, 109, 35, 131, 72, 168, 34, 130, 64, 160, 79, 175, 74, 170, 36, 132)(15, 111, 31, 127, 69, 165, 87, 183, 51, 147, 43, 139, 76, 172, 40, 136)(18, 114, 44, 140, 78, 174, 73, 169, 85, 181, 49, 145, 80, 176, 45, 141)(23, 119, 55, 151, 88, 184, 53, 149, 41, 137, 70, 166, 91, 187, 56, 152)(24, 120, 54, 150, 89, 185, 65, 161, 81, 177, 60, 156, 92, 188, 57, 153)(27, 123, 61, 157, 93, 189, 75, 171, 37, 133, 66, 162, 94, 190, 62, 158)(48, 144, 83, 179, 95, 191, 82, 178, 58, 154, 90, 186, 96, 192, 84, 180) L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 111)(6, 114)(7, 117)(8, 120)(9, 123)(10, 126)(11, 99)(12, 130)(13, 100)(14, 133)(15, 131)(16, 101)(17, 129)(18, 109)(19, 142)(20, 107)(21, 147)(22, 149)(23, 103)(24, 108)(25, 104)(26, 152)(27, 145)(28, 148)(29, 161)(30, 151)(31, 106)(32, 143)(33, 166)(34, 154)(35, 169)(36, 144)(37, 140)(38, 110)(39, 153)(40, 156)(41, 112)(42, 155)(43, 113)(44, 173)(45, 119)(46, 177)(47, 178)(48, 115)(49, 116)(50, 180)(51, 175)(52, 138)(53, 179)(54, 118)(55, 174)(56, 186)(57, 182)(58, 121)(59, 181)(60, 122)(61, 135)(62, 127)(63, 132)(64, 124)(65, 128)(66, 125)(67, 134)(68, 188)(69, 189)(70, 176)(71, 185)(72, 183)(73, 137)(74, 136)(75, 139)(76, 190)(77, 163)(78, 158)(79, 141)(80, 171)(81, 159)(82, 162)(83, 168)(84, 157)(85, 160)(86, 146)(87, 150)(88, 167)(89, 172)(90, 170)(91, 164)(92, 165)(93, 191)(94, 192)(95, 187)(96, 184) local type(s) :: { ( 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6, 4, 6 ) } Outer automorphisms :: reflexible Dual of E23.987 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 12 e = 96 f = 40 degree seq :: [ 16^12 ] E23.992 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 6, 8}) Quotient :: loop Aut^+ = (C2 x SL(2,3)) : C2 (small group id <96, 190>) Aut = $<192, 1485>$ (small group id <192, 1485>) |r| :: 2 Presentation :: [ F^2, T2^4, T2^4, T2^4, (F * T2)^2, (F * T1)^2, T2^-1 * T1^-1 * T2^2 * T1 * T2^-1, T2^2 * T1^-4, T1^-2 * T2 * T1 * T2^-1 * T1^2 * T2^-1 * T1 * T2^-1, T2 * T1^-2 * T2 * T1^-1 * T2^-1 * T1^-2 * T2^-1 * T1^-1, (T2^-1 * T1^-1)^6 ] Map:: non-degenerate R = (1, 97, 3, 99, 10, 106, 5, 101)(2, 98, 7, 103, 21, 117, 8, 104)(4, 100, 12, 108, 17, 113, 14, 110)(6, 102, 18, 114, 13, 109, 19, 115)(9, 105, 26, 122, 15, 111, 27, 123)(11, 107, 28, 124, 16, 112, 30, 126)(20, 116, 40, 136, 23, 119, 41, 137)(22, 118, 42, 138, 24, 120, 44, 140)(25, 121, 45, 141, 29, 125, 46, 142)(31, 127, 56, 152, 33, 129, 57, 153)(32, 128, 58, 154, 34, 130, 60, 156)(35, 131, 62, 158, 37, 133, 63, 159)(36, 132, 64, 160, 38, 134, 66, 162)(39, 135, 67, 163, 43, 139, 68, 164)(47, 143, 79, 175, 49, 145, 80, 176)(48, 144, 81, 177, 50, 146, 82, 178)(51, 147, 83, 179, 53, 149, 84, 180)(52, 148, 85, 181, 54, 150, 86, 182)(55, 151, 78, 174, 59, 155, 77, 173)(61, 157, 87, 183, 65, 161, 88, 184)(69, 165, 89, 185, 71, 167, 90, 186)(70, 166, 91, 187, 72, 168, 92, 188)(73, 169, 93, 189, 75, 171, 94, 190)(74, 170, 95, 191, 76, 172, 96, 192) L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 111)(6, 113)(7, 116)(8, 119)(9, 121)(10, 117)(11, 99)(12, 127)(13, 100)(14, 129)(15, 125)(16, 101)(17, 106)(18, 131)(19, 133)(20, 135)(21, 109)(22, 103)(23, 139)(24, 104)(25, 112)(26, 143)(27, 145)(28, 147)(29, 107)(30, 149)(31, 151)(32, 108)(33, 155)(34, 110)(35, 157)(36, 114)(37, 161)(38, 115)(39, 120)(40, 165)(41, 167)(42, 169)(43, 118)(44, 171)(45, 173)(46, 174)(47, 162)(48, 122)(49, 160)(50, 123)(51, 159)(52, 124)(53, 158)(54, 126)(55, 130)(56, 172)(57, 170)(58, 168)(59, 128)(60, 166)(61, 134)(62, 148)(63, 150)(64, 144)(65, 132)(66, 146)(67, 142)(68, 141)(69, 154)(70, 136)(71, 156)(72, 137)(73, 152)(74, 138)(75, 153)(76, 140)(77, 184)(78, 183)(79, 186)(80, 185)(81, 189)(82, 190)(83, 188)(84, 187)(85, 192)(86, 191)(87, 164)(88, 163)(89, 182)(90, 181)(91, 177)(92, 178)(93, 179)(94, 180)(95, 175)(96, 176) local type(s) :: { ( 6, 8, 6, 8, 6, 8, 6, 8 ) } Outer automorphisms :: reflexible Dual of E23.988 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 24 e = 96 f = 28 degree seq :: [ 8^24 ] E23.993 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 8}) Quotient :: dipole Aut^+ = (C2 x SL(2,3)) : C2 (small group id <96, 190>) Aut = $<192, 1485>$ (small group id <192, 1485>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y1^4, (Y3 * Y1^-1)^2, (R * Y3)^2, (R * Y1)^2, Y3 * Y2 * Y1^2 * Y2^-1 * Y3, (R * Y2 * Y3^-1)^2, Y3 * Y2 * Y3^-1 * Y1 * Y2^-1 * Y1^-1, Y2 * Y1^-2 * Y2^-1 * Y1^-2, Y2^6, Y2^-3 * Y3 * Y2^-3 * Y1^-1, Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y3^-1 * Y2 * Y1^-1, Y2^-1 * Y1 * Y3^-1 * Y2^2 * Y1 * Y3^-1 * Y2^-1, Y2 * Y1^-1 * Y2^3 * Y3 * Y2^2, Y2^2 * Y1 * Y2^-1 * Y3 * Y2^2 * Y1 * Y2^-1 * Y1, Y2^-1 * Y1 * Y2 * R * Y2^2 * Y3 * Y2^-1 * R * Y2^-1, Y2 * Y1 * Y2^-2 * Y1 * Y2 * Y3^-1 * Y2^-2 * Y1^-1, Y2^-2 * Y3 * Y2 * Y1 * Y2^-1 * Y3 * Y2 * Y3^-1 * Y2^-2 * Y1^-1 * Y2^-1 * Y1^-1, (Y3 * Y2^-1)^8 ] Map:: R = (1, 97, 2, 98, 6, 102, 4, 100)(3, 99, 9, 105, 17, 113, 11, 107)(5, 101, 14, 110, 18, 114, 15, 111)(7, 103, 19, 115, 12, 108, 21, 117)(8, 104, 22, 118, 13, 109, 23, 119)(10, 106, 27, 123, 40, 136, 29, 125)(16, 112, 38, 134, 41, 137, 39, 135)(20, 116, 44, 140, 32, 128, 46, 142)(24, 120, 53, 149, 33, 129, 54, 150)(25, 121, 52, 148, 30, 126, 50, 146)(26, 122, 56, 152, 31, 127, 57, 153)(28, 124, 61, 157, 68, 164, 45, 141)(34, 130, 66, 162, 36, 132, 67, 163)(35, 131, 47, 143, 37, 133, 42, 138)(43, 139, 70, 166, 48, 144, 71, 167)(49, 145, 79, 175, 51, 147, 80, 176)(55, 151, 81, 177, 64, 160, 82, 178)(58, 154, 76, 172, 65, 161, 74, 170)(59, 155, 86, 182, 62, 158, 84, 180)(60, 156, 78, 174, 63, 159, 72, 168)(69, 165, 87, 183, 77, 173, 88, 184)(73, 169, 92, 188, 75, 171, 90, 186)(83, 179, 89, 185, 85, 181, 91, 187)(93, 189, 96, 192, 94, 190, 95, 191)(193, 289, 195, 291, 202, 298, 220, 316, 208, 304, 197, 293)(194, 290, 199, 295, 212, 308, 237, 333, 216, 312, 200, 296)(196, 292, 204, 300, 224, 320, 253, 349, 225, 321, 205, 301)(198, 294, 209, 305, 232, 328, 260, 356, 233, 329, 210, 306)(201, 297, 217, 313, 247, 343, 231, 327, 250, 346, 218, 314)(203, 299, 222, 318, 256, 352, 230, 326, 257, 353, 223, 319)(206, 302, 226, 322, 255, 351, 221, 317, 254, 350, 227, 323)(207, 303, 228, 324, 252, 348, 219, 315, 251, 347, 229, 325)(211, 307, 234, 330, 261, 357, 246, 342, 264, 360, 235, 331)(213, 309, 239, 335, 269, 365, 245, 341, 270, 366, 240, 336)(214, 310, 241, 337, 268, 364, 238, 334, 267, 363, 242, 338)(215, 311, 243, 339, 266, 362, 236, 332, 265, 361, 244, 340)(248, 344, 275, 371, 259, 355, 274, 370, 286, 382, 276, 372)(249, 345, 277, 373, 258, 354, 273, 369, 285, 381, 278, 374)(262, 358, 281, 377, 272, 368, 280, 376, 288, 384, 282, 378)(263, 359, 283, 379, 271, 367, 279, 375, 287, 383, 284, 380) L = (1, 196)(2, 193)(3, 203)(4, 198)(5, 207)(6, 194)(7, 213)(8, 215)(9, 195)(10, 221)(11, 209)(12, 211)(13, 214)(14, 197)(15, 210)(16, 231)(17, 201)(18, 206)(19, 199)(20, 238)(21, 204)(22, 200)(23, 205)(24, 246)(25, 242)(26, 249)(27, 202)(28, 237)(29, 232)(30, 244)(31, 248)(32, 236)(33, 245)(34, 259)(35, 234)(36, 258)(37, 239)(38, 208)(39, 233)(40, 219)(41, 230)(42, 229)(43, 263)(44, 212)(45, 260)(46, 224)(47, 227)(48, 262)(49, 272)(50, 222)(51, 271)(52, 217)(53, 216)(54, 225)(55, 274)(56, 218)(57, 223)(58, 266)(59, 276)(60, 264)(61, 220)(62, 278)(63, 270)(64, 273)(65, 268)(66, 226)(67, 228)(68, 253)(69, 280)(70, 235)(71, 240)(72, 255)(73, 282)(74, 257)(75, 284)(76, 250)(77, 279)(78, 252)(79, 241)(80, 243)(81, 247)(82, 256)(83, 283)(84, 254)(85, 281)(86, 251)(87, 261)(88, 269)(89, 275)(90, 267)(91, 277)(92, 265)(93, 287)(94, 288)(95, 286)(96, 285)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 2, 16, 2, 16, 2, 16, 2, 16 ), ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ) } Outer automorphisms :: reflexible Dual of E23.996 Graph:: bipartite v = 40 e = 192 f = 108 degree seq :: [ 8^24, 12^16 ] E23.994 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 8}) Quotient :: dipole Aut^+ = (C2 x SL(2,3)) : C2 (small group id <96, 190>) Aut = $<192, 1485>$ (small group id <192, 1485>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y1 * Y2^-1 * Y1)^2, Y1^6, Y2^-1 * Y1^-1 * Y2^3 * Y1^-1, Y1 * Y2 * Y1^2 * Y2 * Y1 * Y2^2, (Y3^-1 * Y1^-1)^4 ] Map:: R = (1, 97, 2, 98, 6, 102, 18, 114, 13, 109, 4, 100)(3, 99, 9, 105, 27, 123, 49, 145, 20, 116, 11, 107)(5, 101, 15, 111, 35, 131, 73, 169, 41, 137, 16, 112)(7, 103, 21, 117, 51, 147, 79, 175, 45, 141, 23, 119)(8, 104, 24, 120, 12, 108, 34, 130, 58, 154, 25, 121)(10, 106, 30, 126, 55, 151, 78, 174, 62, 158, 31, 127)(14, 110, 37, 133, 44, 140, 77, 173, 67, 163, 38, 134)(17, 113, 33, 129, 70, 166, 80, 176, 75, 171, 43, 139)(19, 115, 46, 142, 81, 177, 63, 159, 36, 132, 48, 144)(22, 118, 53, 149, 83, 179, 72, 168, 87, 183, 54, 150)(26, 122, 56, 152, 90, 186, 74, 170, 40, 136, 60, 156)(28, 124, 52, 148, 42, 138, 59, 155, 85, 181, 64, 160)(29, 125, 65, 161, 32, 128, 47, 143, 82, 178, 66, 162)(39, 135, 57, 153, 86, 182, 50, 146, 84, 180, 61, 157)(68, 164, 92, 188, 69, 165, 93, 189, 95, 191, 91, 187)(71, 167, 89, 185, 76, 172, 94, 190, 96, 192, 88, 184)(193, 289, 195, 291, 202, 298, 213, 309, 244, 340, 230, 326, 209, 305, 197, 293)(194, 290, 199, 295, 214, 310, 238, 334, 234, 330, 208, 304, 218, 314, 200, 296)(196, 292, 204, 300, 221, 317, 201, 297, 220, 316, 255, 351, 231, 327, 206, 302)(198, 294, 211, 307, 239, 335, 269, 365, 251, 347, 217, 313, 242, 338, 212, 308)(203, 299, 224, 320, 260, 356, 222, 318, 259, 355, 278, 374, 263, 359, 225, 321)(205, 301, 227, 323, 264, 360, 226, 322, 256, 352, 271, 367, 266, 362, 228, 324)(207, 303, 223, 319, 261, 357, 279, 375, 243, 339, 235, 331, 268, 364, 232, 328)(210, 306, 236, 332, 270, 366, 265, 361, 277, 373, 241, 337, 272, 368, 237, 333)(215, 311, 247, 343, 280, 376, 245, 341, 233, 329, 262, 358, 283, 379, 248, 344)(216, 312, 246, 342, 281, 377, 257, 353, 273, 369, 252, 348, 284, 380, 249, 345)(219, 315, 253, 349, 285, 381, 267, 363, 229, 325, 258, 354, 286, 382, 254, 350)(240, 336, 275, 371, 287, 383, 274, 370, 250, 346, 282, 378, 288, 384, 276, 372) L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 211)(7, 214)(8, 194)(9, 220)(10, 213)(11, 224)(12, 221)(13, 227)(14, 196)(15, 223)(16, 218)(17, 197)(18, 236)(19, 239)(20, 198)(21, 244)(22, 238)(23, 247)(24, 246)(25, 242)(26, 200)(27, 253)(28, 255)(29, 201)(30, 259)(31, 261)(32, 260)(33, 203)(34, 256)(35, 264)(36, 205)(37, 258)(38, 209)(39, 206)(40, 207)(41, 262)(42, 208)(43, 268)(44, 270)(45, 210)(46, 234)(47, 269)(48, 275)(49, 272)(50, 212)(51, 235)(52, 230)(53, 233)(54, 281)(55, 280)(56, 215)(57, 216)(58, 282)(59, 217)(60, 284)(61, 285)(62, 219)(63, 231)(64, 271)(65, 273)(66, 286)(67, 278)(68, 222)(69, 279)(70, 283)(71, 225)(72, 226)(73, 277)(74, 228)(75, 229)(76, 232)(77, 251)(78, 265)(79, 266)(80, 237)(81, 252)(82, 250)(83, 287)(84, 240)(85, 241)(86, 263)(87, 243)(88, 245)(89, 257)(90, 288)(91, 248)(92, 249)(93, 267)(94, 254)(95, 274)(96, 276)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 2, 8, 2, 8, 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 E23.995 Graph:: bipartite v = 28 e = 192 f = 120 degree seq :: [ 12^16, 16^12 ] E23.995 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 8}) Quotient :: dipole Aut^+ = (C2 x SL(2,3)) : C2 (small group id <96, 190>) Aut = $<192, 1485>$ (small group id <192, 1485>) |r| :: 2 Presentation :: [ Y1, R^2, Y2^4, Y2^4, (R * Y3)^2, Y2^4, (R * Y1)^2, Y3^-3 * Y2^-2 * Y3^-1, (Y2^-1 * R * Y2^-1)^2, (R * Y2 * Y3^-1)^2, Y2 * Y3 * Y2^2 * Y3^-1 * Y2, Y3 * Y2^2 * Y3^3, (Y3^-1 * Y2^-1 * Y3 * Y2^-1 * Y3^-1)^2, Y3^-1 * Y2^-1 * Y3^-2 * Y2 * Y3^-1 * Y2 * Y3^-2 * Y2^-1, Y3 * Y2^-1 * Y3 * Y2 * Y3^-1 * Y2 * Y3 * Y2 * Y3 * Y2^-1 * Y3^-1 * Y2^-1, (Y3^-1 * Y1^-1)^8 ] Map:: R = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)(193, 289, 194, 290, 198, 294, 196, 292)(195, 291, 201, 297, 209, 305, 203, 299)(197, 293, 206, 302, 210, 306, 207, 303)(199, 295, 211, 307, 204, 300, 213, 309)(200, 296, 214, 310, 205, 301, 215, 311)(202, 298, 219, 315, 208, 304, 220, 316)(212, 308, 229, 325, 216, 312, 230, 326)(217, 313, 237, 333, 221, 317, 239, 335)(218, 314, 240, 336, 222, 318, 241, 337)(223, 319, 247, 343, 225, 321, 249, 345)(224, 320, 250, 346, 226, 322, 251, 347)(227, 323, 253, 349, 231, 327, 255, 351)(228, 324, 256, 352, 232, 328, 257, 353)(233, 329, 263, 359, 235, 331, 265, 361)(234, 330, 266, 362, 236, 332, 267, 363)(238, 334, 262, 358, 242, 338, 260, 356)(243, 339, 268, 364, 245, 341, 264, 360)(244, 340, 258, 354, 246, 342, 254, 350)(248, 344, 261, 357, 252, 348, 259, 355)(269, 365, 281, 377, 271, 367, 279, 375)(270, 366, 284, 380, 272, 368, 286, 382)(273, 369, 283, 379, 275, 371, 285, 381)(274, 370, 280, 376, 276, 372, 282, 378)(277, 373, 288, 384, 278, 374, 287, 383) L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 209)(7, 212)(8, 194)(9, 217)(10, 210)(11, 221)(12, 216)(13, 196)(14, 223)(15, 225)(16, 197)(17, 208)(18, 198)(19, 227)(20, 205)(21, 231)(22, 233)(23, 235)(24, 200)(25, 238)(26, 201)(27, 243)(28, 245)(29, 242)(30, 203)(31, 248)(32, 206)(33, 252)(34, 207)(35, 254)(36, 211)(37, 259)(38, 261)(39, 258)(40, 213)(41, 264)(42, 214)(43, 268)(44, 215)(45, 269)(46, 222)(47, 271)(48, 273)(49, 275)(50, 218)(51, 277)(52, 219)(53, 278)(54, 220)(55, 276)(56, 226)(57, 274)(58, 272)(59, 270)(60, 224)(61, 279)(62, 232)(63, 281)(64, 283)(65, 285)(66, 228)(67, 287)(68, 229)(69, 288)(70, 230)(71, 286)(72, 236)(73, 284)(74, 282)(75, 280)(76, 234)(77, 250)(78, 237)(79, 251)(80, 239)(81, 247)(82, 240)(83, 249)(84, 241)(85, 246)(86, 244)(87, 266)(88, 253)(89, 267)(90, 255)(91, 263)(92, 256)(93, 265)(94, 257)(95, 262)(96, 260)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 12, 16 ), ( 12, 16, 12, 16, 12, 16, 12, 16 ) } Outer automorphisms :: reflexible Dual of E23.994 Graph:: simple bipartite v = 120 e = 192 f = 28 degree seq :: [ 2^96, 8^24 ] E23.996 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 8}) Quotient :: dipole Aut^+ = (C2 x SL(2,3)) : C2 (small group id <96, 190>) Aut = $<192, 1485>$ (small group id <192, 1485>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^4, (R * Y1)^2, (R * Y3)^2, Y3 * Y1 * Y3^2 * Y1^-1 * Y3, Y1^-4 * Y3^-2, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^4, (Y3^-1 * Y1 * Y3^-1 * Y1^-2)^2, Y3^-1 * Y1^-2 * Y3 * Y1^-1 * Y3 * Y1^-2 * Y3^-1 * Y1^-1, Y3^-1 * Y1^-1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1^-1 * Y3^-1 * Y1^-1 ] Map:: R = (1, 97, 2, 98, 6, 102, 17, 113, 10, 106, 21, 117, 13, 109, 4, 100)(3, 99, 9, 105, 25, 121, 16, 112, 5, 101, 15, 111, 29, 125, 11, 107)(7, 103, 20, 116, 39, 135, 24, 120, 8, 104, 23, 119, 43, 139, 22, 118)(12, 108, 31, 127, 55, 151, 34, 130, 14, 110, 33, 129, 59, 155, 32, 128)(18, 114, 35, 131, 61, 157, 38, 134, 19, 115, 37, 133, 65, 161, 36, 132)(26, 122, 47, 143, 66, 162, 50, 146, 27, 123, 49, 145, 64, 160, 48, 144)(28, 124, 51, 147, 63, 159, 54, 150, 30, 126, 53, 149, 62, 158, 52, 148)(40, 136, 69, 165, 58, 154, 72, 168, 41, 137, 71, 167, 60, 156, 70, 166)(42, 138, 73, 169, 56, 152, 76, 172, 44, 140, 75, 171, 57, 153, 74, 170)(45, 141, 77, 173, 88, 184, 67, 163, 46, 142, 78, 174, 87, 183, 68, 164)(79, 175, 90, 186, 85, 181, 96, 192, 80, 176, 89, 185, 86, 182, 95, 191)(81, 177, 93, 189, 83, 179, 92, 188, 82, 178, 94, 190, 84, 180, 91, 187)(193, 289)(194, 290)(195, 291)(196, 292)(197, 293)(198, 294)(199, 295)(200, 296)(201, 297)(202, 298)(203, 299)(204, 300)(205, 301)(206, 302)(207, 303)(208, 304)(209, 305)(210, 306)(211, 307)(212, 308)(213, 309)(214, 310)(215, 311)(216, 312)(217, 313)(218, 314)(219, 315)(220, 316)(221, 317)(222, 318)(223, 319)(224, 320)(225, 321)(226, 322)(227, 323)(228, 324)(229, 325)(230, 326)(231, 327)(232, 328)(233, 329)(234, 330)(235, 331)(236, 332)(237, 333)(238, 334)(239, 335)(240, 336)(241, 337)(242, 338)(243, 339)(244, 340)(245, 341)(246, 342)(247, 343)(248, 344)(249, 345)(250, 346)(251, 347)(252, 348)(253, 349)(254, 350)(255, 351)(256, 352)(257, 353)(258, 354)(259, 355)(260, 356)(261, 357)(262, 358)(263, 359)(264, 360)(265, 361)(266, 362)(267, 363)(268, 364)(269, 365)(270, 366)(271, 367)(272, 368)(273, 369)(274, 370)(275, 371)(276, 372)(277, 373)(278, 374)(279, 375)(280, 376)(281, 377)(282, 378)(283, 379)(284, 380)(285, 381)(286, 382)(287, 383)(288, 384) L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 210)(7, 213)(8, 194)(9, 218)(10, 197)(11, 220)(12, 209)(13, 211)(14, 196)(15, 219)(16, 222)(17, 206)(18, 205)(19, 198)(20, 232)(21, 200)(22, 234)(23, 233)(24, 236)(25, 237)(26, 207)(27, 201)(28, 208)(29, 238)(30, 203)(31, 248)(32, 250)(33, 249)(34, 252)(35, 254)(36, 256)(37, 255)(38, 258)(39, 259)(40, 215)(41, 212)(42, 216)(43, 260)(44, 214)(45, 221)(46, 217)(47, 271)(48, 273)(49, 272)(50, 274)(51, 275)(52, 277)(53, 276)(54, 278)(55, 270)(56, 225)(57, 223)(58, 226)(59, 269)(60, 224)(61, 279)(62, 229)(63, 227)(64, 230)(65, 280)(66, 228)(67, 235)(68, 231)(69, 281)(70, 283)(71, 282)(72, 284)(73, 285)(74, 287)(75, 286)(76, 288)(77, 247)(78, 251)(79, 241)(80, 239)(81, 242)(82, 240)(83, 245)(84, 243)(85, 246)(86, 244)(87, 257)(88, 253)(89, 263)(90, 261)(91, 264)(92, 262)(93, 267)(94, 265)(95, 268)(96, 266)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 8, 12 ), ( 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12, 8, 12 ) } Outer automorphisms :: reflexible Dual of E23.993 Graph:: simple bipartite v = 108 e = 192 f = 40 degree seq :: [ 2^96, 16^12 ] E23.997 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 8}) Quotient :: dipole Aut^+ = (C2 x SL(2,3)) : C2 (small group id <96, 190>) Aut = $<192, 1485>$ (small group id <192, 1485>) |r| :: 2 Presentation :: [ R^2, Y1^-1 * Y3^-1, Y1^-1 * Y3^2 * Y1^-1, Y1 * Y3^-2 * Y1, (R * Y1)^2, (Y3 * Y1^-1)^2, Y1^4, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y1 * Y2 * Y1 * Y3^-1 * Y2^-1 * Y3^-1, Y2^-1 * Y3^-1 * Y1 * Y2^-3, Y3 * Y2^-1 * Y3 * Y1^-1 * Y2 * Y1^-1, R * Y2 * R * Y3 * Y2^-3 * Y1^-1, Y2^2 * Y3 * Y2 * Y3 * Y2^2 * Y1^-1 * Y2 * Y1^-1, Y2 * Y3 * Y2^2 * Y1 * Y2 * Y1^-1 * Y2^-2 * Y1^-1, Y2 * Y1 * Y2^2 * Y1 * Y2 * Y3^-1 * Y2^-2 * Y1^-1, Y1 * Y2 * Y3 * Y2 * Y3 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1, Y2 * Y3 * Y2^-1 * Y3 * Y2 * Y1 * Y2^-1 * Y1^-1 * Y2 * Y1^-1 * Y2^-1 * Y1^-1 ] Map:: R = (1, 97, 2, 98, 6, 102, 4, 100)(3, 99, 9, 105, 17, 113, 11, 107)(5, 101, 14, 110, 18, 114, 15, 111)(7, 103, 19, 115, 12, 108, 21, 117)(8, 104, 22, 118, 13, 109, 23, 119)(10, 106, 27, 123, 16, 112, 28, 124)(20, 116, 37, 133, 24, 120, 38, 134)(25, 121, 45, 141, 29, 125, 47, 143)(26, 122, 48, 144, 30, 126, 49, 145)(31, 127, 55, 151, 33, 129, 57, 153)(32, 128, 58, 154, 34, 130, 59, 155)(35, 131, 61, 157, 39, 135, 63, 159)(36, 132, 64, 160, 40, 136, 65, 161)(41, 137, 71, 167, 43, 139, 73, 169)(42, 138, 74, 170, 44, 140, 75, 171)(46, 142, 70, 166, 50, 146, 68, 164)(51, 147, 76, 172, 53, 149, 72, 168)(52, 148, 66, 162, 54, 150, 62, 158)(56, 152, 69, 165, 60, 156, 67, 163)(77, 173, 89, 185, 79, 175, 87, 183)(78, 174, 92, 188, 80, 176, 94, 190)(81, 177, 91, 187, 83, 179, 93, 189)(82, 178, 88, 184, 84, 180, 90, 186)(85, 181, 96, 192, 86, 182, 95, 191)(193, 289, 195, 291, 202, 298, 210, 306, 198, 294, 209, 305, 208, 304, 197, 293)(194, 290, 199, 295, 212, 308, 205, 301, 196, 292, 204, 300, 216, 312, 200, 296)(201, 297, 217, 313, 238, 334, 222, 318, 203, 299, 221, 317, 242, 338, 218, 314)(206, 302, 223, 319, 248, 344, 226, 322, 207, 303, 225, 321, 252, 348, 224, 320)(211, 307, 227, 323, 254, 350, 232, 328, 213, 309, 231, 327, 258, 354, 228, 324)(214, 310, 233, 329, 264, 360, 236, 332, 215, 311, 235, 331, 268, 364, 234, 330)(219, 315, 243, 339, 277, 373, 246, 342, 220, 316, 245, 341, 278, 374, 244, 340)(229, 325, 259, 355, 287, 383, 262, 358, 230, 326, 261, 357, 288, 384, 260, 356)(237, 333, 269, 365, 250, 346, 272, 368, 239, 335, 271, 367, 251, 347, 270, 366)(240, 336, 273, 369, 247, 343, 276, 372, 241, 337, 275, 371, 249, 345, 274, 370)(253, 349, 279, 375, 266, 362, 282, 378, 255, 351, 281, 377, 267, 363, 280, 376)(256, 352, 283, 379, 263, 359, 286, 382, 257, 353, 285, 381, 265, 361, 284, 380) L = (1, 196)(2, 193)(3, 203)(4, 198)(5, 207)(6, 194)(7, 213)(8, 215)(9, 195)(10, 220)(11, 209)(12, 211)(13, 214)(14, 197)(15, 210)(16, 219)(17, 201)(18, 206)(19, 199)(20, 230)(21, 204)(22, 200)(23, 205)(24, 229)(25, 239)(26, 241)(27, 202)(28, 208)(29, 237)(30, 240)(31, 249)(32, 251)(33, 247)(34, 250)(35, 255)(36, 257)(37, 212)(38, 216)(39, 253)(40, 256)(41, 265)(42, 267)(43, 263)(44, 266)(45, 217)(46, 260)(47, 221)(48, 218)(49, 222)(50, 262)(51, 264)(52, 254)(53, 268)(54, 258)(55, 223)(56, 259)(57, 225)(58, 224)(59, 226)(60, 261)(61, 227)(62, 246)(63, 231)(64, 228)(65, 232)(66, 244)(67, 252)(68, 242)(69, 248)(70, 238)(71, 233)(72, 245)(73, 235)(74, 234)(75, 236)(76, 243)(77, 279)(78, 286)(79, 281)(80, 284)(81, 285)(82, 282)(83, 283)(84, 280)(85, 287)(86, 288)(87, 271)(88, 274)(89, 269)(90, 276)(91, 273)(92, 270)(93, 275)(94, 272)(95, 278)(96, 277)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 2, 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 E23.998 Graph:: bipartite v = 36 e = 192 f = 112 degree seq :: [ 8^24, 16^12 ] E23.998 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 6, 8}) Quotient :: dipole Aut^+ = (C2 x SL(2,3)) : C2 (small group id <96, 190>) Aut = $<192, 1485>$ (small group id <192, 1485>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y1 * Y3^-1 * Y1)^2, Y3^-2 * Y1 * Y3 * Y1 * Y3^-1, Y1^6, Y3^-5 * Y1^-1 * Y3^-1 * Y1^-1, Y3^-1 * Y1 * Y3^2 * Y1^-1 * Y3^2 * Y1^-1 * Y3 * Y1^-1, (Y3 * Y2^-1)^8 ] Map:: polytopal R = (1, 97, 2, 98, 6, 102, 18, 114, 13, 109, 4, 100)(3, 99, 9, 105, 27, 123, 49, 145, 20, 116, 11, 107)(5, 101, 15, 111, 35, 131, 73, 169, 41, 137, 16, 112)(7, 103, 21, 117, 51, 147, 79, 175, 45, 141, 23, 119)(8, 104, 24, 120, 12, 108, 34, 130, 58, 154, 25, 121)(10, 106, 30, 126, 55, 151, 78, 174, 62, 158, 31, 127)(14, 110, 37, 133, 44, 140, 77, 173, 67, 163, 38, 134)(17, 113, 33, 129, 70, 166, 80, 176, 75, 171, 43, 139)(19, 115, 46, 142, 81, 177, 63, 159, 36, 132, 48, 144)(22, 118, 53, 149, 83, 179, 72, 168, 87, 183, 54, 150)(26, 122, 56, 152, 90, 186, 74, 170, 40, 136, 60, 156)(28, 124, 52, 148, 42, 138, 59, 155, 85, 181, 64, 160)(29, 125, 65, 161, 32, 128, 47, 143, 82, 178, 66, 162)(39, 135, 57, 153, 86, 182, 50, 146, 84, 180, 61, 157)(68, 164, 92, 188, 69, 165, 93, 189, 95, 191, 91, 187)(71, 167, 89, 185, 76, 172, 94, 190, 96, 192, 88, 184)(193, 289)(194, 290)(195, 291)(196, 292)(197, 293)(198, 294)(199, 295)(200, 296)(201, 297)(202, 298)(203, 299)(204, 300)(205, 301)(206, 302)(207, 303)(208, 304)(209, 305)(210, 306)(211, 307)(212, 308)(213, 309)(214, 310)(215, 311)(216, 312)(217, 313)(218, 314)(219, 315)(220, 316)(221, 317)(222, 318)(223, 319)(224, 320)(225, 321)(226, 322)(227, 323)(228, 324)(229, 325)(230, 326)(231, 327)(232, 328)(233, 329)(234, 330)(235, 331)(236, 332)(237, 333)(238, 334)(239, 335)(240, 336)(241, 337)(242, 338)(243, 339)(244, 340)(245, 341)(246, 342)(247, 343)(248, 344)(249, 345)(250, 346)(251, 347)(252, 348)(253, 349)(254, 350)(255, 351)(256, 352)(257, 353)(258, 354)(259, 355)(260, 356)(261, 357)(262, 358)(263, 359)(264, 360)(265, 361)(266, 362)(267, 363)(268, 364)(269, 365)(270, 366)(271, 367)(272, 368)(273, 369)(274, 370)(275, 371)(276, 372)(277, 373)(278, 374)(279, 375)(280, 376)(281, 377)(282, 378)(283, 379)(284, 380)(285, 381)(286, 382)(287, 383)(288, 384) L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 211)(7, 214)(8, 194)(9, 220)(10, 213)(11, 224)(12, 221)(13, 227)(14, 196)(15, 223)(16, 218)(17, 197)(18, 236)(19, 239)(20, 198)(21, 244)(22, 238)(23, 247)(24, 246)(25, 242)(26, 200)(27, 253)(28, 255)(29, 201)(30, 259)(31, 261)(32, 260)(33, 203)(34, 256)(35, 264)(36, 205)(37, 258)(38, 209)(39, 206)(40, 207)(41, 262)(42, 208)(43, 268)(44, 270)(45, 210)(46, 234)(47, 269)(48, 275)(49, 272)(50, 212)(51, 235)(52, 230)(53, 233)(54, 281)(55, 280)(56, 215)(57, 216)(58, 282)(59, 217)(60, 284)(61, 285)(62, 219)(63, 231)(64, 271)(65, 273)(66, 286)(67, 278)(68, 222)(69, 279)(70, 283)(71, 225)(72, 226)(73, 277)(74, 228)(75, 229)(76, 232)(77, 251)(78, 265)(79, 266)(80, 237)(81, 252)(82, 250)(83, 287)(84, 240)(85, 241)(86, 263)(87, 243)(88, 245)(89, 257)(90, 288)(91, 248)(92, 249)(93, 267)(94, 254)(95, 274)(96, 276)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 8, 16 ), ( 8, 16, 8, 16, 8, 16, 8, 16, 8, 16, 8, 16 ) } Outer automorphisms :: reflexible Dual of E23.997 Graph:: simple bipartite v = 112 e = 192 f = 36 degree seq :: [ 2^96, 12^16 ] E23.999 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 24}) Quotient :: dipole Aut^+ = C2 x D48 (small group id <96, 110>) Aut = $<192, 1299>$ (small group id <192, 1299>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y3)^2, (Y2 * Y1)^2, (R * Y1)^2, (Y3 * Y1)^24 ] Map:: polytopal non-degenerate R = (1, 97, 2, 98)(3, 99, 5, 101)(4, 100, 8, 104)(6, 102, 10, 106)(7, 103, 11, 107)(9, 105, 13, 109)(12, 108, 16, 112)(14, 110, 18, 114)(15, 111, 19, 115)(17, 113, 21, 117)(20, 116, 24, 120)(22, 118, 26, 122)(23, 119, 27, 123)(25, 121, 29, 125)(28, 124, 32, 128)(30, 126, 47, 143)(31, 127, 49, 145)(33, 129, 51, 147)(34, 130, 53, 149)(35, 131, 55, 151)(36, 132, 57, 153)(37, 133, 59, 155)(38, 134, 61, 157)(39, 135, 63, 159)(40, 136, 65, 161)(41, 137, 67, 163)(42, 138, 69, 165)(43, 139, 71, 167)(44, 140, 73, 169)(45, 141, 75, 171)(46, 142, 77, 173)(48, 144, 79, 175)(50, 146, 81, 177)(52, 148, 83, 179)(54, 150, 85, 181)(56, 152, 87, 183)(58, 154, 89, 185)(60, 156, 91, 187)(62, 158, 93, 189)(64, 160, 95, 191)(66, 162, 96, 192)(68, 164, 94, 190)(70, 166, 92, 188)(72, 168, 90, 186)(74, 170, 88, 184)(76, 172, 86, 182)(78, 174, 80, 176)(82, 178, 84, 180)(193, 289, 195, 291)(194, 290, 197, 293)(196, 292, 199, 295)(198, 294, 201, 297)(200, 296, 203, 299)(202, 298, 205, 301)(204, 300, 207, 303)(206, 302, 209, 305)(208, 304, 211, 307)(210, 306, 213, 309)(212, 308, 215, 311)(214, 310, 217, 313)(216, 312, 219, 315)(218, 314, 221, 317)(220, 316, 223, 319)(222, 318, 225, 321)(224, 320, 241, 337)(226, 322, 228, 324)(227, 323, 229, 325)(230, 326, 232, 328)(231, 327, 233, 329)(234, 330, 236, 332)(235, 331, 237, 333)(238, 334, 242, 338)(239, 335, 243, 339)(240, 336, 244, 340)(245, 341, 249, 345)(246, 342, 250, 346)(247, 343, 251, 347)(248, 344, 252, 348)(253, 349, 257, 353)(254, 350, 258, 354)(255, 351, 259, 355)(256, 352, 260, 356)(261, 357, 265, 361)(262, 358, 266, 362)(263, 359, 267, 363)(264, 360, 268, 364)(269, 365, 273, 369)(270, 366, 274, 370)(271, 367, 275, 371)(272, 368, 276, 372)(277, 373, 281, 377)(278, 374, 282, 378)(279, 375, 283, 379)(280, 376, 284, 380)(285, 381, 288, 384)(286, 382, 287, 383) L = (1, 196)(2, 198)(3, 199)(4, 193)(5, 201)(6, 194)(7, 195)(8, 204)(9, 197)(10, 206)(11, 207)(12, 200)(13, 209)(14, 202)(15, 203)(16, 212)(17, 205)(18, 214)(19, 215)(20, 208)(21, 217)(22, 210)(23, 211)(24, 220)(25, 213)(26, 222)(27, 223)(28, 216)(29, 225)(30, 218)(31, 219)(32, 228)(33, 221)(34, 241)(35, 243)(36, 224)(37, 239)(38, 245)(39, 247)(40, 249)(41, 251)(42, 253)(43, 255)(44, 257)(45, 259)(46, 261)(47, 229)(48, 263)(49, 226)(50, 265)(51, 227)(52, 267)(53, 230)(54, 273)(55, 231)(56, 275)(57, 232)(58, 269)(59, 233)(60, 271)(61, 234)(62, 277)(63, 235)(64, 279)(65, 236)(66, 281)(67, 237)(68, 283)(69, 238)(70, 285)(71, 240)(72, 287)(73, 242)(74, 288)(75, 244)(76, 286)(77, 250)(78, 284)(79, 252)(80, 282)(81, 246)(82, 280)(83, 248)(84, 278)(85, 254)(86, 276)(87, 256)(88, 274)(89, 258)(90, 272)(91, 260)(92, 270)(93, 262)(94, 268)(95, 264)(96, 266)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 4, 48, 4, 48 ) } Outer automorphisms :: reflexible Dual of E23.1010 Graph:: simple bipartite v = 96 e = 192 f = 52 degree seq :: [ 4^96 ] E23.1000 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 24}) Quotient :: dipole Aut^+ = (C2 x D24) : C2 (small group id <96, 115>) Aut = $<192, 1305>$ (small group id <192, 1305>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2)^2, (Y1 * Y2)^4, (Y1 * Y3 * Y1 * Y2)^2, Y3 * Y1 * Y3 * Y1 * Y2 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y2 * Y1 ] Map:: polytopal non-degenerate R = (1, 97, 2, 98)(3, 99, 7, 103)(4, 100, 9, 105)(5, 101, 10, 106)(6, 102, 12, 108)(8, 104, 15, 111)(11, 107, 20, 116)(13, 109, 18, 114)(14, 110, 21, 117)(16, 112, 19, 115)(17, 113, 27, 123)(22, 118, 32, 128)(23, 119, 29, 125)(24, 120, 28, 124)(25, 121, 34, 130)(26, 122, 35, 131)(30, 126, 38, 134)(31, 127, 39, 135)(33, 129, 41, 137)(36, 132, 44, 140)(37, 133, 45, 141)(40, 136, 48, 144)(42, 138, 50, 146)(43, 139, 51, 147)(46, 142, 54, 150)(47, 143, 55, 151)(49, 145, 57, 153)(52, 148, 60, 156)(53, 149, 61, 157)(56, 152, 64, 160)(58, 154, 66, 162)(59, 155, 67, 163)(62, 158, 70, 166)(63, 159, 71, 167)(65, 161, 73, 169)(68, 164, 76, 172)(69, 165, 77, 173)(72, 168, 80, 176)(74, 170, 82, 178)(75, 171, 83, 179)(78, 174, 86, 182)(79, 175, 87, 183)(81, 177, 89, 185)(84, 180, 92, 188)(85, 181, 93, 189)(88, 184, 96, 192)(90, 186, 94, 190)(91, 187, 95, 191)(193, 289, 195, 291)(194, 290, 197, 293)(196, 292, 200, 296)(198, 294, 203, 299)(199, 295, 205, 301)(201, 297, 208, 304)(202, 298, 210, 306)(204, 300, 213, 309)(206, 302, 215, 311)(207, 303, 216, 312)(209, 305, 218, 314)(211, 307, 220, 316)(212, 308, 221, 317)(214, 310, 223, 319)(217, 313, 225, 321)(219, 315, 226, 322)(222, 318, 229, 325)(224, 320, 230, 326)(227, 323, 233, 329)(228, 324, 234, 330)(231, 327, 237, 333)(232, 328, 238, 334)(235, 331, 241, 337)(236, 332, 243, 339)(239, 335, 245, 341)(240, 336, 247, 343)(242, 338, 249, 345)(244, 340, 251, 347)(246, 342, 253, 349)(248, 344, 255, 351)(250, 346, 257, 353)(252, 348, 258, 354)(254, 350, 261, 357)(256, 352, 262, 358)(259, 355, 265, 361)(260, 356, 266, 362)(263, 359, 269, 365)(264, 360, 270, 366)(267, 363, 273, 369)(268, 364, 275, 371)(271, 367, 277, 373)(272, 368, 279, 375)(274, 370, 281, 377)(276, 372, 283, 379)(278, 374, 285, 381)(280, 376, 287, 383)(282, 378, 288, 384)(284, 380, 286, 382) L = (1, 196)(2, 198)(3, 200)(4, 193)(5, 203)(6, 194)(7, 206)(8, 195)(9, 209)(10, 211)(11, 197)(12, 214)(13, 215)(14, 199)(15, 217)(16, 218)(17, 201)(18, 220)(19, 202)(20, 222)(21, 223)(22, 204)(23, 205)(24, 225)(25, 207)(26, 208)(27, 228)(28, 210)(29, 229)(30, 212)(31, 213)(32, 232)(33, 216)(34, 234)(35, 235)(36, 219)(37, 221)(38, 238)(39, 239)(40, 224)(41, 241)(42, 226)(43, 227)(44, 244)(45, 245)(46, 230)(47, 231)(48, 248)(49, 233)(50, 250)(51, 251)(52, 236)(53, 237)(54, 254)(55, 255)(56, 240)(57, 257)(58, 242)(59, 243)(60, 260)(61, 261)(62, 246)(63, 247)(64, 264)(65, 249)(66, 266)(67, 267)(68, 252)(69, 253)(70, 270)(71, 271)(72, 256)(73, 273)(74, 258)(75, 259)(76, 276)(77, 277)(78, 262)(79, 263)(80, 280)(81, 265)(82, 282)(83, 283)(84, 268)(85, 269)(86, 286)(87, 287)(88, 272)(89, 288)(90, 274)(91, 275)(92, 285)(93, 284)(94, 278)(95, 279)(96, 281)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 4, 48, 4, 48 ) } Outer automorphisms :: reflexible Dual of E23.1012 Graph:: simple bipartite v = 96 e = 192 f = 52 degree seq :: [ 4^96 ] E23.1001 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 24}) Quotient :: dipole Aut^+ = (C2 x D24) : C2 (small group id <96, 115>) Aut = $<192, 1305>$ (small group id <192, 1305>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y3 * Y1 * Y2 * Y1 * Y3 * Y2 * Y1 * Y2 * Y1 * Y2, (Y3 * Y1 * Y3 * Y2 * Y1)^2, Y3 * Y1 * Y2 * Y1 * Y3 * Y1 * Y2 * Y1 * Y2 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y2 * Y1 * Y3 * Y1 * Y2 * Y1 * Y2 * Y1, (Y3 * Y1)^24 ] Map:: polytopal non-degenerate R = (1, 97, 2, 98)(3, 99, 7, 103)(4, 100, 9, 105)(5, 101, 10, 106)(6, 102, 12, 108)(8, 104, 15, 111)(11, 107, 20, 116)(13, 109, 23, 119)(14, 110, 25, 121)(16, 112, 28, 124)(17, 113, 30, 126)(18, 114, 31, 127)(19, 115, 33, 129)(21, 117, 36, 132)(22, 118, 38, 134)(24, 120, 34, 130)(26, 122, 32, 128)(27, 123, 37, 133)(29, 125, 35, 131)(39, 135, 49, 145)(40, 136, 50, 146)(41, 137, 51, 147)(42, 138, 52, 148)(43, 139, 48, 144)(44, 140, 53, 149)(45, 141, 54, 150)(46, 142, 55, 151)(47, 143, 56, 152)(57, 153, 65, 161)(58, 154, 66, 162)(59, 155, 67, 163)(60, 156, 68, 164)(61, 157, 69, 165)(62, 158, 70, 166)(63, 159, 71, 167)(64, 160, 72, 168)(73, 169, 81, 177)(74, 170, 82, 178)(75, 171, 83, 179)(76, 172, 84, 180)(77, 173, 85, 181)(78, 174, 86, 182)(79, 175, 87, 183)(80, 176, 88, 184)(89, 185, 96, 192)(90, 186, 94, 190)(91, 187, 95, 191)(92, 188, 93, 189)(193, 289, 195, 291)(194, 290, 197, 293)(196, 292, 200, 296)(198, 294, 203, 299)(199, 295, 205, 301)(201, 297, 208, 304)(202, 298, 210, 306)(204, 300, 213, 309)(206, 302, 216, 312)(207, 303, 218, 314)(209, 305, 221, 317)(211, 307, 224, 320)(212, 308, 226, 322)(214, 310, 229, 325)(215, 311, 231, 327)(217, 313, 233, 329)(219, 315, 235, 331)(220, 316, 232, 328)(222, 318, 234, 330)(223, 319, 236, 332)(225, 321, 238, 334)(227, 323, 240, 336)(228, 324, 237, 333)(230, 326, 239, 335)(241, 337, 249, 345)(242, 338, 251, 347)(243, 339, 250, 346)(244, 340, 252, 348)(245, 341, 253, 349)(246, 342, 255, 351)(247, 343, 254, 350)(248, 344, 256, 352)(257, 353, 265, 361)(258, 354, 267, 363)(259, 355, 266, 362)(260, 356, 268, 364)(261, 357, 269, 365)(262, 358, 271, 367)(263, 359, 270, 366)(264, 360, 272, 368)(273, 369, 281, 377)(274, 370, 283, 379)(275, 371, 282, 378)(276, 372, 284, 380)(277, 373, 285, 381)(278, 374, 287, 383)(279, 375, 286, 382)(280, 376, 288, 384) L = (1, 196)(2, 198)(3, 200)(4, 193)(5, 203)(6, 194)(7, 206)(8, 195)(9, 209)(10, 211)(11, 197)(12, 214)(13, 216)(14, 199)(15, 219)(16, 221)(17, 201)(18, 224)(19, 202)(20, 227)(21, 229)(22, 204)(23, 232)(24, 205)(25, 234)(26, 235)(27, 207)(28, 231)(29, 208)(30, 233)(31, 237)(32, 210)(33, 239)(34, 240)(35, 212)(36, 236)(37, 213)(38, 238)(39, 220)(40, 215)(41, 222)(42, 217)(43, 218)(44, 228)(45, 223)(46, 230)(47, 225)(48, 226)(49, 250)(50, 252)(51, 249)(52, 251)(53, 254)(54, 256)(55, 253)(56, 255)(57, 243)(58, 241)(59, 244)(60, 242)(61, 247)(62, 245)(63, 248)(64, 246)(65, 266)(66, 268)(67, 265)(68, 267)(69, 270)(70, 272)(71, 269)(72, 271)(73, 259)(74, 257)(75, 260)(76, 258)(77, 263)(78, 261)(79, 264)(80, 262)(81, 282)(82, 284)(83, 281)(84, 283)(85, 286)(86, 288)(87, 285)(88, 287)(89, 275)(90, 273)(91, 276)(92, 274)(93, 279)(94, 277)(95, 280)(96, 278)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 4, 48, 4, 48 ) } Outer automorphisms :: reflexible Dual of E23.1011 Graph:: simple bipartite v = 96 e = 192 f = 52 degree seq :: [ 4^96 ] E23.1002 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 24}) Quotient :: dipole Aut^+ = (C2 x D24) : C2 (small group id <96, 115>) Aut = $<192, 1311>$ (small group id <192, 1311>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^4, (Y1 * Y2)^2, (Y3 * Y2)^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y1 * Y3^2 * Y1 * Y3^-1, Y3 * Y2 * Y3^-2 * Y2 * Y3, (Y1 * Y3^-1 * Y2 * Y3)^2, Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 ] Map:: polytopal non-degenerate R = (1, 97, 2, 98)(3, 99, 6, 102)(4, 100, 11, 107)(5, 101, 13, 109)(7, 103, 16, 112)(8, 104, 18, 114)(9, 105, 19, 115)(10, 106, 21, 117)(12, 108, 17, 113)(14, 110, 24, 120)(15, 111, 26, 122)(20, 116, 25, 121)(22, 118, 31, 127)(23, 119, 32, 128)(27, 123, 35, 131)(28, 124, 36, 132)(29, 125, 37, 133)(30, 126, 38, 134)(33, 129, 41, 137)(34, 130, 42, 138)(39, 135, 47, 143)(40, 136, 48, 144)(43, 139, 51, 147)(44, 140, 52, 148)(45, 141, 53, 149)(46, 142, 54, 150)(49, 145, 57, 153)(50, 146, 58, 154)(55, 151, 63, 159)(56, 152, 64, 160)(59, 155, 67, 163)(60, 156, 68, 164)(61, 157, 69, 165)(62, 158, 70, 166)(65, 161, 73, 169)(66, 162, 74, 170)(71, 167, 79, 175)(72, 168, 80, 176)(75, 171, 83, 179)(76, 172, 84, 180)(77, 173, 85, 181)(78, 174, 86, 182)(81, 177, 89, 185)(82, 178, 90, 186)(87, 183, 92, 188)(88, 184, 91, 187)(93, 189, 96, 192)(94, 190, 95, 191)(193, 289, 195, 291)(194, 290, 198, 294)(196, 292, 202, 298)(197, 293, 201, 297)(199, 295, 207, 303)(200, 296, 206, 302)(203, 299, 213, 309)(204, 300, 212, 308)(205, 301, 211, 307)(208, 304, 218, 314)(209, 305, 217, 313)(210, 306, 216, 312)(214, 310, 221, 317)(215, 311, 222, 318)(219, 315, 225, 321)(220, 316, 226, 322)(223, 319, 229, 325)(224, 320, 230, 326)(227, 323, 233, 329)(228, 324, 234, 330)(231, 327, 238, 334)(232, 328, 237, 333)(235, 331, 242, 338)(236, 332, 241, 337)(239, 335, 246, 342)(240, 336, 245, 341)(243, 339, 250, 346)(244, 340, 249, 345)(247, 343, 253, 349)(248, 344, 254, 350)(251, 347, 257, 353)(252, 348, 258, 354)(255, 351, 261, 357)(256, 352, 262, 358)(259, 355, 265, 361)(260, 356, 266, 362)(263, 359, 270, 366)(264, 360, 269, 365)(267, 363, 274, 370)(268, 364, 273, 369)(271, 367, 278, 374)(272, 368, 277, 373)(275, 371, 282, 378)(276, 372, 281, 377)(279, 375, 285, 381)(280, 376, 286, 382)(283, 379, 287, 383)(284, 380, 288, 384) L = (1, 196)(2, 199)(3, 201)(4, 204)(5, 193)(6, 206)(7, 209)(8, 194)(9, 212)(10, 195)(11, 214)(12, 197)(13, 215)(14, 217)(15, 198)(16, 219)(17, 200)(18, 220)(19, 221)(20, 202)(21, 222)(22, 205)(23, 203)(24, 225)(25, 207)(26, 226)(27, 210)(28, 208)(29, 213)(30, 211)(31, 231)(32, 232)(33, 218)(34, 216)(35, 235)(36, 236)(37, 237)(38, 238)(39, 224)(40, 223)(41, 241)(42, 242)(43, 228)(44, 227)(45, 230)(46, 229)(47, 247)(48, 248)(49, 234)(50, 233)(51, 251)(52, 252)(53, 253)(54, 254)(55, 240)(56, 239)(57, 257)(58, 258)(59, 244)(60, 243)(61, 246)(62, 245)(63, 263)(64, 264)(65, 250)(66, 249)(67, 267)(68, 268)(69, 269)(70, 270)(71, 256)(72, 255)(73, 273)(74, 274)(75, 260)(76, 259)(77, 262)(78, 261)(79, 279)(80, 280)(81, 266)(82, 265)(83, 283)(84, 284)(85, 285)(86, 286)(87, 272)(88, 271)(89, 287)(90, 288)(91, 276)(92, 275)(93, 278)(94, 277)(95, 282)(96, 281)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 4, 48, 4, 48 ) } Outer automorphisms :: reflexible Dual of E23.1013 Graph:: simple bipartite v = 96 e = 192 f = 52 degree seq :: [ 4^96 ] E23.1003 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 24}) Quotient :: dipole Aut^+ = (C24 x C2) : C2 (small group id <96, 111>) Aut = $<192, 1311>$ (small group id <192, 1311>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^4, (Y3^-1 * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1 * Y3^-1)^2, Y3^-1 * Y1 * Y2 * Y1 * Y2 * Y3^-1, (R * Y2 * Y3^-1)^2, Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 ] Map:: polytopal non-degenerate R = (1, 97, 2, 98)(3, 99, 9, 105)(4, 100, 12, 108)(5, 101, 14, 110)(6, 102, 15, 111)(7, 103, 18, 114)(8, 104, 20, 116)(10, 106, 21, 117)(11, 107, 22, 118)(13, 109, 19, 115)(16, 112, 25, 121)(17, 113, 26, 122)(23, 119, 31, 127)(24, 120, 32, 128)(27, 123, 35, 131)(28, 124, 36, 132)(29, 125, 37, 133)(30, 126, 38, 134)(33, 129, 41, 137)(34, 130, 42, 138)(39, 135, 47, 143)(40, 136, 48, 144)(43, 139, 51, 147)(44, 140, 52, 148)(45, 141, 53, 149)(46, 142, 54, 150)(49, 145, 57, 153)(50, 146, 58, 154)(55, 151, 63, 159)(56, 152, 64, 160)(59, 155, 67, 163)(60, 156, 68, 164)(61, 157, 69, 165)(62, 158, 70, 166)(65, 161, 73, 169)(66, 162, 74, 170)(71, 167, 79, 175)(72, 168, 80, 176)(75, 171, 83, 179)(76, 172, 84, 180)(77, 173, 85, 181)(78, 174, 86, 182)(81, 177, 89, 185)(82, 178, 90, 186)(87, 183, 92, 188)(88, 184, 91, 187)(93, 189, 95, 191)(94, 190, 96, 192)(193, 289, 195, 291)(194, 290, 198, 294)(196, 292, 203, 299)(197, 293, 202, 298)(199, 295, 209, 305)(200, 296, 208, 304)(201, 297, 211, 307)(204, 300, 213, 309)(205, 301, 207, 303)(206, 302, 214, 310)(210, 306, 217, 313)(212, 308, 218, 314)(215, 311, 222, 318)(216, 312, 221, 317)(219, 315, 226, 322)(220, 316, 225, 321)(223, 319, 229, 325)(224, 320, 230, 326)(227, 323, 233, 329)(228, 324, 234, 330)(231, 327, 238, 334)(232, 328, 237, 333)(235, 331, 242, 338)(236, 332, 241, 337)(239, 335, 245, 341)(240, 336, 246, 342)(243, 339, 249, 345)(244, 340, 250, 346)(247, 343, 254, 350)(248, 344, 253, 349)(251, 347, 258, 354)(252, 348, 257, 353)(255, 351, 261, 357)(256, 352, 262, 358)(259, 355, 265, 361)(260, 356, 266, 362)(263, 359, 270, 366)(264, 360, 269, 365)(267, 363, 274, 370)(268, 364, 273, 369)(271, 367, 277, 373)(272, 368, 278, 374)(275, 371, 281, 377)(276, 372, 282, 378)(279, 375, 286, 382)(280, 376, 285, 381)(283, 379, 288, 384)(284, 380, 287, 383) L = (1, 196)(2, 199)(3, 202)(4, 205)(5, 193)(6, 208)(7, 211)(8, 194)(9, 209)(10, 207)(11, 195)(12, 215)(13, 197)(14, 216)(15, 203)(16, 201)(17, 198)(18, 219)(19, 200)(20, 220)(21, 221)(22, 222)(23, 206)(24, 204)(25, 225)(26, 226)(27, 212)(28, 210)(29, 214)(30, 213)(31, 231)(32, 232)(33, 218)(34, 217)(35, 235)(36, 236)(37, 237)(38, 238)(39, 224)(40, 223)(41, 241)(42, 242)(43, 228)(44, 227)(45, 230)(46, 229)(47, 247)(48, 248)(49, 234)(50, 233)(51, 251)(52, 252)(53, 253)(54, 254)(55, 240)(56, 239)(57, 257)(58, 258)(59, 244)(60, 243)(61, 246)(62, 245)(63, 263)(64, 264)(65, 250)(66, 249)(67, 267)(68, 268)(69, 269)(70, 270)(71, 256)(72, 255)(73, 273)(74, 274)(75, 260)(76, 259)(77, 262)(78, 261)(79, 279)(80, 280)(81, 266)(82, 265)(83, 283)(84, 284)(85, 285)(86, 286)(87, 272)(88, 271)(89, 287)(90, 288)(91, 276)(92, 275)(93, 278)(94, 277)(95, 282)(96, 281)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 4, 48, 4, 48 ) } Outer automorphisms :: reflexible Dual of E23.1014 Graph:: simple bipartite v = 96 e = 192 f = 52 degree seq :: [ 4^96 ] E23.1004 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 24}) Quotient :: dipole Aut^+ = D16 x S3 (small group id <96, 117>) Aut = $<192, 1313>$ (small group id <192, 1313>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^2, (Y3 * Y2)^2, (R * Y1)^2, (R * Y3)^2, (R * Y2)^2, (Y1 * Y2 * Y1 * Y3 * Y2)^2, (Y1 * Y3 * Y1 * Y3 * Y1 * Y2)^2, Y2 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y2 * Y1 * Y3 ] Map:: polytopal non-degenerate R = (1, 97, 2, 98)(3, 99, 7, 103)(4, 100, 9, 105)(5, 101, 10, 106)(6, 102, 12, 108)(8, 104, 15, 111)(11, 107, 20, 116)(13, 109, 23, 119)(14, 110, 25, 121)(16, 112, 28, 124)(17, 113, 30, 126)(18, 114, 31, 127)(19, 115, 33, 129)(21, 117, 36, 132)(22, 118, 38, 134)(24, 120, 34, 130)(26, 122, 32, 128)(27, 123, 44, 140)(29, 125, 45, 141)(35, 131, 53, 149)(37, 133, 54, 150)(39, 135, 48, 144)(40, 136, 50, 146)(41, 137, 49, 145)(42, 138, 55, 151)(43, 139, 58, 154)(46, 142, 51, 147)(47, 143, 63, 159)(52, 148, 65, 161)(56, 152, 70, 166)(57, 153, 66, 162)(59, 155, 64, 160)(60, 156, 73, 169)(61, 157, 74, 170)(62, 158, 75, 171)(67, 163, 79, 175)(68, 164, 80, 176)(69, 165, 81, 177)(71, 167, 83, 179)(72, 168, 84, 180)(76, 172, 88, 184)(77, 173, 89, 185)(78, 174, 90, 186)(82, 178, 94, 190)(85, 181, 91, 187)(86, 182, 93, 189)(87, 183, 92, 188)(95, 191, 96, 192)(193, 289, 195, 291)(194, 290, 197, 293)(196, 292, 200, 296)(198, 294, 203, 299)(199, 295, 205, 301)(201, 297, 208, 304)(202, 298, 210, 306)(204, 300, 213, 309)(206, 302, 216, 312)(207, 303, 218, 314)(209, 305, 221, 317)(211, 307, 224, 320)(212, 308, 226, 322)(214, 310, 229, 325)(215, 311, 231, 327)(217, 313, 233, 329)(219, 315, 235, 331)(220, 316, 232, 328)(222, 318, 238, 334)(223, 319, 240, 336)(225, 321, 242, 338)(227, 323, 244, 340)(228, 324, 241, 337)(230, 326, 247, 343)(234, 330, 249, 345)(236, 332, 251, 347)(237, 333, 250, 346)(239, 335, 254, 350)(243, 339, 256, 352)(245, 341, 258, 354)(246, 342, 257, 353)(248, 344, 261, 357)(252, 348, 264, 360)(253, 349, 263, 359)(255, 351, 265, 361)(259, 355, 270, 366)(260, 356, 269, 365)(262, 358, 271, 367)(266, 362, 276, 372)(267, 363, 275, 371)(268, 364, 277, 373)(272, 368, 282, 378)(273, 369, 281, 377)(274, 370, 283, 379)(278, 374, 287, 383)(279, 375, 286, 382)(280, 376, 285, 381)(284, 380, 288, 384) L = (1, 196)(2, 198)(3, 200)(4, 193)(5, 203)(6, 194)(7, 206)(8, 195)(9, 209)(10, 211)(11, 197)(12, 214)(13, 216)(14, 199)(15, 219)(16, 221)(17, 201)(18, 224)(19, 202)(20, 227)(21, 229)(22, 204)(23, 232)(24, 205)(25, 234)(26, 235)(27, 207)(28, 231)(29, 208)(30, 239)(31, 241)(32, 210)(33, 243)(34, 244)(35, 212)(36, 240)(37, 213)(38, 248)(39, 220)(40, 215)(41, 249)(42, 217)(43, 218)(44, 252)(45, 253)(46, 254)(47, 222)(48, 228)(49, 223)(50, 256)(51, 225)(52, 226)(53, 259)(54, 260)(55, 261)(56, 230)(57, 233)(58, 263)(59, 264)(60, 236)(61, 237)(62, 238)(63, 268)(64, 242)(65, 269)(66, 270)(67, 245)(68, 246)(69, 247)(70, 274)(71, 250)(72, 251)(73, 277)(74, 278)(75, 279)(76, 255)(77, 257)(78, 258)(79, 283)(80, 284)(81, 285)(82, 262)(83, 286)(84, 287)(85, 265)(86, 266)(87, 267)(88, 281)(89, 280)(90, 288)(91, 271)(92, 272)(93, 273)(94, 275)(95, 276)(96, 282)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 4, 48, 4, 48 ) } Outer automorphisms :: reflexible Dual of E23.1016 Graph:: simple bipartite v = 96 e = 192 f = 52 degree seq :: [ 4^96 ] E23.1005 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 24}) Quotient :: dipole Aut^+ = D16 x S3 (small group id <96, 117>) Aut = $<192, 1313>$ (small group id <192, 1313>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y3^-1 * Y2)^2, (Y2 * Y1)^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y3^6, Y3^-1 * Y1 * Y3^2 * Y1 * Y3^-1, Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 ] Map:: polytopal non-degenerate R = (1, 97, 2, 98)(3, 99, 6, 102)(4, 100, 11, 107)(5, 101, 13, 109)(7, 103, 17, 113)(8, 104, 19, 115)(9, 105, 21, 117)(10, 106, 23, 119)(12, 108, 18, 114)(14, 110, 20, 116)(15, 111, 29, 125)(16, 112, 31, 127)(22, 118, 30, 126)(24, 120, 32, 128)(25, 121, 41, 137)(26, 122, 43, 139)(27, 123, 42, 138)(28, 124, 44, 140)(33, 129, 49, 145)(34, 130, 51, 147)(35, 131, 50, 146)(36, 132, 52, 148)(37, 133, 53, 149)(38, 134, 55, 151)(39, 135, 54, 150)(40, 136, 56, 152)(45, 141, 60, 156)(46, 142, 62, 158)(47, 143, 61, 157)(48, 144, 63, 159)(57, 153, 70, 166)(58, 154, 71, 167)(59, 155, 72, 168)(64, 160, 76, 172)(65, 161, 77, 173)(66, 162, 78, 174)(67, 163, 79, 175)(68, 164, 80, 176)(69, 165, 81, 177)(73, 169, 85, 181)(74, 170, 86, 182)(75, 171, 87, 183)(82, 178, 88, 184)(83, 179, 89, 185)(84, 180, 90, 186)(91, 187, 94, 190)(92, 188, 95, 191)(93, 189, 96, 192)(193, 289, 195, 291)(194, 290, 198, 294)(196, 292, 202, 298)(197, 293, 201, 297)(199, 295, 208, 304)(200, 296, 207, 303)(203, 299, 215, 311)(204, 300, 216, 312)(205, 301, 213, 309)(206, 302, 214, 310)(209, 305, 223, 319)(210, 306, 224, 320)(211, 307, 221, 317)(212, 308, 222, 318)(217, 313, 232, 328)(218, 314, 230, 326)(219, 315, 231, 327)(220, 316, 229, 325)(225, 321, 240, 336)(226, 322, 238, 334)(227, 323, 239, 335)(228, 324, 237, 333)(233, 329, 248, 344)(234, 330, 246, 342)(235, 331, 247, 343)(236, 332, 245, 341)(241, 337, 255, 351)(242, 338, 253, 349)(243, 339, 254, 350)(244, 340, 252, 348)(249, 345, 259, 355)(250, 346, 261, 357)(251, 347, 260, 356)(256, 352, 265, 361)(257, 353, 267, 363)(258, 354, 266, 362)(262, 358, 271, 367)(263, 359, 273, 369)(264, 360, 272, 368)(268, 364, 277, 373)(269, 365, 279, 375)(270, 366, 278, 374)(274, 370, 284, 380)(275, 371, 283, 379)(276, 372, 285, 381)(280, 376, 287, 383)(281, 377, 286, 382)(282, 378, 288, 384) L = (1, 196)(2, 199)(3, 201)(4, 204)(5, 193)(6, 207)(7, 210)(8, 194)(9, 214)(10, 195)(11, 217)(12, 219)(13, 218)(14, 197)(15, 222)(16, 198)(17, 225)(18, 227)(19, 226)(20, 200)(21, 229)(22, 231)(23, 230)(24, 202)(25, 234)(26, 203)(27, 206)(28, 205)(29, 237)(30, 239)(31, 238)(32, 208)(33, 242)(34, 209)(35, 212)(36, 211)(37, 246)(38, 213)(39, 216)(40, 215)(41, 249)(42, 220)(43, 250)(44, 251)(45, 253)(46, 221)(47, 224)(48, 223)(49, 256)(50, 228)(51, 257)(52, 258)(53, 259)(54, 232)(55, 260)(56, 261)(57, 236)(58, 233)(59, 235)(60, 265)(61, 240)(62, 266)(63, 267)(64, 244)(65, 241)(66, 243)(67, 248)(68, 245)(69, 247)(70, 274)(71, 275)(72, 276)(73, 255)(74, 252)(75, 254)(76, 280)(77, 281)(78, 282)(79, 283)(80, 284)(81, 285)(82, 264)(83, 262)(84, 263)(85, 286)(86, 287)(87, 288)(88, 270)(89, 268)(90, 269)(91, 273)(92, 271)(93, 272)(94, 279)(95, 277)(96, 278)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 4, 48, 4, 48 ) } Outer automorphisms :: reflexible Dual of E23.1017 Graph:: simple bipartite v = 96 e = 192 f = 52 degree seq :: [ 4^96 ] E23.1006 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 24}) Quotient :: dipole Aut^+ = D16 x S3 (small group id <96, 117>) Aut = $<192, 1313>$ (small group id <192, 1313>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^2, (Y3 * Y2)^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y1 * Y3 * Y2 * Y1 * Y2)^2, (Y3 * Y1 * Y3 * Y1 * Y3 * Y2 * Y1)^2, Y2 * Y1 * Y3 * Y1 * Y2 * Y1 * Y3 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1, (Y3 * Y1)^24 ] Map:: polytopal non-degenerate R = (1, 97, 2, 98)(3, 99, 7, 103)(4, 100, 9, 105)(5, 101, 10, 106)(6, 102, 12, 108)(8, 104, 15, 111)(11, 107, 20, 116)(13, 109, 23, 119)(14, 110, 25, 121)(16, 112, 28, 124)(17, 113, 30, 126)(18, 114, 31, 127)(19, 115, 33, 129)(21, 117, 36, 132)(22, 118, 38, 134)(24, 120, 34, 130)(26, 122, 32, 128)(27, 123, 44, 140)(29, 125, 45, 141)(35, 131, 53, 149)(37, 133, 54, 150)(39, 135, 57, 153)(40, 136, 58, 154)(41, 137, 59, 155)(42, 138, 61, 157)(43, 139, 62, 158)(46, 142, 66, 162)(47, 143, 68, 164)(48, 144, 69, 165)(49, 145, 70, 166)(50, 146, 71, 167)(51, 147, 73, 169)(52, 148, 74, 170)(55, 151, 78, 174)(56, 152, 80, 176)(60, 156, 75, 171)(63, 159, 72, 168)(64, 160, 79, 175)(65, 161, 77, 173)(67, 163, 76, 172)(81, 177, 89, 185)(82, 178, 91, 187)(83, 179, 90, 186)(84, 180, 93, 189)(85, 181, 92, 188)(86, 182, 94, 190)(87, 183, 96, 192)(88, 184, 95, 191)(193, 289, 195, 291)(194, 290, 197, 293)(196, 292, 200, 296)(198, 294, 203, 299)(199, 295, 205, 301)(201, 297, 208, 304)(202, 298, 210, 306)(204, 300, 213, 309)(206, 302, 216, 312)(207, 303, 218, 314)(209, 305, 221, 317)(211, 307, 224, 320)(212, 308, 226, 322)(214, 310, 229, 325)(215, 311, 231, 327)(217, 313, 233, 329)(219, 315, 235, 331)(220, 316, 232, 328)(222, 318, 238, 334)(223, 319, 240, 336)(225, 321, 242, 338)(227, 323, 244, 340)(228, 324, 241, 337)(230, 326, 247, 343)(234, 330, 252, 348)(236, 332, 255, 351)(237, 333, 254, 350)(239, 335, 259, 355)(243, 339, 264, 360)(245, 341, 267, 363)(246, 342, 266, 362)(248, 344, 271, 367)(249, 345, 273, 369)(250, 346, 275, 371)(251, 347, 274, 370)(253, 349, 277, 373)(256, 352, 280, 376)(257, 353, 279, 375)(258, 354, 276, 372)(260, 356, 278, 374)(261, 357, 281, 377)(262, 358, 283, 379)(263, 359, 282, 378)(265, 361, 285, 381)(268, 364, 288, 384)(269, 365, 287, 383)(270, 366, 284, 380)(272, 368, 286, 382) L = (1, 196)(2, 198)(3, 200)(4, 193)(5, 203)(6, 194)(7, 206)(8, 195)(9, 209)(10, 211)(11, 197)(12, 214)(13, 216)(14, 199)(15, 219)(16, 221)(17, 201)(18, 224)(19, 202)(20, 227)(21, 229)(22, 204)(23, 232)(24, 205)(25, 234)(26, 235)(27, 207)(28, 231)(29, 208)(30, 239)(31, 241)(32, 210)(33, 243)(34, 244)(35, 212)(36, 240)(37, 213)(38, 248)(39, 220)(40, 215)(41, 252)(42, 217)(43, 218)(44, 256)(45, 257)(46, 259)(47, 222)(48, 228)(49, 223)(50, 264)(51, 225)(52, 226)(53, 268)(54, 269)(55, 271)(56, 230)(57, 274)(58, 276)(59, 273)(60, 233)(61, 278)(62, 279)(63, 280)(64, 236)(65, 237)(66, 275)(67, 238)(68, 277)(69, 282)(70, 284)(71, 281)(72, 242)(73, 286)(74, 287)(75, 288)(76, 245)(77, 246)(78, 283)(79, 247)(80, 285)(81, 251)(82, 249)(83, 258)(84, 250)(85, 260)(86, 253)(87, 254)(88, 255)(89, 263)(90, 261)(91, 270)(92, 262)(93, 272)(94, 265)(95, 266)(96, 267)(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, 48, 4, 48 ) } Outer automorphisms :: reflexible Dual of E23.1015 Graph:: simple bipartite v = 96 e = 192 f = 52 degree seq :: [ 4^96 ] E23.1007 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 24}) Quotient :: dipole Aut^+ = (D8 x S3) : C2 (small group id <96, 121>) Aut = $<192, 1318>$ (small group id <192, 1318>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^2, (Y3 * Y2)^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y3 * Y1 * Y2 * Y1 * Y3 * Y2 * Y1 * Y2 * Y1 * Y2, Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y2 * Y1 * Y2 * Y3 * Y1 * Y3 * Y1, (Y2 * Y1 * Y2 * Y1 * Y3 * Y1 * Y2 * Y1)^2 ] Map:: polytopal non-degenerate R = (1, 97, 2, 98)(3, 99, 7, 103)(4, 100, 9, 105)(5, 101, 10, 106)(6, 102, 12, 108)(8, 104, 15, 111)(11, 107, 20, 116)(13, 109, 23, 119)(14, 110, 25, 121)(16, 112, 28, 124)(17, 113, 30, 126)(18, 114, 31, 127)(19, 115, 33, 129)(21, 117, 36, 132)(22, 118, 38, 134)(24, 120, 34, 130)(26, 122, 32, 128)(27, 123, 44, 140)(29, 125, 45, 141)(35, 131, 53, 149)(37, 133, 54, 150)(39, 135, 57, 153)(40, 136, 58, 154)(41, 137, 59, 155)(42, 138, 61, 157)(43, 139, 62, 158)(46, 142, 66, 162)(47, 143, 68, 164)(48, 144, 69, 165)(49, 145, 70, 166)(50, 146, 71, 167)(51, 147, 73, 169)(52, 148, 74, 170)(55, 151, 78, 174)(56, 152, 80, 176)(60, 156, 75, 171)(63, 159, 72, 168)(64, 160, 76, 172)(65, 161, 86, 182)(67, 163, 79, 175)(77, 173, 93, 189)(81, 177, 88, 184)(82, 178, 90, 186)(83, 179, 89, 185)(84, 180, 92, 188)(85, 181, 91, 187)(87, 183, 95, 191)(94, 190, 96, 192)(193, 289, 195, 291)(194, 290, 197, 293)(196, 292, 200, 296)(198, 294, 203, 299)(199, 295, 205, 301)(201, 297, 208, 304)(202, 298, 210, 306)(204, 300, 213, 309)(206, 302, 216, 312)(207, 303, 218, 314)(209, 305, 221, 317)(211, 307, 224, 320)(212, 308, 226, 322)(214, 310, 229, 325)(215, 311, 231, 327)(217, 313, 233, 329)(219, 315, 235, 331)(220, 316, 232, 328)(222, 318, 238, 334)(223, 319, 240, 336)(225, 321, 242, 338)(227, 323, 244, 340)(228, 324, 241, 337)(230, 326, 247, 343)(234, 330, 252, 348)(236, 332, 255, 351)(237, 333, 254, 350)(239, 335, 259, 355)(243, 339, 264, 360)(245, 341, 267, 363)(246, 342, 266, 362)(248, 344, 271, 367)(249, 345, 273, 369)(250, 346, 275, 371)(251, 347, 274, 370)(253, 349, 277, 373)(256, 352, 279, 375)(257, 353, 272, 368)(258, 354, 276, 372)(260, 356, 269, 365)(261, 357, 280, 376)(262, 358, 282, 378)(263, 359, 281, 377)(265, 361, 284, 380)(268, 364, 286, 382)(270, 366, 283, 379)(278, 374, 287, 383)(285, 381, 288, 384) L = (1, 196)(2, 198)(3, 200)(4, 193)(5, 203)(6, 194)(7, 206)(8, 195)(9, 209)(10, 211)(11, 197)(12, 214)(13, 216)(14, 199)(15, 219)(16, 221)(17, 201)(18, 224)(19, 202)(20, 227)(21, 229)(22, 204)(23, 232)(24, 205)(25, 234)(26, 235)(27, 207)(28, 231)(29, 208)(30, 239)(31, 241)(32, 210)(33, 243)(34, 244)(35, 212)(36, 240)(37, 213)(38, 248)(39, 220)(40, 215)(41, 252)(42, 217)(43, 218)(44, 256)(45, 257)(46, 259)(47, 222)(48, 228)(49, 223)(50, 264)(51, 225)(52, 226)(53, 268)(54, 269)(55, 271)(56, 230)(57, 274)(58, 276)(59, 273)(60, 233)(61, 278)(62, 272)(63, 279)(64, 236)(65, 237)(66, 275)(67, 238)(68, 266)(69, 281)(70, 283)(71, 280)(72, 242)(73, 285)(74, 260)(75, 286)(76, 245)(77, 246)(78, 282)(79, 247)(80, 254)(81, 251)(82, 249)(83, 258)(84, 250)(85, 287)(86, 253)(87, 255)(88, 263)(89, 261)(90, 270)(91, 262)(92, 288)(93, 265)(94, 267)(95, 277)(96, 284)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 4, 48, 4, 48 ) } Outer automorphisms :: reflexible Dual of E23.1019 Graph:: simple bipartite v = 96 e = 192 f = 52 degree seq :: [ 4^96 ] E23.1008 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 24}) Quotient :: dipole Aut^+ = (D8 x S3) : C2 (small group id <96, 121>) Aut = $<192, 1318>$ (small group id <192, 1318>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^2, (Y3 * Y2)^2, (R * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y2 * Y1 * Y2 * Y3 * Y1)^2, Y3 * Y1 * Y2 * Y1 * Y2 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1, (Y2 * Y1)^12 ] Map:: polytopal non-degenerate R = (1, 97, 2, 98)(3, 99, 7, 103)(4, 100, 9, 105)(5, 101, 10, 106)(6, 102, 12, 108)(8, 104, 15, 111)(11, 107, 20, 116)(13, 109, 23, 119)(14, 110, 25, 121)(16, 112, 28, 124)(17, 113, 30, 126)(18, 114, 31, 127)(19, 115, 33, 129)(21, 117, 36, 132)(22, 118, 38, 134)(24, 120, 34, 130)(26, 122, 32, 128)(27, 123, 44, 140)(29, 125, 45, 141)(35, 131, 53, 149)(37, 133, 54, 150)(39, 135, 57, 153)(40, 136, 56, 152)(41, 137, 58, 154)(42, 138, 51, 147)(43, 139, 60, 156)(46, 142, 55, 151)(47, 143, 49, 145)(48, 144, 65, 161)(50, 146, 66, 162)(52, 148, 68, 164)(59, 155, 69, 165)(61, 157, 67, 163)(62, 158, 74, 170)(63, 159, 77, 173)(64, 160, 78, 174)(70, 166, 80, 176)(71, 167, 83, 179)(72, 168, 84, 180)(73, 169, 85, 181)(75, 171, 86, 182)(76, 172, 87, 183)(79, 175, 90, 186)(81, 177, 91, 187)(82, 178, 92, 188)(88, 184, 94, 190)(89, 185, 93, 189)(95, 191, 96, 192)(193, 289, 195, 291)(194, 290, 197, 293)(196, 292, 200, 296)(198, 294, 203, 299)(199, 295, 205, 301)(201, 297, 208, 304)(202, 298, 210, 306)(204, 300, 213, 309)(206, 302, 216, 312)(207, 303, 218, 314)(209, 305, 221, 317)(211, 307, 224, 320)(212, 308, 226, 322)(214, 310, 229, 325)(215, 311, 231, 327)(217, 313, 233, 329)(219, 315, 235, 331)(220, 316, 232, 328)(222, 318, 238, 334)(223, 319, 240, 336)(225, 321, 242, 338)(227, 323, 244, 340)(228, 324, 241, 337)(230, 326, 247, 343)(234, 330, 251, 347)(236, 332, 253, 349)(237, 333, 252, 348)(239, 335, 256, 352)(243, 339, 259, 355)(245, 341, 261, 357)(246, 342, 260, 356)(248, 344, 264, 360)(249, 345, 265, 361)(250, 346, 266, 362)(254, 350, 268, 364)(255, 351, 267, 363)(257, 353, 271, 367)(258, 354, 272, 368)(262, 358, 274, 370)(263, 359, 273, 369)(269, 365, 279, 375)(270, 366, 278, 374)(275, 371, 284, 380)(276, 372, 283, 379)(277, 373, 286, 382)(280, 376, 287, 383)(281, 377, 282, 378)(285, 381, 288, 384) L = (1, 196)(2, 198)(3, 200)(4, 193)(5, 203)(6, 194)(7, 206)(8, 195)(9, 209)(10, 211)(11, 197)(12, 214)(13, 216)(14, 199)(15, 219)(16, 221)(17, 201)(18, 224)(19, 202)(20, 227)(21, 229)(22, 204)(23, 232)(24, 205)(25, 234)(26, 235)(27, 207)(28, 231)(29, 208)(30, 239)(31, 241)(32, 210)(33, 243)(34, 244)(35, 212)(36, 240)(37, 213)(38, 248)(39, 220)(40, 215)(41, 251)(42, 217)(43, 218)(44, 254)(45, 255)(46, 256)(47, 222)(48, 228)(49, 223)(50, 259)(51, 225)(52, 226)(53, 262)(54, 263)(55, 264)(56, 230)(57, 266)(58, 265)(59, 233)(60, 267)(61, 268)(62, 236)(63, 237)(64, 238)(65, 272)(66, 271)(67, 242)(68, 273)(69, 274)(70, 245)(71, 246)(72, 247)(73, 250)(74, 249)(75, 252)(76, 253)(77, 280)(78, 281)(79, 258)(80, 257)(81, 260)(82, 261)(83, 285)(84, 286)(85, 283)(86, 282)(87, 287)(88, 269)(89, 270)(90, 278)(91, 277)(92, 288)(93, 275)(94, 276)(95, 279)(96, 284)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 4, 48, 4, 48 ) } Outer automorphisms :: reflexible Dual of E23.1018 Graph:: simple bipartite v = 96 e = 192 f = 52 degree seq :: [ 4^96 ] E23.1009 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 24}) Quotient :: dipole Aut^+ = (D8 x S3) : C2 (small group id <96, 121>) Aut = $<192, 1328>$ (small group id <192, 1328>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y2 * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^2 * Y1 * Y3^-2 * Y1, Y3^8, Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 ] Map:: polytopal non-degenerate R = (1, 97, 2, 98)(3, 99, 6, 102)(4, 100, 11, 107)(5, 101, 13, 109)(7, 103, 17, 113)(8, 104, 19, 115)(9, 105, 21, 117)(10, 106, 23, 119)(12, 108, 18, 114)(14, 110, 20, 116)(15, 111, 30, 126)(16, 112, 32, 128)(22, 118, 31, 127)(24, 120, 33, 129)(25, 121, 44, 140)(26, 122, 46, 142)(27, 123, 45, 141)(28, 124, 48, 144)(29, 125, 49, 145)(34, 130, 55, 151)(35, 131, 57, 153)(36, 132, 56, 152)(37, 133, 59, 155)(38, 134, 60, 156)(39, 135, 61, 157)(40, 136, 63, 159)(41, 137, 62, 158)(42, 138, 65, 161)(43, 139, 66, 162)(47, 143, 58, 154)(50, 146, 72, 168)(51, 147, 74, 170)(52, 148, 73, 169)(53, 149, 76, 172)(54, 150, 77, 173)(64, 160, 75, 171)(67, 163, 81, 177)(68, 164, 82, 178)(69, 165, 88, 184)(70, 166, 78, 174)(71, 167, 79, 175)(80, 176, 94, 190)(83, 179, 92, 188)(84, 180, 93, 189)(85, 181, 95, 191)(86, 182, 89, 185)(87, 183, 90, 186)(91, 187, 96, 192)(193, 289, 195, 291)(194, 290, 198, 294)(196, 292, 202, 298)(197, 293, 201, 297)(199, 295, 208, 304)(200, 296, 207, 303)(203, 299, 215, 311)(204, 300, 216, 312)(205, 301, 213, 309)(206, 302, 214, 310)(209, 305, 224, 320)(210, 306, 225, 321)(211, 307, 222, 318)(212, 308, 223, 319)(217, 313, 234, 330)(218, 314, 232, 328)(219, 315, 235, 331)(220, 316, 231, 327)(221, 317, 233, 329)(226, 322, 245, 341)(227, 323, 243, 339)(228, 324, 246, 342)(229, 325, 242, 338)(230, 326, 244, 340)(236, 332, 257, 353)(237, 333, 258, 354)(238, 334, 255, 351)(239, 335, 256, 352)(240, 336, 253, 349)(241, 337, 254, 350)(247, 343, 268, 364)(248, 344, 269, 365)(249, 345, 266, 362)(250, 346, 267, 363)(251, 347, 264, 360)(252, 348, 265, 361)(259, 355, 279, 375)(260, 356, 278, 374)(261, 357, 277, 373)(262, 358, 276, 372)(263, 359, 275, 371)(270, 366, 285, 381)(271, 367, 284, 380)(272, 368, 283, 379)(273, 369, 282, 378)(274, 370, 281, 377)(280, 376, 287, 383)(286, 382, 288, 384) L = (1, 196)(2, 199)(3, 201)(4, 204)(5, 193)(6, 207)(7, 210)(8, 194)(9, 214)(10, 195)(11, 217)(12, 219)(13, 218)(14, 197)(15, 223)(16, 198)(17, 226)(18, 228)(19, 227)(20, 200)(21, 231)(22, 233)(23, 232)(24, 202)(25, 237)(26, 203)(27, 239)(28, 205)(29, 206)(30, 242)(31, 244)(32, 243)(33, 208)(34, 248)(35, 209)(36, 250)(37, 211)(38, 212)(39, 254)(40, 213)(41, 256)(42, 215)(43, 216)(44, 259)(45, 261)(46, 260)(47, 221)(48, 262)(49, 220)(50, 265)(51, 222)(52, 267)(53, 224)(54, 225)(55, 270)(56, 272)(57, 271)(58, 230)(59, 273)(60, 229)(61, 275)(62, 277)(63, 276)(64, 235)(65, 278)(66, 234)(67, 280)(68, 236)(69, 241)(70, 238)(71, 240)(72, 281)(73, 283)(74, 282)(75, 246)(76, 284)(77, 245)(78, 286)(79, 247)(80, 252)(81, 249)(82, 251)(83, 287)(84, 253)(85, 258)(86, 255)(87, 257)(88, 263)(89, 288)(90, 264)(91, 269)(92, 266)(93, 268)(94, 274)(95, 279)(96, 285)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 4, 48, 4, 48 ) } Outer automorphisms :: reflexible Dual of E23.1020 Graph:: simple bipartite v = 96 e = 192 f = 52 degree seq :: [ 4^96 ] E23.1010 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 24}) Quotient :: dipole Aut^+ = C2 x D48 (small group id <96, 110>) Aut = $<192, 1299>$ (small group id <192, 1299>) |r| :: 2 Presentation :: [ Y3^2, Y2^2, R^2, (R * Y2)^2, (Y3 * Y2)^2, (Y3 * Y1^-1)^2, (Y1^-1 * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y1^24 ] Map:: polytopal non-degenerate R = (1, 97, 2, 98, 6, 102, 13, 109, 21, 117, 29, 125, 37, 133, 45, 141, 53, 149, 61, 157, 69, 165, 77, 173, 85, 181, 84, 180, 76, 172, 68, 164, 60, 156, 52, 148, 44, 140, 36, 132, 28, 124, 20, 116, 12, 108, 5, 101)(3, 99, 9, 105, 17, 113, 25, 121, 33, 129, 41, 137, 49, 145, 57, 153, 65, 161, 73, 169, 81, 177, 89, 185, 92, 188, 86, 182, 78, 174, 70, 166, 62, 158, 54, 150, 46, 142, 38, 134, 30, 126, 22, 118, 14, 110, 7, 103)(4, 100, 11, 107, 19, 115, 27, 123, 35, 131, 43, 139, 51, 147, 59, 155, 67, 163, 75, 171, 83, 179, 91, 187, 93, 189, 87, 183, 79, 175, 71, 167, 63, 159, 55, 151, 47, 143, 39, 135, 31, 127, 23, 119, 15, 111, 8, 104)(10, 106, 16, 112, 24, 120, 32, 128, 40, 136, 48, 144, 56, 152, 64, 160, 72, 168, 80, 176, 88, 184, 94, 190, 96, 192, 95, 191, 90, 186, 82, 178, 74, 170, 66, 162, 58, 154, 50, 146, 42, 138, 34, 130, 26, 122, 18, 114)(193, 289, 195, 291)(194, 290, 199, 295)(196, 292, 202, 298)(197, 293, 201, 297)(198, 294, 206, 302)(200, 296, 208, 304)(203, 299, 210, 306)(204, 300, 209, 305)(205, 301, 214, 310)(207, 303, 216, 312)(211, 307, 218, 314)(212, 308, 217, 313)(213, 309, 222, 318)(215, 311, 224, 320)(219, 315, 226, 322)(220, 316, 225, 321)(221, 317, 230, 326)(223, 319, 232, 328)(227, 323, 234, 330)(228, 324, 233, 329)(229, 325, 238, 334)(231, 327, 240, 336)(235, 331, 242, 338)(236, 332, 241, 337)(237, 333, 246, 342)(239, 335, 248, 344)(243, 339, 250, 346)(244, 340, 249, 345)(245, 341, 254, 350)(247, 343, 256, 352)(251, 347, 258, 354)(252, 348, 257, 353)(253, 349, 262, 358)(255, 351, 264, 360)(259, 355, 266, 362)(260, 356, 265, 361)(261, 357, 270, 366)(263, 359, 272, 368)(267, 363, 274, 370)(268, 364, 273, 369)(269, 365, 278, 374)(271, 367, 280, 376)(275, 371, 282, 378)(276, 372, 281, 377)(277, 373, 284, 380)(279, 375, 286, 382)(283, 379, 287, 383)(285, 381, 288, 384) L = (1, 196)(2, 200)(3, 202)(4, 193)(5, 203)(6, 207)(7, 208)(8, 194)(9, 210)(10, 195)(11, 197)(12, 211)(13, 215)(14, 216)(15, 198)(16, 199)(17, 218)(18, 201)(19, 204)(20, 219)(21, 223)(22, 224)(23, 205)(24, 206)(25, 226)(26, 209)(27, 212)(28, 227)(29, 231)(30, 232)(31, 213)(32, 214)(33, 234)(34, 217)(35, 220)(36, 235)(37, 239)(38, 240)(39, 221)(40, 222)(41, 242)(42, 225)(43, 228)(44, 243)(45, 247)(46, 248)(47, 229)(48, 230)(49, 250)(50, 233)(51, 236)(52, 251)(53, 255)(54, 256)(55, 237)(56, 238)(57, 258)(58, 241)(59, 244)(60, 259)(61, 263)(62, 264)(63, 245)(64, 246)(65, 266)(66, 249)(67, 252)(68, 267)(69, 271)(70, 272)(71, 253)(72, 254)(73, 274)(74, 257)(75, 260)(76, 275)(77, 279)(78, 280)(79, 261)(80, 262)(81, 282)(82, 265)(83, 268)(84, 283)(85, 285)(86, 286)(87, 269)(88, 270)(89, 287)(90, 273)(91, 276)(92, 288)(93, 277)(94, 278)(95, 281)(96, 284)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 4^4 ), ( 4^48 ) } Outer automorphisms :: reflexible Dual of E23.999 Graph:: simple bipartite v = 52 e = 192 f = 96 degree seq :: [ 4^48, 48^4 ] E23.1011 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 24}) Quotient :: dipole Aut^+ = (C2 x D24) : C2 (small group id <96, 115>) Aut = $<192, 1305>$ (small group id <192, 1305>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (R * Y2)^2, (R * Y3)^2, (Y1^-1 * Y3)^2, (Y3 * Y2)^2, (R * Y1)^2, Y1^-2 * Y2 * Y1^2 * Y2, (Y1 * Y2 * Y1^-1 * Y2)^2, Y2 * Y1 * Y2 * Y1^11, Y1^-6 * Y2 * Y1^-5 * Y2 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 97, 2, 98, 6, 102, 15, 111, 30, 126, 48, 144, 65, 161, 81, 177, 75, 171, 59, 155, 42, 138, 24, 120, 38, 134, 21, 117, 35, 131, 53, 149, 70, 166, 86, 182, 80, 176, 64, 160, 47, 143, 29, 125, 14, 110, 5, 101)(3, 99, 9, 105, 16, 112, 33, 129, 49, 145, 68, 164, 82, 178, 79, 175, 63, 159, 46, 142, 28, 124, 13, 109, 20, 116, 7, 103, 18, 114, 31, 127, 51, 147, 66, 162, 84, 180, 76, 172, 60, 156, 43, 139, 25, 121, 11, 107)(4, 100, 12, 108, 26, 122, 44, 140, 61, 157, 77, 173, 91, 187, 96, 192, 88, 184, 72, 168, 55, 151, 39, 135, 56, 152, 41, 137, 58, 154, 74, 170, 90, 186, 93, 189, 83, 179, 67, 163, 50, 146, 32, 128, 17, 113, 8, 104)(10, 106, 23, 119, 40, 136, 57, 153, 73, 169, 89, 185, 95, 191, 85, 181, 71, 167, 52, 148, 36, 132, 19, 115, 37, 133, 27, 123, 45, 141, 62, 158, 78, 174, 92, 188, 94, 190, 87, 183, 69, 165, 54, 150, 34, 130, 22, 118)(193, 289, 195, 291)(194, 290, 199, 295)(196, 292, 202, 298)(197, 293, 205, 301)(198, 294, 208, 304)(200, 296, 211, 307)(201, 297, 213, 309)(203, 299, 216, 312)(204, 300, 219, 315)(206, 302, 217, 313)(207, 303, 223, 319)(209, 305, 226, 322)(210, 306, 227, 323)(212, 308, 230, 326)(214, 310, 231, 327)(215, 311, 233, 329)(218, 314, 232, 328)(220, 316, 234, 330)(221, 317, 238, 334)(222, 318, 241, 337)(224, 320, 244, 340)(225, 321, 245, 341)(228, 324, 247, 343)(229, 325, 248, 344)(235, 331, 251, 347)(236, 332, 254, 350)(237, 333, 250, 346)(239, 335, 252, 348)(240, 336, 258, 354)(242, 338, 261, 357)(243, 339, 262, 358)(246, 342, 264, 360)(249, 345, 266, 362)(253, 349, 265, 361)(255, 351, 267, 363)(256, 352, 271, 367)(257, 353, 274, 370)(259, 355, 277, 373)(260, 356, 278, 374)(263, 359, 280, 376)(268, 364, 273, 369)(269, 365, 284, 380)(270, 366, 282, 378)(272, 368, 276, 372)(275, 371, 286, 382)(279, 375, 288, 384)(281, 377, 285, 381)(283, 379, 287, 383) L = (1, 196)(2, 200)(3, 202)(4, 193)(5, 204)(6, 209)(7, 211)(8, 194)(9, 214)(10, 195)(11, 215)(12, 197)(13, 219)(14, 218)(15, 224)(16, 226)(17, 198)(18, 228)(19, 199)(20, 229)(21, 231)(22, 201)(23, 203)(24, 233)(25, 232)(26, 206)(27, 205)(28, 237)(29, 236)(30, 242)(31, 244)(32, 207)(33, 246)(34, 208)(35, 247)(36, 210)(37, 212)(38, 248)(39, 213)(40, 217)(41, 216)(42, 250)(43, 249)(44, 221)(45, 220)(46, 254)(47, 253)(48, 259)(49, 261)(50, 222)(51, 263)(52, 223)(53, 264)(54, 225)(55, 227)(56, 230)(57, 235)(58, 234)(59, 266)(60, 265)(61, 239)(62, 238)(63, 270)(64, 269)(65, 275)(66, 277)(67, 240)(68, 279)(69, 241)(70, 280)(71, 243)(72, 245)(73, 252)(74, 251)(75, 282)(76, 281)(77, 256)(78, 255)(79, 284)(80, 283)(81, 285)(82, 286)(83, 257)(84, 287)(85, 258)(86, 288)(87, 260)(88, 262)(89, 268)(90, 267)(91, 272)(92, 271)(93, 273)(94, 274)(95, 276)(96, 278)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 4^4 ), ( 4^48 ) } Outer automorphisms :: reflexible Dual of E23.1001 Graph:: simple bipartite v = 52 e = 192 f = 96 degree seq :: [ 4^48, 48^4 ] E23.1012 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 24}) Quotient :: dipole Aut^+ = (C2 x D24) : C2 (small group id <96, 115>) Aut = $<192, 1305>$ (small group id <192, 1305>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (R * Y2)^2, (Y1^-1 * Y3)^2, (R * Y3)^2, (Y3 * Y2)^2, (R * Y1)^2, (Y2 * Y1^-2)^2, (Y2 * Y1)^4, Y1^-2 * Y2 * Y1 * Y2 * Y1^-9 ] Map:: polytopal non-degenerate R = (1, 97, 2, 98, 6, 102, 15, 111, 30, 126, 48, 144, 65, 161, 81, 177, 76, 172, 58, 154, 42, 138, 22, 118, 35, 131, 25, 121, 38, 134, 54, 150, 71, 167, 87, 183, 80, 176, 64, 160, 47, 143, 29, 125, 14, 110, 5, 101)(3, 99, 9, 105, 21, 117, 39, 135, 57, 153, 73, 169, 85, 181, 66, 162, 52, 148, 31, 127, 20, 116, 7, 103, 18, 114, 13, 109, 28, 124, 46, 142, 63, 159, 79, 175, 82, 178, 69, 165, 49, 145, 34, 130, 16, 112, 11, 107)(4, 100, 12, 108, 26, 122, 44, 140, 61, 157, 77, 173, 91, 187, 96, 192, 88, 184, 72, 168, 56, 152, 43, 139, 55, 151, 41, 137, 60, 156, 75, 171, 90, 186, 93, 189, 83, 179, 67, 163, 50, 146, 32, 128, 17, 113, 8, 104)(10, 106, 24, 120, 33, 129, 53, 149, 68, 164, 86, 182, 94, 190, 92, 188, 78, 174, 62, 158, 45, 141, 27, 123, 36, 132, 19, 115, 37, 133, 51, 147, 70, 166, 84, 180, 95, 191, 89, 185, 74, 170, 59, 155, 40, 136, 23, 119)(193, 289, 195, 291)(194, 290, 199, 295)(196, 292, 202, 298)(197, 293, 205, 301)(198, 294, 208, 304)(200, 296, 211, 307)(201, 297, 214, 310)(203, 299, 217, 313)(204, 300, 219, 315)(206, 302, 213, 309)(207, 303, 223, 319)(209, 305, 225, 321)(210, 306, 227, 323)(212, 308, 230, 326)(215, 311, 233, 329)(216, 312, 235, 331)(218, 314, 232, 328)(220, 316, 234, 330)(221, 317, 238, 334)(222, 318, 241, 337)(224, 320, 243, 339)(226, 322, 246, 342)(228, 324, 247, 343)(229, 325, 248, 344)(231, 327, 250, 346)(236, 332, 254, 350)(237, 333, 252, 348)(239, 335, 249, 345)(240, 336, 258, 354)(242, 338, 260, 356)(244, 340, 263, 359)(245, 341, 264, 360)(251, 347, 267, 363)(253, 349, 266, 362)(255, 351, 268, 364)(256, 352, 271, 367)(257, 353, 274, 370)(259, 355, 276, 372)(261, 357, 279, 375)(262, 358, 280, 376)(265, 361, 273, 369)(269, 365, 284, 380)(270, 366, 282, 378)(272, 368, 277, 373)(275, 371, 286, 382)(278, 374, 288, 384)(281, 377, 285, 381)(283, 379, 287, 383) L = (1, 196)(2, 200)(3, 202)(4, 193)(5, 204)(6, 209)(7, 211)(8, 194)(9, 215)(10, 195)(11, 216)(12, 197)(13, 219)(14, 218)(15, 224)(16, 225)(17, 198)(18, 228)(19, 199)(20, 229)(21, 232)(22, 233)(23, 201)(24, 203)(25, 235)(26, 206)(27, 205)(28, 237)(29, 236)(30, 242)(31, 243)(32, 207)(33, 208)(34, 245)(35, 247)(36, 210)(37, 212)(38, 248)(39, 251)(40, 213)(41, 214)(42, 252)(43, 217)(44, 221)(45, 220)(46, 254)(47, 253)(48, 259)(49, 260)(50, 222)(51, 223)(52, 262)(53, 226)(54, 264)(55, 227)(56, 230)(57, 266)(58, 267)(59, 231)(60, 234)(61, 239)(62, 238)(63, 270)(64, 269)(65, 275)(66, 276)(67, 240)(68, 241)(69, 278)(70, 244)(71, 280)(72, 246)(73, 281)(74, 249)(75, 250)(76, 282)(77, 256)(78, 255)(79, 284)(80, 283)(81, 285)(82, 286)(83, 257)(84, 258)(85, 287)(86, 261)(87, 288)(88, 263)(89, 265)(90, 268)(91, 272)(92, 271)(93, 273)(94, 274)(95, 277)(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) :: { ( 4^4 ), ( 4^48 ) } Outer automorphisms :: reflexible Dual of E23.1000 Graph:: simple bipartite v = 52 e = 192 f = 96 degree seq :: [ 4^48, 48^4 ] E23.1013 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 24}) Quotient :: dipole Aut^+ = (C2 x D24) : C2 (small group id <96, 115>) Aut = $<192, 1311>$ (small group id <192, 1311>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3 * Y2)^2, (R * Y3)^2, (Y3 * Y1^-1)^2, (R * Y1)^2, (Y1^-1 * Y2)^2, (Y3^-1 * Y1^-1)^2, Y3^4, (R * Y2 * Y3^-1)^2, Y3^-2 * Y1^12, Y1^-1 * Y3^-1 * Y1^5 * Y3 * Y1^-6 ] Map:: polytopal non-degenerate R = (1, 97, 2, 98, 7, 103, 18, 114, 33, 129, 49, 145, 65, 161, 81, 177, 78, 174, 62, 158, 46, 142, 30, 126, 15, 111, 24, 120, 39, 135, 55, 151, 71, 167, 87, 183, 80, 176, 64, 160, 48, 144, 32, 128, 17, 113, 5, 101)(3, 99, 11, 107, 25, 121, 41, 137, 57, 153, 73, 169, 89, 185, 96, 192, 88, 184, 72, 168, 56, 152, 40, 136, 28, 124, 44, 140, 60, 156, 76, 172, 92, 188, 93, 189, 82, 178, 66, 162, 50, 146, 34, 130, 19, 115, 8, 104)(4, 100, 14, 110, 29, 125, 45, 141, 61, 157, 77, 173, 84, 180, 67, 163, 52, 148, 35, 131, 21, 117, 9, 105, 6, 102, 16, 112, 31, 127, 47, 143, 63, 159, 79, 175, 83, 179, 68, 164, 51, 147, 36, 132, 20, 116, 10, 106)(12, 108, 23, 119, 37, 133, 54, 150, 69, 165, 86, 182, 94, 190, 90, 186, 75, 171, 58, 154, 43, 139, 26, 122, 13, 109, 22, 118, 38, 134, 53, 149, 70, 166, 85, 181, 95, 191, 91, 187, 74, 170, 59, 155, 42, 138, 27, 123)(193, 289, 195, 291)(194, 290, 200, 296)(196, 292, 205, 301)(197, 293, 203, 299)(198, 294, 204, 300)(199, 295, 211, 307)(201, 297, 215, 311)(202, 298, 214, 310)(206, 302, 218, 314)(207, 303, 220, 316)(208, 304, 219, 315)(209, 305, 217, 313)(210, 306, 226, 322)(212, 308, 230, 326)(213, 309, 229, 325)(216, 312, 232, 328)(221, 317, 235, 331)(222, 318, 236, 332)(223, 319, 234, 330)(224, 320, 233, 329)(225, 321, 242, 338)(227, 323, 246, 342)(228, 324, 245, 341)(231, 327, 248, 344)(237, 333, 250, 346)(238, 334, 252, 348)(239, 335, 251, 347)(240, 336, 249, 345)(241, 337, 258, 354)(243, 339, 262, 358)(244, 340, 261, 357)(247, 343, 264, 360)(253, 349, 267, 363)(254, 350, 268, 364)(255, 351, 266, 362)(256, 352, 265, 361)(257, 353, 274, 370)(259, 355, 278, 374)(260, 356, 277, 373)(263, 359, 280, 376)(269, 365, 282, 378)(270, 366, 284, 380)(271, 367, 283, 379)(272, 368, 281, 377)(273, 369, 285, 381)(275, 371, 287, 383)(276, 372, 286, 382)(279, 375, 288, 384) L = (1, 196)(2, 201)(3, 204)(4, 207)(5, 208)(6, 193)(7, 212)(8, 214)(9, 216)(10, 194)(11, 218)(12, 220)(13, 195)(14, 197)(15, 198)(16, 222)(17, 221)(18, 227)(19, 229)(20, 231)(21, 199)(22, 232)(23, 200)(24, 202)(25, 234)(26, 236)(27, 203)(28, 205)(29, 238)(30, 206)(31, 209)(32, 239)(33, 243)(34, 245)(35, 247)(36, 210)(37, 248)(38, 211)(39, 213)(40, 215)(41, 250)(42, 252)(43, 217)(44, 219)(45, 224)(46, 223)(47, 254)(48, 253)(49, 259)(50, 261)(51, 263)(52, 225)(53, 264)(54, 226)(55, 228)(56, 230)(57, 266)(58, 268)(59, 233)(60, 235)(61, 270)(62, 237)(63, 240)(64, 271)(65, 275)(66, 277)(67, 279)(68, 241)(69, 280)(70, 242)(71, 244)(72, 246)(73, 282)(74, 284)(75, 249)(76, 251)(77, 256)(78, 255)(79, 273)(80, 276)(81, 269)(82, 286)(83, 272)(84, 257)(85, 288)(86, 258)(87, 260)(88, 262)(89, 287)(90, 285)(91, 265)(92, 267)(93, 283)(94, 281)(95, 274)(96, 278)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 4^4 ), ( 4^48 ) } Outer automorphisms :: reflexible Dual of E23.1002 Graph:: simple bipartite v = 52 e = 192 f = 96 degree seq :: [ 4^48, 48^4 ] E23.1014 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 24}) Quotient :: dipole Aut^+ = (C24 x C2) : C2 (small group id <96, 111>) Aut = $<192, 1311>$ (small group id <192, 1311>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3^-1 * Y2)^2, (Y3 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2)^2, Y3^4, (Y3^-1 * Y1^-1)^2, Y1 * Y3^-1 * Y2 * Y3 * Y1 * Y2, (R * Y2 * Y3^-1)^2, (Y2 * Y1^-2)^2, Y1^-2 * Y2 * Y1 * Y2 * Y1^-9 ] Map:: polytopal non-degenerate R = (1, 97, 2, 98, 7, 103, 20, 116, 37, 133, 53, 149, 69, 165, 85, 181, 80, 176, 62, 158, 48, 144, 30, 126, 16, 112, 28, 124, 44, 140, 60, 156, 76, 172, 92, 188, 84, 180, 68, 164, 52, 148, 36, 132, 19, 115, 5, 101)(3, 99, 11, 107, 29, 125, 45, 141, 61, 157, 77, 173, 90, 186, 70, 166, 58, 154, 38, 134, 26, 122, 8, 104, 24, 120, 17, 113, 34, 130, 50, 146, 66, 162, 82, 178, 86, 182, 74, 170, 54, 150, 42, 138, 21, 117, 13, 109)(4, 100, 15, 111, 33, 129, 49, 145, 65, 161, 81, 177, 88, 184, 71, 167, 56, 152, 39, 135, 23, 119, 9, 105, 6, 102, 18, 114, 35, 131, 51, 147, 67, 163, 83, 179, 87, 183, 72, 168, 55, 151, 40, 136, 22, 118, 10, 106)(12, 108, 25, 121, 41, 137, 57, 153, 73, 169, 89, 185, 95, 191, 93, 189, 79, 175, 63, 159, 47, 143, 31, 127, 14, 110, 27, 123, 43, 139, 59, 155, 75, 171, 91, 187, 96, 192, 94, 190, 78, 174, 64, 160, 46, 142, 32, 128)(193, 289, 195, 291)(194, 290, 200, 296)(196, 292, 206, 302)(197, 293, 209, 305)(198, 294, 204, 300)(199, 295, 213, 309)(201, 297, 219, 315)(202, 298, 217, 313)(203, 299, 222, 318)(205, 301, 220, 316)(207, 303, 224, 320)(208, 304, 216, 312)(210, 306, 223, 319)(211, 307, 221, 317)(212, 308, 230, 326)(214, 310, 235, 331)(215, 311, 233, 329)(218, 314, 236, 332)(225, 321, 239, 335)(226, 322, 240, 336)(227, 323, 238, 334)(228, 324, 242, 338)(229, 325, 246, 342)(231, 327, 251, 347)(232, 328, 249, 345)(234, 330, 252, 348)(237, 333, 254, 350)(241, 337, 256, 352)(243, 339, 255, 351)(244, 340, 253, 349)(245, 341, 262, 358)(247, 343, 267, 363)(248, 344, 265, 361)(250, 346, 268, 364)(257, 353, 271, 367)(258, 354, 272, 368)(259, 355, 270, 366)(260, 356, 274, 370)(261, 357, 278, 374)(263, 359, 283, 379)(264, 360, 281, 377)(266, 362, 284, 380)(269, 365, 277, 373)(273, 369, 286, 382)(275, 371, 285, 381)(276, 372, 282, 378)(279, 375, 288, 384)(280, 376, 287, 383) L = (1, 196)(2, 201)(3, 204)(4, 208)(5, 210)(6, 193)(7, 214)(8, 217)(9, 220)(10, 194)(11, 223)(12, 216)(13, 219)(14, 195)(15, 197)(16, 198)(17, 224)(18, 222)(19, 225)(20, 231)(21, 233)(22, 236)(23, 199)(24, 206)(25, 205)(26, 235)(27, 200)(28, 202)(29, 238)(30, 207)(31, 209)(32, 203)(33, 240)(34, 239)(35, 211)(36, 243)(37, 247)(38, 249)(39, 252)(40, 212)(41, 218)(42, 251)(43, 213)(44, 215)(45, 255)(46, 226)(47, 221)(48, 227)(49, 228)(50, 256)(51, 254)(52, 257)(53, 263)(54, 265)(55, 268)(56, 229)(57, 234)(58, 267)(59, 230)(60, 232)(61, 270)(62, 241)(63, 242)(64, 237)(65, 272)(66, 271)(67, 244)(68, 275)(69, 279)(70, 281)(71, 284)(72, 245)(73, 250)(74, 283)(75, 246)(76, 248)(77, 285)(78, 258)(79, 253)(80, 259)(81, 260)(82, 286)(83, 277)(84, 280)(85, 273)(86, 287)(87, 276)(88, 261)(89, 266)(90, 288)(91, 262)(92, 264)(93, 274)(94, 269)(95, 282)(96, 278)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 4^4 ), ( 4^48 ) } Outer automorphisms :: reflexible Dual of E23.1003 Graph:: simple bipartite v = 52 e = 192 f = 96 degree seq :: [ 4^48, 48^4 ] E23.1015 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 24}) Quotient :: dipole Aut^+ = D16 x S3 (small group id <96, 117>) Aut = $<192, 1313>$ (small group id <192, 1313>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y1^-1 * Y3)^2, (Y3 * Y2)^2, Y1^-1 * Y2 * Y1^-1 * Y2 * Y1 * Y2 * Y1 * Y2, Y2 * Y1^3 * Y2 * Y1^-3, Y1^-2 * Y2 * Y1^-1 * Y2 * Y1^-5 ] Map:: polytopal non-degenerate R = (1, 97, 2, 98, 6, 102, 15, 111, 33, 129, 61, 157, 51, 147, 25, 121, 43, 139, 70, 166, 45, 141, 71, 167, 89, 185, 82, 178, 52, 148, 76, 172, 48, 144, 22, 118, 40, 136, 67, 163, 60, 156, 32, 128, 14, 110, 5, 101)(3, 99, 9, 105, 21, 117, 34, 130, 64, 160, 58, 154, 30, 126, 13, 109, 29, 125, 38, 134, 16, 112, 36, 132, 66, 162, 59, 155, 31, 127, 44, 140, 20, 116, 7, 103, 18, 114, 39, 135, 62, 158, 53, 149, 26, 122, 11, 107)(4, 100, 12, 108, 27, 123, 54, 150, 83, 179, 91, 187, 73, 169, 47, 143, 78, 174, 94, 190, 80, 176, 95, 191, 96, 192, 93, 189, 77, 173, 92, 188, 75, 171, 50, 146, 81, 177, 86, 182, 63, 159, 35, 131, 17, 113, 8, 104)(10, 106, 24, 120, 49, 145, 79, 175, 87, 183, 72, 168, 41, 137, 19, 115, 42, 138, 74, 170, 55, 151, 84, 180, 90, 186, 68, 164, 37, 133, 69, 165, 57, 153, 28, 124, 56, 152, 85, 181, 88, 184, 65, 161, 46, 142, 23, 119)(193, 289, 195, 291)(194, 290, 199, 295)(196, 292, 202, 298)(197, 293, 205, 301)(198, 294, 208, 304)(200, 296, 211, 307)(201, 297, 214, 310)(203, 299, 217, 313)(204, 300, 220, 316)(206, 302, 223, 319)(207, 303, 226, 322)(209, 305, 229, 325)(210, 306, 232, 328)(212, 308, 235, 331)(213, 309, 237, 333)(215, 311, 239, 335)(216, 312, 242, 338)(218, 314, 244, 340)(219, 315, 247, 343)(221, 317, 240, 336)(222, 318, 243, 339)(224, 320, 245, 341)(225, 321, 254, 350)(227, 323, 257, 353)(228, 324, 259, 355)(230, 326, 262, 358)(231, 327, 263, 359)(233, 329, 265, 361)(234, 330, 267, 363)(236, 332, 268, 364)(238, 334, 269, 365)(241, 337, 272, 368)(246, 342, 271, 367)(248, 344, 273, 369)(249, 345, 270, 366)(250, 346, 274, 370)(251, 347, 253, 349)(252, 348, 256, 352)(255, 351, 279, 375)(258, 354, 281, 377)(260, 356, 283, 379)(261, 357, 284, 380)(264, 360, 285, 381)(266, 362, 286, 382)(275, 371, 280, 376)(276, 372, 278, 374)(277, 373, 287, 383)(282, 378, 288, 384) L = (1, 196)(2, 200)(3, 202)(4, 193)(5, 204)(6, 209)(7, 211)(8, 194)(9, 215)(10, 195)(11, 216)(12, 197)(13, 220)(14, 219)(15, 227)(16, 229)(17, 198)(18, 233)(19, 199)(20, 234)(21, 238)(22, 239)(23, 201)(24, 203)(25, 242)(26, 241)(27, 206)(28, 205)(29, 249)(30, 248)(31, 247)(32, 246)(33, 255)(34, 257)(35, 207)(36, 260)(37, 208)(38, 261)(39, 264)(40, 265)(41, 210)(42, 212)(43, 267)(44, 266)(45, 269)(46, 213)(47, 214)(48, 270)(49, 218)(50, 217)(51, 273)(52, 272)(53, 271)(54, 224)(55, 223)(56, 222)(57, 221)(58, 277)(59, 276)(60, 275)(61, 278)(62, 279)(63, 225)(64, 280)(65, 226)(66, 282)(67, 283)(68, 228)(69, 230)(70, 284)(71, 285)(72, 231)(73, 232)(74, 236)(75, 235)(76, 286)(77, 237)(78, 240)(79, 245)(80, 244)(81, 243)(82, 287)(83, 252)(84, 251)(85, 250)(86, 253)(87, 254)(88, 256)(89, 288)(90, 258)(91, 259)(92, 262)(93, 263)(94, 268)(95, 274)(96, 281)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 4^4 ), ( 4^48 ) } Outer automorphisms :: reflexible Dual of E23.1006 Graph:: simple bipartite v = 52 e = 192 f = 96 degree seq :: [ 4^48, 48^4 ] E23.1016 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 24}) Quotient :: dipole Aut^+ = D16 x S3 (small group id <96, 117>) Aut = $<192, 1313>$ (small group id <192, 1313>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y1^-1 * Y3)^2, (Y3 * Y2)^2, (Y1^3 * Y2)^2, Y1^-1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2, Y1^-3 * Y2 * Y1 * Y2 * Y1^-4 ] Map:: polytopal non-degenerate R = (1, 97, 2, 98, 6, 102, 15, 111, 33, 129, 61, 157, 49, 145, 22, 118, 40, 136, 66, 162, 53, 149, 76, 172, 92, 188, 79, 175, 46, 142, 71, 167, 52, 148, 25, 121, 43, 139, 69, 165, 60, 156, 32, 128, 14, 110, 5, 101)(3, 99, 9, 105, 21, 117, 45, 141, 62, 158, 44, 140, 20, 116, 7, 103, 18, 114, 39, 135, 31, 127, 59, 155, 70, 166, 38, 134, 16, 112, 36, 132, 30, 126, 13, 109, 29, 125, 58, 154, 65, 161, 34, 130, 26, 122, 11, 107)(4, 100, 12, 108, 27, 123, 54, 150, 83, 179, 91, 187, 75, 171, 51, 147, 82, 178, 93, 189, 78, 174, 95, 191, 96, 192, 94, 190, 81, 177, 89, 185, 73, 169, 48, 144, 80, 176, 86, 182, 63, 159, 35, 131, 17, 113, 8, 104)(10, 106, 24, 120, 50, 146, 64, 160, 88, 184, 85, 181, 57, 153, 28, 124, 56, 152, 67, 163, 37, 133, 68, 164, 90, 186, 84, 180, 55, 151, 72, 168, 41, 137, 19, 115, 42, 138, 74, 170, 87, 183, 77, 173, 47, 143, 23, 119)(193, 289, 195, 291)(194, 290, 199, 295)(196, 292, 202, 298)(197, 293, 205, 301)(198, 294, 208, 304)(200, 296, 211, 307)(201, 297, 214, 310)(203, 299, 217, 313)(204, 300, 220, 316)(206, 302, 223, 319)(207, 303, 226, 322)(209, 305, 229, 325)(210, 306, 232, 328)(212, 308, 235, 331)(213, 309, 238, 334)(215, 311, 240, 336)(216, 312, 243, 339)(218, 314, 245, 341)(219, 315, 247, 343)(221, 317, 241, 337)(222, 318, 244, 340)(224, 320, 237, 333)(225, 321, 254, 350)(227, 323, 256, 352)(228, 324, 258, 354)(230, 326, 261, 357)(231, 327, 263, 359)(233, 329, 265, 361)(234, 330, 267, 363)(236, 332, 268, 364)(239, 335, 270, 366)(242, 338, 273, 369)(246, 342, 269, 365)(248, 344, 274, 370)(249, 345, 272, 368)(250, 346, 271, 367)(251, 347, 253, 349)(252, 348, 257, 353)(255, 351, 279, 375)(259, 355, 281, 377)(260, 356, 283, 379)(262, 358, 284, 380)(264, 360, 285, 381)(266, 362, 286, 382)(275, 371, 280, 376)(276, 372, 278, 374)(277, 373, 287, 383)(282, 378, 288, 384) L = (1, 196)(2, 200)(3, 202)(4, 193)(5, 204)(6, 209)(7, 211)(8, 194)(9, 215)(10, 195)(11, 216)(12, 197)(13, 220)(14, 219)(15, 227)(16, 229)(17, 198)(18, 233)(19, 199)(20, 234)(21, 239)(22, 240)(23, 201)(24, 203)(25, 243)(26, 242)(27, 206)(28, 205)(29, 249)(30, 248)(31, 247)(32, 246)(33, 255)(34, 256)(35, 207)(36, 259)(37, 208)(38, 260)(39, 264)(40, 265)(41, 210)(42, 212)(43, 267)(44, 266)(45, 269)(46, 270)(47, 213)(48, 214)(49, 272)(50, 218)(51, 217)(52, 274)(53, 273)(54, 224)(55, 223)(56, 222)(57, 221)(58, 277)(59, 276)(60, 275)(61, 278)(62, 279)(63, 225)(64, 226)(65, 280)(66, 281)(67, 228)(68, 230)(69, 283)(70, 282)(71, 285)(72, 231)(73, 232)(74, 236)(75, 235)(76, 286)(77, 237)(78, 238)(79, 287)(80, 241)(81, 245)(82, 244)(83, 252)(84, 251)(85, 250)(86, 253)(87, 254)(88, 257)(89, 258)(90, 262)(91, 261)(92, 288)(93, 263)(94, 268)(95, 271)(96, 284)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 4^4 ), ( 4^48 ) } Outer automorphisms :: reflexible Dual of E23.1004 Graph:: simple bipartite v = 52 e = 192 f = 96 degree seq :: [ 4^48, 48^4 ] E23.1017 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 24}) Quotient :: dipole Aut^+ = D16 x S3 (small group id <96, 117>) Aut = $<192, 1313>$ (small group id <192, 1313>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3 * Y2)^2, (R * Y3)^2, (Y1^-1 * Y2)^2, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, (Y1^2 * Y3^-1)^2, Y1 * Y3^-3 * Y1 * Y3^-1, (R * Y2 * Y3^-1)^2, (Y1^-2 * Y3)^2, Y1^-3 * Y3 * Y1 * Y3^-1 * Y1^-4 ] Map:: polytopal non-degenerate R = (1, 97, 2, 98, 7, 103, 21, 117, 44, 140, 69, 165, 64, 160, 39, 135, 20, 116, 30, 126, 52, 148, 77, 173, 91, 187, 87, 183, 65, 161, 40, 136, 15, 111, 27, 123, 50, 146, 75, 171, 68, 164, 43, 139, 18, 114, 5, 101)(3, 99, 11, 107, 31, 127, 57, 153, 81, 177, 94, 190, 80, 176, 56, 152, 37, 133, 62, 158, 86, 182, 95, 191, 96, 192, 92, 188, 78, 174, 53, 149, 34, 130, 60, 156, 84, 180, 88, 184, 70, 166, 45, 141, 22, 118, 8, 104)(4, 100, 14, 110, 38, 134, 63, 159, 71, 167, 47, 143, 28, 124, 9, 105, 6, 102, 19, 115, 42, 138, 67, 163, 72, 168, 51, 147, 23, 119, 10, 106, 29, 125, 17, 113, 41, 137, 66, 162, 76, 172, 46, 142, 24, 120, 16, 112)(12, 108, 26, 122, 55, 151, 73, 169, 90, 186, 83, 179, 61, 157, 32, 128, 13, 109, 36, 132, 48, 144, 74, 170, 93, 189, 85, 181, 58, 154, 33, 129, 54, 150, 25, 121, 49, 145, 79, 175, 89, 185, 82, 178, 59, 155, 35, 131)(193, 289, 195, 291)(194, 290, 200, 296)(196, 292, 205, 301)(197, 293, 203, 299)(198, 294, 204, 300)(199, 295, 214, 310)(201, 297, 218, 314)(202, 298, 217, 313)(206, 302, 224, 320)(207, 303, 229, 325)(208, 304, 228, 324)(209, 305, 225, 321)(210, 306, 223, 319)(211, 307, 227, 323)(212, 308, 226, 322)(213, 309, 237, 333)(215, 311, 241, 337)(216, 312, 240, 336)(219, 315, 248, 344)(220, 316, 247, 343)(221, 317, 246, 342)(222, 318, 245, 341)(230, 326, 253, 349)(231, 327, 252, 348)(232, 328, 254, 350)(233, 329, 250, 346)(234, 330, 251, 347)(235, 331, 249, 345)(236, 332, 262, 358)(238, 334, 266, 362)(239, 335, 265, 361)(242, 338, 272, 368)(243, 339, 271, 367)(244, 340, 270, 366)(255, 351, 275, 371)(256, 352, 276, 372)(257, 353, 278, 374)(258, 354, 277, 373)(259, 355, 274, 370)(260, 356, 273, 369)(261, 357, 280, 376)(263, 359, 282, 378)(264, 360, 281, 377)(267, 363, 286, 382)(268, 364, 285, 381)(269, 365, 284, 380)(279, 375, 287, 383)(283, 379, 288, 384) L = (1, 196)(2, 201)(3, 204)(4, 207)(5, 209)(6, 193)(7, 215)(8, 217)(9, 219)(10, 194)(11, 224)(12, 226)(13, 195)(14, 197)(15, 221)(16, 222)(17, 232)(18, 234)(19, 231)(20, 198)(21, 238)(22, 240)(23, 242)(24, 199)(25, 245)(26, 200)(27, 208)(28, 244)(29, 212)(30, 202)(31, 250)(32, 252)(33, 203)(34, 246)(35, 254)(36, 248)(37, 205)(38, 256)(39, 206)(40, 211)(41, 210)(42, 257)(43, 255)(44, 263)(45, 265)(46, 267)(47, 213)(48, 270)(49, 214)(50, 220)(51, 269)(52, 216)(53, 228)(54, 229)(55, 272)(56, 218)(57, 274)(58, 276)(59, 223)(60, 227)(61, 278)(62, 225)(63, 279)(64, 233)(65, 230)(66, 261)(67, 235)(68, 268)(69, 259)(70, 281)(71, 260)(72, 236)(73, 284)(74, 237)(75, 243)(76, 283)(77, 239)(78, 247)(79, 286)(80, 241)(81, 282)(82, 280)(83, 249)(84, 253)(85, 287)(86, 251)(87, 258)(88, 277)(89, 288)(90, 262)(91, 264)(92, 271)(93, 273)(94, 266)(95, 275)(96, 285)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 4^4 ), ( 4^48 ) } Outer automorphisms :: reflexible Dual of E23.1005 Graph:: simple bipartite v = 52 e = 192 f = 96 degree seq :: [ 4^48, 48^4 ] E23.1018 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 24}) Quotient :: dipole Aut^+ = (D8 x S3) : C2 (small group id <96, 121>) Aut = $<192, 1318>$ (small group id <192, 1318>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (R * Y2)^2, (Y1^-1 * Y3)^2, (Y3 * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y1^-4 * Y2 * Y1^-1 * Y2 * Y1^-1, (Y2 * Y1^2 * Y2 * Y1^-2)^2 ] Map:: polytopal non-degenerate R = (1, 97, 2, 98, 6, 102, 15, 111, 33, 129, 25, 121, 43, 139, 65, 161, 83, 179, 73, 169, 52, 148, 72, 168, 88, 184, 76, 172, 46, 142, 67, 163, 84, 180, 78, 174, 49, 145, 22, 118, 40, 136, 32, 128, 14, 110, 5, 101)(3, 99, 9, 105, 21, 117, 45, 141, 30, 126, 13, 109, 29, 125, 57, 153, 61, 157, 34, 130, 31, 127, 58, 154, 66, 162, 38, 134, 16, 112, 36, 132, 62, 158, 44, 140, 20, 116, 7, 103, 18, 114, 39, 135, 26, 122, 11, 107)(4, 100, 12, 108, 27, 123, 53, 149, 69, 165, 48, 144, 77, 173, 93, 189, 95, 191, 89, 185, 75, 171, 92, 188, 96, 192, 90, 186, 79, 175, 91, 187, 94, 190, 87, 183, 71, 167, 51, 147, 59, 155, 35, 131, 17, 113, 8, 104)(10, 106, 24, 120, 50, 146, 68, 164, 41, 137, 19, 115, 42, 138, 70, 166, 85, 181, 63, 159, 37, 133, 64, 160, 86, 182, 80, 176, 54, 150, 60, 156, 82, 178, 81, 177, 56, 152, 28, 124, 55, 151, 74, 170, 47, 143, 23, 119)(193, 289, 195, 291)(194, 290, 199, 295)(196, 292, 202, 298)(197, 293, 205, 301)(198, 294, 208, 304)(200, 296, 211, 307)(201, 297, 214, 310)(203, 299, 217, 313)(204, 300, 220, 316)(206, 302, 223, 319)(207, 303, 226, 322)(209, 305, 229, 325)(210, 306, 232, 328)(212, 308, 235, 331)(213, 309, 238, 334)(215, 311, 240, 336)(216, 312, 243, 339)(218, 314, 244, 340)(219, 315, 246, 342)(221, 317, 241, 337)(222, 318, 225, 321)(224, 320, 228, 324)(227, 323, 252, 348)(230, 326, 257, 353)(231, 327, 259, 355)(233, 329, 261, 357)(234, 330, 263, 359)(236, 332, 264, 360)(237, 333, 265, 361)(239, 335, 267, 363)(242, 338, 271, 367)(245, 341, 255, 351)(247, 343, 251, 347)(248, 344, 269, 365)(249, 345, 268, 364)(250, 346, 270, 366)(253, 349, 275, 371)(254, 350, 276, 372)(256, 352, 279, 375)(258, 354, 280, 376)(260, 356, 281, 377)(262, 358, 282, 378)(266, 362, 283, 379)(272, 368, 285, 381)(273, 369, 284, 380)(274, 370, 286, 382)(277, 373, 287, 383)(278, 374, 288, 384) L = (1, 196)(2, 200)(3, 202)(4, 193)(5, 204)(6, 209)(7, 211)(8, 194)(9, 215)(10, 195)(11, 216)(12, 197)(13, 220)(14, 219)(15, 227)(16, 229)(17, 198)(18, 233)(19, 199)(20, 234)(21, 239)(22, 240)(23, 201)(24, 203)(25, 243)(26, 242)(27, 206)(28, 205)(29, 248)(30, 247)(31, 246)(32, 245)(33, 251)(34, 252)(35, 207)(36, 255)(37, 208)(38, 256)(39, 260)(40, 261)(41, 210)(42, 212)(43, 263)(44, 262)(45, 266)(46, 267)(47, 213)(48, 214)(49, 269)(50, 218)(51, 217)(52, 271)(53, 224)(54, 223)(55, 222)(56, 221)(57, 273)(58, 272)(59, 225)(60, 226)(61, 274)(62, 277)(63, 228)(64, 230)(65, 279)(66, 278)(67, 281)(68, 231)(69, 232)(70, 236)(71, 235)(72, 282)(73, 283)(74, 237)(75, 238)(76, 284)(77, 241)(78, 285)(79, 244)(80, 250)(81, 249)(82, 253)(83, 286)(84, 287)(85, 254)(86, 258)(87, 257)(88, 288)(89, 259)(90, 264)(91, 265)(92, 268)(93, 270)(94, 275)(95, 276)(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) :: { ( 4^4 ), ( 4^48 ) } Outer automorphisms :: reflexible Dual of E23.1008 Graph:: simple bipartite v = 52 e = 192 f = 96 degree seq :: [ 4^48, 48^4 ] E23.1019 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 24}) Quotient :: dipole Aut^+ = (D8 x S3) : C2 (small group id <96, 121>) Aut = $<192, 1318>$ (small group id <192, 1318>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (R * Y2)^2, (Y1^-1 * Y3)^2, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2)^2, Y1^-4 * Y2 * Y1 * Y2 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 97, 2, 98, 6, 102, 15, 111, 33, 129, 22, 118, 40, 136, 63, 159, 82, 178, 74, 170, 45, 141, 67, 163, 84, 180, 79, 175, 51, 147, 72, 168, 88, 184, 78, 174, 50, 146, 25, 121, 43, 139, 32, 128, 14, 110, 5, 101)(3, 99, 9, 105, 21, 117, 44, 140, 20, 116, 7, 103, 18, 114, 39, 135, 66, 162, 38, 134, 16, 112, 36, 132, 62, 158, 58, 154, 31, 127, 34, 130, 60, 156, 57, 153, 30, 126, 13, 109, 29, 125, 52, 148, 26, 122, 11, 107)(4, 100, 12, 108, 27, 123, 53, 149, 71, 167, 49, 145, 77, 173, 93, 189, 96, 192, 90, 186, 76, 172, 92, 188, 95, 191, 89, 185, 73, 169, 91, 187, 94, 190, 86, 182, 69, 165, 47, 143, 59, 155, 35, 131, 17, 113, 8, 104)(10, 106, 24, 120, 48, 144, 75, 171, 56, 152, 28, 124, 55, 151, 81, 177, 83, 179, 61, 157, 54, 150, 80, 176, 85, 181, 64, 160, 37, 133, 65, 161, 87, 183, 68, 164, 41, 137, 19, 115, 42, 138, 70, 166, 46, 142, 23, 119)(193, 289, 195, 291)(194, 290, 199, 295)(196, 292, 202, 298)(197, 293, 205, 301)(198, 294, 208, 304)(200, 296, 211, 307)(201, 297, 214, 310)(203, 299, 217, 313)(204, 300, 220, 316)(206, 302, 223, 319)(207, 303, 226, 322)(209, 305, 229, 325)(210, 306, 232, 328)(212, 308, 235, 331)(213, 309, 237, 333)(215, 311, 239, 335)(216, 312, 241, 337)(218, 314, 243, 339)(219, 315, 246, 342)(221, 317, 225, 321)(222, 318, 242, 338)(224, 320, 230, 326)(227, 323, 253, 349)(228, 324, 255, 351)(231, 327, 259, 355)(233, 329, 261, 357)(234, 330, 263, 359)(236, 332, 264, 360)(238, 334, 265, 361)(240, 336, 268, 364)(244, 340, 266, 362)(245, 341, 257, 353)(247, 343, 269, 365)(248, 344, 251, 347)(249, 345, 271, 367)(250, 346, 270, 366)(252, 348, 274, 370)(254, 350, 276, 372)(256, 352, 278, 374)(258, 354, 280, 376)(260, 356, 281, 377)(262, 358, 282, 378)(267, 363, 283, 379)(272, 368, 285, 381)(273, 369, 284, 380)(275, 371, 286, 382)(277, 373, 287, 383)(279, 375, 288, 384) L = (1, 196)(2, 200)(3, 202)(4, 193)(5, 204)(6, 209)(7, 211)(8, 194)(9, 215)(10, 195)(11, 216)(12, 197)(13, 220)(14, 219)(15, 227)(16, 229)(17, 198)(18, 233)(19, 199)(20, 234)(21, 238)(22, 239)(23, 201)(24, 203)(25, 241)(26, 240)(27, 206)(28, 205)(29, 248)(30, 247)(31, 246)(32, 245)(33, 251)(34, 253)(35, 207)(36, 256)(37, 208)(38, 257)(39, 260)(40, 261)(41, 210)(42, 212)(43, 263)(44, 262)(45, 265)(46, 213)(47, 214)(48, 218)(49, 217)(50, 269)(51, 268)(52, 267)(53, 224)(54, 223)(55, 222)(56, 221)(57, 273)(58, 272)(59, 225)(60, 275)(61, 226)(62, 277)(63, 278)(64, 228)(65, 230)(66, 279)(67, 281)(68, 231)(69, 232)(70, 236)(71, 235)(72, 282)(73, 237)(74, 283)(75, 244)(76, 243)(77, 242)(78, 285)(79, 284)(80, 250)(81, 249)(82, 286)(83, 252)(84, 287)(85, 254)(86, 255)(87, 258)(88, 288)(89, 259)(90, 264)(91, 266)(92, 271)(93, 270)(94, 274)(95, 276)(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) :: { ( 4^4 ), ( 4^48 ) } Outer automorphisms :: reflexible Dual of E23.1007 Graph:: simple bipartite v = 52 e = 192 f = 96 degree seq :: [ 4^48, 48^4 ] E23.1020 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 24}) Quotient :: dipole Aut^+ = (D8 x S3) : C2 (small group id <96, 121>) Aut = $<192, 1328>$ (small group id <192, 1328>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3^-1 * Y1^-1)^2, (Y3 * Y1)^2, (Y3 * Y2)^2, (Y1 * Y2)^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y3^2 * Y1 * Y3^-2 * Y1^-1, Y3 * Y1^-5 * Y3^-1 * Y1, (Y3^3 * Y1^-1)^2 ] Map:: polytopal non-degenerate R = (1, 97, 2, 98, 7, 103, 21, 117, 49, 145, 39, 135, 20, 116, 30, 126, 58, 154, 83, 179, 78, 174, 48, 144, 66, 162, 42, 138, 63, 159, 88, 184, 79, 175, 41, 137, 15, 111, 27, 123, 55, 151, 46, 142, 18, 114, 5, 101)(3, 99, 11, 107, 31, 127, 67, 163, 87, 183, 62, 158, 37, 133, 73, 169, 93, 189, 96, 192, 92, 188, 77, 173, 89, 185, 74, 170, 94, 190, 95, 191, 84, 180, 59, 155, 34, 130, 70, 166, 80, 176, 50, 146, 22, 118, 8, 104)(4, 100, 14, 110, 38, 134, 64, 160, 28, 124, 9, 105, 6, 102, 19, 115, 47, 143, 56, 152, 23, 119, 10, 106, 29, 125, 65, 161, 45, 141, 51, 147, 24, 120, 57, 153, 40, 136, 17, 113, 44, 140, 52, 148, 43, 139, 16, 112)(12, 108, 26, 122, 61, 157, 91, 187, 71, 167, 32, 128, 13, 109, 36, 132, 76, 172, 81, 177, 68, 164, 33, 129, 72, 168, 85, 181, 53, 149, 82, 178, 69, 165, 90, 186, 60, 156, 25, 121, 54, 150, 86, 182, 75, 171, 35, 131)(193, 289, 195, 291)(194, 290, 200, 296)(196, 292, 205, 301)(197, 293, 203, 299)(198, 294, 204, 300)(199, 295, 214, 310)(201, 297, 218, 314)(202, 298, 217, 313)(206, 302, 224, 320)(207, 303, 229, 325)(208, 304, 228, 324)(209, 305, 225, 321)(210, 306, 223, 319)(211, 307, 227, 323)(212, 308, 226, 322)(213, 309, 242, 338)(215, 311, 246, 342)(216, 312, 245, 341)(219, 315, 254, 350)(220, 316, 253, 349)(221, 317, 252, 348)(222, 318, 251, 347)(230, 326, 263, 359)(231, 327, 262, 358)(232, 328, 264, 360)(233, 329, 265, 361)(234, 330, 269, 365)(235, 331, 268, 364)(236, 332, 260, 356)(237, 333, 261, 357)(238, 334, 259, 355)(239, 335, 267, 363)(240, 336, 266, 362)(241, 337, 272, 368)(243, 339, 274, 370)(244, 340, 273, 369)(247, 343, 279, 375)(248, 344, 278, 374)(249, 345, 277, 373)(250, 346, 276, 372)(255, 351, 284, 380)(256, 352, 283, 379)(257, 353, 282, 378)(258, 354, 281, 377)(270, 366, 286, 382)(271, 367, 285, 381)(275, 371, 287, 383)(280, 376, 288, 384) L = (1, 196)(2, 201)(3, 204)(4, 207)(5, 209)(6, 193)(7, 215)(8, 217)(9, 219)(10, 194)(11, 224)(12, 226)(13, 195)(14, 197)(15, 232)(16, 234)(17, 233)(18, 237)(19, 231)(20, 198)(21, 243)(22, 245)(23, 247)(24, 199)(25, 251)(26, 200)(27, 208)(28, 255)(29, 212)(30, 202)(31, 260)(32, 262)(33, 203)(34, 252)(35, 266)(36, 254)(37, 205)(38, 241)(39, 206)(40, 258)(41, 257)(42, 249)(43, 250)(44, 210)(45, 271)(46, 248)(47, 270)(48, 211)(49, 236)(50, 273)(51, 238)(52, 213)(53, 276)(54, 214)(55, 220)(56, 280)(57, 222)(58, 216)(59, 277)(60, 281)(61, 279)(62, 218)(63, 235)(64, 275)(65, 240)(66, 221)(67, 274)(68, 272)(69, 223)(70, 227)(71, 286)(72, 229)(73, 225)(74, 282)(75, 285)(76, 284)(77, 228)(78, 230)(79, 239)(80, 263)(81, 287)(82, 242)(83, 244)(84, 268)(85, 269)(86, 259)(87, 246)(88, 256)(89, 264)(90, 265)(91, 288)(92, 253)(93, 261)(94, 267)(95, 283)(96, 278)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 4^4 ), ( 4^48 ) } Outer automorphisms :: reflexible Dual of E23.1009 Graph:: simple bipartite v = 52 e = 192 f = 96 degree seq :: [ 4^48, 48^4 ] E23.1021 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 24}) Quotient :: dipole Aut^+ = (D8 x S3) : C2 (small group id <96, 118>) Aut = $<192, 1331>$ (small group id <192, 1331>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^4, (R * Y1)^2, (Y2 * Y3)^2, (R * Y3)^2, (Y1 * Y3^-2)^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y1 * Y3 * Y2 * Y3^-1 * Y2 * Y1 * Y3^-1, Y1 * Y3^-1 * Y1 * Y2 * Y1 * Y3 * Y1 * Y2, Y3 * Y1 * Y2 * Y1 * Y3^-1 * Y1 * Y2 * Y1, Y2 * Y3 * Y1 * Y3 * Y1 * Y2 * Y1 * Y3 * Y1 * Y3^-1, Y2 * Y1 * Y3 * Y2 * Y3^-1 * Y1 * Y2 * Y1 * Y2 * Y1, Y2 * Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y2 * Y1, Y3^-1 * Y1 * Y2 * Y3 * Y1 * Y2 * Y3^2 * Y1 * Y3^-1 * Y2 * Y1 * Y3 * Y2 * Y3^2 * Y1 * Y3^-1 * Y2 * Y1 * Y3 * Y2 * Y3 * Y1 * Y3 * Y2 * Y1 * Y2 ] Map:: polytopal non-degenerate R = (1, 97, 2, 98)(3, 99, 9, 105)(4, 100, 12, 108)(5, 101, 14, 110)(6, 102, 15, 111)(7, 103, 18, 114)(8, 104, 20, 116)(10, 106, 24, 120)(11, 107, 26, 122)(13, 109, 19, 115)(16, 112, 34, 130)(17, 113, 36, 132)(21, 117, 41, 137)(22, 118, 37, 133)(23, 119, 40, 136)(25, 121, 44, 140)(27, 123, 32, 128)(28, 124, 51, 147)(29, 125, 52, 148)(30, 126, 33, 129)(31, 127, 53, 149)(35, 131, 56, 152)(38, 134, 63, 159)(39, 135, 64, 160)(42, 138, 60, 156)(43, 139, 57, 153)(45, 141, 55, 151)(46, 142, 67, 163)(47, 143, 68, 164)(48, 144, 54, 150)(49, 145, 69, 165)(50, 146, 70, 166)(58, 154, 75, 171)(59, 155, 76, 172)(61, 157, 77, 173)(62, 158, 78, 174)(65, 161, 81, 177)(66, 162, 82, 178)(71, 167, 87, 183)(72, 168, 88, 184)(73, 169, 89, 185)(74, 170, 90, 186)(79, 175, 95, 191)(80, 176, 96, 192)(83, 179, 92, 188)(84, 180, 91, 187)(85, 181, 93, 189)(86, 182, 94, 190)(193, 289, 195, 291)(194, 290, 198, 294)(196, 292, 203, 299)(197, 293, 202, 298)(199, 295, 209, 305)(200, 296, 208, 304)(201, 297, 213, 309)(204, 300, 219, 315)(205, 301, 217, 313)(206, 302, 222, 318)(207, 303, 223, 319)(210, 306, 229, 325)(211, 307, 227, 323)(212, 308, 232, 328)(214, 310, 235, 331)(215, 311, 234, 330)(216, 312, 237, 333)(218, 314, 240, 336)(220, 316, 242, 338)(221, 317, 241, 337)(224, 320, 247, 343)(225, 321, 246, 342)(226, 322, 249, 345)(228, 324, 252, 348)(230, 326, 254, 350)(231, 327, 253, 349)(233, 329, 248, 344)(236, 332, 245, 341)(238, 334, 258, 354)(239, 335, 257, 353)(243, 339, 260, 356)(244, 340, 259, 355)(250, 346, 266, 362)(251, 347, 265, 361)(255, 351, 268, 364)(256, 352, 267, 363)(261, 357, 273, 369)(262, 358, 274, 370)(263, 359, 275, 371)(264, 360, 276, 372)(269, 365, 281, 377)(270, 366, 282, 378)(271, 367, 283, 379)(272, 368, 284, 380)(277, 373, 288, 384)(278, 374, 287, 383)(279, 375, 286, 382)(280, 376, 285, 381) L = (1, 196)(2, 199)(3, 202)(4, 205)(5, 193)(6, 208)(7, 211)(8, 194)(9, 214)(10, 217)(11, 195)(12, 220)(13, 197)(14, 221)(15, 224)(16, 227)(17, 198)(18, 230)(19, 200)(20, 231)(21, 234)(22, 236)(23, 201)(24, 238)(25, 203)(26, 239)(27, 241)(28, 206)(29, 204)(30, 242)(31, 246)(32, 248)(33, 207)(34, 250)(35, 209)(36, 251)(37, 253)(38, 212)(39, 210)(40, 254)(41, 247)(42, 245)(43, 213)(44, 215)(45, 257)(46, 218)(47, 216)(48, 258)(49, 222)(50, 219)(51, 263)(52, 264)(53, 235)(54, 233)(55, 223)(56, 225)(57, 265)(58, 228)(59, 226)(60, 266)(61, 232)(62, 229)(63, 271)(64, 272)(65, 240)(66, 237)(67, 275)(68, 276)(69, 277)(70, 278)(71, 244)(72, 243)(73, 252)(74, 249)(75, 283)(76, 284)(77, 285)(78, 286)(79, 256)(80, 255)(81, 287)(82, 288)(83, 260)(84, 259)(85, 262)(86, 261)(87, 282)(88, 281)(89, 279)(90, 280)(91, 268)(92, 267)(93, 270)(94, 269)(95, 274)(96, 273)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 4, 48, 4, 48 ) } Outer automorphisms :: reflexible Dual of E23.1027 Graph:: simple bipartite v = 96 e = 192 f = 52 degree seq :: [ 4^96 ] E23.1022 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 24}) Quotient :: dipole Aut^+ = (D8 x S3) : C2 (small group id <96, 118>) Aut = $<192, 1331>$ (small group id <192, 1331>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y3^-1 * Y2)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y1 * Y3^2 * Y1 * Y3^-2, (Y2 * Y1)^4, Y3^-1 * Y1 * Y3^-2 * Y2 * Y1 * Y2 * Y3^-1, (Y1 * Y3 * Y1 * Y2)^2, Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 ] Map:: polytopal non-degenerate R = (1, 97, 2, 98)(3, 99, 9, 105)(4, 100, 12, 108)(5, 101, 14, 110)(6, 102, 16, 112)(7, 103, 19, 115)(8, 104, 21, 117)(10, 106, 26, 122)(11, 107, 28, 124)(13, 109, 20, 116)(15, 111, 22, 118)(17, 113, 40, 136)(18, 114, 42, 138)(23, 119, 37, 133)(24, 120, 48, 144)(25, 121, 44, 140)(27, 123, 43, 139)(29, 125, 41, 137)(30, 126, 39, 135)(31, 127, 57, 153)(32, 128, 58, 154)(33, 129, 51, 147)(34, 130, 38, 134)(35, 131, 59, 155)(36, 132, 54, 150)(45, 141, 66, 162)(46, 142, 67, 163)(47, 143, 60, 156)(49, 145, 68, 164)(50, 146, 63, 159)(52, 148, 70, 166)(53, 149, 71, 167)(55, 151, 72, 168)(56, 152, 73, 169)(61, 157, 79, 175)(62, 158, 80, 176)(64, 160, 81, 177)(65, 161, 82, 178)(69, 165, 87, 183)(74, 170, 85, 181)(75, 171, 86, 182)(76, 172, 83, 179)(77, 173, 84, 180)(78, 174, 92, 188)(88, 184, 93, 189)(89, 185, 94, 190)(90, 186, 95, 191)(91, 187, 96, 192)(193, 289, 195, 291)(194, 290, 198, 294)(196, 292, 203, 299)(197, 293, 202, 298)(199, 295, 210, 306)(200, 296, 209, 305)(201, 297, 215, 311)(204, 300, 222, 318)(205, 301, 221, 317)(206, 302, 226, 322)(207, 303, 219, 315)(208, 304, 229, 325)(211, 307, 236, 332)(212, 308, 235, 331)(213, 309, 240, 336)(214, 310, 233, 329)(216, 312, 239, 335)(217, 313, 242, 338)(218, 314, 243, 339)(220, 316, 246, 342)(223, 319, 244, 340)(224, 320, 248, 344)(225, 321, 230, 326)(227, 323, 247, 343)(228, 324, 231, 327)(232, 328, 252, 348)(234, 330, 255, 351)(237, 333, 253, 349)(238, 334, 257, 353)(241, 337, 256, 352)(245, 341, 261, 357)(249, 345, 264, 360)(250, 346, 263, 359)(251, 347, 262, 358)(254, 350, 270, 366)(258, 354, 273, 369)(259, 355, 272, 368)(260, 356, 271, 367)(265, 361, 279, 375)(266, 362, 283, 379)(267, 363, 282, 378)(268, 364, 281, 377)(269, 365, 280, 376)(274, 370, 284, 380)(275, 371, 288, 384)(276, 372, 287, 383)(277, 373, 286, 382)(278, 374, 285, 381) L = (1, 196)(2, 199)(3, 202)(4, 205)(5, 193)(6, 209)(7, 212)(8, 194)(9, 216)(10, 219)(11, 195)(12, 223)(13, 225)(14, 224)(15, 197)(16, 230)(17, 233)(18, 198)(19, 237)(20, 239)(21, 238)(22, 200)(23, 242)(24, 235)(25, 201)(26, 244)(27, 231)(28, 245)(29, 203)(30, 248)(31, 243)(32, 204)(33, 229)(34, 247)(35, 206)(36, 207)(37, 228)(38, 221)(39, 208)(40, 253)(41, 217)(42, 254)(43, 210)(44, 257)(45, 252)(46, 211)(47, 215)(48, 256)(49, 213)(50, 214)(51, 261)(52, 222)(53, 218)(54, 227)(55, 220)(56, 226)(57, 266)(58, 267)(59, 268)(60, 270)(61, 236)(62, 232)(63, 241)(64, 234)(65, 240)(66, 275)(67, 276)(68, 277)(69, 246)(70, 280)(71, 281)(72, 282)(73, 283)(74, 279)(75, 249)(76, 250)(77, 251)(78, 255)(79, 285)(80, 286)(81, 287)(82, 288)(83, 284)(84, 258)(85, 259)(86, 260)(87, 269)(88, 265)(89, 262)(90, 263)(91, 264)(92, 278)(93, 274)(94, 271)(95, 272)(96, 273)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 4, 48, 4, 48 ) } Outer automorphisms :: reflexible Dual of E23.1028 Graph:: simple bipartite v = 96 e = 192 f = 52 degree seq :: [ 4^96 ] E23.1023 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 24}) Quotient :: dipole Aut^+ = (C8 x S3) : C2 (small group id <96, 123>) Aut = $<192, 1333>$ (small group id <192, 1333>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y3^-1 * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y1 * Y3^2 * Y1 * Y3^-2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2 * Y3 * Y1 * Y3^2 * Y2 * Y1, (Y1 * Y3 * Y1 * Y2)^2, (Y2 * Y1)^4, Y3 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1, Y1 * Y3^-1 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-3 * Y1 * Y3^-1 * Y1 * Y3^-3 * Y1 * Y3^-1 * Y1 * Y3^-3 * Y1 * Y3^-1 * Y1 * Y3^-3 * Y1 * Y3^-1 * Y1 * Y3^-3 ] Map:: polytopal non-degenerate R = (1, 97, 2, 98)(3, 99, 9, 105)(4, 100, 12, 108)(5, 101, 14, 110)(6, 102, 16, 112)(7, 103, 19, 115)(8, 104, 21, 117)(10, 106, 26, 122)(11, 107, 28, 124)(13, 109, 20, 116)(15, 111, 22, 118)(17, 113, 40, 136)(18, 114, 42, 138)(23, 119, 37, 133)(24, 120, 48, 144)(25, 121, 44, 140)(27, 123, 43, 139)(29, 125, 41, 137)(30, 126, 39, 135)(31, 127, 57, 153)(32, 128, 58, 154)(33, 129, 51, 147)(34, 130, 38, 134)(35, 131, 59, 155)(36, 132, 54, 150)(45, 141, 66, 162)(46, 142, 67, 163)(47, 143, 60, 156)(49, 145, 68, 164)(50, 146, 63, 159)(52, 148, 70, 166)(53, 149, 71, 167)(55, 151, 72, 168)(56, 152, 73, 169)(61, 157, 79, 175)(62, 158, 80, 176)(64, 160, 81, 177)(65, 161, 82, 178)(69, 165, 87, 183)(74, 170, 83, 179)(75, 171, 84, 180)(76, 172, 85, 181)(77, 173, 86, 182)(78, 174, 92, 188)(88, 184, 95, 191)(89, 185, 96, 192)(90, 186, 93, 189)(91, 187, 94, 190)(193, 289, 195, 291)(194, 290, 198, 294)(196, 292, 203, 299)(197, 293, 202, 298)(199, 295, 210, 306)(200, 296, 209, 305)(201, 297, 215, 311)(204, 300, 222, 318)(205, 301, 221, 317)(206, 302, 226, 322)(207, 303, 219, 315)(208, 304, 229, 325)(211, 307, 236, 332)(212, 308, 235, 331)(213, 309, 240, 336)(214, 310, 233, 329)(216, 312, 239, 335)(217, 313, 242, 338)(218, 314, 243, 339)(220, 316, 246, 342)(223, 319, 244, 340)(224, 320, 248, 344)(225, 321, 230, 326)(227, 323, 247, 343)(228, 324, 231, 327)(232, 328, 252, 348)(234, 330, 255, 351)(237, 333, 253, 349)(238, 334, 257, 353)(241, 337, 256, 352)(245, 341, 261, 357)(249, 345, 264, 360)(250, 346, 263, 359)(251, 347, 262, 358)(254, 350, 270, 366)(258, 354, 273, 369)(259, 355, 272, 368)(260, 356, 271, 367)(265, 361, 279, 375)(266, 362, 283, 379)(267, 363, 282, 378)(268, 364, 281, 377)(269, 365, 280, 376)(274, 370, 284, 380)(275, 371, 288, 384)(276, 372, 287, 383)(277, 373, 286, 382)(278, 374, 285, 381) L = (1, 196)(2, 199)(3, 202)(4, 205)(5, 193)(6, 209)(7, 212)(8, 194)(9, 216)(10, 219)(11, 195)(12, 223)(13, 225)(14, 224)(15, 197)(16, 230)(17, 233)(18, 198)(19, 237)(20, 239)(21, 238)(22, 200)(23, 242)(24, 235)(25, 201)(26, 244)(27, 231)(28, 245)(29, 203)(30, 248)(31, 243)(32, 204)(33, 229)(34, 247)(35, 206)(36, 207)(37, 228)(38, 221)(39, 208)(40, 253)(41, 217)(42, 254)(43, 210)(44, 257)(45, 252)(46, 211)(47, 215)(48, 256)(49, 213)(50, 214)(51, 261)(52, 222)(53, 218)(54, 227)(55, 220)(56, 226)(57, 266)(58, 267)(59, 268)(60, 270)(61, 236)(62, 232)(63, 241)(64, 234)(65, 240)(66, 275)(67, 276)(68, 277)(69, 246)(70, 280)(71, 281)(72, 282)(73, 283)(74, 279)(75, 249)(76, 250)(77, 251)(78, 255)(79, 285)(80, 286)(81, 287)(82, 288)(83, 284)(84, 258)(85, 259)(86, 260)(87, 269)(88, 265)(89, 262)(90, 263)(91, 264)(92, 278)(93, 274)(94, 271)(95, 272)(96, 273)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 4, 48, 4, 48 ) } Outer automorphisms :: reflexible Dual of E23.1031 Graph:: simple bipartite v = 96 e = 192 f = 52 degree seq :: [ 4^96 ] E23.1024 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 24}) Quotient :: dipole Aut^+ = (D8 x S3) : C2 (small group id <96, 118>) Aut = $<192, 1333>$ (small group id <192, 1333>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y3 * Y2)^2, Y3^4, (R * Y1)^2, (R * Y3)^2, (Y3^-2 * Y1)^2, (R * Y2 * Y3^-1)^2, Y3 * Y1 * Y2 * Y1 * Y3 * Y2 * Y1 * Y2 * Y1 * Y2, Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y1 * Y2, Y2 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y2 * Y1, Y3^-1 * Y2 * Y1 * Y3 * Y2 * Y3^-2 * Y1 * Y2 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y2 * Y1 ] Map:: polytopal non-degenerate R = (1, 97, 2, 98)(3, 99, 9, 105)(4, 100, 12, 108)(5, 101, 14, 110)(6, 102, 15, 111)(7, 103, 18, 114)(8, 104, 20, 116)(10, 106, 24, 120)(11, 107, 26, 122)(13, 109, 19, 115)(16, 112, 34, 130)(17, 113, 36, 132)(21, 117, 41, 137)(22, 118, 44, 140)(23, 119, 46, 142)(25, 121, 45, 141)(27, 123, 51, 147)(28, 124, 54, 150)(29, 125, 55, 151)(30, 126, 56, 152)(31, 127, 57, 153)(32, 128, 60, 156)(33, 129, 62, 158)(35, 131, 61, 157)(37, 133, 67, 163)(38, 134, 70, 166)(39, 135, 71, 167)(40, 136, 72, 168)(42, 138, 66, 162)(43, 139, 63, 159)(47, 143, 59, 155)(48, 144, 68, 164)(49, 145, 69, 165)(50, 146, 58, 154)(52, 148, 64, 160)(53, 149, 65, 161)(73, 169, 84, 180)(74, 170, 91, 187)(75, 171, 88, 184)(76, 172, 95, 191)(77, 173, 86, 182)(78, 174, 90, 186)(79, 175, 89, 185)(80, 176, 85, 181)(81, 177, 93, 189)(82, 178, 92, 188)(83, 179, 94, 190)(87, 183, 96, 192)(193, 289, 195, 291)(194, 290, 198, 294)(196, 292, 203, 299)(197, 293, 202, 298)(199, 295, 209, 305)(200, 296, 208, 304)(201, 297, 213, 309)(204, 300, 219, 315)(205, 301, 217, 313)(206, 302, 222, 318)(207, 303, 223, 319)(210, 306, 229, 325)(211, 307, 227, 323)(212, 308, 232, 328)(214, 310, 235, 331)(215, 311, 234, 330)(216, 312, 239, 335)(218, 314, 242, 338)(220, 316, 245, 341)(221, 317, 244, 340)(224, 320, 251, 347)(225, 321, 250, 346)(226, 322, 255, 351)(228, 324, 258, 354)(230, 326, 261, 357)(231, 327, 260, 356)(233, 329, 265, 361)(236, 332, 269, 365)(237, 333, 268, 364)(238, 334, 272, 368)(240, 336, 274, 370)(241, 337, 273, 369)(243, 339, 266, 362)(246, 342, 271, 367)(247, 343, 270, 366)(248, 344, 267, 363)(249, 345, 276, 372)(252, 348, 280, 376)(253, 349, 279, 375)(254, 350, 283, 379)(256, 352, 285, 381)(257, 353, 284, 380)(259, 355, 277, 373)(262, 358, 282, 378)(263, 359, 281, 377)(264, 360, 278, 374)(275, 371, 287, 383)(286, 382, 288, 384) L = (1, 196)(2, 199)(3, 202)(4, 205)(5, 193)(6, 208)(7, 211)(8, 194)(9, 214)(10, 217)(11, 195)(12, 220)(13, 197)(14, 221)(15, 224)(16, 227)(17, 198)(18, 230)(19, 200)(20, 231)(21, 234)(22, 237)(23, 201)(24, 240)(25, 203)(26, 241)(27, 244)(28, 206)(29, 204)(30, 245)(31, 250)(32, 253)(33, 207)(34, 256)(35, 209)(36, 257)(37, 260)(38, 212)(39, 210)(40, 261)(41, 266)(42, 268)(43, 213)(44, 270)(45, 215)(46, 271)(47, 273)(48, 218)(49, 216)(50, 274)(51, 265)(52, 222)(53, 219)(54, 272)(55, 269)(56, 275)(57, 277)(58, 279)(59, 223)(60, 281)(61, 225)(62, 282)(63, 284)(64, 228)(65, 226)(66, 285)(67, 276)(68, 232)(69, 229)(70, 283)(71, 280)(72, 286)(73, 248)(74, 287)(75, 233)(76, 235)(77, 246)(78, 238)(79, 236)(80, 247)(81, 242)(82, 239)(83, 243)(84, 264)(85, 288)(86, 249)(87, 251)(88, 262)(89, 254)(90, 252)(91, 263)(92, 258)(93, 255)(94, 259)(95, 267)(96, 278)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 4, 48, 4, 48 ) } Outer automorphisms :: reflexible Dual of E23.1029 Graph:: simple bipartite v = 96 e = 192 f = 52 degree seq :: [ 4^96 ] E23.1025 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 24}) Quotient :: dipole Aut^+ = (C8 x S3) : C2 (small group id <96, 123>) Aut = $<192, 1333>$ (small group id <192, 1333>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^4, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y3 * Y1 * Y3^-2 * Y1 * Y3, Y3^-1 * Y1 * Y3^2 * Y1 * Y3^-1, (R * Y2 * Y3^-1)^2, Y3 * Y1 * Y3 * Y2 * Y1 * Y3 * Y1 * Y3^-1 * Y2 * Y1, Y3 * Y1 * Y2 * Y1 * Y3 * Y2 * Y1 * Y2 * Y1 * Y2, Y2 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y2 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1, (Y3^-1 * Y1)^24 ] Map:: polytopal non-degenerate R = (1, 97, 2, 98)(3, 99, 9, 105)(4, 100, 12, 108)(5, 101, 14, 110)(6, 102, 15, 111)(7, 103, 18, 114)(8, 104, 20, 116)(10, 106, 24, 120)(11, 107, 26, 122)(13, 109, 19, 115)(16, 112, 34, 130)(17, 113, 36, 132)(21, 117, 41, 137)(22, 118, 44, 140)(23, 119, 46, 142)(25, 121, 45, 141)(27, 123, 51, 147)(28, 124, 54, 150)(29, 125, 55, 151)(30, 126, 56, 152)(31, 127, 57, 153)(32, 128, 60, 156)(33, 129, 62, 158)(35, 131, 61, 157)(37, 133, 67, 163)(38, 134, 70, 166)(39, 135, 71, 167)(40, 136, 72, 168)(42, 138, 66, 162)(43, 139, 63, 159)(47, 143, 59, 155)(48, 144, 68, 164)(49, 145, 69, 165)(50, 146, 58, 154)(52, 148, 64, 160)(53, 149, 65, 161)(73, 169, 94, 190)(74, 170, 88, 184)(75, 171, 91, 187)(76, 172, 95, 191)(77, 173, 85, 181)(78, 174, 89, 185)(79, 175, 90, 186)(80, 176, 86, 182)(81, 177, 93, 189)(82, 178, 92, 188)(83, 179, 84, 180)(87, 183, 96, 192)(193, 289, 195, 291)(194, 290, 198, 294)(196, 292, 203, 299)(197, 293, 202, 298)(199, 295, 209, 305)(200, 296, 208, 304)(201, 297, 213, 309)(204, 300, 219, 315)(205, 301, 217, 313)(206, 302, 222, 318)(207, 303, 223, 319)(210, 306, 229, 325)(211, 307, 227, 323)(212, 308, 232, 328)(214, 310, 235, 331)(215, 311, 234, 330)(216, 312, 239, 335)(218, 314, 242, 338)(220, 316, 245, 341)(221, 317, 244, 340)(224, 320, 251, 347)(225, 321, 250, 346)(226, 322, 255, 351)(228, 324, 258, 354)(230, 326, 261, 357)(231, 327, 260, 356)(233, 329, 265, 361)(236, 332, 269, 365)(237, 333, 268, 364)(238, 334, 272, 368)(240, 336, 274, 370)(241, 337, 273, 369)(243, 339, 266, 362)(246, 342, 271, 367)(247, 343, 270, 366)(248, 344, 267, 363)(249, 345, 276, 372)(252, 348, 280, 376)(253, 349, 279, 375)(254, 350, 283, 379)(256, 352, 285, 381)(257, 353, 284, 380)(259, 355, 277, 373)(262, 358, 282, 378)(263, 359, 281, 377)(264, 360, 278, 374)(275, 371, 287, 383)(286, 382, 288, 384) L = (1, 196)(2, 199)(3, 202)(4, 205)(5, 193)(6, 208)(7, 211)(8, 194)(9, 214)(10, 217)(11, 195)(12, 220)(13, 197)(14, 221)(15, 224)(16, 227)(17, 198)(18, 230)(19, 200)(20, 231)(21, 234)(22, 237)(23, 201)(24, 240)(25, 203)(26, 241)(27, 244)(28, 206)(29, 204)(30, 245)(31, 250)(32, 253)(33, 207)(34, 256)(35, 209)(36, 257)(37, 260)(38, 212)(39, 210)(40, 261)(41, 266)(42, 268)(43, 213)(44, 270)(45, 215)(46, 271)(47, 273)(48, 218)(49, 216)(50, 274)(51, 265)(52, 222)(53, 219)(54, 272)(55, 269)(56, 275)(57, 277)(58, 279)(59, 223)(60, 281)(61, 225)(62, 282)(63, 284)(64, 228)(65, 226)(66, 285)(67, 276)(68, 232)(69, 229)(70, 283)(71, 280)(72, 286)(73, 248)(74, 287)(75, 233)(76, 235)(77, 246)(78, 238)(79, 236)(80, 247)(81, 242)(82, 239)(83, 243)(84, 264)(85, 288)(86, 249)(87, 251)(88, 262)(89, 254)(90, 252)(91, 263)(92, 258)(93, 255)(94, 259)(95, 267)(96, 278)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 4, 48, 4, 48 ) } Outer automorphisms :: reflexible Dual of E23.1030 Graph:: simple bipartite v = 96 e = 192 f = 52 degree seq :: [ 4^96 ] E23.1026 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 24}) Quotient :: dipole Aut^+ = (C8 x S3) : C2 (small group id <96, 123>) Aut = $<192, 1336>$ (small group id <192, 1336>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^4, (R * Y1)^2, (R * Y3)^2, (Y2 * Y3)^2, (Y1 * Y3^-2)^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y1 * Y3 * Y2 * Y3^-1 * Y2 * Y1 * Y3^-1, Y1 * Y3 * Y1 * Y2 * Y1 * Y3^-1 * Y1 * Y2, Y2 * Y3 * Y1 * Y3 * Y1 * Y2 * Y1 * Y3 * Y1 * Y3^-1, Y2 * Y1 * Y3 * Y2 * Y3^-1 * Y1 * Y2 * Y1 * Y2 * Y1, Y1 * Y3 * Y1 * Y2 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y2 * Y3^-1 * Y1 * Y3^-1, Y2 * Y3^-1 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y2 * Y1, Y1 * Y3 * Y2 * Y3^-1 * Y1 * Y3^-2 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y3^-1 * Y2 * Y1 * Y2 * Y1 * Y2 ] Map:: polytopal non-degenerate R = (1, 97, 2, 98)(3, 99, 9, 105)(4, 100, 12, 108)(5, 101, 14, 110)(6, 102, 15, 111)(7, 103, 18, 114)(8, 104, 20, 116)(10, 106, 24, 120)(11, 107, 26, 122)(13, 109, 19, 115)(16, 112, 34, 130)(17, 113, 36, 132)(21, 117, 41, 137)(22, 118, 37, 133)(23, 119, 40, 136)(25, 121, 44, 140)(27, 123, 32, 128)(28, 124, 51, 147)(29, 125, 52, 148)(30, 126, 33, 129)(31, 127, 53, 149)(35, 131, 56, 152)(38, 134, 63, 159)(39, 135, 64, 160)(42, 138, 60, 156)(43, 139, 57, 153)(45, 141, 55, 151)(46, 142, 67, 163)(47, 143, 68, 164)(48, 144, 54, 150)(49, 145, 69, 165)(50, 146, 70, 166)(58, 154, 75, 171)(59, 155, 76, 172)(61, 157, 77, 173)(62, 158, 78, 174)(65, 161, 81, 177)(66, 162, 82, 178)(71, 167, 87, 183)(72, 168, 88, 184)(73, 169, 89, 185)(74, 170, 90, 186)(79, 175, 95, 191)(80, 176, 96, 192)(83, 179, 91, 187)(84, 180, 92, 188)(85, 181, 94, 190)(86, 182, 93, 189)(193, 289, 195, 291)(194, 290, 198, 294)(196, 292, 203, 299)(197, 293, 202, 298)(199, 295, 209, 305)(200, 296, 208, 304)(201, 297, 213, 309)(204, 300, 219, 315)(205, 301, 217, 313)(206, 302, 222, 318)(207, 303, 223, 319)(210, 306, 229, 325)(211, 307, 227, 323)(212, 308, 232, 328)(214, 310, 235, 331)(215, 311, 234, 330)(216, 312, 237, 333)(218, 314, 240, 336)(220, 316, 242, 338)(221, 317, 241, 337)(224, 320, 247, 343)(225, 321, 246, 342)(226, 322, 249, 345)(228, 324, 252, 348)(230, 326, 254, 350)(231, 327, 253, 349)(233, 329, 248, 344)(236, 332, 245, 341)(238, 334, 258, 354)(239, 335, 257, 353)(243, 339, 260, 356)(244, 340, 259, 355)(250, 346, 266, 362)(251, 347, 265, 361)(255, 351, 268, 364)(256, 352, 267, 363)(261, 357, 273, 369)(262, 358, 274, 370)(263, 359, 275, 371)(264, 360, 276, 372)(269, 365, 281, 377)(270, 366, 282, 378)(271, 367, 283, 379)(272, 368, 284, 380)(277, 373, 287, 383)(278, 374, 288, 384)(279, 375, 285, 381)(280, 376, 286, 382) L = (1, 196)(2, 199)(3, 202)(4, 205)(5, 193)(6, 208)(7, 211)(8, 194)(9, 214)(10, 217)(11, 195)(12, 220)(13, 197)(14, 221)(15, 224)(16, 227)(17, 198)(18, 230)(19, 200)(20, 231)(21, 234)(22, 236)(23, 201)(24, 238)(25, 203)(26, 239)(27, 241)(28, 206)(29, 204)(30, 242)(31, 246)(32, 248)(33, 207)(34, 250)(35, 209)(36, 251)(37, 253)(38, 212)(39, 210)(40, 254)(41, 247)(42, 245)(43, 213)(44, 215)(45, 257)(46, 218)(47, 216)(48, 258)(49, 222)(50, 219)(51, 263)(52, 264)(53, 235)(54, 233)(55, 223)(56, 225)(57, 265)(58, 228)(59, 226)(60, 266)(61, 232)(62, 229)(63, 271)(64, 272)(65, 240)(66, 237)(67, 275)(68, 276)(69, 277)(70, 278)(71, 244)(72, 243)(73, 252)(74, 249)(75, 283)(76, 284)(77, 285)(78, 286)(79, 256)(80, 255)(81, 288)(82, 287)(83, 260)(84, 259)(85, 262)(86, 261)(87, 281)(88, 282)(89, 280)(90, 279)(91, 268)(92, 267)(93, 270)(94, 269)(95, 273)(96, 274)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 4, 48, 4, 48 ) } Outer automorphisms :: reflexible Dual of E23.1032 Graph:: simple bipartite v = 96 e = 192 f = 52 degree seq :: [ 4^96 ] E23.1027 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 24}) Quotient :: dipole Aut^+ = (D8 x S3) : C2 (small group id <96, 118>) Aut = $<192, 1331>$ (small group id <192, 1331>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3 * Y2)^2, (Y3 * Y1^-1)^2, Y3^4, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y2 * Y1^-2 * R * Y2 * R * Y1^-1, Y3^-1 * Y2 * Y1^2 * Y3 * Y2 * Y1^-2, Y2 * Y1^5 * Y2 * Y1^-1, Y3^-1 * Y1^2 * Y2 * Y3 * Y1^-2 * Y2 ] Map:: polytopal non-degenerate R = (1, 97, 2, 98, 7, 103, 20, 116, 47, 143, 30, 126, 57, 153, 85, 181, 96, 192, 93, 189, 65, 161, 40, 136, 16, 112, 28, 124, 55, 151, 84, 180, 95, 191, 94, 190, 72, 168, 35, 131, 62, 158, 46, 142, 19, 115, 5, 101)(3, 99, 11, 107, 29, 125, 64, 160, 26, 122, 8, 104, 24, 120, 56, 152, 88, 184, 53, 149, 21, 117, 51, 147, 34, 130, 70, 166, 45, 141, 48, 144, 81, 177, 61, 157, 42, 138, 17, 113, 41, 137, 74, 170, 37, 133, 13, 109)(4, 100, 15, 111, 38, 134, 75, 171, 91, 187, 73, 169, 90, 186, 68, 164, 80, 176, 49, 145, 23, 119, 9, 105, 6, 102, 18, 114, 44, 140, 78, 174, 92, 188, 71, 167, 89, 185, 69, 165, 79, 175, 50, 146, 22, 118, 10, 106)(12, 108, 33, 129, 54, 150, 87, 183, 77, 173, 43, 139, 59, 155, 25, 121, 60, 156, 83, 179, 67, 163, 31, 127, 14, 110, 36, 132, 52, 148, 86, 182, 76, 172, 39, 135, 58, 154, 27, 123, 63, 159, 82, 178, 66, 162, 32, 128)(193, 289, 195, 291)(194, 290, 200, 296)(196, 292, 206, 302)(197, 293, 209, 305)(198, 294, 204, 300)(199, 295, 213, 309)(201, 297, 219, 315)(202, 298, 217, 313)(203, 299, 222, 318)(205, 301, 227, 323)(207, 303, 231, 327)(208, 304, 226, 322)(210, 306, 235, 331)(211, 307, 237, 333)(212, 308, 240, 336)(214, 310, 246, 342)(215, 311, 244, 340)(216, 312, 249, 345)(218, 314, 254, 350)(220, 316, 253, 349)(221, 317, 257, 353)(223, 319, 261, 357)(224, 320, 260, 356)(225, 321, 263, 359)(228, 324, 265, 361)(229, 325, 247, 343)(230, 326, 258, 354)(232, 328, 248, 344)(233, 329, 239, 335)(234, 330, 264, 360)(236, 332, 259, 355)(238, 334, 245, 341)(241, 337, 275, 371)(242, 338, 274, 370)(243, 339, 277, 373)(250, 346, 282, 378)(251, 347, 281, 377)(252, 348, 283, 379)(255, 351, 284, 380)(256, 352, 276, 372)(262, 358, 286, 382)(266, 362, 285, 381)(267, 363, 279, 375)(268, 364, 271, 367)(269, 365, 272, 368)(270, 366, 278, 374)(273, 369, 288, 384)(280, 376, 287, 383) L = (1, 196)(2, 201)(3, 204)(4, 208)(5, 210)(6, 193)(7, 214)(8, 217)(9, 220)(10, 194)(11, 223)(12, 226)(13, 228)(14, 195)(15, 197)(16, 198)(17, 231)(18, 232)(19, 230)(20, 241)(21, 244)(22, 247)(23, 199)(24, 250)(25, 253)(26, 255)(27, 200)(28, 202)(29, 258)(30, 260)(31, 262)(32, 203)(33, 205)(34, 206)(35, 263)(36, 243)(37, 246)(38, 257)(39, 248)(40, 207)(41, 269)(42, 251)(43, 209)(44, 211)(45, 259)(46, 270)(47, 271)(48, 274)(49, 276)(50, 212)(51, 225)(52, 229)(53, 279)(54, 213)(55, 215)(56, 235)(57, 281)(58, 234)(59, 216)(60, 218)(61, 219)(62, 283)(63, 273)(64, 275)(65, 236)(66, 237)(67, 221)(68, 286)(69, 222)(70, 224)(71, 277)(72, 282)(73, 227)(74, 278)(75, 238)(76, 233)(77, 280)(78, 285)(79, 287)(80, 239)(81, 252)(82, 256)(83, 240)(84, 242)(85, 265)(86, 245)(87, 266)(88, 268)(89, 264)(90, 249)(91, 288)(92, 254)(93, 267)(94, 261)(95, 272)(96, 284)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 4^4 ), ( 4^48 ) } Outer automorphisms :: reflexible Dual of E23.1021 Graph:: simple bipartite v = 52 e = 192 f = 96 degree seq :: [ 4^48, 48^4 ] E23.1028 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 24}) Quotient :: dipole Aut^+ = (D8 x S3) : C2 (small group id <96, 118>) Aut = $<192, 1331>$ (small group id <192, 1331>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3^-1 * Y2)^2, (R * Y1)^2, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, (Y1^2 * Y2)^2, (Y1^-2 * Y3)^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-2, (Y1 * Y2 * Y1)^2, Y3 * Y1^-1 * Y3^-3 * Y1^-1, (Y1^-1 * Y3 * Y1^-1)^2, (Y2 * Y1^-1)^4, Y3^-1 * Y1 * Y3^-1 * Y2 * R * Y2 * Y1^-1 * R, Y1 * Y2 * Y3^-1 * Y1 * Y2 * Y1^-1 * Y3^-1 * Y1, Y3^-1 * Y2 * Y1^-1 * Y2 * Y3^-1 * Y1^-3, Y1 * Y2 * Y1^-1 * R * Y2 * Y1^-1 * R * Y1, Y2 * Y3^3 * Y2 * Y1^-1 * Y3 * Y1^-1, Y1^-2 * Y2 * Y1 * Y3^-1 * Y2 * Y3 * Y1^-1, Y1^24 ] Map:: polytopal non-degenerate R = (1, 97, 2, 98, 7, 103, 23, 119, 57, 153, 88, 184, 85, 181, 48, 144, 22, 118, 34, 130, 66, 162, 36, 132, 67, 163, 42, 138, 73, 169, 49, 145, 16, 112, 31, 127, 64, 160, 92, 188, 87, 183, 55, 151, 20, 116, 5, 101)(3, 99, 11, 107, 35, 131, 71, 167, 95, 191, 86, 182, 94, 190, 81, 177, 45, 141, 58, 154, 29, 125, 8, 104, 27, 123, 18, 114, 51, 147, 82, 178, 40, 136, 79, 175, 96, 192, 76, 172, 89, 185, 62, 158, 24, 120, 13, 109)(4, 100, 15, 111, 46, 142, 83, 179, 90, 186, 60, 156, 32, 128, 9, 105, 6, 102, 21, 117, 54, 150, 84, 180, 91, 187, 65, 161, 25, 121, 10, 106, 33, 129, 19, 115, 53, 149, 80, 176, 93, 189, 59, 155, 26, 122, 17, 113)(12, 108, 39, 135, 77, 173, 52, 148, 72, 168, 28, 124, 70, 166, 37, 133, 14, 110, 44, 140, 61, 157, 56, 152, 68, 164, 30, 126, 75, 171, 38, 134, 78, 174, 43, 139, 63, 159, 47, 143, 69, 165, 50, 146, 74, 170, 41, 137)(193, 289, 195, 291)(194, 290, 200, 296)(196, 292, 206, 302)(197, 293, 210, 306)(198, 294, 204, 300)(199, 295, 216, 312)(201, 297, 222, 318)(202, 298, 220, 316)(203, 299, 228, 324)(205, 301, 234, 330)(207, 303, 239, 335)(208, 304, 237, 333)(209, 305, 242, 338)(211, 307, 244, 340)(212, 308, 227, 323)(213, 309, 248, 344)(214, 310, 232, 328)(215, 311, 250, 346)(217, 313, 255, 351)(218, 314, 253, 349)(219, 315, 259, 355)(221, 317, 265, 361)(223, 319, 268, 364)(224, 320, 269, 365)(225, 321, 270, 366)(226, 322, 263, 359)(229, 325, 257, 353)(230, 326, 252, 348)(231, 327, 272, 368)(233, 329, 251, 347)(235, 331, 275, 371)(236, 332, 276, 372)(238, 334, 262, 358)(240, 336, 278, 374)(241, 337, 254, 350)(243, 339, 258, 354)(245, 341, 267, 363)(246, 342, 266, 362)(247, 343, 274, 370)(249, 345, 281, 377)(256, 352, 286, 382)(260, 356, 285, 381)(261, 357, 283, 379)(264, 360, 282, 378)(271, 367, 284, 380)(273, 369, 280, 376)(277, 373, 288, 384)(279, 375, 287, 383) L = (1, 196)(2, 201)(3, 204)(4, 208)(5, 211)(6, 193)(7, 217)(8, 220)(9, 223)(10, 194)(11, 229)(12, 232)(13, 235)(14, 195)(15, 197)(16, 225)(17, 226)(18, 239)(19, 241)(20, 246)(21, 240)(22, 198)(23, 251)(24, 253)(25, 256)(26, 199)(27, 260)(28, 263)(29, 266)(30, 200)(31, 209)(32, 258)(33, 214)(34, 202)(35, 267)(36, 252)(37, 271)(38, 203)(39, 205)(40, 270)(41, 250)(42, 272)(43, 274)(44, 273)(45, 206)(46, 277)(47, 278)(48, 207)(49, 213)(50, 268)(51, 269)(52, 210)(53, 212)(54, 265)(55, 275)(56, 254)(57, 282)(58, 230)(59, 284)(60, 215)(61, 243)(62, 244)(63, 216)(64, 224)(65, 228)(66, 218)(67, 283)(68, 287)(69, 219)(70, 221)(71, 242)(72, 281)(73, 238)(74, 227)(75, 288)(76, 222)(77, 286)(78, 237)(79, 233)(80, 280)(81, 231)(82, 236)(83, 234)(84, 247)(85, 245)(86, 248)(87, 285)(88, 276)(89, 261)(90, 279)(91, 249)(92, 257)(93, 259)(94, 255)(95, 264)(96, 262)(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) :: { ( 4^4 ), ( 4^48 ) } Outer automorphisms :: reflexible Dual of E23.1022 Graph:: simple bipartite v = 52 e = 192 f = 96 degree seq :: [ 4^48, 48^4 ] E23.1029 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 24}) Quotient :: dipole Aut^+ = (D8 x S3) : C2 (small group id <96, 118>) Aut = $<192, 1333>$ (small group id <192, 1333>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3 * Y1)^2, (R * Y3)^2, (Y3 * Y1^-1)^2, Y3^4, (Y3 * Y2)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1, Y1^-1 * Y3^-1 * Y2 * Y1^-1 * Y3^-1 * Y1 * Y2 * Y1^-1, Y2 * Y1^2 * Y3 * Y2 * Y3^-1 * Y1^-2, (Y1^3 * Y2)^2, Y1^-7 * Y2 * Y1 * Y2 ] Map:: polytopal non-degenerate R = (1, 97, 2, 98, 7, 103, 20, 116, 47, 143, 81, 177, 67, 163, 30, 126, 57, 153, 89, 185, 75, 171, 40, 136, 16, 112, 28, 124, 55, 151, 88, 184, 72, 168, 35, 131, 62, 158, 92, 188, 80, 176, 46, 142, 19, 115, 5, 101)(3, 99, 11, 107, 29, 125, 65, 161, 82, 178, 64, 160, 26, 122, 8, 104, 24, 120, 56, 152, 45, 141, 71, 167, 34, 130, 53, 149, 21, 117, 51, 147, 42, 138, 17, 113, 41, 137, 61, 157, 86, 182, 48, 144, 37, 133, 13, 109)(4, 100, 15, 111, 38, 134, 76, 172, 94, 190, 66, 162, 95, 191, 73, 169, 84, 180, 49, 145, 23, 119, 9, 105, 6, 102, 18, 114, 44, 140, 79, 175, 93, 189, 68, 164, 96, 192, 70, 166, 83, 179, 50, 146, 22, 118, 10, 106)(12, 108, 33, 129, 69, 165, 87, 183, 59, 155, 25, 121, 60, 156, 43, 139, 78, 174, 91, 187, 52, 148, 31, 127, 14, 110, 36, 132, 74, 170, 85, 181, 58, 154, 27, 123, 63, 159, 39, 135, 77, 173, 90, 186, 54, 150, 32, 128)(193, 289, 195, 291)(194, 290, 200, 296)(196, 292, 206, 302)(197, 293, 209, 305)(198, 294, 204, 300)(199, 295, 213, 309)(201, 297, 219, 315)(202, 298, 217, 313)(203, 299, 222, 318)(205, 301, 227, 323)(207, 303, 231, 327)(208, 304, 226, 322)(210, 306, 235, 331)(211, 307, 237, 333)(212, 308, 240, 336)(214, 310, 246, 342)(215, 311, 244, 340)(216, 312, 249, 345)(218, 314, 254, 350)(220, 316, 253, 349)(221, 317, 247, 343)(223, 319, 260, 356)(224, 320, 258, 354)(225, 321, 262, 358)(228, 324, 265, 361)(229, 325, 267, 363)(230, 326, 261, 357)(232, 328, 256, 352)(233, 329, 259, 355)(234, 330, 264, 360)(236, 332, 266, 362)(238, 334, 257, 353)(239, 335, 274, 370)(241, 337, 279, 375)(242, 338, 277, 373)(243, 339, 281, 377)(245, 341, 284, 380)(248, 344, 280, 376)(250, 346, 286, 382)(251, 347, 285, 381)(252, 348, 287, 383)(255, 351, 288, 384)(263, 359, 273, 369)(268, 364, 283, 379)(269, 365, 276, 372)(270, 366, 275, 371)(271, 367, 282, 378)(272, 368, 278, 374) L = (1, 196)(2, 201)(3, 204)(4, 208)(5, 210)(6, 193)(7, 214)(8, 217)(9, 220)(10, 194)(11, 223)(12, 226)(13, 228)(14, 195)(15, 197)(16, 198)(17, 231)(18, 232)(19, 230)(20, 241)(21, 244)(22, 247)(23, 199)(24, 250)(25, 253)(26, 255)(27, 200)(28, 202)(29, 246)(30, 258)(31, 245)(32, 203)(33, 205)(34, 206)(35, 262)(36, 263)(37, 261)(38, 267)(39, 256)(40, 207)(41, 252)(42, 270)(43, 209)(44, 211)(45, 266)(46, 271)(47, 275)(48, 277)(49, 280)(50, 212)(51, 282)(52, 221)(53, 224)(54, 213)(55, 215)(56, 279)(57, 285)(58, 278)(59, 216)(60, 218)(61, 219)(62, 287)(63, 233)(64, 235)(65, 283)(66, 284)(67, 288)(68, 222)(69, 237)(70, 273)(71, 225)(72, 276)(73, 227)(74, 229)(75, 236)(76, 238)(77, 234)(78, 274)(79, 281)(80, 286)(81, 265)(82, 269)(83, 264)(84, 239)(85, 248)(86, 251)(87, 240)(88, 242)(89, 268)(90, 257)(91, 243)(92, 260)(93, 272)(94, 249)(95, 259)(96, 254)(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) :: { ( 4^4 ), ( 4^48 ) } Outer automorphisms :: reflexible Dual of E23.1024 Graph:: simple bipartite v = 52 e = 192 f = 96 degree seq :: [ 4^48, 48^4 ] E23.1030 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 24}) Quotient :: dipole Aut^+ = (C8 x S3) : C2 (small group id <96, 123>) Aut = $<192, 1333>$ (small group id <192, 1333>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3 * Y1)^2, (R * Y3)^2, (Y3 * Y1^-1)^2, (R * Y1)^2, (Y3 * Y2)^2, Y3^4, Y1 * Y3^2 * Y1^-1 * Y3^-2, (R * Y2 * Y3^-1)^2, Y2 * Y1^2 * Y3 * Y2 * Y3^-1 * Y1^-2, Y1^-4 * Y2 * Y1^-1 * Y2 * Y1^-1, Y1^-1 * Y3^-1 * Y2 * Y1^-1 * Y3^-1 * Y1 * Y2 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 97, 2, 98, 7, 103, 20, 116, 47, 143, 35, 131, 62, 158, 88, 184, 96, 192, 93, 189, 74, 170, 40, 136, 16, 112, 28, 124, 55, 151, 84, 180, 95, 191, 94, 190, 67, 163, 30, 126, 57, 153, 46, 142, 19, 115, 5, 101)(3, 99, 11, 107, 29, 125, 65, 161, 42, 138, 17, 113, 41, 137, 61, 157, 82, 178, 48, 144, 45, 141, 71, 167, 34, 130, 53, 149, 21, 117, 51, 147, 85, 181, 64, 160, 26, 122, 8, 104, 24, 120, 56, 152, 37, 133, 13, 109)(4, 100, 15, 111, 38, 134, 75, 171, 89, 185, 68, 164, 92, 188, 70, 166, 80, 176, 49, 145, 23, 119, 9, 105, 6, 102, 18, 114, 44, 140, 78, 174, 90, 186, 66, 162, 91, 187, 72, 168, 79, 175, 50, 146, 22, 118, 10, 106)(12, 108, 33, 129, 69, 165, 81, 177, 58, 154, 27, 123, 63, 159, 39, 135, 76, 172, 87, 183, 52, 148, 31, 127, 14, 110, 36, 132, 73, 169, 83, 179, 59, 155, 25, 121, 60, 156, 43, 139, 77, 173, 86, 182, 54, 150, 32, 128)(193, 289, 195, 291)(194, 290, 200, 296)(196, 292, 206, 302)(197, 293, 209, 305)(198, 294, 204, 300)(199, 295, 213, 309)(201, 297, 219, 315)(202, 298, 217, 313)(203, 299, 222, 318)(205, 301, 227, 323)(207, 303, 231, 327)(208, 304, 226, 322)(210, 306, 235, 331)(211, 307, 237, 333)(212, 308, 240, 336)(214, 310, 246, 342)(215, 311, 244, 340)(216, 312, 249, 345)(218, 314, 254, 350)(220, 316, 253, 349)(221, 317, 247, 343)(223, 319, 260, 356)(224, 320, 258, 354)(225, 321, 262, 358)(228, 324, 264, 360)(229, 325, 266, 362)(230, 326, 261, 357)(232, 328, 256, 352)(233, 329, 259, 355)(234, 330, 239, 335)(236, 332, 265, 361)(238, 334, 243, 339)(241, 337, 275, 371)(242, 338, 273, 369)(245, 341, 280, 376)(248, 344, 276, 372)(250, 346, 282, 378)(251, 347, 281, 377)(252, 348, 283, 379)(255, 351, 284, 380)(257, 353, 285, 381)(263, 359, 286, 382)(267, 363, 278, 374)(268, 364, 271, 367)(269, 365, 272, 368)(270, 366, 279, 375)(274, 370, 288, 384)(277, 373, 287, 383) L = (1, 196)(2, 201)(3, 204)(4, 208)(5, 210)(6, 193)(7, 214)(8, 217)(9, 220)(10, 194)(11, 223)(12, 226)(13, 228)(14, 195)(15, 197)(16, 198)(17, 231)(18, 232)(19, 230)(20, 241)(21, 244)(22, 247)(23, 199)(24, 250)(25, 253)(26, 255)(27, 200)(28, 202)(29, 246)(30, 258)(31, 245)(32, 203)(33, 205)(34, 206)(35, 262)(36, 263)(37, 261)(38, 266)(39, 256)(40, 207)(41, 252)(42, 269)(43, 209)(44, 211)(45, 265)(46, 270)(47, 271)(48, 273)(49, 276)(50, 212)(51, 278)(52, 221)(53, 224)(54, 213)(55, 215)(56, 275)(57, 281)(58, 274)(59, 216)(60, 218)(61, 219)(62, 283)(63, 233)(64, 235)(65, 279)(66, 280)(67, 284)(68, 222)(69, 237)(70, 286)(71, 225)(72, 227)(73, 229)(74, 236)(75, 238)(76, 234)(77, 277)(78, 285)(79, 287)(80, 239)(81, 248)(82, 251)(83, 240)(84, 242)(85, 268)(86, 257)(87, 243)(88, 260)(89, 288)(90, 249)(91, 259)(92, 254)(93, 267)(94, 264)(95, 272)(96, 282)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 4^4 ), ( 4^48 ) } Outer automorphisms :: reflexible Dual of E23.1025 Graph:: simple bipartite v = 52 e = 192 f = 96 degree seq :: [ 4^48, 48^4 ] E23.1031 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 24}) Quotient :: dipole Aut^+ = (C8 x S3) : C2 (small group id <96, 123>) Aut = $<192, 1333>$ (small group id <192, 1333>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3^-1 * Y1^-1)^2, (R * Y1)^2, (R * Y3)^2, (Y2 * Y3)^2, Y3^-1 * Y1 * Y3^-1 * Y2 * Y1^-1 * Y2, Y3^-1 * Y1^-1 * Y2 * Y3 * Y2 * Y1^-1, Y3^-1 * Y2 * Y1 * Y3 * Y1 * Y2, Y3^2 * Y1 * Y3^-2 * Y1^-1, (Y1 * Y2 * Y1)^2, (R * Y2 * Y3^-1)^2, Y2 * Y1 * Y3^-1 * Y2 * Y1^-1 * Y3, Y3^-1 * Y1^-1 * Y2 * R * Y1 * Y2 * R * Y3^-1, Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1, Y1^2 * Y3^-2 * Y1^4, Y3 * Y1^4 * Y3 * Y1^-2, Y3^8 ] Map:: polytopal non-degenerate R = (1, 97, 2, 98, 7, 103, 23, 119, 56, 152, 49, 145, 16, 112, 31, 127, 63, 159, 91, 187, 80, 176, 36, 132, 67, 163, 42, 138, 72, 168, 94, 190, 85, 181, 47, 143, 22, 118, 34, 130, 66, 162, 54, 150, 20, 116, 5, 101)(3, 99, 11, 107, 35, 131, 77, 173, 93, 189, 74, 170, 40, 136, 81, 177, 89, 185, 57, 153, 29, 125, 8, 104, 27, 123, 18, 114, 51, 147, 86, 182, 96, 192, 71, 167, 44, 140, 83, 179, 87, 183, 61, 157, 24, 120, 13, 109)(4, 100, 15, 111, 45, 141, 58, 154, 26, 122, 65, 161, 48, 144, 19, 115, 52, 148, 64, 160, 25, 121, 10, 106, 33, 129, 76, 172, 53, 149, 75, 171, 32, 128, 9, 105, 6, 102, 21, 117, 55, 151, 59, 155, 50, 146, 17, 113)(12, 108, 39, 135, 73, 169, 90, 186, 79, 175, 46, 142, 69, 165, 43, 139, 62, 158, 88, 184, 78, 174, 38, 134, 68, 164, 30, 126, 60, 156, 92, 188, 82, 178, 37, 133, 14, 110, 28, 124, 70, 166, 95, 191, 84, 180, 41, 137)(193, 289, 195, 291)(194, 290, 200, 296)(196, 292, 206, 302)(197, 293, 210, 306)(198, 294, 204, 300)(199, 295, 216, 312)(201, 297, 222, 318)(202, 298, 220, 316)(203, 299, 228, 324)(205, 301, 234, 330)(207, 303, 238, 334)(208, 304, 236, 332)(209, 305, 235, 331)(211, 307, 233, 329)(212, 308, 227, 323)(213, 309, 230, 326)(214, 310, 232, 328)(215, 311, 249, 345)(217, 313, 254, 350)(218, 314, 252, 348)(219, 315, 259, 355)(221, 317, 264, 360)(223, 319, 266, 362)(224, 320, 265, 361)(225, 321, 261, 357)(226, 322, 263, 359)(229, 325, 268, 364)(231, 327, 257, 353)(237, 333, 274, 370)(239, 335, 275, 371)(240, 336, 260, 356)(241, 337, 273, 369)(242, 338, 262, 358)(243, 339, 272, 368)(244, 340, 270, 366)(245, 341, 271, 367)(246, 342, 278, 374)(247, 343, 276, 372)(248, 344, 279, 375)(250, 346, 282, 378)(251, 347, 280, 376)(253, 349, 286, 382)(255, 351, 288, 384)(256, 352, 287, 383)(258, 354, 285, 381)(267, 363, 284, 380)(269, 365, 283, 379)(277, 373, 281, 377) L = (1, 196)(2, 201)(3, 204)(4, 208)(5, 211)(6, 193)(7, 217)(8, 220)(9, 223)(10, 194)(11, 229)(12, 232)(13, 235)(14, 195)(15, 197)(16, 240)(17, 234)(18, 238)(19, 241)(20, 245)(21, 239)(22, 198)(23, 250)(24, 252)(25, 255)(26, 199)(27, 260)(28, 263)(29, 265)(30, 200)(31, 209)(32, 264)(33, 214)(34, 202)(35, 270)(36, 213)(37, 273)(38, 203)(39, 205)(40, 261)(41, 210)(42, 257)(43, 266)(44, 206)(45, 277)(46, 275)(47, 207)(48, 259)(49, 268)(50, 258)(51, 276)(52, 212)(53, 248)(54, 251)(55, 272)(56, 247)(57, 280)(58, 283)(59, 215)(60, 285)(61, 287)(62, 216)(63, 224)(64, 286)(65, 226)(66, 218)(67, 225)(68, 236)(69, 219)(70, 221)(71, 231)(72, 242)(73, 288)(74, 222)(75, 246)(76, 228)(77, 282)(78, 281)(79, 227)(80, 237)(81, 233)(82, 243)(83, 230)(84, 279)(85, 244)(86, 284)(87, 271)(88, 278)(89, 274)(90, 249)(91, 256)(92, 253)(93, 262)(94, 267)(95, 269)(96, 254)(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) :: { ( 4^4 ), ( 4^48 ) } Outer automorphisms :: reflexible Dual of E23.1023 Graph:: simple bipartite v = 52 e = 192 f = 96 degree seq :: [ 4^48, 48^4 ] E23.1032 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 24}) Quotient :: dipole Aut^+ = (C8 x S3) : C2 (small group id <96, 123>) Aut = $<192, 1336>$ (small group id <192, 1336>) |r| :: 2 Presentation :: [ R^2, Y2^2, (Y3 * Y2)^2, (R * Y3)^2, (Y3^-1 * Y1)^2, (R * Y1)^2, Y3^4, (Y3^-1 * Y1^-1)^2, R * Y3^-1 * Y2 * Y3 * R * Y2, Y2 * Y3^-1 * R * Y2 * R * Y3, Y3^-2 * Y2 * R * Y2 * R, (R * Y2 * Y3^-1)^2, Y1^-1 * Y2 * Y1^-2 * R * Y2 * R * Y1^-1, Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1, Y2 * Y1^3 * Y2 * Y1^-3, Y1^24 ] Map:: polytopal non-degenerate R = (1, 97, 2, 98, 7, 103, 20, 116, 47, 143, 81, 177, 73, 169, 35, 131, 62, 158, 91, 187, 65, 161, 40, 136, 16, 112, 28, 124, 55, 151, 88, 184, 69, 165, 30, 126, 57, 153, 89, 185, 80, 176, 46, 142, 19, 115, 5, 101)(3, 99, 11, 107, 29, 125, 48, 144, 85, 181, 61, 157, 42, 138, 17, 113, 41, 137, 53, 149, 21, 117, 51, 147, 34, 130, 71, 167, 45, 141, 64, 160, 26, 122, 8, 104, 24, 120, 56, 152, 82, 178, 75, 171, 37, 133, 13, 109)(4, 100, 15, 111, 38, 134, 76, 172, 96, 192, 72, 168, 93, 189, 70, 166, 84, 180, 49, 145, 23, 119, 9, 105, 6, 102, 18, 114, 44, 140, 79, 175, 95, 191, 74, 170, 94, 190, 68, 164, 83, 179, 50, 146, 22, 118, 10, 106)(12, 108, 33, 129, 54, 150, 92, 188, 77, 173, 39, 135, 58, 154, 27, 123, 63, 159, 86, 182, 67, 163, 31, 127, 14, 110, 36, 132, 52, 148, 90, 186, 78, 174, 43, 139, 59, 155, 25, 121, 60, 156, 87, 183, 66, 162, 32, 128)(193, 289, 195, 291)(194, 290, 200, 296)(196, 292, 206, 302)(197, 293, 209, 305)(198, 294, 204, 300)(199, 295, 213, 309)(201, 297, 219, 315)(202, 298, 217, 313)(203, 299, 222, 318)(205, 301, 227, 323)(207, 303, 231, 327)(208, 304, 226, 322)(210, 306, 235, 331)(211, 307, 237, 333)(212, 308, 240, 336)(214, 310, 246, 342)(215, 311, 244, 340)(216, 312, 249, 345)(218, 314, 254, 350)(220, 316, 253, 349)(221, 317, 257, 353)(223, 319, 262, 358)(224, 320, 260, 356)(225, 321, 264, 360)(228, 324, 266, 362)(229, 325, 247, 343)(230, 326, 258, 354)(232, 328, 248, 344)(233, 329, 261, 357)(234, 330, 265, 361)(236, 332, 259, 355)(238, 334, 267, 363)(239, 335, 274, 370)(241, 337, 279, 375)(242, 338, 278, 374)(243, 339, 281, 377)(245, 341, 283, 379)(250, 346, 286, 382)(251, 347, 285, 381)(252, 348, 287, 383)(255, 351, 288, 384)(256, 352, 280, 376)(263, 359, 273, 369)(268, 364, 282, 378)(269, 365, 276, 372)(270, 366, 275, 371)(271, 367, 284, 380)(272, 368, 277, 373) L = (1, 196)(2, 201)(3, 204)(4, 208)(5, 210)(6, 193)(7, 214)(8, 217)(9, 220)(10, 194)(11, 223)(12, 226)(13, 228)(14, 195)(15, 197)(16, 198)(17, 231)(18, 232)(19, 230)(20, 241)(21, 244)(22, 247)(23, 199)(24, 250)(25, 253)(26, 255)(27, 200)(28, 202)(29, 258)(30, 260)(31, 263)(32, 203)(33, 205)(34, 206)(35, 264)(36, 243)(37, 246)(38, 257)(39, 248)(40, 207)(41, 270)(42, 251)(43, 209)(44, 211)(45, 259)(46, 271)(47, 275)(48, 278)(49, 280)(50, 212)(51, 225)(52, 229)(53, 284)(54, 213)(55, 215)(56, 235)(57, 285)(58, 234)(59, 216)(60, 218)(61, 219)(62, 287)(63, 277)(64, 279)(65, 236)(66, 237)(67, 221)(68, 273)(69, 276)(70, 222)(71, 224)(72, 281)(73, 286)(74, 227)(75, 282)(76, 238)(77, 233)(78, 274)(79, 283)(80, 288)(81, 262)(82, 269)(83, 261)(84, 239)(85, 252)(86, 256)(87, 240)(88, 242)(89, 266)(90, 245)(91, 268)(92, 267)(93, 265)(94, 249)(95, 272)(96, 254)(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) :: { ( 4^4 ), ( 4^48 ) } Outer automorphisms :: reflexible Dual of E23.1026 Graph:: simple bipartite v = 52 e = 192 f = 96 degree seq :: [ 4^48, 48^4 ] E23.1033 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 4, 24}) Quotient :: edge Aut^+ = (C3 : Q8) : C4 (small group id <96, 23>) Aut = $<192, 293>$ (small group id <192, 293>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^4, T2^4, T2^-1 * T1 * T2^-2 * T1^-1 * T2^-1, T2 * T1^-2 * T2^-1 * T1^-2, T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, (T2 * T1^-1)^24 ] Map:: non-degenerate R = (1, 3, 10, 5)(2, 7, 19, 8)(4, 12, 25, 13)(6, 16, 28, 17)(9, 23, 14, 24)(11, 26, 15, 27)(18, 29, 21, 30)(20, 31, 22, 32)(33, 41, 35, 42)(34, 43, 36, 44)(37, 45, 39, 46)(38, 47, 40, 48)(49, 57, 51, 58)(50, 59, 52, 60)(53, 61, 55, 62)(54, 63, 56, 64)(65, 73, 67, 74)(66, 75, 68, 76)(69, 77, 71, 78)(70, 79, 72, 80)(81, 89, 83, 90)(82, 91, 84, 92)(85, 93, 87, 94)(86, 95, 88, 96)(97, 98, 102, 100)(99, 105, 112, 107)(101, 110, 113, 111)(103, 114, 108, 116)(104, 117, 109, 118)(106, 115, 124, 121)(119, 129, 122, 130)(120, 131, 123, 132)(125, 133, 127, 134)(126, 135, 128, 136)(137, 145, 139, 146)(138, 147, 140, 148)(141, 149, 143, 150)(142, 151, 144, 152)(153, 161, 155, 162)(154, 163, 156, 164)(157, 165, 159, 166)(158, 167, 160, 168)(169, 177, 171, 178)(170, 179, 172, 180)(173, 181, 175, 182)(174, 183, 176, 184)(185, 191, 187, 189)(186, 192, 188, 190) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 48^4 ) } Outer automorphisms :: reflexible Dual of E23.1038 Transitivity :: ET+ Graph:: simple bipartite v = 48 e = 96 f = 4 degree seq :: [ 4^48 ] E23.1034 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 4, 24}) Quotient :: edge Aut^+ = (C3 : Q8) : C4 (small group id <96, 23>) Aut = $<192, 293>$ (small group id <192, 293>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T1 * T2^-1 * T1^2 * T2 * T1, T2^-1 * T1^-1 * T2^-2 * T1 * T2^-1, (T2 * T1^-1)^4, T2^4 * T1^-1 * T2^-8 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 3, 10, 27, 46, 62, 78, 86, 70, 54, 36, 18, 6, 17, 35, 53, 69, 85, 84, 68, 52, 34, 16, 5)(2, 7, 20, 39, 56, 72, 88, 80, 63, 48, 28, 13, 4, 12, 31, 49, 65, 81, 92, 76, 60, 44, 24, 8)(9, 25, 14, 32, 50, 66, 82, 94, 79, 64, 47, 30, 11, 29, 15, 33, 51, 67, 83, 93, 77, 61, 45, 26)(19, 37, 22, 42, 58, 74, 90, 96, 89, 73, 57, 41, 21, 40, 23, 43, 59, 75, 91, 95, 87, 71, 55, 38)(97, 98, 102, 100)(99, 105, 113, 107)(101, 110, 114, 111)(103, 115, 108, 117)(104, 118, 109, 119)(106, 120, 131, 124)(112, 116, 132, 127)(121, 133, 125, 136)(122, 138, 126, 139)(123, 141, 149, 143)(128, 134, 129, 137)(130, 146, 150, 147)(135, 151, 145, 153)(140, 154, 144, 155)(142, 156, 165, 159)(148, 152, 166, 161)(157, 170, 160, 171)(158, 173, 181, 175)(162, 167, 163, 169)(164, 178, 182, 179)(168, 183, 177, 185)(172, 186, 176, 187)(174, 188, 180, 184)(189, 192, 190, 191) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8^4 ), ( 8^24 ) } Outer automorphisms :: reflexible Dual of E23.1036 Transitivity :: ET+ Graph:: bipartite v = 28 e = 96 f = 24 degree seq :: [ 4^24, 24^4 ] E23.1035 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 4, 24}) Quotient :: edge Aut^+ = (C3 : Q8) : C4 (small group id <96, 23>) Aut = $<192, 293>$ (small group id <192, 293>) |r| :: 2 Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, T1 * T2^-1 * T1^2 * T2 * T1, T2 * T1^-1 * T2^2 * T1 * T2, T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2 * T1^-1, T2^9 * T1^-1 * T2^-3 * T1^-1 ] Map:: non-degenerate R = (1, 3, 10, 27, 46, 62, 78, 87, 71, 55, 38, 19, 37, 22, 42, 58, 74, 90, 84, 68, 52, 34, 16, 5)(2, 7, 20, 39, 56, 72, 88, 79, 64, 47, 30, 11, 29, 15, 33, 51, 67, 83, 92, 76, 60, 44, 24, 8)(4, 12, 31, 49, 65, 81, 93, 77, 61, 45, 26, 9, 25, 14, 32, 50, 66, 82, 94, 80, 63, 48, 28, 13)(6, 17, 35, 53, 69, 85, 95, 89, 73, 57, 41, 21, 40, 23, 43, 59, 75, 91, 96, 86, 70, 54, 36, 18)(97, 98, 102, 100)(99, 105, 113, 107)(101, 110, 114, 111)(103, 115, 108, 117)(104, 118, 109, 119)(106, 120, 131, 124)(112, 116, 132, 127)(121, 133, 125, 136)(122, 138, 126, 139)(123, 141, 149, 143)(128, 134, 129, 137)(130, 146, 150, 147)(135, 151, 145, 153)(140, 154, 144, 155)(142, 156, 165, 159)(148, 152, 166, 161)(157, 170, 160, 171)(158, 173, 181, 175)(162, 167, 163, 169)(164, 178, 182, 179)(168, 183, 177, 185)(172, 186, 176, 187)(174, 188, 191, 190)(180, 184, 192, 189) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8^4 ), ( 8^24 ) } Outer automorphisms :: reflexible Dual of E23.1037 Transitivity :: ET+ Graph:: simple bipartite v = 28 e = 96 f = 24 degree seq :: [ 4^24, 24^4 ] E23.1036 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 4, 24}) Quotient :: loop Aut^+ = (C3 : Q8) : C4 (small group id <96, 23>) Aut = $<192, 293>$ (small group id <192, 293>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^4, T2^4, T2^-1 * T1 * T2^-2 * T1^-1 * T2^-1, T2 * T1^-2 * T2^-1 * T1^-2, T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, (T2 * T1^-1)^24 ] Map:: polytopal non-degenerate R = (1, 97, 3, 99, 10, 106, 5, 101)(2, 98, 7, 103, 19, 115, 8, 104)(4, 100, 12, 108, 25, 121, 13, 109)(6, 102, 16, 112, 28, 124, 17, 113)(9, 105, 23, 119, 14, 110, 24, 120)(11, 107, 26, 122, 15, 111, 27, 123)(18, 114, 29, 125, 21, 117, 30, 126)(20, 116, 31, 127, 22, 118, 32, 128)(33, 129, 41, 137, 35, 131, 42, 138)(34, 130, 43, 139, 36, 132, 44, 140)(37, 133, 45, 141, 39, 135, 46, 142)(38, 134, 47, 143, 40, 136, 48, 144)(49, 145, 57, 153, 51, 147, 58, 154)(50, 146, 59, 155, 52, 148, 60, 156)(53, 149, 61, 157, 55, 151, 62, 158)(54, 150, 63, 159, 56, 152, 64, 160)(65, 161, 73, 169, 67, 163, 74, 170)(66, 162, 75, 171, 68, 164, 76, 172)(69, 165, 77, 173, 71, 167, 78, 174)(70, 166, 79, 175, 72, 168, 80, 176)(81, 177, 89, 185, 83, 179, 90, 186)(82, 178, 91, 187, 84, 180, 92, 188)(85, 181, 93, 189, 87, 183, 94, 190)(86, 182, 95, 191, 88, 184, 96, 192) L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 110)(6, 100)(7, 114)(8, 117)(9, 112)(10, 115)(11, 99)(12, 116)(13, 118)(14, 113)(15, 101)(16, 107)(17, 111)(18, 108)(19, 124)(20, 103)(21, 109)(22, 104)(23, 129)(24, 131)(25, 106)(26, 130)(27, 132)(28, 121)(29, 133)(30, 135)(31, 134)(32, 136)(33, 122)(34, 119)(35, 123)(36, 120)(37, 127)(38, 125)(39, 128)(40, 126)(41, 145)(42, 147)(43, 146)(44, 148)(45, 149)(46, 151)(47, 150)(48, 152)(49, 139)(50, 137)(51, 140)(52, 138)(53, 143)(54, 141)(55, 144)(56, 142)(57, 161)(58, 163)(59, 162)(60, 164)(61, 165)(62, 167)(63, 166)(64, 168)(65, 155)(66, 153)(67, 156)(68, 154)(69, 159)(70, 157)(71, 160)(72, 158)(73, 177)(74, 179)(75, 178)(76, 180)(77, 181)(78, 183)(79, 182)(80, 184)(81, 171)(82, 169)(83, 172)(84, 170)(85, 175)(86, 173)(87, 176)(88, 174)(89, 191)(90, 192)(91, 189)(92, 190)(93, 185)(94, 186)(95, 187)(96, 188) local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E23.1034 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 24 e = 96 f = 28 degree seq :: [ 8^24 ] E23.1037 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 4, 24}) Quotient :: loop Aut^+ = (C3 : Q8) : C4 (small group id <96, 23>) Aut = $<192, 293>$ (small group id <192, 293>) |r| :: 2 Presentation :: [ F^2, T2^4, (F * T1)^2, (F * T2)^2, T1^4, T1^-1 * T2 * T1^-2 * T2^-1 * T1^-1, T2^-1 * T1 * T2^-2 * T1^-1 * T2^-1, T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2^-1 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2^-1 * T1^3 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2^-1 * T1 ] Map:: non-degenerate R = (1, 97, 3, 99, 10, 106, 5, 101)(2, 98, 7, 103, 19, 115, 8, 104)(4, 100, 12, 108, 25, 121, 13, 109)(6, 102, 16, 112, 28, 124, 17, 113)(9, 105, 23, 119, 14, 110, 24, 120)(11, 107, 26, 122, 15, 111, 27, 123)(18, 114, 29, 125, 21, 117, 30, 126)(20, 116, 31, 127, 22, 118, 32, 128)(33, 129, 41, 137, 35, 131, 42, 138)(34, 130, 43, 139, 36, 132, 44, 140)(37, 133, 45, 141, 39, 135, 46, 142)(38, 134, 47, 143, 40, 136, 48, 144)(49, 145, 57, 153, 51, 147, 58, 154)(50, 146, 59, 155, 52, 148, 60, 156)(53, 149, 61, 157, 55, 151, 62, 158)(54, 150, 63, 159, 56, 152, 64, 160)(65, 161, 73, 169, 67, 163, 74, 170)(66, 162, 75, 171, 68, 164, 76, 172)(69, 165, 77, 173, 71, 167, 78, 174)(70, 166, 79, 175, 72, 168, 80, 176)(81, 177, 89, 185, 83, 179, 90, 186)(82, 178, 91, 187, 84, 180, 92, 188)(85, 181, 93, 189, 87, 183, 94, 190)(86, 182, 95, 191, 88, 184, 96, 192) L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 110)(6, 100)(7, 114)(8, 117)(9, 112)(10, 115)(11, 99)(12, 116)(13, 118)(14, 113)(15, 101)(16, 107)(17, 111)(18, 108)(19, 124)(20, 103)(21, 109)(22, 104)(23, 129)(24, 131)(25, 106)(26, 130)(27, 132)(28, 121)(29, 133)(30, 135)(31, 134)(32, 136)(33, 122)(34, 119)(35, 123)(36, 120)(37, 127)(38, 125)(39, 128)(40, 126)(41, 145)(42, 147)(43, 146)(44, 148)(45, 149)(46, 151)(47, 150)(48, 152)(49, 139)(50, 137)(51, 140)(52, 138)(53, 143)(54, 141)(55, 144)(56, 142)(57, 161)(58, 163)(59, 162)(60, 164)(61, 165)(62, 167)(63, 166)(64, 168)(65, 155)(66, 153)(67, 156)(68, 154)(69, 159)(70, 157)(71, 160)(72, 158)(73, 177)(74, 179)(75, 178)(76, 180)(77, 181)(78, 183)(79, 182)(80, 184)(81, 171)(82, 169)(83, 172)(84, 170)(85, 175)(86, 173)(87, 176)(88, 174)(89, 190)(90, 189)(91, 192)(92, 191)(93, 188)(94, 187)(95, 186)(96, 185) local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E23.1035 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 24 e = 96 f = 28 degree seq :: [ 8^24 ] E23.1038 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 4, 24}) Quotient :: loop Aut^+ = (C3 : Q8) : C4 (small group id <96, 23>) Aut = $<192, 293>$ (small group id <192, 293>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T1 * T2^-1 * T1^2 * T2 * T1, T2^-1 * T1^-1 * T2^-2 * T1 * T2^-1, (T2 * T1^-1)^4, T2^4 * T1^-1 * T2^-8 * T1^-1 ] Map:: non-degenerate R = (1, 97, 3, 99, 10, 106, 27, 123, 46, 142, 62, 158, 78, 174, 86, 182, 70, 166, 54, 150, 36, 132, 18, 114, 6, 102, 17, 113, 35, 131, 53, 149, 69, 165, 85, 181, 84, 180, 68, 164, 52, 148, 34, 130, 16, 112, 5, 101)(2, 98, 7, 103, 20, 116, 39, 135, 56, 152, 72, 168, 88, 184, 80, 176, 63, 159, 48, 144, 28, 124, 13, 109, 4, 100, 12, 108, 31, 127, 49, 145, 65, 161, 81, 177, 92, 188, 76, 172, 60, 156, 44, 140, 24, 120, 8, 104)(9, 105, 25, 121, 14, 110, 32, 128, 50, 146, 66, 162, 82, 178, 94, 190, 79, 175, 64, 160, 47, 143, 30, 126, 11, 107, 29, 125, 15, 111, 33, 129, 51, 147, 67, 163, 83, 179, 93, 189, 77, 173, 61, 157, 45, 141, 26, 122)(19, 115, 37, 133, 22, 118, 42, 138, 58, 154, 74, 170, 90, 186, 96, 192, 89, 185, 73, 169, 57, 153, 41, 137, 21, 117, 40, 136, 23, 119, 43, 139, 59, 155, 75, 171, 91, 187, 95, 191, 87, 183, 71, 167, 55, 151, 38, 134) L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 110)(6, 100)(7, 115)(8, 118)(9, 113)(10, 120)(11, 99)(12, 117)(13, 119)(14, 114)(15, 101)(16, 116)(17, 107)(18, 111)(19, 108)(20, 132)(21, 103)(22, 109)(23, 104)(24, 131)(25, 133)(26, 138)(27, 141)(28, 106)(29, 136)(30, 139)(31, 112)(32, 134)(33, 137)(34, 146)(35, 124)(36, 127)(37, 125)(38, 129)(39, 151)(40, 121)(41, 128)(42, 126)(43, 122)(44, 154)(45, 149)(46, 156)(47, 123)(48, 155)(49, 153)(50, 150)(51, 130)(52, 152)(53, 143)(54, 147)(55, 145)(56, 166)(57, 135)(58, 144)(59, 140)(60, 165)(61, 170)(62, 173)(63, 142)(64, 171)(65, 148)(66, 167)(67, 169)(68, 178)(69, 159)(70, 161)(71, 163)(72, 183)(73, 162)(74, 160)(75, 157)(76, 186)(77, 181)(78, 188)(79, 158)(80, 187)(81, 185)(82, 182)(83, 164)(84, 184)(85, 175)(86, 179)(87, 177)(88, 174)(89, 168)(90, 176)(91, 172)(92, 180)(93, 192)(94, 191)(95, 189)(96, 190) local type(s) :: { ( 4^48 ) } Outer automorphisms :: reflexible Dual of E23.1033 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 4 e = 96 f = 48 degree seq :: [ 48^4 ] E23.1039 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 24}) Quotient :: dipole Aut^+ = (C3 : Q8) : C4 (small group id <96, 23>) Aut = $<192, 293>$ (small group id <192, 293>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y2^4, Y1^4, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y3 * Y2^-2 * Y3^-1 * Y2^-1, (Y2^-1 * R * Y2^-1)^2, Y2 * Y1^-2 * Y2^-1 * Y1^-2, Y3 * Y2 * Y1 * Y3^-1 * Y2^-1 * Y1^-1, Y2^-2 * Y1 * Y2^-2 * Y1^-1, (R * Y2 * Y3^-1)^2, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, (Y3 * Y2)^24 ] Map:: R = (1, 97, 2, 98, 6, 102, 4, 100)(3, 99, 9, 105, 16, 112, 11, 107)(5, 101, 14, 110, 17, 113, 15, 111)(7, 103, 18, 114, 12, 108, 20, 116)(8, 104, 21, 117, 13, 109, 22, 118)(10, 106, 19, 115, 28, 124, 25, 121)(23, 119, 33, 129, 26, 122, 34, 130)(24, 120, 35, 131, 27, 123, 36, 132)(29, 125, 37, 133, 31, 127, 38, 134)(30, 126, 39, 135, 32, 128, 40, 136)(41, 137, 49, 145, 43, 139, 50, 146)(42, 138, 51, 147, 44, 140, 52, 148)(45, 141, 53, 149, 47, 143, 54, 150)(46, 142, 55, 151, 48, 144, 56, 152)(57, 153, 65, 161, 59, 155, 66, 162)(58, 154, 67, 163, 60, 156, 68, 164)(61, 157, 69, 165, 63, 159, 70, 166)(62, 158, 71, 167, 64, 160, 72, 168)(73, 169, 81, 177, 75, 171, 82, 178)(74, 170, 83, 179, 76, 172, 84, 180)(77, 173, 85, 181, 79, 175, 86, 182)(78, 174, 87, 183, 80, 176, 88, 184)(89, 185, 94, 190, 91, 187, 96, 192)(90, 186, 93, 189, 92, 188, 95, 191)(193, 289, 195, 291, 202, 298, 197, 293)(194, 290, 199, 295, 211, 307, 200, 296)(196, 292, 204, 300, 217, 313, 205, 301)(198, 294, 208, 304, 220, 316, 209, 305)(201, 297, 215, 311, 206, 302, 216, 312)(203, 299, 218, 314, 207, 303, 219, 315)(210, 306, 221, 317, 213, 309, 222, 318)(212, 308, 223, 319, 214, 310, 224, 320)(225, 321, 233, 329, 227, 323, 234, 330)(226, 322, 235, 331, 228, 324, 236, 332)(229, 325, 237, 333, 231, 327, 238, 334)(230, 326, 239, 335, 232, 328, 240, 336)(241, 337, 249, 345, 243, 339, 250, 346)(242, 338, 251, 347, 244, 340, 252, 348)(245, 341, 253, 349, 247, 343, 254, 350)(246, 342, 255, 351, 248, 344, 256, 352)(257, 353, 265, 361, 259, 355, 266, 362)(258, 354, 267, 363, 260, 356, 268, 364)(261, 357, 269, 365, 263, 359, 270, 366)(262, 358, 271, 367, 264, 360, 272, 368)(273, 369, 281, 377, 275, 371, 282, 378)(274, 370, 283, 379, 276, 372, 284, 380)(277, 373, 285, 381, 279, 375, 286, 382)(278, 374, 287, 383, 280, 376, 288, 384) L = (1, 196)(2, 193)(3, 203)(4, 198)(5, 207)(6, 194)(7, 212)(8, 214)(9, 195)(10, 217)(11, 208)(12, 210)(13, 213)(14, 197)(15, 209)(16, 201)(17, 206)(18, 199)(19, 202)(20, 204)(21, 200)(22, 205)(23, 226)(24, 228)(25, 220)(26, 225)(27, 227)(28, 211)(29, 230)(30, 232)(31, 229)(32, 231)(33, 215)(34, 218)(35, 216)(36, 219)(37, 221)(38, 223)(39, 222)(40, 224)(41, 242)(42, 244)(43, 241)(44, 243)(45, 246)(46, 248)(47, 245)(48, 247)(49, 233)(50, 235)(51, 234)(52, 236)(53, 237)(54, 239)(55, 238)(56, 240)(57, 258)(58, 260)(59, 257)(60, 259)(61, 262)(62, 264)(63, 261)(64, 263)(65, 249)(66, 251)(67, 250)(68, 252)(69, 253)(70, 255)(71, 254)(72, 256)(73, 274)(74, 276)(75, 273)(76, 275)(77, 278)(78, 280)(79, 277)(80, 279)(81, 265)(82, 267)(83, 266)(84, 268)(85, 269)(86, 271)(87, 270)(88, 272)(89, 288)(90, 287)(91, 286)(92, 285)(93, 282)(94, 281)(95, 284)(96, 283)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 2, 48, 2, 48, 2, 48, 2, 48 ) } Outer automorphisms :: reflexible Dual of E23.1044 Graph:: bipartite v = 48 e = 192 f = 100 degree seq :: [ 8^48 ] E23.1040 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 24}) Quotient :: dipole Aut^+ = (C3 : Q8) : C4 (small group id <96, 23>) Aut = $<192, 293>$ (small group id <192, 293>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, Y1^4, (R * Y1)^2, (R * Y3)^2, Y1^4, Y1 * Y2^-1 * Y1^2 * Y2 * Y1, Y2^-2 * Y1^-1 * Y2^-2 * Y1, Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2 * Y1^-1, (Y3^-1 * Y1^-1)^4, Y2^-3 * Y1 * Y2^4 * Y1 * Y2^-5 ] Map:: R = (1, 97, 2, 98, 6, 102, 4, 100)(3, 99, 9, 105, 17, 113, 11, 107)(5, 101, 14, 110, 18, 114, 15, 111)(7, 103, 19, 115, 12, 108, 21, 117)(8, 104, 22, 118, 13, 109, 23, 119)(10, 106, 24, 120, 35, 131, 28, 124)(16, 112, 20, 116, 36, 132, 31, 127)(25, 121, 37, 133, 29, 125, 40, 136)(26, 122, 42, 138, 30, 126, 43, 139)(27, 123, 45, 141, 53, 149, 47, 143)(32, 128, 38, 134, 33, 129, 41, 137)(34, 130, 50, 146, 54, 150, 51, 147)(39, 135, 55, 151, 49, 145, 57, 153)(44, 140, 58, 154, 48, 144, 59, 155)(46, 142, 60, 156, 69, 165, 63, 159)(52, 148, 56, 152, 70, 166, 65, 161)(61, 157, 74, 170, 64, 160, 75, 171)(62, 158, 77, 173, 85, 181, 79, 175)(66, 162, 71, 167, 67, 163, 73, 169)(68, 164, 82, 178, 86, 182, 83, 179)(72, 168, 87, 183, 81, 177, 89, 185)(76, 172, 90, 186, 80, 176, 91, 187)(78, 174, 92, 188, 84, 180, 88, 184)(93, 189, 96, 192, 94, 190, 95, 191)(193, 289, 195, 291, 202, 298, 219, 315, 238, 334, 254, 350, 270, 366, 278, 374, 262, 358, 246, 342, 228, 324, 210, 306, 198, 294, 209, 305, 227, 323, 245, 341, 261, 357, 277, 373, 276, 372, 260, 356, 244, 340, 226, 322, 208, 304, 197, 293)(194, 290, 199, 295, 212, 308, 231, 327, 248, 344, 264, 360, 280, 376, 272, 368, 255, 351, 240, 336, 220, 316, 205, 301, 196, 292, 204, 300, 223, 319, 241, 337, 257, 353, 273, 369, 284, 380, 268, 364, 252, 348, 236, 332, 216, 312, 200, 296)(201, 297, 217, 313, 206, 302, 224, 320, 242, 338, 258, 354, 274, 370, 286, 382, 271, 367, 256, 352, 239, 335, 222, 318, 203, 299, 221, 317, 207, 303, 225, 321, 243, 339, 259, 355, 275, 371, 285, 381, 269, 365, 253, 349, 237, 333, 218, 314)(211, 307, 229, 325, 214, 310, 234, 330, 250, 346, 266, 362, 282, 378, 288, 384, 281, 377, 265, 361, 249, 345, 233, 329, 213, 309, 232, 328, 215, 311, 235, 331, 251, 347, 267, 363, 283, 379, 287, 383, 279, 375, 263, 359, 247, 343, 230, 326) L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 209)(7, 212)(8, 194)(9, 217)(10, 219)(11, 221)(12, 223)(13, 196)(14, 224)(15, 225)(16, 197)(17, 227)(18, 198)(19, 229)(20, 231)(21, 232)(22, 234)(23, 235)(24, 200)(25, 206)(26, 201)(27, 238)(28, 205)(29, 207)(30, 203)(31, 241)(32, 242)(33, 243)(34, 208)(35, 245)(36, 210)(37, 214)(38, 211)(39, 248)(40, 215)(41, 213)(42, 250)(43, 251)(44, 216)(45, 218)(46, 254)(47, 222)(48, 220)(49, 257)(50, 258)(51, 259)(52, 226)(53, 261)(54, 228)(55, 230)(56, 264)(57, 233)(58, 266)(59, 267)(60, 236)(61, 237)(62, 270)(63, 240)(64, 239)(65, 273)(66, 274)(67, 275)(68, 244)(69, 277)(70, 246)(71, 247)(72, 280)(73, 249)(74, 282)(75, 283)(76, 252)(77, 253)(78, 278)(79, 256)(80, 255)(81, 284)(82, 286)(83, 285)(84, 260)(85, 276)(86, 262)(87, 263)(88, 272)(89, 265)(90, 288)(91, 287)(92, 268)(93, 269)(94, 271)(95, 279)(96, 281)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 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 E23.1043 Graph:: bipartite v = 28 e = 192 f = 120 degree seq :: [ 8^24, 48^4 ] E23.1041 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 24}) Quotient :: dipole Aut^+ = (C3 : Q8) : C4 (small group id <96, 23>) Aut = $<192, 293>$ (small group id <192, 293>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, Y1^4, (R * Y1)^2, (R * Y3)^2, Y1 * Y2^-1 * Y1^2 * Y2 * Y1, Y2^-1 * Y1 * Y2^-2 * Y1^-1 * Y2^-1, Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2 * Y1^-1, (Y3^-1 * Y1^-1)^4, Y2^9 * Y1^-1 * Y2^-3 * Y1^-1 ] Map:: R = (1, 97, 2, 98, 6, 102, 4, 100)(3, 99, 9, 105, 17, 113, 11, 107)(5, 101, 14, 110, 18, 114, 15, 111)(7, 103, 19, 115, 12, 108, 21, 117)(8, 104, 22, 118, 13, 109, 23, 119)(10, 106, 24, 120, 35, 131, 28, 124)(16, 112, 20, 116, 36, 132, 31, 127)(25, 121, 37, 133, 29, 125, 40, 136)(26, 122, 42, 138, 30, 126, 43, 139)(27, 123, 45, 141, 53, 149, 47, 143)(32, 128, 38, 134, 33, 129, 41, 137)(34, 130, 50, 146, 54, 150, 51, 147)(39, 135, 55, 151, 49, 145, 57, 153)(44, 140, 58, 154, 48, 144, 59, 155)(46, 142, 60, 156, 69, 165, 63, 159)(52, 148, 56, 152, 70, 166, 65, 161)(61, 157, 74, 170, 64, 160, 75, 171)(62, 158, 77, 173, 85, 181, 79, 175)(66, 162, 71, 167, 67, 163, 73, 169)(68, 164, 82, 178, 86, 182, 83, 179)(72, 168, 87, 183, 81, 177, 89, 185)(76, 172, 90, 186, 80, 176, 91, 187)(78, 174, 92, 188, 95, 191, 94, 190)(84, 180, 88, 184, 96, 192, 93, 189)(193, 289, 195, 291, 202, 298, 219, 315, 238, 334, 254, 350, 270, 366, 279, 375, 263, 359, 247, 343, 230, 326, 211, 307, 229, 325, 214, 310, 234, 330, 250, 346, 266, 362, 282, 378, 276, 372, 260, 356, 244, 340, 226, 322, 208, 304, 197, 293)(194, 290, 199, 295, 212, 308, 231, 327, 248, 344, 264, 360, 280, 376, 271, 367, 256, 352, 239, 335, 222, 318, 203, 299, 221, 317, 207, 303, 225, 321, 243, 339, 259, 355, 275, 371, 284, 380, 268, 364, 252, 348, 236, 332, 216, 312, 200, 296)(196, 292, 204, 300, 223, 319, 241, 337, 257, 353, 273, 369, 285, 381, 269, 365, 253, 349, 237, 333, 218, 314, 201, 297, 217, 313, 206, 302, 224, 320, 242, 338, 258, 354, 274, 370, 286, 382, 272, 368, 255, 351, 240, 336, 220, 316, 205, 301)(198, 294, 209, 305, 227, 323, 245, 341, 261, 357, 277, 373, 287, 383, 281, 377, 265, 361, 249, 345, 233, 329, 213, 309, 232, 328, 215, 311, 235, 331, 251, 347, 267, 363, 283, 379, 288, 384, 278, 374, 262, 358, 246, 342, 228, 324, 210, 306) L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 209)(7, 212)(8, 194)(9, 217)(10, 219)(11, 221)(12, 223)(13, 196)(14, 224)(15, 225)(16, 197)(17, 227)(18, 198)(19, 229)(20, 231)(21, 232)(22, 234)(23, 235)(24, 200)(25, 206)(26, 201)(27, 238)(28, 205)(29, 207)(30, 203)(31, 241)(32, 242)(33, 243)(34, 208)(35, 245)(36, 210)(37, 214)(38, 211)(39, 248)(40, 215)(41, 213)(42, 250)(43, 251)(44, 216)(45, 218)(46, 254)(47, 222)(48, 220)(49, 257)(50, 258)(51, 259)(52, 226)(53, 261)(54, 228)(55, 230)(56, 264)(57, 233)(58, 266)(59, 267)(60, 236)(61, 237)(62, 270)(63, 240)(64, 239)(65, 273)(66, 274)(67, 275)(68, 244)(69, 277)(70, 246)(71, 247)(72, 280)(73, 249)(74, 282)(75, 283)(76, 252)(77, 253)(78, 279)(79, 256)(80, 255)(81, 285)(82, 286)(83, 284)(84, 260)(85, 287)(86, 262)(87, 263)(88, 271)(89, 265)(90, 276)(91, 288)(92, 268)(93, 269)(94, 272)(95, 281)(96, 278)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 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 E23.1042 Graph:: bipartite v = 28 e = 192 f = 120 degree seq :: [ 8^24, 48^4 ] E23.1042 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 24}) Quotient :: dipole Aut^+ = (C3 : Q8) : C4 (small group id <96, 23>) Aut = $<192, 293>$ (small group id <192, 293>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, Y2^4, Y3^-1 * Y2^-2 * Y3 * Y2^-2, (R * Y2 * Y3^-1)^2, Y2 * Y3^-2 * Y2^-1 * Y3^-2, Y3^-1 * Y2^-1 * Y3^-1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1, (Y3 * Y2 * Y3 * Y2^-1)^2, Y3^2 * Y2^-1 * Y3^-10 * Y2^-1, (Y3^-1 * Y1^-1)^24 ] Map:: R = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)(193, 289, 194, 290, 198, 294, 196, 292)(195, 291, 201, 297, 209, 305, 203, 299)(197, 293, 206, 302, 210, 306, 207, 303)(199, 295, 211, 307, 204, 300, 213, 309)(200, 296, 214, 310, 205, 301, 215, 311)(202, 298, 216, 312, 227, 323, 220, 316)(208, 304, 212, 308, 228, 324, 223, 319)(217, 313, 229, 325, 221, 317, 232, 328)(218, 314, 234, 330, 222, 318, 235, 331)(219, 315, 237, 333, 245, 341, 239, 335)(224, 320, 230, 326, 225, 321, 233, 329)(226, 322, 242, 338, 246, 342, 243, 339)(231, 327, 247, 343, 241, 337, 249, 345)(236, 332, 250, 346, 240, 336, 251, 347)(238, 334, 252, 348, 261, 357, 255, 351)(244, 340, 248, 344, 262, 358, 257, 353)(253, 349, 266, 362, 256, 352, 267, 363)(254, 350, 269, 365, 277, 373, 271, 367)(258, 354, 263, 359, 259, 355, 265, 361)(260, 356, 274, 370, 278, 374, 275, 371)(264, 360, 279, 375, 273, 369, 281, 377)(268, 364, 282, 378, 272, 368, 283, 379)(270, 366, 284, 380, 276, 372, 280, 376)(285, 381, 288, 384, 286, 382, 287, 383) L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 209)(7, 212)(8, 194)(9, 217)(10, 219)(11, 221)(12, 223)(13, 196)(14, 224)(15, 225)(16, 197)(17, 227)(18, 198)(19, 229)(20, 231)(21, 232)(22, 234)(23, 235)(24, 200)(25, 206)(26, 201)(27, 238)(28, 205)(29, 207)(30, 203)(31, 241)(32, 242)(33, 243)(34, 208)(35, 245)(36, 210)(37, 214)(38, 211)(39, 248)(40, 215)(41, 213)(42, 250)(43, 251)(44, 216)(45, 218)(46, 254)(47, 222)(48, 220)(49, 257)(50, 258)(51, 259)(52, 226)(53, 261)(54, 228)(55, 230)(56, 264)(57, 233)(58, 266)(59, 267)(60, 236)(61, 237)(62, 270)(63, 240)(64, 239)(65, 273)(66, 274)(67, 275)(68, 244)(69, 277)(70, 246)(71, 247)(72, 280)(73, 249)(74, 282)(75, 283)(76, 252)(77, 253)(78, 278)(79, 256)(80, 255)(81, 284)(82, 286)(83, 285)(84, 260)(85, 276)(86, 262)(87, 263)(88, 272)(89, 265)(90, 288)(91, 287)(92, 268)(93, 269)(94, 271)(95, 279)(96, 281)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 8, 48 ), ( 8, 48, 8, 48, 8, 48, 8, 48 ) } Outer automorphisms :: reflexible Dual of E23.1041 Graph:: simple bipartite v = 120 e = 192 f = 28 degree seq :: [ 2^96, 8^24 ] E23.1043 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 24}) Quotient :: dipole Aut^+ = (C3 : Q8) : C4 (small group id <96, 23>) Aut = $<192, 293>$ (small group id <192, 293>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, Y2^4, Y2 * Y3 * Y2^2 * Y3^-1 * Y2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2^-1 * Y3^-2 * Y2 * Y3^-1, Y3^-1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3^-1 * Y2^-1, Y3^9 * Y2^-1 * Y3^-3 * Y2^-1, (Y3^-1 * Y1^-1)^24 ] Map:: polytopal R = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)(193, 289, 194, 290, 198, 294, 196, 292)(195, 291, 201, 297, 209, 305, 203, 299)(197, 293, 206, 302, 210, 306, 207, 303)(199, 295, 211, 307, 204, 300, 213, 309)(200, 296, 214, 310, 205, 301, 215, 311)(202, 298, 216, 312, 227, 323, 220, 316)(208, 304, 212, 308, 228, 324, 223, 319)(217, 313, 229, 325, 221, 317, 232, 328)(218, 314, 234, 330, 222, 318, 235, 331)(219, 315, 237, 333, 245, 341, 239, 335)(224, 320, 230, 326, 225, 321, 233, 329)(226, 322, 242, 338, 246, 342, 243, 339)(231, 327, 247, 343, 241, 337, 249, 345)(236, 332, 250, 346, 240, 336, 251, 347)(238, 334, 252, 348, 261, 357, 255, 351)(244, 340, 248, 344, 262, 358, 257, 353)(253, 349, 266, 362, 256, 352, 267, 363)(254, 350, 269, 365, 277, 373, 271, 367)(258, 354, 263, 359, 259, 355, 265, 361)(260, 356, 274, 370, 278, 374, 275, 371)(264, 360, 279, 375, 273, 369, 281, 377)(268, 364, 282, 378, 272, 368, 283, 379)(270, 366, 284, 380, 287, 383, 286, 382)(276, 372, 280, 376, 288, 384, 285, 381) L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 209)(7, 212)(8, 194)(9, 217)(10, 219)(11, 221)(12, 223)(13, 196)(14, 224)(15, 225)(16, 197)(17, 227)(18, 198)(19, 229)(20, 231)(21, 232)(22, 234)(23, 235)(24, 200)(25, 206)(26, 201)(27, 238)(28, 205)(29, 207)(30, 203)(31, 241)(32, 242)(33, 243)(34, 208)(35, 245)(36, 210)(37, 214)(38, 211)(39, 248)(40, 215)(41, 213)(42, 250)(43, 251)(44, 216)(45, 218)(46, 254)(47, 222)(48, 220)(49, 257)(50, 258)(51, 259)(52, 226)(53, 261)(54, 228)(55, 230)(56, 264)(57, 233)(58, 266)(59, 267)(60, 236)(61, 237)(62, 270)(63, 240)(64, 239)(65, 273)(66, 274)(67, 275)(68, 244)(69, 277)(70, 246)(71, 247)(72, 280)(73, 249)(74, 282)(75, 283)(76, 252)(77, 253)(78, 279)(79, 256)(80, 255)(81, 285)(82, 286)(83, 284)(84, 260)(85, 287)(86, 262)(87, 263)(88, 271)(89, 265)(90, 276)(91, 288)(92, 268)(93, 269)(94, 272)(95, 281)(96, 278)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 8, 48 ), ( 8, 48, 8, 48, 8, 48, 8, 48 ) } Outer automorphisms :: reflexible Dual of E23.1040 Graph:: simple bipartite v = 120 e = 192 f = 28 degree seq :: [ 2^96, 8^24 ] E23.1044 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 24}) Quotient :: dipole Aut^+ = (C3 : Q8) : C4 (small group id <96, 23>) Aut = $<192, 293>$ (small group id <192, 293>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, Y3^4, (R * Y2 * Y3^-1)^2, Y3^-1 * Y1 * Y3^-2 * Y1^-1 * Y3^-1, Y1^-1 * Y3 * Y1^-2 * Y3^-1 * Y1^-1, (Y1^-1 * Y3 * Y1^-1 * Y3^-1)^2, (Y3 * Y1^-1)^4, (Y3 * Y2^-1)^4, Y1^-2 * Y3 * Y1^4 * Y3 * Y1^-6 ] Map:: R = (1, 97, 2, 98, 6, 102, 17, 113, 35, 131, 53, 149, 69, 165, 85, 181, 78, 174, 64, 160, 46, 142, 28, 124, 10, 106, 21, 117, 38, 134, 56, 152, 72, 168, 88, 184, 82, 178, 66, 162, 50, 146, 32, 128, 13, 109, 4, 100)(3, 99, 9, 105, 25, 121, 45, 141, 61, 157, 77, 173, 87, 183, 74, 170, 55, 151, 40, 136, 19, 115, 16, 112, 5, 101, 15, 111, 33, 129, 52, 148, 67, 163, 84, 180, 86, 182, 73, 169, 54, 150, 39, 135, 18, 114, 11, 107)(7, 103, 20, 116, 12, 108, 31, 127, 49, 145, 65, 161, 81, 177, 90, 186, 71, 167, 58, 154, 37, 133, 24, 120, 8, 104, 23, 119, 14, 110, 34, 130, 51, 147, 68, 164, 83, 179, 89, 185, 70, 166, 57, 153, 36, 132, 22, 118)(26, 122, 41, 137, 29, 125, 43, 139, 59, 155, 75, 171, 91, 187, 95, 191, 94, 190, 80, 176, 63, 159, 48, 144, 27, 123, 42, 138, 30, 126, 44, 140, 60, 156, 76, 172, 92, 188, 96, 192, 93, 189, 79, 175, 62, 158, 47, 143)(193, 289)(194, 290)(195, 291)(196, 292)(197, 293)(198, 294)(199, 295)(200, 296)(201, 297)(202, 298)(203, 299)(204, 300)(205, 301)(206, 302)(207, 303)(208, 304)(209, 305)(210, 306)(211, 307)(212, 308)(213, 309)(214, 310)(215, 311)(216, 312)(217, 313)(218, 314)(219, 315)(220, 316)(221, 317)(222, 318)(223, 319)(224, 320)(225, 321)(226, 322)(227, 323)(228, 324)(229, 325)(230, 326)(231, 327)(232, 328)(233, 329)(234, 330)(235, 331)(236, 332)(237, 333)(238, 334)(239, 335)(240, 336)(241, 337)(242, 338)(243, 339)(244, 340)(245, 341)(246, 342)(247, 343)(248, 344)(249, 345)(250, 346)(251, 347)(252, 348)(253, 349)(254, 350)(255, 351)(256, 352)(257, 353)(258, 354)(259, 355)(260, 356)(261, 357)(262, 358)(263, 359)(264, 360)(265, 361)(266, 362)(267, 363)(268, 364)(269, 365)(270, 366)(271, 367)(272, 368)(273, 369)(274, 370)(275, 371)(276, 372)(277, 373)(278, 374)(279, 375)(280, 376)(281, 377)(282, 378)(283, 379)(284, 380)(285, 381)(286, 382)(287, 383)(288, 384) L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 210)(7, 213)(8, 194)(9, 218)(10, 197)(11, 221)(12, 220)(13, 217)(14, 196)(15, 219)(16, 222)(17, 228)(18, 230)(19, 198)(20, 233)(21, 200)(22, 235)(23, 234)(24, 236)(25, 238)(26, 207)(27, 201)(28, 206)(29, 208)(30, 203)(31, 239)(32, 241)(33, 205)(34, 240)(35, 246)(36, 248)(37, 209)(38, 211)(39, 251)(40, 252)(41, 215)(42, 212)(43, 216)(44, 214)(45, 254)(46, 225)(47, 226)(48, 223)(49, 256)(50, 253)(51, 224)(52, 255)(53, 262)(54, 264)(55, 227)(56, 229)(57, 267)(58, 268)(59, 232)(60, 231)(61, 270)(62, 244)(63, 237)(64, 243)(65, 271)(66, 273)(67, 242)(68, 272)(69, 278)(70, 280)(71, 245)(72, 247)(73, 283)(74, 284)(75, 250)(76, 249)(77, 285)(78, 259)(79, 260)(80, 257)(81, 277)(82, 279)(83, 258)(84, 286)(85, 275)(86, 274)(87, 261)(88, 263)(89, 287)(90, 288)(91, 266)(92, 265)(93, 276)(94, 269)(95, 282)(96, 281)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 8, 8 ), ( 8^48 ) } Outer automorphisms :: reflexible Dual of E23.1039 Graph:: simple bipartite v = 100 e = 192 f = 48 degree seq :: [ 2^96, 48^4 ] E23.1045 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 4, 24}) Quotient :: edge Aut^+ = C24 : C4 (small group id <96, 24>) Aut = $<192, 694>$ (small group id <192, 694>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, T1 * T2^-1 * T1^2 * T2 * T1, T2^2 * T1^-1 * T2^2 * T1, T2 * T1^-1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, T2^3 * T1 * T2^-9 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 3, 10, 27, 46, 62, 78, 89, 73, 57, 41, 21, 40, 23, 43, 59, 75, 91, 84, 68, 52, 34, 16, 5)(2, 7, 20, 39, 56, 72, 88, 77, 61, 45, 26, 9, 25, 14, 32, 50, 66, 82, 92, 76, 60, 44, 24, 8)(4, 12, 31, 49, 65, 81, 94, 79, 64, 47, 30, 11, 29, 15, 33, 51, 67, 83, 93, 80, 63, 48, 28, 13)(6, 17, 35, 53, 69, 85, 95, 87, 71, 55, 38, 19, 37, 22, 42, 58, 74, 90, 96, 86, 70, 54, 36, 18)(97, 98, 102, 100)(99, 105, 113, 107)(101, 110, 114, 111)(103, 115, 108, 117)(104, 118, 109, 119)(106, 120, 131, 124)(112, 116, 132, 127)(121, 133, 125, 136)(122, 138, 126, 139)(123, 141, 149, 143)(128, 134, 129, 137)(130, 146, 150, 147)(135, 151, 145, 153)(140, 154, 144, 155)(142, 156, 165, 159)(148, 152, 166, 161)(157, 170, 160, 171)(158, 173, 181, 175)(162, 167, 163, 169)(164, 178, 182, 179)(168, 183, 177, 185)(172, 186, 176, 187)(174, 188, 191, 189)(180, 184, 192, 190) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8^4 ), ( 8^24 ) } Outer automorphisms :: reflexible Dual of E23.1046 Transitivity :: ET+ Graph:: simple bipartite v = 28 e = 96 f = 24 degree seq :: [ 4^24, 24^4 ] E23.1046 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 4, 24}) Quotient :: loop Aut^+ = C24 : C4 (small group id <96, 24>) Aut = $<192, 694>$ (small group id <192, 694>) |r| :: 2 Presentation :: [ F^2, T2^4, T1^4, (F * T1)^2, (F * T2)^2, T2^-2 * T1^-1 * T2^2 * T1, T1^-1 * T2 * T1^2 * T2^-1 * T1^-1, T2^-1 * T1 * T2^2 * T1^-1 * T2^-1, T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 97, 3, 99, 10, 106, 5, 101)(2, 98, 7, 103, 19, 115, 8, 104)(4, 100, 12, 108, 25, 121, 13, 109)(6, 102, 16, 112, 28, 124, 17, 113)(9, 105, 23, 119, 14, 110, 24, 120)(11, 107, 26, 122, 15, 111, 27, 123)(18, 114, 29, 125, 21, 117, 30, 126)(20, 116, 31, 127, 22, 118, 32, 128)(33, 129, 41, 137, 35, 131, 42, 138)(34, 130, 43, 139, 36, 132, 44, 140)(37, 133, 45, 141, 39, 135, 46, 142)(38, 134, 47, 143, 40, 136, 48, 144)(49, 145, 57, 153, 51, 147, 58, 154)(50, 146, 59, 155, 52, 148, 60, 156)(53, 149, 61, 157, 55, 151, 62, 158)(54, 150, 63, 159, 56, 152, 64, 160)(65, 161, 73, 169, 67, 163, 74, 170)(66, 162, 75, 171, 68, 164, 76, 172)(69, 165, 77, 173, 71, 167, 78, 174)(70, 166, 79, 175, 72, 168, 80, 176)(81, 177, 89, 185, 83, 179, 90, 186)(82, 178, 91, 187, 84, 180, 92, 188)(85, 181, 93, 189, 87, 183, 94, 190)(86, 182, 95, 191, 88, 184, 96, 192) L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 110)(6, 100)(7, 114)(8, 117)(9, 112)(10, 115)(11, 99)(12, 116)(13, 118)(14, 113)(15, 101)(16, 107)(17, 111)(18, 108)(19, 124)(20, 103)(21, 109)(22, 104)(23, 129)(24, 131)(25, 106)(26, 130)(27, 132)(28, 121)(29, 133)(30, 135)(31, 134)(32, 136)(33, 122)(34, 119)(35, 123)(36, 120)(37, 127)(38, 125)(39, 128)(40, 126)(41, 145)(42, 147)(43, 146)(44, 148)(45, 149)(46, 151)(47, 150)(48, 152)(49, 139)(50, 137)(51, 140)(52, 138)(53, 143)(54, 141)(55, 144)(56, 142)(57, 161)(58, 163)(59, 162)(60, 164)(61, 165)(62, 167)(63, 166)(64, 168)(65, 155)(66, 153)(67, 156)(68, 154)(69, 159)(70, 157)(71, 160)(72, 158)(73, 177)(74, 179)(75, 178)(76, 180)(77, 181)(78, 183)(79, 182)(80, 184)(81, 171)(82, 169)(83, 172)(84, 170)(85, 175)(86, 173)(87, 176)(88, 174)(89, 192)(90, 191)(91, 190)(92, 189)(93, 186)(94, 185)(95, 188)(96, 187) local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E23.1045 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 24 e = 96 f = 28 degree seq :: [ 8^24 ] E23.1047 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 24}) Quotient :: dipole Aut^+ = C24 : C4 (small group id <96, 24>) Aut = $<192, 694>$ (small group id <192, 694>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y1^4, Y1 * Y2^-1 * Y1^2 * Y2 * Y1, Y2^2 * Y1^-1 * Y2^2 * Y1, Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2 * Y1^-1, (Y3^-1 * Y1^-1)^4, Y2^-4 * Y1^-1 * Y2^3 * Y1 * Y2^-5 ] Map:: R = (1, 97, 2, 98, 6, 102, 4, 100)(3, 99, 9, 105, 17, 113, 11, 107)(5, 101, 14, 110, 18, 114, 15, 111)(7, 103, 19, 115, 12, 108, 21, 117)(8, 104, 22, 118, 13, 109, 23, 119)(10, 106, 24, 120, 35, 131, 28, 124)(16, 112, 20, 116, 36, 132, 31, 127)(25, 121, 37, 133, 29, 125, 40, 136)(26, 122, 42, 138, 30, 126, 43, 139)(27, 123, 45, 141, 53, 149, 47, 143)(32, 128, 38, 134, 33, 129, 41, 137)(34, 130, 50, 146, 54, 150, 51, 147)(39, 135, 55, 151, 49, 145, 57, 153)(44, 140, 58, 154, 48, 144, 59, 155)(46, 142, 60, 156, 69, 165, 63, 159)(52, 148, 56, 152, 70, 166, 65, 161)(61, 157, 74, 170, 64, 160, 75, 171)(62, 158, 77, 173, 85, 181, 79, 175)(66, 162, 71, 167, 67, 163, 73, 169)(68, 164, 82, 178, 86, 182, 83, 179)(72, 168, 87, 183, 81, 177, 89, 185)(76, 172, 90, 186, 80, 176, 91, 187)(78, 174, 92, 188, 95, 191, 93, 189)(84, 180, 88, 184, 96, 192, 94, 190)(193, 289, 195, 291, 202, 298, 219, 315, 238, 334, 254, 350, 270, 366, 281, 377, 265, 361, 249, 345, 233, 329, 213, 309, 232, 328, 215, 311, 235, 331, 251, 347, 267, 363, 283, 379, 276, 372, 260, 356, 244, 340, 226, 322, 208, 304, 197, 293)(194, 290, 199, 295, 212, 308, 231, 327, 248, 344, 264, 360, 280, 376, 269, 365, 253, 349, 237, 333, 218, 314, 201, 297, 217, 313, 206, 302, 224, 320, 242, 338, 258, 354, 274, 370, 284, 380, 268, 364, 252, 348, 236, 332, 216, 312, 200, 296)(196, 292, 204, 300, 223, 319, 241, 337, 257, 353, 273, 369, 286, 382, 271, 367, 256, 352, 239, 335, 222, 318, 203, 299, 221, 317, 207, 303, 225, 321, 243, 339, 259, 355, 275, 371, 285, 381, 272, 368, 255, 351, 240, 336, 220, 316, 205, 301)(198, 294, 209, 305, 227, 323, 245, 341, 261, 357, 277, 373, 287, 383, 279, 375, 263, 359, 247, 343, 230, 326, 211, 307, 229, 325, 214, 310, 234, 330, 250, 346, 266, 362, 282, 378, 288, 384, 278, 374, 262, 358, 246, 342, 228, 324, 210, 306) L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 209)(7, 212)(8, 194)(9, 217)(10, 219)(11, 221)(12, 223)(13, 196)(14, 224)(15, 225)(16, 197)(17, 227)(18, 198)(19, 229)(20, 231)(21, 232)(22, 234)(23, 235)(24, 200)(25, 206)(26, 201)(27, 238)(28, 205)(29, 207)(30, 203)(31, 241)(32, 242)(33, 243)(34, 208)(35, 245)(36, 210)(37, 214)(38, 211)(39, 248)(40, 215)(41, 213)(42, 250)(43, 251)(44, 216)(45, 218)(46, 254)(47, 222)(48, 220)(49, 257)(50, 258)(51, 259)(52, 226)(53, 261)(54, 228)(55, 230)(56, 264)(57, 233)(58, 266)(59, 267)(60, 236)(61, 237)(62, 270)(63, 240)(64, 239)(65, 273)(66, 274)(67, 275)(68, 244)(69, 277)(70, 246)(71, 247)(72, 280)(73, 249)(74, 282)(75, 283)(76, 252)(77, 253)(78, 281)(79, 256)(80, 255)(81, 286)(82, 284)(83, 285)(84, 260)(85, 287)(86, 262)(87, 263)(88, 269)(89, 265)(90, 288)(91, 276)(92, 268)(93, 272)(94, 271)(95, 279)(96, 278)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) } Outer automorphisms :: reflexible Dual of E23.1048 Graph:: bipartite v = 28 e = 192 f = 120 degree seq :: [ 8^24, 48^4 ] E23.1048 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 24}) Quotient :: dipole Aut^+ = C24 : C4 (small group id <96, 24>) Aut = $<192, 694>$ (small group id <192, 694>) |r| :: 2 Presentation :: [ Y1, R^2, (R * Y3)^2, (R * Y1)^2, Y2^4, Y2 * Y3 * Y2^2 * Y3^-1 * Y2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2^-1 * Y3^-2 * Y2 * Y3^-1, Y3^-1 * Y2^-1 * Y3 * Y2^-1 * Y3 * Y2^-1 * Y3^-1 * Y2^-1, Y3^11 * Y2 * Y3^-1 * Y2^-1, (Y3^-1 * Y1^-1)^24 ] Map:: polytopal R = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)(193, 289, 194, 290, 198, 294, 196, 292)(195, 291, 201, 297, 209, 305, 203, 299)(197, 293, 206, 302, 210, 306, 207, 303)(199, 295, 211, 307, 204, 300, 213, 309)(200, 296, 214, 310, 205, 301, 215, 311)(202, 298, 216, 312, 227, 323, 220, 316)(208, 304, 212, 308, 228, 324, 223, 319)(217, 313, 229, 325, 221, 317, 232, 328)(218, 314, 234, 330, 222, 318, 235, 331)(219, 315, 237, 333, 245, 341, 239, 335)(224, 320, 230, 326, 225, 321, 233, 329)(226, 322, 242, 338, 246, 342, 243, 339)(231, 327, 247, 343, 241, 337, 249, 345)(236, 332, 250, 346, 240, 336, 251, 347)(238, 334, 252, 348, 261, 357, 255, 351)(244, 340, 248, 344, 262, 358, 257, 353)(253, 349, 266, 362, 256, 352, 267, 363)(254, 350, 269, 365, 277, 373, 271, 367)(258, 354, 263, 359, 259, 355, 265, 361)(260, 356, 274, 370, 278, 374, 275, 371)(264, 360, 279, 375, 273, 369, 281, 377)(268, 364, 282, 378, 272, 368, 283, 379)(270, 366, 284, 380, 287, 383, 285, 381)(276, 372, 280, 376, 288, 384, 286, 382) L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 209)(7, 212)(8, 194)(9, 217)(10, 219)(11, 221)(12, 223)(13, 196)(14, 224)(15, 225)(16, 197)(17, 227)(18, 198)(19, 229)(20, 231)(21, 232)(22, 234)(23, 235)(24, 200)(25, 206)(26, 201)(27, 238)(28, 205)(29, 207)(30, 203)(31, 241)(32, 242)(33, 243)(34, 208)(35, 245)(36, 210)(37, 214)(38, 211)(39, 248)(40, 215)(41, 213)(42, 250)(43, 251)(44, 216)(45, 218)(46, 254)(47, 222)(48, 220)(49, 257)(50, 258)(51, 259)(52, 226)(53, 261)(54, 228)(55, 230)(56, 264)(57, 233)(58, 266)(59, 267)(60, 236)(61, 237)(62, 270)(63, 240)(64, 239)(65, 273)(66, 274)(67, 275)(68, 244)(69, 277)(70, 246)(71, 247)(72, 280)(73, 249)(74, 282)(75, 283)(76, 252)(77, 253)(78, 281)(79, 256)(80, 255)(81, 286)(82, 284)(83, 285)(84, 260)(85, 287)(86, 262)(87, 263)(88, 269)(89, 265)(90, 288)(91, 276)(92, 268)(93, 272)(94, 271)(95, 279)(96, 278)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 8, 48 ), ( 8, 48, 8, 48, 8, 48, 8, 48 ) } Outer automorphisms :: reflexible Dual of E23.1047 Graph:: simple bipartite v = 120 e = 192 f = 28 degree seq :: [ 2^96, 8^24 ] E23.1049 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 4, 24}) Quotient :: edge Aut^+ = C24 : C4 (small group id <96, 25>) Aut = $<192, 674>$ (small group id <192, 674>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^-1 * T2^-1 * T1 * T2^-1, T1^4, T2^24 ] Map:: non-degenerate R = (1, 3, 9, 17, 25, 33, 41, 49, 57, 65, 73, 81, 89, 84, 76, 68, 60, 52, 44, 36, 28, 20, 12, 5)(2, 7, 15, 23, 31, 39, 47, 55, 63, 71, 79, 87, 94, 88, 80, 72, 64, 56, 48, 40, 32, 24, 16, 8)(4, 11, 19, 27, 35, 43, 51, 59, 67, 75, 83, 91, 95, 90, 82, 74, 66, 58, 50, 42, 34, 26, 18, 10)(6, 13, 21, 29, 37, 45, 53, 61, 69, 77, 85, 92, 96, 93, 86, 78, 70, 62, 54, 46, 38, 30, 22, 14)(97, 98, 102, 100)(99, 104, 109, 106)(101, 103, 110, 107)(105, 112, 117, 114)(108, 111, 118, 115)(113, 120, 125, 122)(116, 119, 126, 123)(121, 128, 133, 130)(124, 127, 134, 131)(129, 136, 141, 138)(132, 135, 142, 139)(137, 144, 149, 146)(140, 143, 150, 147)(145, 152, 157, 154)(148, 151, 158, 155)(153, 160, 165, 162)(156, 159, 166, 163)(161, 168, 173, 170)(164, 167, 174, 171)(169, 176, 181, 178)(172, 175, 182, 179)(177, 184, 188, 186)(180, 183, 189, 187)(185, 190, 192, 191) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8^4 ), ( 8^24 ) } Outer automorphisms :: reflexible Dual of E23.1050 Transitivity :: ET+ Graph:: simple bipartite v = 28 e = 96 f = 24 degree seq :: [ 4^24, 24^4 ] E23.1050 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 4, 24}) Quotient :: loop Aut^+ = C24 : C4 (small group id <96, 25>) Aut = $<192, 674>$ (small group id <192, 674>) |r| :: 2 Presentation :: [ F^2, T1^-1 * T2^-2 * T1^-1, T2^-2 * T1^2, (F * T2)^2, (F * T1)^2, T2^4, (T2 * T1)^24 ] Map:: non-degenerate R = (1, 97, 3, 99, 6, 102, 5, 101)(2, 98, 7, 103, 4, 100, 8, 104)(9, 105, 13, 109, 10, 106, 14, 110)(11, 107, 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, 38, 134, 34, 130, 36, 132)(35, 131, 55, 151, 40, 136, 53, 149)(37, 133, 60, 156, 39, 135, 62, 158)(41, 137, 59, 155, 42, 138, 57, 153)(43, 139, 65, 161, 44, 140, 63, 159)(45, 141, 71, 167, 46, 142, 69, 165)(47, 143, 75, 171, 48, 144, 73, 169)(49, 145, 79, 175, 50, 146, 77, 173)(51, 147, 83, 179, 52, 148, 81, 177)(54, 150, 87, 183, 56, 152, 85, 181)(58, 154, 95, 191, 68, 164, 93, 189)(61, 157, 89, 185, 66, 162, 91, 187)(64, 160, 96, 192, 67, 163, 94, 190)(70, 166, 90, 186, 72, 168, 92, 188)(74, 170, 88, 184, 76, 172, 86, 182)(78, 174, 82, 178, 80, 176, 84, 180) L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 106)(6, 100)(7, 107)(8, 108)(9, 101)(10, 99)(11, 104)(12, 103)(13, 113)(14, 114)(15, 115)(16, 116)(17, 110)(18, 109)(19, 112)(20, 111)(21, 121)(22, 122)(23, 123)(24, 124)(25, 118)(26, 117)(27, 120)(28, 119)(29, 129)(30, 130)(31, 149)(32, 151)(33, 126)(34, 125)(35, 153)(36, 156)(37, 159)(38, 158)(39, 161)(40, 155)(41, 165)(42, 167)(43, 169)(44, 171)(45, 173)(46, 175)(47, 177)(48, 179)(49, 181)(50, 183)(51, 185)(52, 187)(53, 128)(54, 189)(55, 127)(56, 191)(57, 136)(58, 188)(59, 131)(60, 134)(61, 192)(62, 132)(63, 135)(64, 182)(65, 133)(66, 190)(67, 184)(68, 186)(69, 138)(70, 180)(71, 137)(72, 178)(73, 140)(74, 174)(75, 139)(76, 176)(77, 142)(78, 172)(79, 141)(80, 170)(81, 144)(82, 166)(83, 143)(84, 168)(85, 146)(86, 163)(87, 145)(88, 160)(89, 148)(90, 154)(91, 147)(92, 164)(93, 152)(94, 157)(95, 150)(96, 162) local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E23.1049 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 24 e = 96 f = 28 degree seq :: [ 8^24 ] E23.1051 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 24}) Quotient :: dipole Aut^+ = C24 : C4 (small group id <96, 25>) Aut = $<192, 674>$ (small group id <192, 674>) |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, Y2^24 ] Map:: R = (1, 97, 2, 98, 6, 102, 4, 100)(3, 99, 8, 104, 13, 109, 10, 106)(5, 101, 7, 103, 14, 110, 11, 107)(9, 105, 16, 112, 21, 117, 18, 114)(12, 108, 15, 111, 22, 118, 19, 115)(17, 113, 24, 120, 29, 125, 26, 122)(20, 116, 23, 119, 30, 126, 27, 123)(25, 121, 32, 128, 37, 133, 34, 130)(28, 124, 31, 127, 38, 134, 35, 131)(33, 129, 40, 136, 45, 141, 42, 138)(36, 132, 39, 135, 46, 142, 43, 139)(41, 137, 48, 144, 53, 149, 50, 146)(44, 140, 47, 143, 54, 150, 51, 147)(49, 145, 56, 152, 61, 157, 58, 154)(52, 148, 55, 151, 62, 158, 59, 155)(57, 153, 64, 160, 69, 165, 66, 162)(60, 156, 63, 159, 70, 166, 67, 163)(65, 161, 72, 168, 77, 173, 74, 170)(68, 164, 71, 167, 78, 174, 75, 171)(73, 169, 80, 176, 85, 181, 82, 178)(76, 172, 79, 175, 86, 182, 83, 179)(81, 177, 88, 184, 92, 188, 90, 186)(84, 180, 87, 183, 93, 189, 91, 187)(89, 185, 94, 190, 96, 192, 95, 191)(193, 289, 195, 291, 201, 297, 209, 305, 217, 313, 225, 321, 233, 329, 241, 337, 249, 345, 257, 353, 265, 361, 273, 369, 281, 377, 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, 286, 382, 280, 376, 272, 368, 264, 360, 256, 352, 248, 344, 240, 336, 232, 328, 224, 320, 216, 312, 208, 304, 200, 296)(196, 292, 203, 299, 211, 307, 219, 315, 227, 323, 235, 331, 243, 339, 251, 347, 259, 355, 267, 363, 275, 371, 283, 379, 287, 383, 282, 378, 274, 370, 266, 362, 258, 354, 250, 346, 242, 338, 234, 330, 226, 322, 218, 314, 210, 306, 202, 298)(198, 294, 205, 301, 213, 309, 221, 317, 229, 325, 237, 333, 245, 341, 253, 349, 261, 357, 269, 365, 277, 373, 284, 380, 288, 384, 285, 381, 278, 374, 270, 366, 262, 358, 254, 350, 246, 342, 238, 334, 230, 326, 222, 318, 214, 310, 206, 302) L = (1, 195)(2, 199)(3, 201)(4, 203)(5, 193)(6, 205)(7, 207)(8, 194)(9, 209)(10, 196)(11, 211)(12, 197)(13, 213)(14, 198)(15, 215)(16, 200)(17, 217)(18, 202)(19, 219)(20, 204)(21, 221)(22, 206)(23, 223)(24, 208)(25, 225)(26, 210)(27, 227)(28, 212)(29, 229)(30, 214)(31, 231)(32, 216)(33, 233)(34, 218)(35, 235)(36, 220)(37, 237)(38, 222)(39, 239)(40, 224)(41, 241)(42, 226)(43, 243)(44, 228)(45, 245)(46, 230)(47, 247)(48, 232)(49, 249)(50, 234)(51, 251)(52, 236)(53, 253)(54, 238)(55, 255)(56, 240)(57, 257)(58, 242)(59, 259)(60, 244)(61, 261)(62, 246)(63, 263)(64, 248)(65, 265)(66, 250)(67, 267)(68, 252)(69, 269)(70, 254)(71, 271)(72, 256)(73, 273)(74, 258)(75, 275)(76, 260)(77, 277)(78, 262)(79, 279)(80, 264)(81, 281)(82, 266)(83, 283)(84, 268)(85, 284)(86, 270)(87, 286)(88, 272)(89, 276)(90, 274)(91, 287)(92, 288)(93, 278)(94, 280)(95, 282)(96, 285)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 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 E23.1052 Graph:: bipartite v = 28 e = 192 f = 120 degree seq :: [ 8^24, 48^4 ] E23.1052 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 24}) Quotient :: dipole Aut^+ = C24 : C4 (small group id <96, 25>) Aut = $<192, 674>$ (small group id <192, 674>) |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, Y3^11 * Y2 * Y3^-13 * Y2^-1, (Y3^-1 * Y1^-1)^24 ] Map:: R = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)(193, 289, 194, 290, 198, 294, 196, 292)(195, 291, 200, 296, 205, 301, 202, 298)(197, 293, 199, 295, 206, 302, 203, 299)(201, 297, 208, 304, 213, 309, 210, 306)(204, 300, 207, 303, 214, 310, 211, 307)(209, 305, 216, 312, 221, 317, 218, 314)(212, 308, 215, 311, 222, 318, 219, 315)(217, 313, 224, 320, 229, 325, 226, 322)(220, 316, 223, 319, 230, 326, 227, 323)(225, 321, 232, 328, 237, 333, 234, 330)(228, 324, 231, 327, 238, 334, 235, 331)(233, 329, 240, 336, 245, 341, 242, 338)(236, 332, 239, 335, 246, 342, 243, 339)(241, 337, 248, 344, 253, 349, 250, 346)(244, 340, 247, 343, 254, 350, 251, 347)(249, 345, 256, 352, 261, 357, 258, 354)(252, 348, 255, 351, 262, 358, 259, 355)(257, 353, 264, 360, 269, 365, 266, 362)(260, 356, 263, 359, 270, 366, 267, 363)(265, 361, 272, 368, 277, 373, 274, 370)(268, 364, 271, 367, 278, 374, 275, 371)(273, 369, 280, 376, 284, 380, 282, 378)(276, 372, 279, 375, 285, 381, 283, 379)(281, 377, 286, 382, 288, 384, 287, 383) L = (1, 195)(2, 199)(3, 201)(4, 203)(5, 193)(6, 205)(7, 207)(8, 194)(9, 209)(10, 196)(11, 211)(12, 197)(13, 213)(14, 198)(15, 215)(16, 200)(17, 217)(18, 202)(19, 219)(20, 204)(21, 221)(22, 206)(23, 223)(24, 208)(25, 225)(26, 210)(27, 227)(28, 212)(29, 229)(30, 214)(31, 231)(32, 216)(33, 233)(34, 218)(35, 235)(36, 220)(37, 237)(38, 222)(39, 239)(40, 224)(41, 241)(42, 226)(43, 243)(44, 228)(45, 245)(46, 230)(47, 247)(48, 232)(49, 249)(50, 234)(51, 251)(52, 236)(53, 253)(54, 238)(55, 255)(56, 240)(57, 257)(58, 242)(59, 259)(60, 244)(61, 261)(62, 246)(63, 263)(64, 248)(65, 265)(66, 250)(67, 267)(68, 252)(69, 269)(70, 254)(71, 271)(72, 256)(73, 273)(74, 258)(75, 275)(76, 260)(77, 277)(78, 262)(79, 279)(80, 264)(81, 281)(82, 266)(83, 283)(84, 268)(85, 284)(86, 270)(87, 286)(88, 272)(89, 276)(90, 274)(91, 287)(92, 288)(93, 278)(94, 280)(95, 282)(96, 285)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 8, 48 ), ( 8, 48, 8, 48, 8, 48, 8, 48 ) } Outer automorphisms :: reflexible Dual of E23.1051 Graph:: simple bipartite v = 120 e = 192 f = 28 degree seq :: [ 2^96, 8^24 ] E23.1053 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 4, 24}) Quotient :: edge Aut^+ = (C3 x (C8 : C2)) : C2 (small group id <96, 32>) Aut = $<192, 306>$ (small group id <192, 306>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^4, T2^4, (T2^-1 * T1^-1 * T2^-1)^2, T2 * T1^-2 * T2^-1 * T1^-2, T2^-1 * T1^-1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, (T2 * T1 * T2 * T1^-1)^12 ] Map:: non-degenerate R = (1, 3, 10, 5)(2, 7, 19, 8)(4, 12, 25, 13)(6, 16, 28, 17)(9, 23, 15, 24)(11, 26, 14, 27)(18, 29, 22, 30)(20, 31, 21, 32)(33, 41, 36, 42)(34, 43, 35, 44)(37, 45, 40, 46)(38, 47, 39, 48)(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, 98, 102, 100)(99, 105, 112, 107)(101, 110, 113, 111)(103, 114, 108, 116)(104, 117, 109, 118)(106, 121, 124, 115)(119, 129, 122, 130)(120, 131, 123, 132)(125, 133, 127, 134)(126, 135, 128, 136)(137, 145, 139, 146)(138, 147, 140, 148)(141, 149, 143, 150)(142, 151, 144, 152)(153, 161, 155, 162)(154, 163, 156, 164)(157, 165, 159, 166)(158, 167, 160, 168)(169, 177, 171, 178)(170, 179, 172, 180)(173, 181, 175, 182)(174, 183, 176, 184)(185, 189, 187, 191)(186, 192, 188, 190) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 48^4 ) } Outer automorphisms :: reflexible Dual of E23.1058 Transitivity :: ET+ Graph:: simple bipartite v = 48 e = 96 f = 4 degree seq :: [ 4^48 ] E23.1054 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 4, 24}) Quotient :: edge Aut^+ = (C3 x (C8 : C2)) : C2 (small group id <96, 32>) Aut = $<192, 306>$ (small group id <192, 306>) |r| :: 2 Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, T2 * T1^-2 * T2^-1 * T1^-2, (T2^-2 * T1)^2, (T2^2 * T1)^2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1, T2 * T1^-1 * T2^-10 * T1 * T2 ] Map:: polytopal non-degenerate R = (1, 3, 10, 28, 48, 64, 80, 86, 70, 54, 36, 18, 6, 17, 35, 53, 69, 85, 84, 68, 52, 34, 16, 5)(2, 7, 20, 39, 57, 73, 89, 78, 62, 46, 27, 13, 4, 12, 31, 49, 65, 81, 92, 76, 60, 44, 24, 8)(9, 25, 15, 33, 51, 67, 83, 94, 79, 63, 47, 30, 11, 29, 14, 32, 50, 66, 82, 93, 77, 61, 45, 26)(19, 37, 23, 43, 59, 75, 91, 96, 88, 72, 56, 41, 21, 40, 22, 42, 58, 74, 90, 95, 87, 71, 55, 38)(97, 98, 102, 100)(99, 105, 113, 107)(101, 110, 114, 111)(103, 115, 108, 117)(104, 118, 109, 119)(106, 123, 131, 120)(112, 127, 132, 116)(121, 136, 125, 133)(122, 139, 126, 138)(124, 143, 149, 141)(128, 137, 129, 134)(130, 147, 150, 146)(135, 152, 145, 151)(140, 155, 142, 154)(144, 156, 165, 158)(148, 153, 166, 161)(157, 170, 159, 171)(160, 173, 181, 175)(162, 167, 163, 168)(164, 178, 182, 179)(169, 183, 177, 184)(172, 186, 174, 187)(176, 185, 180, 188)(189, 192, 190, 191) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8^4 ), ( 8^24 ) } Outer automorphisms :: reflexible Dual of E23.1056 Transitivity :: ET+ Graph:: bipartite v = 28 e = 96 f = 24 degree seq :: [ 4^24, 24^4 ] E23.1055 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {4, 4, 24}) Quotient :: edge Aut^+ = (C3 x (C8 : C2)) : C2 (small group id <96, 32>) Aut = $<192, 306>$ (small group id <192, 306>) |r| :: 2 Presentation :: [ F^2, (T2 * T1^-1)^2, (F * T1)^2, T1^4, (F * T2)^2, T2^-2 * T1^-1 * T2^-1 * T1^-2 * T2^-1 * T1^-1, (T2^-1 * T1^-1)^4, (T2^3 * T1)^2, T2^6 * T1 * T2^-6 * T1^-1 ] Map:: non-degenerate R = (1, 3, 10, 24, 48, 64, 80, 87, 71, 55, 38, 17, 37, 27, 43, 59, 75, 91, 84, 68, 52, 32, 14, 5)(2, 7, 18, 40, 57, 73, 89, 78, 62, 46, 23, 33, 30, 13, 29, 50, 66, 82, 92, 76, 60, 44, 20, 8)(4, 11, 26, 49, 65, 81, 93, 77, 61, 45, 22, 9, 21, 35, 31, 51, 67, 83, 94, 79, 63, 47, 28, 12)(6, 15, 34, 53, 69, 85, 95, 88, 72, 56, 39, 25, 42, 19, 41, 58, 74, 90, 96, 86, 70, 54, 36, 16)(97, 98, 102, 100)(99, 105, 115, 104)(101, 107, 121, 109)(103, 113, 131, 112)(106, 119, 130, 118)(108, 111, 129, 123)(110, 125, 132, 127)(114, 135, 122, 134)(116, 137, 124, 139)(117, 133, 126, 138)(120, 143, 154, 142)(128, 147, 152, 136)(140, 155, 141, 149)(144, 156, 165, 159)(145, 150, 146, 151)(148, 153, 166, 161)(157, 171, 158, 170)(160, 173, 186, 172)(162, 168, 163, 167)(164, 177, 184, 178)(169, 183, 179, 182)(174, 187, 175, 181)(176, 185, 191, 189)(180, 188, 192, 190) L = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192) local type(s) :: { ( 8^4 ), ( 8^24 ) } Outer automorphisms :: reflexible Dual of E23.1057 Transitivity :: ET+ Graph:: simple bipartite v = 28 e = 96 f = 24 degree seq :: [ 4^24, 24^4 ] E23.1056 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 4, 24}) Quotient :: loop Aut^+ = (C3 x (C8 : C2)) : C2 (small group id <96, 32>) Aut = $<192, 306>$ (small group id <192, 306>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^4, T2^4, (T2^-1 * T1^-1 * T2^-1)^2, T2 * T1^-2 * T2^-1 * T1^-2, T2^-1 * T1^-1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, (T2 * T1 * T2 * T1^-1)^12 ] Map:: polytopal non-degenerate R = (1, 97, 3, 99, 10, 106, 5, 101)(2, 98, 7, 103, 19, 115, 8, 104)(4, 100, 12, 108, 25, 121, 13, 109)(6, 102, 16, 112, 28, 124, 17, 113)(9, 105, 23, 119, 15, 111, 24, 120)(11, 107, 26, 122, 14, 110, 27, 123)(18, 114, 29, 125, 22, 118, 30, 126)(20, 116, 31, 127, 21, 117, 32, 128)(33, 129, 41, 137, 36, 132, 42, 138)(34, 130, 43, 139, 35, 131, 44, 140)(37, 133, 45, 141, 40, 136, 46, 142)(38, 134, 47, 143, 39, 135, 48, 144)(49, 145, 57, 153, 52, 148, 58, 154)(50, 146, 59, 155, 51, 147, 60, 156)(53, 149, 61, 157, 56, 152, 62, 158)(54, 150, 63, 159, 55, 151, 64, 160)(65, 161, 73, 169, 68, 164, 74, 170)(66, 162, 75, 171, 67, 163, 76, 172)(69, 165, 77, 173, 72, 168, 78, 174)(70, 166, 79, 175, 71, 167, 80, 176)(81, 177, 89, 185, 84, 180, 90, 186)(82, 178, 91, 187, 83, 179, 92, 188)(85, 181, 93, 189, 88, 184, 94, 190)(86, 182, 95, 191, 87, 183, 96, 192) L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 110)(6, 100)(7, 114)(8, 117)(9, 112)(10, 121)(11, 99)(12, 116)(13, 118)(14, 113)(15, 101)(16, 107)(17, 111)(18, 108)(19, 106)(20, 103)(21, 109)(22, 104)(23, 129)(24, 131)(25, 124)(26, 130)(27, 132)(28, 115)(29, 133)(30, 135)(31, 134)(32, 136)(33, 122)(34, 119)(35, 123)(36, 120)(37, 127)(38, 125)(39, 128)(40, 126)(41, 145)(42, 147)(43, 146)(44, 148)(45, 149)(46, 151)(47, 150)(48, 152)(49, 139)(50, 137)(51, 140)(52, 138)(53, 143)(54, 141)(55, 144)(56, 142)(57, 161)(58, 163)(59, 162)(60, 164)(61, 165)(62, 167)(63, 166)(64, 168)(65, 155)(66, 153)(67, 156)(68, 154)(69, 159)(70, 157)(71, 160)(72, 158)(73, 177)(74, 179)(75, 178)(76, 180)(77, 181)(78, 183)(79, 182)(80, 184)(81, 171)(82, 169)(83, 172)(84, 170)(85, 175)(86, 173)(87, 176)(88, 174)(89, 189)(90, 192)(91, 191)(92, 190)(93, 187)(94, 186)(95, 185)(96, 188) local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E23.1054 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 24 e = 96 f = 28 degree seq :: [ 8^24 ] E23.1057 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 4, 24}) Quotient :: loop Aut^+ = (C3 x (C8 : C2)) : C2 (small group id <96, 32>) Aut = $<192, 306>$ (small group id <192, 306>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^4, T2^4, (T1^-1 * T2 * T1^-1)^2, T2^-1 * T1 * T2^-2 * T1^-1 * T2^-1, T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1 * T2^-1 * T1^-1, (T2 * T1^-1)^24 ] Map:: non-degenerate R = (1, 97, 3, 99, 10, 106, 5, 101)(2, 98, 7, 103, 19, 115, 8, 104)(4, 100, 12, 108, 25, 121, 13, 109)(6, 102, 16, 112, 28, 124, 17, 113)(9, 105, 23, 119, 14, 110, 24, 120)(11, 107, 26, 122, 15, 111, 27, 123)(18, 114, 29, 125, 21, 117, 30, 126)(20, 116, 31, 127, 22, 118, 32, 128)(33, 129, 41, 137, 35, 131, 42, 138)(34, 130, 43, 139, 36, 132, 44, 140)(37, 133, 45, 141, 39, 135, 46, 142)(38, 134, 47, 143, 40, 136, 48, 144)(49, 145, 57, 153, 51, 147, 58, 154)(50, 146, 59, 155, 52, 148, 60, 156)(53, 149, 61, 157, 55, 151, 62, 158)(54, 150, 63, 159, 56, 152, 64, 160)(65, 161, 73, 169, 67, 163, 74, 170)(66, 162, 75, 171, 68, 164, 76, 172)(69, 165, 77, 173, 71, 167, 78, 174)(70, 166, 79, 175, 72, 168, 80, 176)(81, 177, 89, 185, 83, 179, 90, 186)(82, 178, 91, 187, 84, 180, 92, 188)(85, 181, 93, 189, 87, 183, 94, 190)(86, 182, 95, 191, 88, 184, 96, 192) L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 110)(6, 100)(7, 114)(8, 117)(9, 113)(10, 115)(11, 99)(12, 118)(13, 116)(14, 112)(15, 101)(16, 111)(17, 107)(18, 109)(19, 124)(20, 103)(21, 108)(22, 104)(23, 129)(24, 131)(25, 106)(26, 132)(27, 130)(28, 121)(29, 133)(30, 135)(31, 136)(32, 134)(33, 123)(34, 119)(35, 122)(36, 120)(37, 128)(38, 125)(39, 127)(40, 126)(41, 145)(42, 147)(43, 148)(44, 146)(45, 149)(46, 151)(47, 152)(48, 150)(49, 140)(50, 137)(51, 139)(52, 138)(53, 144)(54, 141)(55, 143)(56, 142)(57, 161)(58, 163)(59, 164)(60, 162)(61, 165)(62, 167)(63, 168)(64, 166)(65, 156)(66, 153)(67, 155)(68, 154)(69, 160)(70, 157)(71, 159)(72, 158)(73, 177)(74, 179)(75, 180)(76, 178)(77, 181)(78, 183)(79, 184)(80, 182)(81, 172)(82, 169)(83, 171)(84, 170)(85, 176)(86, 173)(87, 175)(88, 174)(89, 189)(90, 190)(91, 191)(92, 192)(93, 188)(94, 187)(95, 186)(96, 185) local type(s) :: { ( 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E23.1055 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 24 e = 96 f = 28 degree seq :: [ 8^24 ] E23.1058 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {4, 4, 24}) Quotient :: loop Aut^+ = (C3 x (C8 : C2)) : C2 (small group id <96, 32>) Aut = $<192, 306>$ (small group id <192, 306>) |r| :: 2 Presentation :: [ F^2, T1^4, (F * T2)^2, (F * T1)^2, T2 * T1^-2 * T2^-1 * T1^-2, (T2^-2 * T1)^2, (T2^2 * T1)^2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1, T2 * T1^-1 * T2^-10 * T1 * T2 ] Map:: non-degenerate R = (1, 97, 3, 99, 10, 106, 28, 124, 48, 144, 64, 160, 80, 176, 86, 182, 70, 166, 54, 150, 36, 132, 18, 114, 6, 102, 17, 113, 35, 131, 53, 149, 69, 165, 85, 181, 84, 180, 68, 164, 52, 148, 34, 130, 16, 112, 5, 101)(2, 98, 7, 103, 20, 116, 39, 135, 57, 153, 73, 169, 89, 185, 78, 174, 62, 158, 46, 142, 27, 123, 13, 109, 4, 100, 12, 108, 31, 127, 49, 145, 65, 161, 81, 177, 92, 188, 76, 172, 60, 156, 44, 140, 24, 120, 8, 104)(9, 105, 25, 121, 15, 111, 33, 129, 51, 147, 67, 163, 83, 179, 94, 190, 79, 175, 63, 159, 47, 143, 30, 126, 11, 107, 29, 125, 14, 110, 32, 128, 50, 146, 66, 162, 82, 178, 93, 189, 77, 173, 61, 157, 45, 141, 26, 122)(19, 115, 37, 133, 23, 119, 43, 139, 59, 155, 75, 171, 91, 187, 96, 192, 88, 184, 72, 168, 56, 152, 41, 137, 21, 117, 40, 136, 22, 118, 42, 138, 58, 154, 74, 170, 90, 186, 95, 191, 87, 183, 71, 167, 55, 151, 38, 134) L = (1, 98)(2, 102)(3, 105)(4, 97)(5, 110)(6, 100)(7, 115)(8, 118)(9, 113)(10, 123)(11, 99)(12, 117)(13, 119)(14, 114)(15, 101)(16, 127)(17, 107)(18, 111)(19, 108)(20, 112)(21, 103)(22, 109)(23, 104)(24, 106)(25, 136)(26, 139)(27, 131)(28, 143)(29, 133)(30, 138)(31, 132)(32, 137)(33, 134)(34, 147)(35, 120)(36, 116)(37, 121)(38, 128)(39, 152)(40, 125)(41, 129)(42, 122)(43, 126)(44, 155)(45, 124)(46, 154)(47, 149)(48, 156)(49, 151)(50, 130)(51, 150)(52, 153)(53, 141)(54, 146)(55, 135)(56, 145)(57, 166)(58, 140)(59, 142)(60, 165)(61, 170)(62, 144)(63, 171)(64, 173)(65, 148)(66, 167)(67, 168)(68, 178)(69, 158)(70, 161)(71, 163)(72, 162)(73, 183)(74, 159)(75, 157)(76, 186)(77, 181)(78, 187)(79, 160)(80, 185)(81, 184)(82, 182)(83, 164)(84, 188)(85, 175)(86, 179)(87, 177)(88, 169)(89, 180)(90, 174)(91, 172)(92, 176)(93, 192)(94, 191)(95, 189)(96, 190) local type(s) :: { ( 4^48 ) } Outer automorphisms :: reflexible Dual of E23.1053 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 4 e = 96 f = 48 degree seq :: [ 48^4 ] E23.1059 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 24}) Quotient :: dipole Aut^+ = (C3 x (C8 : C2)) : C2 (small group id <96, 32>) Aut = $<192, 306>$ (small group id <192, 306>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y2^4, Y1^4, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y3 * Y2^-2 * Y3^-1 * Y2^-1, (Y2^-1 * R * Y2^-1)^2, (Y2 * Y1^-2)^2, Y3 * Y2 * Y1 * Y3^-1 * Y2 * Y1^-1, Y2^-2 * Y1 * Y2^-2 * Y1^-1, (R * Y2 * Y3^-1)^2, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1^-1, (Y3 * Y2)^24 ] Map:: R = (1, 97, 2, 98, 6, 102, 4, 100)(3, 99, 9, 105, 17, 113, 11, 107)(5, 101, 14, 110, 16, 112, 15, 111)(7, 103, 18, 114, 13, 109, 20, 116)(8, 104, 21, 117, 12, 108, 22, 118)(10, 106, 19, 115, 28, 124, 25, 121)(23, 119, 33, 129, 27, 123, 34, 130)(24, 120, 35, 131, 26, 122, 36, 132)(29, 125, 37, 133, 32, 128, 38, 134)(30, 126, 39, 135, 31, 127, 40, 136)(41, 137, 49, 145, 44, 140, 50, 146)(42, 138, 51, 147, 43, 139, 52, 148)(45, 141, 53, 149, 48, 144, 54, 150)(46, 142, 55, 151, 47, 143, 56, 152)(57, 153, 65, 161, 60, 156, 66, 162)(58, 154, 67, 163, 59, 155, 68, 164)(61, 157, 69, 165, 64, 160, 70, 166)(62, 158, 71, 167, 63, 159, 72, 168)(73, 169, 81, 177, 76, 172, 82, 178)(74, 170, 83, 179, 75, 171, 84, 180)(77, 173, 85, 181, 80, 176, 86, 182)(78, 174, 87, 183, 79, 175, 88, 184)(89, 185, 93, 189, 92, 188, 96, 192)(90, 186, 94, 190, 91, 187, 95, 191)(193, 289, 195, 291, 202, 298, 197, 293)(194, 290, 199, 295, 211, 307, 200, 296)(196, 292, 204, 300, 217, 313, 205, 301)(198, 294, 208, 304, 220, 316, 209, 305)(201, 297, 215, 311, 206, 302, 216, 312)(203, 299, 218, 314, 207, 303, 219, 315)(210, 306, 221, 317, 213, 309, 222, 318)(212, 308, 223, 319, 214, 310, 224, 320)(225, 321, 233, 329, 227, 323, 234, 330)(226, 322, 235, 331, 228, 324, 236, 332)(229, 325, 237, 333, 231, 327, 238, 334)(230, 326, 239, 335, 232, 328, 240, 336)(241, 337, 249, 345, 243, 339, 250, 346)(242, 338, 251, 347, 244, 340, 252, 348)(245, 341, 253, 349, 247, 343, 254, 350)(246, 342, 255, 351, 248, 344, 256, 352)(257, 353, 265, 361, 259, 355, 266, 362)(258, 354, 267, 363, 260, 356, 268, 364)(261, 357, 269, 365, 263, 359, 270, 366)(262, 358, 271, 367, 264, 360, 272, 368)(273, 369, 281, 377, 275, 371, 282, 378)(274, 370, 283, 379, 276, 372, 284, 380)(277, 373, 285, 381, 279, 375, 286, 382)(278, 374, 287, 383, 280, 376, 288, 384) L = (1, 196)(2, 193)(3, 203)(4, 198)(5, 207)(6, 194)(7, 212)(8, 214)(9, 195)(10, 217)(11, 209)(12, 213)(13, 210)(14, 197)(15, 208)(16, 206)(17, 201)(18, 199)(19, 202)(20, 205)(21, 200)(22, 204)(23, 226)(24, 228)(25, 220)(26, 227)(27, 225)(28, 211)(29, 230)(30, 232)(31, 231)(32, 229)(33, 215)(34, 219)(35, 216)(36, 218)(37, 221)(38, 224)(39, 222)(40, 223)(41, 242)(42, 244)(43, 243)(44, 241)(45, 246)(46, 248)(47, 247)(48, 245)(49, 233)(50, 236)(51, 234)(52, 235)(53, 237)(54, 240)(55, 238)(56, 239)(57, 258)(58, 260)(59, 259)(60, 257)(61, 262)(62, 264)(63, 263)(64, 261)(65, 249)(66, 252)(67, 250)(68, 251)(69, 253)(70, 256)(71, 254)(72, 255)(73, 274)(74, 276)(75, 275)(76, 273)(77, 278)(78, 280)(79, 279)(80, 277)(81, 265)(82, 268)(83, 266)(84, 267)(85, 269)(86, 272)(87, 270)(88, 271)(89, 288)(90, 287)(91, 286)(92, 285)(93, 281)(94, 282)(95, 283)(96, 284)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 2, 48, 2, 48, 2, 48, 2, 48 ) } Outer automorphisms :: reflexible Dual of E23.1064 Graph:: bipartite v = 48 e = 192 f = 100 degree seq :: [ 8^48 ] E23.1060 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 24}) Quotient :: dipole Aut^+ = (C3 x (C8 : C2)) : C2 (small group id <96, 32>) Aut = $<192, 306>$ (small group id <192, 306>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, Y1^4, (R * Y3)^2, (R * Y1)^2, Y2 * Y1^-2 * Y2^-1 * Y1^-2, (Y2^2 * Y1)^2, (Y2^-1 * Y1 * Y2^-1)^2, Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1, (Y3^-1 * Y1^-1)^4, Y2^-3 * Y1^-1 * Y2^8 * Y1^-1 * Y2^-1 ] Map:: R = (1, 97, 2, 98, 6, 102, 4, 100)(3, 99, 9, 105, 17, 113, 11, 107)(5, 101, 14, 110, 18, 114, 15, 111)(7, 103, 19, 115, 12, 108, 21, 117)(8, 104, 22, 118, 13, 109, 23, 119)(10, 106, 27, 123, 35, 131, 24, 120)(16, 112, 31, 127, 36, 132, 20, 116)(25, 121, 40, 136, 29, 125, 37, 133)(26, 122, 43, 139, 30, 126, 42, 138)(28, 124, 47, 143, 53, 149, 45, 141)(32, 128, 41, 137, 33, 129, 38, 134)(34, 130, 51, 147, 54, 150, 50, 146)(39, 135, 56, 152, 49, 145, 55, 151)(44, 140, 59, 155, 46, 142, 58, 154)(48, 144, 60, 156, 69, 165, 62, 158)(52, 148, 57, 153, 70, 166, 65, 161)(61, 157, 74, 170, 63, 159, 75, 171)(64, 160, 77, 173, 85, 181, 79, 175)(66, 162, 71, 167, 67, 163, 72, 168)(68, 164, 82, 178, 86, 182, 83, 179)(73, 169, 87, 183, 81, 177, 88, 184)(76, 172, 90, 186, 78, 174, 91, 187)(80, 176, 89, 185, 84, 180, 92, 188)(93, 189, 96, 192, 94, 190, 95, 191)(193, 289, 195, 291, 202, 298, 220, 316, 240, 336, 256, 352, 272, 368, 278, 374, 262, 358, 246, 342, 228, 324, 210, 306, 198, 294, 209, 305, 227, 323, 245, 341, 261, 357, 277, 373, 276, 372, 260, 356, 244, 340, 226, 322, 208, 304, 197, 293)(194, 290, 199, 295, 212, 308, 231, 327, 249, 345, 265, 361, 281, 377, 270, 366, 254, 350, 238, 334, 219, 315, 205, 301, 196, 292, 204, 300, 223, 319, 241, 337, 257, 353, 273, 369, 284, 380, 268, 364, 252, 348, 236, 332, 216, 312, 200, 296)(201, 297, 217, 313, 207, 303, 225, 321, 243, 339, 259, 355, 275, 371, 286, 382, 271, 367, 255, 351, 239, 335, 222, 318, 203, 299, 221, 317, 206, 302, 224, 320, 242, 338, 258, 354, 274, 370, 285, 381, 269, 365, 253, 349, 237, 333, 218, 314)(211, 307, 229, 325, 215, 311, 235, 331, 251, 347, 267, 363, 283, 379, 288, 384, 280, 376, 264, 360, 248, 344, 233, 329, 213, 309, 232, 328, 214, 310, 234, 330, 250, 346, 266, 362, 282, 378, 287, 383, 279, 375, 263, 359, 247, 343, 230, 326) L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 209)(7, 212)(8, 194)(9, 217)(10, 220)(11, 221)(12, 223)(13, 196)(14, 224)(15, 225)(16, 197)(17, 227)(18, 198)(19, 229)(20, 231)(21, 232)(22, 234)(23, 235)(24, 200)(25, 207)(26, 201)(27, 205)(28, 240)(29, 206)(30, 203)(31, 241)(32, 242)(33, 243)(34, 208)(35, 245)(36, 210)(37, 215)(38, 211)(39, 249)(40, 214)(41, 213)(42, 250)(43, 251)(44, 216)(45, 218)(46, 219)(47, 222)(48, 256)(49, 257)(50, 258)(51, 259)(52, 226)(53, 261)(54, 228)(55, 230)(56, 233)(57, 265)(58, 266)(59, 267)(60, 236)(61, 237)(62, 238)(63, 239)(64, 272)(65, 273)(66, 274)(67, 275)(68, 244)(69, 277)(70, 246)(71, 247)(72, 248)(73, 281)(74, 282)(75, 283)(76, 252)(77, 253)(78, 254)(79, 255)(80, 278)(81, 284)(82, 285)(83, 286)(84, 260)(85, 276)(86, 262)(87, 263)(88, 264)(89, 270)(90, 287)(91, 288)(92, 268)(93, 269)(94, 271)(95, 279)(96, 280)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) } Outer automorphisms :: reflexible Dual of E23.1063 Graph:: bipartite v = 28 e = 192 f = 120 degree seq :: [ 8^24, 48^4 ] E23.1061 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 24}) Quotient :: dipole Aut^+ = (C3 x (C8 : C2)) : C2 (small group id <96, 32>) Aut = $<192, 306>$ (small group id <192, 306>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y3)^2, Y1^4, (Y2^-1 * Y1)^2, (R * Y1)^2, (Y2^3 * Y1)^2, Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1 * Y2 * Y1, (Y2^-3 * Y1^-1)^2, (Y3^-1 * Y1^-1)^4, Y2^10 * Y1 * Y2^-2 * Y1^-1 ] Map:: R = (1, 97, 2, 98, 6, 102, 4, 100)(3, 99, 9, 105, 19, 115, 8, 104)(5, 101, 11, 107, 25, 121, 13, 109)(7, 103, 17, 113, 35, 131, 16, 112)(10, 106, 23, 119, 34, 130, 22, 118)(12, 108, 15, 111, 33, 129, 27, 123)(14, 110, 29, 125, 36, 132, 31, 127)(18, 114, 39, 135, 26, 122, 38, 134)(20, 116, 41, 137, 28, 124, 43, 139)(21, 117, 37, 133, 30, 126, 42, 138)(24, 120, 47, 143, 58, 154, 46, 142)(32, 128, 51, 147, 56, 152, 40, 136)(44, 140, 59, 155, 45, 141, 53, 149)(48, 144, 60, 156, 69, 165, 63, 159)(49, 145, 54, 150, 50, 146, 55, 151)(52, 148, 57, 153, 70, 166, 65, 161)(61, 157, 75, 171, 62, 158, 74, 170)(64, 160, 77, 173, 90, 186, 76, 172)(66, 162, 72, 168, 67, 163, 71, 167)(68, 164, 81, 177, 88, 184, 82, 178)(73, 169, 87, 183, 83, 179, 86, 182)(78, 174, 91, 187, 79, 175, 85, 181)(80, 176, 89, 185, 95, 191, 93, 189)(84, 180, 92, 188, 96, 192, 94, 190)(193, 289, 195, 291, 202, 298, 216, 312, 240, 336, 256, 352, 272, 368, 279, 375, 263, 359, 247, 343, 230, 326, 209, 305, 229, 325, 219, 315, 235, 331, 251, 347, 267, 363, 283, 379, 276, 372, 260, 356, 244, 340, 224, 320, 206, 302, 197, 293)(194, 290, 199, 295, 210, 306, 232, 328, 249, 345, 265, 361, 281, 377, 270, 366, 254, 350, 238, 334, 215, 311, 225, 321, 222, 318, 205, 301, 221, 317, 242, 338, 258, 354, 274, 370, 284, 380, 268, 364, 252, 348, 236, 332, 212, 308, 200, 296)(196, 292, 203, 299, 218, 314, 241, 337, 257, 353, 273, 369, 285, 381, 269, 365, 253, 349, 237, 333, 214, 310, 201, 297, 213, 309, 227, 323, 223, 319, 243, 339, 259, 355, 275, 371, 286, 382, 271, 367, 255, 351, 239, 335, 220, 316, 204, 300)(198, 294, 207, 303, 226, 322, 245, 341, 261, 357, 277, 373, 287, 383, 280, 376, 264, 360, 248, 344, 231, 327, 217, 313, 234, 330, 211, 307, 233, 329, 250, 346, 266, 362, 282, 378, 288, 384, 278, 374, 262, 358, 246, 342, 228, 324, 208, 304) L = (1, 195)(2, 199)(3, 202)(4, 203)(5, 193)(6, 207)(7, 210)(8, 194)(9, 213)(10, 216)(11, 218)(12, 196)(13, 221)(14, 197)(15, 226)(16, 198)(17, 229)(18, 232)(19, 233)(20, 200)(21, 227)(22, 201)(23, 225)(24, 240)(25, 234)(26, 241)(27, 235)(28, 204)(29, 242)(30, 205)(31, 243)(32, 206)(33, 222)(34, 245)(35, 223)(36, 208)(37, 219)(38, 209)(39, 217)(40, 249)(41, 250)(42, 211)(43, 251)(44, 212)(45, 214)(46, 215)(47, 220)(48, 256)(49, 257)(50, 258)(51, 259)(52, 224)(53, 261)(54, 228)(55, 230)(56, 231)(57, 265)(58, 266)(59, 267)(60, 236)(61, 237)(62, 238)(63, 239)(64, 272)(65, 273)(66, 274)(67, 275)(68, 244)(69, 277)(70, 246)(71, 247)(72, 248)(73, 281)(74, 282)(75, 283)(76, 252)(77, 253)(78, 254)(79, 255)(80, 279)(81, 285)(82, 284)(83, 286)(84, 260)(85, 287)(86, 262)(87, 263)(88, 264)(89, 270)(90, 288)(91, 276)(92, 268)(93, 269)(94, 271)(95, 280)(96, 278)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) } Outer automorphisms :: reflexible Dual of E23.1062 Graph:: bipartite v = 28 e = 192 f = 120 degree seq :: [ 8^24, 48^4 ] E23.1062 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 24}) Quotient :: dipole Aut^+ = (C3 x (C8 : C2)) : C2 (small group id <96, 32>) Aut = $<192, 306>$ (small group id <192, 306>) |r| :: 2 Presentation :: [ Y1, R^2, Y2^4, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y3^-1 * Y2^2 * Y3 * Y2^-1, (R * Y2 * Y3^-1)^2, (Y3^2 * Y2)^2, (Y3^2 * Y2^-1)^2, (Y3 * Y2 * Y3 * Y2^-1)^2, Y2^-1 * Y3^-12 * Y2^-1, (Y3^-1 * Y1^-1)^24 ] Map:: R = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)(193, 289, 194, 290, 198, 294, 196, 292)(195, 291, 201, 297, 209, 305, 203, 299)(197, 293, 206, 302, 210, 306, 207, 303)(199, 295, 211, 307, 204, 300, 213, 309)(200, 296, 214, 310, 205, 301, 215, 311)(202, 298, 219, 315, 227, 323, 216, 312)(208, 304, 223, 319, 228, 324, 212, 308)(217, 313, 232, 328, 221, 317, 229, 325)(218, 314, 235, 331, 222, 318, 234, 330)(220, 316, 239, 335, 245, 341, 237, 333)(224, 320, 233, 329, 225, 321, 230, 326)(226, 322, 243, 339, 246, 342, 242, 338)(231, 327, 248, 344, 241, 337, 247, 343)(236, 332, 251, 347, 238, 334, 250, 346)(240, 336, 252, 348, 261, 357, 254, 350)(244, 340, 249, 345, 262, 358, 257, 353)(253, 349, 266, 362, 255, 351, 267, 363)(256, 352, 269, 365, 277, 373, 271, 367)(258, 354, 263, 359, 259, 355, 264, 360)(260, 356, 274, 370, 278, 374, 275, 371)(265, 361, 279, 375, 273, 369, 280, 376)(268, 364, 282, 378, 270, 366, 283, 379)(272, 368, 281, 377, 276, 372, 284, 380)(285, 381, 288, 384, 286, 382, 287, 383) L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 209)(7, 212)(8, 194)(9, 217)(10, 220)(11, 221)(12, 223)(13, 196)(14, 224)(15, 225)(16, 197)(17, 227)(18, 198)(19, 229)(20, 231)(21, 232)(22, 234)(23, 235)(24, 200)(25, 207)(26, 201)(27, 205)(28, 240)(29, 206)(30, 203)(31, 241)(32, 242)(33, 243)(34, 208)(35, 245)(36, 210)(37, 215)(38, 211)(39, 249)(40, 214)(41, 213)(42, 250)(43, 251)(44, 216)(45, 218)(46, 219)(47, 222)(48, 256)(49, 257)(50, 258)(51, 259)(52, 226)(53, 261)(54, 228)(55, 230)(56, 233)(57, 265)(58, 266)(59, 267)(60, 236)(61, 237)(62, 238)(63, 239)(64, 272)(65, 273)(66, 274)(67, 275)(68, 244)(69, 277)(70, 246)(71, 247)(72, 248)(73, 281)(74, 282)(75, 283)(76, 252)(77, 253)(78, 254)(79, 255)(80, 278)(81, 284)(82, 285)(83, 286)(84, 260)(85, 276)(86, 262)(87, 263)(88, 264)(89, 270)(90, 287)(91, 288)(92, 268)(93, 269)(94, 271)(95, 279)(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, 48 ), ( 8, 48, 8, 48, 8, 48, 8, 48 ) } Outer automorphisms :: reflexible Dual of E23.1061 Graph:: simple bipartite v = 120 e = 192 f = 28 degree seq :: [ 2^96, 8^24 ] E23.1063 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 24}) Quotient :: dipole Aut^+ = (C3 x (C8 : C2)) : C2 (small group id <96, 32>) Aut = $<192, 306>$ (small group id <192, 306>) |r| :: 2 Presentation :: [ Y1, R^2, (Y3^-1 * Y2^-1)^2, (R * Y3)^2, (R * Y1)^2, Y2^4, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2 * Y3^-2 * Y2 * Y3^-1 * Y2^2, (Y3 * Y2^-1)^4, (Y3^3 * Y2^-1)^2, Y3 * Y2^-1 * Y3^-11 * Y2^-1, (Y3^-1 * Y1^-1)^24 ] Map:: polytopal R = (1, 97)(2, 98)(3, 99)(4, 100)(5, 101)(6, 102)(7, 103)(8, 104)(9, 105)(10, 106)(11, 107)(12, 108)(13, 109)(14, 110)(15, 111)(16, 112)(17, 113)(18, 114)(19, 115)(20, 116)(21, 117)(22, 118)(23, 119)(24, 120)(25, 121)(26, 122)(27, 123)(28, 124)(29, 125)(30, 126)(31, 127)(32, 128)(33, 129)(34, 130)(35, 131)(36, 132)(37, 133)(38, 134)(39, 135)(40, 136)(41, 137)(42, 138)(43, 139)(44, 140)(45, 141)(46, 142)(47, 143)(48, 144)(49, 145)(50, 146)(51, 147)(52, 148)(53, 149)(54, 150)(55, 151)(56, 152)(57, 153)(58, 154)(59, 155)(60, 156)(61, 157)(62, 158)(63, 159)(64, 160)(65, 161)(66, 162)(67, 163)(68, 164)(69, 165)(70, 166)(71, 167)(72, 168)(73, 169)(74, 170)(75, 171)(76, 172)(77, 173)(78, 174)(79, 175)(80, 176)(81, 177)(82, 178)(83, 179)(84, 180)(85, 181)(86, 182)(87, 183)(88, 184)(89, 185)(90, 186)(91, 187)(92, 188)(93, 189)(94, 190)(95, 191)(96, 192)(193, 289, 194, 290, 198, 294, 196, 292)(195, 291, 201, 297, 213, 309, 203, 299)(197, 293, 205, 301, 210, 306, 199, 295)(200, 296, 211, 307, 226, 322, 207, 303)(202, 298, 215, 311, 225, 321, 217, 313)(204, 300, 208, 304, 227, 323, 220, 316)(206, 302, 223, 319, 228, 324, 221, 317)(209, 305, 229, 325, 219, 315, 231, 327)(212, 308, 235, 331, 214, 310, 233, 329)(216, 312, 239, 335, 251, 347, 236, 332)(218, 314, 232, 328, 222, 318, 234, 330)(224, 320, 241, 337, 247, 343, 243, 339)(230, 326, 248, 344, 242, 338, 246, 342)(237, 333, 245, 341, 238, 334, 250, 346)(240, 336, 252, 348, 261, 357, 253, 349)(244, 340, 249, 345, 262, 358, 257, 353)(254, 350, 267, 363, 255, 351, 266, 362)(256, 352, 269, 365, 283, 379, 270, 366)(258, 354, 264, 360, 259, 355, 263, 359)(260, 356, 274, 370, 279, 375, 265, 361)(268, 364, 282, 378, 271, 367, 277, 373)(272, 368, 281, 377, 287, 383, 286, 382)(273, 369, 278, 374, 275, 371, 280, 376)(276, 372, 284, 380, 288, 384, 285, 381) L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 207)(7, 209)(8, 194)(9, 196)(10, 216)(11, 218)(12, 219)(13, 221)(14, 197)(15, 225)(16, 198)(17, 230)(18, 232)(19, 233)(20, 200)(21, 235)(22, 201)(23, 203)(24, 240)(25, 226)(26, 227)(27, 241)(28, 234)(29, 242)(30, 205)(31, 243)(32, 206)(33, 245)(34, 222)(35, 223)(36, 208)(37, 210)(38, 249)(39, 220)(40, 213)(41, 250)(42, 211)(43, 251)(44, 212)(45, 214)(46, 215)(47, 217)(48, 256)(49, 257)(50, 258)(51, 259)(52, 224)(53, 261)(54, 228)(55, 229)(56, 231)(57, 265)(58, 266)(59, 267)(60, 236)(61, 237)(62, 238)(63, 239)(64, 272)(65, 273)(66, 274)(67, 275)(68, 244)(69, 277)(70, 246)(71, 247)(72, 248)(73, 281)(74, 282)(75, 283)(76, 252)(77, 253)(78, 254)(79, 255)(80, 280)(81, 286)(82, 285)(83, 284)(84, 260)(85, 287)(86, 262)(87, 263)(88, 264)(89, 270)(90, 276)(91, 288)(92, 268)(93, 269)(94, 271)(95, 279)(96, 278)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 8, 48 ), ( 8, 48, 8, 48, 8, 48, 8, 48 ) } Outer automorphisms :: reflexible Dual of E23.1060 Graph:: simple bipartite v = 120 e = 192 f = 28 degree seq :: [ 2^96, 8^24 ] E23.1064 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {4, 4, 24}) Quotient :: dipole Aut^+ = (C3 x (C8 : C2)) : C2 (small group id <96, 32>) Aut = $<192, 306>$ (small group id <192, 306>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, Y3^4, Y3 * Y1 * Y3^2 * Y1^-1 * Y3, (Y1^-1 * Y3^-1 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, (Y1^-1 * Y3 * Y1^-1)^2, Y1^-1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1^-1 * Y3^-1, (Y3 * Y2^-1)^4, Y1^-2 * Y3^-1 * Y1^4 * Y3^-1 * Y1^-6 ] Map:: R = (1, 97, 2, 98, 6, 102, 17, 113, 35, 131, 53, 149, 69, 165, 85, 181, 78, 174, 64, 160, 46, 142, 28, 124, 10, 106, 21, 117, 38, 134, 56, 152, 72, 168, 88, 184, 84, 180, 68, 164, 52, 148, 33, 129, 13, 109, 4, 100)(3, 99, 9, 105, 25, 121, 45, 141, 61, 157, 77, 173, 86, 182, 74, 170, 55, 151, 39, 135, 18, 114, 16, 112, 5, 101, 15, 111, 32, 128, 50, 146, 66, 162, 82, 178, 87, 183, 73, 169, 54, 150, 40, 136, 19, 115, 11, 107)(7, 103, 20, 116, 14, 110, 34, 130, 51, 147, 67, 163, 83, 179, 90, 186, 71, 167, 57, 153, 36, 132, 24, 120, 8, 104, 23, 119, 12, 108, 31, 127, 49, 145, 65, 161, 81, 177, 89, 185, 70, 166, 58, 154, 37, 133, 22, 118)(26, 122, 42, 138, 30, 126, 43, 139, 60, 156, 75, 171, 92, 188, 95, 191, 94, 190, 79, 175, 62, 158, 48, 144, 27, 123, 41, 137, 29, 125, 44, 140, 59, 155, 76, 172, 91, 187, 96, 192, 93, 189, 80, 176, 63, 159, 47, 143)(193, 289)(194, 290)(195, 291)(196, 292)(197, 293)(198, 294)(199, 295)(200, 296)(201, 297)(202, 298)(203, 299)(204, 300)(205, 301)(206, 302)(207, 303)(208, 304)(209, 305)(210, 306)(211, 307)(212, 308)(213, 309)(214, 310)(215, 311)(216, 312)(217, 313)(218, 314)(219, 315)(220, 316)(221, 317)(222, 318)(223, 319)(224, 320)(225, 321)(226, 322)(227, 323)(228, 324)(229, 325)(230, 326)(231, 327)(232, 328)(233, 329)(234, 330)(235, 331)(236, 332)(237, 333)(238, 334)(239, 335)(240, 336)(241, 337)(242, 338)(243, 339)(244, 340)(245, 341)(246, 342)(247, 343)(248, 344)(249, 345)(250, 346)(251, 347)(252, 348)(253, 349)(254, 350)(255, 351)(256, 352)(257, 353)(258, 354)(259, 355)(260, 356)(261, 357)(262, 358)(263, 359)(264, 360)(265, 361)(266, 362)(267, 363)(268, 364)(269, 365)(270, 366)(271, 367)(272, 368)(273, 369)(274, 370)(275, 371)(276, 372)(277, 373)(278, 374)(279, 375)(280, 376)(281, 377)(282, 378)(283, 379)(284, 380)(285, 381)(286, 382)(287, 383)(288, 384) L = (1, 195)(2, 199)(3, 202)(4, 204)(5, 193)(6, 210)(7, 213)(8, 194)(9, 218)(10, 197)(11, 221)(12, 220)(13, 224)(14, 196)(15, 219)(16, 222)(17, 228)(18, 230)(19, 198)(20, 233)(21, 200)(22, 235)(23, 234)(24, 236)(25, 205)(26, 207)(27, 201)(28, 206)(29, 208)(30, 203)(31, 240)(32, 238)(33, 243)(34, 239)(35, 246)(36, 248)(37, 209)(38, 211)(39, 251)(40, 252)(41, 215)(42, 212)(43, 216)(44, 214)(45, 254)(46, 217)(47, 223)(48, 226)(49, 225)(50, 255)(51, 256)(52, 253)(53, 262)(54, 264)(55, 227)(56, 229)(57, 267)(58, 268)(59, 232)(60, 231)(61, 270)(62, 242)(63, 237)(64, 241)(65, 272)(66, 244)(67, 271)(68, 273)(69, 278)(70, 280)(71, 245)(72, 247)(73, 283)(74, 284)(75, 250)(76, 249)(77, 285)(78, 258)(79, 257)(80, 259)(81, 277)(82, 286)(83, 260)(84, 279)(85, 275)(86, 276)(87, 261)(88, 263)(89, 287)(90, 288)(91, 266)(92, 265)(93, 274)(94, 269)(95, 282)(96, 281)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 8, 8 ), ( 8^48 ) } Outer automorphisms :: reflexible Dual of E23.1059 Graph:: simple bipartite v = 100 e = 192 f = 48 degree seq :: [ 2^96, 48^4 ] E23.1065 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 48, 48}) Quotient :: regular Aut^+ = C48 x C2 (small group id <96, 59>) Aut = $<192, 461>$ (small group id <192, 461>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1 * T2 * T1^-1, T1^48 ] Map:: R = (1, 2, 5, 9, 13, 17, 21, 25, 29, 36, 33, 34, 37, 40, 43, 45, 47, 49, 51, 57, 54, 55, 58, 61, 64, 66, 68, 70, 72, 78, 76, 77, 79, 82, 85, 87, 89, 91, 93, 95, 32, 28, 24, 20, 16, 12, 8, 4)(3, 6, 10, 14, 18, 22, 26, 30, 42, 39, 35, 38, 41, 44, 46, 48, 50, 52, 63, 60, 56, 59, 62, 65, 67, 69, 71, 73, 84, 81, 75, 80, 83, 86, 88, 90, 92, 94, 96, 74, 53, 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, 42)(32, 53)(33, 35)(34, 38)(36, 39)(37, 41)(40, 44)(43, 46)(45, 48)(47, 50)(49, 52)(51, 63)(54, 56)(55, 59)(57, 60)(58, 62)(61, 65)(64, 67)(66, 69)(68, 71)(70, 73)(72, 84)(74, 95)(75, 76)(77, 80)(78, 81)(79, 83)(82, 86)(85, 88)(87, 90)(89, 92)(91, 94)(93, 96) local type(s) :: { ( 48^48 ) } Outer automorphisms :: reflexible selfdual Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 2 e = 48 f = 2 degree seq :: [ 48^2 ] E23.1066 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 48, 48}) Quotient :: edge Aut^+ = C48 x C2 (small group id <96, 59>) Aut = $<192, 461>$ (small group id <192, 461>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^48 ] Map:: R = (1, 3, 7, 11, 15, 19, 23, 27, 31, 35, 37, 39, 41, 43, 45, 47, 50, 51, 53, 55, 57, 59, 61, 63, 65, 70, 72, 74, 76, 78, 80, 82, 67, 86, 88, 90, 92, 94, 96, 84, 32, 28, 24, 20, 16, 12, 8, 4)(2, 5, 9, 13, 17, 21, 25, 29, 33, 34, 36, 38, 40, 42, 44, 46, 48, 52, 54, 56, 58, 60, 62, 64, 68, 69, 71, 73, 75, 77, 79, 81, 83, 87, 89, 91, 93, 95, 85, 66, 49, 30, 26, 22, 18, 14, 10, 6)(97, 98)(99, 101)(100, 102)(103, 105)(104, 106)(107, 109)(108, 110)(111, 113)(112, 114)(115, 117)(116, 118)(119, 121)(120, 122)(123, 125)(124, 126)(127, 129)(128, 145)(130, 131)(132, 133)(134, 135)(136, 137)(138, 139)(140, 141)(142, 143)(144, 146)(147, 148)(149, 150)(151, 152)(153, 154)(155, 156)(157, 158)(159, 160)(161, 164)(162, 180)(163, 179)(165, 166)(167, 168)(169, 170)(171, 172)(173, 174)(175, 176)(177, 178)(181, 192)(182, 183)(184, 185)(186, 187)(188, 189)(190, 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) :: { ( 96, 96 ), ( 96^48 ) } Outer automorphisms :: reflexible Dual of E23.1067 Transitivity :: ET+ Graph:: simple bipartite v = 50 e = 96 f = 2 degree seq :: [ 2^48, 48^2 ] E23.1067 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 48, 48}) Quotient :: loop Aut^+ = C48 x C2 (small group id <96, 59>) Aut = $<192, 461>$ (small group id <192, 461>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2 * T1 * T2^-1 * T1, T2^48 ] Map:: R = (1, 97, 3, 99, 7, 103, 11, 107, 15, 111, 19, 115, 23, 119, 27, 123, 31, 127, 42, 138, 38, 134, 34, 130, 37, 133, 41, 137, 45, 141, 47, 143, 49, 145, 51, 147, 53, 149, 67, 163, 63, 159, 59, 155, 56, 152, 58, 154, 62, 158, 66, 162, 69, 165, 71, 167, 73, 169, 75, 171, 77, 173, 88, 184, 84, 180, 80, 176, 83, 179, 87, 183, 91, 187, 93, 189, 95, 191, 96, 192, 32, 128, 28, 124, 24, 120, 20, 116, 16, 112, 12, 108, 8, 104, 4, 100)(2, 98, 5, 101, 9, 105, 13, 109, 17, 113, 21, 117, 25, 121, 29, 125, 44, 140, 40, 136, 36, 132, 33, 129, 35, 131, 39, 135, 43, 139, 46, 142, 48, 144, 50, 146, 52, 148, 54, 150, 65, 161, 61, 157, 57, 153, 60, 156, 64, 160, 68, 164, 70, 166, 72, 168, 74, 170, 76, 172, 90, 186, 86, 182, 82, 178, 79, 175, 81, 177, 85, 181, 89, 185, 92, 188, 94, 190, 78, 174, 55, 151, 30, 126, 26, 122, 22, 118, 18, 114, 14, 110, 10, 106, 6, 102) 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, 140)(32, 151)(33, 130)(34, 129)(35, 133)(36, 134)(37, 131)(38, 132)(39, 137)(40, 138)(41, 135)(42, 136)(43, 141)(44, 127)(45, 139)(46, 143)(47, 142)(48, 145)(49, 144)(50, 147)(51, 146)(52, 149)(53, 148)(54, 163)(55, 128)(56, 153)(57, 152)(58, 156)(59, 157)(60, 154)(61, 155)(62, 160)(63, 161)(64, 158)(65, 159)(66, 164)(67, 150)(68, 162)(69, 166)(70, 165)(71, 168)(72, 167)(73, 170)(74, 169)(75, 172)(76, 171)(77, 186)(78, 192)(79, 176)(80, 175)(81, 179)(82, 180)(83, 177)(84, 178)(85, 183)(86, 184)(87, 181)(88, 182)(89, 187)(90, 173)(91, 185)(92, 189)(93, 188)(94, 191)(95, 190)(96, 174) 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 E23.1066 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 96 f = 50 degree seq :: [ 96^2 ] E23.1068 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 48, 48}) Quotient :: dipole Aut^+ = C48 x C2 (small group id <96, 59>) Aut = $<192, 461>$ (small group id <192, 461>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, Y2^-1 * Y1 * Y2 * Y1, (R * Y2 * Y3^-1)^2, Y2^48, (Y3 * Y2^-1)^48 ] Map:: R = (1, 97, 2, 98)(3, 99, 5, 101)(4, 100, 6, 102)(7, 103, 9, 105)(8, 104, 10, 106)(11, 107, 13, 109)(12, 108, 14, 110)(15, 111, 17, 113)(16, 112, 18, 114)(19, 115, 21, 117)(20, 116, 22, 118)(23, 119, 25, 121)(24, 120, 26, 122)(27, 123, 29, 125)(28, 124, 30, 126)(31, 127, 36, 132)(32, 128, 51, 147)(33, 129, 34, 130)(35, 131, 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, 55, 151)(52, 148, 53, 149)(54, 150, 56, 152)(57, 153, 58, 154)(59, 155, 60, 156)(61, 157, 62, 158)(63, 159, 64, 160)(65, 161, 66, 162)(67, 163, 68, 164)(69, 165, 75, 171)(70, 166, 89, 185)(71, 167, 81, 177)(72, 168, 73, 169)(74, 170, 76, 172)(77, 173, 78, 174)(79, 175, 80, 176)(82, 178, 83, 179)(84, 180, 85, 181)(86, 182, 87, 183)(88, 184, 94, 190)(90, 186, 96, 192)(91, 187, 92, 188)(93, 189, 95, 191)(193, 289, 195, 291, 199, 295, 203, 299, 207, 303, 211, 307, 215, 311, 219, 315, 223, 319, 226, 322, 229, 325, 231, 327, 233, 329, 235, 331, 237, 333, 239, 335, 241, 337, 247, 343, 244, 340, 246, 342, 249, 345, 251, 347, 253, 349, 255, 351, 257, 353, 259, 355, 261, 357, 265, 361, 268, 364, 270, 366, 272, 368, 263, 359, 275, 371, 277, 373, 279, 375, 286, 382, 283, 379, 285, 381, 288, 384, 281, 377, 224, 320, 220, 316, 216, 312, 212, 308, 208, 304, 204, 300, 200, 296, 196, 292)(194, 290, 197, 293, 201, 297, 205, 301, 209, 305, 213, 309, 217, 313, 221, 317, 228, 324, 225, 321, 227, 323, 230, 326, 232, 328, 234, 330, 236, 332, 238, 334, 240, 336, 242, 338, 245, 341, 248, 344, 250, 346, 252, 348, 254, 350, 256, 352, 258, 354, 260, 356, 267, 363, 264, 360, 266, 362, 269, 365, 271, 367, 273, 369, 274, 370, 276, 372, 278, 374, 280, 376, 284, 380, 287, 383, 282, 378, 262, 358, 243, 339, 222, 318, 218, 314, 214, 310, 210, 306, 206, 302, 202, 298, 198, 294) L = (1, 194)(2, 193)(3, 197)(4, 198)(5, 195)(6, 196)(7, 201)(8, 202)(9, 199)(10, 200)(11, 205)(12, 206)(13, 203)(14, 204)(15, 209)(16, 210)(17, 207)(18, 208)(19, 213)(20, 214)(21, 211)(22, 212)(23, 217)(24, 218)(25, 215)(26, 216)(27, 221)(28, 222)(29, 219)(30, 220)(31, 228)(32, 243)(33, 226)(34, 225)(35, 229)(36, 223)(37, 227)(38, 231)(39, 230)(40, 233)(41, 232)(42, 235)(43, 234)(44, 237)(45, 236)(46, 239)(47, 238)(48, 241)(49, 240)(50, 247)(51, 224)(52, 245)(53, 244)(54, 248)(55, 242)(56, 246)(57, 250)(58, 249)(59, 252)(60, 251)(61, 254)(62, 253)(63, 256)(64, 255)(65, 258)(66, 257)(67, 260)(68, 259)(69, 267)(70, 281)(71, 273)(72, 265)(73, 264)(74, 268)(75, 261)(76, 266)(77, 270)(78, 269)(79, 272)(80, 271)(81, 263)(82, 275)(83, 274)(84, 277)(85, 276)(86, 279)(87, 278)(88, 286)(89, 262)(90, 288)(91, 284)(92, 283)(93, 287)(94, 280)(95, 285)(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, 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 E23.1069 Graph:: bipartite v = 50 e = 192 f = 98 degree seq :: [ 4^48, 96^2 ] E23.1069 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 48, 48}) Quotient :: dipole Aut^+ = C48 x C2 (small group id <96, 59>) Aut = $<192, 461>$ (small group id <192, 461>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, (Y3^-1, Y1^-1), (R * Y2 * Y3^-1)^2, Y3^-48, Y1^48 ] Map:: R = (1, 97, 2, 98, 5, 101, 9, 105, 13, 109, 17, 113, 21, 117, 25, 121, 29, 125, 39, 135, 35, 131, 38, 134, 42, 138, 44, 140, 46, 142, 48, 144, 50, 146, 52, 148, 61, 157, 57, 153, 54, 150, 55, 151, 58, 154, 62, 158, 64, 160, 66, 162, 68, 164, 70, 166, 72, 168, 81, 177, 75, 171, 80, 176, 84, 180, 86, 182, 88, 184, 90, 186, 92, 188, 94, 190, 96, 192, 95, 191, 32, 128, 28, 124, 24, 120, 20, 116, 16, 112, 12, 108, 8, 104, 4, 100)(3, 99, 6, 102, 10, 106, 14, 110, 18, 114, 22, 118, 26, 122, 30, 126, 40, 136, 36, 132, 33, 129, 34, 130, 37, 133, 41, 137, 43, 139, 45, 141, 47, 143, 49, 145, 51, 147, 60, 156, 56, 152, 59, 155, 63, 159, 65, 161, 67, 163, 69, 165, 71, 167, 73, 169, 82, 178, 78, 174, 76, 172, 77, 173, 79, 175, 83, 179, 85, 181, 87, 183, 89, 185, 91, 187, 93, 189, 74, 170, 53, 149, 31, 127, 27, 123, 23, 119, 19, 115, 15, 111, 11, 107, 7, 103)(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, 199)(5, 202)(6, 194)(7, 196)(8, 203)(9, 206)(10, 197)(11, 200)(12, 207)(13, 210)(14, 201)(15, 204)(16, 211)(17, 214)(18, 205)(19, 208)(20, 215)(21, 218)(22, 209)(23, 212)(24, 219)(25, 222)(26, 213)(27, 216)(28, 223)(29, 232)(30, 217)(31, 220)(32, 245)(33, 227)(34, 230)(35, 225)(36, 231)(37, 234)(38, 226)(39, 228)(40, 221)(41, 236)(42, 229)(43, 238)(44, 233)(45, 240)(46, 235)(47, 242)(48, 237)(49, 244)(50, 239)(51, 253)(52, 241)(53, 224)(54, 248)(55, 251)(56, 246)(57, 252)(58, 255)(59, 247)(60, 249)(61, 243)(62, 257)(63, 250)(64, 259)(65, 254)(66, 261)(67, 256)(68, 263)(69, 258)(70, 265)(71, 260)(72, 274)(73, 262)(74, 287)(75, 268)(76, 267)(77, 272)(78, 273)(79, 276)(80, 269)(81, 270)(82, 264)(83, 278)(84, 271)(85, 280)(86, 275)(87, 282)(88, 277)(89, 284)(90, 279)(91, 286)(92, 281)(93, 288)(94, 283)(95, 266)(96, 285)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 4, 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 E23.1068 Graph:: simple bipartite v = 98 e = 192 f = 50 degree seq :: [ 2^96, 96^2 ] E23.1070 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 48, 48}) Quotient :: regular Aut^+ = C3 x (C16 : C2) (small group id <96, 60>) Aut = $<192, 467>$ (small group id <192, 467>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^-2 * T2 * T1^2 * T2, (T1 * T2 * T1^-1 * T2)^2, T1^-2 * T2 * T1^-21 * T2 * T1^-1, (T2 * T1^-3)^16 ] Map:: non-degenerate R = (1, 2, 5, 11, 20, 29, 37, 45, 53, 61, 69, 77, 85, 93, 89, 81, 73, 65, 57, 49, 41, 33, 25, 16, 24, 15, 23, 32, 40, 48, 56, 64, 72, 80, 88, 96, 92, 84, 76, 68, 60, 52, 44, 36, 28, 19, 10, 4)(3, 7, 12, 22, 30, 39, 46, 55, 62, 71, 78, 87, 94, 91, 83, 75, 67, 59, 51, 43, 35, 27, 18, 9, 14, 6, 13, 21, 31, 38, 47, 54, 63, 70, 79, 86, 95, 90, 82, 74, 66, 58, 50, 42, 34, 26, 17, 8) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 15)(8, 16)(10, 17)(11, 21)(13, 23)(14, 24)(18, 25)(19, 27)(20, 30)(22, 32)(26, 33)(28, 34)(29, 38)(31, 40)(35, 41)(36, 43)(37, 46)(39, 48)(42, 49)(44, 50)(45, 54)(47, 56)(51, 57)(52, 59)(53, 62)(55, 64)(58, 65)(60, 66)(61, 70)(63, 72)(67, 73)(68, 75)(69, 78)(71, 80)(74, 81)(76, 82)(77, 86)(79, 88)(83, 89)(84, 91)(85, 94)(87, 96)(90, 93)(92, 95) local type(s) :: { ( 48^48 ) } Outer automorphisms :: reflexible selfdual Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 2 e = 48 f = 2 degree seq :: [ 48^2 ] E23.1071 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 48, 48}) Quotient :: edge Aut^+ = C3 x (C16 : C2) (small group id <96, 60>) Aut = $<192, 467>$ (small group id <192, 467>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^2 * T1 * T2^-2 * T1, (T2^-1 * T1 * T2 * T1)^2, T2^23 * T1 * T2 * T1, (T1 * T2^-3)^16 ] Map:: R = (1, 3, 8, 17, 26, 34, 42, 50, 58, 66, 74, 82, 90, 95, 87, 79, 71, 63, 55, 47, 39, 31, 23, 13, 21, 11, 20, 29, 37, 45, 53, 61, 69, 77, 85, 93, 92, 84, 76, 68, 60, 52, 44, 36, 28, 19, 10, 4)(2, 5, 12, 22, 30, 38, 46, 54, 62, 70, 78, 86, 94, 91, 83, 75, 67, 59, 51, 43, 35, 27, 18, 9, 16, 7, 15, 25, 33, 41, 49, 57, 65, 73, 81, 89, 96, 88, 80, 72, 64, 56, 48, 40, 32, 24, 14, 6)(97, 98)(99, 103)(100, 105)(101, 107)(102, 109)(104, 108)(106, 110)(111, 116)(112, 117)(113, 121)(114, 119)(115, 123)(118, 125)(120, 127)(122, 126)(124, 128)(129, 133)(130, 137)(131, 135)(132, 139)(134, 141)(136, 143)(138, 142)(140, 144)(145, 149)(146, 153)(147, 151)(148, 155)(150, 157)(152, 159)(154, 158)(156, 160)(161, 165)(162, 169)(163, 167)(164, 171)(166, 173)(168, 175)(170, 174)(172, 176)(177, 181)(178, 185)(179, 183)(180, 187)(182, 189)(184, 191)(186, 190)(188, 192) 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 ), ( 96^48 ) } Outer automorphisms :: reflexible Dual of E23.1072 Transitivity :: ET+ Graph:: simple bipartite v = 50 e = 96 f = 2 degree seq :: [ 2^48, 48^2 ] E23.1072 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 48, 48}) Quotient :: loop Aut^+ = C3 x (C16 : C2) (small group id <96, 60>) Aut = $<192, 467>$ (small group id <192, 467>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^2 * T1 * T2^-2 * T1, (T2^-1 * T1 * T2 * T1)^2, T2^23 * T1 * T2 * T1, (T1 * T2^-3)^16 ] Map:: R = (1, 97, 3, 99, 8, 104, 17, 113, 26, 122, 34, 130, 42, 138, 50, 146, 58, 154, 66, 162, 74, 170, 82, 178, 90, 186, 95, 191, 87, 183, 79, 175, 71, 167, 63, 159, 55, 151, 47, 143, 39, 135, 31, 127, 23, 119, 13, 109, 21, 117, 11, 107, 20, 116, 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, 19, 115, 10, 106, 4, 100)(2, 98, 5, 101, 12, 108, 22, 118, 30, 126, 38, 134, 46, 142, 54, 150, 62, 158, 70, 166, 78, 174, 86, 182, 94, 190, 91, 187, 83, 179, 75, 171, 67, 163, 59, 155, 51, 147, 43, 139, 35, 131, 27, 123, 18, 114, 9, 105, 16, 112, 7, 103, 15, 111, 25, 121, 33, 129, 41, 137, 49, 145, 57, 153, 65, 161, 73, 169, 81, 177, 89, 185, 96, 192, 88, 184, 80, 176, 72, 168, 64, 160, 56, 152, 48, 144, 40, 136, 32, 128, 24, 120, 14, 110, 6, 102) L = (1, 98)(2, 97)(3, 103)(4, 105)(5, 107)(6, 109)(7, 99)(8, 108)(9, 100)(10, 110)(11, 101)(12, 104)(13, 102)(14, 106)(15, 116)(16, 117)(17, 121)(18, 119)(19, 123)(20, 111)(21, 112)(22, 125)(23, 114)(24, 127)(25, 113)(26, 126)(27, 115)(28, 128)(29, 118)(30, 122)(31, 120)(32, 124)(33, 133)(34, 137)(35, 135)(36, 139)(37, 129)(38, 141)(39, 131)(40, 143)(41, 130)(42, 142)(43, 132)(44, 144)(45, 134)(46, 138)(47, 136)(48, 140)(49, 149)(50, 153)(51, 151)(52, 155)(53, 145)(54, 157)(55, 147)(56, 159)(57, 146)(58, 158)(59, 148)(60, 160)(61, 150)(62, 154)(63, 152)(64, 156)(65, 165)(66, 169)(67, 167)(68, 171)(69, 161)(70, 173)(71, 163)(72, 175)(73, 162)(74, 174)(75, 164)(76, 176)(77, 166)(78, 170)(79, 168)(80, 172)(81, 181)(82, 185)(83, 183)(84, 187)(85, 177)(86, 189)(87, 179)(88, 191)(89, 178)(90, 190)(91, 180)(92, 192)(93, 182)(94, 186)(95, 184)(96, 188) 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 E23.1071 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 96 f = 50 degree seq :: [ 96^2 ] E23.1073 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 48, 48}) Quotient :: dipole Aut^+ = C3 x (C16 : C2) (small group id <96, 60>) Aut = $<192, 467>$ (small group id <192, 467>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^-2 * Y1 * Y2^2 * Y1, (Y2^-1 * R * Y2^-1)^2, (Y2 * Y1 * Y2^-1 * Y1)^2, Y2^23 * Y1 * Y2 * Y1, (Y3 * Y2^-1)^48 ] Map:: R = (1, 97, 2, 98)(3, 99, 7, 103)(4, 100, 9, 105)(5, 101, 11, 107)(6, 102, 13, 109)(8, 104, 12, 108)(10, 106, 14, 110)(15, 111, 20, 116)(16, 112, 21, 117)(17, 113, 25, 121)(18, 114, 23, 119)(19, 115, 27, 123)(22, 118, 29, 125)(24, 120, 31, 127)(26, 122, 30, 126)(28, 124, 32, 128)(33, 129, 37, 133)(34, 130, 41, 137)(35, 131, 39, 135)(36, 132, 43, 139)(38, 134, 45, 141)(40, 136, 47, 143)(42, 138, 46, 142)(44, 140, 48, 144)(49, 145, 53, 149)(50, 146, 57, 153)(51, 147, 55, 151)(52, 148, 59, 155)(54, 150, 61, 157)(56, 152, 63, 159)(58, 154, 62, 158)(60, 156, 64, 160)(65, 161, 69, 165)(66, 162, 73, 169)(67, 163, 71, 167)(68, 164, 75, 171)(70, 166, 77, 173)(72, 168, 79, 175)(74, 170, 78, 174)(76, 172, 80, 176)(81, 177, 85, 181)(82, 178, 89, 185)(83, 179, 87, 183)(84, 180, 91, 187)(86, 182, 93, 189)(88, 184, 95, 191)(90, 186, 94, 190)(92, 188, 96, 192)(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, 287, 383, 279, 375, 271, 367, 263, 359, 255, 351, 247, 343, 239, 335, 231, 327, 223, 319, 215, 311, 205, 301, 213, 309, 203, 299, 212, 308, 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, 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, 283, 379, 275, 371, 267, 363, 259, 355, 251, 347, 243, 339, 235, 331, 227, 323, 219, 315, 210, 306, 201, 297, 208, 304, 199, 295, 207, 303, 217, 313, 225, 321, 233, 329, 241, 337, 249, 345, 257, 353, 265, 361, 273, 369, 281, 377, 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, 204)(9, 196)(10, 206)(11, 197)(12, 200)(13, 198)(14, 202)(15, 212)(16, 213)(17, 217)(18, 215)(19, 219)(20, 207)(21, 208)(22, 221)(23, 210)(24, 223)(25, 209)(26, 222)(27, 211)(28, 224)(29, 214)(30, 218)(31, 216)(32, 220)(33, 229)(34, 233)(35, 231)(36, 235)(37, 225)(38, 237)(39, 227)(40, 239)(41, 226)(42, 238)(43, 228)(44, 240)(45, 230)(46, 234)(47, 232)(48, 236)(49, 245)(50, 249)(51, 247)(52, 251)(53, 241)(54, 253)(55, 243)(56, 255)(57, 242)(58, 254)(59, 244)(60, 256)(61, 246)(62, 250)(63, 248)(64, 252)(65, 261)(66, 265)(67, 263)(68, 267)(69, 257)(70, 269)(71, 259)(72, 271)(73, 258)(74, 270)(75, 260)(76, 272)(77, 262)(78, 266)(79, 264)(80, 268)(81, 277)(82, 281)(83, 279)(84, 283)(85, 273)(86, 285)(87, 275)(88, 287)(89, 274)(90, 286)(91, 276)(92, 288)(93, 278)(94, 282)(95, 280)(96, 284)(97, 289)(98, 290)(99, 291)(100, 292)(101, 293)(102, 294)(103, 295)(104, 296)(105, 297)(106, 298)(107, 299)(108, 300)(109, 301)(110, 302)(111, 303)(112, 304)(113, 305)(114, 306)(115, 307)(116, 308)(117, 309)(118, 310)(119, 311)(120, 312)(121, 313)(122, 314)(123, 315)(124, 316)(125, 317)(126, 318)(127, 319)(128, 320)(129, 321)(130, 322)(131, 323)(132, 324)(133, 325)(134, 326)(135, 327)(136, 328)(137, 329)(138, 330)(139, 331)(140, 332)(141, 333)(142, 334)(143, 335)(144, 336)(145, 337)(146, 338)(147, 339)(148, 340)(149, 341)(150, 342)(151, 343)(152, 344)(153, 345)(154, 346)(155, 347)(156, 348)(157, 349)(158, 350)(159, 351)(160, 352)(161, 353)(162, 354)(163, 355)(164, 356)(165, 357)(166, 358)(167, 359)(168, 360)(169, 361)(170, 362)(171, 363)(172, 364)(173, 365)(174, 366)(175, 367)(176, 368)(177, 369)(178, 370)(179, 371)(180, 372)(181, 373)(182, 374)(183, 375)(184, 376)(185, 377)(186, 378)(187, 379)(188, 380)(189, 381)(190, 382)(191, 383)(192, 384) local type(s) :: { ( 2, 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 E23.1074 Graph:: bipartite v = 50 e = 192 f = 98 degree seq :: [ 4^48, 96^2 ] E23.1074 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 48, 48}) Quotient :: dipole Aut^+ = C3 x (C16 : C2) (small group id <96, 60>) Aut = $<192, 467>$ (small group id <192, 467>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y1)^2, (Y3 * Y2^-1)^2, (R * Y3)^2, Y3 * Y1^2 * Y3 * Y1^-2, (Y1 * Y3 * Y1^-1 * Y3)^2, Y3 * Y1 * Y3 * Y1^23, Y1^-10 * Y3 * Y1^-13 * Y3 * Y1^-1, (Y3 * Y1^-3)^16 ] 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, 89, 185, 81, 177, 73, 169, 65, 161, 57, 153, 49, 145, 41, 137, 33, 129, 25, 121, 16, 112, 24, 120, 15, 111, 23, 119, 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, 12, 108, 22, 118, 30, 126, 39, 135, 46, 142, 55, 151, 62, 158, 71, 167, 78, 174, 87, 183, 94, 190, 91, 187, 83, 179, 75, 171, 67, 163, 59, 155, 51, 147, 43, 139, 35, 131, 27, 123, 18, 114, 9, 105, 14, 110, 6, 102, 13, 109, 21, 117, 31, 127, 38, 134, 47, 143, 54, 150, 63, 159, 70, 166, 79, 175, 86, 182, 95, 191, 90, 186, 82, 178, 74, 170, 66, 162, 58, 154, 50, 146, 42, 138, 34, 130, 26, 122, 17, 113, 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, 207)(8, 208)(9, 196)(10, 209)(11, 213)(12, 197)(13, 215)(14, 216)(15, 199)(16, 200)(17, 202)(18, 217)(19, 219)(20, 222)(21, 203)(22, 224)(23, 205)(24, 206)(25, 210)(26, 225)(27, 211)(28, 226)(29, 230)(30, 212)(31, 232)(32, 214)(33, 218)(34, 220)(35, 233)(36, 235)(37, 238)(38, 221)(39, 240)(40, 223)(41, 227)(42, 241)(43, 228)(44, 242)(45, 246)(46, 229)(47, 248)(48, 231)(49, 234)(50, 236)(51, 249)(52, 251)(53, 254)(54, 237)(55, 256)(56, 239)(57, 243)(58, 257)(59, 244)(60, 258)(61, 262)(62, 245)(63, 264)(64, 247)(65, 250)(66, 252)(67, 265)(68, 267)(69, 270)(70, 253)(71, 272)(72, 255)(73, 259)(74, 273)(75, 260)(76, 274)(77, 278)(78, 261)(79, 280)(80, 263)(81, 266)(82, 268)(83, 281)(84, 283)(85, 286)(86, 269)(87, 288)(88, 271)(89, 275)(90, 285)(91, 276)(92, 287)(93, 282)(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, 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 E23.1073 Graph:: simple bipartite v = 98 e = 192 f = 50 degree seq :: [ 2^96, 96^2 ] E23.1075 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 5, 10}) Quotient :: edge Aut^+ = SL(2,5) (small group id <120, 5>) Aut = SL(2,5) : C2 (small group id <240, 93>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, T2^5, T2^-2 * T1 * T2^-1 * T1^-1 * T2^-1 * T1, (T2 * T1^-1)^4, T1^-1 * T2^-1 * T1^-1 * T2 * T1^-1 * T2^-2 * T1^-1 * T2, T2^2 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1, T1 * T2 * T1 * T2 * T1^2 * T2^-3 * T1, (T2 * T1 * T2)^5 ] Map:: polytopal non-degenerate R = (1, 3, 9, 15, 5)(2, 6, 17, 21, 7)(4, 11, 29, 33, 12)(8, 22, 49, 51, 23)(10, 26, 31, 56, 27)(13, 34, 44, 18, 35)(14, 36, 63, 64, 37)(16, 40, 67, 69, 41)(19, 45, 59, 30, 46)(20, 47, 73, 54, 25)(24, 52, 79, 80, 53)(28, 38, 65, 82, 57)(32, 60, 84, 71, 43)(39, 50, 77, 90, 66)(42, 70, 95, 76, 55)(48, 68, 93, 98, 74)(58, 83, 104, 92, 72)(61, 62, 86, 106, 85)(75, 99, 113, 102, 81)(78, 97, 111, 114, 100)(87, 101, 115, 116, 103)(88, 89, 108, 118, 107)(91, 109, 119, 112, 96)(94, 105, 117, 120, 110)(121, 122, 124)(123, 128, 130)(125, 133, 134)(126, 136, 138)(127, 139, 140)(129, 144, 145)(131, 148, 150)(132, 151, 152)(135, 158, 159)(137, 162, 163)(141, 142, 168)(143, 165, 170)(146, 155, 166)(147, 167, 175)(149, 178, 157)(153, 160, 181)(154, 182, 177)(156, 173, 179)(161, 176, 188)(164, 180, 192)(169, 195, 196)(171, 172, 198)(174, 197, 201)(183, 207, 186)(184, 206, 208)(185, 209, 200)(187, 211, 212)(189, 190, 214)(191, 213, 216)(193, 217, 194)(199, 221, 222)(202, 203, 223)(204, 225, 205)(210, 228, 220)(215, 231, 232)(218, 219, 230)(224, 237, 227)(226, 229, 236)(233, 238, 239)(234, 235, 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) :: { ( 20^3 ), ( 20^5 ) } Outer automorphisms :: reflexible Dual of E23.1079 Transitivity :: ET+ Graph:: simple bipartite v = 64 e = 120 f = 12 degree seq :: [ 3^40, 5^24 ] E23.1076 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 5, 10}) Quotient :: edge Aut^+ = SL(2,5) (small group id <120, 5>) Aut = SL(2,5) : C2 (small group id <240, 93>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^5, (T1^-1 * T2^-1)^3, T2^2 * T1 * T2^-3 * T1, T1^2 * T2^-1 * T1^-1 * T2 * T1^-1 * T2^-1, (T2 * T1^-1 * T2)^3, T2^10, (T2 * T1^-1)^5 ] Map:: polytopal non-degenerate R = (1, 3, 10, 30, 72, 113, 95, 49, 17, 5)(2, 7, 21, 57, 90, 111, 68, 48, 25, 8)(4, 12, 36, 29, 55, 103, 69, 75, 41, 14)(6, 18, 51, 96, 79, 91, 46, 65, 54, 19)(9, 27, 50, 24, 35, 56, 20, 16, 45, 28)(11, 32, 76, 71, 40, 87, 80, 93, 47, 34)(13, 38, 83, 67, 26, 66, 63, 102, 86, 39)(15, 43, 31, 73, 64, 60, 22, 59, 89, 44)(23, 42, 58, 104, 101, 98, 52, 94, 108, 62)(33, 37, 81, 112, 70, 85, 99, 118, 115, 78)(53, 61, 97, 119, 114, 82, 84, 110, 120, 100)(74, 77, 107, 109, 105, 106, 116, 117, 88, 92)(121, 122, 126, 133, 124)(123, 129, 146, 153, 131)(125, 135, 162, 166, 136)(127, 140, 175, 154, 142)(128, 143, 181, 183, 144)(130, 149, 190, 194, 151)(132, 155, 199, 202, 157)(134, 160, 163, 188, 147)(137, 167, 212, 214, 168)(138, 170, 192, 180, 172)(139, 173, 219, 189, 148)(141, 150, 191, 225, 178)(145, 184, 229, 230, 185)(152, 195, 206, 234, 197)(156, 187, 220, 236, 200)(158, 165, 210, 218, 204)(159, 205, 207, 215, 176)(161, 198, 226, 179, 169)(164, 208, 217, 171, 177)(174, 221, 237, 201, 222)(182, 227, 238, 203, 216)(186, 223, 233, 231, 211)(193, 213, 235, 239, 224)(196, 232, 240, 228, 209) 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) :: { ( 6^5 ), ( 6^10 ) } Outer automorphisms :: reflexible Dual of E23.1080 Transitivity :: ET+ Graph:: simple bipartite v = 36 e = 120 f = 40 degree seq :: [ 5^24, 10^12 ] E23.1077 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {3, 5, 10}) Quotient :: edge Aut^+ = SL(2,5) (small group id <120, 5>) Aut = SL(2,5) : C2 (small group id <240, 93>) |r| :: 2 Presentation :: [ F^2, T2^3, (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1^-2 * T2 * T1^-1 * T2^-1, T1^4 * T2 * T1^-1 * T2, (T2 * T1^-1)^4, (T2^-1 * T1^-1)^5 ] Map:: polytopal non-degenerate R = (1, 3, 5)(2, 7, 8)(4, 11, 13)(6, 17, 18)(9, 24, 25)(10, 26, 28)(12, 31, 33)(14, 37, 38)(15, 39, 41)(16, 34, 42)(19, 46, 27)(20, 32, 48)(21, 30, 49)(22, 50, 51)(23, 52, 53)(29, 58, 59)(35, 36, 64)(40, 54, 65)(43, 69, 47)(44, 70, 71)(45, 72, 73)(55, 57, 76)(56, 66, 81)(60, 84, 67)(61, 62, 86)(63, 82, 87)(68, 91, 92)(74, 75, 94)(77, 99, 80)(78, 98, 100)(79, 101, 102)(83, 88, 104)(85, 105, 93)(89, 90, 108)(95, 113, 97)(96, 112, 114)(103, 115, 116)(106, 107, 118)(109, 119, 111)(110, 117, 120)(121, 122, 126, 136, 158, 169, 146, 152, 132, 124)(123, 129, 143, 142, 128, 141, 159, 177, 147, 130)(125, 134, 156, 176, 145, 150, 131, 149, 160, 135)(127, 139, 165, 164, 138, 148, 170, 195, 167, 140)(133, 154, 182, 203, 179, 157, 151, 180, 183, 155)(137, 163, 188, 187, 162, 168, 190, 205, 181, 153)(144, 174, 199, 198, 173, 161, 186, 210, 200, 175)(166, 172, 197, 216, 193, 171, 196, 218, 217, 194)(178, 202, 223, 209, 185, 184, 208, 227, 222, 201)(189, 192, 215, 230, 212, 191, 214, 232, 231, 213)(204, 225, 237, 226, 207, 206, 211, 229, 236, 224)(219, 221, 235, 240, 234, 220, 228, 238, 239, 233) L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 161)(42, 162)(43, 163)(44, 164)(45, 165)(46, 166)(47, 167)(48, 168)(49, 169)(50, 170)(51, 171)(52, 172)(53, 173)(54, 174)(55, 175)(56, 176)(57, 177)(58, 178)(59, 179)(60, 180)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 10^3 ), ( 10^10 ) } Outer automorphisms :: reflexible Dual of E23.1078 Transitivity :: ET+ Graph:: simple bipartite v = 52 e = 120 f = 24 degree seq :: [ 3^40, 10^12 ] E23.1078 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 5, 10}) Quotient :: loop Aut^+ = SL(2,5) (small group id <120, 5>) Aut = SL(2,5) : C2 (small group id <240, 93>) |r| :: 2 Presentation :: [ F^2, T1^3, (F * T2)^2, (F * T1)^2, T2^5, T2^-2 * T1 * T2^-1 * T1^-1 * T2^-1 * T1, (T2 * T1^-1)^4, T1^-1 * T2^-1 * T1^-1 * T2 * T1^-1 * T2^-2 * T1^-1 * T2, T2^2 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1, T1 * T2 * T1 * T2 * T1^2 * T2^-3 * T1, (T2 * T1 * T2)^5 ] Map:: polytopal non-degenerate R = (1, 121, 3, 123, 9, 129, 15, 135, 5, 125)(2, 122, 6, 126, 17, 137, 21, 141, 7, 127)(4, 124, 11, 131, 29, 149, 33, 153, 12, 132)(8, 128, 22, 142, 49, 169, 51, 171, 23, 143)(10, 130, 26, 146, 31, 151, 56, 176, 27, 147)(13, 133, 34, 154, 44, 164, 18, 138, 35, 155)(14, 134, 36, 156, 63, 183, 64, 184, 37, 157)(16, 136, 40, 160, 67, 187, 69, 189, 41, 161)(19, 139, 45, 165, 59, 179, 30, 150, 46, 166)(20, 140, 47, 167, 73, 193, 54, 174, 25, 145)(24, 144, 52, 172, 79, 199, 80, 200, 53, 173)(28, 148, 38, 158, 65, 185, 82, 202, 57, 177)(32, 152, 60, 180, 84, 204, 71, 191, 43, 163)(39, 159, 50, 170, 77, 197, 90, 210, 66, 186)(42, 162, 70, 190, 95, 215, 76, 196, 55, 175)(48, 168, 68, 188, 93, 213, 98, 218, 74, 194)(58, 178, 83, 203, 104, 224, 92, 212, 72, 192)(61, 181, 62, 182, 86, 206, 106, 226, 85, 205)(75, 195, 99, 219, 113, 233, 102, 222, 81, 201)(78, 198, 97, 217, 111, 231, 114, 234, 100, 220)(87, 207, 101, 221, 115, 235, 116, 236, 103, 223)(88, 208, 89, 209, 108, 228, 118, 238, 107, 227)(91, 211, 109, 229, 119, 239, 112, 232, 96, 216)(94, 214, 105, 225, 117, 237, 120, 240, 110, 230) L = (1, 122)(2, 124)(3, 128)(4, 121)(5, 133)(6, 136)(7, 139)(8, 130)(9, 144)(10, 123)(11, 148)(12, 151)(13, 134)(14, 125)(15, 158)(16, 138)(17, 162)(18, 126)(19, 140)(20, 127)(21, 142)(22, 168)(23, 165)(24, 145)(25, 129)(26, 155)(27, 167)(28, 150)(29, 178)(30, 131)(31, 152)(32, 132)(33, 160)(34, 182)(35, 166)(36, 173)(37, 149)(38, 159)(39, 135)(40, 181)(41, 176)(42, 163)(43, 137)(44, 180)(45, 170)(46, 146)(47, 175)(48, 141)(49, 195)(50, 143)(51, 172)(52, 198)(53, 179)(54, 197)(55, 147)(56, 188)(57, 154)(58, 157)(59, 156)(60, 192)(61, 153)(62, 177)(63, 207)(64, 206)(65, 209)(66, 183)(67, 211)(68, 161)(69, 190)(70, 214)(71, 213)(72, 164)(73, 217)(74, 193)(75, 196)(76, 169)(77, 201)(78, 171)(79, 221)(80, 185)(81, 174)(82, 203)(83, 223)(84, 225)(85, 204)(86, 208)(87, 186)(88, 184)(89, 200)(90, 228)(91, 212)(92, 187)(93, 216)(94, 189)(95, 231)(96, 191)(97, 194)(98, 219)(99, 230)(100, 210)(101, 222)(102, 199)(103, 202)(104, 237)(105, 205)(106, 229)(107, 224)(108, 220)(109, 236)(110, 218)(111, 232)(112, 215)(113, 238)(114, 235)(115, 240)(116, 226)(117, 227)(118, 239)(119, 233)(120, 234) local type(s) :: { ( 3, 10, 3, 10, 3, 10, 3, 10, 3, 10 ) } Outer automorphisms :: reflexible Dual of E23.1077 Transitivity :: ET+ VT+ AT Graph:: simple v = 24 e = 120 f = 52 degree seq :: [ 10^24 ] E23.1079 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 5, 10}) Quotient :: loop Aut^+ = SL(2,5) (small group id <120, 5>) Aut = SL(2,5) : C2 (small group id <240, 93>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, T1^5, (T1^-1 * T2^-1)^3, T2^2 * T1 * T2^-3 * T1, T1^2 * T2^-1 * T1^-1 * T2 * T1^-1 * T2^-1, (T2 * T1^-1 * T2)^3, T2^10, (T2 * T1^-1)^5 ] Map:: polytopal non-degenerate R = (1, 121, 3, 123, 10, 130, 30, 150, 72, 192, 113, 233, 95, 215, 49, 169, 17, 137, 5, 125)(2, 122, 7, 127, 21, 141, 57, 177, 90, 210, 111, 231, 68, 188, 48, 168, 25, 145, 8, 128)(4, 124, 12, 132, 36, 156, 29, 149, 55, 175, 103, 223, 69, 189, 75, 195, 41, 161, 14, 134)(6, 126, 18, 138, 51, 171, 96, 216, 79, 199, 91, 211, 46, 166, 65, 185, 54, 174, 19, 139)(9, 129, 27, 147, 50, 170, 24, 144, 35, 155, 56, 176, 20, 140, 16, 136, 45, 165, 28, 148)(11, 131, 32, 152, 76, 196, 71, 191, 40, 160, 87, 207, 80, 200, 93, 213, 47, 167, 34, 154)(13, 133, 38, 158, 83, 203, 67, 187, 26, 146, 66, 186, 63, 183, 102, 222, 86, 206, 39, 159)(15, 135, 43, 163, 31, 151, 73, 193, 64, 184, 60, 180, 22, 142, 59, 179, 89, 209, 44, 164)(23, 143, 42, 162, 58, 178, 104, 224, 101, 221, 98, 218, 52, 172, 94, 214, 108, 228, 62, 182)(33, 153, 37, 157, 81, 201, 112, 232, 70, 190, 85, 205, 99, 219, 118, 238, 115, 235, 78, 198)(53, 173, 61, 181, 97, 217, 119, 239, 114, 234, 82, 202, 84, 204, 110, 230, 120, 240, 100, 220)(74, 194, 77, 197, 107, 227, 109, 229, 105, 225, 106, 226, 116, 236, 117, 237, 88, 208, 92, 212) L = (1, 122)(2, 126)(3, 129)(4, 121)(5, 135)(6, 133)(7, 140)(8, 143)(9, 146)(10, 149)(11, 123)(12, 155)(13, 124)(14, 160)(15, 162)(16, 125)(17, 167)(18, 170)(19, 173)(20, 175)(21, 150)(22, 127)(23, 181)(24, 128)(25, 184)(26, 153)(27, 134)(28, 139)(29, 190)(30, 191)(31, 130)(32, 195)(33, 131)(34, 142)(35, 199)(36, 187)(37, 132)(38, 165)(39, 205)(40, 163)(41, 198)(42, 166)(43, 188)(44, 208)(45, 210)(46, 136)(47, 212)(48, 137)(49, 161)(50, 192)(51, 177)(52, 138)(53, 219)(54, 221)(55, 154)(56, 159)(57, 164)(58, 141)(59, 169)(60, 172)(61, 183)(62, 227)(63, 144)(64, 229)(65, 145)(66, 223)(67, 220)(68, 147)(69, 148)(70, 194)(71, 225)(72, 180)(73, 213)(74, 151)(75, 206)(76, 232)(77, 152)(78, 226)(79, 202)(80, 156)(81, 222)(82, 157)(83, 216)(84, 158)(85, 207)(86, 234)(87, 215)(88, 217)(89, 196)(90, 218)(91, 186)(92, 214)(93, 235)(94, 168)(95, 176)(96, 182)(97, 171)(98, 204)(99, 189)(100, 236)(101, 237)(102, 174)(103, 233)(104, 193)(105, 178)(106, 179)(107, 238)(108, 209)(109, 230)(110, 185)(111, 211)(112, 240)(113, 231)(114, 197)(115, 239)(116, 200)(117, 201)(118, 203)(119, 224)(120, 228) local type(s) :: { ( 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5, 3, 5 ) } Outer automorphisms :: reflexible Dual of E23.1075 Transitivity :: ET+ VT+ AT Graph:: v = 12 e = 120 f = 64 degree seq :: [ 20^12 ] E23.1080 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {3, 5, 10}) Quotient :: loop Aut^+ = SL(2,5) (small group id <120, 5>) Aut = SL(2,5) : C2 (small group id <240, 93>) |r| :: 2 Presentation :: [ F^2, T2^3, (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1^-2 * T2 * T1^-1 * T2^-1, T1^4 * T2 * T1^-1 * T2, (T2 * T1^-1)^4, (T2^-1 * T1^-1)^5 ] Map:: polytopal non-degenerate R = (1, 121, 3, 123, 5, 125)(2, 122, 7, 127, 8, 128)(4, 124, 11, 131, 13, 133)(6, 126, 17, 137, 18, 138)(9, 129, 24, 144, 25, 145)(10, 130, 26, 146, 28, 148)(12, 132, 31, 151, 33, 153)(14, 134, 37, 157, 38, 158)(15, 135, 39, 159, 41, 161)(16, 136, 34, 154, 42, 162)(19, 139, 46, 166, 27, 147)(20, 140, 32, 152, 48, 168)(21, 141, 30, 150, 49, 169)(22, 142, 50, 170, 51, 171)(23, 143, 52, 172, 53, 173)(29, 149, 58, 178, 59, 179)(35, 155, 36, 156, 64, 184)(40, 160, 54, 174, 65, 185)(43, 163, 69, 189, 47, 167)(44, 164, 70, 190, 71, 191)(45, 165, 72, 192, 73, 193)(55, 175, 57, 177, 76, 196)(56, 176, 66, 186, 81, 201)(60, 180, 84, 204, 67, 187)(61, 181, 62, 182, 86, 206)(63, 183, 82, 202, 87, 207)(68, 188, 91, 211, 92, 212)(74, 194, 75, 195, 94, 214)(77, 197, 99, 219, 80, 200)(78, 198, 98, 218, 100, 220)(79, 199, 101, 221, 102, 222)(83, 203, 88, 208, 104, 224)(85, 205, 105, 225, 93, 213)(89, 209, 90, 210, 108, 228)(95, 215, 113, 233, 97, 217)(96, 216, 112, 232, 114, 234)(103, 223, 115, 235, 116, 236)(106, 226, 107, 227, 118, 238)(109, 229, 119, 239, 111, 231)(110, 230, 117, 237, 120, 240) L = (1, 122)(2, 126)(3, 129)(4, 121)(5, 134)(6, 136)(7, 139)(8, 141)(9, 143)(10, 123)(11, 149)(12, 124)(13, 154)(14, 156)(15, 125)(16, 158)(17, 163)(18, 148)(19, 165)(20, 127)(21, 159)(22, 128)(23, 142)(24, 174)(25, 150)(26, 152)(27, 130)(28, 170)(29, 160)(30, 131)(31, 180)(32, 132)(33, 137)(34, 182)(35, 133)(36, 176)(37, 151)(38, 169)(39, 177)(40, 135)(41, 186)(42, 168)(43, 188)(44, 138)(45, 164)(46, 172)(47, 140)(48, 190)(49, 146)(50, 195)(51, 196)(52, 197)(53, 161)(54, 199)(55, 144)(56, 145)(57, 147)(58, 202)(59, 157)(60, 183)(61, 153)(62, 203)(63, 155)(64, 208)(65, 184)(66, 210)(67, 162)(68, 187)(69, 192)(70, 205)(71, 214)(72, 215)(73, 171)(74, 166)(75, 167)(76, 218)(77, 216)(78, 173)(79, 198)(80, 175)(81, 178)(82, 223)(83, 179)(84, 225)(85, 181)(86, 211)(87, 206)(88, 227)(89, 185)(90, 200)(91, 229)(92, 191)(93, 189)(94, 232)(95, 230)(96, 193)(97, 194)(98, 217)(99, 221)(100, 228)(101, 235)(102, 201)(103, 209)(104, 204)(105, 237)(106, 207)(107, 222)(108, 238)(109, 236)(110, 212)(111, 213)(112, 231)(113, 219)(114, 220)(115, 240)(116, 224)(117, 226)(118, 239)(119, 233)(120, 234) local type(s) :: { ( 5, 10, 5, 10, 5, 10 ) } Outer automorphisms :: reflexible Dual of E23.1076 Transitivity :: ET+ VT+ AT Graph:: simple v = 40 e = 120 f = 36 degree seq :: [ 6^40 ] E23.1081 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 5, 10}) Quotient :: dipole Aut^+ = SL(2,5) (small group id <120, 5>) Aut = SL(2,5) : C2 (small group id <240, 93>) |r| :: 2 Presentation :: [ R^2, Y3 * Y1, Y3 * Y1^-2, (R * Y3)^2, (R * Y1)^2, Y2^5, (R * Y2 * Y3^-1)^2, Y2 * Y3 * Y2^2 * Y1^-1 * Y2 * Y1, Y1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1 * Y2^-2, Y1 * Y2^3 * Y3^-1 * Y2^-1 * Y1^-1 * Y2^-1, Y2 * Y3 * Y2^-1 * Y1 * Y2^-1 * Y3^-1 * Y2 * Y1^-1, Y2 * Y1 * Y2 * Y1^-1 * Y2^-1 * Y1^-1 * Y2 * Y3^-1 * Y2 * Y1, Y2 * Y1 * Y2^2 * Y1 * Y2^2 * Y1 * Y2^2 * Y3^-1 * Y2^2 * Y3^-1 * Y2, (Y3 * Y2^-1)^10 ] Map:: R = (1, 121, 2, 122, 4, 124)(3, 123, 8, 128, 10, 130)(5, 125, 13, 133, 14, 134)(6, 126, 16, 136, 18, 138)(7, 127, 19, 139, 20, 140)(9, 129, 24, 144, 25, 145)(11, 131, 28, 148, 30, 150)(12, 132, 31, 151, 32, 152)(15, 135, 38, 158, 39, 159)(17, 137, 42, 162, 43, 163)(21, 141, 22, 142, 48, 168)(23, 143, 45, 165, 50, 170)(26, 146, 35, 155, 46, 166)(27, 147, 47, 167, 55, 175)(29, 149, 58, 178, 37, 157)(33, 153, 40, 160, 61, 181)(34, 154, 62, 182, 57, 177)(36, 156, 53, 173, 59, 179)(41, 161, 56, 176, 68, 188)(44, 164, 60, 180, 72, 192)(49, 169, 75, 195, 76, 196)(51, 171, 52, 172, 78, 198)(54, 174, 77, 197, 81, 201)(63, 183, 87, 207, 66, 186)(64, 184, 86, 206, 88, 208)(65, 185, 89, 209, 80, 200)(67, 187, 91, 211, 92, 212)(69, 189, 70, 190, 94, 214)(71, 191, 93, 213, 96, 216)(73, 193, 97, 217, 74, 194)(79, 199, 101, 221, 102, 222)(82, 202, 83, 203, 103, 223)(84, 204, 105, 225, 85, 205)(90, 210, 108, 228, 100, 220)(95, 215, 111, 231, 112, 232)(98, 218, 99, 219, 110, 230)(104, 224, 117, 237, 107, 227)(106, 226, 109, 229, 116, 236)(113, 233, 118, 238, 119, 239)(114, 234, 115, 235, 120, 240)(241, 361, 243, 363, 249, 369, 255, 375, 245, 365)(242, 362, 246, 366, 257, 377, 261, 381, 247, 367)(244, 364, 251, 371, 269, 389, 273, 393, 252, 372)(248, 368, 262, 382, 289, 409, 291, 411, 263, 383)(250, 370, 266, 386, 271, 391, 296, 416, 267, 387)(253, 373, 274, 394, 284, 404, 258, 378, 275, 395)(254, 374, 276, 396, 303, 423, 304, 424, 277, 397)(256, 376, 280, 400, 307, 427, 309, 429, 281, 401)(259, 379, 285, 405, 299, 419, 270, 390, 286, 406)(260, 380, 287, 407, 313, 433, 294, 414, 265, 385)(264, 384, 292, 412, 319, 439, 320, 440, 293, 413)(268, 388, 278, 398, 305, 425, 322, 442, 297, 417)(272, 392, 300, 420, 324, 444, 311, 431, 283, 403)(279, 399, 290, 410, 317, 437, 330, 450, 306, 426)(282, 402, 310, 430, 335, 455, 316, 436, 295, 415)(288, 408, 308, 428, 333, 453, 338, 458, 314, 434)(298, 418, 323, 443, 344, 464, 332, 452, 312, 432)(301, 421, 302, 422, 326, 446, 346, 466, 325, 445)(315, 435, 339, 459, 353, 473, 342, 462, 321, 441)(318, 438, 337, 457, 351, 471, 354, 474, 340, 460)(327, 447, 341, 461, 355, 475, 356, 476, 343, 463)(328, 448, 329, 449, 348, 468, 358, 478, 347, 467)(331, 451, 349, 469, 359, 479, 352, 472, 336, 456)(334, 454, 345, 465, 357, 477, 360, 480, 350, 470) L = (1, 244)(2, 241)(3, 250)(4, 242)(5, 254)(6, 258)(7, 260)(8, 243)(9, 265)(10, 248)(11, 270)(12, 272)(13, 245)(14, 253)(15, 279)(16, 246)(17, 283)(18, 256)(19, 247)(20, 259)(21, 288)(22, 261)(23, 290)(24, 249)(25, 264)(26, 286)(27, 295)(28, 251)(29, 277)(30, 268)(31, 252)(32, 271)(33, 301)(34, 297)(35, 266)(36, 299)(37, 298)(38, 255)(39, 278)(40, 273)(41, 308)(42, 257)(43, 282)(44, 312)(45, 263)(46, 275)(47, 267)(48, 262)(49, 316)(50, 285)(51, 318)(52, 291)(53, 276)(54, 321)(55, 287)(56, 281)(57, 302)(58, 269)(59, 293)(60, 284)(61, 280)(62, 274)(63, 306)(64, 328)(65, 320)(66, 327)(67, 332)(68, 296)(69, 334)(70, 309)(71, 336)(72, 300)(73, 314)(74, 337)(75, 289)(76, 315)(77, 294)(78, 292)(79, 342)(80, 329)(81, 317)(82, 343)(83, 322)(84, 325)(85, 345)(86, 304)(87, 303)(88, 326)(89, 305)(90, 340)(91, 307)(92, 331)(93, 311)(94, 310)(95, 352)(96, 333)(97, 313)(98, 350)(99, 338)(100, 348)(101, 319)(102, 341)(103, 323)(104, 347)(105, 324)(106, 356)(107, 357)(108, 330)(109, 346)(110, 339)(111, 335)(112, 351)(113, 359)(114, 360)(115, 354)(116, 349)(117, 344)(118, 353)(119, 358)(120, 355)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 2, 20, 2, 20, 2, 20 ), ( 2, 20, 2, 20, 2, 20, 2, 20, 2, 20 ) } Outer automorphisms :: reflexible Dual of E23.1084 Graph:: bipartite v = 64 e = 240 f = 132 degree seq :: [ 6^40, 10^24 ] E23.1082 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 5, 10}) Quotient :: dipole Aut^+ = SL(2,5) (small group id <120, 5>) Aut = SL(2,5) : C2 (small group id <240, 93>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, Y1^5, (Y1^-1 * Y2^-1)^3, (Y3^-1 * Y1^-1)^3, Y1 * Y2^-1 * Y1 * Y2 * Y1^-2 * Y2, Y1 * Y2^2 * Y1 * Y2^-3, (Y2 * Y1^-1 * Y2)^3, Y2^10, (Y2 * Y1^-1)^5 ] Map:: R = (1, 121, 2, 122, 6, 126, 13, 133, 4, 124)(3, 123, 9, 129, 26, 146, 33, 153, 11, 131)(5, 125, 15, 135, 42, 162, 46, 166, 16, 136)(7, 127, 20, 140, 55, 175, 34, 154, 22, 142)(8, 128, 23, 143, 61, 181, 63, 183, 24, 144)(10, 130, 29, 149, 70, 190, 74, 194, 31, 151)(12, 132, 35, 155, 79, 199, 82, 202, 37, 157)(14, 134, 40, 160, 43, 163, 68, 188, 27, 147)(17, 137, 47, 167, 92, 212, 94, 214, 48, 168)(18, 138, 50, 170, 72, 192, 60, 180, 52, 172)(19, 139, 53, 173, 99, 219, 69, 189, 28, 148)(21, 141, 30, 150, 71, 191, 105, 225, 58, 178)(25, 145, 64, 184, 109, 229, 110, 230, 65, 185)(32, 152, 75, 195, 86, 206, 114, 234, 77, 197)(36, 156, 67, 187, 100, 220, 116, 236, 80, 200)(38, 158, 45, 165, 90, 210, 98, 218, 84, 204)(39, 159, 85, 205, 87, 207, 95, 215, 56, 176)(41, 161, 78, 198, 106, 226, 59, 179, 49, 169)(44, 164, 88, 208, 97, 217, 51, 171, 57, 177)(54, 174, 101, 221, 117, 237, 81, 201, 102, 222)(62, 182, 107, 227, 118, 238, 83, 203, 96, 216)(66, 186, 103, 223, 113, 233, 111, 231, 91, 211)(73, 193, 93, 213, 115, 235, 119, 239, 104, 224)(76, 196, 112, 232, 120, 240, 108, 228, 89, 209)(241, 361, 243, 363, 250, 370, 270, 390, 312, 432, 353, 473, 335, 455, 289, 409, 257, 377, 245, 365)(242, 362, 247, 367, 261, 381, 297, 417, 330, 450, 351, 471, 308, 428, 288, 408, 265, 385, 248, 368)(244, 364, 252, 372, 276, 396, 269, 389, 295, 415, 343, 463, 309, 429, 315, 435, 281, 401, 254, 374)(246, 366, 258, 378, 291, 411, 336, 456, 319, 439, 331, 451, 286, 406, 305, 425, 294, 414, 259, 379)(249, 369, 267, 387, 290, 410, 264, 384, 275, 395, 296, 416, 260, 380, 256, 376, 285, 405, 268, 388)(251, 371, 272, 392, 316, 436, 311, 431, 280, 400, 327, 447, 320, 440, 333, 453, 287, 407, 274, 394)(253, 373, 278, 398, 323, 443, 307, 427, 266, 386, 306, 426, 303, 423, 342, 462, 326, 446, 279, 399)(255, 375, 283, 403, 271, 391, 313, 433, 304, 424, 300, 420, 262, 382, 299, 419, 329, 449, 284, 404)(263, 383, 282, 402, 298, 418, 344, 464, 341, 461, 338, 458, 292, 412, 334, 454, 348, 468, 302, 422)(273, 393, 277, 397, 321, 441, 352, 472, 310, 430, 325, 445, 339, 459, 358, 478, 355, 475, 318, 438)(293, 413, 301, 421, 337, 457, 359, 479, 354, 474, 322, 442, 324, 444, 350, 470, 360, 480, 340, 460)(314, 434, 317, 437, 347, 467, 349, 469, 345, 465, 346, 466, 356, 476, 357, 477, 328, 448, 332, 452) L = (1, 243)(2, 247)(3, 250)(4, 252)(5, 241)(6, 258)(7, 261)(8, 242)(9, 267)(10, 270)(11, 272)(12, 276)(13, 278)(14, 244)(15, 283)(16, 285)(17, 245)(18, 291)(19, 246)(20, 256)(21, 297)(22, 299)(23, 282)(24, 275)(25, 248)(26, 306)(27, 290)(28, 249)(29, 295)(30, 312)(31, 313)(32, 316)(33, 277)(34, 251)(35, 296)(36, 269)(37, 321)(38, 323)(39, 253)(40, 327)(41, 254)(42, 298)(43, 271)(44, 255)(45, 268)(46, 305)(47, 274)(48, 265)(49, 257)(50, 264)(51, 336)(52, 334)(53, 301)(54, 259)(55, 343)(56, 260)(57, 330)(58, 344)(59, 329)(60, 262)(61, 337)(62, 263)(63, 342)(64, 300)(65, 294)(66, 303)(67, 266)(68, 288)(69, 315)(70, 325)(71, 280)(72, 353)(73, 304)(74, 317)(75, 281)(76, 311)(77, 347)(78, 273)(79, 331)(80, 333)(81, 352)(82, 324)(83, 307)(84, 350)(85, 339)(86, 279)(87, 320)(88, 332)(89, 284)(90, 351)(91, 286)(92, 314)(93, 287)(94, 348)(95, 289)(96, 319)(97, 359)(98, 292)(99, 358)(100, 293)(101, 338)(102, 326)(103, 309)(104, 341)(105, 346)(106, 356)(107, 349)(108, 302)(109, 345)(110, 360)(111, 308)(112, 310)(113, 335)(114, 322)(115, 318)(116, 357)(117, 328)(118, 355)(119, 354)(120, 340)(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, 6, 2, 6, 2, 6, 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 E23.1083 Graph:: bipartite v = 36 e = 240 f = 160 degree seq :: [ 10^24, 20^12 ] E23.1083 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 5, 10}) Quotient :: dipole Aut^+ = SL(2,5) (small group id <120, 5>) Aut = SL(2,5) : C2 (small group id <240, 93>) |r| :: 2 Presentation :: [ Y1, R^2, Y2^3, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3 * Y2 * Y3^2 * Y2 * Y3 * Y2^-1, Y3 * Y2 * Y3^-4 * Y2, (Y3 * Y2^-1)^5, (Y3^-1 * Y1^-1)^10 ] 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, 244, 364)(243, 363, 248, 368, 250, 370)(245, 365, 253, 373, 254, 374)(246, 366, 256, 376, 258, 378)(247, 367, 259, 379, 260, 380)(249, 369, 264, 384, 266, 386)(251, 371, 269, 389, 271, 391)(252, 372, 272, 392, 273, 393)(255, 375, 279, 399, 280, 400)(257, 377, 276, 396, 284, 404)(261, 381, 289, 409, 290, 410)(262, 382, 282, 402, 278, 398)(263, 383, 291, 411, 292, 412)(265, 385, 294, 414, 275, 395)(267, 387, 274, 394, 297, 417)(268, 388, 298, 418, 281, 401)(270, 390, 287, 407, 300, 420)(277, 397, 285, 405, 304, 424)(283, 403, 307, 427, 286, 406)(288, 408, 301, 421, 312, 432)(293, 413, 317, 437, 318, 438)(295, 415, 299, 419, 321, 441)(296, 416, 315, 435, 322, 442)(302, 422, 305, 425, 326, 446)(303, 423, 327, 447, 328, 448)(306, 426, 319, 439, 330, 450)(308, 428, 309, 429, 333, 453)(310, 430, 313, 433, 334, 454)(311, 431, 335, 455, 336, 456)(314, 434, 331, 451, 338, 458)(316, 436, 323, 443, 340, 460)(320, 440, 341, 461, 342, 462)(324, 444, 325, 445, 346, 466)(329, 449, 343, 463, 348, 468)(332, 452, 347, 467, 349, 469)(337, 457, 350, 470, 352, 472)(339, 459, 351, 471, 353, 473)(344, 464, 345, 465, 357, 477)(354, 474, 360, 480, 358, 478)(355, 475, 356, 476, 359, 479) L = (1, 243)(2, 246)(3, 249)(4, 251)(5, 241)(6, 257)(7, 242)(8, 262)(9, 265)(10, 267)(11, 270)(12, 244)(13, 275)(14, 277)(15, 245)(16, 282)(17, 283)(18, 280)(19, 286)(20, 288)(21, 247)(22, 260)(23, 248)(24, 272)(25, 256)(26, 295)(27, 296)(28, 250)(29, 278)(30, 263)(31, 290)(32, 292)(33, 281)(34, 252)(35, 302)(36, 253)(37, 261)(38, 254)(39, 266)(40, 306)(41, 255)(42, 273)(43, 269)(44, 308)(45, 258)(46, 310)(47, 259)(48, 274)(49, 284)(50, 314)(51, 312)(52, 316)(53, 264)(54, 298)(55, 320)(56, 293)(57, 300)(58, 318)(59, 268)(60, 324)(61, 271)(62, 309)(63, 276)(64, 328)(65, 279)(66, 303)(67, 304)(68, 332)(69, 285)(70, 325)(71, 287)(72, 336)(73, 289)(74, 311)(75, 291)(76, 299)(77, 340)(78, 329)(79, 294)(80, 319)(81, 322)(82, 344)(83, 297)(84, 339)(85, 301)(86, 342)(87, 326)(88, 337)(89, 305)(90, 348)(91, 307)(92, 331)(93, 330)(94, 349)(95, 334)(96, 345)(97, 313)(98, 352)(99, 315)(100, 353)(101, 317)(102, 355)(103, 321)(104, 354)(105, 323)(106, 338)(107, 327)(108, 358)(109, 359)(110, 333)(111, 335)(112, 360)(113, 356)(114, 341)(115, 350)(116, 343)(117, 346)(118, 347)(119, 357)(120, 351)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 10, 20 ), ( 10, 20, 10, 20, 10, 20 ) } Outer automorphisms :: reflexible Dual of E23.1082 Graph:: simple bipartite v = 160 e = 240 f = 36 degree seq :: [ 2^120, 6^40 ] E23.1084 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 5, 10}) Quotient :: dipole Aut^+ = SL(2,5) (small group id <120, 5>) Aut = SL(2,5) : C2 (small group id <240, 93>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^3, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^3, Y1^-1 * Y3 * Y1^-2 * Y3 * Y1^-1 * Y3^-1, Y1 * Y3 * Y1^-1 * Y3 * Y1^3, (Y3 * Y1^-1)^4, (Y3^-1 * Y1^-1)^5 ] Map:: polytopal R = (1, 121, 2, 122, 6, 126, 16, 136, 38, 158, 49, 169, 26, 146, 32, 152, 12, 132, 4, 124)(3, 123, 9, 129, 23, 143, 22, 142, 8, 128, 21, 141, 39, 159, 57, 177, 27, 147, 10, 130)(5, 125, 14, 134, 36, 156, 56, 176, 25, 145, 30, 150, 11, 131, 29, 149, 40, 160, 15, 135)(7, 127, 19, 139, 45, 165, 44, 164, 18, 138, 28, 148, 50, 170, 75, 195, 47, 167, 20, 140)(13, 133, 34, 154, 62, 182, 83, 203, 59, 179, 37, 157, 31, 151, 60, 180, 63, 183, 35, 155)(17, 137, 43, 163, 68, 188, 67, 187, 42, 162, 48, 168, 70, 190, 85, 205, 61, 181, 33, 153)(24, 144, 54, 174, 79, 199, 78, 198, 53, 173, 41, 161, 66, 186, 90, 210, 80, 200, 55, 175)(46, 166, 52, 172, 77, 197, 96, 216, 73, 193, 51, 171, 76, 196, 98, 218, 97, 217, 74, 194)(58, 178, 82, 202, 103, 223, 89, 209, 65, 185, 64, 184, 88, 208, 107, 227, 102, 222, 81, 201)(69, 189, 72, 192, 95, 215, 110, 230, 92, 212, 71, 191, 94, 214, 112, 232, 111, 231, 93, 213)(84, 204, 105, 225, 117, 237, 106, 226, 87, 207, 86, 206, 91, 211, 109, 229, 116, 236, 104, 224)(99, 219, 101, 221, 115, 235, 120, 240, 114, 234, 100, 220, 108, 228, 118, 238, 119, 239, 113, 233)(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, 245)(4, 251)(5, 241)(6, 257)(7, 248)(8, 242)(9, 264)(10, 266)(11, 253)(12, 271)(13, 244)(14, 277)(15, 279)(16, 274)(17, 258)(18, 246)(19, 286)(20, 272)(21, 270)(22, 290)(23, 292)(24, 265)(25, 249)(26, 268)(27, 259)(28, 250)(29, 298)(30, 289)(31, 273)(32, 288)(33, 252)(34, 282)(35, 276)(36, 304)(37, 278)(38, 254)(39, 281)(40, 294)(41, 255)(42, 256)(43, 309)(44, 310)(45, 312)(46, 267)(47, 283)(48, 260)(49, 261)(50, 291)(51, 262)(52, 293)(53, 263)(54, 305)(55, 297)(56, 306)(57, 316)(58, 299)(59, 269)(60, 324)(61, 302)(62, 326)(63, 322)(64, 275)(65, 280)(66, 321)(67, 300)(68, 331)(69, 287)(70, 311)(71, 284)(72, 313)(73, 285)(74, 315)(75, 334)(76, 295)(77, 339)(78, 338)(79, 341)(80, 317)(81, 296)(82, 327)(83, 328)(84, 307)(85, 345)(86, 301)(87, 303)(88, 344)(89, 330)(90, 348)(91, 332)(92, 308)(93, 325)(94, 314)(95, 353)(96, 352)(97, 335)(98, 340)(99, 320)(100, 318)(101, 342)(102, 319)(103, 355)(104, 323)(105, 333)(106, 347)(107, 358)(108, 329)(109, 359)(110, 357)(111, 349)(112, 354)(113, 337)(114, 336)(115, 356)(116, 343)(117, 360)(118, 346)(119, 351)(120, 350)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 6, 10 ), ( 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10 ) } Outer automorphisms :: reflexible Dual of E23.1081 Graph:: simple bipartite v = 132 e = 240 f = 64 degree seq :: [ 2^120, 20^12 ] E23.1085 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 5, 10}) Quotient :: dipole Aut^+ = SL(2,5) (small group id <120, 5>) Aut = SL(2,5) : C2 (small group id <240, 93>) |r| :: 2 Presentation :: [ R^2, Y3^-1 * Y1^-1, Y3^3, Y3 * Y1^-2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2^-1 * Y1 * Y2^4 * Y3^-1, Y2^-2 * Y3^-1 * Y2^-1 * Y1^-1 * Y2^-1 * Y1, Y1 * Y2^-1 * Y3 * Y2^-1 * Y3^-1 * Y2^-2, Y2 * Y3 * Y2 * Y3 * Y2 * Y1^-1 * Y2 * Y1^-1, (Y3 * Y2^-1)^5 ] Map:: R = (1, 121, 2, 122, 4, 124)(3, 123, 8, 128, 10, 130)(5, 125, 13, 133, 14, 134)(6, 126, 16, 136, 18, 138)(7, 127, 19, 139, 20, 140)(9, 129, 24, 144, 26, 146)(11, 131, 29, 149, 31, 151)(12, 132, 32, 152, 33, 153)(15, 135, 39, 159, 40, 160)(17, 137, 44, 164, 45, 165)(21, 141, 22, 142, 49, 169)(23, 143, 41, 161, 52, 172)(25, 145, 37, 157, 55, 175)(27, 147, 36, 156, 47, 167)(28, 148, 48, 168, 57, 177)(30, 150, 59, 179, 38, 158)(34, 154, 42, 162, 61, 181)(35, 155, 62, 182, 58, 178)(43, 163, 50, 170, 68, 188)(46, 166, 60, 180, 72, 192)(51, 171, 75, 195, 76, 196)(53, 173, 54, 174, 78, 198)(56, 176, 77, 197, 81, 201)(63, 183, 87, 207, 66, 186)(64, 184, 86, 206, 88, 208)(65, 185, 89, 209, 80, 200)(67, 187, 91, 211, 92, 212)(69, 189, 70, 190, 94, 214)(71, 191, 93, 213, 96, 216)(73, 193, 97, 217, 74, 194)(79, 199, 101, 221, 102, 222)(82, 202, 83, 203, 103, 223)(84, 204, 105, 225, 85, 205)(90, 210, 108, 228, 100, 220)(95, 215, 111, 231, 112, 232)(98, 218, 99, 219, 110, 230)(104, 224, 117, 237, 107, 227)(106, 226, 109, 229, 116, 236)(113, 233, 118, 238, 119, 239)(114, 234, 115, 235, 120, 240)(241, 361, 243, 363, 249, 369, 265, 385, 271, 391, 287, 407, 259, 379, 281, 401, 255, 375, 245, 365)(242, 362, 246, 366, 257, 377, 268, 388, 250, 370, 267, 387, 272, 392, 290, 410, 261, 381, 247, 367)(244, 364, 251, 371, 270, 390, 286, 406, 258, 378, 276, 396, 253, 373, 275, 395, 274, 394, 252, 372)(248, 368, 262, 382, 291, 411, 296, 416, 266, 386, 260, 380, 288, 408, 313, 433, 293, 413, 263, 383)(254, 374, 277, 397, 303, 423, 322, 442, 298, 418, 269, 389, 279, 399, 305, 425, 304, 424, 278, 398)(256, 376, 282, 402, 307, 427, 311, 431, 285, 405, 273, 393, 300, 420, 324, 444, 309, 429, 283, 403)(264, 384, 294, 414, 319, 439, 320, 440, 295, 415, 292, 412, 317, 437, 330, 450, 306, 426, 280, 400)(284, 404, 310, 430, 335, 455, 316, 436, 297, 417, 308, 428, 333, 453, 338, 458, 314, 434, 289, 409)(299, 419, 323, 443, 344, 464, 332, 452, 312, 432, 302, 422, 326, 446, 346, 466, 325, 445, 301, 421)(315, 435, 339, 459, 353, 473, 342, 462, 321, 441, 337, 457, 351, 471, 354, 474, 340, 460, 318, 438)(327, 447, 341, 461, 355, 475, 356, 476, 343, 463, 329, 449, 348, 468, 358, 478, 347, 467, 328, 448)(331, 451, 349, 469, 359, 479, 352, 472, 336, 456, 345, 465, 357, 477, 360, 480, 350, 470, 334, 454) L = (1, 244)(2, 241)(3, 250)(4, 242)(5, 254)(6, 258)(7, 260)(8, 243)(9, 266)(10, 248)(11, 271)(12, 273)(13, 245)(14, 253)(15, 280)(16, 246)(17, 285)(18, 256)(19, 247)(20, 259)(21, 289)(22, 261)(23, 292)(24, 249)(25, 295)(26, 264)(27, 287)(28, 297)(29, 251)(30, 278)(31, 269)(32, 252)(33, 272)(34, 301)(35, 298)(36, 267)(37, 265)(38, 299)(39, 255)(40, 279)(41, 263)(42, 274)(43, 308)(44, 257)(45, 284)(46, 312)(47, 276)(48, 268)(49, 262)(50, 283)(51, 316)(52, 281)(53, 318)(54, 293)(55, 277)(56, 321)(57, 288)(58, 302)(59, 270)(60, 286)(61, 282)(62, 275)(63, 306)(64, 328)(65, 320)(66, 327)(67, 332)(68, 290)(69, 334)(70, 309)(71, 336)(72, 300)(73, 314)(74, 337)(75, 291)(76, 315)(77, 296)(78, 294)(79, 342)(80, 329)(81, 317)(82, 343)(83, 322)(84, 325)(85, 345)(86, 304)(87, 303)(88, 326)(89, 305)(90, 340)(91, 307)(92, 331)(93, 311)(94, 310)(95, 352)(96, 333)(97, 313)(98, 350)(99, 338)(100, 348)(101, 319)(102, 341)(103, 323)(104, 347)(105, 324)(106, 356)(107, 357)(108, 330)(109, 346)(110, 339)(111, 335)(112, 351)(113, 359)(114, 360)(115, 354)(116, 349)(117, 344)(118, 353)(119, 358)(120, 355)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 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 E23.1086 Graph:: bipartite v = 52 e = 240 f = 144 degree seq :: [ 6^40, 20^12 ] E23.1086 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {3, 5, 10}) Quotient :: dipole Aut^+ = SL(2,5) (small group id <120, 5>) Aut = SL(2,5) : C2 (small group id <240, 93>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, Y1^5, (R * Y2 * Y3^-1)^2, (Y1^-1 * Y3^-1)^3, Y1^2 * Y3^-1 * Y1^-1 * Y3 * Y1^-1 * Y3^-1, Y3 * Y1 * Y3^-3 * Y1 * Y3, (Y3 * Y1^-1 * Y3)^3, (Y3 * Y1^-1)^5, (Y3 * Y2^-1)^10 ] Map:: polytopal R = (1, 121, 2, 122, 6, 126, 13, 133, 4, 124)(3, 123, 9, 129, 26, 146, 33, 153, 11, 131)(5, 125, 15, 135, 42, 162, 46, 166, 16, 136)(7, 127, 20, 140, 55, 175, 34, 154, 22, 142)(8, 128, 23, 143, 61, 181, 63, 183, 24, 144)(10, 130, 29, 149, 70, 190, 74, 194, 31, 151)(12, 132, 35, 155, 79, 199, 82, 202, 37, 157)(14, 134, 40, 160, 43, 163, 68, 188, 27, 147)(17, 137, 47, 167, 92, 212, 94, 214, 48, 168)(18, 138, 50, 170, 72, 192, 60, 180, 52, 172)(19, 139, 53, 173, 99, 219, 69, 189, 28, 148)(21, 141, 30, 150, 71, 191, 105, 225, 58, 178)(25, 145, 64, 184, 109, 229, 110, 230, 65, 185)(32, 152, 75, 195, 86, 206, 114, 234, 77, 197)(36, 156, 67, 187, 100, 220, 116, 236, 80, 200)(38, 158, 45, 165, 90, 210, 98, 218, 84, 204)(39, 159, 85, 205, 87, 207, 95, 215, 56, 176)(41, 161, 78, 198, 106, 226, 59, 179, 49, 169)(44, 164, 88, 208, 97, 217, 51, 171, 57, 177)(54, 174, 101, 221, 117, 237, 81, 201, 102, 222)(62, 182, 107, 227, 118, 238, 83, 203, 96, 216)(66, 186, 103, 223, 113, 233, 111, 231, 91, 211)(73, 193, 93, 213, 115, 235, 119, 239, 104, 224)(76, 196, 112, 232, 120, 240, 108, 228, 89, 209)(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, 258)(7, 261)(8, 242)(9, 267)(10, 270)(11, 272)(12, 276)(13, 278)(14, 244)(15, 283)(16, 285)(17, 245)(18, 291)(19, 246)(20, 256)(21, 297)(22, 299)(23, 282)(24, 275)(25, 248)(26, 306)(27, 290)(28, 249)(29, 295)(30, 312)(31, 313)(32, 316)(33, 277)(34, 251)(35, 296)(36, 269)(37, 321)(38, 323)(39, 253)(40, 327)(41, 254)(42, 298)(43, 271)(44, 255)(45, 268)(46, 305)(47, 274)(48, 265)(49, 257)(50, 264)(51, 336)(52, 334)(53, 301)(54, 259)(55, 343)(56, 260)(57, 330)(58, 344)(59, 329)(60, 262)(61, 337)(62, 263)(63, 342)(64, 300)(65, 294)(66, 303)(67, 266)(68, 288)(69, 315)(70, 325)(71, 280)(72, 353)(73, 304)(74, 317)(75, 281)(76, 311)(77, 347)(78, 273)(79, 331)(80, 333)(81, 352)(82, 324)(83, 307)(84, 350)(85, 339)(86, 279)(87, 320)(88, 332)(89, 284)(90, 351)(91, 286)(92, 314)(93, 287)(94, 348)(95, 289)(96, 319)(97, 359)(98, 292)(99, 358)(100, 293)(101, 338)(102, 326)(103, 309)(104, 341)(105, 346)(106, 356)(107, 349)(108, 302)(109, 345)(110, 360)(111, 308)(112, 310)(113, 335)(114, 322)(115, 318)(116, 357)(117, 328)(118, 355)(119, 354)(120, 340)(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) :: { ( 6, 20 ), ( 6, 20, 6, 20, 6, 20, 6, 20, 6, 20 ) } Outer automorphisms :: reflexible Dual of E23.1085 Graph:: simple bipartite v = 144 e = 240 f = 52 degree seq :: [ 2^120, 10^24 ] E23.1087 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 12, 20}) Quotient :: regular Aut^+ = (C5 x (C3 : C4)) : C2 (small group id <120, 10>) Aut = (C2 x C2 x D30) : C2 (small group id <240, 151>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^2)^2, T1^-2 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-3, T1^20 ] Map:: non-degenerate R = (1, 2, 5, 11, 20, 32, 47, 65, 86, 104, 115, 114, 103, 85, 64, 46, 31, 19, 10, 4)(3, 7, 15, 25, 39, 55, 75, 97, 111, 118, 120, 117, 105, 88, 66, 49, 33, 22, 12, 8)(6, 13, 9, 18, 29, 44, 61, 82, 102, 113, 119, 112, 116, 106, 87, 67, 48, 34, 21, 14)(16, 26, 17, 28, 35, 51, 68, 90, 107, 95, 109, 93, 108, 94, 110, 96, 76, 56, 40, 27)(23, 36, 24, 38, 50, 69, 89, 80, 99, 78, 98, 79, 100, 81, 101, 83, 62, 45, 30, 37)(41, 57, 42, 59, 77, 91, 74, 54, 72, 52, 71, 53, 73, 63, 84, 92, 70, 60, 43, 58) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 15)(11, 21)(13, 23)(14, 24)(18, 30)(19, 29)(20, 33)(22, 35)(25, 40)(26, 41)(27, 42)(28, 43)(31, 39)(32, 48)(34, 50)(36, 52)(37, 53)(38, 54)(44, 62)(45, 63)(46, 61)(47, 66)(49, 68)(51, 70)(55, 76)(56, 77)(57, 78)(58, 79)(59, 80)(60, 81)(64, 75)(65, 87)(67, 89)(69, 91)(71, 93)(72, 94)(73, 95)(74, 96)(82, 101)(83, 92)(84, 90)(85, 102)(86, 105)(88, 107)(97, 110)(98, 112)(99, 106)(100, 113)(103, 111)(104, 116)(108, 118)(109, 117)(114, 119)(115, 120) local type(s) :: { ( 12^20 ) } Outer automorphisms :: reflexible Dual of E23.1088 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 6 e = 60 f = 10 degree seq :: [ 20^6 ] E23.1088 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 12, 20}) Quotient :: regular Aut^+ = (C5 x (C3 : C4)) : C2 (small group id <120, 10>) Aut = (C2 x C2 x D30) : C2 (small group id <240, 151>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^2)^2, T1^12, T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1, T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-6 ] Map:: non-degenerate R = (1, 2, 5, 11, 20, 32, 47, 46, 31, 19, 10, 4)(3, 7, 15, 25, 39, 55, 64, 49, 33, 22, 12, 8)(6, 13, 9, 18, 29, 44, 61, 65, 48, 34, 21, 14)(16, 26, 17, 28, 35, 51, 66, 82, 73, 56, 40, 27)(23, 36, 24, 38, 50, 67, 81, 79, 62, 45, 30, 37)(41, 57, 42, 59, 74, 89, 97, 84, 68, 60, 43, 58)(52, 69, 53, 71, 63, 80, 95, 98, 83, 72, 54, 70)(75, 90, 76, 92, 78, 94, 99, 113, 105, 93, 77, 91)(85, 100, 86, 102, 88, 104, 112, 111, 96, 103, 87, 101)(106, 118, 107, 116, 109, 114, 120, 115, 110, 117, 108, 119) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 15)(11, 21)(13, 23)(14, 24)(18, 30)(19, 29)(20, 33)(22, 35)(25, 40)(26, 41)(27, 42)(28, 43)(31, 39)(32, 48)(34, 50)(36, 52)(37, 53)(38, 54)(44, 62)(45, 63)(46, 61)(47, 64)(49, 66)(51, 68)(55, 73)(56, 74)(57, 75)(58, 76)(59, 77)(60, 78)(65, 81)(67, 83)(69, 85)(70, 86)(71, 87)(72, 88)(79, 95)(80, 96)(82, 97)(84, 99)(89, 105)(90, 106)(91, 107)(92, 108)(93, 109)(94, 110)(98, 112)(100, 114)(101, 115)(102, 116)(103, 117)(104, 118)(111, 119)(113, 120) local type(s) :: { ( 20^12 ) } Outer automorphisms :: reflexible Dual of E23.1087 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 10 e = 60 f = 6 degree seq :: [ 12^10 ] E23.1089 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 12, 20}) Quotient :: edge Aut^+ = (C5 x (C3 : C4)) : C2 (small group id <120, 10>) Aut = (C2 x C2 x D30) : C2 (small group id <240, 151>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, (T2^-1 * T1 * T2^-1)^2, T2^12, T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1, T1 * T2^3 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2^3 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2^3 * T1 * T2^-3 ] Map:: R = (1, 3, 8, 17, 28, 43, 60, 46, 31, 19, 10, 4)(2, 5, 12, 22, 35, 51, 69, 54, 38, 24, 14, 6)(7, 15, 9, 18, 30, 45, 63, 78, 59, 42, 27, 16)(11, 20, 13, 23, 37, 53, 72, 86, 68, 50, 34, 21)(25, 39, 26, 41, 58, 77, 94, 80, 62, 44, 29, 40)(32, 47, 33, 49, 67, 85, 102, 88, 71, 52, 36, 48)(55, 73, 56, 75, 61, 79, 96, 110, 93, 76, 57, 74)(64, 81, 65, 83, 70, 87, 104, 117, 101, 84, 66, 82)(89, 105, 90, 107, 92, 109, 119, 111, 95, 108, 91, 106)(97, 112, 98, 114, 100, 116, 120, 118, 103, 115, 99, 113)(121, 122)(123, 127)(124, 129)(125, 131)(126, 133)(128, 134)(130, 132)(135, 145)(136, 146)(137, 147)(138, 149)(139, 150)(140, 152)(141, 153)(142, 154)(143, 156)(144, 157)(148, 158)(151, 155)(159, 175)(160, 176)(161, 177)(162, 178)(163, 179)(164, 181)(165, 182)(166, 183)(167, 184)(168, 185)(169, 186)(170, 187)(171, 188)(172, 190)(173, 191)(174, 192)(180, 189)(193, 209)(194, 210)(195, 211)(196, 212)(197, 213)(198, 214)(199, 215)(200, 216)(201, 217)(202, 218)(203, 219)(204, 220)(205, 221)(206, 222)(207, 223)(208, 224)(225, 236)(226, 238)(227, 234)(228, 235)(229, 232)(230, 239)(231, 233)(237, 240) L = (1, 121)(2, 122)(3, 123)(4, 124)(5, 125)(6, 126)(7, 127)(8, 128)(9, 129)(10, 130)(11, 131)(12, 132)(13, 133)(14, 134)(15, 135)(16, 136)(17, 137)(18, 138)(19, 139)(20, 140)(21, 141)(22, 142)(23, 143)(24, 144)(25, 145)(26, 146)(27, 147)(28, 148)(29, 149)(30, 150)(31, 151)(32, 152)(33, 153)(34, 154)(35, 155)(36, 156)(37, 157)(38, 158)(39, 159)(40, 160)(41, 161)(42, 162)(43, 163)(44, 164)(45, 165)(46, 166)(47, 167)(48, 168)(49, 169)(50, 170)(51, 171)(52, 172)(53, 173)(54, 174)(55, 175)(56, 176)(57, 177)(58, 178)(59, 179)(60, 180)(61, 181)(62, 182)(63, 183)(64, 184)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 193)(74, 194)(75, 195)(76, 196)(77, 197)(78, 198)(79, 199)(80, 200)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 209)(90, 210)(91, 211)(92, 212)(93, 213)(94, 214)(95, 215)(96, 216)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 225)(106, 226)(107, 227)(108, 228)(109, 229)(110, 230)(111, 231)(112, 232)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240) local type(s) :: { ( 40, 40 ), ( 40^12 ) } Outer automorphisms :: reflexible Dual of E23.1093 Transitivity :: ET+ Graph:: simple bipartite v = 70 e = 120 f = 6 degree seq :: [ 2^60, 12^10 ] E23.1090 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 12, 20}) Quotient :: edge Aut^+ = (C5 x (C3 : C4)) : C2 (small group id <120, 10>) Aut = (C2 x C2 x D30) : C2 (small group id <240, 151>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T2 * T1)^2, (T2 * T1^-1)^2, T2^-1 * T1^-2 * T2^2 * T1^2 * T2^-1, T1^12, T1^-1 * T2^-1 * T1^2 * T2^-9 * T1^-3 ] Map:: polytopal non-degenerate R = (1, 3, 10, 21, 36, 55, 78, 102, 110, 86, 62, 85, 109, 108, 84, 61, 41, 25, 13, 5)(2, 7, 17, 31, 49, 71, 95, 119, 97, 73, 60, 79, 103, 120, 96, 72, 50, 32, 18, 8)(4, 11, 23, 39, 59, 83, 107, 112, 88, 64, 42, 63, 87, 111, 101, 77, 54, 35, 20, 9)(6, 15, 29, 47, 69, 93, 117, 104, 80, 56, 40, 51, 74, 98, 118, 94, 70, 48, 30, 16)(12, 19, 34, 53, 76, 100, 114, 90, 66, 44, 26, 43, 65, 89, 113, 106, 82, 58, 38, 22)(14, 27, 45, 67, 91, 115, 99, 75, 52, 33, 24, 37, 57, 81, 105, 116, 92, 68, 46, 28)(121, 122, 126, 134, 146, 162, 182, 180, 160, 144, 132, 124)(123, 129, 139, 153, 171, 193, 205, 184, 163, 148, 135, 128)(125, 131, 142, 157, 176, 199, 206, 183, 164, 147, 136, 127)(130, 138, 149, 166, 185, 208, 229, 217, 194, 172, 154, 140)(133, 137, 150, 165, 186, 207, 230, 223, 200, 177, 158, 143)(141, 155, 173, 195, 218, 239, 228, 232, 209, 188, 167, 152)(145, 159, 178, 201, 224, 240, 222, 231, 210, 187, 168, 151)(156, 170, 189, 212, 233, 227, 204, 215, 238, 219, 196, 174)(161, 169, 190, 211, 234, 221, 198, 216, 237, 225, 202, 179)(175, 197, 220, 235, 214, 191, 181, 203, 226, 236, 213, 192) 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) :: { ( 4^12 ), ( 4^20 ) } Outer automorphisms :: reflexible Dual of E23.1094 Transitivity :: ET+ Graph:: bipartite v = 16 e = 120 f = 60 degree seq :: [ 12^10, 20^6 ] E23.1091 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 12, 20}) Quotient :: edge Aut^+ = (C5 x (C3 : C4)) : C2 (small group id <120, 10>) Aut = (C2 x C2 x D30) : C2 (small group id <240, 151>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^2)^2, T1^-2 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-3, T1^20 ] Map:: R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 15)(11, 21)(13, 23)(14, 24)(18, 30)(19, 29)(20, 33)(22, 35)(25, 40)(26, 41)(27, 42)(28, 43)(31, 39)(32, 48)(34, 50)(36, 52)(37, 53)(38, 54)(44, 62)(45, 63)(46, 61)(47, 66)(49, 68)(51, 70)(55, 76)(56, 77)(57, 78)(58, 79)(59, 80)(60, 81)(64, 75)(65, 87)(67, 89)(69, 91)(71, 93)(72, 94)(73, 95)(74, 96)(82, 101)(83, 92)(84, 90)(85, 102)(86, 105)(88, 107)(97, 110)(98, 112)(99, 106)(100, 113)(103, 111)(104, 116)(108, 118)(109, 117)(114, 119)(115, 120)(121, 122, 125, 131, 140, 152, 167, 185, 206, 224, 235, 234, 223, 205, 184, 166, 151, 139, 130, 124)(123, 127, 135, 145, 159, 175, 195, 217, 231, 238, 240, 237, 225, 208, 186, 169, 153, 142, 132, 128)(126, 133, 129, 138, 149, 164, 181, 202, 222, 233, 239, 232, 236, 226, 207, 187, 168, 154, 141, 134)(136, 146, 137, 148, 155, 171, 188, 210, 227, 215, 229, 213, 228, 214, 230, 216, 196, 176, 160, 147)(143, 156, 144, 158, 170, 189, 209, 200, 219, 198, 218, 199, 220, 201, 221, 203, 182, 165, 150, 157)(161, 177, 162, 179, 197, 211, 194, 174, 192, 172, 191, 173, 193, 183, 204, 212, 190, 180, 163, 178) 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) :: { ( 24, 24 ), ( 24^20 ) } Outer automorphisms :: reflexible Dual of E23.1092 Transitivity :: ET+ Graph:: simple bipartite v = 66 e = 120 f = 10 degree seq :: [ 2^60, 20^6 ] E23.1092 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 12, 20}) Quotient :: loop Aut^+ = (C5 x (C3 : C4)) : C2 (small group id <120, 10>) Aut = (C2 x C2 x D30) : C2 (small group id <240, 151>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, (T2^-1 * T1 * T2^-1)^2, T2^12, T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1, T1 * T2^3 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2^3 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2^3 * T1 * T2^-3 ] Map:: R = (1, 121, 3, 123, 8, 128, 17, 137, 28, 148, 43, 163, 60, 180, 46, 166, 31, 151, 19, 139, 10, 130, 4, 124)(2, 122, 5, 125, 12, 132, 22, 142, 35, 155, 51, 171, 69, 189, 54, 174, 38, 158, 24, 144, 14, 134, 6, 126)(7, 127, 15, 135, 9, 129, 18, 138, 30, 150, 45, 165, 63, 183, 78, 198, 59, 179, 42, 162, 27, 147, 16, 136)(11, 131, 20, 140, 13, 133, 23, 143, 37, 157, 53, 173, 72, 192, 86, 206, 68, 188, 50, 170, 34, 154, 21, 141)(25, 145, 39, 159, 26, 146, 41, 161, 58, 178, 77, 197, 94, 214, 80, 200, 62, 182, 44, 164, 29, 149, 40, 160)(32, 152, 47, 167, 33, 153, 49, 169, 67, 187, 85, 205, 102, 222, 88, 208, 71, 191, 52, 172, 36, 156, 48, 168)(55, 175, 73, 193, 56, 176, 75, 195, 61, 181, 79, 199, 96, 216, 110, 230, 93, 213, 76, 196, 57, 177, 74, 194)(64, 184, 81, 201, 65, 185, 83, 203, 70, 190, 87, 207, 104, 224, 117, 237, 101, 221, 84, 204, 66, 186, 82, 202)(89, 209, 105, 225, 90, 210, 107, 227, 92, 212, 109, 229, 119, 239, 111, 231, 95, 215, 108, 228, 91, 211, 106, 226)(97, 217, 112, 232, 98, 218, 114, 234, 100, 220, 116, 236, 120, 240, 118, 238, 103, 223, 115, 235, 99, 219, 113, 233) L = (1, 122)(2, 121)(3, 127)(4, 129)(5, 131)(6, 133)(7, 123)(8, 134)(9, 124)(10, 132)(11, 125)(12, 130)(13, 126)(14, 128)(15, 145)(16, 146)(17, 147)(18, 149)(19, 150)(20, 152)(21, 153)(22, 154)(23, 156)(24, 157)(25, 135)(26, 136)(27, 137)(28, 158)(29, 138)(30, 139)(31, 155)(32, 140)(33, 141)(34, 142)(35, 151)(36, 143)(37, 144)(38, 148)(39, 175)(40, 176)(41, 177)(42, 178)(43, 179)(44, 181)(45, 182)(46, 183)(47, 184)(48, 185)(49, 186)(50, 187)(51, 188)(52, 190)(53, 191)(54, 192)(55, 159)(56, 160)(57, 161)(58, 162)(59, 163)(60, 189)(61, 164)(62, 165)(63, 166)(64, 167)(65, 168)(66, 169)(67, 170)(68, 171)(69, 180)(70, 172)(71, 173)(72, 174)(73, 209)(74, 210)(75, 211)(76, 212)(77, 213)(78, 214)(79, 215)(80, 216)(81, 217)(82, 218)(83, 219)(84, 220)(85, 221)(86, 222)(87, 223)(88, 224)(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)(105, 236)(106, 238)(107, 234)(108, 235)(109, 232)(110, 239)(111, 233)(112, 229)(113, 231)(114, 227)(115, 228)(116, 225)(117, 240)(118, 226)(119, 230)(120, 237) local type(s) :: { ( 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20 ) } Outer automorphisms :: reflexible Dual of E23.1091 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 10 e = 120 f = 66 degree seq :: [ 24^10 ] E23.1093 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 12, 20}) Quotient :: loop Aut^+ = (C5 x (C3 : C4)) : C2 (small group id <120, 10>) Aut = (C2 x C2 x D30) : C2 (small group id <240, 151>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, (T2 * T1)^2, (T2 * T1^-1)^2, T2^-1 * T1^-2 * T2^2 * T1^2 * T2^-1, T1^12, T1^-1 * T2^-1 * T1^2 * T2^-9 * T1^-3 ] Map:: R = (1, 121, 3, 123, 10, 130, 21, 141, 36, 156, 55, 175, 78, 198, 102, 222, 110, 230, 86, 206, 62, 182, 85, 205, 109, 229, 108, 228, 84, 204, 61, 181, 41, 161, 25, 145, 13, 133, 5, 125)(2, 122, 7, 127, 17, 137, 31, 151, 49, 169, 71, 191, 95, 215, 119, 239, 97, 217, 73, 193, 60, 180, 79, 199, 103, 223, 120, 240, 96, 216, 72, 192, 50, 170, 32, 152, 18, 138, 8, 128)(4, 124, 11, 131, 23, 143, 39, 159, 59, 179, 83, 203, 107, 227, 112, 232, 88, 208, 64, 184, 42, 162, 63, 183, 87, 207, 111, 231, 101, 221, 77, 197, 54, 174, 35, 155, 20, 140, 9, 129)(6, 126, 15, 135, 29, 149, 47, 167, 69, 189, 93, 213, 117, 237, 104, 224, 80, 200, 56, 176, 40, 160, 51, 171, 74, 194, 98, 218, 118, 238, 94, 214, 70, 190, 48, 168, 30, 150, 16, 136)(12, 132, 19, 139, 34, 154, 53, 173, 76, 196, 100, 220, 114, 234, 90, 210, 66, 186, 44, 164, 26, 146, 43, 163, 65, 185, 89, 209, 113, 233, 106, 226, 82, 202, 58, 178, 38, 158, 22, 142)(14, 134, 27, 147, 45, 165, 67, 187, 91, 211, 115, 235, 99, 219, 75, 195, 52, 172, 33, 153, 24, 144, 37, 157, 57, 177, 81, 201, 105, 225, 116, 236, 92, 212, 68, 188, 46, 166, 28, 148) L = (1, 122)(2, 126)(3, 129)(4, 121)(5, 131)(6, 134)(7, 125)(8, 123)(9, 139)(10, 138)(11, 142)(12, 124)(13, 137)(14, 146)(15, 128)(16, 127)(17, 150)(18, 149)(19, 153)(20, 130)(21, 155)(22, 157)(23, 133)(24, 132)(25, 159)(26, 162)(27, 136)(28, 135)(29, 166)(30, 165)(31, 145)(32, 141)(33, 171)(34, 140)(35, 173)(36, 170)(37, 176)(38, 143)(39, 178)(40, 144)(41, 169)(42, 182)(43, 148)(44, 147)(45, 186)(46, 185)(47, 152)(48, 151)(49, 190)(50, 189)(51, 193)(52, 154)(53, 195)(54, 156)(55, 197)(56, 199)(57, 158)(58, 201)(59, 161)(60, 160)(61, 203)(62, 180)(63, 164)(64, 163)(65, 208)(66, 207)(67, 168)(68, 167)(69, 212)(70, 211)(71, 181)(72, 175)(73, 205)(74, 172)(75, 218)(76, 174)(77, 220)(78, 216)(79, 206)(80, 177)(81, 224)(82, 179)(83, 226)(84, 215)(85, 184)(86, 183)(87, 230)(88, 229)(89, 188)(90, 187)(91, 234)(92, 233)(93, 192)(94, 191)(95, 238)(96, 237)(97, 194)(98, 239)(99, 196)(100, 235)(101, 198)(102, 231)(103, 200)(104, 240)(105, 202)(106, 236)(107, 204)(108, 232)(109, 217)(110, 223)(111, 210)(112, 209)(113, 227)(114, 221)(115, 214)(116, 213)(117, 225)(118, 219)(119, 228)(120, 222) 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 ) } Outer automorphisms :: reflexible Dual of E23.1089 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 6 e = 120 f = 70 degree seq :: [ 40^6 ] E23.1094 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 12, 20}) Quotient :: loop Aut^+ = (C5 x (C3 : C4)) : C2 (small group id <120, 10>) Aut = (C2 x C2 x D30) : C2 (small group id <240, 151>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^2)^2, T1^-2 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-3, T1^20 ] 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, 15, 135)(11, 131, 21, 141)(13, 133, 23, 143)(14, 134, 24, 144)(18, 138, 30, 150)(19, 139, 29, 149)(20, 140, 33, 153)(22, 142, 35, 155)(25, 145, 40, 160)(26, 146, 41, 161)(27, 147, 42, 162)(28, 148, 43, 163)(31, 151, 39, 159)(32, 152, 48, 168)(34, 154, 50, 170)(36, 156, 52, 172)(37, 157, 53, 173)(38, 158, 54, 174)(44, 164, 62, 182)(45, 165, 63, 183)(46, 166, 61, 181)(47, 167, 66, 186)(49, 169, 68, 188)(51, 171, 70, 190)(55, 175, 76, 196)(56, 176, 77, 197)(57, 177, 78, 198)(58, 178, 79, 199)(59, 179, 80, 200)(60, 180, 81, 201)(64, 184, 75, 195)(65, 185, 87, 207)(67, 187, 89, 209)(69, 189, 91, 211)(71, 191, 93, 213)(72, 192, 94, 214)(73, 193, 95, 215)(74, 194, 96, 216)(82, 202, 101, 221)(83, 203, 92, 212)(84, 204, 90, 210)(85, 205, 102, 222)(86, 206, 105, 225)(88, 208, 107, 227)(97, 217, 110, 230)(98, 218, 112, 232)(99, 219, 106, 226)(100, 220, 113, 233)(103, 223, 111, 231)(104, 224, 116, 236)(108, 228, 118, 238)(109, 229, 117, 237)(114, 234, 119, 239)(115, 235, 120, 240) L = (1, 122)(2, 125)(3, 127)(4, 121)(5, 131)(6, 133)(7, 135)(8, 123)(9, 138)(10, 124)(11, 140)(12, 128)(13, 129)(14, 126)(15, 145)(16, 146)(17, 148)(18, 149)(19, 130)(20, 152)(21, 134)(22, 132)(23, 156)(24, 158)(25, 159)(26, 137)(27, 136)(28, 155)(29, 164)(30, 157)(31, 139)(32, 167)(33, 142)(34, 141)(35, 171)(36, 144)(37, 143)(38, 170)(39, 175)(40, 147)(41, 177)(42, 179)(43, 178)(44, 181)(45, 150)(46, 151)(47, 185)(48, 154)(49, 153)(50, 189)(51, 188)(52, 191)(53, 193)(54, 192)(55, 195)(56, 160)(57, 162)(58, 161)(59, 197)(60, 163)(61, 202)(62, 165)(63, 204)(64, 166)(65, 206)(66, 169)(67, 168)(68, 210)(69, 209)(70, 180)(71, 173)(72, 172)(73, 183)(74, 174)(75, 217)(76, 176)(77, 211)(78, 218)(79, 220)(80, 219)(81, 221)(82, 222)(83, 182)(84, 212)(85, 184)(86, 224)(87, 187)(88, 186)(89, 200)(90, 227)(91, 194)(92, 190)(93, 228)(94, 230)(95, 229)(96, 196)(97, 231)(98, 199)(99, 198)(100, 201)(101, 203)(102, 233)(103, 205)(104, 235)(105, 208)(106, 207)(107, 215)(108, 214)(109, 213)(110, 216)(111, 238)(112, 236)(113, 239)(114, 223)(115, 234)(116, 226)(117, 225)(118, 240)(119, 232)(120, 237) local type(s) :: { ( 12, 20, 12, 20 ) } Outer automorphisms :: reflexible Dual of E23.1090 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 60 e = 120 f = 16 degree seq :: [ 4^60 ] E23.1095 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 12, 20}) Quotient :: dipole Aut^+ = (C5 x (C3 : C4)) : C2 (small group id <120, 10>) Aut = (C2 x C2 x D30) : C2 (small group id <240, 151>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y2^2 * Y1)^2, Y2 * R * Y2^-2 * R * Y2, Y2^12, Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1, (Y3 * Y2^-1)^20 ] Map:: R = (1, 121, 2, 122)(3, 123, 7, 127)(4, 124, 9, 129)(5, 125, 11, 131)(6, 126, 13, 133)(8, 128, 14, 134)(10, 130, 12, 132)(15, 135, 25, 145)(16, 136, 26, 146)(17, 137, 27, 147)(18, 138, 29, 149)(19, 139, 30, 150)(20, 140, 32, 152)(21, 141, 33, 153)(22, 142, 34, 154)(23, 143, 36, 156)(24, 144, 37, 157)(28, 148, 38, 158)(31, 151, 35, 155)(39, 159, 55, 175)(40, 160, 56, 176)(41, 161, 57, 177)(42, 162, 58, 178)(43, 163, 59, 179)(44, 164, 61, 181)(45, 165, 62, 182)(46, 166, 63, 183)(47, 167, 64, 184)(48, 168, 65, 185)(49, 169, 66, 186)(50, 170, 67, 187)(51, 171, 68, 188)(52, 172, 70, 190)(53, 173, 71, 191)(54, 174, 72, 192)(60, 180, 69, 189)(73, 193, 89, 209)(74, 194, 90, 210)(75, 195, 91, 211)(76, 196, 92, 212)(77, 197, 93, 213)(78, 198, 94, 214)(79, 199, 95, 215)(80, 200, 96, 216)(81, 201, 97, 217)(82, 202, 98, 218)(83, 203, 99, 219)(84, 204, 100, 220)(85, 205, 101, 221)(86, 206, 102, 222)(87, 207, 103, 223)(88, 208, 104, 224)(105, 225, 116, 236)(106, 226, 118, 238)(107, 227, 114, 234)(108, 228, 115, 235)(109, 229, 112, 232)(110, 230, 119, 239)(111, 231, 113, 233)(117, 237, 120, 240)(241, 361, 243, 363, 248, 368, 257, 377, 268, 388, 283, 403, 300, 420, 286, 406, 271, 391, 259, 379, 250, 370, 244, 364)(242, 362, 245, 365, 252, 372, 262, 382, 275, 395, 291, 411, 309, 429, 294, 414, 278, 398, 264, 384, 254, 374, 246, 366)(247, 367, 255, 375, 249, 369, 258, 378, 270, 390, 285, 405, 303, 423, 318, 438, 299, 419, 282, 402, 267, 387, 256, 376)(251, 371, 260, 380, 253, 373, 263, 383, 277, 397, 293, 413, 312, 432, 326, 446, 308, 428, 290, 410, 274, 394, 261, 381)(265, 385, 279, 399, 266, 386, 281, 401, 298, 418, 317, 437, 334, 454, 320, 440, 302, 422, 284, 404, 269, 389, 280, 400)(272, 392, 287, 407, 273, 393, 289, 409, 307, 427, 325, 445, 342, 462, 328, 448, 311, 431, 292, 412, 276, 396, 288, 408)(295, 415, 313, 433, 296, 416, 315, 435, 301, 421, 319, 439, 336, 456, 350, 470, 333, 453, 316, 436, 297, 417, 314, 434)(304, 424, 321, 441, 305, 425, 323, 443, 310, 430, 327, 447, 344, 464, 357, 477, 341, 461, 324, 444, 306, 426, 322, 442)(329, 449, 345, 465, 330, 450, 347, 467, 332, 452, 349, 469, 359, 479, 351, 471, 335, 455, 348, 468, 331, 451, 346, 466)(337, 457, 352, 472, 338, 458, 354, 474, 340, 460, 356, 476, 360, 480, 358, 478, 343, 463, 355, 475, 339, 459, 353, 473) L = (1, 242)(2, 241)(3, 247)(4, 249)(5, 251)(6, 253)(7, 243)(8, 254)(9, 244)(10, 252)(11, 245)(12, 250)(13, 246)(14, 248)(15, 265)(16, 266)(17, 267)(18, 269)(19, 270)(20, 272)(21, 273)(22, 274)(23, 276)(24, 277)(25, 255)(26, 256)(27, 257)(28, 278)(29, 258)(30, 259)(31, 275)(32, 260)(33, 261)(34, 262)(35, 271)(36, 263)(37, 264)(38, 268)(39, 295)(40, 296)(41, 297)(42, 298)(43, 299)(44, 301)(45, 302)(46, 303)(47, 304)(48, 305)(49, 306)(50, 307)(51, 308)(52, 310)(53, 311)(54, 312)(55, 279)(56, 280)(57, 281)(58, 282)(59, 283)(60, 309)(61, 284)(62, 285)(63, 286)(64, 287)(65, 288)(66, 289)(67, 290)(68, 291)(69, 300)(70, 292)(71, 293)(72, 294)(73, 329)(74, 330)(75, 331)(76, 332)(77, 333)(78, 334)(79, 335)(80, 336)(81, 337)(82, 338)(83, 339)(84, 340)(85, 341)(86, 342)(87, 343)(88, 344)(89, 313)(90, 314)(91, 315)(92, 316)(93, 317)(94, 318)(95, 319)(96, 320)(97, 321)(98, 322)(99, 323)(100, 324)(101, 325)(102, 326)(103, 327)(104, 328)(105, 356)(106, 358)(107, 354)(108, 355)(109, 352)(110, 359)(111, 353)(112, 349)(113, 351)(114, 347)(115, 348)(116, 345)(117, 360)(118, 346)(119, 350)(120, 357)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 2, 40, 2, 40 ), ( 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40, 2, 40 ) } Outer automorphisms :: reflexible Dual of E23.1098 Graph:: bipartite v = 70 e = 240 f = 126 degree seq :: [ 4^60, 24^10 ] E23.1096 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 12, 20}) Quotient :: dipole Aut^+ = (C5 x (C3 : C4)) : C2 (small group id <120, 10>) Aut = (C2 x C2 x D30) : C2 (small group id <240, 151>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-1, (R * Y1)^2, (Y2^-1 * Y1)^2, (Y2 * Y1)^2, R * Y2 * R * Y3, (Y3^-1 * Y1^-1)^2, Y1^12, Y1^-1 * Y2^-1 * Y1^3 * Y2^9 * Y1^-2 ] Map:: R = (1, 121, 2, 122, 6, 126, 14, 134, 26, 146, 42, 162, 62, 182, 60, 180, 40, 160, 24, 144, 12, 132, 4, 124)(3, 123, 9, 129, 19, 139, 33, 153, 51, 171, 73, 193, 85, 205, 64, 184, 43, 163, 28, 148, 15, 135, 8, 128)(5, 125, 11, 131, 22, 142, 37, 157, 56, 176, 79, 199, 86, 206, 63, 183, 44, 164, 27, 147, 16, 136, 7, 127)(10, 130, 18, 138, 29, 149, 46, 166, 65, 185, 88, 208, 109, 229, 97, 217, 74, 194, 52, 172, 34, 154, 20, 140)(13, 133, 17, 137, 30, 150, 45, 165, 66, 186, 87, 207, 110, 230, 103, 223, 80, 200, 57, 177, 38, 158, 23, 143)(21, 141, 35, 155, 53, 173, 75, 195, 98, 218, 119, 239, 108, 228, 112, 232, 89, 209, 68, 188, 47, 167, 32, 152)(25, 145, 39, 159, 58, 178, 81, 201, 104, 224, 120, 240, 102, 222, 111, 231, 90, 210, 67, 187, 48, 168, 31, 151)(36, 156, 50, 170, 69, 189, 92, 212, 113, 233, 107, 227, 84, 204, 95, 215, 118, 238, 99, 219, 76, 196, 54, 174)(41, 161, 49, 169, 70, 190, 91, 211, 114, 234, 101, 221, 78, 198, 96, 216, 117, 237, 105, 225, 82, 202, 59, 179)(55, 175, 77, 197, 100, 220, 115, 235, 94, 214, 71, 191, 61, 181, 83, 203, 106, 226, 116, 236, 93, 213, 72, 192)(241, 361, 243, 363, 250, 370, 261, 381, 276, 396, 295, 415, 318, 438, 342, 462, 350, 470, 326, 446, 302, 422, 325, 445, 349, 469, 348, 468, 324, 444, 301, 421, 281, 401, 265, 385, 253, 373, 245, 365)(242, 362, 247, 367, 257, 377, 271, 391, 289, 409, 311, 431, 335, 455, 359, 479, 337, 457, 313, 433, 300, 420, 319, 439, 343, 463, 360, 480, 336, 456, 312, 432, 290, 410, 272, 392, 258, 378, 248, 368)(244, 364, 251, 371, 263, 383, 279, 399, 299, 419, 323, 443, 347, 467, 352, 472, 328, 448, 304, 424, 282, 402, 303, 423, 327, 447, 351, 471, 341, 461, 317, 437, 294, 414, 275, 395, 260, 380, 249, 369)(246, 366, 255, 375, 269, 389, 287, 407, 309, 429, 333, 453, 357, 477, 344, 464, 320, 440, 296, 416, 280, 400, 291, 411, 314, 434, 338, 458, 358, 478, 334, 454, 310, 430, 288, 408, 270, 390, 256, 376)(252, 372, 259, 379, 274, 394, 293, 413, 316, 436, 340, 460, 354, 474, 330, 450, 306, 426, 284, 404, 266, 386, 283, 403, 305, 425, 329, 449, 353, 473, 346, 466, 322, 442, 298, 418, 278, 398, 262, 382)(254, 374, 267, 387, 285, 405, 307, 427, 331, 451, 355, 475, 339, 459, 315, 435, 292, 412, 273, 393, 264, 384, 277, 397, 297, 417, 321, 441, 345, 465, 356, 476, 332, 452, 308, 428, 286, 406, 268, 388) L = (1, 243)(2, 247)(3, 250)(4, 251)(5, 241)(6, 255)(7, 257)(8, 242)(9, 244)(10, 261)(11, 263)(12, 259)(13, 245)(14, 267)(15, 269)(16, 246)(17, 271)(18, 248)(19, 274)(20, 249)(21, 276)(22, 252)(23, 279)(24, 277)(25, 253)(26, 283)(27, 285)(28, 254)(29, 287)(30, 256)(31, 289)(32, 258)(33, 264)(34, 293)(35, 260)(36, 295)(37, 297)(38, 262)(39, 299)(40, 291)(41, 265)(42, 303)(43, 305)(44, 266)(45, 307)(46, 268)(47, 309)(48, 270)(49, 311)(50, 272)(51, 314)(52, 273)(53, 316)(54, 275)(55, 318)(56, 280)(57, 321)(58, 278)(59, 323)(60, 319)(61, 281)(62, 325)(63, 327)(64, 282)(65, 329)(66, 284)(67, 331)(68, 286)(69, 333)(70, 288)(71, 335)(72, 290)(73, 300)(74, 338)(75, 292)(76, 340)(77, 294)(78, 342)(79, 343)(80, 296)(81, 345)(82, 298)(83, 347)(84, 301)(85, 349)(86, 302)(87, 351)(88, 304)(89, 353)(90, 306)(91, 355)(92, 308)(93, 357)(94, 310)(95, 359)(96, 312)(97, 313)(98, 358)(99, 315)(100, 354)(101, 317)(102, 350)(103, 360)(104, 320)(105, 356)(106, 322)(107, 352)(108, 324)(109, 348)(110, 326)(111, 341)(112, 328)(113, 346)(114, 330)(115, 339)(116, 332)(117, 344)(118, 334)(119, 337)(120, 336)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) } Outer automorphisms :: reflexible Dual of E23.1097 Graph:: bipartite v = 16 e = 240 f = 180 degree seq :: [ 24^10, 40^6 ] E23.1097 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 12, 20}) Quotient :: dipole Aut^+ = (C5 x (C3 : C4)) : C2 (small group id <120, 10>) Aut = (C2 x C2 x D30) : C2 (small group id <240, 151>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3^2 * Y2)^2, Y3 * Y2 * Y3^-5 * Y2 * Y3 * Y2 * Y3^-1 * Y2 * Y3 * Y2 * Y3^-1 * Y2, (Y3^-1 * Y2)^12, (Y3^-1 * Y1^-1)^20 ] 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, 254, 374)(250, 370, 252, 372)(255, 375, 265, 385)(256, 376, 266, 386)(257, 377, 267, 387)(258, 378, 269, 389)(259, 379, 270, 390)(260, 380, 272, 392)(261, 381, 273, 393)(262, 382, 274, 394)(263, 383, 276, 396)(264, 384, 277, 397)(268, 388, 278, 398)(271, 391, 275, 395)(279, 399, 295, 415)(280, 400, 296, 416)(281, 401, 297, 417)(282, 402, 298, 418)(283, 403, 299, 419)(284, 404, 301, 421)(285, 405, 302, 422)(286, 406, 303, 423)(287, 407, 305, 425)(288, 408, 306, 426)(289, 409, 307, 427)(290, 410, 308, 428)(291, 411, 309, 429)(292, 412, 311, 431)(293, 413, 312, 432)(294, 414, 313, 433)(300, 420, 314, 434)(304, 424, 310, 430)(315, 435, 337, 457)(316, 436, 338, 458)(317, 437, 339, 459)(318, 438, 331, 451)(319, 439, 330, 450)(320, 440, 329, 449)(321, 441, 340, 460)(322, 442, 335, 455)(323, 443, 334, 454)(324, 444, 333, 453)(325, 445, 342, 462)(326, 446, 344, 464)(327, 447, 345, 465)(328, 448, 346, 466)(332, 452, 347, 467)(336, 456, 349, 469)(341, 461, 350, 470)(343, 463, 348, 468)(351, 471, 357, 477)(352, 472, 358, 478)(353, 473, 355, 475)(354, 474, 356, 476)(359, 479, 360, 480) L = (1, 243)(2, 245)(3, 248)(4, 241)(5, 252)(6, 242)(7, 255)(8, 257)(9, 258)(10, 244)(11, 260)(12, 262)(13, 263)(14, 246)(15, 249)(16, 247)(17, 268)(18, 270)(19, 250)(20, 253)(21, 251)(22, 275)(23, 277)(24, 254)(25, 279)(26, 281)(27, 256)(28, 283)(29, 280)(30, 285)(31, 259)(32, 287)(33, 289)(34, 261)(35, 291)(36, 288)(37, 293)(38, 264)(39, 266)(40, 265)(41, 298)(42, 267)(43, 300)(44, 269)(45, 303)(46, 271)(47, 273)(48, 272)(49, 308)(50, 274)(51, 310)(52, 276)(53, 313)(54, 278)(55, 315)(56, 317)(57, 316)(58, 319)(59, 282)(60, 321)(61, 322)(62, 284)(63, 324)(64, 286)(65, 326)(66, 328)(67, 327)(68, 330)(69, 290)(70, 332)(71, 333)(72, 292)(73, 335)(74, 294)(75, 296)(76, 295)(77, 301)(78, 297)(79, 329)(80, 299)(81, 341)(82, 334)(83, 302)(84, 342)(85, 304)(86, 306)(87, 305)(88, 311)(89, 307)(90, 318)(91, 309)(92, 348)(93, 323)(94, 312)(95, 349)(96, 314)(97, 351)(98, 347)(99, 352)(100, 320)(101, 353)(102, 346)(103, 325)(104, 355)(105, 340)(106, 356)(107, 331)(108, 357)(109, 339)(110, 336)(111, 338)(112, 337)(113, 359)(114, 343)(115, 345)(116, 344)(117, 360)(118, 350)(119, 354)(120, 358)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 24, 40 ), ( 24, 40, 24, 40 ) } Outer automorphisms :: reflexible Dual of E23.1096 Graph:: simple bipartite v = 180 e = 240 f = 16 degree seq :: [ 2^120, 4^60 ] E23.1098 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 12, 20}) Quotient :: dipole Aut^+ = (C5 x (C3 : C4)) : C2 (small group id <120, 10>) Aut = (C2 x C2 x D30) : C2 (small group id <240, 151>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, (R * Y2 * Y3)^2, (Y1^2 * Y3)^2, Y1^-2 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1^-3, Y1^20, Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 ] Map:: R = (1, 121, 2, 122, 5, 125, 11, 131, 20, 140, 32, 152, 47, 167, 65, 185, 86, 206, 104, 224, 115, 235, 114, 234, 103, 223, 85, 205, 64, 184, 46, 166, 31, 151, 19, 139, 10, 130, 4, 124)(3, 123, 7, 127, 15, 135, 25, 145, 39, 159, 55, 175, 75, 195, 97, 217, 111, 231, 118, 238, 120, 240, 117, 237, 105, 225, 88, 208, 66, 186, 49, 169, 33, 153, 22, 142, 12, 132, 8, 128)(6, 126, 13, 133, 9, 129, 18, 138, 29, 149, 44, 164, 61, 181, 82, 202, 102, 222, 113, 233, 119, 239, 112, 232, 116, 236, 106, 226, 87, 207, 67, 187, 48, 168, 34, 154, 21, 141, 14, 134)(16, 136, 26, 146, 17, 137, 28, 148, 35, 155, 51, 171, 68, 188, 90, 210, 107, 227, 95, 215, 109, 229, 93, 213, 108, 228, 94, 214, 110, 230, 96, 216, 76, 196, 56, 176, 40, 160, 27, 147)(23, 143, 36, 156, 24, 144, 38, 158, 50, 170, 69, 189, 89, 209, 80, 200, 99, 219, 78, 198, 98, 218, 79, 199, 100, 220, 81, 201, 101, 221, 83, 203, 62, 182, 45, 165, 30, 150, 37, 157)(41, 161, 57, 177, 42, 162, 59, 179, 77, 197, 91, 211, 74, 194, 54, 174, 72, 192, 52, 172, 71, 191, 53, 173, 73, 193, 63, 183, 84, 204, 92, 212, 70, 190, 60, 180, 43, 163, 58, 178)(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, 255)(11, 261)(12, 245)(13, 263)(14, 264)(15, 250)(16, 247)(17, 248)(18, 270)(19, 269)(20, 273)(21, 251)(22, 275)(23, 253)(24, 254)(25, 280)(26, 281)(27, 282)(28, 283)(29, 259)(30, 258)(31, 279)(32, 288)(33, 260)(34, 290)(35, 262)(36, 292)(37, 293)(38, 294)(39, 271)(40, 265)(41, 266)(42, 267)(43, 268)(44, 302)(45, 303)(46, 301)(47, 306)(48, 272)(49, 308)(50, 274)(51, 310)(52, 276)(53, 277)(54, 278)(55, 316)(56, 317)(57, 318)(58, 319)(59, 320)(60, 321)(61, 286)(62, 284)(63, 285)(64, 315)(65, 327)(66, 287)(67, 329)(68, 289)(69, 331)(70, 291)(71, 333)(72, 334)(73, 335)(74, 336)(75, 304)(76, 295)(77, 296)(78, 297)(79, 298)(80, 299)(81, 300)(82, 341)(83, 332)(84, 330)(85, 342)(86, 345)(87, 305)(88, 347)(89, 307)(90, 324)(91, 309)(92, 323)(93, 311)(94, 312)(95, 313)(96, 314)(97, 350)(98, 352)(99, 346)(100, 353)(101, 322)(102, 325)(103, 351)(104, 356)(105, 326)(106, 339)(107, 328)(108, 358)(109, 357)(110, 337)(111, 343)(112, 338)(113, 340)(114, 359)(115, 360)(116, 344)(117, 349)(118, 348)(119, 354)(120, 355)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 4, 24 ), ( 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24 ) } Outer automorphisms :: reflexible Dual of E23.1095 Graph:: simple bipartite v = 126 e = 240 f = 70 degree seq :: [ 2^120, 40^6 ] E23.1099 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 12, 20}) Quotient :: dipole Aut^+ = (C5 x (C3 : C4)) : C2 (small group id <120, 10>) Aut = (C2 x C2 x D30) : C2 (small group id <240, 151>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y2^-1 * Y1 * Y2^-1)^2, (Y2^4 * Y1 * Y2^-1 * R)^2, Y2 * Y1 * Y2^-3 * Y1 * Y2 * Y1 * Y2^-3 * Y1 * Y2 * Y1 * Y2^-1 * Y1, Y2^20, (Y3 * Y2^-1)^12 ] Map:: R = (1, 121, 2, 122)(3, 123, 7, 127)(4, 124, 9, 129)(5, 125, 11, 131)(6, 126, 13, 133)(8, 128, 14, 134)(10, 130, 12, 132)(15, 135, 25, 145)(16, 136, 26, 146)(17, 137, 27, 147)(18, 138, 29, 149)(19, 139, 30, 150)(20, 140, 32, 152)(21, 141, 33, 153)(22, 142, 34, 154)(23, 143, 36, 156)(24, 144, 37, 157)(28, 148, 38, 158)(31, 151, 35, 155)(39, 159, 55, 175)(40, 160, 56, 176)(41, 161, 57, 177)(42, 162, 58, 178)(43, 163, 59, 179)(44, 164, 61, 181)(45, 165, 62, 182)(46, 166, 63, 183)(47, 167, 65, 185)(48, 168, 66, 186)(49, 169, 67, 187)(50, 170, 68, 188)(51, 171, 69, 189)(52, 172, 71, 191)(53, 173, 72, 192)(54, 174, 73, 193)(60, 180, 74, 194)(64, 184, 70, 190)(75, 195, 97, 217)(76, 196, 98, 218)(77, 197, 99, 219)(78, 198, 91, 211)(79, 199, 90, 210)(80, 200, 89, 209)(81, 201, 100, 220)(82, 202, 95, 215)(83, 203, 94, 214)(84, 204, 93, 213)(85, 205, 102, 222)(86, 206, 104, 224)(87, 207, 105, 225)(88, 208, 106, 226)(92, 212, 107, 227)(96, 216, 109, 229)(101, 221, 110, 230)(103, 223, 108, 228)(111, 231, 117, 237)(112, 232, 118, 238)(113, 233, 115, 235)(114, 234, 116, 236)(119, 239, 120, 240)(241, 361, 243, 363, 248, 368, 257, 377, 268, 388, 283, 403, 300, 420, 321, 441, 341, 461, 353, 473, 359, 479, 354, 474, 343, 463, 325, 445, 304, 424, 286, 406, 271, 391, 259, 379, 250, 370, 244, 364)(242, 362, 245, 365, 252, 372, 262, 382, 275, 395, 291, 411, 310, 430, 332, 452, 348, 468, 357, 477, 360, 480, 358, 478, 350, 470, 336, 456, 314, 434, 294, 414, 278, 398, 264, 384, 254, 374, 246, 366)(247, 367, 255, 375, 249, 369, 258, 378, 270, 390, 285, 405, 303, 423, 324, 444, 342, 462, 346, 466, 356, 476, 344, 464, 355, 475, 345, 465, 340, 460, 320, 440, 299, 419, 282, 402, 267, 387, 256, 376)(251, 371, 260, 380, 253, 373, 263, 383, 277, 397, 293, 413, 313, 433, 335, 455, 349, 469, 339, 459, 352, 472, 337, 457, 351, 471, 338, 458, 347, 467, 331, 451, 309, 429, 290, 410, 274, 394, 261, 381)(265, 385, 279, 399, 266, 386, 281, 401, 298, 418, 319, 439, 329, 449, 307, 427, 327, 447, 305, 425, 326, 446, 306, 426, 328, 448, 311, 431, 333, 453, 323, 443, 302, 422, 284, 404, 269, 389, 280, 400)(272, 392, 287, 407, 273, 393, 289, 409, 308, 428, 330, 450, 318, 438, 297, 417, 316, 436, 295, 415, 315, 435, 296, 416, 317, 437, 301, 421, 322, 442, 334, 454, 312, 432, 292, 412, 276, 396, 288, 408) L = (1, 242)(2, 241)(3, 247)(4, 249)(5, 251)(6, 253)(7, 243)(8, 254)(9, 244)(10, 252)(11, 245)(12, 250)(13, 246)(14, 248)(15, 265)(16, 266)(17, 267)(18, 269)(19, 270)(20, 272)(21, 273)(22, 274)(23, 276)(24, 277)(25, 255)(26, 256)(27, 257)(28, 278)(29, 258)(30, 259)(31, 275)(32, 260)(33, 261)(34, 262)(35, 271)(36, 263)(37, 264)(38, 268)(39, 295)(40, 296)(41, 297)(42, 298)(43, 299)(44, 301)(45, 302)(46, 303)(47, 305)(48, 306)(49, 307)(50, 308)(51, 309)(52, 311)(53, 312)(54, 313)(55, 279)(56, 280)(57, 281)(58, 282)(59, 283)(60, 314)(61, 284)(62, 285)(63, 286)(64, 310)(65, 287)(66, 288)(67, 289)(68, 290)(69, 291)(70, 304)(71, 292)(72, 293)(73, 294)(74, 300)(75, 337)(76, 338)(77, 339)(78, 331)(79, 330)(80, 329)(81, 340)(82, 335)(83, 334)(84, 333)(85, 342)(86, 344)(87, 345)(88, 346)(89, 320)(90, 319)(91, 318)(92, 347)(93, 324)(94, 323)(95, 322)(96, 349)(97, 315)(98, 316)(99, 317)(100, 321)(101, 350)(102, 325)(103, 348)(104, 326)(105, 327)(106, 328)(107, 332)(108, 343)(109, 336)(110, 341)(111, 357)(112, 358)(113, 355)(114, 356)(115, 353)(116, 354)(117, 351)(118, 352)(119, 360)(120, 359)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 2, 24, 2, 24 ), ( 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24, 2, 24 ) } Outer automorphisms :: reflexible Dual of E23.1100 Graph:: bipartite v = 66 e = 240 f = 130 degree seq :: [ 4^60, 40^6 ] E23.1100 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 12, 20}) Quotient :: dipole Aut^+ = (C5 x (C3 : C4)) : C2 (small group id <120, 10>) Aut = (C2 x C2 x D30) : C2 (small group id <240, 151>) |r| :: 2 Presentation :: [ Y2, R^2, (Y3 * Y1)^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y1^12, Y1^-1 * Y3^-1 * Y1^2 * Y3^-9 * Y1^-3, (Y3 * Y2^-1)^20 ] Map:: R = (1, 121, 2, 122, 6, 126, 14, 134, 26, 146, 42, 162, 62, 182, 60, 180, 40, 160, 24, 144, 12, 132, 4, 124)(3, 123, 9, 129, 19, 139, 33, 153, 51, 171, 73, 193, 85, 205, 64, 184, 43, 163, 28, 148, 15, 135, 8, 128)(5, 125, 11, 131, 22, 142, 37, 157, 56, 176, 79, 199, 86, 206, 63, 183, 44, 164, 27, 147, 16, 136, 7, 127)(10, 130, 18, 138, 29, 149, 46, 166, 65, 185, 88, 208, 109, 229, 97, 217, 74, 194, 52, 172, 34, 154, 20, 140)(13, 133, 17, 137, 30, 150, 45, 165, 66, 186, 87, 207, 110, 230, 103, 223, 80, 200, 57, 177, 38, 158, 23, 143)(21, 141, 35, 155, 53, 173, 75, 195, 98, 218, 119, 239, 108, 228, 112, 232, 89, 209, 68, 188, 47, 167, 32, 152)(25, 145, 39, 159, 58, 178, 81, 201, 104, 224, 120, 240, 102, 222, 111, 231, 90, 210, 67, 187, 48, 168, 31, 151)(36, 156, 50, 170, 69, 189, 92, 212, 113, 233, 107, 227, 84, 204, 95, 215, 118, 238, 99, 219, 76, 196, 54, 174)(41, 161, 49, 169, 70, 190, 91, 211, 114, 234, 101, 221, 78, 198, 96, 216, 117, 237, 105, 225, 82, 202, 59, 179)(55, 175, 77, 197, 100, 220, 115, 235, 94, 214, 71, 191, 61, 181, 83, 203, 106, 226, 116, 236, 93, 213, 72, 192)(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, 251)(5, 241)(6, 255)(7, 257)(8, 242)(9, 244)(10, 261)(11, 263)(12, 259)(13, 245)(14, 267)(15, 269)(16, 246)(17, 271)(18, 248)(19, 274)(20, 249)(21, 276)(22, 252)(23, 279)(24, 277)(25, 253)(26, 283)(27, 285)(28, 254)(29, 287)(30, 256)(31, 289)(32, 258)(33, 264)(34, 293)(35, 260)(36, 295)(37, 297)(38, 262)(39, 299)(40, 291)(41, 265)(42, 303)(43, 305)(44, 266)(45, 307)(46, 268)(47, 309)(48, 270)(49, 311)(50, 272)(51, 314)(52, 273)(53, 316)(54, 275)(55, 318)(56, 280)(57, 321)(58, 278)(59, 323)(60, 319)(61, 281)(62, 325)(63, 327)(64, 282)(65, 329)(66, 284)(67, 331)(68, 286)(69, 333)(70, 288)(71, 335)(72, 290)(73, 300)(74, 338)(75, 292)(76, 340)(77, 294)(78, 342)(79, 343)(80, 296)(81, 345)(82, 298)(83, 347)(84, 301)(85, 349)(86, 302)(87, 351)(88, 304)(89, 353)(90, 306)(91, 355)(92, 308)(93, 357)(94, 310)(95, 359)(96, 312)(97, 313)(98, 358)(99, 315)(100, 354)(101, 317)(102, 350)(103, 360)(104, 320)(105, 356)(106, 322)(107, 352)(108, 324)(109, 348)(110, 326)(111, 341)(112, 328)(113, 346)(114, 330)(115, 339)(116, 332)(117, 344)(118, 334)(119, 337)(120, 336)(121, 361)(122, 362)(123, 363)(124, 364)(125, 365)(126, 366)(127, 367)(128, 368)(129, 369)(130, 370)(131, 371)(132, 372)(133, 373)(134, 374)(135, 375)(136, 376)(137, 377)(138, 378)(139, 379)(140, 380)(141, 381)(142, 382)(143, 383)(144, 384)(145, 385)(146, 386)(147, 387)(148, 388)(149, 389)(150, 390)(151, 391)(152, 392)(153, 393)(154, 394)(155, 395)(156, 396)(157, 397)(158, 398)(159, 399)(160, 400)(161, 401)(162, 402)(163, 403)(164, 404)(165, 405)(166, 406)(167, 407)(168, 408)(169, 409)(170, 410)(171, 411)(172, 412)(173, 413)(174, 414)(175, 415)(176, 416)(177, 417)(178, 418)(179, 419)(180, 420)(181, 421)(182, 422)(183, 423)(184, 424)(185, 425)(186, 426)(187, 427)(188, 428)(189, 429)(190, 430)(191, 431)(192, 432)(193, 433)(194, 434)(195, 435)(196, 436)(197, 437)(198, 438)(199, 439)(200, 440)(201, 441)(202, 442)(203, 443)(204, 444)(205, 445)(206, 446)(207, 447)(208, 448)(209, 449)(210, 450)(211, 451)(212, 452)(213, 453)(214, 454)(215, 455)(216, 456)(217, 457)(218, 458)(219, 459)(220, 460)(221, 461)(222, 462)(223, 463)(224, 464)(225, 465)(226, 466)(227, 467)(228, 468)(229, 469)(230, 470)(231, 471)(232, 472)(233, 473)(234, 474)(235, 475)(236, 476)(237, 477)(238, 478)(239, 479)(240, 480) local type(s) :: { ( 4, 40 ), ( 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40, 4, 40 ) } Outer automorphisms :: reflexible Dual of E23.1099 Graph:: simple bipartite v = 130 e = 240 f = 66 degree seq :: [ 2^120, 24^10 ] E23.1101 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 8, 32}) Quotient :: regular Aut^+ = $<128, 149>$ (small group id <128, 149>) Aut = $<256, 6657>$ (small group id <256, 6657>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1, (T2 * T1^-4)^2, (T1^-2 * T2)^4, T1^10 * T2 * T1^-6 * T2 ] Map:: non-degenerate R = (1, 2, 5, 11, 23, 43, 66, 85, 101, 117, 110, 96, 79, 57, 32, 52, 72, 60, 35, 53, 73, 90, 106, 122, 116, 100, 84, 65, 42, 22, 10, 4)(3, 7, 15, 31, 55, 77, 93, 109, 121, 103, 86, 74, 50, 26, 12, 25, 47, 40, 21, 39, 63, 82, 98, 114, 118, 107, 89, 68, 44, 36, 18, 8)(6, 13, 27, 51, 41, 64, 83, 99, 115, 119, 102, 91, 71, 46, 24, 45, 38, 20, 9, 19, 37, 62, 81, 97, 113, 123, 105, 87, 67, 54, 30, 14)(16, 28, 48, 69, 61, 76, 92, 108, 124, 128, 125, 112, 95, 78, 56, 75, 59, 34, 17, 29, 49, 70, 88, 104, 120, 127, 126, 111, 94, 80, 58, 33) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 35)(19, 33)(20, 34)(22, 41)(23, 44)(25, 48)(26, 49)(27, 52)(30, 53)(31, 56)(36, 61)(37, 57)(38, 60)(39, 58)(40, 59)(42, 55)(43, 67)(45, 69)(46, 70)(47, 72)(50, 73)(51, 75)(54, 76)(62, 78)(63, 79)(64, 80)(65, 81)(66, 86)(68, 88)(71, 90)(74, 92)(77, 94)(82, 95)(83, 96)(84, 98)(85, 102)(87, 104)(89, 106)(91, 108)(93, 110)(97, 111)(99, 112)(100, 115)(101, 118)(103, 120)(105, 122)(107, 124)(109, 125)(113, 117)(114, 126)(116, 121)(119, 127)(123, 128) local type(s) :: { ( 8^32 ) } Outer automorphisms :: reflexible Dual of E23.1103 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 4 e = 64 f = 16 degree seq :: [ 32^4 ] E23.1102 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 8, 32}) Quotient :: regular Aut^+ = $<128, 151>$ (small group id <128, 151>) Aut = $<256, 6657>$ (small group id <256, 6657>) |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^-1 * T2 * T1^-1 * T2, T1^-2 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-11 ] Map:: non-degenerate R = (1, 2, 5, 11, 20, 32, 47, 65, 86, 105, 121, 116, 100, 80, 95, 78, 93, 79, 94, 81, 96, 112, 128, 120, 104, 85, 64, 46, 31, 19, 10, 4)(3, 7, 15, 25, 39, 55, 75, 97, 113, 126, 111, 91, 74, 54, 72, 52, 71, 53, 73, 63, 84, 103, 119, 123, 106, 88, 66, 49, 33, 22, 12, 8)(6, 13, 9, 18, 29, 44, 61, 82, 101, 117, 127, 110, 92, 70, 60, 43, 58, 41, 57, 42, 59, 77, 99, 115, 122, 107, 87, 67, 48, 34, 21, 14)(16, 26, 17, 28, 35, 51, 68, 90, 108, 125, 118, 102, 83, 62, 45, 30, 37, 23, 36, 24, 38, 50, 69, 89, 109, 124, 114, 98, 76, 56, 40, 27) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 15)(11, 21)(13, 23)(14, 24)(18, 30)(19, 29)(20, 33)(22, 35)(25, 40)(26, 41)(27, 42)(28, 43)(31, 39)(32, 48)(34, 50)(36, 52)(37, 53)(38, 54)(44, 62)(45, 63)(46, 61)(47, 66)(49, 68)(51, 70)(55, 76)(56, 77)(57, 78)(58, 79)(59, 80)(60, 81)(64, 75)(65, 87)(67, 89)(69, 91)(71, 93)(72, 94)(73, 95)(74, 96)(82, 102)(83, 103)(84, 100)(85, 101)(86, 106)(88, 108)(90, 110)(92, 112)(97, 114)(98, 115)(99, 116)(104, 113)(105, 122)(107, 124)(109, 126)(111, 128)(117, 125)(118, 123)(119, 121)(120, 127) local type(s) :: { ( 8^32 ) } Outer automorphisms :: reflexible Dual of E23.1104 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 4 e = 64 f = 16 degree seq :: [ 32^4 ] E23.1103 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 8, 32}) Quotient :: regular Aut^+ = $<128, 149>$ (small group id <128, 149>) Aut = $<256, 6657>$ (small group id <256, 6657>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1^2 * T2 * T1^-1, T1^8, T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * 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, (T1^-1 * T2)^32 ] Map:: non-degenerate R = (1, 2, 5, 11, 20, 19, 10, 4)(3, 7, 12, 22, 31, 28, 17, 8)(6, 13, 21, 32, 30, 18, 9, 14)(15, 25, 33, 43, 40, 27, 16, 26)(23, 34, 42, 41, 29, 36, 24, 35)(37, 47, 52, 50, 39, 49, 38, 48)(44, 53, 51, 56, 46, 55, 45, 54)(57, 65, 60, 68, 59, 67, 58, 66)(61, 69, 64, 72, 63, 71, 62, 70)(73, 81, 76, 84, 75, 83, 74, 82)(77, 85, 80, 88, 79, 87, 78, 86)(89, 97, 92, 100, 91, 99, 90, 98)(93, 101, 96, 104, 95, 103, 94, 102)(105, 113, 108, 116, 107, 115, 106, 114)(109, 117, 112, 120, 111, 119, 110, 118)(121, 127, 124, 126, 123, 125, 122, 128) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 15)(8, 16)(10, 17)(11, 21)(13, 23)(14, 24)(18, 29)(19, 30)(20, 31)(22, 33)(25, 37)(26, 38)(27, 39)(28, 40)(32, 42)(34, 44)(35, 45)(36, 46)(41, 51)(43, 52)(47, 57)(48, 58)(49, 59)(50, 60)(53, 61)(54, 62)(55, 63)(56, 64)(65, 73)(66, 74)(67, 75)(68, 76)(69, 77)(70, 78)(71, 79)(72, 80)(81, 89)(82, 90)(83, 91)(84, 92)(85, 93)(86, 94)(87, 95)(88, 96)(97, 105)(98, 106)(99, 107)(100, 108)(101, 109)(102, 110)(103, 111)(104, 112)(113, 121)(114, 122)(115, 123)(116, 124)(117, 125)(118, 126)(119, 127)(120, 128) local type(s) :: { ( 32^8 ) } Outer automorphisms :: reflexible Dual of E23.1101 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 16 e = 64 f = 4 degree seq :: [ 8^16 ] E23.1104 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 8, 32}) Quotient :: regular Aut^+ = $<128, 151>$ (small group id <128, 151>) Aut = $<256, 6657>$ (small group id <256, 6657>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-2)^2, T1^8, (T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1^-1)^2 ] Map:: 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, 81, 74, 83, 76, 84, 75, 82)(77, 85, 78, 87, 80, 88, 79, 86)(89, 97, 90, 99, 92, 100, 91, 98)(93, 101, 94, 103, 96, 104, 95, 102)(105, 113, 106, 115, 108, 116, 107, 114)(109, 117, 110, 119, 112, 120, 111, 118)(121, 128, 122, 127, 124, 125, 123, 126) 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)(81, 89)(82, 90)(83, 91)(84, 92)(85, 93)(86, 94)(87, 95)(88, 96)(97, 105)(98, 106)(99, 107)(100, 108)(101, 109)(102, 110)(103, 111)(104, 112)(113, 121)(114, 122)(115, 123)(116, 124)(117, 125)(118, 126)(119, 127)(120, 128) local type(s) :: { ( 32^8 ) } Outer automorphisms :: reflexible Dual of E23.1102 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 16 e = 64 f = 4 degree seq :: [ 8^16 ] E23.1105 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 8, 32}) Quotient :: edge Aut^+ = $<128, 149>$ (small group id <128, 149>) Aut = $<256, 6657>$ (small group id <256, 6657>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^-1 * T1 * T2^2 * T1 * T2^-1, T2^8, (T2^-1 * T1 * T2^-3)^2, T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1 ] Map:: R = (1, 3, 8, 17, 28, 19, 10, 4)(2, 5, 12, 22, 34, 24, 14, 6)(7, 15, 26, 39, 30, 18, 9, 16)(11, 20, 32, 44, 36, 23, 13, 21)(25, 37, 48, 41, 29, 40, 27, 38)(31, 42, 53, 46, 35, 45, 33, 43)(47, 57, 51, 60, 50, 59, 49, 58)(52, 61, 56, 64, 55, 63, 54, 62)(65, 73, 68, 76, 67, 75, 66, 74)(69, 77, 72, 80, 71, 79, 70, 78)(81, 89, 84, 92, 83, 91, 82, 90)(85, 93, 88, 96, 87, 95, 86, 94)(97, 105, 100, 108, 99, 107, 98, 106)(101, 109, 104, 112, 103, 111, 102, 110)(113, 121, 116, 124, 115, 123, 114, 122)(117, 125, 120, 128, 119, 127, 118, 126)(129, 130)(131, 135)(132, 137)(133, 139)(134, 141)(136, 140)(138, 142)(143, 153)(144, 155)(145, 154)(146, 157)(147, 158)(148, 159)(149, 161)(150, 160)(151, 163)(152, 164)(156, 162)(165, 175)(166, 177)(167, 176)(168, 178)(169, 179)(170, 180)(171, 182)(172, 181)(173, 183)(174, 184)(185, 193)(186, 194)(187, 195)(188, 196)(189, 197)(190, 198)(191, 199)(192, 200)(201, 209)(202, 210)(203, 211)(204, 212)(205, 213)(206, 214)(207, 215)(208, 216)(217, 225)(218, 226)(219, 227)(220, 228)(221, 229)(222, 230)(223, 231)(224, 232)(233, 241)(234, 242)(235, 243)(236, 244)(237, 245)(238, 246)(239, 247)(240, 248)(249, 255)(250, 256)(251, 253)(252, 254) L = (1, 129)(2, 130)(3, 131)(4, 132)(5, 133)(6, 134)(7, 135)(8, 136)(9, 137)(10, 138)(11, 139)(12, 140)(13, 141)(14, 142)(15, 143)(16, 144)(17, 145)(18, 146)(19, 147)(20, 148)(21, 149)(22, 150)(23, 151)(24, 152)(25, 153)(26, 154)(27, 155)(28, 156)(29, 157)(30, 158)(31, 159)(32, 160)(33, 161)(34, 162)(35, 163)(36, 164)(37, 165)(38, 166)(39, 167)(40, 168)(41, 169)(42, 170)(43, 171)(44, 172)(45, 173)(46, 174)(47, 175)(48, 176)(49, 177)(50, 178)(51, 179)(52, 180)(53, 181)(54, 182)(55, 183)(56, 184)(57, 185)(58, 186)(59, 187)(60, 188)(61, 189)(62, 190)(63, 191)(64, 192)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 64, 64 ), ( 64^8 ) } Outer automorphisms :: reflexible Dual of E23.1113 Transitivity :: ET+ Graph:: simple bipartite v = 80 e = 128 f = 4 degree seq :: [ 2^64, 8^16 ] E23.1106 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 8, 32}) Quotient :: edge Aut^+ = $<128, 151>$ (small group id <128, 151>) Aut = $<256, 6657>$ (small group id <256, 6657>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, (T1 * T2^2)^2, T2^8, T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 ] Map:: 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, 89, 82, 91, 84, 92, 83, 90)(85, 93, 86, 95, 88, 96, 87, 94)(97, 105, 98, 107, 100, 108, 99, 106)(101, 109, 102, 111, 104, 112, 103, 110)(113, 121, 114, 123, 116, 124, 115, 122)(117, 125, 118, 127, 120, 128, 119, 126)(129, 130)(131, 135)(132, 137)(133, 139)(134, 141)(136, 142)(138, 140)(143, 153)(144, 154)(145, 155)(146, 157)(147, 158)(148, 159)(149, 160)(150, 161)(151, 163)(152, 164)(156, 162)(165, 175)(166, 176)(167, 177)(168, 178)(169, 179)(170, 180)(171, 181)(172, 182)(173, 183)(174, 184)(185, 193)(186, 194)(187, 195)(188, 196)(189, 197)(190, 198)(191, 199)(192, 200)(201, 209)(202, 210)(203, 211)(204, 212)(205, 213)(206, 214)(207, 215)(208, 216)(217, 225)(218, 226)(219, 227)(220, 228)(221, 229)(222, 230)(223, 231)(224, 232)(233, 241)(234, 242)(235, 243)(236, 244)(237, 245)(238, 246)(239, 247)(240, 248)(249, 256)(250, 254)(251, 255)(252, 253) L = (1, 129)(2, 130)(3, 131)(4, 132)(5, 133)(6, 134)(7, 135)(8, 136)(9, 137)(10, 138)(11, 139)(12, 140)(13, 141)(14, 142)(15, 143)(16, 144)(17, 145)(18, 146)(19, 147)(20, 148)(21, 149)(22, 150)(23, 151)(24, 152)(25, 153)(26, 154)(27, 155)(28, 156)(29, 157)(30, 158)(31, 159)(32, 160)(33, 161)(34, 162)(35, 163)(36, 164)(37, 165)(38, 166)(39, 167)(40, 168)(41, 169)(42, 170)(43, 171)(44, 172)(45, 173)(46, 174)(47, 175)(48, 176)(49, 177)(50, 178)(51, 179)(52, 180)(53, 181)(54, 182)(55, 183)(56, 184)(57, 185)(58, 186)(59, 187)(60, 188)(61, 189)(62, 190)(63, 191)(64, 192)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 64, 64 ), ( 64^8 ) } Outer automorphisms :: reflexible Dual of E23.1114 Transitivity :: ET+ Graph:: simple bipartite v = 80 e = 128 f = 4 degree seq :: [ 2^64, 8^16 ] E23.1107 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 8, 32}) Quotient :: edge Aut^+ = $<128, 149>$ (small group id <128, 149>) Aut = $<256, 6657>$ (small group id <256, 6657>) |r| :: 2 Presentation :: [ F^2, (T2^-1 * T1^-1)^2, (T1^-1 * T2^-1)^2, (F * T1)^2, (F * T2)^2, T1^-2 * T2 * T1^2 * T2^-1, T1 * T2^-2 * T1^3 * T2^-2, T1^8, T2^13 * T1^-1 * T2^-3 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 3, 10, 25, 48, 64, 80, 96, 112, 120, 104, 88, 72, 56, 41, 30, 34, 21, 42, 58, 74, 90, 106, 122, 116, 100, 84, 68, 52, 33, 15, 5)(2, 7, 19, 40, 57, 73, 89, 105, 121, 110, 94, 78, 62, 46, 24, 11, 27, 37, 32, 51, 67, 83, 99, 115, 124, 108, 92, 76, 60, 44, 22, 8)(4, 12, 29, 49, 65, 81, 97, 113, 126, 111, 95, 79, 63, 47, 26, 35, 16, 14, 31, 50, 66, 82, 98, 114, 125, 109, 93, 77, 61, 45, 23, 9)(6, 17, 36, 53, 69, 85, 101, 117, 127, 119, 103, 87, 71, 55, 39, 20, 13, 28, 43, 59, 75, 91, 107, 123, 128, 118, 102, 86, 70, 54, 38, 18)(129, 130, 134, 144, 162, 155, 141, 132)(131, 137, 145, 136, 149, 163, 156, 139)(133, 142, 146, 165, 158, 140, 148, 135)(138, 152, 164, 151, 170, 150, 171, 154)(143, 160, 166, 157, 169, 147, 167, 159)(153, 175, 181, 174, 186, 173, 187, 172)(161, 177, 182, 168, 184, 178, 183, 179)(176, 188, 197, 191, 202, 190, 203, 189)(180, 185, 198, 194, 200, 195, 199, 193)(192, 205, 213, 204, 218, 207, 219, 206)(196, 210, 214, 211, 216, 209, 215, 201)(208, 222, 229, 221, 234, 220, 235, 223)(212, 227, 230, 225, 232, 217, 231, 226)(224, 239, 245, 238, 250, 237, 251, 236)(228, 241, 246, 233, 248, 242, 247, 243)(240, 252, 255, 254, 244, 249, 256, 253) L = (1, 129)(2, 130)(3, 131)(4, 132)(5, 133)(6, 134)(7, 135)(8, 136)(9, 137)(10, 138)(11, 139)(12, 140)(13, 141)(14, 142)(15, 143)(16, 144)(17, 145)(18, 146)(19, 147)(20, 148)(21, 149)(22, 150)(23, 151)(24, 152)(25, 153)(26, 154)(27, 155)(28, 156)(29, 157)(30, 158)(31, 159)(32, 160)(33, 161)(34, 162)(35, 163)(36, 164)(37, 165)(38, 166)(39, 167)(40, 168)(41, 169)(42, 170)(43, 171)(44, 172)(45, 173)(46, 174)(47, 175)(48, 176)(49, 177)(50, 178)(51, 179)(52, 180)(53, 181)(54, 182)(55, 183)(56, 184)(57, 185)(58, 186)(59, 187)(60, 188)(61, 189)(62, 190)(63, 191)(64, 192)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4^8 ), ( 4^32 ) } Outer automorphisms :: reflexible Dual of E23.1115 Transitivity :: ET+ Graph:: bipartite v = 20 e = 128 f = 64 degree seq :: [ 8^16, 32^4 ] E23.1108 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 8, 32}) Quotient :: edge Aut^+ = $<128, 151>$ (small group id <128, 151>) Aut = $<256, 6657>$ (small group id <256, 6657>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2 * T1)^2, (T2 * T1^-1)^2, T1^8, T1^-1 * T2^-1 * T1^2 * T2^-15 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 3, 10, 21, 36, 52, 68, 84, 100, 116, 122, 106, 90, 74, 58, 42, 26, 41, 57, 73, 89, 105, 121, 120, 104, 88, 72, 56, 40, 25, 13, 5)(2, 7, 17, 31, 47, 63, 79, 95, 111, 127, 113, 97, 81, 65, 49, 33, 24, 37, 53, 69, 85, 101, 117, 128, 112, 96, 80, 64, 48, 32, 18, 8)(4, 11, 23, 39, 55, 71, 87, 103, 119, 124, 108, 92, 76, 60, 44, 28, 14, 27, 43, 59, 75, 91, 107, 123, 115, 99, 83, 67, 51, 35, 20, 9)(6, 15, 29, 45, 61, 77, 93, 109, 125, 118, 102, 86, 70, 54, 38, 22, 12, 19, 34, 50, 66, 82, 98, 114, 126, 110, 94, 78, 62, 46, 30, 16)(129, 130, 134, 142, 154, 152, 140, 132)(131, 137, 147, 161, 169, 156, 143, 136)(133, 139, 150, 165, 170, 155, 144, 135)(138, 146, 157, 172, 185, 177, 162, 148)(141, 145, 158, 171, 186, 181, 166, 151)(149, 163, 178, 193, 201, 188, 173, 160)(153, 167, 182, 197, 202, 187, 174, 159)(164, 176, 189, 204, 217, 209, 194, 179)(168, 175, 190, 203, 218, 213, 198, 183)(180, 195, 210, 225, 233, 220, 205, 192)(184, 199, 214, 229, 234, 219, 206, 191)(196, 208, 221, 236, 249, 241, 226, 211)(200, 207, 222, 235, 250, 245, 230, 215)(212, 227, 242, 255, 248, 252, 237, 224)(216, 231, 246, 256, 244, 251, 238, 223)(228, 240, 253, 247, 232, 239, 254, 243) L = (1, 129)(2, 130)(3, 131)(4, 132)(5, 133)(6, 134)(7, 135)(8, 136)(9, 137)(10, 138)(11, 139)(12, 140)(13, 141)(14, 142)(15, 143)(16, 144)(17, 145)(18, 146)(19, 147)(20, 148)(21, 149)(22, 150)(23, 151)(24, 152)(25, 153)(26, 154)(27, 155)(28, 156)(29, 157)(30, 158)(31, 159)(32, 160)(33, 161)(34, 162)(35, 163)(36, 164)(37, 165)(38, 166)(39, 167)(40, 168)(41, 169)(42, 170)(43, 171)(44, 172)(45, 173)(46, 174)(47, 175)(48, 176)(49, 177)(50, 178)(51, 179)(52, 180)(53, 181)(54, 182)(55, 183)(56, 184)(57, 185)(58, 186)(59, 187)(60, 188)(61, 189)(62, 190)(63, 191)(64, 192)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 4^8 ), ( 4^32 ) } Outer automorphisms :: reflexible Dual of E23.1116 Transitivity :: ET+ Graph:: bipartite v = 20 e = 128 f = 64 degree seq :: [ 8^16, 32^4 ] E23.1109 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 8, 32}) Quotient :: edge Aut^+ = $<128, 149>$ (small group id <128, 149>) Aut = $<256, 6657>$ (small group id <256, 6657>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1, (T2 * T1^-4)^2, (T1^-2 * T2)^4, T1^10 * T2 * T1^-6 * T2 ] Map:: R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 35)(19, 33)(20, 34)(22, 41)(23, 44)(25, 48)(26, 49)(27, 52)(30, 53)(31, 56)(36, 61)(37, 57)(38, 60)(39, 58)(40, 59)(42, 55)(43, 67)(45, 69)(46, 70)(47, 72)(50, 73)(51, 75)(54, 76)(62, 78)(63, 79)(64, 80)(65, 81)(66, 86)(68, 88)(71, 90)(74, 92)(77, 94)(82, 95)(83, 96)(84, 98)(85, 102)(87, 104)(89, 106)(91, 108)(93, 110)(97, 111)(99, 112)(100, 115)(101, 118)(103, 120)(105, 122)(107, 124)(109, 125)(113, 117)(114, 126)(116, 121)(119, 127)(123, 128)(129, 130, 133, 139, 151, 171, 194, 213, 229, 245, 238, 224, 207, 185, 160, 180, 200, 188, 163, 181, 201, 218, 234, 250, 244, 228, 212, 193, 170, 150, 138, 132)(131, 135, 143, 159, 183, 205, 221, 237, 249, 231, 214, 202, 178, 154, 140, 153, 175, 168, 149, 167, 191, 210, 226, 242, 246, 235, 217, 196, 172, 164, 146, 136)(134, 141, 155, 179, 169, 192, 211, 227, 243, 247, 230, 219, 199, 174, 152, 173, 166, 148, 137, 147, 165, 190, 209, 225, 241, 251, 233, 215, 195, 182, 158, 142)(144, 156, 176, 197, 189, 204, 220, 236, 252, 256, 253, 240, 223, 206, 184, 203, 187, 162, 145, 157, 177, 198, 216, 232, 248, 255, 254, 239, 222, 208, 186, 161) L = (1, 129)(2, 130)(3, 131)(4, 132)(5, 133)(6, 134)(7, 135)(8, 136)(9, 137)(10, 138)(11, 139)(12, 140)(13, 141)(14, 142)(15, 143)(16, 144)(17, 145)(18, 146)(19, 147)(20, 148)(21, 149)(22, 150)(23, 151)(24, 152)(25, 153)(26, 154)(27, 155)(28, 156)(29, 157)(30, 158)(31, 159)(32, 160)(33, 161)(34, 162)(35, 163)(36, 164)(37, 165)(38, 166)(39, 167)(40, 168)(41, 169)(42, 170)(43, 171)(44, 172)(45, 173)(46, 174)(47, 175)(48, 176)(49, 177)(50, 178)(51, 179)(52, 180)(53, 181)(54, 182)(55, 183)(56, 184)(57, 185)(58, 186)(59, 187)(60, 188)(61, 189)(62, 190)(63, 191)(64, 192)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 16, 16 ), ( 16^32 ) } Outer automorphisms :: reflexible Dual of E23.1111 Transitivity :: ET+ Graph:: simple bipartite v = 68 e = 128 f = 16 degree seq :: [ 2^64, 32^4 ] E23.1110 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 8, 32}) Quotient :: edge Aut^+ = $<128, 151>$ (small group id <128, 151>) Aut = $<256, 6657>$ (small group id <256, 6657>) |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 * T2 * T1^-1 * T2 * T1^-1, T1^-2 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-11 ] Map:: R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 15)(11, 21)(13, 23)(14, 24)(18, 30)(19, 29)(20, 33)(22, 35)(25, 40)(26, 41)(27, 42)(28, 43)(31, 39)(32, 48)(34, 50)(36, 52)(37, 53)(38, 54)(44, 62)(45, 63)(46, 61)(47, 66)(49, 68)(51, 70)(55, 76)(56, 77)(57, 78)(58, 79)(59, 80)(60, 81)(64, 75)(65, 87)(67, 89)(69, 91)(71, 93)(72, 94)(73, 95)(74, 96)(82, 102)(83, 103)(84, 100)(85, 101)(86, 106)(88, 108)(90, 110)(92, 112)(97, 114)(98, 115)(99, 116)(104, 113)(105, 122)(107, 124)(109, 126)(111, 128)(117, 125)(118, 123)(119, 121)(120, 127)(129, 130, 133, 139, 148, 160, 175, 193, 214, 233, 249, 244, 228, 208, 223, 206, 221, 207, 222, 209, 224, 240, 256, 248, 232, 213, 192, 174, 159, 147, 138, 132)(131, 135, 143, 153, 167, 183, 203, 225, 241, 254, 239, 219, 202, 182, 200, 180, 199, 181, 201, 191, 212, 231, 247, 251, 234, 216, 194, 177, 161, 150, 140, 136)(134, 141, 137, 146, 157, 172, 189, 210, 229, 245, 255, 238, 220, 198, 188, 171, 186, 169, 185, 170, 187, 205, 227, 243, 250, 235, 215, 195, 176, 162, 149, 142)(144, 154, 145, 156, 163, 179, 196, 218, 236, 253, 246, 230, 211, 190, 173, 158, 165, 151, 164, 152, 166, 178, 197, 217, 237, 252, 242, 226, 204, 184, 168, 155) L = (1, 129)(2, 130)(3, 131)(4, 132)(5, 133)(6, 134)(7, 135)(8, 136)(9, 137)(10, 138)(11, 139)(12, 140)(13, 141)(14, 142)(15, 143)(16, 144)(17, 145)(18, 146)(19, 147)(20, 148)(21, 149)(22, 150)(23, 151)(24, 152)(25, 153)(26, 154)(27, 155)(28, 156)(29, 157)(30, 158)(31, 159)(32, 160)(33, 161)(34, 162)(35, 163)(36, 164)(37, 165)(38, 166)(39, 167)(40, 168)(41, 169)(42, 170)(43, 171)(44, 172)(45, 173)(46, 174)(47, 175)(48, 176)(49, 177)(50, 178)(51, 179)(52, 180)(53, 181)(54, 182)(55, 183)(56, 184)(57, 185)(58, 186)(59, 187)(60, 188)(61, 189)(62, 190)(63, 191)(64, 192)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256) local type(s) :: { ( 16, 16 ), ( 16^32 ) } Outer automorphisms :: reflexible Dual of E23.1112 Transitivity :: ET+ Graph:: simple bipartite v = 68 e = 128 f = 16 degree seq :: [ 2^64, 32^4 ] E23.1111 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 8, 32}) Quotient :: loop Aut^+ = $<128, 149>$ (small group id <128, 149>) Aut = $<256, 6657>$ (small group id <256, 6657>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^-1 * T1 * T2^2 * T1 * T2^-1, T2^8, (T2^-1 * T1 * T2^-3)^2, T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1 ] Map:: R = (1, 129, 3, 131, 8, 136, 17, 145, 28, 156, 19, 147, 10, 138, 4, 132)(2, 130, 5, 133, 12, 140, 22, 150, 34, 162, 24, 152, 14, 142, 6, 134)(7, 135, 15, 143, 26, 154, 39, 167, 30, 158, 18, 146, 9, 137, 16, 144)(11, 139, 20, 148, 32, 160, 44, 172, 36, 164, 23, 151, 13, 141, 21, 149)(25, 153, 37, 165, 48, 176, 41, 169, 29, 157, 40, 168, 27, 155, 38, 166)(31, 159, 42, 170, 53, 181, 46, 174, 35, 163, 45, 173, 33, 161, 43, 171)(47, 175, 57, 185, 51, 179, 60, 188, 50, 178, 59, 187, 49, 177, 58, 186)(52, 180, 61, 189, 56, 184, 64, 192, 55, 183, 63, 191, 54, 182, 62, 190)(65, 193, 73, 201, 68, 196, 76, 204, 67, 195, 75, 203, 66, 194, 74, 202)(69, 197, 77, 205, 72, 200, 80, 208, 71, 199, 79, 207, 70, 198, 78, 206)(81, 209, 89, 217, 84, 212, 92, 220, 83, 211, 91, 219, 82, 210, 90, 218)(85, 213, 93, 221, 88, 216, 96, 224, 87, 215, 95, 223, 86, 214, 94, 222)(97, 225, 105, 233, 100, 228, 108, 236, 99, 227, 107, 235, 98, 226, 106, 234)(101, 229, 109, 237, 104, 232, 112, 240, 103, 231, 111, 239, 102, 230, 110, 238)(113, 241, 121, 249, 116, 244, 124, 252, 115, 243, 123, 251, 114, 242, 122, 250)(117, 245, 125, 253, 120, 248, 128, 256, 119, 247, 127, 255, 118, 246, 126, 254) L = (1, 130)(2, 129)(3, 135)(4, 137)(5, 139)(6, 141)(7, 131)(8, 140)(9, 132)(10, 142)(11, 133)(12, 136)(13, 134)(14, 138)(15, 153)(16, 155)(17, 154)(18, 157)(19, 158)(20, 159)(21, 161)(22, 160)(23, 163)(24, 164)(25, 143)(26, 145)(27, 144)(28, 162)(29, 146)(30, 147)(31, 148)(32, 150)(33, 149)(34, 156)(35, 151)(36, 152)(37, 175)(38, 177)(39, 176)(40, 178)(41, 179)(42, 180)(43, 182)(44, 181)(45, 183)(46, 184)(47, 165)(48, 167)(49, 166)(50, 168)(51, 169)(52, 170)(53, 172)(54, 171)(55, 173)(56, 174)(57, 193)(58, 194)(59, 195)(60, 196)(61, 197)(62, 198)(63, 199)(64, 200)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 209)(74, 210)(75, 211)(76, 212)(77, 213)(78, 214)(79, 215)(80, 216)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 225)(90, 226)(91, 227)(92, 228)(93, 229)(94, 230)(95, 231)(96, 232)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 241)(106, 242)(107, 243)(108, 244)(109, 245)(110, 246)(111, 247)(112, 248)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)(121, 255)(122, 256)(123, 253)(124, 254)(125, 251)(126, 252)(127, 249)(128, 250) local type(s) :: { ( 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32 ) } Outer automorphisms :: reflexible Dual of E23.1109 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 16 e = 128 f = 68 degree seq :: [ 16^16 ] E23.1112 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 8, 32}) Quotient :: loop Aut^+ = $<128, 151>$ (small group id <128, 151>) Aut = $<256, 6657>$ (small group id <256, 6657>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, (T1 * T2^2)^2, T2^8, T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 ] Map:: R = (1, 129, 3, 131, 8, 136, 17, 145, 28, 156, 19, 147, 10, 138, 4, 132)(2, 130, 5, 133, 12, 140, 22, 150, 34, 162, 24, 152, 14, 142, 6, 134)(7, 135, 15, 143, 9, 137, 18, 146, 30, 158, 40, 168, 27, 155, 16, 144)(11, 139, 20, 148, 13, 141, 23, 151, 36, 164, 45, 173, 33, 161, 21, 149)(25, 153, 37, 165, 26, 154, 39, 167, 50, 178, 41, 169, 29, 157, 38, 166)(31, 159, 42, 170, 32, 160, 44, 172, 55, 183, 46, 174, 35, 163, 43, 171)(47, 175, 57, 185, 48, 176, 59, 187, 51, 179, 60, 188, 49, 177, 58, 186)(52, 180, 61, 189, 53, 181, 63, 191, 56, 184, 64, 192, 54, 182, 62, 190)(65, 193, 73, 201, 66, 194, 75, 203, 68, 196, 76, 204, 67, 195, 74, 202)(69, 197, 77, 205, 70, 198, 79, 207, 72, 200, 80, 208, 71, 199, 78, 206)(81, 209, 89, 217, 82, 210, 91, 219, 84, 212, 92, 220, 83, 211, 90, 218)(85, 213, 93, 221, 86, 214, 95, 223, 88, 216, 96, 224, 87, 215, 94, 222)(97, 225, 105, 233, 98, 226, 107, 235, 100, 228, 108, 236, 99, 227, 106, 234)(101, 229, 109, 237, 102, 230, 111, 239, 104, 232, 112, 240, 103, 231, 110, 238)(113, 241, 121, 249, 114, 242, 123, 251, 116, 244, 124, 252, 115, 243, 122, 250)(117, 245, 125, 253, 118, 246, 127, 255, 120, 248, 128, 256, 119, 247, 126, 254) L = (1, 130)(2, 129)(3, 135)(4, 137)(5, 139)(6, 141)(7, 131)(8, 142)(9, 132)(10, 140)(11, 133)(12, 138)(13, 134)(14, 136)(15, 153)(16, 154)(17, 155)(18, 157)(19, 158)(20, 159)(21, 160)(22, 161)(23, 163)(24, 164)(25, 143)(26, 144)(27, 145)(28, 162)(29, 146)(30, 147)(31, 148)(32, 149)(33, 150)(34, 156)(35, 151)(36, 152)(37, 175)(38, 176)(39, 177)(40, 178)(41, 179)(42, 180)(43, 181)(44, 182)(45, 183)(46, 184)(47, 165)(48, 166)(49, 167)(50, 168)(51, 169)(52, 170)(53, 171)(54, 172)(55, 173)(56, 174)(57, 193)(58, 194)(59, 195)(60, 196)(61, 197)(62, 198)(63, 199)(64, 200)(65, 185)(66, 186)(67, 187)(68, 188)(69, 189)(70, 190)(71, 191)(72, 192)(73, 209)(74, 210)(75, 211)(76, 212)(77, 213)(78, 214)(79, 215)(80, 216)(81, 201)(82, 202)(83, 203)(84, 204)(85, 205)(86, 206)(87, 207)(88, 208)(89, 225)(90, 226)(91, 227)(92, 228)(93, 229)(94, 230)(95, 231)(96, 232)(97, 217)(98, 218)(99, 219)(100, 220)(101, 221)(102, 222)(103, 223)(104, 224)(105, 241)(106, 242)(107, 243)(108, 244)(109, 245)(110, 246)(111, 247)(112, 248)(113, 233)(114, 234)(115, 235)(116, 236)(117, 237)(118, 238)(119, 239)(120, 240)(121, 256)(122, 254)(123, 255)(124, 253)(125, 252)(126, 250)(127, 251)(128, 249) local type(s) :: { ( 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32, 2, 32 ) } Outer automorphisms :: reflexible Dual of E23.1110 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 16 e = 128 f = 68 degree seq :: [ 16^16 ] E23.1113 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 8, 32}) Quotient :: loop Aut^+ = $<128, 149>$ (small group id <128, 149>) Aut = $<256, 6657>$ (small group id <256, 6657>) |r| :: 2 Presentation :: [ F^2, (T2^-1 * T1^-1)^2, (T1^-1 * T2^-1)^2, (F * T1)^2, (F * T2)^2, T1^-2 * T2 * T1^2 * T2^-1, T1 * T2^-2 * T1^3 * T2^-2, T1^8, T2^13 * T1^-1 * T2^-3 * T1^-1 ] Map:: R = (1, 129, 3, 131, 10, 138, 25, 153, 48, 176, 64, 192, 80, 208, 96, 224, 112, 240, 120, 248, 104, 232, 88, 216, 72, 200, 56, 184, 41, 169, 30, 158, 34, 162, 21, 149, 42, 170, 58, 186, 74, 202, 90, 218, 106, 234, 122, 250, 116, 244, 100, 228, 84, 212, 68, 196, 52, 180, 33, 161, 15, 143, 5, 133)(2, 130, 7, 135, 19, 147, 40, 168, 57, 185, 73, 201, 89, 217, 105, 233, 121, 249, 110, 238, 94, 222, 78, 206, 62, 190, 46, 174, 24, 152, 11, 139, 27, 155, 37, 165, 32, 160, 51, 179, 67, 195, 83, 211, 99, 227, 115, 243, 124, 252, 108, 236, 92, 220, 76, 204, 60, 188, 44, 172, 22, 150, 8, 136)(4, 132, 12, 140, 29, 157, 49, 177, 65, 193, 81, 209, 97, 225, 113, 241, 126, 254, 111, 239, 95, 223, 79, 207, 63, 191, 47, 175, 26, 154, 35, 163, 16, 144, 14, 142, 31, 159, 50, 178, 66, 194, 82, 210, 98, 226, 114, 242, 125, 253, 109, 237, 93, 221, 77, 205, 61, 189, 45, 173, 23, 151, 9, 137)(6, 134, 17, 145, 36, 164, 53, 181, 69, 197, 85, 213, 101, 229, 117, 245, 127, 255, 119, 247, 103, 231, 87, 215, 71, 199, 55, 183, 39, 167, 20, 148, 13, 141, 28, 156, 43, 171, 59, 187, 75, 203, 91, 219, 107, 235, 123, 251, 128, 256, 118, 246, 102, 230, 86, 214, 70, 198, 54, 182, 38, 166, 18, 146) L = (1, 130)(2, 134)(3, 137)(4, 129)(5, 142)(6, 144)(7, 133)(8, 149)(9, 145)(10, 152)(11, 131)(12, 148)(13, 132)(14, 146)(15, 160)(16, 162)(17, 136)(18, 165)(19, 167)(20, 135)(21, 163)(22, 171)(23, 170)(24, 164)(25, 175)(26, 138)(27, 141)(28, 139)(29, 169)(30, 140)(31, 143)(32, 166)(33, 177)(34, 155)(35, 156)(36, 151)(37, 158)(38, 157)(39, 159)(40, 184)(41, 147)(42, 150)(43, 154)(44, 153)(45, 187)(46, 186)(47, 181)(48, 188)(49, 182)(50, 183)(51, 161)(52, 185)(53, 174)(54, 168)(55, 179)(56, 178)(57, 198)(58, 173)(59, 172)(60, 197)(61, 176)(62, 203)(63, 202)(64, 205)(65, 180)(66, 200)(67, 199)(68, 210)(69, 191)(70, 194)(71, 193)(72, 195)(73, 196)(74, 190)(75, 189)(76, 218)(77, 213)(78, 192)(79, 219)(80, 222)(81, 215)(82, 214)(83, 216)(84, 227)(85, 204)(86, 211)(87, 201)(88, 209)(89, 231)(90, 207)(91, 206)(92, 235)(93, 234)(94, 229)(95, 208)(96, 239)(97, 232)(98, 212)(99, 230)(100, 241)(101, 221)(102, 225)(103, 226)(104, 217)(105, 248)(106, 220)(107, 223)(108, 224)(109, 251)(110, 250)(111, 245)(112, 252)(113, 246)(114, 247)(115, 228)(116, 249)(117, 238)(118, 233)(119, 243)(120, 242)(121, 256)(122, 237)(123, 236)(124, 255)(125, 240)(126, 244)(127, 254)(128, 253) 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 E23.1105 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 4 e = 128 f = 80 degree seq :: [ 64^4 ] E23.1114 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 8, 32}) Quotient :: loop Aut^+ = $<128, 151>$ (small group id <128, 151>) Aut = $<256, 6657>$ (small group id <256, 6657>) |r| :: 2 Presentation :: [ F^2, (F * T1)^2, (F * T2)^2, (T2 * T1)^2, (T2 * T1^-1)^2, T1^8, T1^-1 * T2^-1 * T1^2 * T2^-15 * T1^-1 ] Map:: R = (1, 129, 3, 131, 10, 138, 21, 149, 36, 164, 52, 180, 68, 196, 84, 212, 100, 228, 116, 244, 122, 250, 106, 234, 90, 218, 74, 202, 58, 186, 42, 170, 26, 154, 41, 169, 57, 185, 73, 201, 89, 217, 105, 233, 121, 249, 120, 248, 104, 232, 88, 216, 72, 200, 56, 184, 40, 168, 25, 153, 13, 141, 5, 133)(2, 130, 7, 135, 17, 145, 31, 159, 47, 175, 63, 191, 79, 207, 95, 223, 111, 239, 127, 255, 113, 241, 97, 225, 81, 209, 65, 193, 49, 177, 33, 161, 24, 152, 37, 165, 53, 181, 69, 197, 85, 213, 101, 229, 117, 245, 128, 256, 112, 240, 96, 224, 80, 208, 64, 192, 48, 176, 32, 160, 18, 146, 8, 136)(4, 132, 11, 139, 23, 151, 39, 167, 55, 183, 71, 199, 87, 215, 103, 231, 119, 247, 124, 252, 108, 236, 92, 220, 76, 204, 60, 188, 44, 172, 28, 156, 14, 142, 27, 155, 43, 171, 59, 187, 75, 203, 91, 219, 107, 235, 123, 251, 115, 243, 99, 227, 83, 211, 67, 195, 51, 179, 35, 163, 20, 148, 9, 137)(6, 134, 15, 143, 29, 157, 45, 173, 61, 189, 77, 205, 93, 221, 109, 237, 125, 253, 118, 246, 102, 230, 86, 214, 70, 198, 54, 182, 38, 166, 22, 150, 12, 140, 19, 147, 34, 162, 50, 178, 66, 194, 82, 210, 98, 226, 114, 242, 126, 254, 110, 238, 94, 222, 78, 206, 62, 190, 46, 174, 30, 158, 16, 144) L = (1, 130)(2, 134)(3, 137)(4, 129)(5, 139)(6, 142)(7, 133)(8, 131)(9, 147)(10, 146)(11, 150)(12, 132)(13, 145)(14, 154)(15, 136)(16, 135)(17, 158)(18, 157)(19, 161)(20, 138)(21, 163)(22, 165)(23, 141)(24, 140)(25, 167)(26, 152)(27, 144)(28, 143)(29, 172)(30, 171)(31, 153)(32, 149)(33, 169)(34, 148)(35, 178)(36, 176)(37, 170)(38, 151)(39, 182)(40, 175)(41, 156)(42, 155)(43, 186)(44, 185)(45, 160)(46, 159)(47, 190)(48, 189)(49, 162)(50, 193)(51, 164)(52, 195)(53, 166)(54, 197)(55, 168)(56, 199)(57, 177)(58, 181)(59, 174)(60, 173)(61, 204)(62, 203)(63, 184)(64, 180)(65, 201)(66, 179)(67, 210)(68, 208)(69, 202)(70, 183)(71, 214)(72, 207)(73, 188)(74, 187)(75, 218)(76, 217)(77, 192)(78, 191)(79, 222)(80, 221)(81, 194)(82, 225)(83, 196)(84, 227)(85, 198)(86, 229)(87, 200)(88, 231)(89, 209)(90, 213)(91, 206)(92, 205)(93, 236)(94, 235)(95, 216)(96, 212)(97, 233)(98, 211)(99, 242)(100, 240)(101, 234)(102, 215)(103, 246)(104, 239)(105, 220)(106, 219)(107, 250)(108, 249)(109, 224)(110, 223)(111, 254)(112, 253)(113, 226)(114, 255)(115, 228)(116, 251)(117, 230)(118, 256)(119, 232)(120, 252)(121, 241)(122, 245)(123, 238)(124, 237)(125, 247)(126, 243)(127, 248)(128, 244) 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 E23.1106 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 4 e = 128 f = 80 degree seq :: [ 64^4 ] E23.1115 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 8, 32}) Quotient :: loop Aut^+ = $<128, 149>$ (small group id <128, 149>) Aut = $<256, 6657>$ (small group id <256, 6657>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1^-1, (T2 * T1^-4)^2, (T1^-2 * T2)^4, T1^10 * T2 * T1^-6 * T2 ] Map:: polytopal non-degenerate R = (1, 129, 3, 131)(2, 130, 6, 134)(4, 132, 9, 137)(5, 133, 12, 140)(7, 135, 16, 144)(8, 136, 17, 145)(10, 138, 21, 149)(11, 139, 24, 152)(13, 141, 28, 156)(14, 142, 29, 157)(15, 143, 32, 160)(18, 146, 35, 163)(19, 147, 33, 161)(20, 148, 34, 162)(22, 150, 41, 169)(23, 151, 44, 172)(25, 153, 48, 176)(26, 154, 49, 177)(27, 155, 52, 180)(30, 158, 53, 181)(31, 159, 56, 184)(36, 164, 61, 189)(37, 165, 57, 185)(38, 166, 60, 188)(39, 167, 58, 186)(40, 168, 59, 187)(42, 170, 55, 183)(43, 171, 67, 195)(45, 173, 69, 197)(46, 174, 70, 198)(47, 175, 72, 200)(50, 178, 73, 201)(51, 179, 75, 203)(54, 182, 76, 204)(62, 190, 78, 206)(63, 191, 79, 207)(64, 192, 80, 208)(65, 193, 81, 209)(66, 194, 86, 214)(68, 196, 88, 216)(71, 199, 90, 218)(74, 202, 92, 220)(77, 205, 94, 222)(82, 210, 95, 223)(83, 211, 96, 224)(84, 212, 98, 226)(85, 213, 102, 230)(87, 215, 104, 232)(89, 217, 106, 234)(91, 219, 108, 236)(93, 221, 110, 238)(97, 225, 111, 239)(99, 227, 112, 240)(100, 228, 115, 243)(101, 229, 118, 246)(103, 231, 120, 248)(105, 233, 122, 250)(107, 235, 124, 252)(109, 237, 125, 253)(113, 241, 117, 245)(114, 242, 126, 254)(116, 244, 121, 249)(119, 247, 127, 255)(123, 251, 128, 256) L = (1, 130)(2, 133)(3, 135)(4, 129)(5, 139)(6, 141)(7, 143)(8, 131)(9, 147)(10, 132)(11, 151)(12, 153)(13, 155)(14, 134)(15, 159)(16, 156)(17, 157)(18, 136)(19, 165)(20, 137)(21, 167)(22, 138)(23, 171)(24, 173)(25, 175)(26, 140)(27, 179)(28, 176)(29, 177)(30, 142)(31, 183)(32, 180)(33, 144)(34, 145)(35, 181)(36, 146)(37, 190)(38, 148)(39, 191)(40, 149)(41, 192)(42, 150)(43, 194)(44, 164)(45, 166)(46, 152)(47, 168)(48, 197)(49, 198)(50, 154)(51, 169)(52, 200)(53, 201)(54, 158)(55, 205)(56, 203)(57, 160)(58, 161)(59, 162)(60, 163)(61, 204)(62, 209)(63, 210)(64, 211)(65, 170)(66, 213)(67, 182)(68, 172)(69, 189)(70, 216)(71, 174)(72, 188)(73, 218)(74, 178)(75, 187)(76, 220)(77, 221)(78, 184)(79, 185)(80, 186)(81, 225)(82, 226)(83, 227)(84, 193)(85, 229)(86, 202)(87, 195)(88, 232)(89, 196)(90, 234)(91, 199)(92, 236)(93, 237)(94, 208)(95, 206)(96, 207)(97, 241)(98, 242)(99, 243)(100, 212)(101, 245)(102, 219)(103, 214)(104, 248)(105, 215)(106, 250)(107, 217)(108, 252)(109, 249)(110, 224)(111, 222)(112, 223)(113, 251)(114, 246)(115, 247)(116, 228)(117, 238)(118, 235)(119, 230)(120, 255)(121, 231)(122, 244)(123, 233)(124, 256)(125, 240)(126, 239)(127, 254)(128, 253) local type(s) :: { ( 8, 32, 8, 32 ) } Outer automorphisms :: reflexible Dual of E23.1107 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 64 e = 128 f = 20 degree seq :: [ 4^64 ] E23.1116 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 8, 32}) Quotient :: loop Aut^+ = $<128, 151>$ (small group id <128, 151>) Aut = $<256, 6657>$ (small group id <256, 6657>) |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 * T2 * T1^-1 * T2 * T1^-1, T1^-2 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1^-11 ] Map:: polytopal non-degenerate R = (1, 129, 3, 131)(2, 130, 6, 134)(4, 132, 9, 137)(5, 133, 12, 140)(7, 135, 16, 144)(8, 136, 17, 145)(10, 138, 15, 143)(11, 139, 21, 149)(13, 141, 23, 151)(14, 142, 24, 152)(18, 146, 30, 158)(19, 147, 29, 157)(20, 148, 33, 161)(22, 150, 35, 163)(25, 153, 40, 168)(26, 154, 41, 169)(27, 155, 42, 170)(28, 156, 43, 171)(31, 159, 39, 167)(32, 160, 48, 176)(34, 162, 50, 178)(36, 164, 52, 180)(37, 165, 53, 181)(38, 166, 54, 182)(44, 172, 62, 190)(45, 173, 63, 191)(46, 174, 61, 189)(47, 175, 66, 194)(49, 177, 68, 196)(51, 179, 70, 198)(55, 183, 76, 204)(56, 184, 77, 205)(57, 185, 78, 206)(58, 186, 79, 207)(59, 187, 80, 208)(60, 188, 81, 209)(64, 192, 75, 203)(65, 193, 87, 215)(67, 195, 89, 217)(69, 197, 91, 219)(71, 199, 93, 221)(72, 200, 94, 222)(73, 201, 95, 223)(74, 202, 96, 224)(82, 210, 102, 230)(83, 211, 103, 231)(84, 212, 100, 228)(85, 213, 101, 229)(86, 214, 106, 234)(88, 216, 108, 236)(90, 218, 110, 238)(92, 220, 112, 240)(97, 225, 114, 242)(98, 226, 115, 243)(99, 227, 116, 244)(104, 232, 113, 241)(105, 233, 122, 250)(107, 235, 124, 252)(109, 237, 126, 254)(111, 239, 128, 256)(117, 245, 125, 253)(118, 246, 123, 251)(119, 247, 121, 249)(120, 248, 127, 255) L = (1, 130)(2, 133)(3, 135)(4, 129)(5, 139)(6, 141)(7, 143)(8, 131)(9, 146)(10, 132)(11, 148)(12, 136)(13, 137)(14, 134)(15, 153)(16, 154)(17, 156)(18, 157)(19, 138)(20, 160)(21, 142)(22, 140)(23, 164)(24, 166)(25, 167)(26, 145)(27, 144)(28, 163)(29, 172)(30, 165)(31, 147)(32, 175)(33, 150)(34, 149)(35, 179)(36, 152)(37, 151)(38, 178)(39, 183)(40, 155)(41, 185)(42, 187)(43, 186)(44, 189)(45, 158)(46, 159)(47, 193)(48, 162)(49, 161)(50, 197)(51, 196)(52, 199)(53, 201)(54, 200)(55, 203)(56, 168)(57, 170)(58, 169)(59, 205)(60, 171)(61, 210)(62, 173)(63, 212)(64, 174)(65, 214)(66, 177)(67, 176)(68, 218)(69, 217)(70, 188)(71, 181)(72, 180)(73, 191)(74, 182)(75, 225)(76, 184)(77, 227)(78, 221)(79, 222)(80, 223)(81, 224)(82, 229)(83, 190)(84, 231)(85, 192)(86, 233)(87, 195)(88, 194)(89, 237)(90, 236)(91, 202)(92, 198)(93, 207)(94, 209)(95, 206)(96, 240)(97, 241)(98, 204)(99, 243)(100, 208)(101, 245)(102, 211)(103, 247)(104, 213)(105, 249)(106, 216)(107, 215)(108, 253)(109, 252)(110, 220)(111, 219)(112, 256)(113, 254)(114, 226)(115, 250)(116, 228)(117, 255)(118, 230)(119, 251)(120, 232)(121, 244)(122, 235)(123, 234)(124, 242)(125, 246)(126, 239)(127, 238)(128, 248) local type(s) :: { ( 8, 32, 8, 32 ) } Outer automorphisms :: reflexible Dual of E23.1108 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 64 e = 128 f = 20 degree seq :: [ 4^64 ] E23.1117 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 32}) Quotient :: dipole Aut^+ = $<128, 149>$ (small group id <128, 149>) Aut = $<256, 6657>$ (small group id <256, 6657>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^-1 * Y1 * Y2^2 * Y1 * Y2^-1, (Y2^-1 * R * Y2^-1)^2, Y2^8, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1, (Y3 * Y2^-1)^32 ] Map:: R = (1, 129, 2, 130)(3, 131, 7, 135)(4, 132, 9, 137)(5, 133, 11, 139)(6, 134, 13, 141)(8, 136, 12, 140)(10, 138, 14, 142)(15, 143, 25, 153)(16, 144, 27, 155)(17, 145, 26, 154)(18, 146, 29, 157)(19, 147, 30, 158)(20, 148, 31, 159)(21, 149, 33, 161)(22, 150, 32, 160)(23, 151, 35, 163)(24, 152, 36, 164)(28, 156, 34, 162)(37, 165, 47, 175)(38, 166, 49, 177)(39, 167, 48, 176)(40, 168, 50, 178)(41, 169, 51, 179)(42, 170, 52, 180)(43, 171, 54, 182)(44, 172, 53, 181)(45, 173, 55, 183)(46, 174, 56, 184)(57, 185, 65, 193)(58, 186, 66, 194)(59, 187, 67, 195)(60, 188, 68, 196)(61, 189, 69, 197)(62, 190, 70, 198)(63, 191, 71, 199)(64, 192, 72, 200)(73, 201, 81, 209)(74, 202, 82, 210)(75, 203, 83, 211)(76, 204, 84, 212)(77, 205, 85, 213)(78, 206, 86, 214)(79, 207, 87, 215)(80, 208, 88, 216)(89, 217, 97, 225)(90, 218, 98, 226)(91, 219, 99, 227)(92, 220, 100, 228)(93, 221, 101, 229)(94, 222, 102, 230)(95, 223, 103, 231)(96, 224, 104, 232)(105, 233, 113, 241)(106, 234, 114, 242)(107, 235, 115, 243)(108, 236, 116, 244)(109, 237, 117, 245)(110, 238, 118, 246)(111, 239, 119, 247)(112, 240, 120, 248)(121, 249, 127, 255)(122, 250, 128, 256)(123, 251, 125, 253)(124, 252, 126, 254)(257, 385, 259, 387, 264, 392, 273, 401, 284, 412, 275, 403, 266, 394, 260, 388)(258, 386, 261, 389, 268, 396, 278, 406, 290, 418, 280, 408, 270, 398, 262, 390)(263, 391, 271, 399, 282, 410, 295, 423, 286, 414, 274, 402, 265, 393, 272, 400)(267, 395, 276, 404, 288, 416, 300, 428, 292, 420, 279, 407, 269, 397, 277, 405)(281, 409, 293, 421, 304, 432, 297, 425, 285, 413, 296, 424, 283, 411, 294, 422)(287, 415, 298, 426, 309, 437, 302, 430, 291, 419, 301, 429, 289, 417, 299, 427)(303, 431, 313, 441, 307, 435, 316, 444, 306, 434, 315, 443, 305, 433, 314, 442)(308, 436, 317, 445, 312, 440, 320, 448, 311, 439, 319, 447, 310, 438, 318, 446)(321, 449, 329, 457, 324, 452, 332, 460, 323, 451, 331, 459, 322, 450, 330, 458)(325, 453, 333, 461, 328, 456, 336, 464, 327, 455, 335, 463, 326, 454, 334, 462)(337, 465, 345, 473, 340, 468, 348, 476, 339, 467, 347, 475, 338, 466, 346, 474)(341, 469, 349, 477, 344, 472, 352, 480, 343, 471, 351, 479, 342, 470, 350, 478)(353, 481, 361, 489, 356, 484, 364, 492, 355, 483, 363, 491, 354, 482, 362, 490)(357, 485, 365, 493, 360, 488, 368, 496, 359, 487, 367, 495, 358, 486, 366, 494)(369, 497, 377, 505, 372, 500, 380, 508, 371, 499, 379, 507, 370, 498, 378, 506)(373, 501, 381, 509, 376, 504, 384, 512, 375, 503, 383, 511, 374, 502, 382, 510) L = (1, 258)(2, 257)(3, 263)(4, 265)(5, 267)(6, 269)(7, 259)(8, 268)(9, 260)(10, 270)(11, 261)(12, 264)(13, 262)(14, 266)(15, 281)(16, 283)(17, 282)(18, 285)(19, 286)(20, 287)(21, 289)(22, 288)(23, 291)(24, 292)(25, 271)(26, 273)(27, 272)(28, 290)(29, 274)(30, 275)(31, 276)(32, 278)(33, 277)(34, 284)(35, 279)(36, 280)(37, 303)(38, 305)(39, 304)(40, 306)(41, 307)(42, 308)(43, 310)(44, 309)(45, 311)(46, 312)(47, 293)(48, 295)(49, 294)(50, 296)(51, 297)(52, 298)(53, 300)(54, 299)(55, 301)(56, 302)(57, 321)(58, 322)(59, 323)(60, 324)(61, 325)(62, 326)(63, 327)(64, 328)(65, 313)(66, 314)(67, 315)(68, 316)(69, 317)(70, 318)(71, 319)(72, 320)(73, 337)(74, 338)(75, 339)(76, 340)(77, 341)(78, 342)(79, 343)(80, 344)(81, 329)(82, 330)(83, 331)(84, 332)(85, 333)(86, 334)(87, 335)(88, 336)(89, 353)(90, 354)(91, 355)(92, 356)(93, 357)(94, 358)(95, 359)(96, 360)(97, 345)(98, 346)(99, 347)(100, 348)(101, 349)(102, 350)(103, 351)(104, 352)(105, 369)(106, 370)(107, 371)(108, 372)(109, 373)(110, 374)(111, 375)(112, 376)(113, 361)(114, 362)(115, 363)(116, 364)(117, 365)(118, 366)(119, 367)(120, 368)(121, 383)(122, 384)(123, 381)(124, 382)(125, 379)(126, 380)(127, 377)(128, 378)(129, 385)(130, 386)(131, 387)(132, 388)(133, 389)(134, 390)(135, 391)(136, 392)(137, 393)(138, 394)(139, 395)(140, 396)(141, 397)(142, 398)(143, 399)(144, 400)(145, 401)(146, 402)(147, 403)(148, 404)(149, 405)(150, 406)(151, 407)(152, 408)(153, 409)(154, 410)(155, 411)(156, 412)(157, 413)(158, 414)(159, 415)(160, 416)(161, 417)(162, 418)(163, 419)(164, 420)(165, 421)(166, 422)(167, 423)(168, 424)(169, 425)(170, 426)(171, 427)(172, 428)(173, 429)(174, 430)(175, 431)(176, 432)(177, 433)(178, 434)(179, 435)(180, 436)(181, 437)(182, 438)(183, 439)(184, 440)(185, 441)(186, 442)(187, 443)(188, 444)(189, 445)(190, 446)(191, 447)(192, 448)(193, 449)(194, 450)(195, 451)(196, 452)(197, 453)(198, 454)(199, 455)(200, 456)(201, 457)(202, 458)(203, 459)(204, 460)(205, 461)(206, 462)(207, 463)(208, 464)(209, 465)(210, 466)(211, 467)(212, 468)(213, 469)(214, 470)(215, 471)(216, 472)(217, 473)(218, 474)(219, 475)(220, 476)(221, 477)(222, 478)(223, 479)(224, 480)(225, 481)(226, 482)(227, 483)(228, 484)(229, 485)(230, 486)(231, 487)(232, 488)(233, 489)(234, 490)(235, 491)(236, 492)(237, 493)(238, 494)(239, 495)(240, 496)(241, 497)(242, 498)(243, 499)(244, 500)(245, 501)(246, 502)(247, 503)(248, 504)(249, 505)(250, 506)(251, 507)(252, 508)(253, 509)(254, 510)(255, 511)(256, 512) local type(s) :: { ( 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 E23.1123 Graph:: bipartite v = 80 e = 256 f = 132 degree seq :: [ 4^64, 16^16 ] E23.1118 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 32}) Quotient :: dipole Aut^+ = $<128, 151>$ (small group id <128, 151>) Aut = $<256, 6657>$ (small group id <256, 6657>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y1 * Y2^-2)^2, Y2^-1 * R * Y2^2 * R * Y2^-1, Y2^8, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1, (Y3 * Y2^-1)^32 ] Map:: R = (1, 129, 2, 130)(3, 131, 7, 135)(4, 132, 9, 137)(5, 133, 11, 139)(6, 134, 13, 141)(8, 136, 14, 142)(10, 138, 12, 140)(15, 143, 25, 153)(16, 144, 26, 154)(17, 145, 27, 155)(18, 146, 29, 157)(19, 147, 30, 158)(20, 148, 31, 159)(21, 149, 32, 160)(22, 150, 33, 161)(23, 151, 35, 163)(24, 152, 36, 164)(28, 156, 34, 162)(37, 165, 47, 175)(38, 166, 48, 176)(39, 167, 49, 177)(40, 168, 50, 178)(41, 169, 51, 179)(42, 170, 52, 180)(43, 171, 53, 181)(44, 172, 54, 182)(45, 173, 55, 183)(46, 174, 56, 184)(57, 185, 65, 193)(58, 186, 66, 194)(59, 187, 67, 195)(60, 188, 68, 196)(61, 189, 69, 197)(62, 190, 70, 198)(63, 191, 71, 199)(64, 192, 72, 200)(73, 201, 81, 209)(74, 202, 82, 210)(75, 203, 83, 211)(76, 204, 84, 212)(77, 205, 85, 213)(78, 206, 86, 214)(79, 207, 87, 215)(80, 208, 88, 216)(89, 217, 97, 225)(90, 218, 98, 226)(91, 219, 99, 227)(92, 220, 100, 228)(93, 221, 101, 229)(94, 222, 102, 230)(95, 223, 103, 231)(96, 224, 104, 232)(105, 233, 113, 241)(106, 234, 114, 242)(107, 235, 115, 243)(108, 236, 116, 244)(109, 237, 117, 245)(110, 238, 118, 246)(111, 239, 119, 247)(112, 240, 120, 248)(121, 249, 128, 256)(122, 250, 126, 254)(123, 251, 127, 255)(124, 252, 125, 253)(257, 385, 259, 387, 264, 392, 273, 401, 284, 412, 275, 403, 266, 394, 260, 388)(258, 386, 261, 389, 268, 396, 278, 406, 290, 418, 280, 408, 270, 398, 262, 390)(263, 391, 271, 399, 265, 393, 274, 402, 286, 414, 296, 424, 283, 411, 272, 400)(267, 395, 276, 404, 269, 397, 279, 407, 292, 420, 301, 429, 289, 417, 277, 405)(281, 409, 293, 421, 282, 410, 295, 423, 306, 434, 297, 425, 285, 413, 294, 422)(287, 415, 298, 426, 288, 416, 300, 428, 311, 439, 302, 430, 291, 419, 299, 427)(303, 431, 313, 441, 304, 432, 315, 443, 307, 435, 316, 444, 305, 433, 314, 442)(308, 436, 317, 445, 309, 437, 319, 447, 312, 440, 320, 448, 310, 438, 318, 446)(321, 449, 329, 457, 322, 450, 331, 459, 324, 452, 332, 460, 323, 451, 330, 458)(325, 453, 333, 461, 326, 454, 335, 463, 328, 456, 336, 464, 327, 455, 334, 462)(337, 465, 345, 473, 338, 466, 347, 475, 340, 468, 348, 476, 339, 467, 346, 474)(341, 469, 349, 477, 342, 470, 351, 479, 344, 472, 352, 480, 343, 471, 350, 478)(353, 481, 361, 489, 354, 482, 363, 491, 356, 484, 364, 492, 355, 483, 362, 490)(357, 485, 365, 493, 358, 486, 367, 495, 360, 488, 368, 496, 359, 487, 366, 494)(369, 497, 377, 505, 370, 498, 379, 507, 372, 500, 380, 508, 371, 499, 378, 506)(373, 501, 381, 509, 374, 502, 383, 511, 376, 504, 384, 512, 375, 503, 382, 510) L = (1, 258)(2, 257)(3, 263)(4, 265)(5, 267)(6, 269)(7, 259)(8, 270)(9, 260)(10, 268)(11, 261)(12, 266)(13, 262)(14, 264)(15, 281)(16, 282)(17, 283)(18, 285)(19, 286)(20, 287)(21, 288)(22, 289)(23, 291)(24, 292)(25, 271)(26, 272)(27, 273)(28, 290)(29, 274)(30, 275)(31, 276)(32, 277)(33, 278)(34, 284)(35, 279)(36, 280)(37, 303)(38, 304)(39, 305)(40, 306)(41, 307)(42, 308)(43, 309)(44, 310)(45, 311)(46, 312)(47, 293)(48, 294)(49, 295)(50, 296)(51, 297)(52, 298)(53, 299)(54, 300)(55, 301)(56, 302)(57, 321)(58, 322)(59, 323)(60, 324)(61, 325)(62, 326)(63, 327)(64, 328)(65, 313)(66, 314)(67, 315)(68, 316)(69, 317)(70, 318)(71, 319)(72, 320)(73, 337)(74, 338)(75, 339)(76, 340)(77, 341)(78, 342)(79, 343)(80, 344)(81, 329)(82, 330)(83, 331)(84, 332)(85, 333)(86, 334)(87, 335)(88, 336)(89, 353)(90, 354)(91, 355)(92, 356)(93, 357)(94, 358)(95, 359)(96, 360)(97, 345)(98, 346)(99, 347)(100, 348)(101, 349)(102, 350)(103, 351)(104, 352)(105, 369)(106, 370)(107, 371)(108, 372)(109, 373)(110, 374)(111, 375)(112, 376)(113, 361)(114, 362)(115, 363)(116, 364)(117, 365)(118, 366)(119, 367)(120, 368)(121, 384)(122, 382)(123, 383)(124, 381)(125, 380)(126, 378)(127, 379)(128, 377)(129, 385)(130, 386)(131, 387)(132, 388)(133, 389)(134, 390)(135, 391)(136, 392)(137, 393)(138, 394)(139, 395)(140, 396)(141, 397)(142, 398)(143, 399)(144, 400)(145, 401)(146, 402)(147, 403)(148, 404)(149, 405)(150, 406)(151, 407)(152, 408)(153, 409)(154, 410)(155, 411)(156, 412)(157, 413)(158, 414)(159, 415)(160, 416)(161, 417)(162, 418)(163, 419)(164, 420)(165, 421)(166, 422)(167, 423)(168, 424)(169, 425)(170, 426)(171, 427)(172, 428)(173, 429)(174, 430)(175, 431)(176, 432)(177, 433)(178, 434)(179, 435)(180, 436)(181, 437)(182, 438)(183, 439)(184, 440)(185, 441)(186, 442)(187, 443)(188, 444)(189, 445)(190, 446)(191, 447)(192, 448)(193, 449)(194, 450)(195, 451)(196, 452)(197, 453)(198, 454)(199, 455)(200, 456)(201, 457)(202, 458)(203, 459)(204, 460)(205, 461)(206, 462)(207, 463)(208, 464)(209, 465)(210, 466)(211, 467)(212, 468)(213, 469)(214, 470)(215, 471)(216, 472)(217, 473)(218, 474)(219, 475)(220, 476)(221, 477)(222, 478)(223, 479)(224, 480)(225, 481)(226, 482)(227, 483)(228, 484)(229, 485)(230, 486)(231, 487)(232, 488)(233, 489)(234, 490)(235, 491)(236, 492)(237, 493)(238, 494)(239, 495)(240, 496)(241, 497)(242, 498)(243, 499)(244, 500)(245, 501)(246, 502)(247, 503)(248, 504)(249, 505)(250, 506)(251, 507)(252, 508)(253, 509)(254, 510)(255, 511)(256, 512) local type(s) :: { ( 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 E23.1124 Graph:: bipartite v = 80 e = 256 f = 132 degree seq :: [ 4^64, 16^16 ] E23.1119 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 32}) Quotient :: dipole Aut^+ = $<128, 149>$ (small group id <128, 149>) Aut = $<256, 6657>$ (small group id <256, 6657>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (Y2 * Y1)^2, (Y3^-1 * Y1^-1)^2, (R * Y3)^2, (R * Y1)^2, Y2^-1 * Y1^-2 * Y2 * Y1^2, Y1^-1 * Y2^-1 * Y1^2 * Y2 * Y1^-1, Y1^-1 * Y2^2 * Y1^-3 * Y2^2, Y1^8, Y2 * Y1^-1 * Y2^-15 * Y1^-1 ] Map:: R = (1, 129, 2, 130, 6, 134, 16, 144, 34, 162, 27, 155, 13, 141, 4, 132)(3, 131, 9, 137, 17, 145, 8, 136, 21, 149, 35, 163, 28, 156, 11, 139)(5, 133, 14, 142, 18, 146, 37, 165, 30, 158, 12, 140, 20, 148, 7, 135)(10, 138, 24, 152, 36, 164, 23, 151, 42, 170, 22, 150, 43, 171, 26, 154)(15, 143, 32, 160, 38, 166, 29, 157, 41, 169, 19, 147, 39, 167, 31, 159)(25, 153, 47, 175, 53, 181, 46, 174, 58, 186, 45, 173, 59, 187, 44, 172)(33, 161, 49, 177, 54, 182, 40, 168, 56, 184, 50, 178, 55, 183, 51, 179)(48, 176, 60, 188, 69, 197, 63, 191, 74, 202, 62, 190, 75, 203, 61, 189)(52, 180, 57, 185, 70, 198, 66, 194, 72, 200, 67, 195, 71, 199, 65, 193)(64, 192, 77, 205, 85, 213, 76, 204, 90, 218, 79, 207, 91, 219, 78, 206)(68, 196, 82, 210, 86, 214, 83, 211, 88, 216, 81, 209, 87, 215, 73, 201)(80, 208, 94, 222, 101, 229, 93, 221, 106, 234, 92, 220, 107, 235, 95, 223)(84, 212, 99, 227, 102, 230, 97, 225, 104, 232, 89, 217, 103, 231, 98, 226)(96, 224, 111, 239, 117, 245, 110, 238, 122, 250, 109, 237, 123, 251, 108, 236)(100, 228, 113, 241, 118, 246, 105, 233, 120, 248, 114, 242, 119, 247, 115, 243)(112, 240, 124, 252, 127, 255, 126, 254, 116, 244, 121, 249, 128, 256, 125, 253)(257, 385, 259, 387, 266, 394, 281, 409, 304, 432, 320, 448, 336, 464, 352, 480, 368, 496, 376, 504, 360, 488, 344, 472, 328, 456, 312, 440, 297, 425, 286, 414, 290, 418, 277, 405, 298, 426, 314, 442, 330, 458, 346, 474, 362, 490, 378, 506, 372, 500, 356, 484, 340, 468, 324, 452, 308, 436, 289, 417, 271, 399, 261, 389)(258, 386, 263, 391, 275, 403, 296, 424, 313, 441, 329, 457, 345, 473, 361, 489, 377, 505, 366, 494, 350, 478, 334, 462, 318, 446, 302, 430, 280, 408, 267, 395, 283, 411, 293, 421, 288, 416, 307, 435, 323, 451, 339, 467, 355, 483, 371, 499, 380, 508, 364, 492, 348, 476, 332, 460, 316, 444, 300, 428, 278, 406, 264, 392)(260, 388, 268, 396, 285, 413, 305, 433, 321, 449, 337, 465, 353, 481, 369, 497, 382, 510, 367, 495, 351, 479, 335, 463, 319, 447, 303, 431, 282, 410, 291, 419, 272, 400, 270, 398, 287, 415, 306, 434, 322, 450, 338, 466, 354, 482, 370, 498, 381, 509, 365, 493, 349, 477, 333, 461, 317, 445, 301, 429, 279, 407, 265, 393)(262, 390, 273, 401, 292, 420, 309, 437, 325, 453, 341, 469, 357, 485, 373, 501, 383, 511, 375, 503, 359, 487, 343, 471, 327, 455, 311, 439, 295, 423, 276, 404, 269, 397, 284, 412, 299, 427, 315, 443, 331, 459, 347, 475, 363, 491, 379, 507, 384, 512, 374, 502, 358, 486, 342, 470, 326, 454, 310, 438, 294, 422, 274, 402) L = (1, 259)(2, 263)(3, 266)(4, 268)(5, 257)(6, 273)(7, 275)(8, 258)(9, 260)(10, 281)(11, 283)(12, 285)(13, 284)(14, 287)(15, 261)(16, 270)(17, 292)(18, 262)(19, 296)(20, 269)(21, 298)(22, 264)(23, 265)(24, 267)(25, 304)(26, 291)(27, 293)(28, 299)(29, 305)(30, 290)(31, 306)(32, 307)(33, 271)(34, 277)(35, 272)(36, 309)(37, 288)(38, 274)(39, 276)(40, 313)(41, 286)(42, 314)(43, 315)(44, 278)(45, 279)(46, 280)(47, 282)(48, 320)(49, 321)(50, 322)(51, 323)(52, 289)(53, 325)(54, 294)(55, 295)(56, 297)(57, 329)(58, 330)(59, 331)(60, 300)(61, 301)(62, 302)(63, 303)(64, 336)(65, 337)(66, 338)(67, 339)(68, 308)(69, 341)(70, 310)(71, 311)(72, 312)(73, 345)(74, 346)(75, 347)(76, 316)(77, 317)(78, 318)(79, 319)(80, 352)(81, 353)(82, 354)(83, 355)(84, 324)(85, 357)(86, 326)(87, 327)(88, 328)(89, 361)(90, 362)(91, 363)(92, 332)(93, 333)(94, 334)(95, 335)(96, 368)(97, 369)(98, 370)(99, 371)(100, 340)(101, 373)(102, 342)(103, 343)(104, 344)(105, 377)(106, 378)(107, 379)(108, 348)(109, 349)(110, 350)(111, 351)(112, 376)(113, 382)(114, 381)(115, 380)(116, 356)(117, 383)(118, 358)(119, 359)(120, 360)(121, 366)(122, 372)(123, 384)(124, 364)(125, 365)(126, 367)(127, 375)(128, 374)(129, 385)(130, 386)(131, 387)(132, 388)(133, 389)(134, 390)(135, 391)(136, 392)(137, 393)(138, 394)(139, 395)(140, 396)(141, 397)(142, 398)(143, 399)(144, 400)(145, 401)(146, 402)(147, 403)(148, 404)(149, 405)(150, 406)(151, 407)(152, 408)(153, 409)(154, 410)(155, 411)(156, 412)(157, 413)(158, 414)(159, 415)(160, 416)(161, 417)(162, 418)(163, 419)(164, 420)(165, 421)(166, 422)(167, 423)(168, 424)(169, 425)(170, 426)(171, 427)(172, 428)(173, 429)(174, 430)(175, 431)(176, 432)(177, 433)(178, 434)(179, 435)(180, 436)(181, 437)(182, 438)(183, 439)(184, 440)(185, 441)(186, 442)(187, 443)(188, 444)(189, 445)(190, 446)(191, 447)(192, 448)(193, 449)(194, 450)(195, 451)(196, 452)(197, 453)(198, 454)(199, 455)(200, 456)(201, 457)(202, 458)(203, 459)(204, 460)(205, 461)(206, 462)(207, 463)(208, 464)(209, 465)(210, 466)(211, 467)(212, 468)(213, 469)(214, 470)(215, 471)(216, 472)(217, 473)(218, 474)(219, 475)(220, 476)(221, 477)(222, 478)(223, 479)(224, 480)(225, 481)(226, 482)(227, 483)(228, 484)(229, 485)(230, 486)(231, 487)(232, 488)(233, 489)(234, 490)(235, 491)(236, 492)(237, 493)(238, 494)(239, 495)(240, 496)(241, 497)(242, 498)(243, 499)(244, 500)(245, 501)(246, 502)(247, 503)(248, 504)(249, 505)(250, 506)(251, 507)(252, 508)(253, 509)(254, 510)(255, 511)(256, 512) 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 E23.1121 Graph:: bipartite v = 20 e = 256 f = 192 degree seq :: [ 16^16, 64^4 ] E23.1120 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 32}) Quotient :: dipole Aut^+ = $<128, 151>$ (small group id <128, 151>) Aut = $<256, 6657>$ (small group id <256, 6657>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y3)^2, (Y2 * Y1^-1)^2, (R * Y1)^2, (Y2^-1 * Y1^-1)^2, (Y3^-1 * Y1^-1)^2, Y1^8, Y1^-1 * Y2^-1 * Y1 * Y2^15 * Y1^-2 ] Map:: R = (1, 129, 2, 130, 6, 134, 14, 142, 26, 154, 24, 152, 12, 140, 4, 132)(3, 131, 9, 137, 19, 147, 33, 161, 41, 169, 28, 156, 15, 143, 8, 136)(5, 133, 11, 139, 22, 150, 37, 165, 42, 170, 27, 155, 16, 144, 7, 135)(10, 138, 18, 146, 29, 157, 44, 172, 57, 185, 49, 177, 34, 162, 20, 148)(13, 141, 17, 145, 30, 158, 43, 171, 58, 186, 53, 181, 38, 166, 23, 151)(21, 149, 35, 163, 50, 178, 65, 193, 73, 201, 60, 188, 45, 173, 32, 160)(25, 153, 39, 167, 54, 182, 69, 197, 74, 202, 59, 187, 46, 174, 31, 159)(36, 164, 48, 176, 61, 189, 76, 204, 89, 217, 81, 209, 66, 194, 51, 179)(40, 168, 47, 175, 62, 190, 75, 203, 90, 218, 85, 213, 70, 198, 55, 183)(52, 180, 67, 195, 82, 210, 97, 225, 105, 233, 92, 220, 77, 205, 64, 192)(56, 184, 71, 199, 86, 214, 101, 229, 106, 234, 91, 219, 78, 206, 63, 191)(68, 196, 80, 208, 93, 221, 108, 236, 121, 249, 113, 241, 98, 226, 83, 211)(72, 200, 79, 207, 94, 222, 107, 235, 122, 250, 117, 245, 102, 230, 87, 215)(84, 212, 99, 227, 114, 242, 127, 255, 120, 248, 124, 252, 109, 237, 96, 224)(88, 216, 103, 231, 118, 246, 128, 256, 116, 244, 123, 251, 110, 238, 95, 223)(100, 228, 112, 240, 125, 253, 119, 247, 104, 232, 111, 239, 126, 254, 115, 243)(257, 385, 259, 387, 266, 394, 277, 405, 292, 420, 308, 436, 324, 452, 340, 468, 356, 484, 372, 500, 378, 506, 362, 490, 346, 474, 330, 458, 314, 442, 298, 426, 282, 410, 297, 425, 313, 441, 329, 457, 345, 473, 361, 489, 377, 505, 376, 504, 360, 488, 344, 472, 328, 456, 312, 440, 296, 424, 281, 409, 269, 397, 261, 389)(258, 386, 263, 391, 273, 401, 287, 415, 303, 431, 319, 447, 335, 463, 351, 479, 367, 495, 383, 511, 369, 497, 353, 481, 337, 465, 321, 449, 305, 433, 289, 417, 280, 408, 293, 421, 309, 437, 325, 453, 341, 469, 357, 485, 373, 501, 384, 512, 368, 496, 352, 480, 336, 464, 320, 448, 304, 432, 288, 416, 274, 402, 264, 392)(260, 388, 267, 395, 279, 407, 295, 423, 311, 439, 327, 455, 343, 471, 359, 487, 375, 503, 380, 508, 364, 492, 348, 476, 332, 460, 316, 444, 300, 428, 284, 412, 270, 398, 283, 411, 299, 427, 315, 443, 331, 459, 347, 475, 363, 491, 379, 507, 371, 499, 355, 483, 339, 467, 323, 451, 307, 435, 291, 419, 276, 404, 265, 393)(262, 390, 271, 399, 285, 413, 301, 429, 317, 445, 333, 461, 349, 477, 365, 493, 381, 509, 374, 502, 358, 486, 342, 470, 326, 454, 310, 438, 294, 422, 278, 406, 268, 396, 275, 403, 290, 418, 306, 434, 322, 450, 338, 466, 354, 482, 370, 498, 382, 510, 366, 494, 350, 478, 334, 462, 318, 446, 302, 430, 286, 414, 272, 400) L = (1, 259)(2, 263)(3, 266)(4, 267)(5, 257)(6, 271)(7, 273)(8, 258)(9, 260)(10, 277)(11, 279)(12, 275)(13, 261)(14, 283)(15, 285)(16, 262)(17, 287)(18, 264)(19, 290)(20, 265)(21, 292)(22, 268)(23, 295)(24, 293)(25, 269)(26, 297)(27, 299)(28, 270)(29, 301)(30, 272)(31, 303)(32, 274)(33, 280)(34, 306)(35, 276)(36, 308)(37, 309)(38, 278)(39, 311)(40, 281)(41, 313)(42, 282)(43, 315)(44, 284)(45, 317)(46, 286)(47, 319)(48, 288)(49, 289)(50, 322)(51, 291)(52, 324)(53, 325)(54, 294)(55, 327)(56, 296)(57, 329)(58, 298)(59, 331)(60, 300)(61, 333)(62, 302)(63, 335)(64, 304)(65, 305)(66, 338)(67, 307)(68, 340)(69, 341)(70, 310)(71, 343)(72, 312)(73, 345)(74, 314)(75, 347)(76, 316)(77, 349)(78, 318)(79, 351)(80, 320)(81, 321)(82, 354)(83, 323)(84, 356)(85, 357)(86, 326)(87, 359)(88, 328)(89, 361)(90, 330)(91, 363)(92, 332)(93, 365)(94, 334)(95, 367)(96, 336)(97, 337)(98, 370)(99, 339)(100, 372)(101, 373)(102, 342)(103, 375)(104, 344)(105, 377)(106, 346)(107, 379)(108, 348)(109, 381)(110, 350)(111, 383)(112, 352)(113, 353)(114, 382)(115, 355)(116, 378)(117, 384)(118, 358)(119, 380)(120, 360)(121, 376)(122, 362)(123, 371)(124, 364)(125, 374)(126, 366)(127, 369)(128, 368)(129, 385)(130, 386)(131, 387)(132, 388)(133, 389)(134, 390)(135, 391)(136, 392)(137, 393)(138, 394)(139, 395)(140, 396)(141, 397)(142, 398)(143, 399)(144, 400)(145, 401)(146, 402)(147, 403)(148, 404)(149, 405)(150, 406)(151, 407)(152, 408)(153, 409)(154, 410)(155, 411)(156, 412)(157, 413)(158, 414)(159, 415)(160, 416)(161, 417)(162, 418)(163, 419)(164, 420)(165, 421)(166, 422)(167, 423)(168, 424)(169, 425)(170, 426)(171, 427)(172, 428)(173, 429)(174, 430)(175, 431)(176, 432)(177, 433)(178, 434)(179, 435)(180, 436)(181, 437)(182, 438)(183, 439)(184, 440)(185, 441)(186, 442)(187, 443)(188, 444)(189, 445)(190, 446)(191, 447)(192, 448)(193, 449)(194, 450)(195, 451)(196, 452)(197, 453)(198, 454)(199, 455)(200, 456)(201, 457)(202, 458)(203, 459)(204, 460)(205, 461)(206, 462)(207, 463)(208, 464)(209, 465)(210, 466)(211, 467)(212, 468)(213, 469)(214, 470)(215, 471)(216, 472)(217, 473)(218, 474)(219, 475)(220, 476)(221, 477)(222, 478)(223, 479)(224, 480)(225, 481)(226, 482)(227, 483)(228, 484)(229, 485)(230, 486)(231, 487)(232, 488)(233, 489)(234, 490)(235, 491)(236, 492)(237, 493)(238, 494)(239, 495)(240, 496)(241, 497)(242, 498)(243, 499)(244, 500)(245, 501)(246, 502)(247, 503)(248, 504)(249, 505)(250, 506)(251, 507)(252, 508)(253, 509)(254, 510)(255, 511)(256, 512) 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 E23.1122 Graph:: bipartite v = 20 e = 256 f = 192 degree seq :: [ 16^16, 64^4 ] E23.1121 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 32}) Quotient :: dipole Aut^+ = $<128, 149>$ (small group id <128, 149>) Aut = $<256, 6657>$ (small group id <256, 6657>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3^-1 * Y2, (Y3^4 * Y2)^2, (Y3^-2 * Y2)^4, Y3^-13 * Y2 * Y3^2 * Y2 * Y3^-1, (Y3^-1 * Y1^-1)^32 ] Map:: polytopal R = (1, 129)(2, 130)(3, 131)(4, 132)(5, 133)(6, 134)(7, 135)(8, 136)(9, 137)(10, 138)(11, 139)(12, 140)(13, 141)(14, 142)(15, 143)(16, 144)(17, 145)(18, 146)(19, 147)(20, 148)(21, 149)(22, 150)(23, 151)(24, 152)(25, 153)(26, 154)(27, 155)(28, 156)(29, 157)(30, 158)(31, 159)(32, 160)(33, 161)(34, 162)(35, 163)(36, 164)(37, 165)(38, 166)(39, 167)(40, 168)(41, 169)(42, 170)(43, 171)(44, 172)(45, 173)(46, 174)(47, 175)(48, 176)(49, 177)(50, 178)(51, 179)(52, 180)(53, 181)(54, 182)(55, 183)(56, 184)(57, 185)(58, 186)(59, 187)(60, 188)(61, 189)(62, 190)(63, 191)(64, 192)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)(257, 385, 258, 386)(259, 387, 263, 391)(260, 388, 265, 393)(261, 389, 267, 395)(262, 390, 269, 397)(264, 392, 273, 401)(266, 394, 277, 405)(268, 396, 281, 409)(270, 398, 285, 413)(271, 399, 279, 407)(272, 400, 283, 411)(274, 402, 291, 419)(275, 403, 280, 408)(276, 404, 284, 412)(278, 406, 297, 425)(282, 410, 303, 431)(286, 414, 309, 437)(287, 415, 301, 429)(288, 416, 307, 435)(289, 417, 299, 427)(290, 418, 305, 433)(292, 420, 310, 438)(293, 421, 302, 430)(294, 422, 308, 436)(295, 423, 300, 428)(296, 424, 306, 434)(298, 426, 304, 432)(311, 439, 326, 454)(312, 440, 331, 459)(313, 441, 324, 452)(314, 442, 330, 458)(315, 443, 322, 450)(316, 444, 329, 457)(317, 445, 333, 461)(318, 446, 327, 455)(319, 447, 325, 453)(320, 448, 323, 451)(321, 449, 337, 465)(328, 456, 341, 469)(332, 460, 345, 473)(334, 462, 347, 475)(335, 463, 346, 474)(336, 464, 350, 478)(338, 466, 343, 471)(339, 467, 342, 470)(340, 468, 354, 482)(344, 472, 358, 486)(348, 476, 362, 490)(349, 477, 361, 489)(351, 479, 363, 491)(352, 480, 367, 495)(353, 481, 357, 485)(355, 483, 359, 487)(356, 484, 371, 499)(360, 488, 375, 503)(364, 492, 379, 507)(365, 493, 378, 506)(366, 494, 377, 505)(368, 496, 380, 508)(369, 497, 374, 502)(370, 498, 373, 501)(372, 500, 376, 504)(381, 509, 384, 512)(382, 510, 383, 511) L = (1, 259)(2, 261)(3, 264)(4, 257)(5, 268)(6, 258)(7, 271)(8, 274)(9, 275)(10, 260)(11, 279)(12, 282)(13, 283)(14, 262)(15, 287)(16, 263)(17, 289)(18, 292)(19, 293)(20, 265)(21, 295)(22, 266)(23, 299)(24, 267)(25, 301)(26, 304)(27, 305)(28, 269)(29, 307)(30, 270)(31, 311)(32, 272)(33, 313)(34, 273)(35, 315)(36, 317)(37, 318)(38, 276)(39, 319)(40, 277)(41, 320)(42, 278)(43, 322)(44, 280)(45, 324)(46, 281)(47, 326)(48, 328)(49, 329)(50, 284)(51, 330)(52, 285)(53, 331)(54, 286)(55, 297)(56, 288)(57, 296)(58, 290)(59, 294)(60, 291)(61, 336)(62, 337)(63, 338)(64, 339)(65, 298)(66, 309)(67, 300)(68, 308)(69, 302)(70, 306)(71, 303)(72, 344)(73, 345)(74, 346)(75, 347)(76, 310)(77, 312)(78, 314)(79, 316)(80, 352)(81, 353)(82, 354)(83, 355)(84, 321)(85, 323)(86, 325)(87, 327)(88, 360)(89, 361)(90, 362)(91, 363)(92, 332)(93, 333)(94, 334)(95, 335)(96, 368)(97, 369)(98, 370)(99, 371)(100, 340)(101, 341)(102, 342)(103, 343)(104, 376)(105, 377)(106, 378)(107, 379)(108, 348)(109, 349)(110, 350)(111, 351)(112, 374)(113, 381)(114, 380)(115, 382)(116, 356)(117, 357)(118, 358)(119, 359)(120, 366)(121, 383)(122, 372)(123, 384)(124, 364)(125, 365)(126, 367)(127, 373)(128, 375)(129, 385)(130, 386)(131, 387)(132, 388)(133, 389)(134, 390)(135, 391)(136, 392)(137, 393)(138, 394)(139, 395)(140, 396)(141, 397)(142, 398)(143, 399)(144, 400)(145, 401)(146, 402)(147, 403)(148, 404)(149, 405)(150, 406)(151, 407)(152, 408)(153, 409)(154, 410)(155, 411)(156, 412)(157, 413)(158, 414)(159, 415)(160, 416)(161, 417)(162, 418)(163, 419)(164, 420)(165, 421)(166, 422)(167, 423)(168, 424)(169, 425)(170, 426)(171, 427)(172, 428)(173, 429)(174, 430)(175, 431)(176, 432)(177, 433)(178, 434)(179, 435)(180, 436)(181, 437)(182, 438)(183, 439)(184, 440)(185, 441)(186, 442)(187, 443)(188, 444)(189, 445)(190, 446)(191, 447)(192, 448)(193, 449)(194, 450)(195, 451)(196, 452)(197, 453)(198, 454)(199, 455)(200, 456)(201, 457)(202, 458)(203, 459)(204, 460)(205, 461)(206, 462)(207, 463)(208, 464)(209, 465)(210, 466)(211, 467)(212, 468)(213, 469)(214, 470)(215, 471)(216, 472)(217, 473)(218, 474)(219, 475)(220, 476)(221, 477)(222, 478)(223, 479)(224, 480)(225, 481)(226, 482)(227, 483)(228, 484)(229, 485)(230, 486)(231, 487)(232, 488)(233, 489)(234, 490)(235, 491)(236, 492)(237, 493)(238, 494)(239, 495)(240, 496)(241, 497)(242, 498)(243, 499)(244, 500)(245, 501)(246, 502)(247, 503)(248, 504)(249, 505)(250, 506)(251, 507)(252, 508)(253, 509)(254, 510)(255, 511)(256, 512) local type(s) :: { ( 16, 64 ), ( 16, 64, 16, 64 ) } Outer automorphisms :: reflexible Dual of E23.1119 Graph:: simple bipartite v = 192 e = 256 f = 20 degree seq :: [ 2^128, 4^64 ] E23.1122 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 32}) Quotient :: dipole Aut^+ = $<128, 151>$ (small group id <128, 151>) Aut = $<256, 6657>$ (small group id <256, 6657>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3^2 * Y2)^2, (Y3^-1 * Y2)^8, Y3^3 * Y2 * Y3^-5 * Y2 * Y3^7 * Y2 * Y3^-1 * Y2, (Y3^-1 * Y1^-1)^32 ] Map:: polytopal R = (1, 129)(2, 130)(3, 131)(4, 132)(5, 133)(6, 134)(7, 135)(8, 136)(9, 137)(10, 138)(11, 139)(12, 140)(13, 141)(14, 142)(15, 143)(16, 144)(17, 145)(18, 146)(19, 147)(20, 148)(21, 149)(22, 150)(23, 151)(24, 152)(25, 153)(26, 154)(27, 155)(28, 156)(29, 157)(30, 158)(31, 159)(32, 160)(33, 161)(34, 162)(35, 163)(36, 164)(37, 165)(38, 166)(39, 167)(40, 168)(41, 169)(42, 170)(43, 171)(44, 172)(45, 173)(46, 174)(47, 175)(48, 176)(49, 177)(50, 178)(51, 179)(52, 180)(53, 181)(54, 182)(55, 183)(56, 184)(57, 185)(58, 186)(59, 187)(60, 188)(61, 189)(62, 190)(63, 191)(64, 192)(65, 193)(66, 194)(67, 195)(68, 196)(69, 197)(70, 198)(71, 199)(72, 200)(73, 201)(74, 202)(75, 203)(76, 204)(77, 205)(78, 206)(79, 207)(80, 208)(81, 209)(82, 210)(83, 211)(84, 212)(85, 213)(86, 214)(87, 215)(88, 216)(89, 217)(90, 218)(91, 219)(92, 220)(93, 221)(94, 222)(95, 223)(96, 224)(97, 225)(98, 226)(99, 227)(100, 228)(101, 229)(102, 230)(103, 231)(104, 232)(105, 233)(106, 234)(107, 235)(108, 236)(109, 237)(110, 238)(111, 239)(112, 240)(113, 241)(114, 242)(115, 243)(116, 244)(117, 245)(118, 246)(119, 247)(120, 248)(121, 249)(122, 250)(123, 251)(124, 252)(125, 253)(126, 254)(127, 255)(128, 256)(257, 385, 258, 386)(259, 387, 263, 391)(260, 388, 265, 393)(261, 389, 267, 395)(262, 390, 269, 397)(264, 392, 270, 398)(266, 394, 268, 396)(271, 399, 281, 409)(272, 400, 282, 410)(273, 401, 283, 411)(274, 402, 285, 413)(275, 403, 286, 414)(276, 404, 288, 416)(277, 405, 289, 417)(278, 406, 290, 418)(279, 407, 292, 420)(280, 408, 293, 421)(284, 412, 294, 422)(287, 415, 291, 419)(295, 423, 311, 439)(296, 424, 312, 440)(297, 425, 313, 441)(298, 426, 314, 442)(299, 427, 315, 443)(300, 428, 317, 445)(301, 429, 318, 446)(302, 430, 319, 447)(303, 431, 321, 449)(304, 432, 322, 450)(305, 433, 323, 451)(306, 434, 324, 452)(307, 435, 325, 453)(308, 436, 327, 455)(309, 437, 328, 456)(310, 438, 329, 457)(316, 444, 330, 458)(320, 448, 326, 454)(331, 459, 342, 470)(332, 460, 344, 472)(333, 461, 343, 471)(334, 462, 349, 477)(335, 463, 353, 481)(336, 464, 354, 482)(337, 465, 355, 483)(338, 466, 345, 473)(339, 467, 357, 485)(340, 468, 358, 486)(341, 469, 359, 487)(346, 474, 361, 489)(347, 475, 362, 490)(348, 476, 363, 491)(350, 478, 365, 493)(351, 479, 366, 494)(352, 480, 367, 495)(356, 484, 368, 496)(360, 488, 364, 492)(369, 497, 381, 509)(370, 498, 380, 508)(371, 499, 379, 507)(372, 500, 378, 506)(373, 501, 377, 505)(374, 502, 384, 512)(375, 503, 383, 511)(376, 504, 382, 510) L = (1, 259)(2, 261)(3, 264)(4, 257)(5, 268)(6, 258)(7, 271)(8, 273)(9, 274)(10, 260)(11, 276)(12, 278)(13, 279)(14, 262)(15, 265)(16, 263)(17, 284)(18, 286)(19, 266)(20, 269)(21, 267)(22, 291)(23, 293)(24, 270)(25, 295)(26, 297)(27, 272)(28, 299)(29, 296)(30, 301)(31, 275)(32, 303)(33, 305)(34, 277)(35, 307)(36, 304)(37, 309)(38, 280)(39, 282)(40, 281)(41, 314)(42, 283)(43, 316)(44, 285)(45, 319)(46, 287)(47, 289)(48, 288)(49, 324)(50, 290)(51, 326)(52, 292)(53, 329)(54, 294)(55, 331)(56, 333)(57, 332)(58, 335)(59, 298)(60, 337)(61, 338)(62, 300)(63, 340)(64, 302)(65, 342)(66, 344)(67, 343)(68, 346)(69, 306)(70, 348)(71, 349)(72, 308)(73, 351)(74, 310)(75, 312)(76, 311)(77, 317)(78, 313)(79, 354)(80, 315)(81, 356)(82, 357)(83, 318)(84, 359)(85, 320)(86, 322)(87, 321)(88, 327)(89, 323)(90, 362)(91, 325)(92, 364)(93, 365)(94, 328)(95, 367)(96, 330)(97, 334)(98, 370)(99, 336)(100, 372)(101, 373)(102, 339)(103, 375)(104, 341)(105, 345)(106, 378)(107, 347)(108, 380)(109, 381)(110, 350)(111, 383)(112, 352)(113, 353)(114, 379)(115, 355)(116, 377)(117, 384)(118, 358)(119, 382)(120, 360)(121, 361)(122, 371)(123, 363)(124, 369)(125, 376)(126, 366)(127, 374)(128, 368)(129, 385)(130, 386)(131, 387)(132, 388)(133, 389)(134, 390)(135, 391)(136, 392)(137, 393)(138, 394)(139, 395)(140, 396)(141, 397)(142, 398)(143, 399)(144, 400)(145, 401)(146, 402)(147, 403)(148, 404)(149, 405)(150, 406)(151, 407)(152, 408)(153, 409)(154, 410)(155, 411)(156, 412)(157, 413)(158, 414)(159, 415)(160, 416)(161, 417)(162, 418)(163, 419)(164, 420)(165, 421)(166, 422)(167, 423)(168, 424)(169, 425)(170, 426)(171, 427)(172, 428)(173, 429)(174, 430)(175, 431)(176, 432)(177, 433)(178, 434)(179, 435)(180, 436)(181, 437)(182, 438)(183, 439)(184, 440)(185, 441)(186, 442)(187, 443)(188, 444)(189, 445)(190, 446)(191, 447)(192, 448)(193, 449)(194, 450)(195, 451)(196, 452)(197, 453)(198, 454)(199, 455)(200, 456)(201, 457)(202, 458)(203, 459)(204, 460)(205, 461)(206, 462)(207, 463)(208, 464)(209, 465)(210, 466)(211, 467)(212, 468)(213, 469)(214, 470)(215, 471)(216, 472)(217, 473)(218, 474)(219, 475)(220, 476)(221, 477)(222, 478)(223, 479)(224, 480)(225, 481)(226, 482)(227, 483)(228, 484)(229, 485)(230, 486)(231, 487)(232, 488)(233, 489)(234, 490)(235, 491)(236, 492)(237, 493)(238, 494)(239, 495)(240, 496)(241, 497)(242, 498)(243, 499)(244, 500)(245, 501)(246, 502)(247, 503)(248, 504)(249, 505)(250, 506)(251, 507)(252, 508)(253, 509)(254, 510)(255, 511)(256, 512) local type(s) :: { ( 16, 64 ), ( 16, 64, 16, 64 ) } Outer automorphisms :: reflexible Dual of E23.1120 Graph:: simple bipartite v = 192 e = 256 f = 20 degree seq :: [ 2^128, 4^64 ] E23.1123 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 32}) Quotient :: dipole Aut^+ = $<128, 149>$ (small group id <128, 149>) Aut = $<256, 6657>$ (small group id <256, 6657>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1, (Y1^-4 * Y3)^2, (Y1^-2 * Y3)^4, Y1^-4 * Y3 * Y1^6 * Y3 * Y1^-6 ] Map:: R = (1, 129, 2, 130, 5, 133, 11, 139, 23, 151, 43, 171, 66, 194, 85, 213, 101, 229, 117, 245, 110, 238, 96, 224, 79, 207, 57, 185, 32, 160, 52, 180, 72, 200, 60, 188, 35, 163, 53, 181, 73, 201, 90, 218, 106, 234, 122, 250, 116, 244, 100, 228, 84, 212, 65, 193, 42, 170, 22, 150, 10, 138, 4, 132)(3, 131, 7, 135, 15, 143, 31, 159, 55, 183, 77, 205, 93, 221, 109, 237, 121, 249, 103, 231, 86, 214, 74, 202, 50, 178, 26, 154, 12, 140, 25, 153, 47, 175, 40, 168, 21, 149, 39, 167, 63, 191, 82, 210, 98, 226, 114, 242, 118, 246, 107, 235, 89, 217, 68, 196, 44, 172, 36, 164, 18, 146, 8, 136)(6, 134, 13, 141, 27, 155, 51, 179, 41, 169, 64, 192, 83, 211, 99, 227, 115, 243, 119, 247, 102, 230, 91, 219, 71, 199, 46, 174, 24, 152, 45, 173, 38, 166, 20, 148, 9, 137, 19, 147, 37, 165, 62, 190, 81, 209, 97, 225, 113, 241, 123, 251, 105, 233, 87, 215, 67, 195, 54, 182, 30, 158, 14, 142)(16, 144, 28, 156, 48, 176, 69, 197, 61, 189, 76, 204, 92, 220, 108, 236, 124, 252, 128, 256, 125, 253, 112, 240, 95, 223, 78, 206, 56, 184, 75, 203, 59, 187, 34, 162, 17, 145, 29, 157, 49, 177, 70, 198, 88, 216, 104, 232, 120, 248, 127, 255, 126, 254, 111, 239, 94, 222, 80, 208, 58, 186, 33, 161)(257, 385)(258, 386)(259, 387)(260, 388)(261, 389)(262, 390)(263, 391)(264, 392)(265, 393)(266, 394)(267, 395)(268, 396)(269, 397)(270, 398)(271, 399)(272, 400)(273, 401)(274, 402)(275, 403)(276, 404)(277, 405)(278, 406)(279, 407)(280, 408)(281, 409)(282, 410)(283, 411)(284, 412)(285, 413)(286, 414)(287, 415)(288, 416)(289, 417)(290, 418)(291, 419)(292, 420)(293, 421)(294, 422)(295, 423)(296, 424)(297, 425)(298, 426)(299, 427)(300, 428)(301, 429)(302, 430)(303, 431)(304, 432)(305, 433)(306, 434)(307, 435)(308, 436)(309, 437)(310, 438)(311, 439)(312, 440)(313, 441)(314, 442)(315, 443)(316, 444)(317, 445)(318, 446)(319, 447)(320, 448)(321, 449)(322, 450)(323, 451)(324, 452)(325, 453)(326, 454)(327, 455)(328, 456)(329, 457)(330, 458)(331, 459)(332, 460)(333, 461)(334, 462)(335, 463)(336, 464)(337, 465)(338, 466)(339, 467)(340, 468)(341, 469)(342, 470)(343, 471)(344, 472)(345, 473)(346, 474)(347, 475)(348, 476)(349, 477)(350, 478)(351, 479)(352, 480)(353, 481)(354, 482)(355, 483)(356, 484)(357, 485)(358, 486)(359, 487)(360, 488)(361, 489)(362, 490)(363, 491)(364, 492)(365, 493)(366, 494)(367, 495)(368, 496)(369, 497)(370, 498)(371, 499)(372, 500)(373, 501)(374, 502)(375, 503)(376, 504)(377, 505)(378, 506)(379, 507)(380, 508)(381, 509)(382, 510)(383, 511)(384, 512) L = (1, 259)(2, 262)(3, 257)(4, 265)(5, 268)(6, 258)(7, 272)(8, 273)(9, 260)(10, 277)(11, 280)(12, 261)(13, 284)(14, 285)(15, 288)(16, 263)(17, 264)(18, 291)(19, 289)(20, 290)(21, 266)(22, 297)(23, 300)(24, 267)(25, 304)(26, 305)(27, 308)(28, 269)(29, 270)(30, 309)(31, 312)(32, 271)(33, 275)(34, 276)(35, 274)(36, 317)(37, 313)(38, 316)(39, 314)(40, 315)(41, 278)(42, 311)(43, 323)(44, 279)(45, 325)(46, 326)(47, 328)(48, 281)(49, 282)(50, 329)(51, 331)(52, 283)(53, 286)(54, 332)(55, 298)(56, 287)(57, 293)(58, 295)(59, 296)(60, 294)(61, 292)(62, 334)(63, 335)(64, 336)(65, 337)(66, 342)(67, 299)(68, 344)(69, 301)(70, 302)(71, 346)(72, 303)(73, 306)(74, 348)(75, 307)(76, 310)(77, 350)(78, 318)(79, 319)(80, 320)(81, 321)(82, 351)(83, 352)(84, 354)(85, 358)(86, 322)(87, 360)(88, 324)(89, 362)(90, 327)(91, 364)(92, 330)(93, 366)(94, 333)(95, 338)(96, 339)(97, 367)(98, 340)(99, 368)(100, 371)(101, 374)(102, 341)(103, 376)(104, 343)(105, 378)(106, 345)(107, 380)(108, 347)(109, 381)(110, 349)(111, 353)(112, 355)(113, 373)(114, 382)(115, 356)(116, 377)(117, 369)(118, 357)(119, 383)(120, 359)(121, 372)(122, 361)(123, 384)(124, 363)(125, 365)(126, 370)(127, 375)(128, 379)(129, 385)(130, 386)(131, 387)(132, 388)(133, 389)(134, 390)(135, 391)(136, 392)(137, 393)(138, 394)(139, 395)(140, 396)(141, 397)(142, 398)(143, 399)(144, 400)(145, 401)(146, 402)(147, 403)(148, 404)(149, 405)(150, 406)(151, 407)(152, 408)(153, 409)(154, 410)(155, 411)(156, 412)(157, 413)(158, 414)(159, 415)(160, 416)(161, 417)(162, 418)(163, 419)(164, 420)(165, 421)(166, 422)(167, 423)(168, 424)(169, 425)(170, 426)(171, 427)(172, 428)(173, 429)(174, 430)(175, 431)(176, 432)(177, 433)(178, 434)(179, 435)(180, 436)(181, 437)(182, 438)(183, 439)(184, 440)(185, 441)(186, 442)(187, 443)(188, 444)(189, 445)(190, 446)(191, 447)(192, 448)(193, 449)(194, 450)(195, 451)(196, 452)(197, 453)(198, 454)(199, 455)(200, 456)(201, 457)(202, 458)(203, 459)(204, 460)(205, 461)(206, 462)(207, 463)(208, 464)(209, 465)(210, 466)(211, 467)(212, 468)(213, 469)(214, 470)(215, 471)(216, 472)(217, 473)(218, 474)(219, 475)(220, 476)(221, 477)(222, 478)(223, 479)(224, 480)(225, 481)(226, 482)(227, 483)(228, 484)(229, 485)(230, 486)(231, 487)(232, 488)(233, 489)(234, 490)(235, 491)(236, 492)(237, 493)(238, 494)(239, 495)(240, 496)(241, 497)(242, 498)(243, 499)(244, 500)(245, 501)(246, 502)(247, 503)(248, 504)(249, 505)(250, 506)(251, 507)(252, 508)(253, 509)(254, 510)(255, 511)(256, 512) local type(s) :: { ( 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E23.1117 Graph:: simple bipartite v = 132 e = 256 f = 80 degree seq :: [ 2^128, 64^4 ] E23.1124 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 32}) Quotient :: dipole Aut^+ = $<128, 151>$ (small group id <128, 151>) Aut = $<256, 6657>$ (small group id <256, 6657>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, (R * Y2 * Y3)^2, (Y3 * Y1^-2)^2, (Y3 * Y1)^8, Y1^-2 * Y3 * Y1^3 * Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1^-9 ] Map:: R = (1, 129, 2, 130, 5, 133, 11, 139, 20, 148, 32, 160, 47, 175, 65, 193, 86, 214, 105, 233, 121, 249, 116, 244, 100, 228, 80, 208, 95, 223, 78, 206, 93, 221, 79, 207, 94, 222, 81, 209, 96, 224, 112, 240, 128, 256, 120, 248, 104, 232, 85, 213, 64, 192, 46, 174, 31, 159, 19, 147, 10, 138, 4, 132)(3, 131, 7, 135, 15, 143, 25, 153, 39, 167, 55, 183, 75, 203, 97, 225, 113, 241, 126, 254, 111, 239, 91, 219, 74, 202, 54, 182, 72, 200, 52, 180, 71, 199, 53, 181, 73, 201, 63, 191, 84, 212, 103, 231, 119, 247, 123, 251, 106, 234, 88, 216, 66, 194, 49, 177, 33, 161, 22, 150, 12, 140, 8, 136)(6, 134, 13, 141, 9, 137, 18, 146, 29, 157, 44, 172, 61, 189, 82, 210, 101, 229, 117, 245, 127, 255, 110, 238, 92, 220, 70, 198, 60, 188, 43, 171, 58, 186, 41, 169, 57, 185, 42, 170, 59, 187, 77, 205, 99, 227, 115, 243, 122, 250, 107, 235, 87, 215, 67, 195, 48, 176, 34, 162, 21, 149, 14, 142)(16, 144, 26, 154, 17, 145, 28, 156, 35, 163, 51, 179, 68, 196, 90, 218, 108, 236, 125, 253, 118, 246, 102, 230, 83, 211, 62, 190, 45, 173, 30, 158, 37, 165, 23, 151, 36, 164, 24, 152, 38, 166, 50, 178, 69, 197, 89, 217, 109, 237, 124, 252, 114, 242, 98, 226, 76, 204, 56, 184, 40, 168, 27, 155)(257, 385)(258, 386)(259, 387)(260, 388)(261, 389)(262, 390)(263, 391)(264, 392)(265, 393)(266, 394)(267, 395)(268, 396)(269, 397)(270, 398)(271, 399)(272, 400)(273, 401)(274, 402)(275, 403)(276, 404)(277, 405)(278, 406)(279, 407)(280, 408)(281, 409)(282, 410)(283, 411)(284, 412)(285, 413)(286, 414)(287, 415)(288, 416)(289, 417)(290, 418)(291, 419)(292, 420)(293, 421)(294, 422)(295, 423)(296, 424)(297, 425)(298, 426)(299, 427)(300, 428)(301, 429)(302, 430)(303, 431)(304, 432)(305, 433)(306, 434)(307, 435)(308, 436)(309, 437)(310, 438)(311, 439)(312, 440)(313, 441)(314, 442)(315, 443)(316, 444)(317, 445)(318, 446)(319, 447)(320, 448)(321, 449)(322, 450)(323, 451)(324, 452)(325, 453)(326, 454)(327, 455)(328, 456)(329, 457)(330, 458)(331, 459)(332, 460)(333, 461)(334, 462)(335, 463)(336, 464)(337, 465)(338, 466)(339, 467)(340, 468)(341, 469)(342, 470)(343, 471)(344, 472)(345, 473)(346, 474)(347, 475)(348, 476)(349, 477)(350, 478)(351, 479)(352, 480)(353, 481)(354, 482)(355, 483)(356, 484)(357, 485)(358, 486)(359, 487)(360, 488)(361, 489)(362, 490)(363, 491)(364, 492)(365, 493)(366, 494)(367, 495)(368, 496)(369, 497)(370, 498)(371, 499)(372, 500)(373, 501)(374, 502)(375, 503)(376, 504)(377, 505)(378, 506)(379, 507)(380, 508)(381, 509)(382, 510)(383, 511)(384, 512) L = (1, 259)(2, 262)(3, 257)(4, 265)(5, 268)(6, 258)(7, 272)(8, 273)(9, 260)(10, 271)(11, 277)(12, 261)(13, 279)(14, 280)(15, 266)(16, 263)(17, 264)(18, 286)(19, 285)(20, 289)(21, 267)(22, 291)(23, 269)(24, 270)(25, 296)(26, 297)(27, 298)(28, 299)(29, 275)(30, 274)(31, 295)(32, 304)(33, 276)(34, 306)(35, 278)(36, 308)(37, 309)(38, 310)(39, 287)(40, 281)(41, 282)(42, 283)(43, 284)(44, 318)(45, 319)(46, 317)(47, 322)(48, 288)(49, 324)(50, 290)(51, 326)(52, 292)(53, 293)(54, 294)(55, 332)(56, 333)(57, 334)(58, 335)(59, 336)(60, 337)(61, 302)(62, 300)(63, 301)(64, 331)(65, 343)(66, 303)(67, 345)(68, 305)(69, 347)(70, 307)(71, 349)(72, 350)(73, 351)(74, 352)(75, 320)(76, 311)(77, 312)(78, 313)(79, 314)(80, 315)(81, 316)(82, 358)(83, 359)(84, 356)(85, 357)(86, 362)(87, 321)(88, 364)(89, 323)(90, 366)(91, 325)(92, 368)(93, 327)(94, 328)(95, 329)(96, 330)(97, 370)(98, 371)(99, 372)(100, 340)(101, 341)(102, 338)(103, 339)(104, 369)(105, 378)(106, 342)(107, 380)(108, 344)(109, 382)(110, 346)(111, 384)(112, 348)(113, 360)(114, 353)(115, 354)(116, 355)(117, 381)(118, 379)(119, 377)(120, 383)(121, 375)(122, 361)(123, 374)(124, 363)(125, 373)(126, 365)(127, 376)(128, 367)(129, 385)(130, 386)(131, 387)(132, 388)(133, 389)(134, 390)(135, 391)(136, 392)(137, 393)(138, 394)(139, 395)(140, 396)(141, 397)(142, 398)(143, 399)(144, 400)(145, 401)(146, 402)(147, 403)(148, 404)(149, 405)(150, 406)(151, 407)(152, 408)(153, 409)(154, 410)(155, 411)(156, 412)(157, 413)(158, 414)(159, 415)(160, 416)(161, 417)(162, 418)(163, 419)(164, 420)(165, 421)(166, 422)(167, 423)(168, 424)(169, 425)(170, 426)(171, 427)(172, 428)(173, 429)(174, 430)(175, 431)(176, 432)(177, 433)(178, 434)(179, 435)(180, 436)(181, 437)(182, 438)(183, 439)(184, 440)(185, 441)(186, 442)(187, 443)(188, 444)(189, 445)(190, 446)(191, 447)(192, 448)(193, 449)(194, 450)(195, 451)(196, 452)(197, 453)(198, 454)(199, 455)(200, 456)(201, 457)(202, 458)(203, 459)(204, 460)(205, 461)(206, 462)(207, 463)(208, 464)(209, 465)(210, 466)(211, 467)(212, 468)(213, 469)(214, 470)(215, 471)(216, 472)(217, 473)(218, 474)(219, 475)(220, 476)(221, 477)(222, 478)(223, 479)(224, 480)(225, 481)(226, 482)(227, 483)(228, 484)(229, 485)(230, 486)(231, 487)(232, 488)(233, 489)(234, 490)(235, 491)(236, 492)(237, 493)(238, 494)(239, 495)(240, 496)(241, 497)(242, 498)(243, 499)(244, 500)(245, 501)(246, 502)(247, 503)(248, 504)(249, 505)(250, 506)(251, 507)(252, 508)(253, 509)(254, 510)(255, 511)(256, 512) local type(s) :: { ( 4, 16 ), ( 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16, 4, 16 ) } Outer automorphisms :: reflexible Dual of E23.1118 Graph:: simple bipartite v = 132 e = 256 f = 80 degree seq :: [ 2^128, 64^4 ] E23.1125 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 32}) Quotient :: dipole Aut^+ = $<128, 149>$ (small group id <128, 149>) Aut = $<256, 6657>$ (small group id <256, 6657>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1, (Y2^4 * Y1)^2, (Y2^2 * Y1)^4, (Y2^-1 * Y1 * R * Y2^-5)^2, (Y3 * Y2^-1)^8, Y2^-13 * Y1 * Y2^2 * Y1 * Y2^-1 ] Map:: R = (1, 129, 2, 130)(3, 131, 7, 135)(4, 132, 9, 137)(5, 133, 11, 139)(6, 134, 13, 141)(8, 136, 17, 145)(10, 138, 21, 149)(12, 140, 25, 153)(14, 142, 29, 157)(15, 143, 23, 151)(16, 144, 27, 155)(18, 146, 35, 163)(19, 147, 24, 152)(20, 148, 28, 156)(22, 150, 41, 169)(26, 154, 47, 175)(30, 158, 53, 181)(31, 159, 45, 173)(32, 160, 51, 179)(33, 161, 43, 171)(34, 162, 49, 177)(36, 164, 54, 182)(37, 165, 46, 174)(38, 166, 52, 180)(39, 167, 44, 172)(40, 168, 50, 178)(42, 170, 48, 176)(55, 183, 70, 198)(56, 184, 75, 203)(57, 185, 68, 196)(58, 186, 74, 202)(59, 187, 66, 194)(60, 188, 73, 201)(61, 189, 77, 205)(62, 190, 71, 199)(63, 191, 69, 197)(64, 192, 67, 195)(65, 193, 81, 209)(72, 200, 85, 213)(76, 204, 89, 217)(78, 206, 91, 219)(79, 207, 90, 218)(80, 208, 94, 222)(82, 210, 87, 215)(83, 211, 86, 214)(84, 212, 98, 226)(88, 216, 102, 230)(92, 220, 106, 234)(93, 221, 105, 233)(95, 223, 107, 235)(96, 224, 111, 239)(97, 225, 101, 229)(99, 227, 103, 231)(100, 228, 115, 243)(104, 232, 119, 247)(108, 236, 123, 251)(109, 237, 122, 250)(110, 238, 121, 249)(112, 240, 124, 252)(113, 241, 118, 246)(114, 242, 117, 245)(116, 244, 120, 248)(125, 253, 128, 256)(126, 254, 127, 255)(257, 385, 259, 387, 264, 392, 274, 402, 292, 420, 317, 445, 336, 464, 352, 480, 368, 496, 374, 502, 358, 486, 342, 470, 325, 453, 302, 430, 281, 409, 301, 429, 324, 452, 308, 436, 285, 413, 307, 435, 330, 458, 346, 474, 362, 490, 378, 506, 372, 500, 356, 484, 340, 468, 321, 449, 298, 426, 278, 406, 266, 394, 260, 388)(258, 386, 261, 389, 268, 396, 282, 410, 304, 432, 328, 456, 344, 472, 360, 488, 376, 504, 366, 494, 350, 478, 334, 462, 314, 442, 290, 418, 273, 401, 289, 417, 313, 441, 296, 424, 277, 405, 295, 423, 319, 447, 338, 466, 354, 482, 370, 498, 380, 508, 364, 492, 348, 476, 332, 460, 310, 438, 286, 414, 270, 398, 262, 390)(263, 391, 271, 399, 287, 415, 311, 439, 297, 425, 320, 448, 339, 467, 355, 483, 371, 499, 382, 510, 367, 495, 351, 479, 335, 463, 316, 444, 291, 419, 315, 443, 294, 422, 276, 404, 265, 393, 275, 403, 293, 421, 318, 446, 337, 465, 353, 481, 369, 497, 381, 509, 365, 493, 349, 477, 333, 461, 312, 440, 288, 416, 272, 400)(267, 395, 279, 407, 299, 427, 322, 450, 309, 437, 331, 459, 347, 475, 363, 491, 379, 507, 384, 512, 375, 503, 359, 487, 343, 471, 327, 455, 303, 431, 326, 454, 306, 434, 284, 412, 269, 397, 283, 411, 305, 433, 329, 457, 345, 473, 361, 489, 377, 505, 383, 511, 373, 501, 357, 485, 341, 469, 323, 451, 300, 428, 280, 408) L = (1, 258)(2, 257)(3, 263)(4, 265)(5, 267)(6, 269)(7, 259)(8, 273)(9, 260)(10, 277)(11, 261)(12, 281)(13, 262)(14, 285)(15, 279)(16, 283)(17, 264)(18, 291)(19, 280)(20, 284)(21, 266)(22, 297)(23, 271)(24, 275)(25, 268)(26, 303)(27, 272)(28, 276)(29, 270)(30, 309)(31, 301)(32, 307)(33, 299)(34, 305)(35, 274)(36, 310)(37, 302)(38, 308)(39, 300)(40, 306)(41, 278)(42, 304)(43, 289)(44, 295)(45, 287)(46, 293)(47, 282)(48, 298)(49, 290)(50, 296)(51, 288)(52, 294)(53, 286)(54, 292)(55, 326)(56, 331)(57, 324)(58, 330)(59, 322)(60, 329)(61, 333)(62, 327)(63, 325)(64, 323)(65, 337)(66, 315)(67, 320)(68, 313)(69, 319)(70, 311)(71, 318)(72, 341)(73, 316)(74, 314)(75, 312)(76, 345)(77, 317)(78, 347)(79, 346)(80, 350)(81, 321)(82, 343)(83, 342)(84, 354)(85, 328)(86, 339)(87, 338)(88, 358)(89, 332)(90, 335)(91, 334)(92, 362)(93, 361)(94, 336)(95, 363)(96, 367)(97, 357)(98, 340)(99, 359)(100, 371)(101, 353)(102, 344)(103, 355)(104, 375)(105, 349)(106, 348)(107, 351)(108, 379)(109, 378)(110, 377)(111, 352)(112, 380)(113, 374)(114, 373)(115, 356)(116, 376)(117, 370)(118, 369)(119, 360)(120, 372)(121, 366)(122, 365)(123, 364)(124, 368)(125, 384)(126, 383)(127, 382)(128, 381)(129, 385)(130, 386)(131, 387)(132, 388)(133, 389)(134, 390)(135, 391)(136, 392)(137, 393)(138, 394)(139, 395)(140, 396)(141, 397)(142, 398)(143, 399)(144, 400)(145, 401)(146, 402)(147, 403)(148, 404)(149, 405)(150, 406)(151, 407)(152, 408)(153, 409)(154, 410)(155, 411)(156, 412)(157, 413)(158, 414)(159, 415)(160, 416)(161, 417)(162, 418)(163, 419)(164, 420)(165, 421)(166, 422)(167, 423)(168, 424)(169, 425)(170, 426)(171, 427)(172, 428)(173, 429)(174, 430)(175, 431)(176, 432)(177, 433)(178, 434)(179, 435)(180, 436)(181, 437)(182, 438)(183, 439)(184, 440)(185, 441)(186, 442)(187, 443)(188, 444)(189, 445)(190, 446)(191, 447)(192, 448)(193, 449)(194, 450)(195, 451)(196, 452)(197, 453)(198, 454)(199, 455)(200, 456)(201, 457)(202, 458)(203, 459)(204, 460)(205, 461)(206, 462)(207, 463)(208, 464)(209, 465)(210, 466)(211, 467)(212, 468)(213, 469)(214, 470)(215, 471)(216, 472)(217, 473)(218, 474)(219, 475)(220, 476)(221, 477)(222, 478)(223, 479)(224, 480)(225, 481)(226, 482)(227, 483)(228, 484)(229, 485)(230, 486)(231, 487)(232, 488)(233, 489)(234, 490)(235, 491)(236, 492)(237, 493)(238, 494)(239, 495)(240, 496)(241, 497)(242, 498)(243, 499)(244, 500)(245, 501)(246, 502)(247, 503)(248, 504)(249, 505)(250, 506)(251, 507)(252, 508)(253, 509)(254, 510)(255, 511)(256, 512) local type(s) :: { ( 2, 16, 2, 16 ), ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ) } Outer automorphisms :: reflexible Dual of E23.1127 Graph:: bipartite v = 68 e = 256 f = 144 degree seq :: [ 4^64, 64^4 ] E23.1126 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 32}) Quotient :: dipole Aut^+ = $<128, 151>$ (small group id <128, 151>) Aut = $<256, 6657>$ (small group id <256, 6657>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y2^2 * Y1)^2, (Y3 * Y2^-1)^8, Y2^3 * Y1 * Y2^-4 * R * Y2^7 * Y1 * R, Y2 * Y1 * Y2^-1 * R * Y2^-7 * R * Y2^-5 * Y1 * Y2^2, Y2^3 * Y1 * Y2^-5 * Y1 * Y2^7 * Y1 * Y2^-1 * Y1, Y2^32 ] Map:: R = (1, 129, 2, 130)(3, 131, 7, 135)(4, 132, 9, 137)(5, 133, 11, 139)(6, 134, 13, 141)(8, 136, 14, 142)(10, 138, 12, 140)(15, 143, 25, 153)(16, 144, 26, 154)(17, 145, 27, 155)(18, 146, 29, 157)(19, 147, 30, 158)(20, 148, 32, 160)(21, 149, 33, 161)(22, 150, 34, 162)(23, 151, 36, 164)(24, 152, 37, 165)(28, 156, 38, 166)(31, 159, 35, 163)(39, 167, 55, 183)(40, 168, 56, 184)(41, 169, 57, 185)(42, 170, 58, 186)(43, 171, 59, 187)(44, 172, 61, 189)(45, 173, 62, 190)(46, 174, 63, 191)(47, 175, 65, 193)(48, 176, 66, 194)(49, 177, 67, 195)(50, 178, 68, 196)(51, 179, 69, 197)(52, 180, 71, 199)(53, 181, 72, 200)(54, 182, 73, 201)(60, 188, 74, 202)(64, 192, 70, 198)(75, 203, 86, 214)(76, 204, 88, 216)(77, 205, 87, 215)(78, 206, 93, 221)(79, 207, 97, 225)(80, 208, 98, 226)(81, 209, 99, 227)(82, 210, 89, 217)(83, 211, 101, 229)(84, 212, 102, 230)(85, 213, 103, 231)(90, 218, 105, 233)(91, 219, 106, 234)(92, 220, 107, 235)(94, 222, 109, 237)(95, 223, 110, 238)(96, 224, 111, 239)(100, 228, 112, 240)(104, 232, 108, 236)(113, 241, 125, 253)(114, 242, 124, 252)(115, 243, 123, 251)(116, 244, 122, 250)(117, 245, 121, 249)(118, 246, 128, 256)(119, 247, 127, 255)(120, 248, 126, 254)(257, 385, 259, 387, 264, 392, 273, 401, 284, 412, 299, 427, 316, 444, 337, 465, 356, 484, 372, 500, 377, 505, 361, 489, 345, 473, 323, 451, 343, 471, 321, 449, 342, 470, 322, 450, 344, 472, 327, 455, 349, 477, 365, 493, 381, 509, 376, 504, 360, 488, 341, 469, 320, 448, 302, 430, 287, 415, 275, 403, 266, 394, 260, 388)(258, 386, 261, 389, 268, 396, 278, 406, 291, 419, 307, 435, 326, 454, 348, 476, 364, 492, 380, 508, 369, 497, 353, 481, 334, 462, 313, 441, 332, 460, 311, 439, 331, 459, 312, 440, 333, 461, 317, 445, 338, 466, 357, 485, 373, 501, 384, 512, 368, 496, 352, 480, 330, 458, 310, 438, 294, 422, 280, 408, 270, 398, 262, 390)(263, 391, 271, 399, 265, 393, 274, 402, 286, 414, 301, 429, 319, 447, 340, 468, 359, 487, 375, 503, 382, 510, 366, 494, 350, 478, 328, 456, 308, 436, 292, 420, 304, 432, 288, 416, 303, 431, 289, 417, 305, 433, 324, 452, 346, 474, 362, 490, 378, 506, 371, 499, 355, 483, 336, 464, 315, 443, 298, 426, 283, 411, 272, 400)(267, 395, 276, 404, 269, 397, 279, 407, 293, 421, 309, 437, 329, 457, 351, 479, 367, 495, 383, 511, 374, 502, 358, 486, 339, 467, 318, 446, 300, 428, 285, 413, 296, 424, 281, 409, 295, 423, 282, 410, 297, 425, 314, 442, 335, 463, 354, 482, 370, 498, 379, 507, 363, 491, 347, 475, 325, 453, 306, 434, 290, 418, 277, 405) L = (1, 258)(2, 257)(3, 263)(4, 265)(5, 267)(6, 269)(7, 259)(8, 270)(9, 260)(10, 268)(11, 261)(12, 266)(13, 262)(14, 264)(15, 281)(16, 282)(17, 283)(18, 285)(19, 286)(20, 288)(21, 289)(22, 290)(23, 292)(24, 293)(25, 271)(26, 272)(27, 273)(28, 294)(29, 274)(30, 275)(31, 291)(32, 276)(33, 277)(34, 278)(35, 287)(36, 279)(37, 280)(38, 284)(39, 311)(40, 312)(41, 313)(42, 314)(43, 315)(44, 317)(45, 318)(46, 319)(47, 321)(48, 322)(49, 323)(50, 324)(51, 325)(52, 327)(53, 328)(54, 329)(55, 295)(56, 296)(57, 297)(58, 298)(59, 299)(60, 330)(61, 300)(62, 301)(63, 302)(64, 326)(65, 303)(66, 304)(67, 305)(68, 306)(69, 307)(70, 320)(71, 308)(72, 309)(73, 310)(74, 316)(75, 342)(76, 344)(77, 343)(78, 349)(79, 353)(80, 354)(81, 355)(82, 345)(83, 357)(84, 358)(85, 359)(86, 331)(87, 333)(88, 332)(89, 338)(90, 361)(91, 362)(92, 363)(93, 334)(94, 365)(95, 366)(96, 367)(97, 335)(98, 336)(99, 337)(100, 368)(101, 339)(102, 340)(103, 341)(104, 364)(105, 346)(106, 347)(107, 348)(108, 360)(109, 350)(110, 351)(111, 352)(112, 356)(113, 381)(114, 380)(115, 379)(116, 378)(117, 377)(118, 384)(119, 383)(120, 382)(121, 373)(122, 372)(123, 371)(124, 370)(125, 369)(126, 376)(127, 375)(128, 374)(129, 385)(130, 386)(131, 387)(132, 388)(133, 389)(134, 390)(135, 391)(136, 392)(137, 393)(138, 394)(139, 395)(140, 396)(141, 397)(142, 398)(143, 399)(144, 400)(145, 401)(146, 402)(147, 403)(148, 404)(149, 405)(150, 406)(151, 407)(152, 408)(153, 409)(154, 410)(155, 411)(156, 412)(157, 413)(158, 414)(159, 415)(160, 416)(161, 417)(162, 418)(163, 419)(164, 420)(165, 421)(166, 422)(167, 423)(168, 424)(169, 425)(170, 426)(171, 427)(172, 428)(173, 429)(174, 430)(175, 431)(176, 432)(177, 433)(178, 434)(179, 435)(180, 436)(181, 437)(182, 438)(183, 439)(184, 440)(185, 441)(186, 442)(187, 443)(188, 444)(189, 445)(190, 446)(191, 447)(192, 448)(193, 449)(194, 450)(195, 451)(196, 452)(197, 453)(198, 454)(199, 455)(200, 456)(201, 457)(202, 458)(203, 459)(204, 460)(205, 461)(206, 462)(207, 463)(208, 464)(209, 465)(210, 466)(211, 467)(212, 468)(213, 469)(214, 470)(215, 471)(216, 472)(217, 473)(218, 474)(219, 475)(220, 476)(221, 477)(222, 478)(223, 479)(224, 480)(225, 481)(226, 482)(227, 483)(228, 484)(229, 485)(230, 486)(231, 487)(232, 488)(233, 489)(234, 490)(235, 491)(236, 492)(237, 493)(238, 494)(239, 495)(240, 496)(241, 497)(242, 498)(243, 499)(244, 500)(245, 501)(246, 502)(247, 503)(248, 504)(249, 505)(250, 506)(251, 507)(252, 508)(253, 509)(254, 510)(255, 511)(256, 512) local type(s) :: { ( 2, 16, 2, 16 ), ( 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16, 2, 16 ) } Outer automorphisms :: reflexible Dual of E23.1128 Graph:: bipartite v = 68 e = 256 f = 144 degree seq :: [ 4^64, 64^4 ] E23.1127 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 32}) Quotient :: dipole Aut^+ = $<128, 149>$ (small group id <128, 149>) Aut = $<256, 6657>$ (small group id <256, 6657>) |r| :: 2 Presentation :: [ Y2, R^2, (Y3^-1 * Y1^-1)^2, (Y3^-1 * Y1^-1)^2, (R * Y3)^2, (R * Y1)^2, Y3 * Y1^-1 * Y3 * Y1^3, (R * Y2 * Y3^-1)^2, (Y1^-1 * Y3 * Y1^-2)^2, Y3^2 * Y1^-1 * Y3^-14 * Y1, (Y3 * Y2^-1)^32 ] Map:: R = (1, 129, 2, 130, 6, 134, 16, 144, 34, 162, 27, 155, 13, 141, 4, 132)(3, 131, 9, 137, 17, 145, 8, 136, 21, 149, 35, 163, 28, 156, 11, 139)(5, 133, 14, 142, 18, 146, 37, 165, 30, 158, 12, 140, 20, 148, 7, 135)(10, 138, 24, 152, 36, 164, 23, 151, 42, 170, 22, 150, 43, 171, 26, 154)(15, 143, 32, 160, 38, 166, 29, 157, 41, 169, 19, 147, 39, 167, 31, 159)(25, 153, 47, 175, 53, 181, 46, 174, 58, 186, 45, 173, 59, 187, 44, 172)(33, 161, 49, 177, 54, 182, 40, 168, 56, 184, 50, 178, 55, 183, 51, 179)(48, 176, 60, 188, 69, 197, 63, 191, 74, 202, 62, 190, 75, 203, 61, 189)(52, 180, 57, 185, 70, 198, 66, 194, 72, 200, 67, 195, 71, 199, 65, 193)(64, 192, 77, 205, 85, 213, 76, 204, 90, 218, 79, 207, 91, 219, 78, 206)(68, 196, 82, 210, 86, 214, 83, 211, 88, 216, 81, 209, 87, 215, 73, 201)(80, 208, 94, 222, 101, 229, 93, 221, 106, 234, 92, 220, 107, 235, 95, 223)(84, 212, 99, 227, 102, 230, 97, 225, 104, 232, 89, 217, 103, 231, 98, 226)(96, 224, 111, 239, 117, 245, 110, 238, 122, 250, 109, 237, 123, 251, 108, 236)(100, 228, 113, 241, 118, 246, 105, 233, 120, 248, 114, 242, 119, 247, 115, 243)(112, 240, 124, 252, 127, 255, 126, 254, 116, 244, 121, 249, 128, 256, 125, 253)(257, 385)(258, 386)(259, 387)(260, 388)(261, 389)(262, 390)(263, 391)(264, 392)(265, 393)(266, 394)(267, 395)(268, 396)(269, 397)(270, 398)(271, 399)(272, 400)(273, 401)(274, 402)(275, 403)(276, 404)(277, 405)(278, 406)(279, 407)(280, 408)(281, 409)(282, 410)(283, 411)(284, 412)(285, 413)(286, 414)(287, 415)(288, 416)(289, 417)(290, 418)(291, 419)(292, 420)(293, 421)(294, 422)(295, 423)(296, 424)(297, 425)(298, 426)(299, 427)(300, 428)(301, 429)(302, 430)(303, 431)(304, 432)(305, 433)(306, 434)(307, 435)(308, 436)(309, 437)(310, 438)(311, 439)(312, 440)(313, 441)(314, 442)(315, 443)(316, 444)(317, 445)(318, 446)(319, 447)(320, 448)(321, 449)(322, 450)(323, 451)(324, 452)(325, 453)(326, 454)(327, 455)(328, 456)(329, 457)(330, 458)(331, 459)(332, 460)(333, 461)(334, 462)(335, 463)(336, 464)(337, 465)(338, 466)(339, 467)(340, 468)(341, 469)(342, 470)(343, 471)(344, 472)(345, 473)(346, 474)(347, 475)(348, 476)(349, 477)(350, 478)(351, 479)(352, 480)(353, 481)(354, 482)(355, 483)(356, 484)(357, 485)(358, 486)(359, 487)(360, 488)(361, 489)(362, 490)(363, 491)(364, 492)(365, 493)(366, 494)(367, 495)(368, 496)(369, 497)(370, 498)(371, 499)(372, 500)(373, 501)(374, 502)(375, 503)(376, 504)(377, 505)(378, 506)(379, 507)(380, 508)(381, 509)(382, 510)(383, 511)(384, 512) L = (1, 259)(2, 263)(3, 266)(4, 268)(5, 257)(6, 273)(7, 275)(8, 258)(9, 260)(10, 281)(11, 283)(12, 285)(13, 284)(14, 287)(15, 261)(16, 270)(17, 292)(18, 262)(19, 296)(20, 269)(21, 298)(22, 264)(23, 265)(24, 267)(25, 304)(26, 291)(27, 293)(28, 299)(29, 305)(30, 290)(31, 306)(32, 307)(33, 271)(34, 277)(35, 272)(36, 309)(37, 288)(38, 274)(39, 276)(40, 313)(41, 286)(42, 314)(43, 315)(44, 278)(45, 279)(46, 280)(47, 282)(48, 320)(49, 321)(50, 322)(51, 323)(52, 289)(53, 325)(54, 294)(55, 295)(56, 297)(57, 329)(58, 330)(59, 331)(60, 300)(61, 301)(62, 302)(63, 303)(64, 336)(65, 337)(66, 338)(67, 339)(68, 308)(69, 341)(70, 310)(71, 311)(72, 312)(73, 345)(74, 346)(75, 347)(76, 316)(77, 317)(78, 318)(79, 319)(80, 352)(81, 353)(82, 354)(83, 355)(84, 324)(85, 357)(86, 326)(87, 327)(88, 328)(89, 361)(90, 362)(91, 363)(92, 332)(93, 333)(94, 334)(95, 335)(96, 368)(97, 369)(98, 370)(99, 371)(100, 340)(101, 373)(102, 342)(103, 343)(104, 344)(105, 377)(106, 378)(107, 379)(108, 348)(109, 349)(110, 350)(111, 351)(112, 376)(113, 382)(114, 381)(115, 380)(116, 356)(117, 383)(118, 358)(119, 359)(120, 360)(121, 366)(122, 372)(123, 384)(124, 364)(125, 365)(126, 367)(127, 375)(128, 374)(129, 385)(130, 386)(131, 387)(132, 388)(133, 389)(134, 390)(135, 391)(136, 392)(137, 393)(138, 394)(139, 395)(140, 396)(141, 397)(142, 398)(143, 399)(144, 400)(145, 401)(146, 402)(147, 403)(148, 404)(149, 405)(150, 406)(151, 407)(152, 408)(153, 409)(154, 410)(155, 411)(156, 412)(157, 413)(158, 414)(159, 415)(160, 416)(161, 417)(162, 418)(163, 419)(164, 420)(165, 421)(166, 422)(167, 423)(168, 424)(169, 425)(170, 426)(171, 427)(172, 428)(173, 429)(174, 430)(175, 431)(176, 432)(177, 433)(178, 434)(179, 435)(180, 436)(181, 437)(182, 438)(183, 439)(184, 440)(185, 441)(186, 442)(187, 443)(188, 444)(189, 445)(190, 446)(191, 447)(192, 448)(193, 449)(194, 450)(195, 451)(196, 452)(197, 453)(198, 454)(199, 455)(200, 456)(201, 457)(202, 458)(203, 459)(204, 460)(205, 461)(206, 462)(207, 463)(208, 464)(209, 465)(210, 466)(211, 467)(212, 468)(213, 469)(214, 470)(215, 471)(216, 472)(217, 473)(218, 474)(219, 475)(220, 476)(221, 477)(222, 478)(223, 479)(224, 480)(225, 481)(226, 482)(227, 483)(228, 484)(229, 485)(230, 486)(231, 487)(232, 488)(233, 489)(234, 490)(235, 491)(236, 492)(237, 493)(238, 494)(239, 495)(240, 496)(241, 497)(242, 498)(243, 499)(244, 500)(245, 501)(246, 502)(247, 503)(248, 504)(249, 505)(250, 506)(251, 507)(252, 508)(253, 509)(254, 510)(255, 511)(256, 512) local type(s) :: { ( 4, 64 ), ( 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64 ) } Outer automorphisms :: reflexible Dual of E23.1125 Graph:: simple bipartite v = 144 e = 256 f = 68 degree seq :: [ 2^128, 16^16 ] E23.1128 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 8, 32}) Quotient :: dipole Aut^+ = $<128, 151>$ (small group id <128, 151>) Aut = $<256, 6657>$ (small group id <256, 6657>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y1)^2, (Y3 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, Y1^8, Y1^-1 * Y3^-1 * Y1 * Y3^15 * Y1^-2, (Y3 * Y2^-1)^32 ] Map:: R = (1, 129, 2, 130, 6, 134, 14, 142, 26, 154, 24, 152, 12, 140, 4, 132)(3, 131, 9, 137, 19, 147, 33, 161, 41, 169, 28, 156, 15, 143, 8, 136)(5, 133, 11, 139, 22, 150, 37, 165, 42, 170, 27, 155, 16, 144, 7, 135)(10, 138, 18, 146, 29, 157, 44, 172, 57, 185, 49, 177, 34, 162, 20, 148)(13, 141, 17, 145, 30, 158, 43, 171, 58, 186, 53, 181, 38, 166, 23, 151)(21, 149, 35, 163, 50, 178, 65, 193, 73, 201, 60, 188, 45, 173, 32, 160)(25, 153, 39, 167, 54, 182, 69, 197, 74, 202, 59, 187, 46, 174, 31, 159)(36, 164, 48, 176, 61, 189, 76, 204, 89, 217, 81, 209, 66, 194, 51, 179)(40, 168, 47, 175, 62, 190, 75, 203, 90, 218, 85, 213, 70, 198, 55, 183)(52, 180, 67, 195, 82, 210, 97, 225, 105, 233, 92, 220, 77, 205, 64, 192)(56, 184, 71, 199, 86, 214, 101, 229, 106, 234, 91, 219, 78, 206, 63, 191)(68, 196, 80, 208, 93, 221, 108, 236, 121, 249, 113, 241, 98, 226, 83, 211)(72, 200, 79, 207, 94, 222, 107, 235, 122, 250, 117, 245, 102, 230, 87, 215)(84, 212, 99, 227, 114, 242, 127, 255, 120, 248, 124, 252, 109, 237, 96, 224)(88, 216, 103, 231, 118, 246, 128, 256, 116, 244, 123, 251, 110, 238, 95, 223)(100, 228, 112, 240, 125, 253, 119, 247, 104, 232, 111, 239, 126, 254, 115, 243)(257, 385)(258, 386)(259, 387)(260, 388)(261, 389)(262, 390)(263, 391)(264, 392)(265, 393)(266, 394)(267, 395)(268, 396)(269, 397)(270, 398)(271, 399)(272, 400)(273, 401)(274, 402)(275, 403)(276, 404)(277, 405)(278, 406)(279, 407)(280, 408)(281, 409)(282, 410)(283, 411)(284, 412)(285, 413)(286, 414)(287, 415)(288, 416)(289, 417)(290, 418)(291, 419)(292, 420)(293, 421)(294, 422)(295, 423)(296, 424)(297, 425)(298, 426)(299, 427)(300, 428)(301, 429)(302, 430)(303, 431)(304, 432)(305, 433)(306, 434)(307, 435)(308, 436)(309, 437)(310, 438)(311, 439)(312, 440)(313, 441)(314, 442)(315, 443)(316, 444)(317, 445)(318, 446)(319, 447)(320, 448)(321, 449)(322, 450)(323, 451)(324, 452)(325, 453)(326, 454)(327, 455)(328, 456)(329, 457)(330, 458)(331, 459)(332, 460)(333, 461)(334, 462)(335, 463)(336, 464)(337, 465)(338, 466)(339, 467)(340, 468)(341, 469)(342, 470)(343, 471)(344, 472)(345, 473)(346, 474)(347, 475)(348, 476)(349, 477)(350, 478)(351, 479)(352, 480)(353, 481)(354, 482)(355, 483)(356, 484)(357, 485)(358, 486)(359, 487)(360, 488)(361, 489)(362, 490)(363, 491)(364, 492)(365, 493)(366, 494)(367, 495)(368, 496)(369, 497)(370, 498)(371, 499)(372, 500)(373, 501)(374, 502)(375, 503)(376, 504)(377, 505)(378, 506)(379, 507)(380, 508)(381, 509)(382, 510)(383, 511)(384, 512) L = (1, 259)(2, 263)(3, 266)(4, 267)(5, 257)(6, 271)(7, 273)(8, 258)(9, 260)(10, 277)(11, 279)(12, 275)(13, 261)(14, 283)(15, 285)(16, 262)(17, 287)(18, 264)(19, 290)(20, 265)(21, 292)(22, 268)(23, 295)(24, 293)(25, 269)(26, 297)(27, 299)(28, 270)(29, 301)(30, 272)(31, 303)(32, 274)(33, 280)(34, 306)(35, 276)(36, 308)(37, 309)(38, 278)(39, 311)(40, 281)(41, 313)(42, 282)(43, 315)(44, 284)(45, 317)(46, 286)(47, 319)(48, 288)(49, 289)(50, 322)(51, 291)(52, 324)(53, 325)(54, 294)(55, 327)(56, 296)(57, 329)(58, 298)(59, 331)(60, 300)(61, 333)(62, 302)(63, 335)(64, 304)(65, 305)(66, 338)(67, 307)(68, 340)(69, 341)(70, 310)(71, 343)(72, 312)(73, 345)(74, 314)(75, 347)(76, 316)(77, 349)(78, 318)(79, 351)(80, 320)(81, 321)(82, 354)(83, 323)(84, 356)(85, 357)(86, 326)(87, 359)(88, 328)(89, 361)(90, 330)(91, 363)(92, 332)(93, 365)(94, 334)(95, 367)(96, 336)(97, 337)(98, 370)(99, 339)(100, 372)(101, 373)(102, 342)(103, 375)(104, 344)(105, 377)(106, 346)(107, 379)(108, 348)(109, 381)(110, 350)(111, 383)(112, 352)(113, 353)(114, 382)(115, 355)(116, 378)(117, 384)(118, 358)(119, 380)(120, 360)(121, 376)(122, 362)(123, 371)(124, 364)(125, 374)(126, 366)(127, 369)(128, 368)(129, 385)(130, 386)(131, 387)(132, 388)(133, 389)(134, 390)(135, 391)(136, 392)(137, 393)(138, 394)(139, 395)(140, 396)(141, 397)(142, 398)(143, 399)(144, 400)(145, 401)(146, 402)(147, 403)(148, 404)(149, 405)(150, 406)(151, 407)(152, 408)(153, 409)(154, 410)(155, 411)(156, 412)(157, 413)(158, 414)(159, 415)(160, 416)(161, 417)(162, 418)(163, 419)(164, 420)(165, 421)(166, 422)(167, 423)(168, 424)(169, 425)(170, 426)(171, 427)(172, 428)(173, 429)(174, 430)(175, 431)(176, 432)(177, 433)(178, 434)(179, 435)(180, 436)(181, 437)(182, 438)(183, 439)(184, 440)(185, 441)(186, 442)(187, 443)(188, 444)(189, 445)(190, 446)(191, 447)(192, 448)(193, 449)(194, 450)(195, 451)(196, 452)(197, 453)(198, 454)(199, 455)(200, 456)(201, 457)(202, 458)(203, 459)(204, 460)(205, 461)(206, 462)(207, 463)(208, 464)(209, 465)(210, 466)(211, 467)(212, 468)(213, 469)(214, 470)(215, 471)(216, 472)(217, 473)(218, 474)(219, 475)(220, 476)(221, 477)(222, 478)(223, 479)(224, 480)(225, 481)(226, 482)(227, 483)(228, 484)(229, 485)(230, 486)(231, 487)(232, 488)(233, 489)(234, 490)(235, 491)(236, 492)(237, 493)(238, 494)(239, 495)(240, 496)(241, 497)(242, 498)(243, 499)(244, 500)(245, 501)(246, 502)(247, 503)(248, 504)(249, 505)(250, 506)(251, 507)(252, 508)(253, 509)(254, 510)(255, 511)(256, 512) local type(s) :: { ( 4, 64 ), ( 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64, 4, 64 ) } Outer automorphisms :: reflexible Dual of E23.1126 Graph:: simple bipartite v = 144 e = 256 f = 68 degree seq :: [ 2^128, 16^16 ] E23.1129 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 2, 6}) Quotient :: halfedge^2 Aut^+ = S3 x D22 (small group id <132, 5>) Aut = C2 x S3 x D22 (small group id <264, 34>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, R * Y3 * R * Y2, (R * Y1)^2, Y3 * Y1 * Y3 * Y2 * Y1 * Y2, (Y3 * Y2)^3, (Y3 * Y1)^22 ] Map:: non-degenerate R = (1, 134, 2, 133)(3, 139, 7, 135)(4, 141, 9, 136)(5, 143, 11, 137)(6, 145, 13, 138)(8, 144, 12, 140)(10, 146, 14, 142)(15, 155, 23, 147)(16, 156, 24, 148)(17, 157, 25, 149)(18, 158, 26, 150)(19, 159, 27, 151)(20, 160, 28, 152)(21, 161, 29, 153)(22, 162, 30, 154)(31, 169, 37, 163)(32, 170, 38, 164)(33, 171, 39, 165)(34, 172, 40, 166)(35, 173, 41, 167)(36, 174, 42, 168)(43, 181, 49, 175)(44, 182, 50, 176)(45, 183, 51, 177)(46, 184, 52, 178)(47, 185, 53, 179)(48, 186, 54, 180)(55, 217, 85, 187)(56, 219, 87, 188)(57, 221, 89, 189)(58, 223, 91, 190)(59, 225, 93, 191)(60, 227, 95, 192)(61, 229, 97, 193)(62, 232, 100, 194)(63, 230, 98, 195)(64, 233, 101, 196)(65, 237, 105, 197)(66, 239, 107, 198)(67, 240, 108, 199)(68, 243, 111, 200)(69, 245, 113, 201)(70, 247, 115, 202)(71, 248, 116, 203)(72, 251, 119, 204)(73, 253, 121, 205)(74, 255, 123, 206)(75, 257, 125, 207)(76, 259, 127, 208)(77, 261, 129, 209)(78, 263, 131, 210)(79, 264, 132, 211)(80, 262, 130, 212)(81, 260, 128, 213)(82, 258, 126, 214)(83, 256, 124, 215)(84, 254, 122, 216)(86, 252, 120, 218)(88, 249, 117, 220)(90, 246, 114, 222)(92, 238, 106, 224)(94, 231, 99, 226)(96, 234, 102, 228)(103, 241, 109, 235)(104, 244, 112, 236)(110, 250, 118, 242) L = (1, 3)(2, 5)(4, 10)(6, 14)(7, 15)(8, 17)(9, 18)(11, 19)(12, 21)(13, 22)(16, 25)(20, 29)(23, 31)(24, 33)(26, 32)(27, 34)(28, 36)(30, 35)(37, 43)(38, 45)(39, 44)(40, 46)(41, 48)(42, 47)(49, 55)(50, 57)(51, 56)(52, 64)(53, 58)(54, 63)(59, 87)(60, 89)(61, 98)(62, 91)(65, 95)(66, 93)(67, 85)(68, 108)(69, 100)(70, 97)(71, 101)(72, 116)(73, 107)(74, 105)(75, 111)(76, 115)(77, 113)(78, 119)(79, 123)(80, 121)(81, 125)(82, 129)(83, 127)(84, 131)(86, 130)(88, 132)(90, 128)(92, 122)(94, 114)(96, 120)(99, 106)(102, 112)(103, 126)(104, 124)(109, 118)(110, 117)(133, 136)(134, 138)(135, 140)(137, 144)(139, 148)(141, 147)(142, 149)(143, 152)(145, 151)(146, 153)(150, 157)(154, 161)(155, 164)(156, 163)(158, 165)(159, 167)(160, 166)(162, 168)(169, 176)(170, 175)(171, 177)(172, 179)(173, 178)(174, 180)(181, 188)(182, 187)(183, 189)(184, 195)(185, 196)(186, 190)(191, 221)(192, 217)(193, 223)(194, 233)(197, 225)(198, 240)(199, 219)(200, 227)(201, 229)(202, 248)(203, 230)(204, 232)(205, 237)(206, 243)(207, 239)(208, 245)(209, 251)(210, 247)(211, 253)(212, 257)(213, 255)(214, 259)(215, 263)(216, 261)(218, 264)(220, 260)(222, 262)(224, 256)(226, 249)(228, 246)(231, 241)(234, 238)(235, 254)(236, 258)(242, 252)(244, 250) local type(s) :: { ( 12^4 ) } Outer automorphisms :: reflexible Dual of E23.1130 Transitivity :: VT+ AT Graph:: simple bipartite v = 66 e = 132 f = 22 degree seq :: [ 4^66 ] E23.1130 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 2, 6}) Quotient :: halfedge^2 Aut^+ = S3 x D22 (small group id <132, 5>) Aut = C2 x S3 x D22 (small group id <264, 34>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y1^-1 * Y3 * Y2 * Y1^-1, R * Y3 * R * Y2, (R * Y1)^2, (Y3 * Y2)^3, Y1^6, Y2 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y3 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 ] Map:: non-degenerate R = (1, 134, 2, 138, 6, 146, 14, 142, 10, 137, 5, 133)(3, 141, 9, 147, 15, 144, 12, 136, 4, 143, 11, 135)(7, 148, 16, 145, 13, 150, 18, 140, 8, 149, 17, 139)(19, 157, 25, 153, 21, 159, 27, 152, 20, 158, 26, 151)(22, 160, 28, 156, 24, 162, 30, 155, 23, 161, 29, 154)(31, 169, 37, 165, 33, 171, 39, 164, 32, 170, 38, 163)(34, 172, 40, 168, 36, 174, 42, 167, 35, 173, 41, 166)(43, 181, 49, 177, 45, 183, 51, 176, 44, 182, 50, 175)(46, 184, 52, 180, 48, 186, 54, 179, 47, 185, 53, 178)(55, 241, 109, 189, 57, 243, 111, 188, 56, 242, 110, 187)(58, 239, 107, 199, 67, 240, 108, 195, 63, 238, 106, 190)(59, 235, 103, 194, 62, 236, 104, 203, 71, 237, 105, 191)(60, 247, 115, 193, 61, 246, 114, 204, 72, 250, 118, 192)(64, 244, 112, 197, 65, 252, 120, 202, 70, 245, 113, 196)(66, 229, 97, 200, 68, 230, 98, 201, 69, 231, 99, 198)(73, 227, 95, 206, 74, 228, 96, 207, 75, 226, 94, 205)(76, 248, 116, 209, 77, 251, 119, 210, 78, 249, 117, 208)(79, 253, 121, 212, 80, 255, 123, 213, 81, 254, 122, 211)(82, 218, 86, 215, 83, 219, 87, 216, 84, 217, 85, 214)(88, 256, 124, 221, 89, 258, 126, 222, 90, 257, 125, 220)(91, 259, 127, 224, 92, 261, 129, 225, 93, 260, 128, 223)(100, 262, 130, 233, 101, 264, 132, 234, 102, 263, 131, 232) L = (1, 3)(2, 7)(4, 6)(5, 13)(8, 14)(9, 19)(10, 15)(11, 21)(12, 20)(16, 22)(17, 24)(18, 23)(25, 31)(26, 33)(27, 32)(28, 34)(29, 36)(30, 35)(37, 43)(38, 45)(39, 44)(40, 46)(41, 48)(42, 47)(49, 55)(50, 57)(51, 56)(52, 101)(53, 102)(54, 100)(58, 112)(59, 114)(60, 116)(61, 117)(62, 115)(63, 120)(64, 121)(65, 122)(66, 108)(67, 113)(68, 107)(69, 106)(70, 123)(71, 118)(72, 119)(73, 104)(74, 103)(75, 105)(76, 124)(77, 125)(78, 126)(79, 127)(80, 128)(81, 129)(82, 98)(83, 97)(84, 99)(85, 96)(86, 95)(87, 94)(88, 130)(89, 131)(90, 132)(91, 111)(92, 109)(93, 110)(133, 136)(134, 140)(135, 142)(137, 139)(138, 147)(141, 152)(143, 151)(144, 153)(145, 146)(148, 155)(149, 154)(150, 156)(157, 164)(158, 163)(159, 165)(160, 167)(161, 166)(162, 168)(169, 176)(170, 175)(171, 177)(172, 179)(173, 178)(174, 180)(181, 188)(182, 187)(183, 189)(184, 232)(185, 233)(186, 234)(190, 245)(191, 247)(192, 249)(193, 251)(194, 250)(195, 244)(196, 254)(197, 255)(198, 239)(199, 252)(200, 238)(201, 240)(202, 253)(203, 246)(204, 248)(205, 235)(206, 237)(207, 236)(208, 257)(209, 258)(210, 256)(211, 260)(212, 261)(213, 259)(214, 229)(215, 231)(216, 230)(217, 227)(218, 226)(219, 228)(220, 263)(221, 264)(222, 262)(223, 241)(224, 242)(225, 243) local type(s) :: { ( 4^12 ) } Outer automorphisms :: reflexible Dual of E23.1129 Transitivity :: VT+ AT Graph:: bipartite v = 22 e = 132 f = 66 degree seq :: [ 12^22 ] E23.1131 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 2, 6}) Quotient :: edge^2 Aut^+ = S3 x D22 (small group id <132, 5>) Aut = C2 x S3 x D22 (small group id <264, 34>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, (R * Y3)^2, R * Y1 * R * Y2, Y2 * Y3 * Y2 * Y1 * Y3 * Y1, (Y2 * Y1)^3, (Y3 * Y2)^22 ] Map:: R = (1, 133, 4, 136)(2, 134, 6, 138)(3, 135, 8, 140)(5, 137, 12, 144)(7, 139, 15, 147)(9, 141, 17, 149)(10, 142, 18, 150)(11, 143, 19, 151)(13, 145, 21, 153)(14, 146, 22, 154)(16, 148, 23, 155)(20, 152, 27, 159)(24, 156, 31, 163)(25, 157, 32, 164)(26, 158, 33, 165)(28, 160, 34, 166)(29, 161, 35, 167)(30, 162, 36, 168)(37, 169, 43, 175)(38, 170, 44, 176)(39, 171, 45, 177)(40, 172, 46, 178)(41, 173, 47, 179)(42, 174, 48, 180)(49, 181, 55, 187)(50, 182, 56, 188)(51, 183, 57, 189)(52, 184, 85, 217)(53, 185, 87, 219)(54, 186, 89, 221)(58, 190, 91, 223)(59, 191, 93, 225)(60, 192, 95, 227)(61, 193, 97, 229)(62, 194, 99, 231)(63, 195, 101, 233)(64, 196, 103, 235)(65, 197, 105, 237)(66, 198, 107, 239)(67, 199, 109, 241)(68, 200, 111, 243)(69, 201, 113, 245)(70, 202, 115, 247)(71, 203, 117, 249)(72, 204, 119, 251)(73, 205, 121, 253)(74, 206, 123, 255)(75, 207, 125, 257)(76, 208, 127, 259)(77, 209, 129, 261)(78, 210, 131, 263)(79, 211, 128, 260)(80, 212, 132, 264)(81, 213, 130, 262)(82, 214, 122, 254)(83, 215, 126, 258)(84, 216, 124, 256)(86, 218, 116, 248)(88, 220, 120, 252)(90, 222, 118, 250)(92, 224, 108, 240)(94, 226, 102, 234)(96, 228, 104, 236)(98, 230, 110, 242)(100, 232, 112, 244)(106, 238, 114, 246)(265, 266)(267, 271)(268, 273)(269, 275)(270, 277)(272, 280)(274, 279)(276, 284)(278, 283)(281, 288)(282, 290)(285, 292)(286, 294)(287, 293)(289, 291)(295, 301)(296, 303)(297, 302)(298, 304)(299, 306)(300, 305)(307, 313)(308, 315)(309, 314)(310, 316)(311, 318)(312, 317)(319, 322)(320, 325)(321, 326)(323, 349)(324, 351)(327, 355)(328, 363)(329, 353)(330, 357)(331, 369)(332, 359)(333, 361)(334, 365)(335, 377)(336, 367)(337, 371)(338, 375)(339, 373)(340, 379)(341, 383)(342, 381)(343, 385)(344, 389)(345, 387)(346, 391)(347, 395)(348, 393)(350, 392)(352, 394)(354, 396)(356, 386)(358, 380)(360, 384)(362, 390)(364, 388)(366, 372)(368, 376)(370, 382)(374, 378)(397, 399)(398, 401)(400, 406)(402, 410)(403, 407)(404, 409)(405, 408)(411, 416)(412, 415)(413, 421)(414, 420)(417, 425)(418, 424)(419, 426)(422, 423)(427, 434)(428, 433)(429, 435)(430, 437)(431, 436)(432, 438)(439, 446)(440, 445)(441, 447)(442, 449)(443, 448)(444, 450)(451, 458)(452, 454)(453, 457)(455, 483)(456, 485)(459, 495)(460, 493)(461, 481)(462, 501)(463, 491)(464, 489)(465, 487)(466, 509)(467, 499)(468, 497)(469, 507)(470, 505)(471, 503)(472, 515)(473, 513)(474, 511)(475, 521)(476, 519)(477, 517)(478, 527)(479, 525)(480, 523)(482, 526)(484, 528)(486, 524)(488, 520)(490, 514)(492, 512)(494, 518)(496, 522)(498, 506)(500, 504)(502, 516)(508, 510) L = (1, 265)(2, 266)(3, 267)(4, 268)(5, 269)(6, 270)(7, 271)(8, 272)(9, 273)(10, 274)(11, 275)(12, 276)(13, 277)(14, 278)(15, 279)(16, 280)(17, 281)(18, 282)(19, 283)(20, 284)(21, 285)(22, 286)(23, 287)(24, 288)(25, 289)(26, 290)(27, 291)(28, 292)(29, 293)(30, 294)(31, 295)(32, 296)(33, 297)(34, 298)(35, 299)(36, 300)(37, 301)(38, 302)(39, 303)(40, 304)(41, 305)(42, 306)(43, 307)(44, 308)(45, 309)(46, 310)(47, 311)(48, 312)(49, 313)(50, 314)(51, 315)(52, 316)(53, 317)(54, 318)(55, 319)(56, 320)(57, 321)(58, 322)(59, 323)(60, 324)(61, 325)(62, 326)(63, 327)(64, 328)(65, 329)(66, 330)(67, 331)(68, 332)(69, 333)(70, 334)(71, 335)(72, 336)(73, 337)(74, 338)(75, 339)(76, 340)(77, 341)(78, 342)(79, 343)(80, 344)(81, 345)(82, 346)(83, 347)(84, 348)(85, 349)(86, 350)(87, 351)(88, 352)(89, 353)(90, 354)(91, 355)(92, 356)(93, 357)(94, 358)(95, 359)(96, 360)(97, 361)(98, 362)(99, 363)(100, 364)(101, 365)(102, 366)(103, 367)(104, 368)(105, 369)(106, 370)(107, 371)(108, 372)(109, 373)(110, 374)(111, 375)(112, 376)(113, 377)(114, 378)(115, 379)(116, 380)(117, 381)(118, 382)(119, 383)(120, 384)(121, 385)(122, 386)(123, 387)(124, 388)(125, 389)(126, 390)(127, 391)(128, 392)(129, 393)(130, 394)(131, 395)(132, 396)(133, 397)(134, 398)(135, 399)(136, 400)(137, 401)(138, 402)(139, 403)(140, 404)(141, 405)(142, 406)(143, 407)(144, 408)(145, 409)(146, 410)(147, 411)(148, 412)(149, 413)(150, 414)(151, 415)(152, 416)(153, 417)(154, 418)(155, 419)(156, 420)(157, 421)(158, 422)(159, 423)(160, 424)(161, 425)(162, 426)(163, 427)(164, 428)(165, 429)(166, 430)(167, 431)(168, 432)(169, 433)(170, 434)(171, 435)(172, 436)(173, 437)(174, 438)(175, 439)(176, 440)(177, 441)(178, 442)(179, 443)(180, 444)(181, 445)(182, 446)(183, 447)(184, 448)(185, 449)(186, 450)(187, 451)(188, 452)(189, 453)(190, 454)(191, 455)(192, 456)(193, 457)(194, 458)(195, 459)(196, 460)(197, 461)(198, 462)(199, 463)(200, 464)(201, 465)(202, 466)(203, 467)(204, 468)(205, 469)(206, 470)(207, 471)(208, 472)(209, 473)(210, 474)(211, 475)(212, 476)(213, 477)(214, 478)(215, 479)(216, 480)(217, 481)(218, 482)(219, 483)(220, 484)(221, 485)(222, 486)(223, 487)(224, 488)(225, 489)(226, 490)(227, 491)(228, 492)(229, 493)(230, 494)(231, 495)(232, 496)(233, 497)(234, 498)(235, 499)(236, 500)(237, 501)(238, 502)(239, 503)(240, 504)(241, 505)(242, 506)(243, 507)(244, 508)(245, 509)(246, 510)(247, 511)(248, 512)(249, 513)(250, 514)(251, 515)(252, 516)(253, 517)(254, 518)(255, 519)(256, 520)(257, 521)(258, 522)(259, 523)(260, 524)(261, 525)(262, 526)(263, 527)(264, 528) local type(s) :: { ( 24, 24 ), ( 24^4 ) } Outer automorphisms :: reflexible Dual of E23.1134 Graph:: simple bipartite v = 198 e = 264 f = 22 degree seq :: [ 2^132, 4^66 ] E23.1132 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 2, 6}) Quotient :: edge^2 Aut^+ = S3 x D22 (small group id <132, 5>) Aut = C2 x S3 x D22 (small group id <264, 34>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y1 * Y3^2, R * Y2 * R * Y1, (R * Y3)^2, Y1 * Y2 * Y3^4, Y3 * Y2 * Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ] Map:: R = (1, 133, 4, 136, 6, 138, 15, 147, 9, 141, 5, 137)(2, 134, 7, 139, 3, 135, 10, 142, 14, 146, 8, 140)(11, 143, 19, 151, 12, 144, 21, 153, 13, 145, 20, 152)(16, 148, 22, 154, 17, 149, 24, 156, 18, 150, 23, 155)(25, 157, 31, 163, 26, 158, 33, 165, 27, 159, 32, 164)(28, 160, 34, 166, 29, 161, 36, 168, 30, 162, 35, 167)(37, 169, 43, 175, 38, 170, 45, 177, 39, 171, 44, 176)(40, 172, 46, 178, 41, 173, 48, 180, 42, 174, 47, 179)(49, 181, 55, 187, 50, 182, 57, 189, 51, 183, 56, 188)(52, 184, 69, 201, 53, 185, 70, 202, 54, 186, 68, 200)(58, 190, 99, 231, 63, 195, 113, 245, 66, 198, 101, 233)(59, 191, 92, 224, 60, 192, 94, 226, 71, 203, 91, 223)(61, 193, 103, 235, 72, 204, 105, 237, 62, 194, 102, 234)(64, 196, 98, 230, 67, 199, 112, 244, 65, 197, 97, 229)(73, 205, 108, 240, 75, 207, 110, 242, 74, 206, 107, 239)(76, 208, 116, 248, 78, 210, 118, 250, 77, 209, 115, 247)(79, 211, 128, 260, 81, 213, 130, 262, 80, 212, 127, 259)(82, 214, 132, 264, 84, 216, 131, 263, 83, 215, 129, 261)(85, 217, 117, 249, 87, 219, 121, 253, 86, 218, 119, 251)(88, 220, 109, 241, 90, 222, 126, 258, 89, 221, 111, 243)(93, 225, 114, 246, 96, 228, 120, 252, 95, 227, 100, 232)(104, 236, 123, 255, 106, 238, 124, 256, 125, 257, 122, 254)(265, 266)(267, 273)(268, 275)(269, 276)(270, 278)(271, 280)(272, 281)(274, 282)(277, 279)(283, 289)(284, 290)(285, 291)(286, 292)(287, 293)(288, 294)(295, 301)(296, 302)(297, 303)(298, 304)(299, 305)(300, 306)(307, 313)(308, 314)(309, 315)(310, 316)(311, 317)(312, 318)(319, 355)(320, 356)(321, 358)(322, 361)(323, 366)(324, 369)(325, 371)(326, 372)(327, 376)(328, 379)(329, 380)(330, 362)(331, 382)(332, 363)(333, 365)(334, 377)(335, 367)(336, 374)(337, 391)(338, 392)(339, 394)(340, 393)(341, 396)(342, 395)(343, 383)(344, 381)(345, 385)(346, 375)(347, 373)(348, 390)(349, 364)(350, 378)(351, 384)(352, 368)(353, 370)(354, 389)(357, 386)(359, 387)(360, 388)(397, 399)(398, 402)(400, 408)(401, 409)(403, 413)(404, 414)(405, 410)(406, 412)(407, 411)(415, 422)(416, 423)(417, 421)(418, 425)(419, 426)(420, 424)(427, 434)(428, 435)(429, 433)(430, 437)(431, 438)(432, 436)(439, 446)(440, 447)(441, 445)(442, 449)(443, 450)(444, 448)(451, 488)(452, 490)(453, 487)(454, 494)(455, 499)(456, 498)(457, 504)(458, 506)(459, 493)(460, 512)(461, 514)(462, 508)(463, 511)(464, 509)(465, 495)(466, 497)(467, 501)(468, 503)(469, 524)(470, 526)(471, 523)(472, 528)(473, 527)(474, 525)(475, 513)(476, 517)(477, 515)(478, 505)(479, 522)(480, 507)(481, 510)(482, 516)(483, 496)(484, 502)(485, 521)(486, 500)(489, 519)(491, 520)(492, 518) L = (1, 265)(2, 266)(3, 267)(4, 268)(5, 269)(6, 270)(7, 271)(8, 272)(9, 273)(10, 274)(11, 275)(12, 276)(13, 277)(14, 278)(15, 279)(16, 280)(17, 281)(18, 282)(19, 283)(20, 284)(21, 285)(22, 286)(23, 287)(24, 288)(25, 289)(26, 290)(27, 291)(28, 292)(29, 293)(30, 294)(31, 295)(32, 296)(33, 297)(34, 298)(35, 299)(36, 300)(37, 301)(38, 302)(39, 303)(40, 304)(41, 305)(42, 306)(43, 307)(44, 308)(45, 309)(46, 310)(47, 311)(48, 312)(49, 313)(50, 314)(51, 315)(52, 316)(53, 317)(54, 318)(55, 319)(56, 320)(57, 321)(58, 322)(59, 323)(60, 324)(61, 325)(62, 326)(63, 327)(64, 328)(65, 329)(66, 330)(67, 331)(68, 332)(69, 333)(70, 334)(71, 335)(72, 336)(73, 337)(74, 338)(75, 339)(76, 340)(77, 341)(78, 342)(79, 343)(80, 344)(81, 345)(82, 346)(83, 347)(84, 348)(85, 349)(86, 350)(87, 351)(88, 352)(89, 353)(90, 354)(91, 355)(92, 356)(93, 357)(94, 358)(95, 359)(96, 360)(97, 361)(98, 362)(99, 363)(100, 364)(101, 365)(102, 366)(103, 367)(104, 368)(105, 369)(106, 370)(107, 371)(108, 372)(109, 373)(110, 374)(111, 375)(112, 376)(113, 377)(114, 378)(115, 379)(116, 380)(117, 381)(118, 382)(119, 383)(120, 384)(121, 385)(122, 386)(123, 387)(124, 388)(125, 389)(126, 390)(127, 391)(128, 392)(129, 393)(130, 394)(131, 395)(132, 396)(133, 397)(134, 398)(135, 399)(136, 400)(137, 401)(138, 402)(139, 403)(140, 404)(141, 405)(142, 406)(143, 407)(144, 408)(145, 409)(146, 410)(147, 411)(148, 412)(149, 413)(150, 414)(151, 415)(152, 416)(153, 417)(154, 418)(155, 419)(156, 420)(157, 421)(158, 422)(159, 423)(160, 424)(161, 425)(162, 426)(163, 427)(164, 428)(165, 429)(166, 430)(167, 431)(168, 432)(169, 433)(170, 434)(171, 435)(172, 436)(173, 437)(174, 438)(175, 439)(176, 440)(177, 441)(178, 442)(179, 443)(180, 444)(181, 445)(182, 446)(183, 447)(184, 448)(185, 449)(186, 450)(187, 451)(188, 452)(189, 453)(190, 454)(191, 455)(192, 456)(193, 457)(194, 458)(195, 459)(196, 460)(197, 461)(198, 462)(199, 463)(200, 464)(201, 465)(202, 466)(203, 467)(204, 468)(205, 469)(206, 470)(207, 471)(208, 472)(209, 473)(210, 474)(211, 475)(212, 476)(213, 477)(214, 478)(215, 479)(216, 480)(217, 481)(218, 482)(219, 483)(220, 484)(221, 485)(222, 486)(223, 487)(224, 488)(225, 489)(226, 490)(227, 491)(228, 492)(229, 493)(230, 494)(231, 495)(232, 496)(233, 497)(234, 498)(235, 499)(236, 500)(237, 501)(238, 502)(239, 503)(240, 504)(241, 505)(242, 506)(243, 507)(244, 508)(245, 509)(246, 510)(247, 511)(248, 512)(249, 513)(250, 514)(251, 515)(252, 516)(253, 517)(254, 518)(255, 519)(256, 520)(257, 521)(258, 522)(259, 523)(260, 524)(261, 525)(262, 526)(263, 527)(264, 528) local type(s) :: { ( 8, 8 ), ( 8^12 ) } Outer automorphisms :: reflexible Dual of E23.1133 Graph:: simple bipartite v = 154 e = 264 f = 66 degree seq :: [ 2^132, 12^22 ] E23.1133 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 2, 6}) Quotient :: loop^2 Aut^+ = S3 x D22 (small group id <132, 5>) Aut = C2 x S3 x D22 (small group id <264, 34>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, (R * Y3)^2, R * Y1 * R * Y2, Y2 * Y3 * Y2 * Y1 * Y3 * Y1, (Y2 * Y1)^3, (Y3 * Y2)^22 ] Map:: R = (1, 133, 265, 397, 4, 136, 268, 400)(2, 134, 266, 398, 6, 138, 270, 402)(3, 135, 267, 399, 8, 140, 272, 404)(5, 137, 269, 401, 12, 144, 276, 408)(7, 139, 271, 403, 15, 147, 279, 411)(9, 141, 273, 405, 17, 149, 281, 413)(10, 142, 274, 406, 18, 150, 282, 414)(11, 143, 275, 407, 19, 151, 283, 415)(13, 145, 277, 409, 21, 153, 285, 417)(14, 146, 278, 410, 22, 154, 286, 418)(16, 148, 280, 412, 23, 155, 287, 419)(20, 152, 284, 416, 27, 159, 291, 423)(24, 156, 288, 420, 31, 163, 295, 427)(25, 157, 289, 421, 32, 164, 296, 428)(26, 158, 290, 422, 33, 165, 297, 429)(28, 160, 292, 424, 34, 166, 298, 430)(29, 161, 293, 425, 35, 167, 299, 431)(30, 162, 294, 426, 36, 168, 300, 432)(37, 169, 301, 433, 43, 175, 307, 439)(38, 170, 302, 434, 44, 176, 308, 440)(39, 171, 303, 435, 45, 177, 309, 441)(40, 172, 304, 436, 46, 178, 310, 442)(41, 173, 305, 437, 47, 179, 311, 443)(42, 174, 306, 438, 48, 180, 312, 444)(49, 181, 313, 445, 55, 187, 319, 451)(50, 182, 314, 446, 56, 188, 320, 452)(51, 183, 315, 447, 57, 189, 321, 453)(52, 184, 316, 448, 91, 223, 355, 487)(53, 185, 317, 449, 93, 225, 357, 489)(54, 186, 318, 450, 95, 227, 359, 491)(58, 190, 322, 454, 99, 231, 363, 495)(59, 191, 323, 455, 103, 235, 367, 499)(60, 192, 324, 456, 106, 238, 370, 502)(61, 193, 325, 457, 105, 237, 369, 501)(62, 194, 326, 458, 110, 242, 374, 506)(63, 195, 327, 459, 109, 241, 373, 505)(64, 196, 328, 460, 113, 245, 377, 509)(65, 197, 329, 461, 97, 229, 361, 493)(66, 198, 330, 462, 116, 248, 380, 512)(67, 199, 331, 463, 118, 250, 382, 514)(68, 200, 332, 464, 120, 252, 384, 516)(69, 201, 333, 465, 101, 233, 365, 497)(70, 202, 334, 466, 123, 255, 387, 519)(71, 203, 335, 467, 125, 257, 389, 521)(72, 204, 336, 468, 102, 234, 366, 498)(73, 205, 337, 469, 128, 260, 392, 524)(74, 206, 338, 470, 98, 230, 362, 494)(75, 207, 339, 471, 131, 263, 395, 527)(76, 208, 340, 472, 129, 261, 393, 525)(77, 209, 341, 473, 124, 256, 388, 520)(78, 210, 342, 474, 126, 258, 390, 522)(79, 211, 343, 475, 132, 264, 396, 528)(80, 212, 344, 476, 117, 249, 381, 513)(81, 213, 345, 477, 119, 251, 383, 515)(82, 214, 346, 478, 121, 253, 385, 517)(83, 215, 347, 479, 104, 236, 368, 500)(84, 216, 348, 480, 107, 239, 371, 503)(85, 217, 349, 481, 114, 246, 378, 510)(86, 218, 350, 482, 100, 232, 364, 496)(87, 219, 351, 483, 111, 243, 375, 507)(88, 220, 352, 484, 127, 259, 391, 523)(89, 221, 353, 485, 108, 240, 372, 504)(90, 222, 354, 486, 122, 254, 386, 518)(92, 224, 356, 488, 130, 262, 394, 526)(94, 226, 358, 490, 112, 244, 376, 508)(96, 228, 360, 492, 115, 247, 379, 511) L = (1, 134)(2, 133)(3, 139)(4, 141)(5, 143)(6, 145)(7, 135)(8, 148)(9, 136)(10, 147)(11, 137)(12, 152)(13, 138)(14, 151)(15, 142)(16, 140)(17, 156)(18, 158)(19, 146)(20, 144)(21, 160)(22, 162)(23, 161)(24, 149)(25, 159)(26, 150)(27, 157)(28, 153)(29, 155)(30, 154)(31, 169)(32, 171)(33, 170)(34, 172)(35, 174)(36, 173)(37, 163)(38, 165)(39, 164)(40, 166)(41, 168)(42, 167)(43, 181)(44, 183)(45, 182)(46, 184)(47, 186)(48, 185)(49, 175)(50, 177)(51, 176)(52, 178)(53, 180)(54, 179)(55, 206)(56, 197)(57, 195)(58, 229)(59, 233)(60, 237)(61, 227)(62, 241)(63, 189)(64, 230)(65, 188)(66, 242)(67, 231)(68, 234)(69, 225)(70, 238)(71, 235)(72, 223)(73, 252)(74, 187)(75, 245)(76, 250)(77, 248)(78, 263)(79, 257)(80, 255)(81, 260)(82, 256)(83, 261)(84, 258)(85, 249)(86, 264)(87, 251)(88, 236)(89, 253)(90, 239)(91, 204)(92, 232)(93, 201)(94, 246)(95, 193)(96, 243)(97, 190)(98, 196)(99, 199)(100, 224)(101, 191)(102, 200)(103, 203)(104, 220)(105, 192)(106, 202)(107, 222)(108, 262)(109, 194)(110, 198)(111, 228)(112, 259)(113, 207)(114, 226)(115, 254)(116, 209)(117, 217)(118, 208)(119, 219)(120, 205)(121, 221)(122, 247)(123, 212)(124, 214)(125, 211)(126, 216)(127, 244)(128, 213)(129, 215)(130, 240)(131, 210)(132, 218)(265, 399)(266, 401)(267, 397)(268, 406)(269, 398)(270, 410)(271, 407)(272, 409)(273, 408)(274, 400)(275, 403)(276, 405)(277, 404)(278, 402)(279, 416)(280, 415)(281, 421)(282, 420)(283, 412)(284, 411)(285, 425)(286, 424)(287, 426)(288, 414)(289, 413)(290, 423)(291, 422)(292, 418)(293, 417)(294, 419)(295, 434)(296, 433)(297, 435)(298, 437)(299, 436)(300, 438)(301, 428)(302, 427)(303, 429)(304, 431)(305, 430)(306, 432)(307, 446)(308, 445)(309, 447)(310, 449)(311, 448)(312, 450)(313, 440)(314, 439)(315, 441)(316, 443)(317, 442)(318, 444)(319, 459)(320, 470)(321, 461)(322, 494)(323, 498)(324, 497)(325, 487)(326, 493)(327, 451)(328, 505)(329, 453)(330, 509)(331, 506)(332, 501)(333, 491)(334, 516)(335, 502)(336, 489)(337, 499)(338, 452)(339, 495)(340, 527)(341, 514)(342, 512)(343, 524)(344, 521)(345, 519)(346, 522)(347, 520)(348, 525)(349, 515)(350, 513)(351, 528)(352, 503)(353, 500)(354, 517)(355, 457)(356, 507)(357, 468)(358, 496)(359, 465)(360, 510)(361, 458)(362, 454)(363, 471)(364, 490)(365, 456)(366, 455)(367, 469)(368, 485)(369, 464)(370, 467)(371, 484)(372, 508)(373, 460)(374, 463)(375, 488)(376, 504)(377, 462)(378, 492)(379, 523)(380, 474)(381, 482)(382, 473)(383, 481)(384, 466)(385, 486)(386, 526)(387, 477)(388, 479)(389, 476)(390, 478)(391, 511)(392, 475)(393, 480)(394, 518)(395, 472)(396, 483) local type(s) :: { ( 2, 12, 2, 12, 2, 12, 2, 12 ) } Outer automorphisms :: reflexible Dual of E23.1132 Transitivity :: VT+ Graph:: bipartite v = 66 e = 264 f = 154 degree seq :: [ 8^66 ] E23.1134 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 2, 6}) Quotient :: loop^2 Aut^+ = S3 x D22 (small group id <132, 5>) Aut = C2 x S3 x D22 (small group id <264, 34>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y2 * Y1 * Y3^2, R * Y2 * R * Y1, (R * Y3)^2, Y1 * Y2 * Y3^4, Y3 * Y2 * Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ] Map:: R = (1, 133, 265, 397, 4, 136, 268, 400, 6, 138, 270, 402, 15, 147, 279, 411, 9, 141, 273, 405, 5, 137, 269, 401)(2, 134, 266, 398, 7, 139, 271, 403, 3, 135, 267, 399, 10, 142, 274, 406, 14, 146, 278, 410, 8, 140, 272, 404)(11, 143, 275, 407, 19, 151, 283, 415, 12, 144, 276, 408, 21, 153, 285, 417, 13, 145, 277, 409, 20, 152, 284, 416)(16, 148, 280, 412, 22, 154, 286, 418, 17, 149, 281, 413, 24, 156, 288, 420, 18, 150, 282, 414, 23, 155, 287, 419)(25, 157, 289, 421, 31, 163, 295, 427, 26, 158, 290, 422, 33, 165, 297, 429, 27, 159, 291, 423, 32, 164, 296, 428)(28, 160, 292, 424, 34, 166, 298, 430, 29, 161, 293, 425, 36, 168, 300, 432, 30, 162, 294, 426, 35, 167, 299, 431)(37, 169, 301, 433, 43, 175, 307, 439, 38, 170, 302, 434, 45, 177, 309, 441, 39, 171, 303, 435, 44, 176, 308, 440)(40, 172, 304, 436, 46, 178, 310, 442, 41, 173, 305, 437, 48, 180, 312, 444, 42, 174, 306, 438, 47, 179, 311, 443)(49, 181, 313, 445, 55, 187, 319, 451, 50, 182, 314, 446, 57, 189, 321, 453, 51, 183, 315, 447, 56, 188, 320, 452)(52, 184, 316, 448, 61, 193, 325, 457, 53, 185, 317, 449, 58, 190, 322, 454, 54, 186, 318, 450, 64, 196, 328, 460)(59, 191, 323, 455, 88, 220, 352, 484, 60, 192, 324, 456, 85, 217, 349, 481, 66, 198, 330, 462, 86, 218, 350, 482)(62, 194, 326, 458, 91, 223, 355, 487, 63, 195, 327, 459, 92, 224, 356, 488, 65, 197, 329, 461, 99, 231, 363, 495)(67, 199, 331, 463, 94, 226, 358, 490, 68, 200, 332, 464, 95, 227, 359, 491, 69, 201, 333, 465, 97, 229, 361, 493)(70, 202, 334, 466, 101, 233, 365, 497, 71, 203, 335, 467, 102, 234, 366, 498, 72, 204, 336, 468, 104, 236, 368, 500)(73, 205, 337, 469, 109, 241, 373, 505, 74, 206, 338, 470, 110, 242, 374, 506, 75, 207, 339, 471, 112, 244, 376, 508)(76, 208, 340, 472, 115, 247, 379, 511, 77, 209, 341, 473, 116, 248, 380, 512, 78, 210, 342, 474, 118, 250, 382, 514)(79, 211, 343, 475, 121, 253, 385, 517, 80, 212, 344, 476, 122, 254, 386, 518, 81, 213, 345, 477, 124, 256, 388, 520)(82, 214, 346, 478, 127, 259, 391, 523, 83, 215, 347, 479, 128, 260, 392, 524, 84, 216, 348, 480, 130, 262, 394, 526)(87, 219, 351, 483, 132, 264, 396, 528, 89, 221, 353, 485, 131, 263, 395, 527, 90, 222, 354, 486, 129, 261, 393, 525)(93, 225, 357, 489, 123, 255, 387, 519, 100, 232, 364, 496, 126, 258, 390, 522, 106, 238, 370, 502, 125, 257, 389, 521)(96, 228, 360, 492, 120, 252, 384, 516, 108, 240, 372, 504, 119, 251, 383, 515, 98, 230, 362, 494, 117, 249, 381, 513)(103, 235, 367, 499, 114, 246, 378, 510, 107, 239, 371, 503, 113, 245, 377, 509, 105, 237, 369, 501, 111, 243, 375, 507) L = (1, 134)(2, 133)(3, 141)(4, 143)(5, 144)(6, 146)(7, 148)(8, 149)(9, 135)(10, 150)(11, 136)(12, 137)(13, 147)(14, 138)(15, 145)(16, 139)(17, 140)(18, 142)(19, 157)(20, 158)(21, 159)(22, 160)(23, 161)(24, 162)(25, 151)(26, 152)(27, 153)(28, 154)(29, 155)(30, 156)(31, 169)(32, 170)(33, 171)(34, 172)(35, 173)(36, 174)(37, 163)(38, 164)(39, 165)(40, 166)(41, 167)(42, 168)(43, 181)(44, 182)(45, 183)(46, 184)(47, 185)(48, 186)(49, 175)(50, 176)(51, 177)(52, 178)(53, 179)(54, 180)(55, 217)(56, 218)(57, 220)(58, 223)(59, 226)(60, 229)(61, 224)(62, 233)(63, 236)(64, 231)(65, 234)(66, 227)(67, 241)(68, 244)(69, 242)(70, 247)(71, 250)(72, 248)(73, 253)(74, 256)(75, 254)(76, 259)(77, 262)(78, 260)(79, 264)(80, 261)(81, 263)(82, 258)(83, 255)(84, 257)(85, 187)(86, 188)(87, 251)(88, 189)(89, 252)(90, 249)(91, 190)(92, 193)(93, 243)(94, 191)(95, 198)(96, 237)(97, 192)(98, 235)(99, 196)(100, 245)(101, 194)(102, 197)(103, 230)(104, 195)(105, 228)(106, 246)(107, 240)(108, 239)(109, 199)(110, 201)(111, 225)(112, 200)(113, 232)(114, 238)(115, 202)(116, 204)(117, 222)(118, 203)(119, 219)(120, 221)(121, 205)(122, 207)(123, 215)(124, 206)(125, 216)(126, 214)(127, 208)(128, 210)(129, 212)(130, 209)(131, 213)(132, 211)(265, 399)(266, 402)(267, 397)(268, 408)(269, 409)(270, 398)(271, 413)(272, 414)(273, 410)(274, 412)(275, 411)(276, 400)(277, 401)(278, 405)(279, 407)(280, 406)(281, 403)(282, 404)(283, 422)(284, 423)(285, 421)(286, 425)(287, 426)(288, 424)(289, 417)(290, 415)(291, 416)(292, 420)(293, 418)(294, 419)(295, 434)(296, 435)(297, 433)(298, 437)(299, 438)(300, 436)(301, 429)(302, 427)(303, 428)(304, 432)(305, 430)(306, 431)(307, 446)(308, 447)(309, 445)(310, 449)(311, 450)(312, 448)(313, 441)(314, 439)(315, 440)(316, 444)(317, 442)(318, 443)(319, 482)(320, 484)(321, 481)(322, 488)(323, 491)(324, 490)(325, 495)(326, 498)(327, 497)(328, 487)(329, 500)(330, 493)(331, 506)(332, 505)(333, 508)(334, 512)(335, 511)(336, 514)(337, 518)(338, 517)(339, 520)(340, 524)(341, 523)(342, 526)(343, 527)(344, 528)(345, 525)(346, 521)(347, 522)(348, 519)(349, 453)(350, 451)(351, 513)(352, 452)(353, 515)(354, 516)(355, 460)(356, 454)(357, 510)(358, 456)(359, 455)(360, 499)(361, 462)(362, 503)(363, 457)(364, 507)(365, 459)(366, 458)(367, 492)(368, 461)(369, 504)(370, 509)(371, 494)(372, 501)(373, 464)(374, 463)(375, 496)(376, 465)(377, 502)(378, 489)(379, 467)(380, 466)(381, 483)(382, 468)(383, 485)(384, 486)(385, 470)(386, 469)(387, 480)(388, 471)(389, 478)(390, 479)(391, 473)(392, 472)(393, 477)(394, 474)(395, 475)(396, 476) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) } Outer automorphisms :: reflexible Dual of E23.1131 Transitivity :: VT+ Graph:: bipartite v = 22 e = 264 f = 198 degree seq :: [ 24^22 ] E23.1135 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 6}) Quotient :: dipole Aut^+ = S3 x D22 (small group id <132, 5>) Aut = C2 x S3 x D22 (small group id <264, 34>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^2, (Y2 * Y3)^2, (R * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y1 * Y3 * Y1 * Y2)^2, (Y3 * Y1)^6, Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y3 * Y1 * Y2 * Y1 * Y2 * Y1 * Y3 * Y2 * Y1 * Y3 * Y2 ] Map:: polytopal non-degenerate R = (1, 133, 2, 134)(3, 135, 7, 139)(4, 136, 9, 141)(5, 137, 10, 142)(6, 138, 12, 144)(8, 140, 15, 147)(11, 143, 20, 152)(13, 145, 23, 155)(14, 146, 21, 153)(16, 148, 19, 151)(17, 149, 28, 160)(18, 150, 29, 161)(22, 154, 34, 166)(24, 156, 37, 169)(25, 157, 36, 168)(26, 158, 39, 171)(27, 159, 40, 172)(30, 162, 44, 176)(31, 163, 43, 175)(32, 164, 46, 178)(33, 165, 47, 179)(35, 167, 49, 181)(38, 170, 53, 185)(41, 173, 48, 180)(42, 174, 57, 189)(45, 177, 61, 193)(50, 182, 67, 199)(51, 183, 66, 198)(52, 184, 63, 195)(54, 186, 64, 196)(55, 187, 60, 192)(56, 188, 62, 194)(58, 190, 74, 206)(59, 191, 73, 205)(65, 197, 79, 211)(68, 200, 83, 215)(69, 201, 82, 214)(70, 202, 78, 210)(71, 203, 77, 209)(72, 204, 85, 217)(75, 207, 89, 221)(76, 208, 88, 220)(80, 212, 93, 225)(81, 213, 92, 224)(84, 216, 96, 228)(86, 218, 99, 231)(87, 219, 98, 230)(90, 222, 102, 234)(91, 223, 103, 235)(94, 226, 107, 239)(95, 227, 106, 238)(97, 229, 109, 241)(100, 232, 113, 245)(101, 233, 112, 244)(104, 236, 117, 249)(105, 237, 116, 248)(108, 240, 120, 252)(110, 242, 123, 255)(111, 243, 122, 254)(114, 246, 126, 258)(115, 247, 127, 259)(118, 250, 131, 263)(119, 251, 130, 262)(121, 253, 132, 264)(124, 256, 128, 260)(125, 257, 129, 261)(265, 397, 267, 399)(266, 398, 269, 401)(268, 400, 272, 404)(270, 402, 275, 407)(271, 403, 277, 409)(273, 405, 280, 412)(274, 406, 282, 414)(276, 408, 285, 417)(278, 410, 288, 420)(279, 411, 289, 421)(281, 413, 291, 423)(283, 415, 294, 426)(284, 416, 295, 427)(286, 418, 297, 429)(287, 419, 299, 431)(290, 422, 302, 434)(292, 424, 303, 435)(293, 425, 306, 438)(296, 428, 309, 441)(298, 430, 310, 442)(300, 432, 314, 446)(301, 433, 315, 447)(304, 436, 319, 451)(305, 437, 318, 450)(307, 439, 322, 454)(308, 440, 323, 455)(311, 443, 327, 459)(312, 444, 326, 458)(313, 445, 329, 461)(316, 448, 332, 464)(317, 449, 333, 465)(320, 452, 335, 467)(321, 453, 336, 468)(324, 456, 339, 471)(325, 457, 340, 472)(328, 460, 342, 474)(330, 462, 344, 476)(331, 463, 345, 477)(334, 466, 348, 480)(337, 469, 350, 482)(338, 470, 351, 483)(341, 473, 354, 486)(343, 475, 355, 487)(346, 478, 358, 490)(347, 479, 359, 491)(349, 481, 361, 493)(352, 484, 364, 496)(353, 485, 365, 497)(356, 488, 368, 500)(357, 489, 369, 501)(360, 492, 372, 504)(362, 494, 374, 506)(363, 495, 375, 507)(366, 498, 378, 510)(367, 499, 379, 511)(370, 502, 382, 514)(371, 503, 383, 515)(373, 505, 385, 517)(376, 508, 388, 520)(377, 509, 389, 521)(380, 512, 392, 524)(381, 513, 393, 525)(384, 516, 396, 528)(386, 518, 395, 527)(387, 519, 394, 526)(390, 522, 391, 523) L = (1, 268)(2, 270)(3, 272)(4, 265)(5, 275)(6, 266)(7, 278)(8, 267)(9, 281)(10, 283)(11, 269)(12, 286)(13, 288)(14, 271)(15, 290)(16, 291)(17, 273)(18, 294)(19, 274)(20, 296)(21, 297)(22, 276)(23, 300)(24, 277)(25, 302)(26, 279)(27, 280)(28, 305)(29, 307)(30, 282)(31, 309)(32, 284)(33, 285)(34, 312)(35, 314)(36, 287)(37, 316)(38, 289)(39, 318)(40, 320)(41, 292)(42, 322)(43, 293)(44, 324)(45, 295)(46, 326)(47, 328)(48, 298)(49, 330)(50, 299)(51, 332)(52, 301)(53, 334)(54, 303)(55, 335)(56, 304)(57, 337)(58, 306)(59, 339)(60, 308)(61, 341)(62, 310)(63, 342)(64, 311)(65, 344)(66, 313)(67, 346)(68, 315)(69, 348)(70, 317)(71, 319)(72, 350)(73, 321)(74, 352)(75, 323)(76, 354)(77, 325)(78, 327)(79, 356)(80, 329)(81, 358)(82, 331)(83, 360)(84, 333)(85, 362)(86, 336)(87, 364)(88, 338)(89, 366)(90, 340)(91, 368)(92, 343)(93, 370)(94, 345)(95, 372)(96, 347)(97, 374)(98, 349)(99, 376)(100, 351)(101, 378)(102, 353)(103, 380)(104, 355)(105, 382)(106, 357)(107, 384)(108, 359)(109, 386)(110, 361)(111, 388)(112, 363)(113, 390)(114, 365)(115, 392)(116, 367)(117, 394)(118, 369)(119, 396)(120, 371)(121, 395)(122, 373)(123, 393)(124, 375)(125, 391)(126, 377)(127, 389)(128, 379)(129, 387)(130, 381)(131, 385)(132, 383)(133, 397)(134, 398)(135, 399)(136, 400)(137, 401)(138, 402)(139, 403)(140, 404)(141, 405)(142, 406)(143, 407)(144, 408)(145, 409)(146, 410)(147, 411)(148, 412)(149, 413)(150, 414)(151, 415)(152, 416)(153, 417)(154, 418)(155, 419)(156, 420)(157, 421)(158, 422)(159, 423)(160, 424)(161, 425)(162, 426)(163, 427)(164, 428)(165, 429)(166, 430)(167, 431)(168, 432)(169, 433)(170, 434)(171, 435)(172, 436)(173, 437)(174, 438)(175, 439)(176, 440)(177, 441)(178, 442)(179, 443)(180, 444)(181, 445)(182, 446)(183, 447)(184, 448)(185, 449)(186, 450)(187, 451)(188, 452)(189, 453)(190, 454)(191, 455)(192, 456)(193, 457)(194, 458)(195, 459)(196, 460)(197, 461)(198, 462)(199, 463)(200, 464)(201, 465)(202, 466)(203, 467)(204, 468)(205, 469)(206, 470)(207, 471)(208, 472)(209, 473)(210, 474)(211, 475)(212, 476)(213, 477)(214, 478)(215, 479)(216, 480)(217, 481)(218, 482)(219, 483)(220, 484)(221, 485)(222, 486)(223, 487)(224, 488)(225, 489)(226, 490)(227, 491)(228, 492)(229, 493)(230, 494)(231, 495)(232, 496)(233, 497)(234, 498)(235, 499)(236, 500)(237, 501)(238, 502)(239, 503)(240, 504)(241, 505)(242, 506)(243, 507)(244, 508)(245, 509)(246, 510)(247, 511)(248, 512)(249, 513)(250, 514)(251, 515)(252, 516)(253, 517)(254, 518)(255, 519)(256, 520)(257, 521)(258, 522)(259, 523)(260, 524)(261, 525)(262, 526)(263, 527)(264, 528) local type(s) :: { ( 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E23.1139 Graph:: simple bipartite v = 132 e = 264 f = 88 degree seq :: [ 4^132 ] E23.1136 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 6}) Quotient :: dipole Aut^+ = S3 x D22 (small group id <132, 5>) Aut = C2 x S3 x D22 (small group id <264, 34>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2 * Y3^-1 * Y1 * Y2 * Y1 * Y3, (Y3^2 * Y1)^2, Y1 * Y3 * Y1 * Y2 * Y3^-1 * Y1 * Y3, Y3^22, Y3^-10 * Y2 * Y3^2 * Y1 * Y3^-8 * Y2 * Y1 ] Map:: non-degenerate R = (1, 133, 2, 134)(3, 135, 9, 141)(4, 136, 12, 144)(5, 137, 14, 146)(6, 138, 16, 148)(7, 139, 19, 151)(8, 140, 21, 153)(10, 142, 24, 156)(11, 143, 26, 158)(13, 145, 22, 154)(15, 147, 20, 152)(17, 149, 29, 161)(18, 150, 28, 160)(23, 155, 31, 163)(25, 157, 37, 169)(27, 159, 33, 165)(30, 162, 42, 174)(32, 164, 38, 170)(34, 166, 45, 177)(35, 167, 39, 171)(36, 168, 41, 173)(40, 172, 51, 183)(43, 175, 48, 180)(44, 176, 47, 179)(46, 178, 54, 186)(49, 181, 50, 182)(52, 184, 61, 193)(53, 185, 57, 189)(55, 187, 66, 198)(56, 188, 62, 194)(58, 190, 69, 201)(59, 191, 63, 195)(60, 192, 65, 197)(64, 196, 75, 207)(67, 199, 72, 204)(68, 200, 71, 203)(70, 202, 78, 210)(73, 205, 74, 206)(76, 208, 85, 217)(77, 209, 81, 213)(79, 211, 90, 222)(80, 212, 86, 218)(82, 214, 93, 225)(83, 215, 87, 219)(84, 216, 89, 221)(88, 220, 99, 231)(91, 223, 96, 228)(92, 224, 95, 227)(94, 226, 102, 234)(97, 229, 98, 230)(100, 232, 109, 241)(101, 233, 105, 237)(103, 235, 114, 246)(104, 236, 110, 242)(106, 238, 117, 249)(107, 239, 111, 243)(108, 240, 113, 245)(112, 244, 123, 255)(115, 247, 120, 252)(116, 248, 119, 251)(118, 250, 126, 258)(121, 253, 122, 254)(124, 256, 129, 261)(125, 257, 128, 260)(127, 259, 131, 263)(130, 262, 132, 264)(265, 397, 267, 399)(266, 398, 270, 402)(268, 400, 275, 407)(269, 401, 274, 406)(271, 403, 282, 414)(272, 404, 281, 413)(273, 405, 284, 416)(276, 408, 291, 423)(277, 409, 280, 412)(278, 410, 290, 422)(279, 411, 289, 421)(283, 415, 295, 427)(285, 417, 292, 424)(286, 418, 298, 430)(287, 419, 299, 431)(288, 420, 302, 434)(293, 425, 305, 437)(294, 426, 297, 429)(296, 428, 304, 436)(300, 432, 310, 442)(301, 433, 311, 443)(303, 435, 314, 446)(306, 438, 317, 449)(307, 439, 309, 441)(308, 440, 316, 448)(312, 444, 322, 454)(313, 445, 323, 455)(315, 447, 326, 458)(318, 450, 329, 461)(319, 451, 321, 453)(320, 452, 328, 460)(324, 456, 334, 466)(325, 457, 335, 467)(327, 459, 338, 470)(330, 462, 341, 473)(331, 463, 333, 465)(332, 464, 340, 472)(336, 468, 346, 478)(337, 469, 347, 479)(339, 471, 350, 482)(342, 474, 353, 485)(343, 475, 345, 477)(344, 476, 352, 484)(348, 480, 358, 490)(349, 481, 359, 491)(351, 483, 362, 494)(354, 486, 365, 497)(355, 487, 357, 489)(356, 488, 364, 496)(360, 492, 370, 502)(361, 493, 371, 503)(363, 495, 374, 506)(366, 498, 377, 509)(367, 499, 369, 501)(368, 500, 376, 508)(372, 504, 382, 514)(373, 505, 383, 515)(375, 507, 386, 518)(378, 510, 389, 521)(379, 511, 381, 513)(380, 512, 388, 520)(384, 516, 393, 525)(385, 517, 394, 526)(387, 519, 395, 527)(390, 522, 396, 528)(391, 523, 392, 524) L = (1, 268)(2, 271)(3, 274)(4, 277)(5, 265)(6, 281)(7, 284)(8, 266)(9, 282)(10, 289)(11, 267)(12, 292)(13, 294)(14, 295)(15, 269)(16, 275)(17, 298)(18, 270)(19, 290)(20, 299)(21, 291)(22, 272)(23, 273)(24, 283)(25, 304)(26, 285)(27, 305)(28, 278)(29, 276)(30, 307)(31, 302)(32, 279)(33, 280)(34, 310)(35, 311)(36, 286)(37, 287)(38, 314)(39, 288)(40, 316)(41, 317)(42, 293)(43, 319)(44, 296)(45, 297)(46, 322)(47, 323)(48, 300)(49, 301)(50, 326)(51, 303)(52, 328)(53, 329)(54, 306)(55, 331)(56, 308)(57, 309)(58, 334)(59, 335)(60, 312)(61, 313)(62, 338)(63, 315)(64, 340)(65, 341)(66, 318)(67, 343)(68, 320)(69, 321)(70, 346)(71, 347)(72, 324)(73, 325)(74, 350)(75, 327)(76, 352)(77, 353)(78, 330)(79, 355)(80, 332)(81, 333)(82, 358)(83, 359)(84, 336)(85, 337)(86, 362)(87, 339)(88, 364)(89, 365)(90, 342)(91, 367)(92, 344)(93, 345)(94, 370)(95, 371)(96, 348)(97, 349)(98, 374)(99, 351)(100, 376)(101, 377)(102, 354)(103, 379)(104, 356)(105, 357)(106, 382)(107, 383)(108, 360)(109, 361)(110, 386)(111, 363)(112, 388)(113, 389)(114, 366)(115, 391)(116, 368)(117, 369)(118, 393)(119, 394)(120, 372)(121, 373)(122, 395)(123, 375)(124, 392)(125, 396)(126, 378)(127, 380)(128, 381)(129, 385)(130, 384)(131, 390)(132, 387)(133, 397)(134, 398)(135, 399)(136, 400)(137, 401)(138, 402)(139, 403)(140, 404)(141, 405)(142, 406)(143, 407)(144, 408)(145, 409)(146, 410)(147, 411)(148, 412)(149, 413)(150, 414)(151, 415)(152, 416)(153, 417)(154, 418)(155, 419)(156, 420)(157, 421)(158, 422)(159, 423)(160, 424)(161, 425)(162, 426)(163, 427)(164, 428)(165, 429)(166, 430)(167, 431)(168, 432)(169, 433)(170, 434)(171, 435)(172, 436)(173, 437)(174, 438)(175, 439)(176, 440)(177, 441)(178, 442)(179, 443)(180, 444)(181, 445)(182, 446)(183, 447)(184, 448)(185, 449)(186, 450)(187, 451)(188, 452)(189, 453)(190, 454)(191, 455)(192, 456)(193, 457)(194, 458)(195, 459)(196, 460)(197, 461)(198, 462)(199, 463)(200, 464)(201, 465)(202, 466)(203, 467)(204, 468)(205, 469)(206, 470)(207, 471)(208, 472)(209, 473)(210, 474)(211, 475)(212, 476)(213, 477)(214, 478)(215, 479)(216, 480)(217, 481)(218, 482)(219, 483)(220, 484)(221, 485)(222, 486)(223, 487)(224, 488)(225, 489)(226, 490)(227, 491)(228, 492)(229, 493)(230, 494)(231, 495)(232, 496)(233, 497)(234, 498)(235, 499)(236, 500)(237, 501)(238, 502)(239, 503)(240, 504)(241, 505)(242, 506)(243, 507)(244, 508)(245, 509)(246, 510)(247, 511)(248, 512)(249, 513)(250, 514)(251, 515)(252, 516)(253, 517)(254, 518)(255, 519)(256, 520)(257, 521)(258, 522)(259, 523)(260, 524)(261, 525)(262, 526)(263, 527)(264, 528) local type(s) :: { ( 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E23.1140 Graph:: simple bipartite v = 132 e = 264 f = 88 degree seq :: [ 4^132 ] E23.1137 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 6}) Quotient :: dipole Aut^+ = S3 x D22 (small group id <132, 5>) Aut = C2 x S3 x D22 (small group id <264, 34>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y1 * Y3 * Y2 * Y1)^2, (Y3 * Y1 * Y2 * Y1 * Y2 * Y1)^2, (Y3 * Y1)^6, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y3 * Y1 * Y2 * Y3 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 ] Map:: polytopal non-degenerate R = (1, 133, 2, 134)(3, 135, 7, 139)(4, 136, 9, 141)(5, 137, 10, 142)(6, 138, 12, 144)(8, 140, 15, 147)(11, 143, 20, 152)(13, 145, 23, 155)(14, 146, 25, 157)(16, 148, 28, 160)(17, 149, 30, 162)(18, 150, 31, 163)(19, 151, 33, 165)(21, 153, 36, 168)(22, 154, 38, 170)(24, 156, 41, 173)(26, 158, 44, 176)(27, 159, 37, 169)(29, 161, 35, 167)(32, 164, 50, 182)(34, 166, 53, 185)(39, 171, 57, 189)(40, 172, 55, 187)(42, 174, 51, 183)(43, 175, 56, 188)(45, 177, 60, 192)(46, 178, 49, 181)(47, 179, 52, 184)(48, 180, 64, 196)(54, 186, 67, 199)(58, 190, 73, 205)(59, 191, 74, 206)(61, 193, 72, 204)(62, 194, 70, 202)(63, 195, 69, 201)(65, 197, 79, 211)(66, 198, 80, 212)(68, 200, 78, 210)(71, 203, 83, 215)(75, 207, 86, 218)(76, 208, 88, 220)(77, 209, 89, 221)(81, 213, 92, 224)(82, 214, 94, 226)(84, 216, 97, 229)(85, 217, 98, 230)(87, 219, 96, 228)(90, 222, 103, 235)(91, 223, 104, 236)(93, 225, 102, 234)(95, 227, 107, 239)(99, 231, 110, 242)(100, 232, 112, 244)(101, 233, 113, 245)(105, 237, 116, 248)(106, 238, 118, 250)(108, 240, 121, 253)(109, 241, 122, 254)(111, 243, 120, 252)(114, 246, 127, 259)(115, 247, 128, 260)(117, 249, 126, 258)(119, 251, 129, 261)(123, 255, 125, 257)(124, 256, 131, 263)(130, 262, 132, 264)(265, 397, 267, 399)(266, 398, 269, 401)(268, 400, 272, 404)(270, 402, 275, 407)(271, 403, 277, 409)(273, 405, 280, 412)(274, 406, 282, 414)(276, 408, 285, 417)(278, 410, 288, 420)(279, 411, 290, 422)(281, 413, 293, 425)(283, 415, 296, 428)(284, 416, 298, 430)(286, 418, 301, 433)(287, 419, 303, 435)(289, 421, 306, 438)(291, 423, 309, 441)(292, 424, 310, 442)(294, 426, 307, 439)(295, 427, 312, 444)(297, 429, 315, 447)(299, 431, 318, 450)(300, 432, 319, 451)(302, 434, 316, 448)(304, 436, 322, 454)(305, 437, 323, 455)(308, 440, 325, 457)(311, 443, 327, 459)(313, 445, 329, 461)(314, 446, 330, 462)(317, 449, 332, 464)(320, 452, 334, 466)(321, 453, 335, 467)(324, 456, 339, 471)(326, 458, 340, 472)(328, 460, 341, 473)(331, 463, 345, 477)(333, 465, 346, 478)(336, 468, 348, 480)(337, 469, 349, 481)(338, 470, 351, 483)(342, 474, 354, 486)(343, 475, 355, 487)(344, 476, 357, 489)(347, 479, 359, 491)(350, 482, 363, 495)(352, 484, 364, 496)(353, 485, 365, 497)(356, 488, 369, 501)(358, 490, 370, 502)(360, 492, 372, 504)(361, 493, 373, 505)(362, 494, 375, 507)(366, 498, 378, 510)(367, 499, 379, 511)(368, 500, 381, 513)(371, 503, 383, 515)(374, 506, 387, 519)(376, 508, 388, 520)(377, 509, 389, 521)(380, 512, 393, 525)(382, 514, 394, 526)(384, 516, 391, 523)(385, 517, 390, 522)(386, 518, 392, 524)(395, 527, 396, 528) L = (1, 268)(2, 270)(3, 272)(4, 265)(5, 275)(6, 266)(7, 278)(8, 267)(9, 281)(10, 283)(11, 269)(12, 286)(13, 288)(14, 271)(15, 291)(16, 293)(17, 273)(18, 296)(19, 274)(20, 299)(21, 301)(22, 276)(23, 304)(24, 277)(25, 307)(26, 309)(27, 279)(28, 311)(29, 280)(30, 306)(31, 313)(32, 282)(33, 316)(34, 318)(35, 284)(36, 320)(37, 285)(38, 315)(39, 322)(40, 287)(41, 324)(42, 294)(43, 289)(44, 326)(45, 290)(46, 327)(47, 292)(48, 329)(49, 295)(50, 331)(51, 302)(52, 297)(53, 333)(54, 298)(55, 334)(56, 300)(57, 336)(58, 303)(59, 339)(60, 305)(61, 340)(62, 308)(63, 310)(64, 342)(65, 312)(66, 345)(67, 314)(68, 346)(69, 317)(70, 319)(71, 348)(72, 321)(73, 350)(74, 352)(75, 323)(76, 325)(77, 354)(78, 328)(79, 356)(80, 358)(81, 330)(82, 332)(83, 360)(84, 335)(85, 363)(86, 337)(87, 364)(88, 338)(89, 366)(90, 341)(91, 369)(92, 343)(93, 370)(94, 344)(95, 372)(96, 347)(97, 374)(98, 376)(99, 349)(100, 351)(101, 378)(102, 353)(103, 380)(104, 382)(105, 355)(106, 357)(107, 384)(108, 359)(109, 387)(110, 361)(111, 388)(112, 362)(113, 390)(114, 365)(115, 393)(116, 367)(117, 394)(118, 368)(119, 391)(120, 371)(121, 389)(122, 395)(123, 373)(124, 375)(125, 385)(126, 377)(127, 383)(128, 396)(129, 379)(130, 381)(131, 386)(132, 392)(133, 397)(134, 398)(135, 399)(136, 400)(137, 401)(138, 402)(139, 403)(140, 404)(141, 405)(142, 406)(143, 407)(144, 408)(145, 409)(146, 410)(147, 411)(148, 412)(149, 413)(150, 414)(151, 415)(152, 416)(153, 417)(154, 418)(155, 419)(156, 420)(157, 421)(158, 422)(159, 423)(160, 424)(161, 425)(162, 426)(163, 427)(164, 428)(165, 429)(166, 430)(167, 431)(168, 432)(169, 433)(170, 434)(171, 435)(172, 436)(173, 437)(174, 438)(175, 439)(176, 440)(177, 441)(178, 442)(179, 443)(180, 444)(181, 445)(182, 446)(183, 447)(184, 448)(185, 449)(186, 450)(187, 451)(188, 452)(189, 453)(190, 454)(191, 455)(192, 456)(193, 457)(194, 458)(195, 459)(196, 460)(197, 461)(198, 462)(199, 463)(200, 464)(201, 465)(202, 466)(203, 467)(204, 468)(205, 469)(206, 470)(207, 471)(208, 472)(209, 473)(210, 474)(211, 475)(212, 476)(213, 477)(214, 478)(215, 479)(216, 480)(217, 481)(218, 482)(219, 483)(220, 484)(221, 485)(222, 486)(223, 487)(224, 488)(225, 489)(226, 490)(227, 491)(228, 492)(229, 493)(230, 494)(231, 495)(232, 496)(233, 497)(234, 498)(235, 499)(236, 500)(237, 501)(238, 502)(239, 503)(240, 504)(241, 505)(242, 506)(243, 507)(244, 508)(245, 509)(246, 510)(247, 511)(248, 512)(249, 513)(250, 514)(251, 515)(252, 516)(253, 517)(254, 518)(255, 519)(256, 520)(257, 521)(258, 522)(259, 523)(260, 524)(261, 525)(262, 526)(263, 527)(264, 528) local type(s) :: { ( 4, 12, 4, 12 ) } Outer automorphisms :: reflexible Dual of E23.1138 Graph:: simple bipartite v = 132 e = 264 f = 88 degree seq :: [ 4^132 ] E23.1138 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 6}) Quotient :: dipole Aut^+ = S3 x D22 (small group id <132, 5>) Aut = C2 x S3 x D22 (small group id <264, 34>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (R * Y2)^2, (Y1^-1 * Y3)^2, (R * Y1)^2, (Y3 * Y2)^2, (R * Y3)^2, Y1^6, Y1^-1 * Y2 * Y1^2 * Y2 * Y1^-1, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1 ] Map:: polytopal non-degenerate R = (1, 133, 2, 134, 6, 138, 15, 147, 14, 146, 5, 137)(3, 135, 9, 141, 16, 148, 31, 163, 25, 157, 11, 143)(4, 136, 12, 144, 26, 158, 30, 162, 17, 149, 8, 140)(7, 139, 18, 150, 29, 161, 28, 160, 13, 145, 20, 152)(10, 142, 23, 155, 40, 172, 47, 179, 32, 164, 22, 154)(19, 151, 35, 167, 27, 159, 43, 175, 45, 177, 34, 166)(21, 153, 37, 169, 46, 178, 42, 174, 24, 156, 39, 171)(33, 165, 48, 180, 44, 176, 52, 184, 36, 168, 50, 182)(38, 170, 55, 187, 41, 173, 57, 189, 60, 192, 54, 186)(49, 181, 63, 195, 51, 183, 65, 197, 59, 191, 62, 194)(53, 185, 67, 199, 58, 190, 71, 203, 56, 188, 69, 201)(61, 193, 73, 205, 66, 198, 77, 209, 64, 196, 75, 207)(68, 200, 81, 213, 70, 202, 83, 215, 72, 204, 80, 212)(74, 206, 87, 219, 76, 208, 89, 221, 78, 210, 86, 218)(79, 211, 91, 223, 84, 216, 95, 227, 82, 214, 93, 225)(85, 217, 97, 229, 90, 222, 101, 233, 88, 220, 99, 231)(92, 224, 105, 237, 94, 226, 107, 239, 96, 228, 104, 236)(98, 230, 111, 243, 100, 232, 113, 245, 102, 234, 110, 242)(103, 235, 115, 247, 108, 240, 119, 251, 106, 238, 117, 249)(109, 241, 121, 253, 114, 246, 125, 257, 112, 244, 123, 255)(116, 248, 128, 260, 118, 250, 129, 261, 120, 252, 127, 259)(122, 254, 131, 263, 124, 256, 132, 264, 126, 258, 130, 262)(265, 397, 267, 399)(266, 398, 271, 403)(268, 400, 274, 406)(269, 401, 277, 409)(270, 402, 280, 412)(272, 404, 283, 415)(273, 405, 285, 417)(275, 407, 288, 420)(276, 408, 291, 423)(278, 410, 289, 421)(279, 411, 293, 425)(281, 413, 296, 428)(282, 414, 297, 429)(284, 416, 300, 432)(286, 418, 302, 434)(287, 419, 305, 437)(290, 422, 304, 436)(292, 424, 308, 440)(294, 426, 309, 441)(295, 427, 310, 442)(298, 430, 313, 445)(299, 431, 315, 447)(301, 433, 317, 449)(303, 435, 320, 452)(306, 438, 322, 454)(307, 439, 323, 455)(311, 443, 324, 456)(312, 444, 325, 457)(314, 446, 328, 460)(316, 448, 330, 462)(318, 450, 332, 464)(319, 451, 334, 466)(321, 453, 336, 468)(326, 458, 338, 470)(327, 459, 340, 472)(329, 461, 342, 474)(331, 463, 343, 475)(333, 465, 346, 478)(335, 467, 348, 480)(337, 469, 349, 481)(339, 471, 352, 484)(341, 473, 354, 486)(344, 476, 356, 488)(345, 477, 358, 490)(347, 479, 360, 492)(350, 482, 362, 494)(351, 483, 364, 496)(353, 485, 366, 498)(355, 487, 367, 499)(357, 489, 370, 502)(359, 491, 372, 504)(361, 493, 373, 505)(363, 495, 376, 508)(365, 497, 378, 510)(368, 500, 380, 512)(369, 501, 382, 514)(371, 503, 384, 516)(374, 506, 386, 518)(375, 507, 388, 520)(377, 509, 390, 522)(379, 511, 389, 521)(381, 513, 385, 517)(383, 515, 387, 519)(391, 523, 396, 528)(392, 524, 394, 526)(393, 525, 395, 527) L = (1, 268)(2, 272)(3, 274)(4, 265)(5, 276)(6, 281)(7, 283)(8, 266)(9, 286)(10, 267)(11, 287)(12, 269)(13, 291)(14, 290)(15, 294)(16, 296)(17, 270)(18, 298)(19, 271)(20, 299)(21, 302)(22, 273)(23, 275)(24, 305)(25, 304)(26, 278)(27, 277)(28, 307)(29, 309)(30, 279)(31, 311)(32, 280)(33, 313)(34, 282)(35, 284)(36, 315)(37, 318)(38, 285)(39, 319)(40, 289)(41, 288)(42, 321)(43, 292)(44, 323)(45, 293)(46, 324)(47, 295)(48, 326)(49, 297)(50, 327)(51, 300)(52, 329)(53, 332)(54, 301)(55, 303)(56, 334)(57, 306)(58, 336)(59, 308)(60, 310)(61, 338)(62, 312)(63, 314)(64, 340)(65, 316)(66, 342)(67, 344)(68, 317)(69, 345)(70, 320)(71, 347)(72, 322)(73, 350)(74, 325)(75, 351)(76, 328)(77, 353)(78, 330)(79, 356)(80, 331)(81, 333)(82, 358)(83, 335)(84, 360)(85, 362)(86, 337)(87, 339)(88, 364)(89, 341)(90, 366)(91, 368)(92, 343)(93, 369)(94, 346)(95, 371)(96, 348)(97, 374)(98, 349)(99, 375)(100, 352)(101, 377)(102, 354)(103, 380)(104, 355)(105, 357)(106, 382)(107, 359)(108, 384)(109, 386)(110, 361)(111, 363)(112, 388)(113, 365)(114, 390)(115, 391)(116, 367)(117, 392)(118, 370)(119, 393)(120, 372)(121, 394)(122, 373)(123, 395)(124, 376)(125, 396)(126, 378)(127, 379)(128, 381)(129, 383)(130, 385)(131, 387)(132, 389)(133, 397)(134, 398)(135, 399)(136, 400)(137, 401)(138, 402)(139, 403)(140, 404)(141, 405)(142, 406)(143, 407)(144, 408)(145, 409)(146, 410)(147, 411)(148, 412)(149, 413)(150, 414)(151, 415)(152, 416)(153, 417)(154, 418)(155, 419)(156, 420)(157, 421)(158, 422)(159, 423)(160, 424)(161, 425)(162, 426)(163, 427)(164, 428)(165, 429)(166, 430)(167, 431)(168, 432)(169, 433)(170, 434)(171, 435)(172, 436)(173, 437)(174, 438)(175, 439)(176, 440)(177, 441)(178, 442)(179, 443)(180, 444)(181, 445)(182, 446)(183, 447)(184, 448)(185, 449)(186, 450)(187, 451)(188, 452)(189, 453)(190, 454)(191, 455)(192, 456)(193, 457)(194, 458)(195, 459)(196, 460)(197, 461)(198, 462)(199, 463)(200, 464)(201, 465)(202, 466)(203, 467)(204, 468)(205, 469)(206, 470)(207, 471)(208, 472)(209, 473)(210, 474)(211, 475)(212, 476)(213, 477)(214, 478)(215, 479)(216, 480)(217, 481)(218, 482)(219, 483)(220, 484)(221, 485)(222, 486)(223, 487)(224, 488)(225, 489)(226, 490)(227, 491)(228, 492)(229, 493)(230, 494)(231, 495)(232, 496)(233, 497)(234, 498)(235, 499)(236, 500)(237, 501)(238, 502)(239, 503)(240, 504)(241, 505)(242, 506)(243, 507)(244, 508)(245, 509)(246, 510)(247, 511)(248, 512)(249, 513)(250, 514)(251, 515)(252, 516)(253, 517)(254, 518)(255, 519)(256, 520)(257, 521)(258, 522)(259, 523)(260, 524)(261, 525)(262, 526)(263, 527)(264, 528) local type(s) :: { ( 4^4 ), ( 4^12 ) } Outer automorphisms :: reflexible Dual of E23.1137 Graph:: simple bipartite v = 88 e = 264 f = 132 degree seq :: [ 4^66, 12^22 ] E23.1139 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 6}) Quotient :: dipole Aut^+ = S3 x D22 (small group id <132, 5>) Aut = C2 x S3 x D22 (small group id <264, 34>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (Y1^-1 * Y3)^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y1)^2, (R * Y3)^2, Y1^6, (Y1^-1 * Y2 * Y1^-1)^2, Y1^-4 * Y3 * Y1^2 * Y3, Y1^-1 * Y2 * Y1^-1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y3 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 ] Map:: polytopal non-degenerate R = (1, 133, 2, 134, 6, 138, 15, 147, 14, 146, 5, 137)(3, 135, 9, 141, 21, 153, 32, 164, 16, 148, 11, 143)(4, 136, 12, 144, 26, 158, 30, 162, 17, 149, 8, 140)(7, 139, 18, 150, 13, 145, 28, 160, 29, 161, 20, 152)(10, 142, 24, 156, 31, 163, 46, 178, 37, 169, 23, 155)(19, 151, 35, 167, 45, 177, 43, 175, 27, 159, 34, 166)(22, 154, 38, 170, 25, 157, 42, 174, 47, 179, 40, 172)(33, 165, 48, 180, 36, 168, 52, 184, 44, 176, 50, 182)(39, 171, 55, 187, 60, 192, 57, 189, 41, 173, 54, 186)(49, 181, 63, 195, 59, 191, 65, 197, 51, 183, 62, 194)(53, 185, 67, 199, 56, 188, 71, 203, 58, 190, 69, 201)(61, 193, 73, 205, 64, 196, 77, 209, 66, 198, 75, 207)(68, 200, 81, 213, 72, 204, 83, 215, 70, 202, 80, 212)(74, 206, 87, 219, 78, 210, 89, 221, 76, 208, 86, 218)(79, 211, 91, 223, 82, 214, 95, 227, 84, 216, 93, 225)(85, 217, 97, 229, 88, 220, 101, 233, 90, 222, 99, 231)(92, 224, 105, 237, 96, 228, 107, 239, 94, 226, 104, 236)(98, 230, 111, 243, 102, 234, 113, 245, 100, 232, 110, 242)(103, 235, 115, 247, 106, 238, 119, 251, 108, 240, 117, 249)(109, 241, 121, 253, 112, 244, 125, 257, 114, 246, 123, 255)(116, 248, 129, 261, 120, 252, 131, 263, 118, 250, 128, 260)(122, 254, 127, 259, 126, 258, 130, 262, 124, 256, 132, 264)(265, 397, 267, 399)(266, 398, 271, 403)(268, 400, 274, 406)(269, 401, 277, 409)(270, 402, 280, 412)(272, 404, 283, 415)(273, 405, 286, 418)(275, 407, 289, 421)(276, 408, 291, 423)(278, 410, 285, 417)(279, 411, 293, 425)(281, 413, 295, 427)(282, 414, 297, 429)(284, 416, 300, 432)(287, 419, 303, 435)(288, 420, 305, 437)(290, 422, 301, 433)(292, 424, 308, 440)(294, 426, 309, 441)(296, 428, 311, 443)(298, 430, 313, 445)(299, 431, 315, 447)(302, 434, 317, 449)(304, 436, 320, 452)(306, 438, 322, 454)(307, 439, 323, 455)(310, 442, 324, 456)(312, 444, 325, 457)(314, 446, 328, 460)(316, 448, 330, 462)(318, 450, 332, 464)(319, 451, 334, 466)(321, 453, 336, 468)(326, 458, 338, 470)(327, 459, 340, 472)(329, 461, 342, 474)(331, 463, 343, 475)(333, 465, 346, 478)(335, 467, 348, 480)(337, 469, 349, 481)(339, 471, 352, 484)(341, 473, 354, 486)(344, 476, 356, 488)(345, 477, 358, 490)(347, 479, 360, 492)(350, 482, 362, 494)(351, 483, 364, 496)(353, 485, 366, 498)(355, 487, 367, 499)(357, 489, 370, 502)(359, 491, 372, 504)(361, 493, 373, 505)(363, 495, 376, 508)(365, 497, 378, 510)(368, 500, 380, 512)(369, 501, 382, 514)(371, 503, 384, 516)(374, 506, 386, 518)(375, 507, 388, 520)(377, 509, 390, 522)(379, 511, 391, 523)(381, 513, 394, 526)(383, 515, 396, 528)(385, 517, 395, 527)(387, 519, 392, 524)(389, 521, 393, 525) L = (1, 268)(2, 272)(3, 274)(4, 265)(5, 276)(6, 281)(7, 283)(8, 266)(9, 287)(10, 267)(11, 288)(12, 269)(13, 291)(14, 290)(15, 294)(16, 295)(17, 270)(18, 298)(19, 271)(20, 299)(21, 301)(22, 303)(23, 273)(24, 275)(25, 305)(26, 278)(27, 277)(28, 307)(29, 309)(30, 279)(31, 280)(32, 310)(33, 313)(34, 282)(35, 284)(36, 315)(37, 285)(38, 318)(39, 286)(40, 319)(41, 289)(42, 321)(43, 292)(44, 323)(45, 293)(46, 296)(47, 324)(48, 326)(49, 297)(50, 327)(51, 300)(52, 329)(53, 332)(54, 302)(55, 304)(56, 334)(57, 306)(58, 336)(59, 308)(60, 311)(61, 338)(62, 312)(63, 314)(64, 340)(65, 316)(66, 342)(67, 344)(68, 317)(69, 345)(70, 320)(71, 347)(72, 322)(73, 350)(74, 325)(75, 351)(76, 328)(77, 353)(78, 330)(79, 356)(80, 331)(81, 333)(82, 358)(83, 335)(84, 360)(85, 362)(86, 337)(87, 339)(88, 364)(89, 341)(90, 366)(91, 368)(92, 343)(93, 369)(94, 346)(95, 371)(96, 348)(97, 374)(98, 349)(99, 375)(100, 352)(101, 377)(102, 354)(103, 380)(104, 355)(105, 357)(106, 382)(107, 359)(108, 384)(109, 386)(110, 361)(111, 363)(112, 388)(113, 365)(114, 390)(115, 392)(116, 367)(117, 393)(118, 370)(119, 395)(120, 372)(121, 396)(122, 373)(123, 391)(124, 376)(125, 394)(126, 378)(127, 387)(128, 379)(129, 381)(130, 389)(131, 383)(132, 385)(133, 397)(134, 398)(135, 399)(136, 400)(137, 401)(138, 402)(139, 403)(140, 404)(141, 405)(142, 406)(143, 407)(144, 408)(145, 409)(146, 410)(147, 411)(148, 412)(149, 413)(150, 414)(151, 415)(152, 416)(153, 417)(154, 418)(155, 419)(156, 420)(157, 421)(158, 422)(159, 423)(160, 424)(161, 425)(162, 426)(163, 427)(164, 428)(165, 429)(166, 430)(167, 431)(168, 432)(169, 433)(170, 434)(171, 435)(172, 436)(173, 437)(174, 438)(175, 439)(176, 440)(177, 441)(178, 442)(179, 443)(180, 444)(181, 445)(182, 446)(183, 447)(184, 448)(185, 449)(186, 450)(187, 451)(188, 452)(189, 453)(190, 454)(191, 455)(192, 456)(193, 457)(194, 458)(195, 459)(196, 460)(197, 461)(198, 462)(199, 463)(200, 464)(201, 465)(202, 466)(203, 467)(204, 468)(205, 469)(206, 470)(207, 471)(208, 472)(209, 473)(210, 474)(211, 475)(212, 476)(213, 477)(214, 478)(215, 479)(216, 480)(217, 481)(218, 482)(219, 483)(220, 484)(221, 485)(222, 486)(223, 487)(224, 488)(225, 489)(226, 490)(227, 491)(228, 492)(229, 493)(230, 494)(231, 495)(232, 496)(233, 497)(234, 498)(235, 499)(236, 500)(237, 501)(238, 502)(239, 503)(240, 504)(241, 505)(242, 506)(243, 507)(244, 508)(245, 509)(246, 510)(247, 511)(248, 512)(249, 513)(250, 514)(251, 515)(252, 516)(253, 517)(254, 518)(255, 519)(256, 520)(257, 521)(258, 522)(259, 523)(260, 524)(261, 525)(262, 526)(263, 527)(264, 528) local type(s) :: { ( 4^4 ), ( 4^12 ) } Outer automorphisms :: reflexible Dual of E23.1135 Graph:: simple bipartite v = 88 e = 264 f = 132 degree seq :: [ 4^66, 12^22 ] E23.1140 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 6}) Quotient :: dipole Aut^+ = S3 x D22 (small group id <132, 5>) Aut = C2 x S3 x D22 (small group id <264, 34>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^3, Y1^2 * Y3^-1, (Y2 * Y3^-1)^2, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y3 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y3^-1, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 ] Map:: non-degenerate R = (1, 133, 2, 134, 4, 136, 8, 140, 6, 138, 5, 137)(3, 135, 9, 141, 10, 142, 18, 150, 12, 144, 11, 143)(7, 139, 14, 146, 13, 145, 20, 152, 16, 148, 15, 147)(17, 149, 23, 155, 19, 151, 26, 158, 25, 157, 24, 156)(21, 153, 28, 160, 22, 154, 30, 162, 27, 159, 29, 161)(31, 163, 37, 169, 32, 164, 39, 171, 33, 165, 38, 170)(34, 166, 40, 172, 35, 167, 42, 174, 36, 168, 41, 173)(43, 175, 49, 181, 44, 176, 51, 183, 45, 177, 50, 182)(46, 178, 52, 184, 47, 179, 54, 186, 48, 180, 53, 185)(55, 187, 91, 223, 56, 188, 92, 224, 57, 189, 93, 225)(58, 190, 94, 226, 61, 193, 101, 233, 63, 195, 95, 227)(59, 191, 96, 228, 64, 196, 102, 234, 62, 194, 98, 230)(60, 192, 99, 231, 66, 198, 97, 229, 68, 200, 100, 232)(65, 197, 103, 235, 71, 203, 105, 237, 67, 199, 104, 236)(69, 201, 106, 238, 72, 204, 108, 240, 70, 202, 107, 239)(73, 205, 109, 241, 75, 207, 111, 243, 74, 206, 110, 242)(76, 208, 112, 244, 78, 210, 114, 246, 77, 209, 113, 245)(79, 211, 115, 247, 81, 213, 117, 249, 80, 212, 116, 248)(82, 214, 118, 250, 84, 216, 120, 252, 83, 215, 119, 251)(85, 217, 121, 253, 87, 219, 123, 255, 86, 218, 122, 254)(88, 220, 124, 256, 90, 222, 126, 258, 89, 221, 125, 257)(127, 259, 131, 263, 129, 261, 130, 262, 128, 260, 132, 264)(265, 397, 267, 399)(266, 398, 271, 403)(268, 400, 276, 408)(269, 401, 277, 409)(270, 402, 274, 406)(272, 404, 280, 412)(273, 405, 281, 413)(275, 407, 283, 415)(278, 410, 285, 417)(279, 411, 286, 418)(282, 414, 289, 421)(284, 416, 291, 423)(287, 419, 295, 427)(288, 420, 296, 428)(290, 422, 297, 429)(292, 424, 298, 430)(293, 425, 299, 431)(294, 426, 300, 432)(301, 433, 307, 439)(302, 434, 308, 440)(303, 435, 309, 441)(304, 436, 310, 442)(305, 437, 311, 443)(306, 438, 312, 444)(313, 445, 319, 451)(314, 446, 320, 452)(315, 447, 321, 453)(316, 448, 332, 464)(317, 449, 324, 456)(318, 450, 330, 462)(322, 454, 357, 489)(323, 455, 361, 493)(325, 457, 356, 488)(326, 458, 364, 496)(327, 459, 355, 487)(328, 460, 363, 495)(329, 461, 365, 497)(331, 463, 359, 491)(333, 465, 366, 498)(334, 466, 362, 494)(335, 467, 358, 490)(336, 468, 360, 492)(337, 469, 369, 501)(338, 470, 368, 500)(339, 471, 367, 499)(340, 472, 372, 504)(341, 473, 371, 503)(342, 474, 370, 502)(343, 475, 375, 507)(344, 476, 374, 506)(345, 477, 373, 505)(346, 478, 378, 510)(347, 479, 377, 509)(348, 480, 376, 508)(349, 481, 381, 513)(350, 482, 380, 512)(351, 483, 379, 511)(352, 484, 384, 516)(353, 485, 383, 515)(354, 486, 382, 514)(385, 517, 393, 525)(386, 518, 392, 524)(387, 519, 391, 523)(388, 520, 395, 527)(389, 521, 394, 526)(390, 522, 396, 528) L = (1, 268)(2, 272)(3, 274)(4, 270)(5, 266)(6, 265)(7, 277)(8, 269)(9, 282)(10, 276)(11, 273)(12, 267)(13, 280)(14, 284)(15, 278)(16, 271)(17, 283)(18, 275)(19, 289)(20, 279)(21, 286)(22, 291)(23, 290)(24, 287)(25, 281)(26, 288)(27, 285)(28, 294)(29, 292)(30, 293)(31, 296)(32, 297)(33, 295)(34, 299)(35, 300)(36, 298)(37, 303)(38, 301)(39, 302)(40, 306)(41, 304)(42, 305)(43, 308)(44, 309)(45, 307)(46, 311)(47, 312)(48, 310)(49, 315)(50, 313)(51, 314)(52, 318)(53, 316)(54, 317)(55, 320)(56, 321)(57, 319)(58, 325)(59, 328)(60, 330)(61, 327)(62, 323)(63, 322)(64, 326)(65, 335)(66, 332)(67, 329)(68, 324)(69, 336)(70, 333)(71, 331)(72, 334)(73, 339)(74, 337)(75, 338)(76, 342)(77, 340)(78, 341)(79, 345)(80, 343)(81, 344)(82, 348)(83, 346)(84, 347)(85, 351)(86, 349)(87, 350)(88, 354)(89, 352)(90, 353)(91, 356)(92, 357)(93, 355)(94, 365)(95, 358)(96, 366)(97, 364)(98, 360)(99, 361)(100, 363)(101, 359)(102, 362)(103, 369)(104, 367)(105, 368)(106, 372)(107, 370)(108, 371)(109, 375)(110, 373)(111, 374)(112, 378)(113, 376)(114, 377)(115, 381)(116, 379)(117, 380)(118, 384)(119, 382)(120, 383)(121, 387)(122, 385)(123, 386)(124, 390)(125, 388)(126, 389)(127, 393)(128, 391)(129, 392)(130, 396)(131, 394)(132, 395)(133, 397)(134, 398)(135, 399)(136, 400)(137, 401)(138, 402)(139, 403)(140, 404)(141, 405)(142, 406)(143, 407)(144, 408)(145, 409)(146, 410)(147, 411)(148, 412)(149, 413)(150, 414)(151, 415)(152, 416)(153, 417)(154, 418)(155, 419)(156, 420)(157, 421)(158, 422)(159, 423)(160, 424)(161, 425)(162, 426)(163, 427)(164, 428)(165, 429)(166, 430)(167, 431)(168, 432)(169, 433)(170, 434)(171, 435)(172, 436)(173, 437)(174, 438)(175, 439)(176, 440)(177, 441)(178, 442)(179, 443)(180, 444)(181, 445)(182, 446)(183, 447)(184, 448)(185, 449)(186, 450)(187, 451)(188, 452)(189, 453)(190, 454)(191, 455)(192, 456)(193, 457)(194, 458)(195, 459)(196, 460)(197, 461)(198, 462)(199, 463)(200, 464)(201, 465)(202, 466)(203, 467)(204, 468)(205, 469)(206, 470)(207, 471)(208, 472)(209, 473)(210, 474)(211, 475)(212, 476)(213, 477)(214, 478)(215, 479)(216, 480)(217, 481)(218, 482)(219, 483)(220, 484)(221, 485)(222, 486)(223, 487)(224, 488)(225, 489)(226, 490)(227, 491)(228, 492)(229, 493)(230, 494)(231, 495)(232, 496)(233, 497)(234, 498)(235, 499)(236, 500)(237, 501)(238, 502)(239, 503)(240, 504)(241, 505)(242, 506)(243, 507)(244, 508)(245, 509)(246, 510)(247, 511)(248, 512)(249, 513)(250, 514)(251, 515)(252, 516)(253, 517)(254, 518)(255, 519)(256, 520)(257, 521)(258, 522)(259, 523)(260, 524)(261, 525)(262, 526)(263, 527)(264, 528) local type(s) :: { ( 4^4 ), ( 4^12 ) } Outer automorphisms :: reflexible Dual of E23.1136 Graph:: bipartite v = 88 e = 264 f = 132 degree seq :: [ 4^66, 12^22 ] E23.1141 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 6, 69}) Quotient :: regular Aut^+ = C3 x D46 (small group id <138, 2>) Aut = S3 x D46 (small group id <276, 5>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-3)^2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1, T1^9 * T2 * T1^-13 * T2 * T1 ] Map:: non-degenerate R = (1, 2, 5, 11, 23, 39, 53, 65, 77, 89, 101, 113, 125, 132, 121, 109, 96, 85, 73, 60, 49, 33, 16, 28, 42, 35, 46, 58, 70, 82, 94, 106, 118, 130, 137, 138, 133, 120, 108, 97, 84, 72, 61, 48, 32, 45, 34, 17, 29, 43, 56, 68, 80, 92, 104, 116, 128, 136, 124, 112, 100, 88, 76, 64, 52, 38, 22, 10, 4)(3, 7, 15, 31, 47, 59, 71, 83, 95, 107, 119, 131, 127, 114, 105, 91, 78, 69, 55, 40, 30, 14, 6, 13, 27, 21, 37, 51, 63, 75, 87, 99, 111, 123, 135, 126, 117, 103, 90, 81, 67, 54, 44, 26, 12, 25, 20, 9, 19, 36, 50, 62, 74, 86, 98, 110, 122, 134, 129, 115, 102, 93, 79, 66, 57, 41, 24, 18, 8) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 35)(19, 33)(20, 34)(22, 31)(23, 40)(25, 42)(26, 43)(27, 45)(30, 46)(36, 48)(37, 49)(38, 50)(39, 54)(41, 56)(44, 58)(47, 60)(51, 61)(52, 63)(53, 66)(55, 68)(57, 70)(59, 72)(62, 73)(64, 71)(65, 78)(67, 80)(69, 82)(74, 84)(75, 85)(76, 86)(77, 90)(79, 92)(81, 94)(83, 96)(87, 97)(88, 99)(89, 102)(91, 104)(93, 106)(95, 108)(98, 109)(100, 107)(101, 114)(103, 116)(105, 118)(110, 120)(111, 121)(112, 122)(113, 126)(115, 128)(117, 130)(119, 132)(123, 133)(124, 135)(125, 134)(127, 136)(129, 137)(131, 138) local type(s) :: { ( 6^69 ) } Outer automorphisms :: reflexible Dual of E23.1142 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 2 e = 69 f = 23 degree seq :: [ 69^2 ] E23.1142 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 6, 69}) Quotient :: regular Aut^+ = C3 x D46 (small group id <138, 2>) Aut = S3 x D46 (small group id <276, 5>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^6, T1^-1 * T2 * T1^2 * T2 * T1^-1, T1^-2 * T2 * T1^-2 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1 * T2 * T1^2 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-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 * 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 ] Map:: non-degenerate R = (1, 2, 5, 11, 10, 4)(3, 7, 12, 20, 17, 8)(6, 13, 19, 18, 9, 14)(15, 23, 27, 25, 16, 24)(21, 28, 26, 30, 22, 29)(31, 37, 33, 39, 32, 38)(34, 40, 36, 42, 35, 41)(43, 49, 45, 51, 44, 50)(46, 52, 48, 54, 47, 53)(55, 91, 57, 93, 56, 92)(58, 94, 62, 101, 65, 95)(59, 96, 66, 100, 61, 98)(60, 97, 67, 105, 70, 99)(63, 102, 72, 104, 64, 103)(68, 106, 71, 108, 69, 107)(73, 109, 75, 111, 74, 110)(76, 112, 78, 114, 77, 113)(79, 115, 81, 117, 80, 116)(82, 118, 84, 120, 83, 119)(85, 121, 87, 123, 86, 122)(88, 124, 90, 126, 89, 125)(127, 134, 129, 132, 128, 136)(130, 135, 137, 133, 131, 138) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 15)(8, 16)(10, 17)(11, 19)(13, 21)(14, 22)(18, 26)(20, 27)(23, 31)(24, 32)(25, 33)(28, 34)(29, 35)(30, 36)(37, 43)(38, 44)(39, 45)(40, 46)(41, 47)(42, 48)(49, 55)(50, 56)(51, 57)(52, 67)(53, 60)(54, 70)(58, 92)(59, 97)(61, 99)(62, 91)(63, 94)(64, 95)(65, 93)(66, 105)(68, 96)(69, 98)(71, 100)(72, 101)(73, 102)(74, 103)(75, 104)(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)(121, 127)(122, 128)(123, 129)(124, 138)(125, 133)(126, 135)(130, 136)(131, 132)(134, 137) local type(s) :: { ( 69^6 ) } Outer automorphisms :: reflexible Dual of E23.1141 Transitivity :: ET+ VT+ AT+ REG+ Graph:: v = 23 e = 69 f = 2 degree seq :: [ 6^23 ] E23.1143 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 6, 69}) Quotient :: edge Aut^+ = C3 x D46 (small group id <138, 2>) Aut = S3 x D46 (small group id <276, 5>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^6, T2^-1 * T1 * T2^2 * T1 * T2^-1, T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * 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 * T1, (T2^-1 * T1)^69 ] Map:: R = (1, 3, 8, 17, 10, 4)(2, 5, 12, 21, 14, 6)(7, 15, 24, 18, 9, 16)(11, 19, 28, 22, 13, 20)(23, 31, 26, 33, 25, 32)(27, 34, 30, 36, 29, 35)(37, 43, 39, 45, 38, 44)(40, 46, 42, 48, 41, 47)(49, 55, 51, 57, 50, 56)(52, 88, 54, 90, 53, 89)(58, 107, 65, 120, 67, 108)(59, 110, 69, 125, 71, 111)(60, 112, 74, 114, 61, 113)(62, 115, 78, 117, 63, 116)(64, 119, 81, 122, 66, 106)(68, 124, 85, 127, 70, 109)(72, 128, 75, 130, 73, 129)(76, 103, 79, 105, 77, 104)(80, 132, 83, 121, 82, 118)(84, 136, 87, 126, 86, 123)(91, 134, 93, 133, 92, 131)(94, 138, 96, 137, 95, 135)(97, 101, 99, 100, 98, 102)(139, 140)(141, 145)(142, 147)(143, 149)(144, 151)(146, 150)(148, 152)(153, 161)(154, 163)(155, 162)(156, 164)(157, 165)(158, 167)(159, 166)(160, 168)(169, 175)(170, 176)(171, 177)(172, 178)(173, 179)(174, 180)(181, 187)(182, 188)(183, 189)(184, 190)(185, 191)(186, 192)(193, 241)(194, 242)(195, 243)(196, 244)(197, 247)(198, 248)(199, 249)(200, 245)(201, 246)(202, 256)(203, 257)(204, 259)(205, 260)(206, 261)(207, 262)(208, 264)(209, 265)(210, 250)(211, 251)(212, 263)(213, 252)(214, 253)(215, 254)(216, 258)(217, 255)(218, 269)(219, 270)(220, 271)(221, 272)(222, 273)(223, 274)(224, 275)(225, 276)(226, 266)(227, 267)(228, 268)(229, 240)(230, 238)(231, 239)(232, 237)(233, 235)(234, 236) L = (1, 139)(2, 140)(3, 141)(4, 142)(5, 143)(6, 144)(7, 145)(8, 146)(9, 147)(10, 148)(11, 149)(12, 150)(13, 151)(14, 152)(15, 153)(16, 154)(17, 155)(18, 156)(19, 157)(20, 158)(21, 159)(22, 160)(23, 161)(24, 162)(25, 163)(26, 164)(27, 165)(28, 166)(29, 167)(30, 168)(31, 169)(32, 170)(33, 171)(34, 172)(35, 173)(36, 174)(37, 175)(38, 176)(39, 177)(40, 178)(41, 179)(42, 180)(43, 181)(44, 182)(45, 183)(46, 184)(47, 185)(48, 186)(49, 187)(50, 188)(51, 189)(52, 190)(53, 191)(54, 192)(55, 193)(56, 194)(57, 195)(58, 196)(59, 197)(60, 198)(61, 199)(62, 200)(63, 201)(64, 202)(65, 203)(66, 204)(67, 205)(68, 206)(69, 207)(70, 208)(71, 209)(72, 210)(73, 211)(74, 212)(75, 213)(76, 214)(77, 215)(78, 216)(79, 217)(80, 218)(81, 219)(82, 220)(83, 221)(84, 222)(85, 223)(86, 224)(87, 225)(88, 226)(89, 227)(90, 228)(91, 229)(92, 230)(93, 231)(94, 232)(95, 233)(96, 234)(97, 235)(98, 236)(99, 237)(100, 238)(101, 239)(102, 240)(103, 241)(104, 242)(105, 243)(106, 244)(107, 245)(108, 246)(109, 247)(110, 248)(111, 249)(112, 250)(113, 251)(114, 252)(115, 253)(116, 254)(117, 255)(118, 256)(119, 257)(120, 258)(121, 259)(122, 260)(123, 261)(124, 262)(125, 263)(126, 264)(127, 265)(128, 266)(129, 267)(130, 268)(131, 269)(132, 270)(133, 271)(134, 272)(135, 273)(136, 274)(137, 275)(138, 276) local type(s) :: { ( 138, 138 ), ( 138^6 ) } Outer automorphisms :: reflexible Dual of E23.1147 Transitivity :: ET+ Graph:: simple bipartite v = 92 e = 138 f = 2 degree seq :: [ 2^69, 6^23 ] E23.1144 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 6, 69}) Quotient :: edge Aut^+ = C3 x D46 (small group id <138, 2>) Aut = S3 x D46 (small group id <276, 5>) |r| :: 2 Presentation :: [ F^2, (T2^-1 * T1^-1)^2, (T2 * T1)^2, (F * T1)^2, (F * T2)^2, T1^-1 * T2^-1 * T1^2 * T2 * T1^-1, (T2 * T1^-1 * T2)^2, T1^-1 * T2^-1 * T1 * T2^22 ] Map:: polytopal non-degenerate R = (1, 3, 10, 25, 37, 49, 61, 73, 85, 97, 109, 121, 133, 127, 115, 103, 91, 79, 67, 55, 43, 31, 20, 13, 21, 33, 45, 57, 69, 81, 93, 105, 117, 129, 138, 137, 126, 114, 102, 90, 78, 66, 54, 42, 30, 18, 6, 17, 29, 41, 53, 65, 77, 89, 101, 113, 125, 136, 124, 112, 100, 88, 76, 64, 52, 40, 28, 15, 5)(2, 7, 19, 32, 44, 56, 68, 80, 92, 104, 116, 128, 131, 119, 107, 95, 83, 71, 59, 47, 35, 23, 9, 4, 12, 26, 38, 50, 62, 74, 86, 98, 110, 122, 134, 132, 120, 108, 96, 84, 72, 60, 48, 36, 24, 11, 16, 14, 27, 39, 51, 63, 75, 87, 99, 111, 123, 135, 130, 118, 106, 94, 82, 70, 58, 46, 34, 22, 8)(139, 140, 144, 154, 151, 142)(141, 147, 155, 146, 159, 149)(143, 152, 156, 150, 158, 145)(148, 162, 167, 161, 171, 160)(153, 164, 168, 157, 169, 165)(163, 172, 179, 174, 183, 173)(166, 170, 180, 177, 181, 176)(175, 185, 191, 184, 195, 186)(178, 189, 192, 188, 193, 182)(187, 198, 203, 197, 207, 196)(190, 200, 204, 194, 205, 201)(199, 208, 215, 210, 219, 209)(202, 206, 216, 213, 217, 212)(211, 221, 227, 220, 231, 222)(214, 225, 228, 224, 229, 218)(223, 234, 239, 233, 243, 232)(226, 236, 240, 230, 241, 237)(235, 244, 251, 246, 255, 245)(238, 242, 252, 249, 253, 248)(247, 257, 263, 256, 267, 258)(250, 261, 264, 260, 265, 254)(259, 270, 274, 269, 276, 268)(262, 272, 275, 266, 271, 273) L = (1, 139)(2, 140)(3, 141)(4, 142)(5, 143)(6, 144)(7, 145)(8, 146)(9, 147)(10, 148)(11, 149)(12, 150)(13, 151)(14, 152)(15, 153)(16, 154)(17, 155)(18, 156)(19, 157)(20, 158)(21, 159)(22, 160)(23, 161)(24, 162)(25, 163)(26, 164)(27, 165)(28, 166)(29, 167)(30, 168)(31, 169)(32, 170)(33, 171)(34, 172)(35, 173)(36, 174)(37, 175)(38, 176)(39, 177)(40, 178)(41, 179)(42, 180)(43, 181)(44, 182)(45, 183)(46, 184)(47, 185)(48, 186)(49, 187)(50, 188)(51, 189)(52, 190)(53, 191)(54, 192)(55, 193)(56, 194)(57, 195)(58, 196)(59, 197)(60, 198)(61, 199)(62, 200)(63, 201)(64, 202)(65, 203)(66, 204)(67, 205)(68, 206)(69, 207)(70, 208)(71, 209)(72, 210)(73, 211)(74, 212)(75, 213)(76, 214)(77, 215)(78, 216)(79, 217)(80, 218)(81, 219)(82, 220)(83, 221)(84, 222)(85, 223)(86, 224)(87, 225)(88, 226)(89, 227)(90, 228)(91, 229)(92, 230)(93, 231)(94, 232)(95, 233)(96, 234)(97, 235)(98, 236)(99, 237)(100, 238)(101, 239)(102, 240)(103, 241)(104, 242)(105, 243)(106, 244)(107, 245)(108, 246)(109, 247)(110, 248)(111, 249)(112, 250)(113, 251)(114, 252)(115, 253)(116, 254)(117, 255)(118, 256)(119, 257)(120, 258)(121, 259)(122, 260)(123, 261)(124, 262)(125, 263)(126, 264)(127, 265)(128, 266)(129, 267)(130, 268)(131, 269)(132, 270)(133, 271)(134, 272)(135, 273)(136, 274)(137, 275)(138, 276) local type(s) :: { ( 4^6 ), ( 4^69 ) } Outer automorphisms :: reflexible Dual of E23.1148 Transitivity :: ET+ Graph:: bipartite v = 25 e = 138 f = 69 degree seq :: [ 6^23, 69^2 ] E23.1145 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 6, 69}) Quotient :: edge Aut^+ = C3 x D46 (small group id <138, 2>) Aut = S3 x D46 (small group id <276, 5>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-3)^2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1, T1^9 * T2 * T1^-13 * T2 * T1 ] Map:: R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 35)(19, 33)(20, 34)(22, 31)(23, 40)(25, 42)(26, 43)(27, 45)(30, 46)(36, 48)(37, 49)(38, 50)(39, 54)(41, 56)(44, 58)(47, 60)(51, 61)(52, 63)(53, 66)(55, 68)(57, 70)(59, 72)(62, 73)(64, 71)(65, 78)(67, 80)(69, 82)(74, 84)(75, 85)(76, 86)(77, 90)(79, 92)(81, 94)(83, 96)(87, 97)(88, 99)(89, 102)(91, 104)(93, 106)(95, 108)(98, 109)(100, 107)(101, 114)(103, 116)(105, 118)(110, 120)(111, 121)(112, 122)(113, 126)(115, 128)(117, 130)(119, 132)(123, 133)(124, 135)(125, 134)(127, 136)(129, 137)(131, 138)(139, 140, 143, 149, 161, 177, 191, 203, 215, 227, 239, 251, 263, 270, 259, 247, 234, 223, 211, 198, 187, 171, 154, 166, 180, 173, 184, 196, 208, 220, 232, 244, 256, 268, 275, 276, 271, 258, 246, 235, 222, 210, 199, 186, 170, 183, 172, 155, 167, 181, 194, 206, 218, 230, 242, 254, 266, 274, 262, 250, 238, 226, 214, 202, 190, 176, 160, 148, 142)(141, 145, 153, 169, 185, 197, 209, 221, 233, 245, 257, 269, 265, 252, 243, 229, 216, 207, 193, 178, 168, 152, 144, 151, 165, 159, 175, 189, 201, 213, 225, 237, 249, 261, 273, 264, 255, 241, 228, 219, 205, 192, 182, 164, 150, 163, 158, 147, 157, 174, 188, 200, 212, 224, 236, 248, 260, 272, 267, 253, 240, 231, 217, 204, 195, 179, 162, 156, 146) L = (1, 139)(2, 140)(3, 141)(4, 142)(5, 143)(6, 144)(7, 145)(8, 146)(9, 147)(10, 148)(11, 149)(12, 150)(13, 151)(14, 152)(15, 153)(16, 154)(17, 155)(18, 156)(19, 157)(20, 158)(21, 159)(22, 160)(23, 161)(24, 162)(25, 163)(26, 164)(27, 165)(28, 166)(29, 167)(30, 168)(31, 169)(32, 170)(33, 171)(34, 172)(35, 173)(36, 174)(37, 175)(38, 176)(39, 177)(40, 178)(41, 179)(42, 180)(43, 181)(44, 182)(45, 183)(46, 184)(47, 185)(48, 186)(49, 187)(50, 188)(51, 189)(52, 190)(53, 191)(54, 192)(55, 193)(56, 194)(57, 195)(58, 196)(59, 197)(60, 198)(61, 199)(62, 200)(63, 201)(64, 202)(65, 203)(66, 204)(67, 205)(68, 206)(69, 207)(70, 208)(71, 209)(72, 210)(73, 211)(74, 212)(75, 213)(76, 214)(77, 215)(78, 216)(79, 217)(80, 218)(81, 219)(82, 220)(83, 221)(84, 222)(85, 223)(86, 224)(87, 225)(88, 226)(89, 227)(90, 228)(91, 229)(92, 230)(93, 231)(94, 232)(95, 233)(96, 234)(97, 235)(98, 236)(99, 237)(100, 238)(101, 239)(102, 240)(103, 241)(104, 242)(105, 243)(106, 244)(107, 245)(108, 246)(109, 247)(110, 248)(111, 249)(112, 250)(113, 251)(114, 252)(115, 253)(116, 254)(117, 255)(118, 256)(119, 257)(120, 258)(121, 259)(122, 260)(123, 261)(124, 262)(125, 263)(126, 264)(127, 265)(128, 266)(129, 267)(130, 268)(131, 269)(132, 270)(133, 271)(134, 272)(135, 273)(136, 274)(137, 275)(138, 276) local type(s) :: { ( 12, 12 ), ( 12^69 ) } Outer automorphisms :: reflexible Dual of E23.1146 Transitivity :: ET+ Graph:: simple bipartite v = 71 e = 138 f = 23 degree seq :: [ 2^69, 69^2 ] E23.1146 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 6, 69}) Quotient :: loop Aut^+ = C3 x D46 (small group id <138, 2>) Aut = S3 x D46 (small group id <276, 5>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T2)^2, (F * T1)^2, T2^6, T2^-1 * T1 * T2^2 * T1 * T2^-1, T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * 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 * T1, (T2^-1 * T1)^69 ] Map:: R = (1, 139, 3, 141, 8, 146, 17, 155, 10, 148, 4, 142)(2, 140, 5, 143, 12, 150, 21, 159, 14, 152, 6, 144)(7, 145, 15, 153, 24, 162, 18, 156, 9, 147, 16, 154)(11, 149, 19, 157, 28, 166, 22, 160, 13, 151, 20, 158)(23, 161, 31, 169, 26, 164, 33, 171, 25, 163, 32, 170)(27, 165, 34, 172, 30, 168, 36, 174, 29, 167, 35, 173)(37, 175, 43, 181, 39, 177, 45, 183, 38, 176, 44, 182)(40, 178, 46, 184, 42, 180, 48, 186, 41, 179, 47, 185)(49, 187, 55, 193, 51, 189, 57, 195, 50, 188, 56, 194)(52, 190, 60, 198, 54, 192, 70, 208, 53, 191, 61, 199)(58, 196, 91, 229, 63, 201, 93, 231, 65, 203, 92, 230)(59, 197, 96, 234, 67, 205, 104, 242, 69, 207, 97, 235)(62, 200, 99, 237, 72, 210, 101, 239, 64, 202, 94, 232)(66, 204, 103, 241, 76, 214, 106, 244, 68, 206, 95, 233)(71, 209, 108, 246, 74, 212, 100, 238, 73, 211, 98, 236)(75, 213, 112, 250, 78, 216, 105, 243, 77, 215, 102, 240)(79, 217, 110, 248, 81, 219, 109, 247, 80, 218, 107, 245)(82, 220, 114, 252, 84, 222, 113, 251, 83, 221, 111, 249)(85, 223, 117, 255, 87, 225, 116, 254, 86, 224, 115, 253)(88, 226, 120, 258, 90, 228, 119, 257, 89, 227, 118, 256)(121, 259, 127, 265, 123, 261, 129, 267, 122, 260, 128, 266)(124, 262, 134, 272, 126, 264, 136, 274, 125, 263, 135, 273)(130, 268, 133, 271, 137, 275, 132, 270, 131, 269, 138, 276) L = (1, 140)(2, 139)(3, 145)(4, 147)(5, 149)(6, 151)(7, 141)(8, 150)(9, 142)(10, 152)(11, 143)(12, 146)(13, 144)(14, 148)(15, 161)(16, 163)(17, 162)(18, 164)(19, 165)(20, 167)(21, 166)(22, 168)(23, 153)(24, 155)(25, 154)(26, 156)(27, 157)(28, 159)(29, 158)(30, 160)(31, 175)(32, 176)(33, 177)(34, 178)(35, 179)(36, 180)(37, 169)(38, 170)(39, 171)(40, 172)(41, 173)(42, 174)(43, 187)(44, 188)(45, 189)(46, 190)(47, 191)(48, 192)(49, 181)(50, 182)(51, 183)(52, 184)(53, 185)(54, 186)(55, 229)(56, 230)(57, 231)(58, 232)(59, 233)(60, 234)(61, 235)(62, 236)(63, 237)(64, 238)(65, 239)(66, 240)(67, 241)(68, 243)(69, 244)(70, 242)(71, 245)(72, 246)(73, 247)(74, 248)(75, 249)(76, 250)(77, 251)(78, 252)(79, 253)(80, 254)(81, 255)(82, 256)(83, 257)(84, 258)(85, 259)(86, 260)(87, 261)(88, 262)(89, 263)(90, 264)(91, 193)(92, 194)(93, 195)(94, 196)(95, 197)(96, 198)(97, 199)(98, 200)(99, 201)(100, 202)(101, 203)(102, 204)(103, 205)(104, 208)(105, 206)(106, 207)(107, 209)(108, 210)(109, 211)(110, 212)(111, 213)(112, 214)(113, 215)(114, 216)(115, 217)(116, 218)(117, 219)(118, 220)(119, 221)(120, 222)(121, 223)(122, 224)(123, 225)(124, 226)(125, 227)(126, 228)(127, 271)(128, 276)(129, 270)(130, 274)(131, 272)(132, 267)(133, 265)(134, 269)(135, 275)(136, 268)(137, 273)(138, 266) local type(s) :: { ( 2, 69, 2, 69, 2, 69, 2, 69, 2, 69, 2, 69 ) } Outer automorphisms :: reflexible Dual of E23.1145 Transitivity :: ET+ VT+ AT Graph:: v = 23 e = 138 f = 71 degree seq :: [ 12^23 ] E23.1147 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 6, 69}) Quotient :: loop Aut^+ = C3 x D46 (small group id <138, 2>) Aut = S3 x D46 (small group id <276, 5>) |r| :: 2 Presentation :: [ F^2, (T2^-1 * T1^-1)^2, (T2 * T1)^2, (F * T1)^2, (F * T2)^2, T1^-1 * T2^-1 * T1^2 * T2 * T1^-1, (T2 * T1^-1 * T2)^2, T1^-1 * T2^-1 * T1 * T2^22 ] Map:: R = (1, 139, 3, 141, 10, 148, 25, 163, 37, 175, 49, 187, 61, 199, 73, 211, 85, 223, 97, 235, 109, 247, 121, 259, 133, 271, 127, 265, 115, 253, 103, 241, 91, 229, 79, 217, 67, 205, 55, 193, 43, 181, 31, 169, 20, 158, 13, 151, 21, 159, 33, 171, 45, 183, 57, 195, 69, 207, 81, 219, 93, 231, 105, 243, 117, 255, 129, 267, 138, 276, 137, 275, 126, 264, 114, 252, 102, 240, 90, 228, 78, 216, 66, 204, 54, 192, 42, 180, 30, 168, 18, 156, 6, 144, 17, 155, 29, 167, 41, 179, 53, 191, 65, 203, 77, 215, 89, 227, 101, 239, 113, 251, 125, 263, 136, 274, 124, 262, 112, 250, 100, 238, 88, 226, 76, 214, 64, 202, 52, 190, 40, 178, 28, 166, 15, 153, 5, 143)(2, 140, 7, 145, 19, 157, 32, 170, 44, 182, 56, 194, 68, 206, 80, 218, 92, 230, 104, 242, 116, 254, 128, 266, 131, 269, 119, 257, 107, 245, 95, 233, 83, 221, 71, 209, 59, 197, 47, 185, 35, 173, 23, 161, 9, 147, 4, 142, 12, 150, 26, 164, 38, 176, 50, 188, 62, 200, 74, 212, 86, 224, 98, 236, 110, 248, 122, 260, 134, 272, 132, 270, 120, 258, 108, 246, 96, 234, 84, 222, 72, 210, 60, 198, 48, 186, 36, 174, 24, 162, 11, 149, 16, 154, 14, 152, 27, 165, 39, 177, 51, 189, 63, 201, 75, 213, 87, 225, 99, 237, 111, 249, 123, 261, 135, 273, 130, 268, 118, 256, 106, 244, 94, 232, 82, 220, 70, 208, 58, 196, 46, 184, 34, 172, 22, 160, 8, 146) L = (1, 140)(2, 144)(3, 147)(4, 139)(5, 152)(6, 154)(7, 143)(8, 159)(9, 155)(10, 162)(11, 141)(12, 158)(13, 142)(14, 156)(15, 164)(16, 151)(17, 146)(18, 150)(19, 169)(20, 145)(21, 149)(22, 148)(23, 171)(24, 167)(25, 172)(26, 168)(27, 153)(28, 170)(29, 161)(30, 157)(31, 165)(32, 180)(33, 160)(34, 179)(35, 163)(36, 183)(37, 185)(38, 166)(39, 181)(40, 189)(41, 174)(42, 177)(43, 176)(44, 178)(45, 173)(46, 195)(47, 191)(48, 175)(49, 198)(50, 193)(51, 192)(52, 200)(53, 184)(54, 188)(55, 182)(56, 205)(57, 186)(58, 187)(59, 207)(60, 203)(61, 208)(62, 204)(63, 190)(64, 206)(65, 197)(66, 194)(67, 201)(68, 216)(69, 196)(70, 215)(71, 199)(72, 219)(73, 221)(74, 202)(75, 217)(76, 225)(77, 210)(78, 213)(79, 212)(80, 214)(81, 209)(82, 231)(83, 227)(84, 211)(85, 234)(86, 229)(87, 228)(88, 236)(89, 220)(90, 224)(91, 218)(92, 241)(93, 222)(94, 223)(95, 243)(96, 239)(97, 244)(98, 240)(99, 226)(100, 242)(101, 233)(102, 230)(103, 237)(104, 252)(105, 232)(106, 251)(107, 235)(108, 255)(109, 257)(110, 238)(111, 253)(112, 261)(113, 246)(114, 249)(115, 248)(116, 250)(117, 245)(118, 267)(119, 263)(120, 247)(121, 270)(122, 265)(123, 264)(124, 272)(125, 256)(126, 260)(127, 254)(128, 271)(129, 258)(130, 259)(131, 276)(132, 274)(133, 273)(134, 275)(135, 262)(136, 269)(137, 266)(138, 268) local type(s) :: { ( 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6, 2, 6 ) } Outer automorphisms :: reflexible Dual of E23.1143 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 138 f = 92 degree seq :: [ 138^2 ] E23.1148 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 6, 69}) Quotient :: loop Aut^+ = C3 x D46 (small group id <138, 2>) Aut = S3 x D46 (small group id <276, 5>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-3)^2, T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1, T1^9 * T2 * T1^-13 * T2 * T1 ] Map:: polytopal non-degenerate R = (1, 139, 3, 141)(2, 140, 6, 144)(4, 142, 9, 147)(5, 143, 12, 150)(7, 145, 16, 154)(8, 146, 17, 155)(10, 148, 21, 159)(11, 149, 24, 162)(13, 151, 28, 166)(14, 152, 29, 167)(15, 153, 32, 170)(18, 156, 35, 173)(19, 157, 33, 171)(20, 158, 34, 172)(22, 160, 31, 169)(23, 161, 40, 178)(25, 163, 42, 180)(26, 164, 43, 181)(27, 165, 45, 183)(30, 168, 46, 184)(36, 174, 48, 186)(37, 175, 49, 187)(38, 176, 50, 188)(39, 177, 54, 192)(41, 179, 56, 194)(44, 182, 58, 196)(47, 185, 60, 198)(51, 189, 61, 199)(52, 190, 63, 201)(53, 191, 66, 204)(55, 193, 68, 206)(57, 195, 70, 208)(59, 197, 72, 210)(62, 200, 73, 211)(64, 202, 71, 209)(65, 203, 78, 216)(67, 205, 80, 218)(69, 207, 82, 220)(74, 212, 84, 222)(75, 213, 85, 223)(76, 214, 86, 224)(77, 215, 90, 228)(79, 217, 92, 230)(81, 219, 94, 232)(83, 221, 96, 234)(87, 225, 97, 235)(88, 226, 99, 237)(89, 227, 102, 240)(91, 229, 104, 242)(93, 231, 106, 244)(95, 233, 108, 246)(98, 236, 109, 247)(100, 238, 107, 245)(101, 239, 114, 252)(103, 241, 116, 254)(105, 243, 118, 256)(110, 248, 120, 258)(111, 249, 121, 259)(112, 250, 122, 260)(113, 251, 126, 264)(115, 253, 128, 266)(117, 255, 130, 268)(119, 257, 132, 270)(123, 261, 133, 271)(124, 262, 135, 273)(125, 263, 134, 272)(127, 265, 136, 274)(129, 267, 137, 275)(131, 269, 138, 276) L = (1, 140)(2, 143)(3, 145)(4, 139)(5, 149)(6, 151)(7, 153)(8, 141)(9, 157)(10, 142)(11, 161)(12, 163)(13, 165)(14, 144)(15, 169)(16, 166)(17, 167)(18, 146)(19, 174)(20, 147)(21, 175)(22, 148)(23, 177)(24, 156)(25, 158)(26, 150)(27, 159)(28, 180)(29, 181)(30, 152)(31, 185)(32, 183)(33, 154)(34, 155)(35, 184)(36, 188)(37, 189)(38, 160)(39, 191)(40, 168)(41, 162)(42, 173)(43, 194)(44, 164)(45, 172)(46, 196)(47, 197)(48, 170)(49, 171)(50, 200)(51, 201)(52, 176)(53, 203)(54, 182)(55, 178)(56, 206)(57, 179)(58, 208)(59, 209)(60, 187)(61, 186)(62, 212)(63, 213)(64, 190)(65, 215)(66, 195)(67, 192)(68, 218)(69, 193)(70, 220)(71, 221)(72, 199)(73, 198)(74, 224)(75, 225)(76, 202)(77, 227)(78, 207)(79, 204)(80, 230)(81, 205)(82, 232)(83, 233)(84, 210)(85, 211)(86, 236)(87, 237)(88, 214)(89, 239)(90, 219)(91, 216)(92, 242)(93, 217)(94, 244)(95, 245)(96, 223)(97, 222)(98, 248)(99, 249)(100, 226)(101, 251)(102, 231)(103, 228)(104, 254)(105, 229)(106, 256)(107, 257)(108, 235)(109, 234)(110, 260)(111, 261)(112, 238)(113, 263)(114, 243)(115, 240)(116, 266)(117, 241)(118, 268)(119, 269)(120, 246)(121, 247)(122, 272)(123, 273)(124, 250)(125, 270)(126, 255)(127, 252)(128, 274)(129, 253)(130, 275)(131, 265)(132, 259)(133, 258)(134, 267)(135, 264)(136, 262)(137, 276)(138, 271) local type(s) :: { ( 6, 69, 6, 69 ) } Outer automorphisms :: reflexible Dual of E23.1144 Transitivity :: ET+ VT+ AT Graph:: simple v = 69 e = 138 f = 25 degree seq :: [ 4^69 ] E23.1149 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 69}) Quotient :: dipole Aut^+ = C3 x D46 (small group id <138, 2>) Aut = S3 x D46 (small group id <276, 5>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y2^6, Y2^-1 * Y1 * Y2^2 * Y1 * Y2^-1, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1, (Y3 * Y2^-1)^69 ] Map:: R = (1, 139, 2, 140)(3, 141, 7, 145)(4, 142, 9, 147)(5, 143, 11, 149)(6, 144, 13, 151)(8, 146, 12, 150)(10, 148, 14, 152)(15, 153, 23, 161)(16, 154, 25, 163)(17, 155, 24, 162)(18, 156, 26, 164)(19, 157, 27, 165)(20, 158, 29, 167)(21, 159, 28, 166)(22, 160, 30, 168)(31, 169, 37, 175)(32, 170, 38, 176)(33, 171, 39, 177)(34, 172, 40, 178)(35, 173, 41, 179)(36, 174, 42, 180)(43, 181, 49, 187)(44, 182, 50, 188)(45, 183, 51, 189)(46, 184, 52, 190)(47, 185, 53, 191)(48, 186, 54, 192)(55, 193, 85, 223)(56, 194, 87, 225)(57, 195, 89, 227)(58, 196, 91, 229)(59, 197, 93, 231)(60, 198, 95, 233)(61, 199, 97, 235)(62, 200, 100, 238)(63, 201, 98, 236)(64, 202, 102, 240)(65, 203, 105, 243)(66, 204, 108, 246)(67, 205, 106, 244)(68, 206, 111, 249)(69, 207, 113, 251)(70, 208, 116, 254)(71, 209, 114, 252)(72, 210, 119, 257)(73, 211, 121, 259)(74, 212, 123, 261)(75, 213, 125, 263)(76, 214, 127, 265)(77, 215, 129, 267)(78, 216, 131, 269)(79, 217, 133, 271)(80, 218, 135, 273)(81, 219, 137, 275)(82, 220, 138, 276)(83, 221, 134, 272)(84, 222, 136, 274)(86, 224, 130, 268)(88, 226, 132, 270)(90, 228, 128, 266)(92, 230, 122, 260)(94, 232, 120, 258)(96, 234, 115, 253)(99, 237, 112, 250)(101, 239, 107, 245)(103, 241, 126, 264)(104, 242, 124, 262)(109, 247, 118, 256)(110, 248, 117, 255)(277, 415, 279, 417, 284, 422, 293, 431, 286, 424, 280, 418)(278, 416, 281, 419, 288, 426, 297, 435, 290, 428, 282, 420)(283, 421, 291, 429, 300, 438, 294, 432, 285, 423, 292, 430)(287, 425, 295, 433, 304, 442, 298, 436, 289, 427, 296, 434)(299, 437, 307, 445, 302, 440, 309, 447, 301, 439, 308, 446)(303, 441, 310, 448, 306, 444, 312, 450, 305, 443, 311, 449)(313, 451, 319, 457, 315, 453, 321, 459, 314, 452, 320, 458)(316, 454, 322, 460, 318, 456, 324, 462, 317, 455, 323, 461)(325, 463, 331, 469, 327, 465, 333, 471, 326, 464, 332, 470)(328, 466, 340, 478, 330, 468, 334, 472, 329, 467, 339, 477)(335, 473, 363, 501, 343, 481, 361, 499, 336, 474, 365, 503)(337, 475, 374, 512, 347, 485, 378, 516, 338, 476, 367, 505)(341, 479, 382, 520, 344, 482, 371, 509, 342, 480, 369, 507)(345, 483, 390, 528, 348, 486, 376, 514, 346, 484, 373, 511)(349, 487, 387, 525, 351, 489, 384, 522, 350, 488, 381, 519)(352, 490, 395, 533, 354, 492, 392, 530, 353, 491, 389, 527)(355, 493, 401, 539, 357, 495, 399, 537, 356, 494, 397, 535)(358, 496, 407, 545, 360, 498, 405, 543, 359, 497, 403, 541)(362, 500, 413, 551, 366, 504, 411, 549, 364, 502, 409, 547)(368, 506, 410, 548, 379, 517, 414, 552, 380, 518, 412, 550)(370, 508, 408, 546, 386, 524, 406, 544, 372, 510, 404, 542)(375, 513, 402, 540, 394, 532, 400, 538, 377, 515, 398, 536)(383, 521, 393, 531, 388, 526, 391, 529, 385, 523, 396, 534) L = (1, 278)(2, 277)(3, 283)(4, 285)(5, 287)(6, 289)(7, 279)(8, 288)(9, 280)(10, 290)(11, 281)(12, 284)(13, 282)(14, 286)(15, 299)(16, 301)(17, 300)(18, 302)(19, 303)(20, 305)(21, 304)(22, 306)(23, 291)(24, 293)(25, 292)(26, 294)(27, 295)(28, 297)(29, 296)(30, 298)(31, 313)(32, 314)(33, 315)(34, 316)(35, 317)(36, 318)(37, 307)(38, 308)(39, 309)(40, 310)(41, 311)(42, 312)(43, 325)(44, 326)(45, 327)(46, 328)(47, 329)(48, 330)(49, 319)(50, 320)(51, 321)(52, 322)(53, 323)(54, 324)(55, 361)(56, 363)(57, 365)(58, 367)(59, 369)(60, 371)(61, 373)(62, 376)(63, 374)(64, 378)(65, 381)(66, 384)(67, 382)(68, 387)(69, 389)(70, 392)(71, 390)(72, 395)(73, 397)(74, 399)(75, 401)(76, 403)(77, 405)(78, 407)(79, 409)(80, 411)(81, 413)(82, 414)(83, 410)(84, 412)(85, 331)(86, 406)(87, 332)(88, 408)(89, 333)(90, 404)(91, 334)(92, 398)(93, 335)(94, 396)(95, 336)(96, 391)(97, 337)(98, 339)(99, 388)(100, 338)(101, 383)(102, 340)(103, 402)(104, 400)(105, 341)(106, 343)(107, 377)(108, 342)(109, 394)(110, 393)(111, 344)(112, 375)(113, 345)(114, 347)(115, 372)(116, 346)(117, 386)(118, 385)(119, 348)(120, 370)(121, 349)(122, 368)(123, 350)(124, 380)(125, 351)(126, 379)(127, 352)(128, 366)(129, 353)(130, 362)(131, 354)(132, 364)(133, 355)(134, 359)(135, 356)(136, 360)(137, 357)(138, 358)(139, 415)(140, 416)(141, 417)(142, 418)(143, 419)(144, 420)(145, 421)(146, 422)(147, 423)(148, 424)(149, 425)(150, 426)(151, 427)(152, 428)(153, 429)(154, 430)(155, 431)(156, 432)(157, 433)(158, 434)(159, 435)(160, 436)(161, 437)(162, 438)(163, 439)(164, 440)(165, 441)(166, 442)(167, 443)(168, 444)(169, 445)(170, 446)(171, 447)(172, 448)(173, 449)(174, 450)(175, 451)(176, 452)(177, 453)(178, 454)(179, 455)(180, 456)(181, 457)(182, 458)(183, 459)(184, 460)(185, 461)(186, 462)(187, 463)(188, 464)(189, 465)(190, 466)(191, 467)(192, 468)(193, 469)(194, 470)(195, 471)(196, 472)(197, 473)(198, 474)(199, 475)(200, 476)(201, 477)(202, 478)(203, 479)(204, 480)(205, 481)(206, 482)(207, 483)(208, 484)(209, 485)(210, 486)(211, 487)(212, 488)(213, 489)(214, 490)(215, 491)(216, 492)(217, 493)(218, 494)(219, 495)(220, 496)(221, 497)(222, 498)(223, 499)(224, 500)(225, 501)(226, 502)(227, 503)(228, 504)(229, 505)(230, 506)(231, 507)(232, 508)(233, 509)(234, 510)(235, 511)(236, 512)(237, 513)(238, 514)(239, 515)(240, 516)(241, 517)(242, 518)(243, 519)(244, 520)(245, 521)(246, 522)(247, 523)(248, 524)(249, 525)(250, 526)(251, 527)(252, 528)(253, 529)(254, 530)(255, 531)(256, 532)(257, 533)(258, 534)(259, 535)(260, 536)(261, 537)(262, 538)(263, 539)(264, 540)(265, 541)(266, 542)(267, 543)(268, 544)(269, 545)(270, 546)(271, 547)(272, 548)(273, 549)(274, 550)(275, 551)(276, 552) local type(s) :: { ( 2, 138, 2, 138 ), ( 2, 138, 2, 138, 2, 138, 2, 138, 2, 138, 2, 138 ) } Outer automorphisms :: reflexible Dual of E23.1152 Graph:: bipartite v = 92 e = 276 f = 140 degree seq :: [ 4^69, 12^23 ] E23.1150 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 69}) Quotient :: dipole Aut^+ = C3 x D46 (small group id <138, 2>) Aut = S3 x D46 (small group id <276, 5>) |r| :: 2 Presentation :: [ R^2, Y3 * Y2^-1, (Y2^-1 * Y1^-1)^2, (Y2^-1 * Y1^-1)^2, (R * Y1)^2, R * Y2 * R * Y3, (Y3^-1 * Y1^-1)^2, Y1^-1 * Y2^-1 * Y1^2 * Y2 * Y1^-1, Y1^6, (Y2^-2 * Y1)^2, Y1^-1 * Y2^-1 * Y1 * Y2^22 ] Map:: R = (1, 139, 2, 140, 6, 144, 16, 154, 13, 151, 4, 142)(3, 141, 9, 147, 17, 155, 8, 146, 21, 159, 11, 149)(5, 143, 14, 152, 18, 156, 12, 150, 20, 158, 7, 145)(10, 148, 24, 162, 29, 167, 23, 161, 33, 171, 22, 160)(15, 153, 26, 164, 30, 168, 19, 157, 31, 169, 27, 165)(25, 163, 34, 172, 41, 179, 36, 174, 45, 183, 35, 173)(28, 166, 32, 170, 42, 180, 39, 177, 43, 181, 38, 176)(37, 175, 47, 185, 53, 191, 46, 184, 57, 195, 48, 186)(40, 178, 51, 189, 54, 192, 50, 188, 55, 193, 44, 182)(49, 187, 60, 198, 65, 203, 59, 197, 69, 207, 58, 196)(52, 190, 62, 200, 66, 204, 56, 194, 67, 205, 63, 201)(61, 199, 70, 208, 77, 215, 72, 210, 81, 219, 71, 209)(64, 202, 68, 206, 78, 216, 75, 213, 79, 217, 74, 212)(73, 211, 83, 221, 89, 227, 82, 220, 93, 231, 84, 222)(76, 214, 87, 225, 90, 228, 86, 224, 91, 229, 80, 218)(85, 223, 96, 234, 101, 239, 95, 233, 105, 243, 94, 232)(88, 226, 98, 236, 102, 240, 92, 230, 103, 241, 99, 237)(97, 235, 106, 244, 113, 251, 108, 246, 117, 255, 107, 245)(100, 238, 104, 242, 114, 252, 111, 249, 115, 253, 110, 248)(109, 247, 119, 257, 125, 263, 118, 256, 129, 267, 120, 258)(112, 250, 123, 261, 126, 264, 122, 260, 127, 265, 116, 254)(121, 259, 132, 270, 136, 274, 131, 269, 138, 276, 130, 268)(124, 262, 134, 272, 137, 275, 128, 266, 133, 271, 135, 273)(277, 415, 279, 417, 286, 424, 301, 439, 313, 451, 325, 463, 337, 475, 349, 487, 361, 499, 373, 511, 385, 523, 397, 535, 409, 547, 403, 541, 391, 529, 379, 517, 367, 505, 355, 493, 343, 481, 331, 469, 319, 457, 307, 445, 296, 434, 289, 427, 297, 435, 309, 447, 321, 459, 333, 471, 345, 483, 357, 495, 369, 507, 381, 519, 393, 531, 405, 543, 414, 552, 413, 551, 402, 540, 390, 528, 378, 516, 366, 504, 354, 492, 342, 480, 330, 468, 318, 456, 306, 444, 294, 432, 282, 420, 293, 431, 305, 443, 317, 455, 329, 467, 341, 479, 353, 491, 365, 503, 377, 515, 389, 527, 401, 539, 412, 550, 400, 538, 388, 526, 376, 514, 364, 502, 352, 490, 340, 478, 328, 466, 316, 454, 304, 442, 291, 429, 281, 419)(278, 416, 283, 421, 295, 433, 308, 446, 320, 458, 332, 470, 344, 482, 356, 494, 368, 506, 380, 518, 392, 530, 404, 542, 407, 545, 395, 533, 383, 521, 371, 509, 359, 497, 347, 485, 335, 473, 323, 461, 311, 449, 299, 437, 285, 423, 280, 418, 288, 426, 302, 440, 314, 452, 326, 464, 338, 476, 350, 488, 362, 500, 374, 512, 386, 524, 398, 536, 410, 548, 408, 546, 396, 534, 384, 522, 372, 510, 360, 498, 348, 486, 336, 474, 324, 462, 312, 450, 300, 438, 287, 425, 292, 430, 290, 428, 303, 441, 315, 453, 327, 465, 339, 477, 351, 489, 363, 501, 375, 513, 387, 525, 399, 537, 411, 549, 406, 544, 394, 532, 382, 520, 370, 508, 358, 496, 346, 484, 334, 472, 322, 460, 310, 448, 298, 436, 284, 422) L = (1, 279)(2, 283)(3, 286)(4, 288)(5, 277)(6, 293)(7, 295)(8, 278)(9, 280)(10, 301)(11, 292)(12, 302)(13, 297)(14, 303)(15, 281)(16, 290)(17, 305)(18, 282)(19, 308)(20, 289)(21, 309)(22, 284)(23, 285)(24, 287)(25, 313)(26, 314)(27, 315)(28, 291)(29, 317)(30, 294)(31, 296)(32, 320)(33, 321)(34, 298)(35, 299)(36, 300)(37, 325)(38, 326)(39, 327)(40, 304)(41, 329)(42, 306)(43, 307)(44, 332)(45, 333)(46, 310)(47, 311)(48, 312)(49, 337)(50, 338)(51, 339)(52, 316)(53, 341)(54, 318)(55, 319)(56, 344)(57, 345)(58, 322)(59, 323)(60, 324)(61, 349)(62, 350)(63, 351)(64, 328)(65, 353)(66, 330)(67, 331)(68, 356)(69, 357)(70, 334)(71, 335)(72, 336)(73, 361)(74, 362)(75, 363)(76, 340)(77, 365)(78, 342)(79, 343)(80, 368)(81, 369)(82, 346)(83, 347)(84, 348)(85, 373)(86, 374)(87, 375)(88, 352)(89, 377)(90, 354)(91, 355)(92, 380)(93, 381)(94, 358)(95, 359)(96, 360)(97, 385)(98, 386)(99, 387)(100, 364)(101, 389)(102, 366)(103, 367)(104, 392)(105, 393)(106, 370)(107, 371)(108, 372)(109, 397)(110, 398)(111, 399)(112, 376)(113, 401)(114, 378)(115, 379)(116, 404)(117, 405)(118, 382)(119, 383)(120, 384)(121, 409)(122, 410)(123, 411)(124, 388)(125, 412)(126, 390)(127, 391)(128, 407)(129, 414)(130, 394)(131, 395)(132, 396)(133, 403)(134, 408)(135, 406)(136, 400)(137, 402)(138, 413)(139, 415)(140, 416)(141, 417)(142, 418)(143, 419)(144, 420)(145, 421)(146, 422)(147, 423)(148, 424)(149, 425)(150, 426)(151, 427)(152, 428)(153, 429)(154, 430)(155, 431)(156, 432)(157, 433)(158, 434)(159, 435)(160, 436)(161, 437)(162, 438)(163, 439)(164, 440)(165, 441)(166, 442)(167, 443)(168, 444)(169, 445)(170, 446)(171, 447)(172, 448)(173, 449)(174, 450)(175, 451)(176, 452)(177, 453)(178, 454)(179, 455)(180, 456)(181, 457)(182, 458)(183, 459)(184, 460)(185, 461)(186, 462)(187, 463)(188, 464)(189, 465)(190, 466)(191, 467)(192, 468)(193, 469)(194, 470)(195, 471)(196, 472)(197, 473)(198, 474)(199, 475)(200, 476)(201, 477)(202, 478)(203, 479)(204, 480)(205, 481)(206, 482)(207, 483)(208, 484)(209, 485)(210, 486)(211, 487)(212, 488)(213, 489)(214, 490)(215, 491)(216, 492)(217, 493)(218, 494)(219, 495)(220, 496)(221, 497)(222, 498)(223, 499)(224, 500)(225, 501)(226, 502)(227, 503)(228, 504)(229, 505)(230, 506)(231, 507)(232, 508)(233, 509)(234, 510)(235, 511)(236, 512)(237, 513)(238, 514)(239, 515)(240, 516)(241, 517)(242, 518)(243, 519)(244, 520)(245, 521)(246, 522)(247, 523)(248, 524)(249, 525)(250, 526)(251, 527)(252, 528)(253, 529)(254, 530)(255, 531)(256, 532)(257, 533)(258, 534)(259, 535)(260, 536)(261, 537)(262, 538)(263, 539)(264, 540)(265, 541)(266, 542)(267, 543)(268, 544)(269, 545)(270, 546)(271, 547)(272, 548)(273, 549)(274, 550)(275, 551)(276, 552) 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 E23.1151 Graph:: bipartite v = 25 e = 276 f = 207 degree seq :: [ 12^23, 138^2 ] E23.1151 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 69}) Quotient :: dipole Aut^+ = C3 x D46 (small group id <138, 2>) Aut = S3 x D46 (small group id <276, 5>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3^3 * Y2)^2, Y3^-1 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3^-1 * Y2, Y3^-21 * Y2 * Y3 * Y2 * Y3^-1, (Y3^-1 * Y1^-1)^69 ] Map:: polytopal R = (1, 139)(2, 140)(3, 141)(4, 142)(5, 143)(6, 144)(7, 145)(8, 146)(9, 147)(10, 148)(11, 149)(12, 150)(13, 151)(14, 152)(15, 153)(16, 154)(17, 155)(18, 156)(19, 157)(20, 158)(21, 159)(22, 160)(23, 161)(24, 162)(25, 163)(26, 164)(27, 165)(28, 166)(29, 167)(30, 168)(31, 169)(32, 170)(33, 171)(34, 172)(35, 173)(36, 174)(37, 175)(38, 176)(39, 177)(40, 178)(41, 179)(42, 180)(43, 181)(44, 182)(45, 183)(46, 184)(47, 185)(48, 186)(49, 187)(50, 188)(51, 189)(52, 190)(53, 191)(54, 192)(55, 193)(56, 194)(57, 195)(58, 196)(59, 197)(60, 198)(61, 199)(62, 200)(63, 201)(64, 202)(65, 203)(66, 204)(67, 205)(68, 206)(69, 207)(70, 208)(71, 209)(72, 210)(73, 211)(74, 212)(75, 213)(76, 214)(77, 215)(78, 216)(79, 217)(80, 218)(81, 219)(82, 220)(83, 221)(84, 222)(85, 223)(86, 224)(87, 225)(88, 226)(89, 227)(90, 228)(91, 229)(92, 230)(93, 231)(94, 232)(95, 233)(96, 234)(97, 235)(98, 236)(99, 237)(100, 238)(101, 239)(102, 240)(103, 241)(104, 242)(105, 243)(106, 244)(107, 245)(108, 246)(109, 247)(110, 248)(111, 249)(112, 250)(113, 251)(114, 252)(115, 253)(116, 254)(117, 255)(118, 256)(119, 257)(120, 258)(121, 259)(122, 260)(123, 261)(124, 262)(125, 263)(126, 264)(127, 265)(128, 266)(129, 267)(130, 268)(131, 269)(132, 270)(133, 271)(134, 272)(135, 273)(136, 274)(137, 275)(138, 276)(277, 415, 278, 416)(279, 417, 283, 421)(280, 418, 285, 423)(281, 419, 287, 425)(282, 420, 289, 427)(284, 422, 293, 431)(286, 424, 297, 435)(288, 426, 301, 439)(290, 428, 305, 443)(291, 429, 299, 437)(292, 430, 303, 441)(294, 432, 306, 444)(295, 433, 300, 438)(296, 434, 304, 442)(298, 436, 302, 440)(307, 445, 317, 455)(308, 446, 321, 459)(309, 447, 315, 453)(310, 448, 320, 458)(311, 449, 323, 461)(312, 450, 318, 456)(313, 451, 316, 454)(314, 452, 326, 464)(319, 457, 329, 467)(322, 460, 332, 470)(324, 462, 333, 471)(325, 463, 336, 474)(327, 465, 330, 468)(328, 466, 339, 477)(331, 469, 342, 480)(334, 472, 345, 483)(335, 473, 344, 482)(337, 475, 346, 484)(338, 476, 341, 479)(340, 478, 343, 481)(347, 485, 357, 495)(348, 486, 356, 494)(349, 487, 359, 497)(350, 488, 354, 492)(351, 489, 353, 491)(352, 490, 362, 500)(355, 493, 365, 503)(358, 496, 368, 506)(360, 498, 369, 507)(361, 499, 372, 510)(363, 501, 366, 504)(364, 502, 375, 513)(367, 505, 378, 516)(370, 508, 381, 519)(371, 509, 380, 518)(373, 511, 382, 520)(374, 512, 377, 515)(376, 514, 379, 517)(383, 521, 393, 531)(384, 522, 392, 530)(385, 523, 395, 533)(386, 524, 390, 528)(387, 525, 389, 527)(388, 526, 398, 536)(391, 529, 401, 539)(394, 532, 404, 542)(396, 534, 405, 543)(397, 535, 408, 546)(399, 537, 402, 540)(400, 538, 411, 549)(403, 541, 413, 551)(406, 544, 414, 552)(407, 545, 412, 550)(409, 547, 410, 548) L = (1, 279)(2, 281)(3, 284)(4, 277)(5, 288)(6, 278)(7, 291)(8, 294)(9, 295)(10, 280)(11, 299)(12, 302)(13, 303)(14, 282)(15, 307)(16, 283)(17, 309)(18, 311)(19, 312)(20, 285)(21, 313)(22, 286)(23, 315)(24, 287)(25, 317)(26, 319)(27, 320)(28, 289)(29, 321)(30, 290)(31, 297)(32, 292)(33, 296)(34, 293)(35, 325)(36, 326)(37, 327)(38, 298)(39, 305)(40, 300)(41, 304)(42, 301)(43, 331)(44, 332)(45, 333)(46, 306)(47, 308)(48, 310)(49, 337)(50, 338)(51, 339)(52, 314)(53, 316)(54, 318)(55, 343)(56, 344)(57, 345)(58, 322)(59, 323)(60, 324)(61, 349)(62, 350)(63, 351)(64, 328)(65, 329)(66, 330)(67, 355)(68, 356)(69, 357)(70, 334)(71, 335)(72, 336)(73, 361)(74, 362)(75, 363)(76, 340)(77, 341)(78, 342)(79, 367)(80, 368)(81, 369)(82, 346)(83, 347)(84, 348)(85, 373)(86, 374)(87, 375)(88, 352)(89, 353)(90, 354)(91, 379)(92, 380)(93, 381)(94, 358)(95, 359)(96, 360)(97, 385)(98, 386)(99, 387)(100, 364)(101, 365)(102, 366)(103, 391)(104, 392)(105, 393)(106, 370)(107, 371)(108, 372)(109, 397)(110, 398)(111, 399)(112, 376)(113, 377)(114, 378)(115, 403)(116, 404)(117, 405)(118, 382)(119, 383)(120, 384)(121, 409)(122, 410)(123, 411)(124, 388)(125, 389)(126, 390)(127, 407)(128, 412)(129, 414)(130, 394)(131, 395)(132, 396)(133, 401)(134, 406)(135, 408)(136, 400)(137, 402)(138, 413)(139, 415)(140, 416)(141, 417)(142, 418)(143, 419)(144, 420)(145, 421)(146, 422)(147, 423)(148, 424)(149, 425)(150, 426)(151, 427)(152, 428)(153, 429)(154, 430)(155, 431)(156, 432)(157, 433)(158, 434)(159, 435)(160, 436)(161, 437)(162, 438)(163, 439)(164, 440)(165, 441)(166, 442)(167, 443)(168, 444)(169, 445)(170, 446)(171, 447)(172, 448)(173, 449)(174, 450)(175, 451)(176, 452)(177, 453)(178, 454)(179, 455)(180, 456)(181, 457)(182, 458)(183, 459)(184, 460)(185, 461)(186, 462)(187, 463)(188, 464)(189, 465)(190, 466)(191, 467)(192, 468)(193, 469)(194, 470)(195, 471)(196, 472)(197, 473)(198, 474)(199, 475)(200, 476)(201, 477)(202, 478)(203, 479)(204, 480)(205, 481)(206, 482)(207, 483)(208, 484)(209, 485)(210, 486)(211, 487)(212, 488)(213, 489)(214, 490)(215, 491)(216, 492)(217, 493)(218, 494)(219, 495)(220, 496)(221, 497)(222, 498)(223, 499)(224, 500)(225, 501)(226, 502)(227, 503)(228, 504)(229, 505)(230, 506)(231, 507)(232, 508)(233, 509)(234, 510)(235, 511)(236, 512)(237, 513)(238, 514)(239, 515)(240, 516)(241, 517)(242, 518)(243, 519)(244, 520)(245, 521)(246, 522)(247, 523)(248, 524)(249, 525)(250, 526)(251, 527)(252, 528)(253, 529)(254, 530)(255, 531)(256, 532)(257, 533)(258, 534)(259, 535)(260, 536)(261, 537)(262, 538)(263, 539)(264, 540)(265, 541)(266, 542)(267, 543)(268, 544)(269, 545)(270, 546)(271, 547)(272, 548)(273, 549)(274, 550)(275, 551)(276, 552) local type(s) :: { ( 12, 138 ), ( 12, 138, 12, 138 ) } Outer automorphisms :: reflexible Dual of E23.1150 Graph:: simple bipartite v = 207 e = 276 f = 25 degree seq :: [ 2^138, 4^69 ] E23.1152 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 69}) Quotient :: dipole Aut^+ = C3 x D46 (small group id <138, 2>) Aut = S3 x D46 (small group id <276, 5>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, (Y1^-1 * Y3 * Y1^-2)^2, Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1^-1, Y1^7 * Y3 * Y1^-16 * Y3 ] Map:: R = (1, 139, 2, 140, 5, 143, 11, 149, 23, 161, 39, 177, 53, 191, 65, 203, 77, 215, 89, 227, 101, 239, 113, 251, 125, 263, 132, 270, 121, 259, 109, 247, 96, 234, 85, 223, 73, 211, 60, 198, 49, 187, 33, 171, 16, 154, 28, 166, 42, 180, 35, 173, 46, 184, 58, 196, 70, 208, 82, 220, 94, 232, 106, 244, 118, 256, 130, 268, 137, 275, 138, 276, 133, 271, 120, 258, 108, 246, 97, 235, 84, 222, 72, 210, 61, 199, 48, 186, 32, 170, 45, 183, 34, 172, 17, 155, 29, 167, 43, 181, 56, 194, 68, 206, 80, 218, 92, 230, 104, 242, 116, 254, 128, 266, 136, 274, 124, 262, 112, 250, 100, 238, 88, 226, 76, 214, 64, 202, 52, 190, 38, 176, 22, 160, 10, 148, 4, 142)(3, 141, 7, 145, 15, 153, 31, 169, 47, 185, 59, 197, 71, 209, 83, 221, 95, 233, 107, 245, 119, 257, 131, 269, 127, 265, 114, 252, 105, 243, 91, 229, 78, 216, 69, 207, 55, 193, 40, 178, 30, 168, 14, 152, 6, 144, 13, 151, 27, 165, 21, 159, 37, 175, 51, 189, 63, 201, 75, 213, 87, 225, 99, 237, 111, 249, 123, 261, 135, 273, 126, 264, 117, 255, 103, 241, 90, 228, 81, 219, 67, 205, 54, 192, 44, 182, 26, 164, 12, 150, 25, 163, 20, 158, 9, 147, 19, 157, 36, 174, 50, 188, 62, 200, 74, 212, 86, 224, 98, 236, 110, 248, 122, 260, 134, 272, 129, 267, 115, 253, 102, 240, 93, 231, 79, 217, 66, 204, 57, 195, 41, 179, 24, 162, 18, 156, 8, 146)(277, 415)(278, 416)(279, 417)(280, 418)(281, 419)(282, 420)(283, 421)(284, 422)(285, 423)(286, 424)(287, 425)(288, 426)(289, 427)(290, 428)(291, 429)(292, 430)(293, 431)(294, 432)(295, 433)(296, 434)(297, 435)(298, 436)(299, 437)(300, 438)(301, 439)(302, 440)(303, 441)(304, 442)(305, 443)(306, 444)(307, 445)(308, 446)(309, 447)(310, 448)(311, 449)(312, 450)(313, 451)(314, 452)(315, 453)(316, 454)(317, 455)(318, 456)(319, 457)(320, 458)(321, 459)(322, 460)(323, 461)(324, 462)(325, 463)(326, 464)(327, 465)(328, 466)(329, 467)(330, 468)(331, 469)(332, 470)(333, 471)(334, 472)(335, 473)(336, 474)(337, 475)(338, 476)(339, 477)(340, 478)(341, 479)(342, 480)(343, 481)(344, 482)(345, 483)(346, 484)(347, 485)(348, 486)(349, 487)(350, 488)(351, 489)(352, 490)(353, 491)(354, 492)(355, 493)(356, 494)(357, 495)(358, 496)(359, 497)(360, 498)(361, 499)(362, 500)(363, 501)(364, 502)(365, 503)(366, 504)(367, 505)(368, 506)(369, 507)(370, 508)(371, 509)(372, 510)(373, 511)(374, 512)(375, 513)(376, 514)(377, 515)(378, 516)(379, 517)(380, 518)(381, 519)(382, 520)(383, 521)(384, 522)(385, 523)(386, 524)(387, 525)(388, 526)(389, 527)(390, 528)(391, 529)(392, 530)(393, 531)(394, 532)(395, 533)(396, 534)(397, 535)(398, 536)(399, 537)(400, 538)(401, 539)(402, 540)(403, 541)(404, 542)(405, 543)(406, 544)(407, 545)(408, 546)(409, 547)(410, 548)(411, 549)(412, 550)(413, 551)(414, 552) L = (1, 279)(2, 282)(3, 277)(4, 285)(5, 288)(6, 278)(7, 292)(8, 293)(9, 280)(10, 297)(11, 300)(12, 281)(13, 304)(14, 305)(15, 308)(16, 283)(17, 284)(18, 311)(19, 309)(20, 310)(21, 286)(22, 307)(23, 316)(24, 287)(25, 318)(26, 319)(27, 321)(28, 289)(29, 290)(30, 322)(31, 298)(32, 291)(33, 295)(34, 296)(35, 294)(36, 324)(37, 325)(38, 326)(39, 330)(40, 299)(41, 332)(42, 301)(43, 302)(44, 334)(45, 303)(46, 306)(47, 336)(48, 312)(49, 313)(50, 314)(51, 337)(52, 339)(53, 342)(54, 315)(55, 344)(56, 317)(57, 346)(58, 320)(59, 348)(60, 323)(61, 327)(62, 349)(63, 328)(64, 347)(65, 354)(66, 329)(67, 356)(68, 331)(69, 358)(70, 333)(71, 340)(72, 335)(73, 338)(74, 360)(75, 361)(76, 362)(77, 366)(78, 341)(79, 368)(80, 343)(81, 370)(82, 345)(83, 372)(84, 350)(85, 351)(86, 352)(87, 373)(88, 375)(89, 378)(90, 353)(91, 380)(92, 355)(93, 382)(94, 357)(95, 384)(96, 359)(97, 363)(98, 385)(99, 364)(100, 383)(101, 390)(102, 365)(103, 392)(104, 367)(105, 394)(106, 369)(107, 376)(108, 371)(109, 374)(110, 396)(111, 397)(112, 398)(113, 402)(114, 377)(115, 404)(116, 379)(117, 406)(118, 381)(119, 408)(120, 386)(121, 387)(122, 388)(123, 409)(124, 411)(125, 410)(126, 389)(127, 412)(128, 391)(129, 413)(130, 393)(131, 414)(132, 395)(133, 399)(134, 401)(135, 400)(136, 403)(137, 405)(138, 407)(139, 415)(140, 416)(141, 417)(142, 418)(143, 419)(144, 420)(145, 421)(146, 422)(147, 423)(148, 424)(149, 425)(150, 426)(151, 427)(152, 428)(153, 429)(154, 430)(155, 431)(156, 432)(157, 433)(158, 434)(159, 435)(160, 436)(161, 437)(162, 438)(163, 439)(164, 440)(165, 441)(166, 442)(167, 443)(168, 444)(169, 445)(170, 446)(171, 447)(172, 448)(173, 449)(174, 450)(175, 451)(176, 452)(177, 453)(178, 454)(179, 455)(180, 456)(181, 457)(182, 458)(183, 459)(184, 460)(185, 461)(186, 462)(187, 463)(188, 464)(189, 465)(190, 466)(191, 467)(192, 468)(193, 469)(194, 470)(195, 471)(196, 472)(197, 473)(198, 474)(199, 475)(200, 476)(201, 477)(202, 478)(203, 479)(204, 480)(205, 481)(206, 482)(207, 483)(208, 484)(209, 485)(210, 486)(211, 487)(212, 488)(213, 489)(214, 490)(215, 491)(216, 492)(217, 493)(218, 494)(219, 495)(220, 496)(221, 497)(222, 498)(223, 499)(224, 500)(225, 501)(226, 502)(227, 503)(228, 504)(229, 505)(230, 506)(231, 507)(232, 508)(233, 509)(234, 510)(235, 511)(236, 512)(237, 513)(238, 514)(239, 515)(240, 516)(241, 517)(242, 518)(243, 519)(244, 520)(245, 521)(246, 522)(247, 523)(248, 524)(249, 525)(250, 526)(251, 527)(252, 528)(253, 529)(254, 530)(255, 531)(256, 532)(257, 533)(258, 534)(259, 535)(260, 536)(261, 537)(262, 538)(263, 539)(264, 540)(265, 541)(266, 542)(267, 543)(268, 544)(269, 545)(270, 546)(271, 547)(272, 548)(273, 549)(274, 550)(275, 551)(276, 552) local type(s) :: { ( 4, 12 ), ( 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 4, 12, 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 E23.1149 Graph:: simple bipartite v = 140 e = 276 f = 92 degree seq :: [ 2^138, 138^2 ] E23.1153 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 69}) Quotient :: dipole Aut^+ = C3 x D46 (small group id <138, 2>) Aut = S3 x D46 (small group id <276, 5>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y2^3 * Y1)^2, Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1, (Y3 * Y2^-1)^6, Y2^3 * Y1 * Y2^-19 * Y1 * Y2 ] Map:: R = (1, 139, 2, 140)(3, 141, 7, 145)(4, 142, 9, 147)(5, 143, 11, 149)(6, 144, 13, 151)(8, 146, 17, 155)(10, 148, 21, 159)(12, 150, 25, 163)(14, 152, 29, 167)(15, 153, 23, 161)(16, 154, 27, 165)(18, 156, 30, 168)(19, 157, 24, 162)(20, 158, 28, 166)(22, 160, 26, 164)(31, 169, 41, 179)(32, 170, 45, 183)(33, 171, 39, 177)(34, 172, 44, 182)(35, 173, 47, 185)(36, 174, 42, 180)(37, 175, 40, 178)(38, 176, 50, 188)(43, 181, 53, 191)(46, 184, 56, 194)(48, 186, 57, 195)(49, 187, 60, 198)(51, 189, 54, 192)(52, 190, 63, 201)(55, 193, 66, 204)(58, 196, 69, 207)(59, 197, 68, 206)(61, 199, 70, 208)(62, 200, 65, 203)(64, 202, 67, 205)(71, 209, 81, 219)(72, 210, 80, 218)(73, 211, 83, 221)(74, 212, 78, 216)(75, 213, 77, 215)(76, 214, 86, 224)(79, 217, 89, 227)(82, 220, 92, 230)(84, 222, 93, 231)(85, 223, 96, 234)(87, 225, 90, 228)(88, 226, 99, 237)(91, 229, 102, 240)(94, 232, 105, 243)(95, 233, 104, 242)(97, 235, 106, 244)(98, 236, 101, 239)(100, 238, 103, 241)(107, 245, 117, 255)(108, 246, 116, 254)(109, 247, 119, 257)(110, 248, 114, 252)(111, 249, 113, 251)(112, 250, 122, 260)(115, 253, 125, 263)(118, 256, 128, 266)(120, 258, 129, 267)(121, 259, 132, 270)(123, 261, 126, 264)(124, 262, 135, 273)(127, 265, 137, 275)(130, 268, 138, 276)(131, 269, 136, 274)(133, 271, 134, 272)(277, 415, 279, 417, 284, 422, 294, 432, 311, 449, 325, 463, 337, 475, 349, 487, 361, 499, 373, 511, 385, 523, 397, 535, 409, 547, 401, 539, 389, 527, 377, 515, 365, 503, 353, 491, 341, 479, 329, 467, 316, 454, 300, 438, 287, 425, 299, 437, 315, 453, 305, 443, 321, 459, 333, 471, 345, 483, 357, 495, 369, 507, 381, 519, 393, 531, 405, 543, 414, 552, 413, 551, 402, 540, 390, 528, 378, 516, 366, 504, 354, 492, 342, 480, 330, 468, 318, 456, 301, 439, 317, 455, 304, 442, 289, 427, 303, 441, 320, 458, 332, 470, 344, 482, 356, 494, 368, 506, 380, 518, 392, 530, 404, 542, 412, 550, 400, 538, 388, 526, 376, 514, 364, 502, 352, 490, 340, 478, 328, 466, 314, 452, 298, 436, 286, 424, 280, 418)(278, 416, 281, 419, 288, 426, 302, 440, 319, 457, 331, 469, 343, 481, 355, 493, 367, 505, 379, 517, 391, 529, 403, 541, 407, 545, 395, 533, 383, 521, 371, 509, 359, 497, 347, 485, 335, 473, 323, 461, 308, 446, 292, 430, 283, 421, 291, 429, 307, 445, 297, 435, 313, 451, 327, 465, 339, 477, 351, 489, 363, 501, 375, 513, 387, 525, 399, 537, 411, 549, 408, 546, 396, 534, 384, 522, 372, 510, 360, 498, 348, 486, 336, 474, 324, 462, 310, 448, 293, 431, 309, 447, 296, 434, 285, 423, 295, 433, 312, 450, 326, 464, 338, 476, 350, 488, 362, 500, 374, 512, 386, 524, 398, 536, 410, 548, 406, 544, 394, 532, 382, 520, 370, 508, 358, 496, 346, 484, 334, 472, 322, 460, 306, 444, 290, 428, 282, 420) L = (1, 278)(2, 277)(3, 283)(4, 285)(5, 287)(6, 289)(7, 279)(8, 293)(9, 280)(10, 297)(11, 281)(12, 301)(13, 282)(14, 305)(15, 299)(16, 303)(17, 284)(18, 306)(19, 300)(20, 304)(21, 286)(22, 302)(23, 291)(24, 295)(25, 288)(26, 298)(27, 292)(28, 296)(29, 290)(30, 294)(31, 317)(32, 321)(33, 315)(34, 320)(35, 323)(36, 318)(37, 316)(38, 326)(39, 309)(40, 313)(41, 307)(42, 312)(43, 329)(44, 310)(45, 308)(46, 332)(47, 311)(48, 333)(49, 336)(50, 314)(51, 330)(52, 339)(53, 319)(54, 327)(55, 342)(56, 322)(57, 324)(58, 345)(59, 344)(60, 325)(61, 346)(62, 341)(63, 328)(64, 343)(65, 338)(66, 331)(67, 340)(68, 335)(69, 334)(70, 337)(71, 357)(72, 356)(73, 359)(74, 354)(75, 353)(76, 362)(77, 351)(78, 350)(79, 365)(80, 348)(81, 347)(82, 368)(83, 349)(84, 369)(85, 372)(86, 352)(87, 366)(88, 375)(89, 355)(90, 363)(91, 378)(92, 358)(93, 360)(94, 381)(95, 380)(96, 361)(97, 382)(98, 377)(99, 364)(100, 379)(101, 374)(102, 367)(103, 376)(104, 371)(105, 370)(106, 373)(107, 393)(108, 392)(109, 395)(110, 390)(111, 389)(112, 398)(113, 387)(114, 386)(115, 401)(116, 384)(117, 383)(118, 404)(119, 385)(120, 405)(121, 408)(122, 388)(123, 402)(124, 411)(125, 391)(126, 399)(127, 413)(128, 394)(129, 396)(130, 414)(131, 412)(132, 397)(133, 410)(134, 409)(135, 400)(136, 407)(137, 403)(138, 406)(139, 415)(140, 416)(141, 417)(142, 418)(143, 419)(144, 420)(145, 421)(146, 422)(147, 423)(148, 424)(149, 425)(150, 426)(151, 427)(152, 428)(153, 429)(154, 430)(155, 431)(156, 432)(157, 433)(158, 434)(159, 435)(160, 436)(161, 437)(162, 438)(163, 439)(164, 440)(165, 441)(166, 442)(167, 443)(168, 444)(169, 445)(170, 446)(171, 447)(172, 448)(173, 449)(174, 450)(175, 451)(176, 452)(177, 453)(178, 454)(179, 455)(180, 456)(181, 457)(182, 458)(183, 459)(184, 460)(185, 461)(186, 462)(187, 463)(188, 464)(189, 465)(190, 466)(191, 467)(192, 468)(193, 469)(194, 470)(195, 471)(196, 472)(197, 473)(198, 474)(199, 475)(200, 476)(201, 477)(202, 478)(203, 479)(204, 480)(205, 481)(206, 482)(207, 483)(208, 484)(209, 485)(210, 486)(211, 487)(212, 488)(213, 489)(214, 490)(215, 491)(216, 492)(217, 493)(218, 494)(219, 495)(220, 496)(221, 497)(222, 498)(223, 499)(224, 500)(225, 501)(226, 502)(227, 503)(228, 504)(229, 505)(230, 506)(231, 507)(232, 508)(233, 509)(234, 510)(235, 511)(236, 512)(237, 513)(238, 514)(239, 515)(240, 516)(241, 517)(242, 518)(243, 519)(244, 520)(245, 521)(246, 522)(247, 523)(248, 524)(249, 525)(250, 526)(251, 527)(252, 528)(253, 529)(254, 530)(255, 531)(256, 532)(257, 533)(258, 534)(259, 535)(260, 536)(261, 537)(262, 538)(263, 539)(264, 540)(265, 541)(266, 542)(267, 543)(268, 544)(269, 545)(270, 546)(271, 547)(272, 548)(273, 549)(274, 550)(275, 551)(276, 552) local type(s) :: { ( 2, 12, 2, 12 ), ( 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12, 2, 12 ) } Outer automorphisms :: reflexible Dual of E23.1154 Graph:: bipartite v = 71 e = 276 f = 161 degree seq :: [ 4^69, 138^2 ] E23.1154 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 6, 69}) Quotient :: dipole Aut^+ = C3 x D46 (small group id <138, 2>) Aut = S3 x D46 (small group id <276, 5>) |r| :: 2 Presentation :: [ Y2, R^2, (Y3^-1 * Y1^-1)^2, (Y3 * Y1)^2, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y3^-1 * Y1^2 * Y3 * Y1^-1, (Y3^-2 * Y1)^2, Y1^6, Y1^-1 * Y3^-1 * Y1 * Y3^22, (Y3 * Y2^-1)^69 ] Map:: R = (1, 139, 2, 140, 6, 144, 16, 154, 13, 151, 4, 142)(3, 141, 9, 147, 17, 155, 8, 146, 21, 159, 11, 149)(5, 143, 14, 152, 18, 156, 12, 150, 20, 158, 7, 145)(10, 148, 24, 162, 29, 167, 23, 161, 33, 171, 22, 160)(15, 153, 26, 164, 30, 168, 19, 157, 31, 169, 27, 165)(25, 163, 34, 172, 41, 179, 36, 174, 45, 183, 35, 173)(28, 166, 32, 170, 42, 180, 39, 177, 43, 181, 38, 176)(37, 175, 47, 185, 53, 191, 46, 184, 57, 195, 48, 186)(40, 178, 51, 189, 54, 192, 50, 188, 55, 193, 44, 182)(49, 187, 60, 198, 65, 203, 59, 197, 69, 207, 58, 196)(52, 190, 62, 200, 66, 204, 56, 194, 67, 205, 63, 201)(61, 199, 70, 208, 77, 215, 72, 210, 81, 219, 71, 209)(64, 202, 68, 206, 78, 216, 75, 213, 79, 217, 74, 212)(73, 211, 83, 221, 89, 227, 82, 220, 93, 231, 84, 222)(76, 214, 87, 225, 90, 228, 86, 224, 91, 229, 80, 218)(85, 223, 96, 234, 101, 239, 95, 233, 105, 243, 94, 232)(88, 226, 98, 236, 102, 240, 92, 230, 103, 241, 99, 237)(97, 235, 106, 244, 113, 251, 108, 246, 117, 255, 107, 245)(100, 238, 104, 242, 114, 252, 111, 249, 115, 253, 110, 248)(109, 247, 119, 257, 125, 263, 118, 256, 129, 267, 120, 258)(112, 250, 123, 261, 126, 264, 122, 260, 127, 265, 116, 254)(121, 259, 132, 270, 136, 274, 131, 269, 138, 276, 130, 268)(124, 262, 134, 272, 137, 275, 128, 266, 133, 271, 135, 273)(277, 415)(278, 416)(279, 417)(280, 418)(281, 419)(282, 420)(283, 421)(284, 422)(285, 423)(286, 424)(287, 425)(288, 426)(289, 427)(290, 428)(291, 429)(292, 430)(293, 431)(294, 432)(295, 433)(296, 434)(297, 435)(298, 436)(299, 437)(300, 438)(301, 439)(302, 440)(303, 441)(304, 442)(305, 443)(306, 444)(307, 445)(308, 446)(309, 447)(310, 448)(311, 449)(312, 450)(313, 451)(314, 452)(315, 453)(316, 454)(317, 455)(318, 456)(319, 457)(320, 458)(321, 459)(322, 460)(323, 461)(324, 462)(325, 463)(326, 464)(327, 465)(328, 466)(329, 467)(330, 468)(331, 469)(332, 470)(333, 471)(334, 472)(335, 473)(336, 474)(337, 475)(338, 476)(339, 477)(340, 478)(341, 479)(342, 480)(343, 481)(344, 482)(345, 483)(346, 484)(347, 485)(348, 486)(349, 487)(350, 488)(351, 489)(352, 490)(353, 491)(354, 492)(355, 493)(356, 494)(357, 495)(358, 496)(359, 497)(360, 498)(361, 499)(362, 500)(363, 501)(364, 502)(365, 503)(366, 504)(367, 505)(368, 506)(369, 507)(370, 508)(371, 509)(372, 510)(373, 511)(374, 512)(375, 513)(376, 514)(377, 515)(378, 516)(379, 517)(380, 518)(381, 519)(382, 520)(383, 521)(384, 522)(385, 523)(386, 524)(387, 525)(388, 526)(389, 527)(390, 528)(391, 529)(392, 530)(393, 531)(394, 532)(395, 533)(396, 534)(397, 535)(398, 536)(399, 537)(400, 538)(401, 539)(402, 540)(403, 541)(404, 542)(405, 543)(406, 544)(407, 545)(408, 546)(409, 547)(410, 548)(411, 549)(412, 550)(413, 551)(414, 552) L = (1, 279)(2, 283)(3, 286)(4, 288)(5, 277)(6, 293)(7, 295)(8, 278)(9, 280)(10, 301)(11, 292)(12, 302)(13, 297)(14, 303)(15, 281)(16, 290)(17, 305)(18, 282)(19, 308)(20, 289)(21, 309)(22, 284)(23, 285)(24, 287)(25, 313)(26, 314)(27, 315)(28, 291)(29, 317)(30, 294)(31, 296)(32, 320)(33, 321)(34, 298)(35, 299)(36, 300)(37, 325)(38, 326)(39, 327)(40, 304)(41, 329)(42, 306)(43, 307)(44, 332)(45, 333)(46, 310)(47, 311)(48, 312)(49, 337)(50, 338)(51, 339)(52, 316)(53, 341)(54, 318)(55, 319)(56, 344)(57, 345)(58, 322)(59, 323)(60, 324)(61, 349)(62, 350)(63, 351)(64, 328)(65, 353)(66, 330)(67, 331)(68, 356)(69, 357)(70, 334)(71, 335)(72, 336)(73, 361)(74, 362)(75, 363)(76, 340)(77, 365)(78, 342)(79, 343)(80, 368)(81, 369)(82, 346)(83, 347)(84, 348)(85, 373)(86, 374)(87, 375)(88, 352)(89, 377)(90, 354)(91, 355)(92, 380)(93, 381)(94, 358)(95, 359)(96, 360)(97, 385)(98, 386)(99, 387)(100, 364)(101, 389)(102, 366)(103, 367)(104, 392)(105, 393)(106, 370)(107, 371)(108, 372)(109, 397)(110, 398)(111, 399)(112, 376)(113, 401)(114, 378)(115, 379)(116, 404)(117, 405)(118, 382)(119, 383)(120, 384)(121, 409)(122, 410)(123, 411)(124, 388)(125, 412)(126, 390)(127, 391)(128, 407)(129, 414)(130, 394)(131, 395)(132, 396)(133, 403)(134, 408)(135, 406)(136, 400)(137, 402)(138, 413)(139, 415)(140, 416)(141, 417)(142, 418)(143, 419)(144, 420)(145, 421)(146, 422)(147, 423)(148, 424)(149, 425)(150, 426)(151, 427)(152, 428)(153, 429)(154, 430)(155, 431)(156, 432)(157, 433)(158, 434)(159, 435)(160, 436)(161, 437)(162, 438)(163, 439)(164, 440)(165, 441)(166, 442)(167, 443)(168, 444)(169, 445)(170, 446)(171, 447)(172, 448)(173, 449)(174, 450)(175, 451)(176, 452)(177, 453)(178, 454)(179, 455)(180, 456)(181, 457)(182, 458)(183, 459)(184, 460)(185, 461)(186, 462)(187, 463)(188, 464)(189, 465)(190, 466)(191, 467)(192, 468)(193, 469)(194, 470)(195, 471)(196, 472)(197, 473)(198, 474)(199, 475)(200, 476)(201, 477)(202, 478)(203, 479)(204, 480)(205, 481)(206, 482)(207, 483)(208, 484)(209, 485)(210, 486)(211, 487)(212, 488)(213, 489)(214, 490)(215, 491)(216, 492)(217, 493)(218, 494)(219, 495)(220, 496)(221, 497)(222, 498)(223, 499)(224, 500)(225, 501)(226, 502)(227, 503)(228, 504)(229, 505)(230, 506)(231, 507)(232, 508)(233, 509)(234, 510)(235, 511)(236, 512)(237, 513)(238, 514)(239, 515)(240, 516)(241, 517)(242, 518)(243, 519)(244, 520)(245, 521)(246, 522)(247, 523)(248, 524)(249, 525)(250, 526)(251, 527)(252, 528)(253, 529)(254, 530)(255, 531)(256, 532)(257, 533)(258, 534)(259, 535)(260, 536)(261, 537)(262, 538)(263, 539)(264, 540)(265, 541)(266, 542)(267, 543)(268, 544)(269, 545)(270, 546)(271, 547)(272, 548)(273, 549)(274, 550)(275, 551)(276, 552) local type(s) :: { ( 4, 138 ), ( 4, 138, 4, 138, 4, 138, 4, 138, 4, 138, 4, 138 ) } Outer automorphisms :: reflexible Dual of E23.1153 Graph:: simple bipartite v = 161 e = 276 f = 71 degree seq :: [ 2^138, 12^23 ] E23.1155 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 2, 4}) Quotient :: halfedge^2 Aut^+ = D8 x D22 (small group id <176, 31>) Aut = D16 x D22 (small group id <352, 105>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, R * Y3 * R * Y2, (R * Y1)^2, Y3 * Y1 * Y3 * Y2 * Y1 * Y2, (Y2 * Y3)^4, (Y3 * Y1)^22 ] Map:: polytopal non-degenerate R = (1, 178, 2, 177)(3, 183, 7, 179)(4, 185, 9, 180)(5, 187, 11, 181)(6, 189, 13, 182)(8, 188, 12, 184)(10, 190, 14, 186)(15, 201, 25, 191)(16, 202, 26, 192)(17, 203, 27, 193)(18, 205, 29, 194)(19, 206, 30, 195)(20, 207, 31, 196)(21, 208, 32, 197)(22, 209, 33, 198)(23, 211, 35, 199)(24, 212, 36, 200)(28, 210, 34, 204)(37, 223, 47, 213)(38, 224, 48, 214)(39, 225, 49, 215)(40, 226, 50, 216)(41, 227, 51, 217)(42, 228, 52, 218)(43, 229, 53, 219)(44, 230, 54, 220)(45, 231, 55, 221)(46, 232, 56, 222)(57, 241, 65, 233)(58, 242, 66, 234)(59, 243, 67, 235)(60, 244, 68, 236)(61, 245, 69, 237)(62, 246, 70, 238)(63, 247, 71, 239)(64, 248, 72, 240)(73, 256, 80, 249)(74, 253, 77, 250)(75, 266, 90, 251)(76, 258, 82, 252)(78, 290, 114, 254)(79, 303, 127, 255)(81, 298, 122, 257)(83, 312, 136, 259)(84, 289, 113, 260)(85, 301, 125, 261)(86, 294, 118, 262)(87, 308, 132, 263)(88, 305, 129, 264)(89, 310, 134, 265)(91, 326, 150, 267)(92, 297, 121, 268)(93, 317, 141, 269)(94, 314, 138, 270)(95, 319, 143, 271)(96, 292, 116, 272)(97, 337, 161, 273)(98, 300, 124, 274)(99, 324, 148, 275)(100, 322, 146, 276)(101, 329, 153, 277)(102, 304, 128, 278)(103, 321, 145, 279)(104, 335, 159, 280)(105, 333, 157, 281)(106, 340, 164, 282)(107, 313, 137, 283)(108, 332, 156, 284)(109, 346, 170, 285)(110, 344, 168, 286)(111, 348, 172, 287)(112, 343, 167, 288)(115, 347, 171, 291)(117, 345, 169, 293)(119, 351, 175, 295)(120, 349, 173, 296)(123, 334, 158, 299)(126, 323, 147, 302)(130, 315, 139, 306)(131, 336, 160, 307)(133, 318, 142, 309)(135, 341, 165, 311)(140, 325, 149, 316)(144, 330, 154, 320)(151, 338, 162, 327)(152, 352, 176, 328)(155, 342, 166, 331)(163, 350, 174, 339) L = (1, 3)(2, 5)(4, 10)(6, 14)(7, 15)(8, 17)(9, 18)(11, 20)(12, 22)(13, 23)(16, 27)(19, 28)(21, 33)(24, 34)(25, 37)(26, 39)(29, 38)(30, 40)(31, 42)(32, 44)(35, 43)(36, 45)(41, 50)(46, 55)(47, 57)(48, 59)(49, 58)(51, 60)(52, 61)(53, 63)(54, 62)(56, 64)(65, 73)(66, 75)(67, 74)(68, 76)(69, 113)(70, 116)(71, 114)(72, 118)(77, 121)(78, 124)(79, 128)(80, 122)(81, 129)(82, 134)(83, 137)(84, 125)(85, 138)(86, 143)(87, 145)(88, 146)(89, 150)(90, 127)(91, 153)(92, 132)(93, 156)(94, 157)(95, 161)(96, 136)(97, 164)(98, 141)(99, 167)(100, 168)(101, 172)(102, 148)(103, 170)(104, 173)(105, 169)(106, 175)(107, 159)(108, 171)(109, 165)(110, 158)(111, 176)(112, 160)(115, 154)(117, 147)(119, 174)(120, 149)(123, 139)(126, 130)(131, 162)(133, 144)(135, 142)(140, 151)(152, 166)(155, 163)(177, 180)(178, 182)(179, 184)(181, 188)(183, 192)(185, 191)(186, 195)(187, 197)(189, 196)(190, 200)(193, 204)(194, 206)(198, 210)(199, 212)(201, 214)(202, 213)(203, 216)(205, 217)(207, 219)(208, 218)(209, 221)(211, 222)(215, 226)(220, 231)(223, 234)(224, 233)(225, 236)(227, 235)(228, 238)(229, 237)(230, 240)(232, 239)(241, 250)(242, 249)(243, 252)(244, 251)(245, 290)(246, 289)(247, 294)(248, 292)(253, 298)(254, 301)(255, 305)(256, 303)(257, 308)(258, 297)(259, 314)(260, 312)(261, 317)(262, 300)(263, 322)(264, 324)(265, 304)(266, 310)(267, 321)(268, 326)(269, 333)(270, 335)(271, 313)(272, 319)(273, 332)(274, 337)(275, 344)(276, 346)(277, 343)(278, 329)(279, 348)(280, 345)(281, 347)(282, 349)(283, 340)(284, 351)(285, 334)(286, 336)(287, 341)(288, 352)(291, 323)(293, 325)(295, 330)(296, 350)(299, 318)(302, 309)(306, 316)(307, 315)(311, 342)(320, 331)(327, 339)(328, 338) local type(s) :: { ( 8^4 ) } Outer automorphisms :: reflexible Dual of E23.1157 Transitivity :: VT+ AT Graph:: simple bipartite v = 88 e = 176 f = 44 degree seq :: [ 4^88 ] E23.1156 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 2, 4}) Quotient :: halfedge^2 Aut^+ = (C4 x D22) : C2 (small group id <176, 34>) Aut = (D8 x D22) : C2 (small group id <352, 109>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, R * Y3 * R * Y2, (R * Y1)^2, Y3 * Y1 * Y3 * Y2 * Y1 * Y2, (Y2 * Y3)^4, Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y2 * Y1 * Y3 * Y1 * Y2 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 ] Map:: polytopal non-degenerate R = (1, 178, 2, 177)(3, 183, 7, 179)(4, 185, 9, 180)(5, 187, 11, 181)(6, 189, 13, 182)(8, 188, 12, 184)(10, 190, 14, 186)(15, 201, 25, 191)(16, 202, 26, 192)(17, 203, 27, 193)(18, 205, 29, 194)(19, 206, 30, 195)(20, 207, 31, 196)(21, 208, 32, 197)(22, 209, 33, 198)(23, 211, 35, 199)(24, 212, 36, 200)(28, 210, 34, 204)(37, 223, 47, 213)(38, 224, 48, 214)(39, 225, 49, 215)(40, 226, 50, 216)(41, 227, 51, 217)(42, 228, 52, 218)(43, 229, 53, 219)(44, 230, 54, 220)(45, 231, 55, 221)(46, 232, 56, 222)(57, 241, 65, 233)(58, 242, 66, 234)(59, 243, 67, 235)(60, 244, 68, 236)(61, 245, 69, 237)(62, 246, 70, 238)(63, 247, 71, 239)(64, 248, 72, 240)(73, 289, 113, 249)(74, 291, 115, 250)(75, 293, 117, 251)(76, 295, 119, 252)(77, 297, 121, 253)(78, 299, 123, 254)(79, 301, 125, 255)(80, 303, 127, 256)(81, 306, 130, 257)(82, 309, 133, 258)(83, 304, 128, 259)(84, 312, 136, 260)(85, 315, 139, 261)(86, 313, 137, 262)(87, 319, 143, 263)(88, 316, 140, 264)(89, 322, 146, 265)(90, 325, 149, 266)(91, 323, 147, 267)(92, 329, 153, 268)(93, 326, 150, 269)(94, 307, 131, 270)(95, 333, 157, 271)(96, 335, 159, 272)(97, 338, 162, 273)(98, 336, 160, 274)(99, 341, 165, 275)(100, 343, 167, 276)(101, 345, 169, 277)(102, 348, 172, 278)(103, 346, 170, 279)(104, 351, 175, 280)(105, 352, 176, 281)(106, 347, 171, 282)(107, 349, 173, 283)(108, 344, 168, 284)(109, 342, 166, 285)(110, 337, 161, 286)(111, 339, 163, 287)(112, 334, 158, 288)(114, 350, 174, 290)(116, 327, 151, 292)(118, 330, 154, 294)(120, 324, 148, 296)(122, 340, 164, 298)(124, 331, 155, 300)(126, 328, 152, 302)(129, 321, 145, 305)(132, 318, 142, 308)(134, 320, 144, 310)(135, 317, 141, 311)(138, 332, 156, 314) L = (1, 3)(2, 5)(4, 10)(6, 14)(7, 15)(8, 17)(9, 18)(11, 20)(12, 22)(13, 23)(16, 27)(19, 28)(21, 33)(24, 34)(25, 37)(26, 39)(29, 38)(30, 40)(31, 42)(32, 44)(35, 43)(36, 45)(41, 50)(46, 55)(47, 57)(48, 59)(49, 58)(51, 60)(52, 61)(53, 63)(54, 62)(56, 64)(65, 73)(66, 75)(67, 74)(68, 76)(69, 77)(70, 82)(71, 83)(72, 94)(78, 113)(79, 115)(80, 121)(81, 128)(84, 123)(85, 137)(86, 117)(87, 125)(88, 119)(89, 127)(90, 147)(91, 133)(92, 130)(93, 131)(95, 136)(96, 143)(97, 139)(98, 140)(99, 160)(100, 146)(101, 153)(102, 149)(103, 150)(104, 170)(105, 157)(106, 162)(107, 159)(108, 165)(109, 167)(110, 172)(111, 169)(112, 175)(114, 176)(116, 173)(118, 171)(120, 168)(122, 166)(124, 174)(126, 151)(129, 164)(132, 141)(134, 161)(135, 163)(138, 155)(142, 154)(144, 152)(145, 148)(156, 158)(177, 180)(178, 182)(179, 184)(181, 188)(183, 192)(185, 191)(186, 195)(187, 197)(189, 196)(190, 200)(193, 204)(194, 206)(198, 210)(199, 212)(201, 214)(202, 213)(203, 216)(205, 217)(207, 219)(208, 218)(209, 221)(211, 222)(215, 226)(220, 231)(223, 234)(224, 233)(225, 236)(227, 235)(228, 238)(229, 237)(230, 240)(232, 239)(241, 250)(242, 249)(243, 252)(244, 251)(245, 259)(246, 253)(247, 270)(248, 258)(254, 291)(255, 295)(256, 304)(257, 307)(260, 313)(261, 316)(262, 289)(263, 299)(264, 293)(265, 323)(266, 326)(267, 297)(268, 303)(269, 309)(271, 319)(272, 336)(273, 312)(274, 301)(275, 315)(276, 329)(277, 346)(278, 322)(279, 306)(280, 325)(281, 338)(282, 341)(283, 333)(284, 335)(285, 348)(286, 351)(287, 343)(288, 345)(290, 349)(292, 344)(294, 352)(296, 347)(298, 339)(300, 330)(302, 350)(305, 320)(308, 340)(310, 342)(311, 334)(314, 328)(317, 331)(318, 324)(321, 327)(332, 337) local type(s) :: { ( 8^4 ) } Outer automorphisms :: reflexible Dual of E23.1158 Transitivity :: VT+ AT Graph:: simple bipartite v = 88 e = 176 f = 44 degree seq :: [ 4^88 ] E23.1157 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 2, 4}) Quotient :: halfedge^2 Aut^+ = D8 x D22 (small group id <176, 31>) Aut = D16 x D22 (small group id <352, 105>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y1^4, R * Y3 * R * Y2, (R * Y1)^2, (Y1^-1 * Y3 * Y1^-1)^2, (Y1^-1 * Y2 * Y1^-1)^2, (Y2 * Y3 * Y1^-1)^2, Y3 * Y1 * Y3 * Y2 * Y1^-1 * Y2, Y3 * Y1 * Y3 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 178, 2, 182, 6, 181, 5, 177)(3, 185, 9, 193, 17, 187, 11, 179)(4, 188, 12, 194, 18, 190, 14, 180)(7, 195, 19, 191, 15, 197, 21, 183)(8, 198, 22, 192, 16, 200, 24, 184)(10, 196, 20, 189, 13, 199, 23, 186)(25, 209, 33, 203, 27, 210, 34, 201)(26, 211, 35, 204, 28, 212, 36, 202)(29, 213, 37, 207, 31, 214, 38, 205)(30, 215, 39, 208, 32, 216, 40, 206)(41, 225, 49, 219, 43, 226, 50, 217)(42, 227, 51, 220, 44, 228, 52, 218)(45, 229, 53, 223, 47, 230, 54, 221)(46, 231, 55, 224, 48, 232, 56, 222)(57, 241, 65, 235, 59, 242, 66, 233)(58, 243, 67, 236, 60, 244, 68, 234)(61, 245, 69, 239, 63, 246, 70, 237)(62, 247, 71, 240, 64, 248, 72, 238)(73, 305, 129, 251, 75, 307, 131, 249)(74, 306, 130, 252, 76, 308, 132, 250)(77, 309, 133, 258, 82, 312, 136, 253)(78, 313, 137, 257, 81, 316, 140, 254)(79, 314, 138, 269, 93, 319, 143, 255)(80, 320, 144, 270, 94, 315, 139, 256)(83, 322, 146, 267, 91, 310, 134, 259)(84, 311, 135, 268, 92, 323, 147, 260)(85, 324, 148, 263, 87, 326, 150, 261)(86, 327, 151, 265, 89, 325, 149, 262)(88, 328, 152, 266, 90, 329, 153, 264)(95, 331, 155, 273, 97, 333, 157, 271)(96, 334, 158, 275, 99, 332, 156, 272)(98, 335, 159, 276, 100, 336, 160, 274)(101, 321, 145, 279, 103, 317, 141, 277)(102, 318, 142, 280, 104, 330, 154, 278)(105, 337, 161, 282, 106, 338, 162, 281)(107, 339, 163, 284, 108, 340, 164, 283)(109, 341, 165, 286, 110, 342, 166, 285)(111, 343, 167, 288, 112, 344, 168, 287)(113, 345, 169, 290, 114, 346, 170, 289)(115, 347, 171, 292, 116, 348, 172, 291)(117, 349, 173, 294, 118, 350, 174, 293)(119, 351, 175, 296, 120, 352, 176, 295)(121, 302, 126, 298, 122, 301, 125, 297)(123, 304, 128, 300, 124, 303, 127, 299) L = (1, 3)(2, 7)(4, 13)(5, 15)(6, 17)(8, 23)(9, 25)(10, 18)(11, 27)(12, 28)(14, 26)(16, 20)(19, 29)(21, 31)(22, 32)(24, 30)(33, 41)(34, 43)(35, 44)(36, 42)(37, 45)(38, 47)(39, 48)(40, 46)(49, 57)(50, 59)(51, 60)(52, 58)(53, 61)(54, 63)(55, 64)(56, 62)(65, 73)(66, 75)(67, 76)(68, 74)(69, 103)(70, 101)(71, 104)(72, 102)(77, 134)(78, 138)(79, 141)(80, 142)(81, 143)(82, 146)(83, 131)(84, 132)(85, 133)(86, 135)(87, 136)(88, 149)(89, 147)(90, 151)(91, 129)(92, 130)(93, 145)(94, 154)(95, 137)(96, 139)(97, 140)(98, 156)(99, 144)(100, 158)(105, 148)(106, 150)(107, 153)(108, 152)(109, 155)(110, 157)(111, 160)(112, 159)(113, 161)(114, 162)(115, 164)(116, 163)(117, 165)(118, 166)(119, 168)(120, 167)(121, 169)(122, 170)(123, 172)(124, 171)(125, 173)(126, 174)(127, 176)(128, 175)(177, 180)(178, 184)(179, 186)(181, 192)(182, 194)(183, 196)(185, 202)(187, 204)(188, 201)(189, 193)(190, 203)(191, 199)(195, 206)(197, 208)(198, 205)(200, 207)(209, 218)(210, 220)(211, 217)(212, 219)(213, 222)(214, 224)(215, 221)(216, 223)(225, 234)(226, 236)(227, 233)(228, 235)(229, 238)(230, 240)(231, 237)(232, 239)(241, 250)(242, 252)(243, 249)(244, 251)(245, 278)(246, 280)(247, 279)(248, 277)(253, 311)(254, 315)(255, 318)(256, 321)(257, 320)(258, 323)(259, 308)(260, 305)(261, 325)(262, 322)(263, 327)(264, 312)(265, 310)(266, 309)(267, 306)(268, 307)(269, 330)(270, 317)(271, 332)(272, 319)(273, 334)(274, 316)(275, 314)(276, 313)(281, 329)(282, 328)(283, 326)(284, 324)(285, 336)(286, 335)(287, 333)(288, 331)(289, 340)(290, 339)(291, 338)(292, 337)(293, 344)(294, 343)(295, 342)(296, 341)(297, 348)(298, 347)(299, 346)(300, 345)(301, 352)(302, 351)(303, 350)(304, 349) local type(s) :: { ( 4^8 ) } Outer automorphisms :: reflexible Dual of E23.1155 Transitivity :: VT+ AT Graph:: bipartite v = 44 e = 176 f = 88 degree seq :: [ 8^44 ] E23.1158 :: Family: { 2P } :: Oriented family(ies): { E2 } Signature :: (0; {2, 2, 2, 4}) Quotient :: halfedge^2 Aut^+ = (C4 x D22) : C2 (small group id <176, 34>) Aut = (D8 x D22) : C2 (small group id <352, 109>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, R * Y3 * R * Y2, (R * Y1)^2, Y1^4, (Y1^-1 * Y3 * Y1^-1)^2, (Y1^-1 * Y2 * Y1^-1)^2, (Y2 * Y3 * Y1^-1)^2, Y3 * Y1 * Y3 * Y2 * Y1^-1 * Y2, Y3 * Y1 * Y3 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 178, 2, 182, 6, 181, 5, 177)(3, 185, 9, 193, 17, 187, 11, 179)(4, 188, 12, 194, 18, 190, 14, 180)(7, 195, 19, 191, 15, 197, 21, 183)(8, 198, 22, 192, 16, 200, 24, 184)(10, 196, 20, 189, 13, 199, 23, 186)(25, 209, 33, 203, 27, 210, 34, 201)(26, 211, 35, 204, 28, 212, 36, 202)(29, 213, 37, 207, 31, 214, 38, 205)(30, 215, 39, 208, 32, 216, 40, 206)(41, 225, 49, 219, 43, 226, 50, 217)(42, 227, 51, 220, 44, 228, 52, 218)(45, 229, 53, 223, 47, 230, 54, 221)(46, 231, 55, 224, 48, 232, 56, 222)(57, 241, 65, 235, 59, 242, 66, 233)(58, 243, 67, 236, 60, 244, 68, 234)(61, 245, 69, 239, 63, 246, 70, 237)(62, 247, 71, 240, 64, 248, 72, 238)(73, 268, 92, 251, 75, 267, 91, 249)(74, 257, 81, 252, 76, 254, 78, 250)(77, 296, 120, 258, 82, 294, 118, 253)(79, 305, 129, 265, 89, 303, 127, 255)(80, 304, 128, 266, 90, 309, 133, 256)(83, 301, 125, 263, 87, 310, 134, 259)(84, 311, 135, 264, 88, 302, 126, 260)(85, 295, 119, 262, 86, 293, 117, 261)(93, 306, 130, 271, 95, 308, 132, 269)(94, 316, 140, 272, 96, 307, 131, 270)(97, 312, 136, 275, 99, 314, 138, 273)(98, 315, 139, 276, 100, 313, 137, 274)(101, 317, 141, 279, 103, 319, 143, 277)(102, 320, 144, 280, 104, 318, 142, 278)(105, 321, 145, 283, 107, 323, 147, 281)(106, 324, 148, 284, 108, 322, 146, 282)(109, 325, 149, 287, 111, 327, 151, 285)(110, 328, 152, 288, 112, 326, 150, 286)(113, 329, 153, 291, 115, 331, 155, 289)(114, 332, 156, 292, 116, 330, 154, 290)(121, 333, 157, 299, 123, 335, 159, 297)(122, 336, 160, 300, 124, 334, 158, 298)(161, 343, 167, 339, 163, 341, 165, 337)(162, 342, 166, 340, 164, 344, 168, 338)(169, 350, 174, 347, 171, 352, 176, 345)(170, 349, 173, 348, 172, 351, 175, 346) L = (1, 3)(2, 7)(4, 13)(5, 15)(6, 17)(8, 23)(9, 25)(10, 18)(11, 27)(12, 28)(14, 26)(16, 20)(19, 29)(21, 31)(22, 32)(24, 30)(33, 41)(34, 43)(35, 44)(36, 42)(37, 45)(38, 47)(39, 48)(40, 46)(49, 57)(50, 59)(51, 60)(52, 58)(53, 61)(54, 63)(55, 64)(56, 62)(65, 73)(66, 75)(67, 76)(68, 74)(69, 117)(70, 119)(71, 120)(72, 118)(77, 125)(78, 127)(79, 130)(80, 131)(81, 129)(82, 134)(83, 136)(84, 137)(85, 126)(86, 135)(87, 138)(88, 139)(89, 132)(90, 140)(91, 128)(92, 133)(93, 141)(94, 142)(95, 143)(96, 144)(97, 145)(98, 146)(99, 147)(100, 148)(101, 149)(102, 150)(103, 151)(104, 152)(105, 153)(106, 154)(107, 155)(108, 156)(109, 157)(110, 158)(111, 159)(112, 160)(113, 161)(114, 162)(115, 163)(116, 164)(121, 169)(122, 170)(123, 171)(124, 172)(165, 174)(166, 173)(167, 176)(168, 175)(177, 180)(178, 184)(179, 186)(181, 192)(182, 194)(183, 196)(185, 202)(187, 204)(188, 201)(189, 193)(190, 203)(191, 199)(195, 206)(197, 208)(198, 205)(200, 207)(209, 218)(210, 220)(211, 217)(212, 219)(213, 222)(214, 224)(215, 221)(216, 223)(225, 234)(226, 236)(227, 233)(228, 235)(229, 238)(230, 240)(231, 237)(232, 239)(241, 250)(242, 252)(243, 249)(244, 251)(245, 294)(246, 296)(247, 293)(248, 295)(253, 302)(254, 304)(255, 307)(256, 308)(257, 309)(258, 311)(259, 313)(260, 314)(261, 310)(262, 301)(263, 315)(264, 312)(265, 316)(266, 306)(267, 305)(268, 303)(269, 318)(270, 319)(271, 320)(272, 317)(273, 322)(274, 323)(275, 324)(276, 321)(277, 326)(278, 327)(279, 328)(280, 325)(281, 330)(282, 331)(283, 332)(284, 329)(285, 334)(286, 335)(287, 336)(288, 333)(289, 338)(290, 339)(291, 340)(292, 337)(297, 346)(298, 347)(299, 348)(300, 345)(341, 349)(342, 352)(343, 351)(344, 350) local type(s) :: { ( 4^8 ) } Outer automorphisms :: reflexible Dual of E23.1156 Transitivity :: VT+ AT Graph:: bipartite v = 44 e = 176 f = 88 degree seq :: [ 8^44 ] E23.1159 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 2, 4}) Quotient :: edge^2 Aut^+ = D8 x D22 (small group id <176, 31>) Aut = D16 x D22 (small group id <352, 105>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, (R * Y3)^2, R * Y1 * R * Y2, Y2 * Y3 * Y2 * Y1 * Y3 * Y1, (Y1 * Y2)^4, (Y3 * Y2)^22 ] Map:: polytopal R = (1, 177, 4, 180)(2, 178, 6, 182)(3, 179, 8, 184)(5, 181, 12, 188)(7, 183, 16, 192)(9, 185, 18, 194)(10, 186, 19, 195)(11, 187, 21, 197)(13, 189, 23, 199)(14, 190, 24, 200)(15, 191, 25, 201)(17, 193, 27, 203)(20, 196, 31, 207)(22, 198, 33, 209)(26, 202, 37, 213)(28, 204, 39, 215)(29, 205, 40, 216)(30, 206, 41, 217)(32, 208, 42, 218)(34, 210, 44, 220)(35, 211, 45, 221)(36, 212, 46, 222)(38, 214, 47, 223)(43, 219, 52, 228)(48, 224, 57, 233)(49, 225, 58, 234)(50, 226, 59, 235)(51, 227, 60, 236)(53, 229, 61, 237)(54, 230, 62, 238)(55, 231, 63, 239)(56, 232, 64, 240)(65, 241, 73, 249)(66, 242, 74, 250)(67, 243, 75, 251)(68, 244, 76, 252)(69, 245, 117, 293)(70, 246, 118, 294)(71, 247, 119, 295)(72, 248, 120, 296)(77, 253, 125, 301)(78, 254, 126, 302)(79, 255, 127, 303)(80, 256, 130, 306)(81, 257, 131, 307)(82, 258, 134, 310)(83, 259, 133, 309)(84, 260, 135, 311)(85, 261, 129, 305)(86, 262, 136, 312)(87, 263, 128, 304)(88, 264, 137, 313)(89, 265, 139, 315)(90, 266, 140, 316)(91, 267, 132, 308)(92, 268, 141, 317)(93, 269, 143, 319)(94, 270, 144, 320)(95, 271, 142, 318)(96, 272, 145, 321)(97, 273, 138, 314)(98, 274, 146, 322)(99, 275, 147, 323)(100, 276, 148, 324)(101, 277, 149, 325)(102, 278, 150, 326)(103, 279, 151, 327)(104, 280, 152, 328)(105, 281, 153, 329)(106, 282, 154, 330)(107, 283, 155, 331)(108, 284, 156, 332)(109, 285, 157, 333)(110, 286, 158, 334)(111, 287, 159, 335)(112, 288, 160, 336)(113, 289, 161, 337)(114, 290, 162, 338)(115, 291, 163, 339)(116, 292, 164, 340)(121, 297, 169, 345)(122, 298, 170, 346)(123, 299, 171, 347)(124, 300, 172, 348)(165, 341, 175, 351)(166, 342, 176, 352)(167, 343, 174, 350)(168, 344, 173, 349)(353, 354)(355, 359)(356, 361)(357, 363)(358, 365)(360, 369)(362, 368)(364, 374)(366, 373)(367, 372)(370, 380)(371, 382)(375, 386)(376, 388)(377, 384)(378, 383)(379, 387)(381, 385)(389, 395)(390, 394)(391, 400)(392, 402)(393, 401)(396, 405)(397, 407)(398, 406)(399, 408)(403, 404)(409, 417)(410, 419)(411, 418)(412, 420)(413, 421)(414, 423)(415, 422)(416, 424)(425, 431)(426, 430)(427, 439)(428, 437)(429, 470)(432, 480)(433, 469)(434, 484)(435, 472)(436, 483)(438, 479)(440, 481)(441, 490)(442, 488)(443, 471)(444, 485)(445, 494)(446, 487)(447, 477)(448, 493)(449, 478)(450, 489)(451, 482)(452, 499)(453, 492)(454, 498)(455, 486)(456, 503)(457, 496)(458, 497)(459, 495)(460, 491)(461, 508)(462, 501)(463, 502)(464, 500)(465, 507)(466, 505)(467, 506)(468, 504)(473, 512)(474, 510)(475, 511)(476, 509)(513, 518)(514, 519)(515, 520)(516, 517)(521, 528)(522, 526)(523, 525)(524, 527)(529, 531)(530, 533)(532, 538)(534, 542)(535, 543)(536, 541)(537, 540)(539, 548)(544, 554)(545, 553)(546, 557)(547, 556)(549, 560)(550, 559)(551, 563)(552, 562)(555, 566)(558, 565)(561, 571)(564, 570)(567, 577)(568, 576)(569, 579)(572, 582)(573, 581)(574, 584)(575, 583)(578, 580)(585, 594)(586, 593)(587, 596)(588, 595)(589, 598)(590, 597)(591, 600)(592, 599)(601, 615)(602, 607)(603, 613)(604, 606)(605, 648)(608, 657)(609, 646)(610, 661)(611, 647)(612, 660)(614, 656)(616, 654)(617, 665)(618, 666)(619, 645)(620, 653)(621, 669)(622, 670)(623, 659)(624, 662)(625, 655)(626, 658)(627, 664)(628, 674)(629, 675)(630, 667)(631, 663)(632, 673)(633, 679)(634, 671)(635, 672)(636, 668)(637, 678)(638, 684)(639, 676)(640, 677)(641, 682)(642, 683)(643, 680)(644, 681)(649, 687)(650, 688)(651, 685)(652, 686)(689, 696)(690, 694)(691, 693)(692, 695)(697, 701)(698, 704)(699, 703)(700, 702) L = (1, 353)(2, 354)(3, 355)(4, 356)(5, 357)(6, 358)(7, 359)(8, 360)(9, 361)(10, 362)(11, 363)(12, 364)(13, 365)(14, 366)(15, 367)(16, 368)(17, 369)(18, 370)(19, 371)(20, 372)(21, 373)(22, 374)(23, 375)(24, 376)(25, 377)(26, 378)(27, 379)(28, 380)(29, 381)(30, 382)(31, 383)(32, 384)(33, 385)(34, 386)(35, 387)(36, 388)(37, 389)(38, 390)(39, 391)(40, 392)(41, 393)(42, 394)(43, 395)(44, 396)(45, 397)(46, 398)(47, 399)(48, 400)(49, 401)(50, 402)(51, 403)(52, 404)(53, 405)(54, 406)(55, 407)(56, 408)(57, 409)(58, 410)(59, 411)(60, 412)(61, 413)(62, 414)(63, 415)(64, 416)(65, 417)(66, 418)(67, 419)(68, 420)(69, 421)(70, 422)(71, 423)(72, 424)(73, 425)(74, 426)(75, 427)(76, 428)(77, 429)(78, 430)(79, 431)(80, 432)(81, 433)(82, 434)(83, 435)(84, 436)(85, 437)(86, 438)(87, 439)(88, 440)(89, 441)(90, 442)(91, 443)(92, 444)(93, 445)(94, 446)(95, 447)(96, 448)(97, 449)(98, 450)(99, 451)(100, 452)(101, 453)(102, 454)(103, 455)(104, 456)(105, 457)(106, 458)(107, 459)(108, 460)(109, 461)(110, 462)(111, 463)(112, 464)(113, 465)(114, 466)(115, 467)(116, 468)(117, 469)(118, 470)(119, 471)(120, 472)(121, 473)(122, 474)(123, 475)(124, 476)(125, 477)(126, 478)(127, 479)(128, 480)(129, 481)(130, 482)(131, 483)(132, 484)(133, 485)(134, 486)(135, 487)(136, 488)(137, 489)(138, 490)(139, 491)(140, 492)(141, 493)(142, 494)(143, 495)(144, 496)(145, 497)(146, 498)(147, 499)(148, 500)(149, 501)(150, 502)(151, 503)(152, 504)(153, 505)(154, 506)(155, 507)(156, 508)(157, 509)(158, 510)(159, 511)(160, 512)(161, 513)(162, 514)(163, 515)(164, 516)(165, 517)(166, 518)(167, 519)(168, 520)(169, 521)(170, 522)(171, 523)(172, 524)(173, 525)(174, 526)(175, 527)(176, 528)(177, 529)(178, 530)(179, 531)(180, 532)(181, 533)(182, 534)(183, 535)(184, 536)(185, 537)(186, 538)(187, 539)(188, 540)(189, 541)(190, 542)(191, 543)(192, 544)(193, 545)(194, 546)(195, 547)(196, 548)(197, 549)(198, 550)(199, 551)(200, 552)(201, 553)(202, 554)(203, 555)(204, 556)(205, 557)(206, 558)(207, 559)(208, 560)(209, 561)(210, 562)(211, 563)(212, 564)(213, 565)(214, 566)(215, 567)(216, 568)(217, 569)(218, 570)(219, 571)(220, 572)(221, 573)(222, 574)(223, 575)(224, 576)(225, 577)(226, 578)(227, 579)(228, 580)(229, 581)(230, 582)(231, 583)(232, 584)(233, 585)(234, 586)(235, 587)(236, 588)(237, 589)(238, 590)(239, 591)(240, 592)(241, 593)(242, 594)(243, 595)(244, 596)(245, 597)(246, 598)(247, 599)(248, 600)(249, 601)(250, 602)(251, 603)(252, 604)(253, 605)(254, 606)(255, 607)(256, 608)(257, 609)(258, 610)(259, 611)(260, 612)(261, 613)(262, 614)(263, 615)(264, 616)(265, 617)(266, 618)(267, 619)(268, 620)(269, 621)(270, 622)(271, 623)(272, 624)(273, 625)(274, 626)(275, 627)(276, 628)(277, 629)(278, 630)(279, 631)(280, 632)(281, 633)(282, 634)(283, 635)(284, 636)(285, 637)(286, 638)(287, 639)(288, 640)(289, 641)(290, 642)(291, 643)(292, 644)(293, 645)(294, 646)(295, 647)(296, 648)(297, 649)(298, 650)(299, 651)(300, 652)(301, 653)(302, 654)(303, 655)(304, 656)(305, 657)(306, 658)(307, 659)(308, 660)(309, 661)(310, 662)(311, 663)(312, 664)(313, 665)(314, 666)(315, 667)(316, 668)(317, 669)(318, 670)(319, 671)(320, 672)(321, 673)(322, 674)(323, 675)(324, 676)(325, 677)(326, 678)(327, 679)(328, 680)(329, 681)(330, 682)(331, 683)(332, 684)(333, 685)(334, 686)(335, 687)(336, 688)(337, 689)(338, 690)(339, 691)(340, 692)(341, 693)(342, 694)(343, 695)(344, 696)(345, 697)(346, 698)(347, 699)(348, 700)(349, 701)(350, 702)(351, 703)(352, 704) local type(s) :: { ( 16, 16 ), ( 16^4 ) } Outer automorphisms :: reflexible Dual of E23.1165 Graph:: simple bipartite v = 264 e = 352 f = 44 degree seq :: [ 2^176, 4^88 ] E23.1160 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 2, 4}) Quotient :: edge^2 Aut^+ = (C4 x D22) : C2 (small group id <176, 34>) Aut = (D8 x D22) : C2 (small group id <352, 109>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, (R * Y3)^2, R * Y1 * R * Y2, Y2 * Y3 * Y2 * Y1 * Y3 * Y1, (Y1 * Y2)^4, Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y1 * Y3 * Y2 * Y3 * Y1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 ] Map:: polytopal R = (1, 177, 4, 180)(2, 178, 6, 182)(3, 179, 8, 184)(5, 181, 12, 188)(7, 183, 16, 192)(9, 185, 18, 194)(10, 186, 19, 195)(11, 187, 21, 197)(13, 189, 23, 199)(14, 190, 24, 200)(15, 191, 25, 201)(17, 193, 27, 203)(20, 196, 31, 207)(22, 198, 33, 209)(26, 202, 37, 213)(28, 204, 39, 215)(29, 205, 40, 216)(30, 206, 41, 217)(32, 208, 42, 218)(34, 210, 44, 220)(35, 211, 45, 221)(36, 212, 46, 222)(38, 214, 47, 223)(43, 219, 52, 228)(48, 224, 57, 233)(49, 225, 58, 234)(50, 226, 59, 235)(51, 227, 60, 236)(53, 229, 61, 237)(54, 230, 62, 238)(55, 231, 63, 239)(56, 232, 64, 240)(65, 241, 73, 249)(66, 242, 74, 250)(67, 243, 75, 251)(68, 244, 76, 252)(69, 245, 81, 257)(70, 246, 87, 263)(71, 247, 77, 253)(72, 248, 79, 255)(78, 254, 116, 292)(80, 256, 127, 303)(82, 258, 122, 298)(83, 259, 118, 294)(84, 260, 113, 289)(85, 261, 136, 312)(86, 262, 125, 301)(88, 264, 132, 308)(89, 265, 134, 310)(90, 266, 130, 306)(91, 267, 121, 297)(92, 268, 146, 322)(93, 269, 114, 290)(94, 270, 138, 314)(95, 271, 124, 300)(96, 272, 143, 319)(97, 273, 141, 317)(98, 274, 157, 333)(99, 275, 129, 305)(100, 276, 151, 327)(101, 277, 149, 325)(102, 278, 154, 330)(103, 279, 148, 324)(104, 280, 140, 316)(105, 281, 163, 339)(106, 282, 161, 337)(107, 283, 165, 341)(108, 284, 160, 336)(109, 285, 171, 347)(110, 286, 169, 345)(111, 287, 173, 349)(112, 288, 168, 344)(115, 291, 172, 348)(117, 293, 170, 346)(119, 295, 175, 351)(120, 296, 174, 350)(123, 299, 176, 352)(126, 302, 167, 343)(128, 304, 166, 342)(131, 307, 159, 335)(133, 309, 164, 340)(135, 311, 158, 334)(137, 313, 155, 331)(139, 315, 152, 328)(142, 318, 153, 329)(144, 320, 147, 323)(145, 321, 162, 338)(150, 326, 156, 332)(353, 354)(355, 359)(356, 361)(357, 363)(358, 365)(360, 369)(362, 368)(364, 374)(366, 373)(367, 372)(370, 380)(371, 382)(375, 386)(376, 388)(377, 384)(378, 383)(379, 387)(381, 385)(389, 395)(390, 394)(391, 400)(392, 402)(393, 401)(396, 405)(397, 407)(398, 406)(399, 408)(403, 404)(409, 417)(410, 419)(411, 418)(412, 420)(413, 421)(414, 423)(415, 422)(416, 424)(425, 465)(426, 468)(427, 466)(428, 470)(429, 473)(430, 476)(431, 474)(432, 481)(433, 484)(434, 482)(435, 477)(436, 490)(437, 492)(438, 493)(439, 479)(440, 498)(441, 500)(442, 501)(443, 486)(444, 506)(445, 488)(446, 509)(447, 495)(448, 512)(449, 513)(450, 517)(451, 503)(452, 520)(453, 521)(454, 525)(455, 523)(456, 515)(457, 526)(458, 522)(459, 527)(460, 524)(461, 518)(462, 514)(463, 528)(464, 516)(467, 507)(469, 502)(471, 519)(472, 504)(475, 511)(478, 505)(480, 496)(483, 508)(485, 510)(487, 489)(491, 499)(494, 497)(529, 531)(530, 533)(532, 538)(534, 542)(535, 543)(536, 541)(537, 540)(539, 548)(544, 554)(545, 553)(546, 557)(547, 556)(549, 560)(550, 559)(551, 563)(552, 562)(555, 566)(558, 565)(561, 571)(564, 570)(567, 577)(568, 576)(569, 579)(572, 582)(573, 581)(574, 584)(575, 583)(578, 580)(585, 594)(586, 593)(587, 596)(588, 595)(589, 598)(590, 597)(591, 600)(592, 599)(601, 642)(602, 641)(603, 646)(604, 644)(605, 650)(606, 653)(607, 655)(608, 658)(609, 649)(610, 662)(611, 664)(612, 652)(613, 669)(614, 671)(615, 660)(616, 657)(617, 677)(618, 679)(619, 674)(620, 676)(621, 666)(622, 668)(623, 685)(624, 689)(625, 691)(626, 688)(627, 682)(628, 697)(629, 699)(630, 696)(631, 701)(632, 693)(633, 698)(634, 700)(635, 702)(636, 703)(637, 690)(638, 692)(639, 694)(640, 704)(643, 678)(645, 680)(647, 683)(648, 695)(651, 686)(654, 675)(656, 687)(659, 667)(661, 670)(663, 684)(665, 681)(672, 673) L = (1, 353)(2, 354)(3, 355)(4, 356)(5, 357)(6, 358)(7, 359)(8, 360)(9, 361)(10, 362)(11, 363)(12, 364)(13, 365)(14, 366)(15, 367)(16, 368)(17, 369)(18, 370)(19, 371)(20, 372)(21, 373)(22, 374)(23, 375)(24, 376)(25, 377)(26, 378)(27, 379)(28, 380)(29, 381)(30, 382)(31, 383)(32, 384)(33, 385)(34, 386)(35, 387)(36, 388)(37, 389)(38, 390)(39, 391)(40, 392)(41, 393)(42, 394)(43, 395)(44, 396)(45, 397)(46, 398)(47, 399)(48, 400)(49, 401)(50, 402)(51, 403)(52, 404)(53, 405)(54, 406)(55, 407)(56, 408)(57, 409)(58, 410)(59, 411)(60, 412)(61, 413)(62, 414)(63, 415)(64, 416)(65, 417)(66, 418)(67, 419)(68, 420)(69, 421)(70, 422)(71, 423)(72, 424)(73, 425)(74, 426)(75, 427)(76, 428)(77, 429)(78, 430)(79, 431)(80, 432)(81, 433)(82, 434)(83, 435)(84, 436)(85, 437)(86, 438)(87, 439)(88, 440)(89, 441)(90, 442)(91, 443)(92, 444)(93, 445)(94, 446)(95, 447)(96, 448)(97, 449)(98, 450)(99, 451)(100, 452)(101, 453)(102, 454)(103, 455)(104, 456)(105, 457)(106, 458)(107, 459)(108, 460)(109, 461)(110, 462)(111, 463)(112, 464)(113, 465)(114, 466)(115, 467)(116, 468)(117, 469)(118, 470)(119, 471)(120, 472)(121, 473)(122, 474)(123, 475)(124, 476)(125, 477)(126, 478)(127, 479)(128, 480)(129, 481)(130, 482)(131, 483)(132, 484)(133, 485)(134, 486)(135, 487)(136, 488)(137, 489)(138, 490)(139, 491)(140, 492)(141, 493)(142, 494)(143, 495)(144, 496)(145, 497)(146, 498)(147, 499)(148, 500)(149, 501)(150, 502)(151, 503)(152, 504)(153, 505)(154, 506)(155, 507)(156, 508)(157, 509)(158, 510)(159, 511)(160, 512)(161, 513)(162, 514)(163, 515)(164, 516)(165, 517)(166, 518)(167, 519)(168, 520)(169, 521)(170, 522)(171, 523)(172, 524)(173, 525)(174, 526)(175, 527)(176, 528)(177, 529)(178, 530)(179, 531)(180, 532)(181, 533)(182, 534)(183, 535)(184, 536)(185, 537)(186, 538)(187, 539)(188, 540)(189, 541)(190, 542)(191, 543)(192, 544)(193, 545)(194, 546)(195, 547)(196, 548)(197, 549)(198, 550)(199, 551)(200, 552)(201, 553)(202, 554)(203, 555)(204, 556)(205, 557)(206, 558)(207, 559)(208, 560)(209, 561)(210, 562)(211, 563)(212, 564)(213, 565)(214, 566)(215, 567)(216, 568)(217, 569)(218, 570)(219, 571)(220, 572)(221, 573)(222, 574)(223, 575)(224, 576)(225, 577)(226, 578)(227, 579)(228, 580)(229, 581)(230, 582)(231, 583)(232, 584)(233, 585)(234, 586)(235, 587)(236, 588)(237, 589)(238, 590)(239, 591)(240, 592)(241, 593)(242, 594)(243, 595)(244, 596)(245, 597)(246, 598)(247, 599)(248, 600)(249, 601)(250, 602)(251, 603)(252, 604)(253, 605)(254, 606)(255, 607)(256, 608)(257, 609)(258, 610)(259, 611)(260, 612)(261, 613)(262, 614)(263, 615)(264, 616)(265, 617)(266, 618)(267, 619)(268, 620)(269, 621)(270, 622)(271, 623)(272, 624)(273, 625)(274, 626)(275, 627)(276, 628)(277, 629)(278, 630)(279, 631)(280, 632)(281, 633)(282, 634)(283, 635)(284, 636)(285, 637)(286, 638)(287, 639)(288, 640)(289, 641)(290, 642)(291, 643)(292, 644)(293, 645)(294, 646)(295, 647)(296, 648)(297, 649)(298, 650)(299, 651)(300, 652)(301, 653)(302, 654)(303, 655)(304, 656)(305, 657)(306, 658)(307, 659)(308, 660)(309, 661)(310, 662)(311, 663)(312, 664)(313, 665)(314, 666)(315, 667)(316, 668)(317, 669)(318, 670)(319, 671)(320, 672)(321, 673)(322, 674)(323, 675)(324, 676)(325, 677)(326, 678)(327, 679)(328, 680)(329, 681)(330, 682)(331, 683)(332, 684)(333, 685)(334, 686)(335, 687)(336, 688)(337, 689)(338, 690)(339, 691)(340, 692)(341, 693)(342, 694)(343, 695)(344, 696)(345, 697)(346, 698)(347, 699)(348, 700)(349, 701)(350, 702)(351, 703)(352, 704) local type(s) :: { ( 16, 16 ), ( 16^4 ) } Outer automorphisms :: reflexible Dual of E23.1166 Graph:: simple bipartite v = 264 e = 352 f = 44 degree seq :: [ 2^176, 4^88 ] E23.1161 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 2, 4}) Quotient :: edge^2 Aut^+ = D8 x D22 (small group id <176, 31>) Aut = D16 x D22 (small group id <352, 105>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (R * Y3)^2, R * Y1 * R * Y2, Y3^4, (Y3^-1 * Y2 * Y3^-1)^2, Y2 * Y1 * Y2 * Y3^-2 * Y1, (Y3^-1 * Y1 * Y3^-1)^2, Y2 * Y3^-1 * Y2 * Y1 * Y3 * Y1, (Y1 * Y3^-1 * Y2)^2, Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ] Map:: polytopal R = (1, 177, 4, 180, 14, 190, 5, 181)(2, 178, 7, 183, 22, 198, 8, 184)(3, 179, 10, 186, 17, 193, 11, 187)(6, 182, 18, 194, 9, 185, 19, 195)(12, 188, 25, 201, 15, 191, 26, 202)(13, 189, 27, 203, 16, 192, 28, 204)(20, 196, 29, 205, 23, 199, 30, 206)(21, 197, 31, 207, 24, 200, 32, 208)(33, 209, 41, 217, 35, 211, 42, 218)(34, 210, 43, 219, 36, 212, 44, 220)(37, 213, 45, 221, 39, 215, 46, 222)(38, 214, 47, 223, 40, 216, 48, 224)(49, 225, 57, 233, 51, 227, 58, 234)(50, 226, 59, 235, 52, 228, 60, 236)(53, 229, 61, 237, 55, 231, 62, 238)(54, 230, 63, 239, 56, 232, 64, 240)(65, 241, 73, 249, 67, 243, 74, 250)(66, 242, 75, 251, 68, 244, 76, 252)(69, 245, 113, 289, 71, 247, 117, 293)(70, 246, 115, 291, 72, 248, 119, 295)(77, 253, 121, 297, 84, 260, 123, 299)(78, 254, 124, 300, 90, 266, 126, 302)(79, 255, 127, 303, 87, 263, 129, 305)(80, 256, 130, 306, 81, 257, 132, 308)(82, 258, 134, 310, 85, 261, 136, 312)(83, 259, 137, 313, 86, 262, 139, 315)(88, 264, 144, 320, 91, 267, 146, 322)(89, 265, 147, 323, 92, 268, 149, 325)(93, 269, 153, 329, 95, 271, 155, 331)(94, 270, 156, 332, 96, 272, 158, 334)(97, 273, 161, 337, 99, 275, 163, 339)(98, 274, 164, 340, 100, 276, 166, 342)(101, 277, 169, 345, 103, 279, 171, 347)(102, 278, 172, 348, 104, 280, 174, 350)(105, 281, 175, 351, 107, 283, 170, 346)(106, 282, 173, 349, 108, 284, 176, 352)(109, 285, 162, 338, 111, 287, 167, 343)(110, 286, 168, 344, 112, 288, 165, 341)(114, 290, 154, 330, 118, 294, 159, 335)(116, 292, 160, 336, 120, 296, 157, 333)(122, 298, 151, 327, 140, 316, 145, 321)(125, 301, 141, 317, 150, 326, 135, 311)(128, 304, 142, 318, 143, 319, 138, 314)(131, 307, 152, 328, 133, 309, 148, 324)(353, 354)(355, 361)(356, 364)(357, 367)(358, 369)(359, 372)(360, 375)(362, 376)(363, 373)(365, 371)(366, 374)(368, 370)(377, 385)(378, 387)(379, 388)(380, 386)(381, 389)(382, 391)(383, 392)(384, 390)(393, 401)(394, 403)(395, 404)(396, 402)(397, 405)(398, 407)(399, 408)(400, 406)(409, 417)(410, 419)(411, 420)(412, 418)(413, 421)(414, 423)(415, 424)(416, 422)(425, 429)(426, 436)(427, 432)(428, 433)(430, 465)(431, 467)(434, 473)(435, 484)(437, 475)(438, 482)(439, 471)(440, 476)(441, 481)(442, 469)(443, 478)(444, 479)(445, 486)(446, 491)(447, 488)(448, 489)(449, 496)(450, 501)(451, 498)(452, 499)(453, 505)(454, 510)(455, 507)(456, 508)(457, 513)(458, 518)(459, 515)(460, 516)(461, 521)(462, 526)(463, 523)(464, 524)(466, 527)(468, 528)(470, 522)(472, 525)(474, 514)(477, 506)(480, 512)(483, 520)(485, 517)(487, 503)(490, 500)(492, 519)(493, 497)(494, 504)(495, 509)(502, 511)(529, 531)(530, 534)(532, 541)(533, 544)(535, 549)(536, 552)(537, 550)(538, 548)(539, 551)(540, 546)(542, 545)(543, 547)(553, 562)(554, 564)(555, 561)(556, 563)(557, 566)(558, 568)(559, 565)(560, 567)(569, 578)(570, 580)(571, 577)(572, 579)(573, 582)(574, 584)(575, 581)(576, 583)(585, 594)(586, 596)(587, 593)(588, 595)(589, 598)(590, 600)(591, 597)(592, 599)(601, 609)(602, 608)(603, 605)(604, 612)(606, 643)(607, 645)(610, 660)(611, 651)(613, 658)(614, 649)(615, 641)(616, 657)(617, 654)(618, 647)(619, 655)(620, 652)(621, 667)(622, 664)(623, 665)(624, 662)(625, 677)(626, 674)(627, 675)(628, 672)(629, 686)(630, 683)(631, 684)(632, 681)(633, 694)(634, 691)(635, 692)(636, 689)(637, 702)(638, 699)(639, 700)(640, 697)(642, 704)(644, 698)(646, 701)(648, 703)(650, 693)(653, 685)(656, 682)(659, 690)(661, 695)(663, 680)(666, 679)(668, 696)(669, 676)(670, 673)(671, 687)(678, 688) L = (1, 353)(2, 354)(3, 355)(4, 356)(5, 357)(6, 358)(7, 359)(8, 360)(9, 361)(10, 362)(11, 363)(12, 364)(13, 365)(14, 366)(15, 367)(16, 368)(17, 369)(18, 370)(19, 371)(20, 372)(21, 373)(22, 374)(23, 375)(24, 376)(25, 377)(26, 378)(27, 379)(28, 380)(29, 381)(30, 382)(31, 383)(32, 384)(33, 385)(34, 386)(35, 387)(36, 388)(37, 389)(38, 390)(39, 391)(40, 392)(41, 393)(42, 394)(43, 395)(44, 396)(45, 397)(46, 398)(47, 399)(48, 400)(49, 401)(50, 402)(51, 403)(52, 404)(53, 405)(54, 406)(55, 407)(56, 408)(57, 409)(58, 410)(59, 411)(60, 412)(61, 413)(62, 414)(63, 415)(64, 416)(65, 417)(66, 418)(67, 419)(68, 420)(69, 421)(70, 422)(71, 423)(72, 424)(73, 425)(74, 426)(75, 427)(76, 428)(77, 429)(78, 430)(79, 431)(80, 432)(81, 433)(82, 434)(83, 435)(84, 436)(85, 437)(86, 438)(87, 439)(88, 440)(89, 441)(90, 442)(91, 443)(92, 444)(93, 445)(94, 446)(95, 447)(96, 448)(97, 449)(98, 450)(99, 451)(100, 452)(101, 453)(102, 454)(103, 455)(104, 456)(105, 457)(106, 458)(107, 459)(108, 460)(109, 461)(110, 462)(111, 463)(112, 464)(113, 465)(114, 466)(115, 467)(116, 468)(117, 469)(118, 470)(119, 471)(120, 472)(121, 473)(122, 474)(123, 475)(124, 476)(125, 477)(126, 478)(127, 479)(128, 480)(129, 481)(130, 482)(131, 483)(132, 484)(133, 485)(134, 486)(135, 487)(136, 488)(137, 489)(138, 490)(139, 491)(140, 492)(141, 493)(142, 494)(143, 495)(144, 496)(145, 497)(146, 498)(147, 499)(148, 500)(149, 501)(150, 502)(151, 503)(152, 504)(153, 505)(154, 506)(155, 507)(156, 508)(157, 509)(158, 510)(159, 511)(160, 512)(161, 513)(162, 514)(163, 515)(164, 516)(165, 517)(166, 518)(167, 519)(168, 520)(169, 521)(170, 522)(171, 523)(172, 524)(173, 525)(174, 526)(175, 527)(176, 528)(177, 529)(178, 530)(179, 531)(180, 532)(181, 533)(182, 534)(183, 535)(184, 536)(185, 537)(186, 538)(187, 539)(188, 540)(189, 541)(190, 542)(191, 543)(192, 544)(193, 545)(194, 546)(195, 547)(196, 548)(197, 549)(198, 550)(199, 551)(200, 552)(201, 553)(202, 554)(203, 555)(204, 556)(205, 557)(206, 558)(207, 559)(208, 560)(209, 561)(210, 562)(211, 563)(212, 564)(213, 565)(214, 566)(215, 567)(216, 568)(217, 569)(218, 570)(219, 571)(220, 572)(221, 573)(222, 574)(223, 575)(224, 576)(225, 577)(226, 578)(227, 579)(228, 580)(229, 581)(230, 582)(231, 583)(232, 584)(233, 585)(234, 586)(235, 587)(236, 588)(237, 589)(238, 590)(239, 591)(240, 592)(241, 593)(242, 594)(243, 595)(244, 596)(245, 597)(246, 598)(247, 599)(248, 600)(249, 601)(250, 602)(251, 603)(252, 604)(253, 605)(254, 606)(255, 607)(256, 608)(257, 609)(258, 610)(259, 611)(260, 612)(261, 613)(262, 614)(263, 615)(264, 616)(265, 617)(266, 618)(267, 619)(268, 620)(269, 621)(270, 622)(271, 623)(272, 624)(273, 625)(274, 626)(275, 627)(276, 628)(277, 629)(278, 630)(279, 631)(280, 632)(281, 633)(282, 634)(283, 635)(284, 636)(285, 637)(286, 638)(287, 639)(288, 640)(289, 641)(290, 642)(291, 643)(292, 644)(293, 645)(294, 646)(295, 647)(296, 648)(297, 649)(298, 650)(299, 651)(300, 652)(301, 653)(302, 654)(303, 655)(304, 656)(305, 657)(306, 658)(307, 659)(308, 660)(309, 661)(310, 662)(311, 663)(312, 664)(313, 665)(314, 666)(315, 667)(316, 668)(317, 669)(318, 670)(319, 671)(320, 672)(321, 673)(322, 674)(323, 675)(324, 676)(325, 677)(326, 678)(327, 679)(328, 680)(329, 681)(330, 682)(331, 683)(332, 684)(333, 685)(334, 686)(335, 687)(336, 688)(337, 689)(338, 690)(339, 691)(340, 692)(341, 693)(342, 694)(343, 695)(344, 696)(345, 697)(346, 698)(347, 699)(348, 700)(349, 701)(350, 702)(351, 703)(352, 704) local type(s) :: { ( 8, 8 ), ( 8^8 ) } Outer automorphisms :: reflexible Dual of E23.1163 Graph:: simple bipartite v = 220 e = 352 f = 88 degree seq :: [ 2^176, 8^44 ] E23.1162 :: Family: { 4 } :: Oriented family(ies): { E4 } Signature :: (0; {2, 2, 2, 4}) Quotient :: edge^2 Aut^+ = (C4 x D22) : C2 (small group id <176, 34>) Aut = (D8 x D22) : C2 (small group id <352, 109>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (R * Y3)^2, R * Y1 * R * Y2, Y3^4, (Y3^-1 * Y2 * Y3^-1)^2, Y2 * Y1 * Y2 * Y3^-2 * Y1, (Y3^-1 * Y1 * Y3^-1)^2, Y2 * Y3^-1 * Y2 * Y1 * Y3 * Y1, (Y1 * Y3^-1 * Y2)^2, Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ] Map:: polytopal R = (1, 177, 4, 180, 14, 190, 5, 181)(2, 178, 7, 183, 22, 198, 8, 184)(3, 179, 10, 186, 17, 193, 11, 187)(6, 182, 18, 194, 9, 185, 19, 195)(12, 188, 25, 201, 15, 191, 26, 202)(13, 189, 27, 203, 16, 192, 28, 204)(20, 196, 29, 205, 23, 199, 30, 206)(21, 197, 31, 207, 24, 200, 32, 208)(33, 209, 41, 217, 35, 211, 42, 218)(34, 210, 43, 219, 36, 212, 44, 220)(37, 213, 45, 221, 39, 215, 46, 222)(38, 214, 47, 223, 40, 216, 48, 224)(49, 225, 57, 233, 51, 227, 58, 234)(50, 226, 59, 235, 52, 228, 60, 236)(53, 229, 61, 237, 55, 231, 62, 238)(54, 230, 63, 239, 56, 232, 64, 240)(65, 241, 73, 249, 67, 243, 74, 250)(66, 242, 75, 251, 68, 244, 76, 252)(69, 245, 91, 267, 71, 247, 90, 266)(70, 246, 81, 257, 72, 248, 80, 256)(77, 253, 124, 300, 86, 262, 122, 298)(78, 254, 129, 305, 94, 270, 130, 306)(79, 255, 132, 308, 89, 265, 133, 309)(82, 258, 123, 299, 83, 259, 121, 297)(84, 260, 125, 301, 87, 263, 134, 310)(85, 261, 135, 311, 88, 264, 126, 302)(92, 268, 127, 303, 95, 271, 131, 307)(93, 269, 140, 316, 96, 272, 128, 304)(97, 273, 136, 312, 99, 275, 138, 314)(98, 274, 139, 315, 100, 276, 137, 313)(101, 277, 141, 317, 103, 279, 143, 319)(102, 278, 144, 320, 104, 280, 142, 318)(105, 281, 145, 321, 107, 283, 147, 323)(106, 282, 148, 324, 108, 284, 146, 322)(109, 285, 149, 325, 111, 287, 151, 327)(110, 286, 152, 328, 112, 288, 150, 326)(113, 289, 153, 329, 115, 291, 155, 331)(114, 290, 156, 332, 116, 292, 154, 330)(117, 293, 157, 333, 119, 295, 159, 335)(118, 294, 160, 336, 120, 296, 158, 334)(161, 337, 171, 347, 163, 339, 169, 345)(162, 338, 170, 346, 164, 340, 172, 348)(165, 341, 175, 351, 167, 343, 176, 352)(166, 342, 174, 350, 168, 344, 173, 349)(353, 354)(355, 361)(356, 364)(357, 367)(358, 369)(359, 372)(360, 375)(362, 376)(363, 373)(365, 371)(366, 374)(368, 370)(377, 385)(378, 387)(379, 388)(380, 386)(381, 389)(382, 391)(383, 392)(384, 390)(393, 401)(394, 403)(395, 404)(396, 402)(397, 405)(398, 407)(399, 408)(400, 406)(409, 417)(410, 419)(411, 420)(412, 418)(413, 421)(414, 423)(415, 424)(416, 422)(425, 473)(426, 475)(427, 476)(428, 474)(429, 477)(430, 479)(431, 480)(432, 482)(433, 481)(434, 478)(435, 487)(436, 488)(437, 489)(438, 486)(439, 490)(440, 491)(441, 492)(442, 484)(443, 485)(444, 493)(445, 494)(446, 483)(447, 495)(448, 496)(449, 497)(450, 498)(451, 499)(452, 500)(453, 501)(454, 502)(455, 503)(456, 504)(457, 505)(458, 506)(459, 507)(460, 508)(461, 509)(462, 510)(463, 511)(464, 512)(465, 513)(466, 514)(467, 515)(468, 516)(469, 517)(470, 518)(471, 519)(472, 520)(521, 527)(522, 526)(523, 528)(524, 525)(529, 531)(530, 534)(532, 541)(533, 544)(535, 549)(536, 552)(537, 550)(538, 548)(539, 551)(540, 546)(542, 545)(543, 547)(553, 562)(554, 564)(555, 561)(556, 563)(557, 566)(558, 568)(559, 565)(560, 567)(569, 578)(570, 580)(571, 577)(572, 579)(573, 582)(574, 584)(575, 581)(576, 583)(585, 594)(586, 596)(587, 593)(588, 595)(589, 598)(590, 600)(591, 597)(592, 599)(601, 650)(602, 652)(603, 649)(604, 651)(605, 654)(606, 656)(607, 659)(608, 660)(609, 661)(610, 662)(611, 653)(612, 665)(613, 666)(614, 663)(615, 667)(616, 664)(617, 655)(618, 657)(619, 658)(620, 670)(621, 671)(622, 668)(623, 672)(624, 669)(625, 674)(626, 675)(627, 676)(628, 673)(629, 678)(630, 679)(631, 680)(632, 677)(633, 682)(634, 683)(635, 684)(636, 681)(637, 686)(638, 687)(639, 688)(640, 685)(641, 690)(642, 691)(643, 692)(644, 689)(645, 694)(646, 695)(647, 696)(648, 693)(697, 702)(698, 704)(699, 701)(700, 703) L = (1, 353)(2, 354)(3, 355)(4, 356)(5, 357)(6, 358)(7, 359)(8, 360)(9, 361)(10, 362)(11, 363)(12, 364)(13, 365)(14, 366)(15, 367)(16, 368)(17, 369)(18, 370)(19, 371)(20, 372)(21, 373)(22, 374)(23, 375)(24, 376)(25, 377)(26, 378)(27, 379)(28, 380)(29, 381)(30, 382)(31, 383)(32, 384)(33, 385)(34, 386)(35, 387)(36, 388)(37, 389)(38, 390)(39, 391)(40, 392)(41, 393)(42, 394)(43, 395)(44, 396)(45, 397)(46, 398)(47, 399)(48, 400)(49, 401)(50, 402)(51, 403)(52, 404)(53, 405)(54, 406)(55, 407)(56, 408)(57, 409)(58, 410)(59, 411)(60, 412)(61, 413)(62, 414)(63, 415)(64, 416)(65, 417)(66, 418)(67, 419)(68, 420)(69, 421)(70, 422)(71, 423)(72, 424)(73, 425)(74, 426)(75, 427)(76, 428)(77, 429)(78, 430)(79, 431)(80, 432)(81, 433)(82, 434)(83, 435)(84, 436)(85, 437)(86, 438)(87, 439)(88, 440)(89, 441)(90, 442)(91, 443)(92, 444)(93, 445)(94, 446)(95, 447)(96, 448)(97, 449)(98, 450)(99, 451)(100, 452)(101, 453)(102, 454)(103, 455)(104, 456)(105, 457)(106, 458)(107, 459)(108, 460)(109, 461)(110, 462)(111, 463)(112, 464)(113, 465)(114, 466)(115, 467)(116, 468)(117, 469)(118, 470)(119, 471)(120, 472)(121, 473)(122, 474)(123, 475)(124, 476)(125, 477)(126, 478)(127, 479)(128, 480)(129, 481)(130, 482)(131, 483)(132, 484)(133, 485)(134, 486)(135, 487)(136, 488)(137, 489)(138, 490)(139, 491)(140, 492)(141, 493)(142, 494)(143, 495)(144, 496)(145, 497)(146, 498)(147, 499)(148, 500)(149, 501)(150, 502)(151, 503)(152, 504)(153, 505)(154, 506)(155, 507)(156, 508)(157, 509)(158, 510)(159, 511)(160, 512)(161, 513)(162, 514)(163, 515)(164, 516)(165, 517)(166, 518)(167, 519)(168, 520)(169, 521)(170, 522)(171, 523)(172, 524)(173, 525)(174, 526)(175, 527)(176, 528)(177, 529)(178, 530)(179, 531)(180, 532)(181, 533)(182, 534)(183, 535)(184, 536)(185, 537)(186, 538)(187, 539)(188, 540)(189, 541)(190, 542)(191, 543)(192, 544)(193, 545)(194, 546)(195, 547)(196, 548)(197, 549)(198, 550)(199, 551)(200, 552)(201, 553)(202, 554)(203, 555)(204, 556)(205, 557)(206, 558)(207, 559)(208, 560)(209, 561)(210, 562)(211, 563)(212, 564)(213, 565)(214, 566)(215, 567)(216, 568)(217, 569)(218, 570)(219, 571)(220, 572)(221, 573)(222, 574)(223, 575)(224, 576)(225, 577)(226, 578)(227, 579)(228, 580)(229, 581)(230, 582)(231, 583)(232, 584)(233, 585)(234, 586)(235, 587)(236, 588)(237, 589)(238, 590)(239, 591)(240, 592)(241, 593)(242, 594)(243, 595)(244, 596)(245, 597)(246, 598)(247, 599)(248, 600)(249, 601)(250, 602)(251, 603)(252, 604)(253, 605)(254, 606)(255, 607)(256, 608)(257, 609)(258, 610)(259, 611)(260, 612)(261, 613)(262, 614)(263, 615)(264, 616)(265, 617)(266, 618)(267, 619)(268, 620)(269, 621)(270, 622)(271, 623)(272, 624)(273, 625)(274, 626)(275, 627)(276, 628)(277, 629)(278, 630)(279, 631)(280, 632)(281, 633)(282, 634)(283, 635)(284, 636)(285, 637)(286, 638)(287, 639)(288, 640)(289, 641)(290, 642)(291, 643)(292, 644)(293, 645)(294, 646)(295, 647)(296, 648)(297, 649)(298, 650)(299, 651)(300, 652)(301, 653)(302, 654)(303, 655)(304, 656)(305, 657)(306, 658)(307, 659)(308, 660)(309, 661)(310, 662)(311, 663)(312, 664)(313, 665)(314, 666)(315, 667)(316, 668)(317, 669)(318, 670)(319, 671)(320, 672)(321, 673)(322, 674)(323, 675)(324, 676)(325, 677)(326, 678)(327, 679)(328, 680)(329, 681)(330, 682)(331, 683)(332, 684)(333, 685)(334, 686)(335, 687)(336, 688)(337, 689)(338, 690)(339, 691)(340, 692)(341, 693)(342, 694)(343, 695)(344, 696)(345, 697)(346, 698)(347, 699)(348, 700)(349, 701)(350, 702)(351, 703)(352, 704) local type(s) :: { ( 8, 8 ), ( 8^8 ) } Outer automorphisms :: reflexible Dual of E23.1164 Graph:: simple bipartite v = 220 e = 352 f = 88 degree seq :: [ 2^176, 8^44 ] E23.1163 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 2, 4}) Quotient :: loop^2 Aut^+ = D8 x D22 (small group id <176, 31>) Aut = D16 x D22 (small group id <352, 105>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, (R * Y3)^2, R * Y1 * R * Y2, Y2 * Y3 * Y2 * Y1 * Y3 * Y1, (Y1 * Y2)^4, (Y3 * Y2)^22 ] Map:: R = (1, 177, 353, 529, 4, 180, 356, 532)(2, 178, 354, 530, 6, 182, 358, 534)(3, 179, 355, 531, 8, 184, 360, 536)(5, 181, 357, 533, 12, 188, 364, 540)(7, 183, 359, 535, 16, 192, 368, 544)(9, 185, 361, 537, 18, 194, 370, 546)(10, 186, 362, 538, 19, 195, 371, 547)(11, 187, 363, 539, 21, 197, 373, 549)(13, 189, 365, 541, 23, 199, 375, 551)(14, 190, 366, 542, 24, 200, 376, 552)(15, 191, 367, 543, 25, 201, 377, 553)(17, 193, 369, 545, 27, 203, 379, 555)(20, 196, 372, 548, 31, 207, 383, 559)(22, 198, 374, 550, 33, 209, 385, 561)(26, 202, 378, 554, 37, 213, 389, 565)(28, 204, 380, 556, 39, 215, 391, 567)(29, 205, 381, 557, 40, 216, 392, 568)(30, 206, 382, 558, 41, 217, 393, 569)(32, 208, 384, 560, 42, 218, 394, 570)(34, 210, 386, 562, 44, 220, 396, 572)(35, 211, 387, 563, 45, 221, 397, 573)(36, 212, 388, 564, 46, 222, 398, 574)(38, 214, 390, 566, 47, 223, 399, 575)(43, 219, 395, 571, 52, 228, 404, 580)(48, 224, 400, 576, 57, 233, 409, 585)(49, 225, 401, 577, 58, 234, 410, 586)(50, 226, 402, 578, 59, 235, 411, 587)(51, 227, 403, 579, 60, 236, 412, 588)(53, 229, 405, 581, 61, 237, 413, 589)(54, 230, 406, 582, 62, 238, 414, 590)(55, 231, 407, 583, 63, 239, 415, 591)(56, 232, 408, 584, 64, 240, 416, 592)(65, 241, 417, 593, 73, 249, 425, 601)(66, 242, 418, 594, 74, 250, 426, 602)(67, 243, 419, 595, 75, 251, 427, 603)(68, 244, 420, 596, 76, 252, 428, 604)(69, 245, 421, 597, 77, 253, 429, 605)(70, 246, 422, 598, 81, 257, 433, 609)(71, 247, 423, 599, 79, 255, 431, 607)(72, 248, 424, 600, 87, 263, 439, 615)(78, 254, 430, 606, 113, 289, 465, 641)(80, 256, 432, 608, 121, 297, 473, 649)(82, 258, 434, 610, 132, 308, 484, 660)(83, 259, 435, 611, 116, 292, 468, 644)(84, 260, 436, 612, 114, 290, 466, 642)(85, 261, 437, 613, 124, 300, 476, 652)(86, 262, 438, 614, 138, 314, 490, 666)(88, 264, 440, 616, 122, 298, 474, 650)(89, 265, 441, 617, 129, 305, 481, 657)(90, 266, 442, 618, 146, 322, 498, 674)(91, 267, 443, 619, 127, 303, 479, 655)(92, 268, 444, 620, 130, 306, 482, 658)(93, 269, 445, 621, 118, 294, 470, 646)(94, 270, 446, 622, 125, 301, 477, 653)(95, 271, 447, 623, 136, 312, 488, 664)(96, 272, 448, 624, 140, 316, 492, 668)(97, 273, 449, 625, 157, 333, 509, 685)(98, 274, 450, 626, 141, 317, 493, 669)(99, 275, 451, 627, 134, 310, 486, 662)(100, 276, 452, 628, 148, 324, 500, 676)(101, 277, 453, 629, 154, 330, 506, 682)(102, 278, 454, 630, 149, 325, 501, 677)(103, 279, 455, 631, 151, 327, 503, 679)(104, 280, 456, 632, 143, 319, 495, 671)(105, 281, 457, 633, 160, 336, 512, 688)(106, 282, 458, 634, 165, 341, 517, 693)(107, 283, 459, 635, 161, 337, 513, 689)(108, 284, 460, 636, 163, 339, 515, 691)(109, 285, 461, 637, 168, 344, 520, 696)(110, 286, 462, 638, 173, 349, 525, 701)(111, 287, 463, 639, 169, 345, 521, 697)(112, 288, 464, 640, 171, 347, 523, 699)(115, 291, 467, 643, 170, 346, 522, 698)(117, 293, 469, 645, 174, 350, 526, 702)(119, 295, 471, 647, 172, 348, 524, 700)(120, 296, 472, 648, 175, 351, 527, 703)(123, 299, 475, 651, 162, 338, 514, 690)(126, 302, 478, 654, 150, 326, 502, 678)(128, 304, 480, 656, 164, 340, 516, 692)(131, 307, 483, 659, 142, 318, 494, 670)(133, 309, 485, 661, 166, 342, 518, 694)(135, 311, 487, 663, 144, 320, 496, 672)(137, 313, 489, 665, 152, 328, 504, 680)(139, 315, 491, 667, 155, 331, 507, 683)(145, 321, 497, 673, 176, 352, 528, 704)(147, 323, 499, 675, 158, 334, 510, 686)(153, 329, 505, 681, 159, 335, 511, 687)(156, 332, 508, 684, 167, 343, 519, 695) L = (1, 178)(2, 177)(3, 183)(4, 185)(5, 187)(6, 189)(7, 179)(8, 193)(9, 180)(10, 192)(11, 181)(12, 198)(13, 182)(14, 197)(15, 196)(16, 186)(17, 184)(18, 204)(19, 206)(20, 191)(21, 190)(22, 188)(23, 210)(24, 212)(25, 208)(26, 207)(27, 211)(28, 194)(29, 209)(30, 195)(31, 202)(32, 201)(33, 205)(34, 199)(35, 203)(36, 200)(37, 219)(38, 218)(39, 224)(40, 226)(41, 225)(42, 214)(43, 213)(44, 229)(45, 231)(46, 230)(47, 232)(48, 215)(49, 217)(50, 216)(51, 228)(52, 227)(53, 220)(54, 222)(55, 221)(56, 223)(57, 241)(58, 243)(59, 242)(60, 244)(61, 245)(62, 247)(63, 246)(64, 248)(65, 233)(66, 235)(67, 234)(68, 236)(69, 237)(70, 239)(71, 238)(72, 240)(73, 289)(74, 292)(75, 290)(76, 294)(77, 297)(78, 300)(79, 298)(80, 305)(81, 308)(82, 306)(83, 301)(84, 314)(85, 316)(86, 317)(87, 303)(88, 322)(89, 324)(90, 325)(91, 310)(92, 330)(93, 312)(94, 333)(95, 319)(96, 336)(97, 337)(98, 341)(99, 327)(100, 344)(101, 345)(102, 349)(103, 347)(104, 339)(105, 346)(106, 348)(107, 350)(108, 351)(109, 338)(110, 340)(111, 342)(112, 352)(113, 249)(114, 251)(115, 326)(116, 250)(117, 328)(118, 252)(119, 331)(120, 343)(121, 253)(122, 255)(123, 318)(124, 254)(125, 259)(126, 307)(127, 263)(128, 334)(129, 256)(130, 258)(131, 302)(132, 257)(133, 320)(134, 267)(135, 315)(136, 269)(137, 323)(138, 260)(139, 311)(140, 261)(141, 262)(142, 299)(143, 271)(144, 309)(145, 335)(146, 264)(147, 313)(148, 265)(149, 266)(150, 291)(151, 275)(152, 293)(153, 332)(154, 268)(155, 295)(156, 329)(157, 270)(158, 304)(159, 321)(160, 272)(161, 273)(162, 285)(163, 280)(164, 286)(165, 274)(166, 287)(167, 296)(168, 276)(169, 277)(170, 281)(171, 279)(172, 282)(173, 278)(174, 283)(175, 284)(176, 288)(353, 531)(354, 533)(355, 529)(356, 538)(357, 530)(358, 542)(359, 543)(360, 541)(361, 540)(362, 532)(363, 548)(364, 537)(365, 536)(366, 534)(367, 535)(368, 554)(369, 553)(370, 557)(371, 556)(372, 539)(373, 560)(374, 559)(375, 563)(376, 562)(377, 545)(378, 544)(379, 566)(380, 547)(381, 546)(382, 565)(383, 550)(384, 549)(385, 571)(386, 552)(387, 551)(388, 570)(389, 558)(390, 555)(391, 577)(392, 576)(393, 579)(394, 564)(395, 561)(396, 582)(397, 581)(398, 584)(399, 583)(400, 568)(401, 567)(402, 580)(403, 569)(404, 578)(405, 573)(406, 572)(407, 575)(408, 574)(409, 594)(410, 593)(411, 596)(412, 595)(413, 598)(414, 597)(415, 600)(416, 599)(417, 586)(418, 585)(419, 588)(420, 587)(421, 590)(422, 589)(423, 592)(424, 591)(425, 642)(426, 641)(427, 646)(428, 644)(429, 650)(430, 653)(431, 655)(432, 658)(433, 649)(434, 662)(435, 664)(436, 652)(437, 669)(438, 671)(439, 660)(440, 657)(441, 677)(442, 679)(443, 674)(444, 676)(445, 666)(446, 668)(447, 685)(448, 689)(449, 691)(450, 688)(451, 682)(452, 697)(453, 699)(454, 696)(455, 701)(456, 693)(457, 700)(458, 703)(459, 698)(460, 702)(461, 692)(462, 704)(463, 690)(464, 694)(465, 602)(466, 601)(467, 680)(468, 604)(469, 695)(470, 603)(471, 678)(472, 683)(473, 609)(474, 605)(475, 672)(476, 612)(477, 606)(478, 663)(479, 607)(480, 670)(481, 616)(482, 608)(483, 665)(484, 615)(485, 687)(486, 610)(487, 654)(488, 611)(489, 659)(490, 621)(491, 681)(492, 622)(493, 613)(494, 656)(495, 614)(496, 651)(497, 686)(498, 619)(499, 684)(500, 620)(501, 617)(502, 647)(503, 618)(504, 643)(505, 667)(506, 627)(507, 648)(508, 675)(509, 623)(510, 673)(511, 661)(512, 626)(513, 624)(514, 639)(515, 625)(516, 637)(517, 632)(518, 640)(519, 645)(520, 630)(521, 628)(522, 635)(523, 629)(524, 633)(525, 631)(526, 636)(527, 634)(528, 638) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8 ) } Outer automorphisms :: reflexible Dual of E23.1161 Transitivity :: VT+ Graph:: bipartite v = 88 e = 352 f = 220 degree seq :: [ 8^88 ] E23.1164 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 2, 4}) Quotient :: loop^2 Aut^+ = (C4 x D22) : C2 (small group id <176, 34>) Aut = (D8 x D22) : C2 (small group id <352, 109>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, Y3^2, R^2, (R * Y3)^2, R * Y1 * R * Y2, Y2 * Y3 * Y2 * Y1 * Y3 * Y1, (Y1 * Y2)^4, Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y1 * Y3 * Y2 * Y3 * Y1 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 * Y3 * Y2 ] Map:: R = (1, 177, 353, 529, 4, 180, 356, 532)(2, 178, 354, 530, 6, 182, 358, 534)(3, 179, 355, 531, 8, 184, 360, 536)(5, 181, 357, 533, 12, 188, 364, 540)(7, 183, 359, 535, 16, 192, 368, 544)(9, 185, 361, 537, 18, 194, 370, 546)(10, 186, 362, 538, 19, 195, 371, 547)(11, 187, 363, 539, 21, 197, 373, 549)(13, 189, 365, 541, 23, 199, 375, 551)(14, 190, 366, 542, 24, 200, 376, 552)(15, 191, 367, 543, 25, 201, 377, 553)(17, 193, 369, 545, 27, 203, 379, 555)(20, 196, 372, 548, 31, 207, 383, 559)(22, 198, 374, 550, 33, 209, 385, 561)(26, 202, 378, 554, 37, 213, 389, 565)(28, 204, 380, 556, 39, 215, 391, 567)(29, 205, 381, 557, 40, 216, 392, 568)(30, 206, 382, 558, 41, 217, 393, 569)(32, 208, 384, 560, 42, 218, 394, 570)(34, 210, 386, 562, 44, 220, 396, 572)(35, 211, 387, 563, 45, 221, 397, 573)(36, 212, 388, 564, 46, 222, 398, 574)(38, 214, 390, 566, 47, 223, 399, 575)(43, 219, 395, 571, 52, 228, 404, 580)(48, 224, 400, 576, 57, 233, 409, 585)(49, 225, 401, 577, 58, 234, 410, 586)(50, 226, 402, 578, 59, 235, 411, 587)(51, 227, 403, 579, 60, 236, 412, 588)(53, 229, 405, 581, 61, 237, 413, 589)(54, 230, 406, 582, 62, 238, 414, 590)(55, 231, 407, 583, 63, 239, 415, 591)(56, 232, 408, 584, 64, 240, 416, 592)(65, 241, 417, 593, 73, 249, 425, 601)(66, 242, 418, 594, 74, 250, 426, 602)(67, 243, 419, 595, 75, 251, 427, 603)(68, 244, 420, 596, 76, 252, 428, 604)(69, 245, 421, 597, 87, 263, 439, 615)(70, 246, 422, 598, 79, 255, 431, 607)(71, 247, 423, 599, 81, 257, 433, 609)(72, 248, 424, 600, 77, 253, 429, 605)(78, 254, 430, 606, 118, 294, 470, 646)(80, 256, 432, 608, 121, 297, 473, 649)(82, 258, 434, 610, 132, 308, 484, 660)(83, 259, 435, 611, 114, 290, 466, 642)(84, 260, 436, 612, 116, 292, 468, 644)(85, 261, 437, 613, 124, 300, 476, 652)(86, 262, 438, 614, 138, 314, 490, 666)(88, 264, 440, 616, 122, 298, 474, 650)(89, 265, 441, 617, 129, 305, 481, 657)(90, 266, 442, 618, 146, 322, 498, 674)(91, 267, 443, 619, 127, 303, 479, 655)(92, 268, 444, 620, 130, 306, 482, 658)(93, 269, 445, 621, 113, 289, 465, 641)(94, 270, 446, 622, 125, 301, 477, 653)(95, 271, 447, 623, 136, 312, 488, 664)(96, 272, 448, 624, 140, 316, 492, 668)(97, 273, 449, 625, 157, 333, 509, 685)(98, 274, 450, 626, 141, 317, 493, 669)(99, 275, 451, 627, 134, 310, 486, 662)(100, 276, 452, 628, 148, 324, 500, 676)(101, 277, 453, 629, 154, 330, 506, 682)(102, 278, 454, 630, 149, 325, 501, 677)(103, 279, 455, 631, 151, 327, 503, 679)(104, 280, 456, 632, 143, 319, 495, 671)(105, 281, 457, 633, 160, 336, 512, 688)(106, 282, 458, 634, 165, 341, 517, 693)(107, 283, 459, 635, 161, 337, 513, 689)(108, 284, 460, 636, 163, 339, 515, 691)(109, 285, 461, 637, 168, 344, 520, 696)(110, 286, 462, 638, 173, 349, 525, 701)(111, 287, 463, 639, 169, 345, 521, 697)(112, 288, 464, 640, 171, 347, 523, 699)(115, 291, 467, 643, 170, 346, 522, 698)(117, 293, 469, 645, 174, 350, 526, 702)(119, 295, 471, 647, 172, 348, 524, 700)(120, 296, 472, 648, 175, 351, 527, 703)(123, 299, 475, 651, 176, 352, 528, 704)(126, 302, 478, 654, 167, 343, 519, 695)(128, 304, 480, 656, 166, 342, 518, 694)(131, 307, 483, 659, 159, 335, 511, 687)(133, 309, 485, 661, 164, 340, 516, 692)(135, 311, 487, 663, 158, 334, 510, 686)(137, 313, 489, 665, 155, 331, 507, 683)(139, 315, 491, 667, 152, 328, 504, 680)(142, 318, 494, 670, 153, 329, 505, 681)(144, 320, 496, 672, 147, 323, 499, 675)(145, 321, 497, 673, 162, 338, 514, 690)(150, 326, 502, 678, 156, 332, 508, 684) L = (1, 178)(2, 177)(3, 183)(4, 185)(5, 187)(6, 189)(7, 179)(8, 193)(9, 180)(10, 192)(11, 181)(12, 198)(13, 182)(14, 197)(15, 196)(16, 186)(17, 184)(18, 204)(19, 206)(20, 191)(21, 190)(22, 188)(23, 210)(24, 212)(25, 208)(26, 207)(27, 211)(28, 194)(29, 209)(30, 195)(31, 202)(32, 201)(33, 205)(34, 199)(35, 203)(36, 200)(37, 219)(38, 218)(39, 224)(40, 226)(41, 225)(42, 214)(43, 213)(44, 229)(45, 231)(46, 230)(47, 232)(48, 215)(49, 217)(50, 216)(51, 228)(52, 227)(53, 220)(54, 222)(55, 221)(56, 223)(57, 241)(58, 243)(59, 242)(60, 244)(61, 245)(62, 247)(63, 246)(64, 248)(65, 233)(66, 235)(67, 234)(68, 236)(69, 237)(70, 239)(71, 238)(72, 240)(73, 289)(74, 292)(75, 290)(76, 294)(77, 297)(78, 300)(79, 298)(80, 305)(81, 308)(82, 306)(83, 301)(84, 314)(85, 316)(86, 317)(87, 303)(88, 322)(89, 324)(90, 325)(91, 310)(92, 330)(93, 312)(94, 333)(95, 319)(96, 336)(97, 337)(98, 341)(99, 327)(100, 344)(101, 345)(102, 349)(103, 347)(104, 339)(105, 346)(106, 348)(107, 350)(108, 351)(109, 338)(110, 340)(111, 342)(112, 352)(113, 249)(114, 251)(115, 326)(116, 250)(117, 328)(118, 252)(119, 331)(120, 343)(121, 253)(122, 255)(123, 335)(124, 254)(125, 259)(126, 329)(127, 263)(128, 320)(129, 256)(130, 258)(131, 332)(132, 257)(133, 334)(134, 267)(135, 313)(136, 269)(137, 311)(138, 260)(139, 323)(140, 261)(141, 262)(142, 321)(143, 271)(144, 304)(145, 318)(146, 264)(147, 315)(148, 265)(149, 266)(150, 291)(151, 275)(152, 293)(153, 302)(154, 268)(155, 295)(156, 307)(157, 270)(158, 309)(159, 299)(160, 272)(161, 273)(162, 285)(163, 280)(164, 286)(165, 274)(166, 287)(167, 296)(168, 276)(169, 277)(170, 281)(171, 279)(172, 282)(173, 278)(174, 283)(175, 284)(176, 288)(353, 531)(354, 533)(355, 529)(356, 538)(357, 530)(358, 542)(359, 543)(360, 541)(361, 540)(362, 532)(363, 548)(364, 537)(365, 536)(366, 534)(367, 535)(368, 554)(369, 553)(370, 557)(371, 556)(372, 539)(373, 560)(374, 559)(375, 563)(376, 562)(377, 545)(378, 544)(379, 566)(380, 547)(381, 546)(382, 565)(383, 550)(384, 549)(385, 571)(386, 552)(387, 551)(388, 570)(389, 558)(390, 555)(391, 577)(392, 576)(393, 579)(394, 564)(395, 561)(396, 582)(397, 581)(398, 584)(399, 583)(400, 568)(401, 567)(402, 580)(403, 569)(404, 578)(405, 573)(406, 572)(407, 575)(408, 574)(409, 594)(410, 593)(411, 596)(412, 595)(413, 598)(414, 597)(415, 600)(416, 599)(417, 586)(418, 585)(419, 588)(420, 587)(421, 590)(422, 589)(423, 592)(424, 591)(425, 642)(426, 641)(427, 646)(428, 644)(429, 650)(430, 653)(431, 655)(432, 658)(433, 649)(434, 662)(435, 664)(436, 652)(437, 669)(438, 671)(439, 660)(440, 657)(441, 677)(442, 679)(443, 674)(444, 676)(445, 666)(446, 668)(447, 685)(448, 689)(449, 691)(450, 688)(451, 682)(452, 697)(453, 699)(454, 696)(455, 701)(456, 693)(457, 700)(458, 703)(459, 698)(460, 702)(461, 692)(462, 704)(463, 690)(464, 694)(465, 602)(466, 601)(467, 680)(468, 604)(469, 695)(470, 603)(471, 678)(472, 683)(473, 609)(474, 605)(475, 686)(476, 612)(477, 606)(478, 675)(479, 607)(480, 687)(481, 616)(482, 608)(483, 667)(484, 615)(485, 670)(486, 610)(487, 684)(488, 611)(489, 681)(490, 621)(491, 659)(492, 622)(493, 613)(494, 661)(495, 614)(496, 673)(497, 672)(498, 619)(499, 654)(500, 620)(501, 617)(502, 647)(503, 618)(504, 643)(505, 665)(506, 627)(507, 648)(508, 663)(509, 623)(510, 651)(511, 656)(512, 626)(513, 624)(514, 639)(515, 625)(516, 637)(517, 632)(518, 640)(519, 645)(520, 630)(521, 628)(522, 635)(523, 629)(524, 633)(525, 631)(526, 636)(527, 634)(528, 638) local type(s) :: { ( 2, 8, 2, 8, 2, 8, 2, 8 ) } Outer automorphisms :: reflexible Dual of E23.1162 Transitivity :: VT+ Graph:: bipartite v = 88 e = 352 f = 220 degree seq :: [ 8^88 ] E23.1165 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 2, 4}) Quotient :: loop^2 Aut^+ = D8 x D22 (small group id <176, 31>) Aut = D16 x D22 (small group id <352, 105>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (R * Y3)^2, R * Y1 * R * Y2, Y3^4, (Y3^-1 * Y2 * Y3^-1)^2, Y2 * Y1 * Y2 * Y3^-2 * Y1, (Y3^-1 * Y1 * Y3^-1)^2, Y2 * Y3^-1 * Y2 * Y1 * Y3 * Y1, (Y1 * Y3^-1 * Y2)^2, Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ] Map:: R = (1, 177, 353, 529, 4, 180, 356, 532, 14, 190, 366, 542, 5, 181, 357, 533)(2, 178, 354, 530, 7, 183, 359, 535, 22, 198, 374, 550, 8, 184, 360, 536)(3, 179, 355, 531, 10, 186, 362, 538, 17, 193, 369, 545, 11, 187, 363, 539)(6, 182, 358, 534, 18, 194, 370, 546, 9, 185, 361, 537, 19, 195, 371, 547)(12, 188, 364, 540, 25, 201, 377, 553, 15, 191, 367, 543, 26, 202, 378, 554)(13, 189, 365, 541, 27, 203, 379, 555, 16, 192, 368, 544, 28, 204, 380, 556)(20, 196, 372, 548, 29, 205, 381, 557, 23, 199, 375, 551, 30, 206, 382, 558)(21, 197, 373, 549, 31, 207, 383, 559, 24, 200, 376, 552, 32, 208, 384, 560)(33, 209, 385, 561, 41, 217, 393, 569, 35, 211, 387, 563, 42, 218, 394, 570)(34, 210, 386, 562, 43, 219, 395, 571, 36, 212, 388, 564, 44, 220, 396, 572)(37, 213, 389, 565, 45, 221, 397, 573, 39, 215, 391, 567, 46, 222, 398, 574)(38, 214, 390, 566, 47, 223, 399, 575, 40, 216, 392, 568, 48, 224, 400, 576)(49, 225, 401, 577, 57, 233, 409, 585, 51, 227, 403, 579, 58, 234, 410, 586)(50, 226, 402, 578, 59, 235, 411, 587, 52, 228, 404, 580, 60, 236, 412, 588)(53, 229, 405, 581, 61, 237, 413, 589, 55, 231, 407, 583, 62, 238, 414, 590)(54, 230, 406, 582, 63, 239, 415, 591, 56, 232, 408, 584, 64, 240, 416, 592)(65, 241, 417, 593, 73, 249, 425, 601, 67, 243, 419, 595, 74, 250, 426, 602)(66, 242, 418, 594, 75, 251, 427, 603, 68, 244, 420, 596, 76, 252, 428, 604)(69, 245, 421, 597, 80, 256, 432, 608, 71, 247, 423, 599, 83, 259, 435, 611)(70, 246, 422, 598, 77, 253, 429, 605, 72, 248, 424, 600, 86, 262, 438, 614)(78, 254, 430, 606, 117, 293, 469, 645, 79, 255, 431, 607, 114, 290, 466, 642)(81, 257, 433, 609, 121, 297, 473, 649, 82, 258, 434, 610, 130, 306, 482, 658)(84, 260, 436, 612, 138, 314, 490, 666, 85, 261, 437, 613, 122, 298, 474, 650)(87, 263, 439, 615, 116, 292, 468, 644, 88, 264, 440, 616, 113, 289, 465, 641)(89, 265, 441, 617, 124, 300, 476, 652, 90, 266, 442, 618, 127, 303, 479, 655)(91, 267, 443, 619, 128, 304, 480, 656, 92, 268, 444, 620, 125, 301, 477, 653)(93, 269, 445, 621, 132, 308, 484, 660, 94, 270, 446, 622, 135, 311, 487, 663)(95, 271, 447, 623, 136, 312, 488, 664, 96, 272, 448, 624, 133, 309, 485, 661)(97, 273, 449, 625, 145, 321, 497, 673, 98, 274, 450, 626, 148, 324, 500, 676)(99, 275, 451, 627, 149, 325, 501, 677, 100, 276, 452, 628, 146, 322, 498, 674)(101, 277, 453, 629, 153, 329, 505, 681, 102, 278, 454, 630, 156, 332, 508, 684)(103, 279, 455, 631, 157, 333, 509, 685, 104, 280, 456, 632, 154, 330, 506, 682)(105, 281, 457, 633, 161, 337, 513, 689, 106, 282, 458, 634, 164, 340, 516, 692)(107, 283, 459, 635, 165, 341, 517, 693, 108, 284, 460, 636, 162, 338, 514, 690)(109, 285, 461, 637, 169, 345, 521, 697, 110, 286, 462, 638, 172, 348, 524, 700)(111, 287, 463, 639, 173, 349, 525, 701, 112, 288, 464, 640, 170, 346, 522, 698)(115, 291, 467, 643, 175, 351, 527, 703, 118, 294, 470, 646, 176, 352, 528, 704)(119, 295, 471, 647, 171, 347, 523, 699, 120, 296, 472, 648, 174, 350, 526, 702)(123, 299, 475, 651, 163, 339, 515, 691, 142, 318, 494, 670, 166, 342, 518, 694)(126, 302, 478, 654, 158, 334, 510, 686, 129, 305, 481, 657, 155, 331, 507, 683)(131, 307, 483, 659, 167, 343, 519, 695, 139, 315, 491, 667, 168, 344, 520, 696)(134, 310, 486, 662, 150, 326, 502, 678, 137, 313, 489, 665, 147, 323, 499, 675)(140, 316, 492, 668, 152, 328, 504, 680, 141, 317, 493, 669, 151, 327, 503, 679)(143, 319, 495, 671, 160, 336, 512, 688, 144, 320, 496, 672, 159, 335, 511, 687) L = (1, 178)(2, 177)(3, 185)(4, 188)(5, 191)(6, 193)(7, 196)(8, 199)(9, 179)(10, 200)(11, 197)(12, 180)(13, 195)(14, 198)(15, 181)(16, 194)(17, 182)(18, 192)(19, 189)(20, 183)(21, 187)(22, 190)(23, 184)(24, 186)(25, 209)(26, 211)(27, 212)(28, 210)(29, 213)(30, 215)(31, 216)(32, 214)(33, 201)(34, 204)(35, 202)(36, 203)(37, 205)(38, 208)(39, 206)(40, 207)(41, 225)(42, 227)(43, 228)(44, 226)(45, 229)(46, 231)(47, 232)(48, 230)(49, 217)(50, 220)(51, 218)(52, 219)(53, 221)(54, 224)(55, 222)(56, 223)(57, 241)(58, 243)(59, 244)(60, 242)(61, 245)(62, 247)(63, 248)(64, 246)(65, 233)(66, 236)(67, 234)(68, 235)(69, 237)(70, 240)(71, 238)(72, 239)(73, 289)(74, 292)(75, 293)(76, 290)(77, 297)(78, 300)(79, 303)(80, 298)(81, 308)(82, 311)(83, 314)(84, 309)(85, 312)(86, 306)(87, 301)(88, 304)(89, 321)(90, 324)(91, 322)(92, 325)(93, 329)(94, 332)(95, 330)(96, 333)(97, 337)(98, 340)(99, 338)(100, 341)(101, 345)(102, 348)(103, 346)(104, 349)(105, 351)(106, 352)(107, 350)(108, 347)(109, 343)(110, 344)(111, 342)(112, 339)(113, 249)(114, 252)(115, 336)(116, 250)(117, 251)(118, 335)(119, 331)(120, 334)(121, 253)(122, 256)(123, 323)(124, 254)(125, 263)(126, 313)(127, 255)(128, 264)(129, 310)(130, 262)(131, 328)(132, 257)(133, 260)(134, 305)(135, 258)(136, 261)(137, 302)(138, 259)(139, 327)(140, 319)(141, 320)(142, 326)(143, 316)(144, 317)(145, 265)(146, 267)(147, 299)(148, 266)(149, 268)(150, 318)(151, 315)(152, 307)(153, 269)(154, 271)(155, 295)(156, 270)(157, 272)(158, 296)(159, 294)(160, 291)(161, 273)(162, 275)(163, 288)(164, 274)(165, 276)(166, 287)(167, 285)(168, 286)(169, 277)(170, 279)(171, 284)(172, 278)(173, 280)(174, 283)(175, 281)(176, 282)(353, 531)(354, 534)(355, 529)(356, 541)(357, 544)(358, 530)(359, 549)(360, 552)(361, 550)(362, 548)(363, 551)(364, 546)(365, 532)(366, 545)(367, 547)(368, 533)(369, 542)(370, 540)(371, 543)(372, 538)(373, 535)(374, 537)(375, 539)(376, 536)(377, 562)(378, 564)(379, 561)(380, 563)(381, 566)(382, 568)(383, 565)(384, 567)(385, 555)(386, 553)(387, 556)(388, 554)(389, 559)(390, 557)(391, 560)(392, 558)(393, 578)(394, 580)(395, 577)(396, 579)(397, 582)(398, 584)(399, 581)(400, 583)(401, 571)(402, 569)(403, 572)(404, 570)(405, 575)(406, 573)(407, 576)(408, 574)(409, 594)(410, 596)(411, 593)(412, 595)(413, 598)(414, 600)(415, 597)(416, 599)(417, 587)(418, 585)(419, 588)(420, 586)(421, 591)(422, 589)(423, 592)(424, 590)(425, 642)(426, 645)(427, 641)(428, 644)(429, 650)(430, 653)(431, 656)(432, 658)(433, 661)(434, 664)(435, 649)(436, 663)(437, 660)(438, 666)(439, 655)(440, 652)(441, 674)(442, 677)(443, 676)(444, 673)(445, 682)(446, 685)(447, 684)(448, 681)(449, 690)(450, 693)(451, 692)(452, 689)(453, 698)(454, 701)(455, 700)(456, 697)(457, 702)(458, 699)(459, 704)(460, 703)(461, 694)(462, 691)(463, 696)(464, 695)(465, 603)(466, 601)(467, 683)(468, 604)(469, 602)(470, 686)(471, 687)(472, 688)(473, 611)(474, 605)(475, 679)(476, 616)(477, 606)(478, 669)(479, 615)(480, 607)(481, 668)(482, 608)(483, 675)(484, 613)(485, 609)(486, 672)(487, 612)(488, 610)(489, 671)(490, 614)(491, 678)(492, 657)(493, 654)(494, 680)(495, 665)(496, 662)(497, 620)(498, 617)(499, 659)(500, 619)(501, 618)(502, 667)(503, 651)(504, 670)(505, 624)(506, 621)(507, 643)(508, 623)(509, 622)(510, 646)(511, 647)(512, 648)(513, 628)(514, 625)(515, 638)(516, 627)(517, 626)(518, 637)(519, 640)(520, 639)(521, 632)(522, 629)(523, 634)(524, 631)(525, 630)(526, 633)(527, 636)(528, 635) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) } Outer automorphisms :: reflexible Dual of E23.1159 Transitivity :: VT+ Graph:: bipartite v = 44 e = 352 f = 264 degree seq :: [ 16^44 ] E23.1166 :: Family: { 4* } :: Oriented family(ies): { E4* } Signature :: (0; {2, 2, 2, 4}) Quotient :: loop^2 Aut^+ = (C4 x D22) : C2 (small group id <176, 34>) Aut = (D8 x D22) : C2 (small group id <352, 109>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (R * Y3)^2, R * Y1 * R * Y2, Y3^4, (Y3^-1 * Y2 * Y3^-1)^2, Y2 * Y1 * Y2 * Y3^-2 * Y1, (Y3^-1 * Y1 * Y3^-1)^2, Y2 * Y3^-1 * Y2 * Y1 * Y3 * Y1, (Y1 * Y3^-1 * Y2)^2, Y3^-1 * Y1 * Y3^-1 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1 ] Map:: R = (1, 177, 353, 529, 4, 180, 356, 532, 14, 190, 366, 542, 5, 181, 357, 533)(2, 178, 354, 530, 7, 183, 359, 535, 22, 198, 374, 550, 8, 184, 360, 536)(3, 179, 355, 531, 10, 186, 362, 538, 17, 193, 369, 545, 11, 187, 363, 539)(6, 182, 358, 534, 18, 194, 370, 546, 9, 185, 361, 537, 19, 195, 371, 547)(12, 188, 364, 540, 25, 201, 377, 553, 15, 191, 367, 543, 26, 202, 378, 554)(13, 189, 365, 541, 27, 203, 379, 555, 16, 192, 368, 544, 28, 204, 380, 556)(20, 196, 372, 548, 29, 205, 381, 557, 23, 199, 375, 551, 30, 206, 382, 558)(21, 197, 373, 549, 31, 207, 383, 559, 24, 200, 376, 552, 32, 208, 384, 560)(33, 209, 385, 561, 41, 217, 393, 569, 35, 211, 387, 563, 42, 218, 394, 570)(34, 210, 386, 562, 43, 219, 395, 571, 36, 212, 388, 564, 44, 220, 396, 572)(37, 213, 389, 565, 45, 221, 397, 573, 39, 215, 391, 567, 46, 222, 398, 574)(38, 214, 390, 566, 47, 223, 399, 575, 40, 216, 392, 568, 48, 224, 400, 576)(49, 225, 401, 577, 57, 233, 409, 585, 51, 227, 403, 579, 58, 234, 410, 586)(50, 226, 402, 578, 59, 235, 411, 587, 52, 228, 404, 580, 60, 236, 412, 588)(53, 229, 405, 581, 61, 237, 413, 589, 55, 231, 407, 583, 62, 238, 414, 590)(54, 230, 406, 582, 63, 239, 415, 591, 56, 232, 408, 584, 64, 240, 416, 592)(65, 241, 417, 593, 73, 249, 425, 601, 67, 243, 419, 595, 74, 250, 426, 602)(66, 242, 418, 594, 75, 251, 427, 603, 68, 244, 420, 596, 76, 252, 428, 604)(69, 245, 421, 597, 80, 256, 432, 608, 71, 247, 423, 599, 83, 259, 435, 611)(70, 246, 422, 598, 77, 253, 429, 605, 72, 248, 424, 600, 86, 262, 438, 614)(78, 254, 430, 606, 117, 293, 469, 645, 79, 255, 431, 607, 114, 290, 466, 642)(81, 257, 433, 609, 121, 297, 473, 649, 82, 258, 434, 610, 130, 306, 482, 658)(84, 260, 436, 612, 138, 314, 490, 666, 85, 261, 437, 613, 122, 298, 474, 650)(87, 263, 439, 615, 116, 292, 468, 644, 88, 264, 440, 616, 113, 289, 465, 641)(89, 265, 441, 617, 124, 300, 476, 652, 90, 266, 442, 618, 127, 303, 479, 655)(91, 267, 443, 619, 128, 304, 480, 656, 92, 268, 444, 620, 125, 301, 477, 653)(93, 269, 445, 621, 132, 308, 484, 660, 94, 270, 446, 622, 135, 311, 487, 663)(95, 271, 447, 623, 136, 312, 488, 664, 96, 272, 448, 624, 133, 309, 485, 661)(97, 273, 449, 625, 145, 321, 497, 673, 98, 274, 450, 626, 148, 324, 500, 676)(99, 275, 451, 627, 149, 325, 501, 677, 100, 276, 452, 628, 146, 322, 498, 674)(101, 277, 453, 629, 153, 329, 505, 681, 102, 278, 454, 630, 156, 332, 508, 684)(103, 279, 455, 631, 157, 333, 509, 685, 104, 280, 456, 632, 154, 330, 506, 682)(105, 281, 457, 633, 161, 337, 513, 689, 106, 282, 458, 634, 164, 340, 516, 692)(107, 283, 459, 635, 165, 341, 517, 693, 108, 284, 460, 636, 162, 338, 514, 690)(109, 285, 461, 637, 169, 345, 521, 697, 110, 286, 462, 638, 172, 348, 524, 700)(111, 287, 463, 639, 173, 349, 525, 701, 112, 288, 464, 640, 170, 346, 522, 698)(115, 291, 467, 643, 176, 352, 528, 704, 118, 294, 470, 646, 175, 351, 527, 703)(119, 295, 471, 647, 174, 350, 526, 702, 120, 296, 472, 648, 171, 347, 523, 699)(123, 299, 475, 651, 166, 342, 518, 694, 142, 318, 494, 670, 163, 339, 515, 691)(126, 302, 478, 654, 155, 331, 507, 683, 129, 305, 481, 657, 158, 334, 510, 686)(131, 307, 483, 659, 168, 344, 520, 696, 139, 315, 491, 667, 167, 343, 519, 695)(134, 310, 486, 662, 147, 323, 499, 675, 137, 313, 489, 665, 150, 326, 502, 678)(140, 316, 492, 668, 151, 327, 503, 679, 141, 317, 493, 669, 152, 328, 504, 680)(143, 319, 495, 671, 159, 335, 511, 687, 144, 320, 496, 672, 160, 336, 512, 688) L = (1, 178)(2, 177)(3, 185)(4, 188)(5, 191)(6, 193)(7, 196)(8, 199)(9, 179)(10, 200)(11, 197)(12, 180)(13, 195)(14, 198)(15, 181)(16, 194)(17, 182)(18, 192)(19, 189)(20, 183)(21, 187)(22, 190)(23, 184)(24, 186)(25, 209)(26, 211)(27, 212)(28, 210)(29, 213)(30, 215)(31, 216)(32, 214)(33, 201)(34, 204)(35, 202)(36, 203)(37, 205)(38, 208)(39, 206)(40, 207)(41, 225)(42, 227)(43, 228)(44, 226)(45, 229)(46, 231)(47, 232)(48, 230)(49, 217)(50, 220)(51, 218)(52, 219)(53, 221)(54, 224)(55, 222)(56, 223)(57, 241)(58, 243)(59, 244)(60, 242)(61, 245)(62, 247)(63, 248)(64, 246)(65, 233)(66, 236)(67, 234)(68, 235)(69, 237)(70, 240)(71, 238)(72, 239)(73, 289)(74, 292)(75, 293)(76, 290)(77, 297)(78, 300)(79, 303)(80, 298)(81, 308)(82, 311)(83, 314)(84, 309)(85, 312)(86, 306)(87, 301)(88, 304)(89, 321)(90, 324)(91, 322)(92, 325)(93, 329)(94, 332)(95, 330)(96, 333)(97, 337)(98, 340)(99, 338)(100, 341)(101, 345)(102, 348)(103, 346)(104, 349)(105, 352)(106, 351)(107, 347)(108, 350)(109, 344)(110, 343)(111, 339)(112, 342)(113, 249)(114, 252)(115, 335)(116, 250)(117, 251)(118, 336)(119, 334)(120, 331)(121, 253)(122, 256)(123, 326)(124, 254)(125, 263)(126, 310)(127, 255)(128, 264)(129, 313)(130, 262)(131, 327)(132, 257)(133, 260)(134, 302)(135, 258)(136, 261)(137, 305)(138, 259)(139, 328)(140, 320)(141, 319)(142, 323)(143, 317)(144, 316)(145, 265)(146, 267)(147, 318)(148, 266)(149, 268)(150, 299)(151, 307)(152, 315)(153, 269)(154, 271)(155, 296)(156, 270)(157, 272)(158, 295)(159, 291)(160, 294)(161, 273)(162, 275)(163, 287)(164, 274)(165, 276)(166, 288)(167, 286)(168, 285)(169, 277)(170, 279)(171, 283)(172, 278)(173, 280)(174, 284)(175, 282)(176, 281)(353, 531)(354, 534)(355, 529)(356, 541)(357, 544)(358, 530)(359, 549)(360, 552)(361, 550)(362, 548)(363, 551)(364, 546)(365, 532)(366, 545)(367, 547)(368, 533)(369, 542)(370, 540)(371, 543)(372, 538)(373, 535)(374, 537)(375, 539)(376, 536)(377, 562)(378, 564)(379, 561)(380, 563)(381, 566)(382, 568)(383, 565)(384, 567)(385, 555)(386, 553)(387, 556)(388, 554)(389, 559)(390, 557)(391, 560)(392, 558)(393, 578)(394, 580)(395, 577)(396, 579)(397, 582)(398, 584)(399, 581)(400, 583)(401, 571)(402, 569)(403, 572)(404, 570)(405, 575)(406, 573)(407, 576)(408, 574)(409, 594)(410, 596)(411, 593)(412, 595)(413, 598)(414, 600)(415, 597)(416, 599)(417, 587)(418, 585)(419, 588)(420, 586)(421, 591)(422, 589)(423, 592)(424, 590)(425, 642)(426, 645)(427, 641)(428, 644)(429, 650)(430, 653)(431, 656)(432, 658)(433, 661)(434, 664)(435, 649)(436, 663)(437, 660)(438, 666)(439, 655)(440, 652)(441, 674)(442, 677)(443, 676)(444, 673)(445, 682)(446, 685)(447, 684)(448, 681)(449, 690)(450, 693)(451, 692)(452, 689)(453, 698)(454, 701)(455, 700)(456, 697)(457, 699)(458, 702)(459, 703)(460, 704)(461, 691)(462, 694)(463, 695)(464, 696)(465, 603)(466, 601)(467, 686)(468, 604)(469, 602)(470, 683)(471, 688)(472, 687)(473, 611)(474, 605)(475, 680)(476, 616)(477, 606)(478, 668)(479, 615)(480, 607)(481, 669)(482, 608)(483, 678)(484, 613)(485, 609)(486, 671)(487, 612)(488, 610)(489, 672)(490, 614)(491, 675)(492, 654)(493, 657)(494, 679)(495, 662)(496, 665)(497, 620)(498, 617)(499, 667)(500, 619)(501, 618)(502, 659)(503, 670)(504, 651)(505, 624)(506, 621)(507, 646)(508, 623)(509, 622)(510, 643)(511, 648)(512, 647)(513, 628)(514, 625)(515, 637)(516, 627)(517, 626)(518, 638)(519, 639)(520, 640)(521, 632)(522, 629)(523, 633)(524, 631)(525, 630)(526, 634)(527, 635)(528, 636) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) } Outer automorphisms :: reflexible Dual of E23.1160 Transitivity :: VT+ Graph:: bipartite v = 44 e = 352 f = 264 degree seq :: [ 16^44 ] E23.1167 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 4}) Quotient :: dipole Aut^+ = D8 x D22 (small group id <176, 31>) Aut = C2 x D8 x D22 (small group id <352, 177>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y1 * Y2 * Y1)^2, (Y3 * Y1)^4, (Y2 * Y1)^22 ] Map:: polytopal non-degenerate R = (1, 177, 2, 178)(3, 179, 7, 183)(4, 180, 9, 185)(5, 181, 10, 186)(6, 182, 12, 188)(8, 184, 15, 191)(11, 187, 20, 196)(13, 189, 23, 199)(14, 190, 21, 197)(16, 192, 19, 195)(17, 193, 22, 198)(18, 194, 28, 204)(24, 200, 35, 211)(25, 201, 34, 210)(26, 202, 32, 208)(27, 203, 31, 207)(29, 205, 39, 215)(30, 206, 38, 214)(33, 209, 41, 217)(36, 212, 44, 220)(37, 213, 45, 221)(40, 216, 48, 224)(42, 218, 51, 227)(43, 219, 50, 226)(46, 222, 55, 231)(47, 223, 54, 230)(49, 225, 57, 233)(52, 228, 60, 236)(53, 229, 61, 237)(56, 232, 64, 240)(58, 234, 67, 243)(59, 235, 66, 242)(62, 238, 98, 274)(63, 239, 97, 273)(65, 241, 101, 277)(68, 244, 103, 279)(69, 245, 105, 281)(70, 246, 107, 283)(71, 247, 109, 285)(72, 248, 111, 287)(73, 249, 113, 289)(74, 250, 115, 291)(75, 251, 117, 293)(76, 252, 119, 295)(77, 253, 121, 297)(78, 254, 123, 299)(79, 255, 125, 301)(80, 256, 127, 303)(81, 257, 129, 305)(82, 258, 131, 307)(83, 259, 133, 309)(84, 260, 135, 311)(85, 261, 137, 313)(86, 262, 139, 315)(87, 263, 141, 317)(88, 264, 143, 319)(89, 265, 145, 321)(90, 266, 147, 323)(91, 267, 149, 325)(92, 268, 151, 327)(93, 269, 153, 329)(94, 270, 155, 331)(95, 271, 157, 333)(96, 272, 159, 335)(99, 275, 162, 338)(100, 276, 161, 337)(102, 278, 165, 341)(104, 280, 167, 343)(106, 282, 169, 345)(108, 284, 171, 347)(110, 286, 166, 342)(112, 288, 173, 349)(114, 290, 174, 350)(116, 292, 154, 330)(118, 294, 175, 351)(120, 296, 150, 326)(122, 298, 176, 352)(124, 300, 164, 340)(126, 302, 163, 339)(128, 304, 172, 348)(130, 306, 160, 336)(132, 308, 158, 334)(134, 310, 138, 314)(136, 312, 170, 346)(140, 316, 168, 344)(142, 318, 148, 324)(144, 320, 146, 322)(152, 328, 156, 332)(353, 529, 355, 531)(354, 530, 357, 533)(356, 532, 360, 536)(358, 534, 363, 539)(359, 535, 365, 541)(361, 537, 368, 544)(362, 538, 370, 546)(364, 540, 373, 549)(366, 542, 376, 552)(367, 543, 377, 553)(369, 545, 379, 555)(371, 547, 381, 557)(372, 548, 382, 558)(374, 550, 384, 560)(375, 551, 385, 561)(378, 554, 388, 564)(380, 556, 389, 565)(383, 559, 392, 568)(386, 562, 394, 570)(387, 563, 395, 571)(390, 566, 398, 574)(391, 567, 399, 575)(393, 569, 401, 577)(396, 572, 404, 580)(397, 573, 405, 581)(400, 576, 408, 584)(402, 578, 410, 586)(403, 579, 411, 587)(406, 582, 414, 590)(407, 583, 415, 591)(409, 585, 417, 593)(412, 588, 420, 596)(413, 589, 432, 608)(416, 592, 421, 597)(418, 594, 429, 605)(419, 595, 424, 600)(422, 598, 455, 631)(423, 599, 457, 633)(425, 601, 450, 626)(426, 602, 459, 635)(427, 603, 449, 625)(428, 604, 461, 637)(430, 606, 473, 649)(431, 607, 463, 639)(433, 609, 469, 645)(434, 610, 465, 641)(435, 611, 467, 643)(436, 612, 453, 629)(437, 613, 471, 647)(438, 614, 479, 655)(439, 615, 477, 653)(440, 616, 475, 651)(441, 617, 483, 659)(442, 618, 481, 657)(443, 619, 485, 661)(444, 620, 487, 663)(445, 621, 489, 665)(446, 622, 491, 667)(447, 623, 495, 671)(448, 624, 493, 669)(451, 627, 499, 675)(452, 628, 497, 673)(454, 630, 501, 677)(456, 632, 503, 679)(458, 634, 507, 683)(460, 636, 519, 695)(462, 638, 521, 697)(464, 640, 509, 685)(466, 642, 514, 690)(468, 644, 523, 699)(470, 646, 513, 689)(472, 648, 518, 694)(474, 650, 511, 687)(476, 652, 528, 704)(478, 654, 525, 701)(480, 656, 505, 681)(482, 658, 527, 703)(484, 660, 526, 702)(486, 662, 506, 682)(488, 664, 517, 693)(490, 666, 502, 678)(492, 668, 524, 700)(494, 670, 515, 691)(496, 672, 516, 692)(498, 674, 510, 686)(500, 676, 512, 688)(504, 680, 522, 698)(508, 684, 520, 696) L = (1, 356)(2, 358)(3, 360)(4, 353)(5, 363)(6, 354)(7, 366)(8, 355)(9, 369)(10, 371)(11, 357)(12, 374)(13, 376)(14, 359)(15, 378)(16, 379)(17, 361)(18, 381)(19, 362)(20, 383)(21, 384)(22, 364)(23, 386)(24, 365)(25, 388)(26, 367)(27, 368)(28, 390)(29, 370)(30, 392)(31, 372)(32, 373)(33, 394)(34, 375)(35, 396)(36, 377)(37, 398)(38, 380)(39, 400)(40, 382)(41, 402)(42, 385)(43, 404)(44, 387)(45, 406)(46, 389)(47, 408)(48, 391)(49, 410)(50, 393)(51, 412)(52, 395)(53, 414)(54, 397)(55, 416)(56, 399)(57, 418)(58, 401)(59, 420)(60, 403)(61, 449)(62, 405)(63, 421)(64, 407)(65, 429)(66, 409)(67, 455)(68, 411)(69, 415)(70, 424)(71, 425)(72, 422)(73, 423)(74, 430)(75, 432)(76, 433)(77, 417)(78, 426)(79, 436)(80, 427)(81, 428)(82, 438)(83, 439)(84, 431)(85, 441)(86, 434)(87, 435)(88, 444)(89, 437)(90, 446)(91, 447)(92, 440)(93, 451)(94, 442)(95, 443)(96, 456)(97, 413)(98, 457)(99, 445)(100, 458)(101, 463)(102, 474)(103, 419)(104, 448)(105, 450)(106, 452)(107, 473)(108, 464)(109, 469)(110, 466)(111, 453)(112, 460)(113, 479)(114, 462)(115, 477)(116, 476)(117, 461)(118, 480)(119, 483)(120, 482)(121, 459)(122, 454)(123, 487)(124, 468)(125, 467)(126, 488)(127, 465)(128, 470)(129, 491)(130, 472)(131, 471)(132, 492)(133, 495)(134, 494)(135, 475)(136, 478)(137, 499)(138, 498)(139, 481)(140, 484)(141, 503)(142, 486)(143, 485)(144, 504)(145, 507)(146, 490)(147, 489)(148, 508)(149, 511)(150, 510)(151, 493)(152, 496)(153, 513)(154, 515)(155, 497)(156, 500)(157, 519)(158, 502)(159, 501)(160, 520)(161, 505)(162, 521)(163, 506)(164, 522)(165, 525)(166, 527)(167, 509)(168, 512)(169, 514)(170, 516)(171, 528)(172, 526)(173, 517)(174, 524)(175, 518)(176, 523)(177, 529)(178, 530)(179, 531)(180, 532)(181, 533)(182, 534)(183, 535)(184, 536)(185, 537)(186, 538)(187, 539)(188, 540)(189, 541)(190, 542)(191, 543)(192, 544)(193, 545)(194, 546)(195, 547)(196, 548)(197, 549)(198, 550)(199, 551)(200, 552)(201, 553)(202, 554)(203, 555)(204, 556)(205, 557)(206, 558)(207, 559)(208, 560)(209, 561)(210, 562)(211, 563)(212, 564)(213, 565)(214, 566)(215, 567)(216, 568)(217, 569)(218, 570)(219, 571)(220, 572)(221, 573)(222, 574)(223, 575)(224, 576)(225, 577)(226, 578)(227, 579)(228, 580)(229, 581)(230, 582)(231, 583)(232, 584)(233, 585)(234, 586)(235, 587)(236, 588)(237, 589)(238, 590)(239, 591)(240, 592)(241, 593)(242, 594)(243, 595)(244, 596)(245, 597)(246, 598)(247, 599)(248, 600)(249, 601)(250, 602)(251, 603)(252, 604)(253, 605)(254, 606)(255, 607)(256, 608)(257, 609)(258, 610)(259, 611)(260, 612)(261, 613)(262, 614)(263, 615)(264, 616)(265, 617)(266, 618)(267, 619)(268, 620)(269, 621)(270, 622)(271, 623)(272, 624)(273, 625)(274, 626)(275, 627)(276, 628)(277, 629)(278, 630)(279, 631)(280, 632)(281, 633)(282, 634)(283, 635)(284, 636)(285, 637)(286, 638)(287, 639)(288, 640)(289, 641)(290, 642)(291, 643)(292, 644)(293, 645)(294, 646)(295, 647)(296, 648)(297, 649)(298, 650)(299, 651)(300, 652)(301, 653)(302, 654)(303, 655)(304, 656)(305, 657)(306, 658)(307, 659)(308, 660)(309, 661)(310, 662)(311, 663)(312, 664)(313, 665)(314, 666)(315, 667)(316, 668)(317, 669)(318, 670)(319, 671)(320, 672)(321, 673)(322, 674)(323, 675)(324, 676)(325, 677)(326, 678)(327, 679)(328, 680)(329, 681)(330, 682)(331, 683)(332, 684)(333, 685)(334, 686)(335, 687)(336, 688)(337, 689)(338, 690)(339, 691)(340, 692)(341, 693)(342, 694)(343, 695)(344, 696)(345, 697)(346, 698)(347, 699)(348, 700)(349, 701)(350, 702)(351, 703)(352, 704) local type(s) :: { ( 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E23.1172 Graph:: simple bipartite v = 176 e = 352 f = 132 degree seq :: [ 4^176 ] E23.1168 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 4}) Quotient :: dipole Aut^+ = D8 x D22 (small group id <176, 31>) Aut = C2 x D8 x D22 (small group id <352, 177>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y1 * Y3 * Y2 * Y3^-1 * Y1 * Y2, (R * Y2 * Y3^-1)^2, (Y3^2 * Y1)^2, Y3 * Y1 * Y3 * Y1 * Y3^-1 * Y1 * Y3^-1 * Y1, Y3^22, Y3^-10 * Y2 * Y3^2 * Y1 * Y3^-8 * Y2 * Y1 ] Map:: polytopal non-degenerate R = (1, 177, 2, 178)(3, 179, 9, 185)(4, 180, 12, 188)(5, 181, 14, 190)(6, 182, 16, 192)(7, 183, 19, 195)(8, 184, 21, 197)(10, 186, 24, 200)(11, 187, 26, 202)(13, 189, 22, 198)(15, 191, 20, 196)(17, 193, 34, 210)(18, 194, 36, 212)(23, 199, 37, 213)(25, 201, 43, 219)(27, 203, 33, 209)(28, 204, 38, 214)(29, 205, 41, 217)(30, 206, 50, 226)(31, 207, 39, 215)(32, 208, 44, 220)(35, 211, 53, 229)(40, 216, 60, 236)(42, 218, 54, 230)(45, 221, 58, 234)(46, 222, 59, 235)(47, 223, 65, 241)(48, 224, 55, 231)(49, 225, 56, 232)(51, 227, 62, 238)(52, 228, 61, 237)(57, 233, 73, 249)(63, 239, 75, 251)(64, 240, 76, 252)(66, 242, 79, 255)(67, 243, 71, 247)(68, 244, 72, 248)(69, 245, 84, 260)(70, 246, 80, 256)(74, 250, 87, 263)(77, 253, 92, 268)(78, 254, 88, 264)(81, 257, 91, 267)(82, 258, 97, 273)(83, 259, 89, 265)(85, 261, 94, 270)(86, 262, 93, 269)(90, 266, 105, 281)(95, 271, 107, 283)(96, 272, 108, 284)(98, 274, 111, 287)(99, 275, 103, 279)(100, 276, 104, 280)(101, 277, 116, 292)(102, 278, 112, 288)(106, 282, 119, 295)(109, 285, 124, 300)(110, 286, 120, 296)(113, 289, 123, 299)(114, 290, 129, 305)(115, 291, 121, 297)(117, 293, 126, 302)(118, 294, 125, 301)(122, 298, 137, 313)(127, 303, 139, 315)(128, 304, 140, 316)(130, 306, 143, 319)(131, 307, 135, 311)(132, 308, 136, 312)(133, 309, 148, 324)(134, 310, 144, 320)(138, 314, 151, 327)(141, 317, 156, 332)(142, 318, 152, 328)(145, 321, 155, 331)(146, 322, 161, 337)(147, 323, 153, 329)(149, 325, 158, 334)(150, 326, 157, 333)(154, 330, 168, 344)(159, 335, 170, 346)(160, 336, 171, 347)(162, 338, 169, 345)(163, 339, 166, 342)(164, 340, 167, 343)(165, 341, 173, 349)(172, 348, 175, 351)(174, 350, 176, 352)(353, 529, 355, 531)(354, 530, 358, 534)(356, 532, 363, 539)(357, 533, 362, 538)(359, 535, 370, 546)(360, 536, 369, 545)(361, 537, 372, 548)(364, 540, 379, 555)(365, 541, 368, 544)(366, 542, 378, 554)(367, 543, 377, 553)(371, 547, 389, 565)(373, 549, 388, 564)(374, 550, 387, 563)(375, 551, 392, 568)(376, 552, 396, 572)(380, 556, 400, 576)(381, 557, 401, 577)(382, 558, 385, 561)(383, 559, 397, 573)(384, 560, 399, 575)(386, 562, 406, 582)(390, 566, 410, 586)(391, 567, 411, 587)(393, 569, 407, 583)(394, 570, 409, 585)(395, 571, 413, 589)(398, 574, 416, 592)(402, 578, 419, 595)(403, 579, 405, 581)(404, 580, 418, 594)(408, 584, 424, 600)(412, 588, 427, 603)(414, 590, 426, 602)(415, 591, 429, 605)(417, 593, 432, 608)(420, 596, 435, 611)(421, 597, 423, 599)(422, 598, 434, 610)(425, 601, 440, 616)(428, 604, 443, 619)(430, 606, 442, 618)(431, 607, 445, 621)(433, 609, 448, 624)(436, 612, 451, 627)(437, 613, 439, 615)(438, 614, 450, 626)(441, 617, 456, 632)(444, 620, 459, 635)(446, 622, 458, 634)(447, 623, 461, 637)(449, 625, 464, 640)(452, 628, 467, 643)(453, 629, 455, 631)(454, 630, 466, 642)(457, 633, 472, 648)(460, 636, 475, 651)(462, 638, 474, 650)(463, 639, 477, 653)(465, 641, 480, 656)(468, 644, 483, 659)(469, 645, 471, 647)(470, 646, 482, 658)(473, 649, 488, 664)(476, 652, 491, 667)(478, 654, 490, 666)(479, 655, 493, 669)(481, 657, 496, 672)(484, 660, 499, 675)(485, 661, 487, 663)(486, 662, 498, 674)(489, 665, 504, 680)(492, 668, 507, 683)(494, 670, 506, 682)(495, 671, 509, 685)(497, 673, 512, 688)(500, 676, 515, 691)(501, 677, 503, 679)(502, 678, 514, 690)(505, 681, 519, 695)(508, 684, 522, 698)(510, 686, 521, 697)(511, 687, 524, 700)(513, 689, 525, 701)(516, 692, 526, 702)(517, 693, 518, 694)(520, 696, 527, 703)(523, 699, 528, 704) L = (1, 356)(2, 359)(3, 362)(4, 365)(5, 353)(6, 369)(7, 372)(8, 354)(9, 370)(10, 377)(11, 355)(12, 380)(13, 382)(14, 383)(15, 357)(16, 363)(17, 387)(18, 358)(19, 390)(20, 392)(21, 393)(22, 360)(23, 361)(24, 397)(25, 399)(26, 400)(27, 401)(28, 366)(29, 364)(30, 403)(31, 396)(32, 367)(33, 368)(34, 407)(35, 409)(36, 410)(37, 411)(38, 373)(39, 371)(40, 413)(41, 406)(42, 374)(43, 375)(44, 416)(45, 378)(46, 376)(47, 418)(48, 379)(49, 419)(50, 381)(51, 421)(52, 384)(53, 385)(54, 424)(55, 388)(56, 386)(57, 426)(58, 389)(59, 427)(60, 391)(61, 429)(62, 394)(63, 395)(64, 432)(65, 398)(66, 434)(67, 435)(68, 402)(69, 437)(70, 404)(71, 405)(72, 440)(73, 408)(74, 442)(75, 443)(76, 412)(77, 445)(78, 414)(79, 415)(80, 448)(81, 417)(82, 450)(83, 451)(84, 420)(85, 453)(86, 422)(87, 423)(88, 456)(89, 425)(90, 458)(91, 459)(92, 428)(93, 461)(94, 430)(95, 431)(96, 464)(97, 433)(98, 466)(99, 467)(100, 436)(101, 469)(102, 438)(103, 439)(104, 472)(105, 441)(106, 474)(107, 475)(108, 444)(109, 477)(110, 446)(111, 447)(112, 480)(113, 449)(114, 482)(115, 483)(116, 452)(117, 485)(118, 454)(119, 455)(120, 488)(121, 457)(122, 490)(123, 491)(124, 460)(125, 493)(126, 462)(127, 463)(128, 496)(129, 465)(130, 498)(131, 499)(132, 468)(133, 501)(134, 470)(135, 471)(136, 504)(137, 473)(138, 506)(139, 507)(140, 476)(141, 509)(142, 478)(143, 479)(144, 512)(145, 481)(146, 514)(147, 515)(148, 484)(149, 517)(150, 486)(151, 487)(152, 519)(153, 489)(154, 521)(155, 522)(156, 492)(157, 524)(158, 494)(159, 495)(160, 525)(161, 497)(162, 518)(163, 526)(164, 500)(165, 502)(166, 503)(167, 527)(168, 505)(169, 511)(170, 528)(171, 508)(172, 510)(173, 516)(174, 513)(175, 523)(176, 520)(177, 529)(178, 530)(179, 531)(180, 532)(181, 533)(182, 534)(183, 535)(184, 536)(185, 537)(186, 538)(187, 539)(188, 540)(189, 541)(190, 542)(191, 543)(192, 544)(193, 545)(194, 546)(195, 547)(196, 548)(197, 549)(198, 550)(199, 551)(200, 552)(201, 553)(202, 554)(203, 555)(204, 556)(205, 557)(206, 558)(207, 559)(208, 560)(209, 561)(210, 562)(211, 563)(212, 564)(213, 565)(214, 566)(215, 567)(216, 568)(217, 569)(218, 570)(219, 571)(220, 572)(221, 573)(222, 574)(223, 575)(224, 576)(225, 577)(226, 578)(227, 579)(228, 580)(229, 581)(230, 582)(231, 583)(232, 584)(233, 585)(234, 586)(235, 587)(236, 588)(237, 589)(238, 590)(239, 591)(240, 592)(241, 593)(242, 594)(243, 595)(244, 596)(245, 597)(246, 598)(247, 599)(248, 600)(249, 601)(250, 602)(251, 603)(252, 604)(253, 605)(254, 606)(255, 607)(256, 608)(257, 609)(258, 610)(259, 611)(260, 612)(261, 613)(262, 614)(263, 615)(264, 616)(265, 617)(266, 618)(267, 619)(268, 620)(269, 621)(270, 622)(271, 623)(272, 624)(273, 625)(274, 626)(275, 627)(276, 628)(277, 629)(278, 630)(279, 631)(280, 632)(281, 633)(282, 634)(283, 635)(284, 636)(285, 637)(286, 638)(287, 639)(288, 640)(289, 641)(290, 642)(291, 643)(292, 644)(293, 645)(294, 646)(295, 647)(296, 648)(297, 649)(298, 650)(299, 651)(300, 652)(301, 653)(302, 654)(303, 655)(304, 656)(305, 657)(306, 658)(307, 659)(308, 660)(309, 661)(310, 662)(311, 663)(312, 664)(313, 665)(314, 666)(315, 667)(316, 668)(317, 669)(318, 670)(319, 671)(320, 672)(321, 673)(322, 674)(323, 675)(324, 676)(325, 677)(326, 678)(327, 679)(328, 680)(329, 681)(330, 682)(331, 683)(332, 684)(333, 685)(334, 686)(335, 687)(336, 688)(337, 689)(338, 690)(339, 691)(340, 692)(341, 693)(342, 694)(343, 695)(344, 696)(345, 697)(346, 698)(347, 699)(348, 700)(349, 701)(350, 702)(351, 703)(352, 704) local type(s) :: { ( 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E23.1173 Graph:: simple bipartite v = 176 e = 352 f = 132 degree seq :: [ 4^176 ] E23.1169 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 4}) Quotient :: dipole Aut^+ = D8 x D22 (small group id <176, 31>) Aut = C2 x D8 x D22 (small group id <352, 177>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^2, (R * Y2)^2, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y1 * Y2 * Y1)^2, (Y3 * Y1)^4, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y3 * Y1 * Y2 * Y3 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 ] Map:: polytopal non-degenerate R = (1, 177, 2, 178)(3, 179, 7, 183)(4, 180, 9, 185)(5, 181, 10, 186)(6, 182, 12, 188)(8, 184, 15, 191)(11, 187, 20, 196)(13, 189, 23, 199)(14, 190, 21, 197)(16, 192, 19, 195)(17, 193, 22, 198)(18, 194, 28, 204)(24, 200, 35, 211)(25, 201, 34, 210)(26, 202, 32, 208)(27, 203, 31, 207)(29, 205, 39, 215)(30, 206, 38, 214)(33, 209, 41, 217)(36, 212, 44, 220)(37, 213, 45, 221)(40, 216, 48, 224)(42, 218, 51, 227)(43, 219, 50, 226)(46, 222, 55, 231)(47, 223, 54, 230)(49, 225, 57, 233)(52, 228, 60, 236)(53, 229, 61, 237)(56, 232, 64, 240)(58, 234, 67, 243)(59, 235, 66, 242)(62, 238, 119, 295)(63, 239, 117, 293)(65, 241, 121, 297)(68, 244, 123, 299)(69, 245, 125, 301)(70, 246, 127, 303)(71, 247, 128, 304)(72, 248, 130, 306)(73, 249, 126, 302)(74, 250, 132, 308)(75, 251, 134, 310)(76, 252, 135, 311)(77, 253, 137, 313)(78, 254, 138, 314)(79, 255, 139, 315)(80, 256, 141, 317)(81, 257, 129, 305)(82, 258, 142, 318)(83, 259, 143, 319)(84, 260, 131, 307)(85, 261, 145, 321)(86, 262, 147, 323)(87, 263, 148, 324)(88, 264, 133, 309)(89, 265, 150, 326)(90, 266, 152, 328)(91, 267, 149, 325)(92, 268, 136, 312)(93, 269, 153, 329)(94, 270, 151, 327)(95, 271, 155, 331)(96, 272, 144, 320)(97, 273, 140, 316)(98, 274, 156, 332)(99, 275, 146, 322)(100, 276, 158, 334)(101, 277, 159, 335)(102, 278, 157, 333)(103, 279, 161, 337)(104, 280, 162, 338)(105, 281, 154, 330)(106, 282, 163, 339)(107, 283, 164, 340)(108, 284, 165, 341)(109, 285, 166, 342)(110, 286, 167, 343)(111, 287, 168, 344)(112, 288, 160, 336)(113, 289, 169, 345)(114, 290, 170, 346)(115, 291, 171, 347)(116, 292, 172, 348)(118, 294, 174, 350)(120, 296, 176, 352)(122, 298, 173, 349)(124, 300, 175, 351)(353, 529, 355, 531)(354, 530, 357, 533)(356, 532, 360, 536)(358, 534, 363, 539)(359, 535, 365, 541)(361, 537, 368, 544)(362, 538, 370, 546)(364, 540, 373, 549)(366, 542, 376, 552)(367, 543, 377, 553)(369, 545, 379, 555)(371, 547, 381, 557)(372, 548, 382, 558)(374, 550, 384, 560)(375, 551, 385, 561)(378, 554, 388, 564)(380, 556, 389, 565)(383, 559, 392, 568)(386, 562, 394, 570)(387, 563, 395, 571)(390, 566, 398, 574)(391, 567, 399, 575)(393, 569, 401, 577)(396, 572, 404, 580)(397, 573, 405, 581)(400, 576, 408, 584)(402, 578, 410, 586)(403, 579, 411, 587)(406, 582, 414, 590)(407, 583, 415, 591)(409, 585, 417, 593)(412, 588, 420, 596)(413, 589, 433, 609)(416, 592, 464, 640)(418, 594, 448, 624)(419, 595, 449, 625)(421, 597, 478, 654)(422, 598, 480, 656)(423, 599, 481, 657)(424, 600, 483, 659)(425, 601, 473, 649)(426, 602, 485, 661)(427, 603, 477, 653)(428, 604, 488, 664)(429, 605, 487, 663)(430, 606, 479, 655)(431, 607, 492, 668)(432, 608, 491, 667)(434, 610, 493, 669)(435, 611, 482, 658)(436, 612, 496, 672)(437, 613, 498, 674)(438, 614, 489, 665)(439, 615, 484, 660)(440, 616, 501, 677)(441, 617, 503, 679)(442, 618, 486, 662)(443, 619, 469, 645)(444, 620, 471, 647)(445, 621, 502, 678)(446, 622, 506, 682)(447, 623, 490, 666)(450, 626, 497, 673)(451, 627, 509, 685)(452, 628, 495, 671)(453, 629, 494, 670)(454, 630, 512, 688)(455, 631, 500, 676)(456, 632, 499, 675)(457, 633, 475, 651)(458, 634, 504, 680)(459, 635, 505, 681)(460, 636, 507, 683)(461, 637, 508, 684)(462, 638, 511, 687)(463, 639, 510, 686)(465, 641, 514, 690)(466, 642, 513, 689)(467, 643, 515, 691)(468, 644, 516, 692)(470, 646, 517, 693)(472, 648, 518, 694)(474, 650, 520, 696)(476, 652, 519, 695)(521, 697, 527, 703)(522, 698, 525, 701)(523, 699, 528, 704)(524, 700, 526, 702) L = (1, 356)(2, 358)(3, 360)(4, 353)(5, 363)(6, 354)(7, 366)(8, 355)(9, 369)(10, 371)(11, 357)(12, 374)(13, 376)(14, 359)(15, 378)(16, 379)(17, 361)(18, 381)(19, 362)(20, 383)(21, 384)(22, 364)(23, 386)(24, 365)(25, 388)(26, 367)(27, 368)(28, 390)(29, 370)(30, 392)(31, 372)(32, 373)(33, 394)(34, 375)(35, 396)(36, 377)(37, 398)(38, 380)(39, 400)(40, 382)(41, 402)(42, 385)(43, 404)(44, 387)(45, 406)(46, 389)(47, 408)(48, 391)(49, 410)(50, 393)(51, 412)(52, 395)(53, 414)(54, 397)(55, 416)(56, 399)(57, 418)(58, 401)(59, 420)(60, 403)(61, 469)(62, 405)(63, 464)(64, 407)(65, 448)(66, 409)(67, 475)(68, 411)(69, 424)(70, 426)(71, 428)(72, 421)(73, 431)(74, 422)(75, 434)(76, 423)(77, 437)(78, 438)(79, 425)(80, 441)(81, 443)(82, 427)(83, 445)(84, 446)(85, 429)(86, 430)(87, 450)(88, 451)(89, 432)(90, 452)(91, 433)(92, 454)(93, 435)(94, 436)(95, 455)(96, 417)(97, 457)(98, 439)(99, 440)(100, 442)(101, 459)(102, 444)(103, 447)(104, 461)(105, 449)(106, 462)(107, 453)(108, 465)(109, 456)(110, 458)(111, 468)(112, 415)(113, 460)(114, 472)(115, 474)(116, 463)(117, 413)(118, 525)(119, 512)(120, 466)(121, 492)(122, 467)(123, 419)(124, 526)(125, 493)(126, 483)(127, 489)(128, 485)(129, 488)(130, 502)(131, 478)(132, 497)(133, 480)(134, 495)(135, 498)(136, 481)(137, 479)(138, 500)(139, 503)(140, 473)(141, 477)(142, 505)(143, 486)(144, 506)(145, 484)(146, 487)(147, 508)(148, 490)(149, 509)(150, 482)(151, 491)(152, 511)(153, 494)(154, 496)(155, 514)(156, 499)(157, 501)(158, 516)(159, 504)(160, 471)(161, 518)(162, 507)(163, 520)(164, 510)(165, 522)(166, 513)(167, 524)(168, 515)(169, 528)(170, 517)(171, 527)(172, 519)(173, 470)(174, 476)(175, 523)(176, 521)(177, 529)(178, 530)(179, 531)(180, 532)(181, 533)(182, 534)(183, 535)(184, 536)(185, 537)(186, 538)(187, 539)(188, 540)(189, 541)(190, 542)(191, 543)(192, 544)(193, 545)(194, 546)(195, 547)(196, 548)(197, 549)(198, 550)(199, 551)(200, 552)(201, 553)(202, 554)(203, 555)(204, 556)(205, 557)(206, 558)(207, 559)(208, 560)(209, 561)(210, 562)(211, 563)(212, 564)(213, 565)(214, 566)(215, 567)(216, 568)(217, 569)(218, 570)(219, 571)(220, 572)(221, 573)(222, 574)(223, 575)(224, 576)(225, 577)(226, 578)(227, 579)(228, 580)(229, 581)(230, 582)(231, 583)(232, 584)(233, 585)(234, 586)(235, 587)(236, 588)(237, 589)(238, 590)(239, 591)(240, 592)(241, 593)(242, 594)(243, 595)(244, 596)(245, 597)(246, 598)(247, 599)(248, 600)(249, 601)(250, 602)(251, 603)(252, 604)(253, 605)(254, 606)(255, 607)(256, 608)(257, 609)(258, 610)(259, 611)(260, 612)(261, 613)(262, 614)(263, 615)(264, 616)(265, 617)(266, 618)(267, 619)(268, 620)(269, 621)(270, 622)(271, 623)(272, 624)(273, 625)(274, 626)(275, 627)(276, 628)(277, 629)(278, 630)(279, 631)(280, 632)(281, 633)(282, 634)(283, 635)(284, 636)(285, 637)(286, 638)(287, 639)(288, 640)(289, 641)(290, 642)(291, 643)(292, 644)(293, 645)(294, 646)(295, 647)(296, 648)(297, 649)(298, 650)(299, 651)(300, 652)(301, 653)(302, 654)(303, 655)(304, 656)(305, 657)(306, 658)(307, 659)(308, 660)(309, 661)(310, 662)(311, 663)(312, 664)(313, 665)(314, 666)(315, 667)(316, 668)(317, 669)(318, 670)(319, 671)(320, 672)(321, 673)(322, 674)(323, 675)(324, 676)(325, 677)(326, 678)(327, 679)(328, 680)(329, 681)(330, 682)(331, 683)(332, 684)(333, 685)(334, 686)(335, 687)(336, 688)(337, 689)(338, 690)(339, 691)(340, 692)(341, 693)(342, 694)(343, 695)(344, 696)(345, 697)(346, 698)(347, 699)(348, 700)(349, 701)(350, 702)(351, 703)(352, 704) local type(s) :: { ( 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E23.1171 Graph:: simple bipartite v = 176 e = 352 f = 132 degree seq :: [ 4^176 ] E23.1170 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 4}) Quotient :: dipole Aut^+ = (C4 x D22) : C2 (small group id <176, 34>) Aut = (D8 x D22) : C2 (small group id <352, 184>) |r| :: 2 Presentation :: [ Y1^2, Y2^2, R^2, Y3^4, (Y3 * Y2)^2, (R * Y3)^2, (R * Y1)^2, Y3 * Y1 * Y3^-1 * Y1, (R * Y2 * Y3^-1)^2, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y3 * Y2 * Y3^-1 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 ] Map:: polytopal non-degenerate R = (1, 177, 2, 178)(3, 179, 9, 185)(4, 180, 7, 183)(5, 181, 8, 184)(6, 182, 13, 189)(10, 186, 18, 194)(11, 187, 19, 195)(12, 188, 16, 192)(14, 190, 22, 198)(15, 191, 23, 199)(17, 193, 25, 201)(20, 196, 28, 204)(21, 197, 29, 205)(24, 200, 32, 208)(26, 202, 34, 210)(27, 203, 35, 211)(30, 206, 38, 214)(31, 207, 39, 215)(33, 209, 41, 217)(36, 212, 44, 220)(37, 213, 45, 221)(40, 216, 48, 224)(42, 218, 50, 226)(43, 219, 51, 227)(46, 222, 54, 230)(47, 223, 55, 231)(49, 225, 57, 233)(52, 228, 60, 236)(53, 229, 61, 237)(56, 232, 64, 240)(58, 234, 66, 242)(59, 235, 67, 243)(62, 238, 116, 292)(63, 239, 101, 277)(65, 241, 99, 275)(68, 244, 112, 288)(69, 245, 129, 305)(70, 246, 132, 308)(71, 247, 135, 311)(72, 248, 138, 314)(73, 249, 140, 316)(74, 250, 142, 318)(75, 251, 145, 321)(76, 252, 147, 323)(77, 253, 146, 322)(78, 254, 150, 326)(79, 255, 152, 328)(80, 256, 143, 319)(81, 257, 139, 315)(82, 258, 154, 330)(83, 259, 156, 332)(84, 260, 136, 312)(85, 261, 157, 333)(86, 262, 134, 310)(87, 263, 141, 317)(88, 264, 158, 334)(89, 265, 126, 302)(90, 266, 131, 307)(91, 267, 148, 324)(92, 268, 161, 337)(93, 269, 151, 327)(94, 270, 165, 341)(95, 271, 121, 297)(96, 272, 130, 306)(97, 273, 155, 331)(98, 274, 168, 344)(100, 276, 133, 309)(102, 278, 137, 313)(103, 279, 160, 336)(104, 280, 170, 346)(105, 281, 144, 320)(106, 282, 163, 339)(107, 283, 125, 301)(108, 284, 166, 342)(109, 285, 123, 299)(110, 286, 149, 325)(111, 287, 169, 345)(113, 289, 153, 329)(114, 290, 159, 335)(115, 291, 172, 348)(117, 293, 162, 338)(118, 294, 173, 349)(119, 295, 174, 350)(120, 296, 164, 340)(122, 298, 175, 351)(124, 300, 167, 343)(127, 303, 171, 347)(128, 304, 176, 352)(353, 529, 355, 531)(354, 530, 358, 534)(356, 532, 363, 539)(357, 533, 362, 538)(359, 535, 367, 543)(360, 536, 366, 542)(361, 537, 369, 545)(364, 540, 372, 548)(365, 541, 373, 549)(368, 544, 376, 552)(370, 546, 379, 555)(371, 547, 378, 554)(374, 550, 383, 559)(375, 551, 382, 558)(377, 553, 385, 561)(380, 556, 388, 564)(381, 557, 389, 565)(384, 560, 392, 568)(386, 562, 395, 571)(387, 563, 394, 570)(390, 566, 399, 575)(391, 567, 398, 574)(393, 569, 401, 577)(396, 572, 404, 580)(397, 573, 405, 581)(400, 576, 408, 584)(402, 578, 411, 587)(403, 579, 410, 586)(406, 582, 415, 591)(407, 583, 414, 590)(409, 585, 417, 593)(412, 588, 420, 596)(413, 589, 473, 649)(416, 592, 475, 651)(418, 594, 478, 654)(419, 595, 477, 653)(421, 597, 482, 658)(422, 598, 485, 661)(423, 599, 488, 664)(424, 600, 486, 662)(425, 601, 493, 669)(426, 602, 495, 671)(427, 603, 483, 659)(428, 604, 500, 676)(429, 605, 501, 677)(430, 606, 497, 673)(431, 607, 499, 675)(432, 608, 498, 674)(433, 609, 505, 681)(434, 610, 490, 666)(435, 611, 492, 668)(436, 612, 491, 667)(437, 613, 510, 686)(438, 614, 489, 665)(439, 615, 512, 688)(440, 616, 484, 660)(441, 617, 513, 689)(442, 618, 496, 672)(443, 619, 515, 691)(444, 620, 481, 657)(445, 621, 516, 692)(446, 622, 502, 678)(447, 623, 504, 680)(448, 624, 503, 679)(449, 625, 519, 695)(450, 626, 506, 682)(451, 627, 508, 684)(452, 628, 507, 683)(453, 629, 522, 698)(454, 630, 511, 687)(455, 631, 524, 700)(456, 632, 487, 663)(457, 633, 514, 690)(458, 634, 525, 701)(459, 635, 494, 670)(460, 636, 474, 650)(461, 637, 517, 693)(462, 638, 518, 694)(463, 639, 471, 647)(464, 640, 520, 696)(465, 641, 521, 697)(466, 642, 523, 699)(467, 643, 528, 704)(468, 644, 509, 685)(469, 645, 480, 656)(470, 646, 479, 655)(472, 648, 526, 702)(476, 652, 527, 703) L = (1, 356)(2, 359)(3, 362)(4, 364)(5, 353)(6, 366)(7, 368)(8, 354)(9, 370)(10, 372)(11, 355)(12, 357)(13, 374)(14, 376)(15, 358)(16, 360)(17, 378)(18, 380)(19, 361)(20, 363)(21, 382)(22, 384)(23, 365)(24, 367)(25, 386)(26, 388)(27, 369)(28, 371)(29, 390)(30, 392)(31, 373)(32, 375)(33, 394)(34, 396)(35, 377)(36, 379)(37, 398)(38, 400)(39, 381)(40, 383)(41, 402)(42, 404)(43, 385)(44, 387)(45, 406)(46, 408)(47, 389)(48, 391)(49, 410)(50, 412)(51, 393)(52, 395)(53, 414)(54, 416)(55, 397)(56, 399)(57, 418)(58, 420)(59, 401)(60, 403)(61, 468)(62, 475)(63, 405)(64, 407)(65, 477)(66, 464)(67, 409)(68, 411)(69, 425)(70, 428)(71, 431)(72, 421)(73, 432)(74, 435)(75, 422)(76, 436)(77, 439)(78, 423)(79, 440)(80, 424)(81, 443)(82, 426)(83, 444)(84, 427)(85, 447)(86, 429)(87, 448)(88, 430)(89, 451)(90, 433)(91, 452)(92, 434)(93, 455)(94, 437)(95, 456)(96, 438)(97, 458)(98, 441)(99, 459)(100, 442)(101, 413)(102, 445)(103, 462)(104, 446)(105, 449)(106, 465)(107, 450)(108, 467)(109, 453)(110, 454)(111, 470)(112, 419)(113, 457)(114, 460)(115, 472)(116, 461)(117, 463)(118, 476)(119, 480)(120, 466)(121, 522)(122, 523)(123, 415)(124, 469)(125, 520)(126, 417)(127, 471)(128, 527)(129, 492)(130, 486)(131, 491)(132, 499)(133, 483)(134, 498)(135, 504)(136, 497)(137, 503)(138, 481)(139, 500)(140, 495)(141, 482)(142, 508)(143, 490)(144, 507)(145, 484)(146, 493)(147, 488)(148, 485)(149, 489)(150, 487)(151, 512)(152, 510)(153, 496)(154, 494)(155, 515)(156, 513)(157, 473)(158, 502)(159, 518)(160, 501)(161, 506)(162, 521)(163, 505)(164, 511)(165, 509)(166, 524)(167, 514)(168, 478)(169, 525)(170, 517)(171, 526)(172, 516)(173, 519)(174, 528)(175, 479)(176, 474)(177, 529)(178, 530)(179, 531)(180, 532)(181, 533)(182, 534)(183, 535)(184, 536)(185, 537)(186, 538)(187, 539)(188, 540)(189, 541)(190, 542)(191, 543)(192, 544)(193, 545)(194, 546)(195, 547)(196, 548)(197, 549)(198, 550)(199, 551)(200, 552)(201, 553)(202, 554)(203, 555)(204, 556)(205, 557)(206, 558)(207, 559)(208, 560)(209, 561)(210, 562)(211, 563)(212, 564)(213, 565)(214, 566)(215, 567)(216, 568)(217, 569)(218, 570)(219, 571)(220, 572)(221, 573)(222, 574)(223, 575)(224, 576)(225, 577)(226, 578)(227, 579)(228, 580)(229, 581)(230, 582)(231, 583)(232, 584)(233, 585)(234, 586)(235, 587)(236, 588)(237, 589)(238, 590)(239, 591)(240, 592)(241, 593)(242, 594)(243, 595)(244, 596)(245, 597)(246, 598)(247, 599)(248, 600)(249, 601)(250, 602)(251, 603)(252, 604)(253, 605)(254, 606)(255, 607)(256, 608)(257, 609)(258, 610)(259, 611)(260, 612)(261, 613)(262, 614)(263, 615)(264, 616)(265, 617)(266, 618)(267, 619)(268, 620)(269, 621)(270, 622)(271, 623)(272, 624)(273, 625)(274, 626)(275, 627)(276, 628)(277, 629)(278, 630)(279, 631)(280, 632)(281, 633)(282, 634)(283, 635)(284, 636)(285, 637)(286, 638)(287, 639)(288, 640)(289, 641)(290, 642)(291, 643)(292, 644)(293, 645)(294, 646)(295, 647)(296, 648)(297, 649)(298, 650)(299, 651)(300, 652)(301, 653)(302, 654)(303, 655)(304, 656)(305, 657)(306, 658)(307, 659)(308, 660)(309, 661)(310, 662)(311, 663)(312, 664)(313, 665)(314, 666)(315, 667)(316, 668)(317, 669)(318, 670)(319, 671)(320, 672)(321, 673)(322, 674)(323, 675)(324, 676)(325, 677)(326, 678)(327, 679)(328, 680)(329, 681)(330, 682)(331, 683)(332, 684)(333, 685)(334, 686)(335, 687)(336, 688)(337, 689)(338, 690)(339, 691)(340, 692)(341, 693)(342, 694)(343, 695)(344, 696)(345, 697)(346, 698)(347, 699)(348, 700)(349, 701)(350, 702)(351, 703)(352, 704) local type(s) :: { ( 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E23.1174 Graph:: simple bipartite v = 176 e = 352 f = 132 degree seq :: [ 4^176 ] E23.1171 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 4}) Quotient :: dipole Aut^+ = D8 x D22 (small group id <176, 31>) Aut = C2 x D8 x D22 (small group id <352, 177>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, (R * Y2)^2, (R * Y3)^2, (Y3 * Y2)^2, (Y3 * Y1^-1)^2, Y1^4, (R * Y1)^2, (Y1^-1 * Y2 * Y1^-1)^2, Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 177, 2, 178, 6, 182, 5, 181)(3, 179, 9, 185, 14, 190, 11, 187)(4, 180, 12, 188, 15, 191, 8, 184)(7, 183, 16, 192, 13, 189, 18, 194)(10, 186, 21, 197, 24, 200, 20, 196)(17, 193, 27, 203, 23, 199, 26, 202)(19, 195, 29, 205, 22, 198, 31, 207)(25, 201, 33, 209, 28, 204, 35, 211)(30, 206, 39, 215, 32, 208, 38, 214)(34, 210, 43, 219, 36, 212, 42, 218)(37, 213, 45, 221, 40, 216, 47, 223)(41, 217, 49, 225, 44, 220, 51, 227)(46, 222, 55, 231, 48, 224, 54, 230)(50, 226, 59, 235, 52, 228, 58, 234)(53, 229, 61, 237, 56, 232, 63, 239)(57, 233, 65, 241, 60, 236, 67, 243)(62, 238, 71, 247, 64, 240, 70, 246)(66, 242, 110, 286, 68, 244, 109, 285)(69, 245, 113, 289, 72, 248, 115, 291)(73, 249, 117, 293, 76, 252, 119, 295)(74, 250, 120, 296, 82, 258, 122, 298)(75, 251, 123, 299, 83, 259, 125, 301)(77, 253, 127, 303, 81, 257, 129, 305)(78, 254, 130, 306, 80, 256, 132, 308)(79, 255, 133, 309, 88, 264, 135, 311)(84, 260, 140, 316, 87, 263, 142, 318)(85, 261, 143, 319, 86, 262, 145, 321)(89, 265, 149, 325, 90, 266, 151, 327)(91, 267, 153, 329, 92, 268, 155, 331)(93, 269, 157, 333, 94, 270, 159, 335)(95, 271, 161, 337, 96, 272, 163, 339)(97, 273, 165, 341, 98, 274, 167, 343)(99, 275, 169, 345, 100, 276, 171, 347)(101, 277, 173, 349, 102, 278, 175, 351)(103, 279, 166, 342, 104, 280, 168, 344)(105, 281, 164, 340, 106, 282, 162, 338)(107, 283, 174, 350, 108, 284, 176, 352)(111, 287, 172, 348, 112, 288, 170, 346)(114, 290, 152, 328, 116, 292, 150, 326)(118, 294, 144, 320, 126, 302, 146, 322)(121, 297, 128, 304, 138, 314, 137, 313)(124, 300, 156, 332, 139, 315, 154, 330)(131, 307, 160, 336, 136, 312, 158, 334)(134, 310, 147, 323, 148, 324, 141, 317)(353, 529, 355, 531)(354, 530, 359, 535)(356, 532, 362, 538)(357, 533, 365, 541)(358, 534, 366, 542)(360, 536, 369, 545)(361, 537, 371, 547)(363, 539, 374, 550)(364, 540, 375, 551)(367, 543, 376, 552)(368, 544, 377, 553)(370, 546, 380, 556)(372, 548, 382, 558)(373, 549, 384, 560)(378, 554, 386, 562)(379, 555, 388, 564)(381, 557, 389, 565)(383, 559, 392, 568)(385, 561, 393, 569)(387, 563, 396, 572)(390, 566, 398, 574)(391, 567, 400, 576)(394, 570, 402, 578)(395, 571, 404, 580)(397, 573, 405, 581)(399, 575, 408, 584)(401, 577, 409, 585)(403, 579, 412, 588)(406, 582, 414, 590)(407, 583, 416, 592)(410, 586, 418, 594)(411, 587, 420, 596)(413, 589, 421, 597)(415, 591, 424, 600)(417, 593, 425, 601)(419, 595, 428, 604)(422, 598, 430, 606)(423, 599, 432, 608)(426, 602, 465, 641)(427, 603, 462, 638)(429, 605, 469, 645)(431, 607, 482, 658)(433, 609, 471, 647)(434, 610, 467, 643)(435, 611, 461, 637)(436, 612, 477, 653)(437, 613, 472, 648)(438, 614, 474, 650)(439, 615, 475, 651)(440, 616, 484, 660)(441, 617, 479, 655)(442, 618, 481, 657)(443, 619, 487, 663)(444, 620, 485, 661)(445, 621, 494, 670)(446, 622, 492, 668)(447, 623, 495, 671)(448, 624, 497, 673)(449, 625, 501, 677)(450, 626, 503, 679)(451, 627, 507, 683)(452, 628, 505, 681)(453, 629, 511, 687)(454, 630, 509, 685)(455, 631, 513, 689)(456, 632, 515, 691)(457, 633, 517, 693)(458, 634, 519, 695)(459, 635, 523, 699)(460, 636, 521, 697)(463, 639, 527, 703)(464, 640, 525, 701)(466, 642, 518, 694)(468, 644, 520, 696)(470, 646, 516, 692)(473, 649, 504, 680)(476, 652, 524, 700)(478, 654, 514, 690)(480, 656, 496, 672)(483, 659, 528, 704)(486, 662, 512, 688)(488, 664, 526, 702)(489, 665, 498, 674)(490, 666, 502, 678)(491, 667, 522, 698)(493, 669, 506, 682)(499, 675, 508, 684)(500, 676, 510, 686) L = (1, 356)(2, 360)(3, 362)(4, 353)(5, 364)(6, 367)(7, 369)(8, 354)(9, 372)(10, 355)(11, 373)(12, 357)(13, 375)(14, 376)(15, 358)(16, 378)(17, 359)(18, 379)(19, 382)(20, 361)(21, 363)(22, 384)(23, 365)(24, 366)(25, 386)(26, 368)(27, 370)(28, 388)(29, 390)(30, 371)(31, 391)(32, 374)(33, 394)(34, 377)(35, 395)(36, 380)(37, 398)(38, 381)(39, 383)(40, 400)(41, 402)(42, 385)(43, 387)(44, 404)(45, 406)(46, 389)(47, 407)(48, 392)(49, 410)(50, 393)(51, 411)(52, 396)(53, 414)(54, 397)(55, 399)(56, 416)(57, 418)(58, 401)(59, 403)(60, 420)(61, 422)(62, 405)(63, 423)(64, 408)(65, 461)(66, 409)(67, 462)(68, 412)(69, 430)(70, 413)(71, 415)(72, 432)(73, 435)(74, 440)(75, 428)(76, 427)(77, 439)(78, 421)(79, 434)(80, 424)(81, 436)(82, 431)(83, 425)(84, 433)(85, 444)(86, 443)(87, 429)(88, 426)(89, 446)(90, 445)(91, 438)(92, 437)(93, 442)(94, 441)(95, 452)(96, 451)(97, 454)(98, 453)(99, 448)(100, 447)(101, 450)(102, 449)(103, 460)(104, 459)(105, 464)(106, 463)(107, 456)(108, 455)(109, 417)(110, 419)(111, 458)(112, 457)(113, 484)(114, 488)(115, 482)(116, 483)(117, 475)(118, 476)(119, 477)(120, 485)(121, 486)(122, 487)(123, 469)(124, 470)(125, 471)(126, 491)(127, 492)(128, 493)(129, 494)(130, 467)(131, 468)(132, 465)(133, 472)(134, 473)(135, 474)(136, 466)(137, 499)(138, 500)(139, 478)(140, 479)(141, 480)(142, 481)(143, 505)(144, 506)(145, 507)(146, 508)(147, 489)(148, 490)(149, 509)(150, 510)(151, 511)(152, 512)(153, 495)(154, 496)(155, 497)(156, 498)(157, 501)(158, 502)(159, 503)(160, 504)(161, 521)(162, 522)(163, 523)(164, 524)(165, 525)(166, 526)(167, 527)(168, 528)(169, 513)(170, 514)(171, 515)(172, 516)(173, 517)(174, 518)(175, 519)(176, 520)(177, 529)(178, 530)(179, 531)(180, 532)(181, 533)(182, 534)(183, 535)(184, 536)(185, 537)(186, 538)(187, 539)(188, 540)(189, 541)(190, 542)(191, 543)(192, 544)(193, 545)(194, 546)(195, 547)(196, 548)(197, 549)(198, 550)(199, 551)(200, 552)(201, 553)(202, 554)(203, 555)(204, 556)(205, 557)(206, 558)(207, 559)(208, 560)(209, 561)(210, 562)(211, 563)(212, 564)(213, 565)(214, 566)(215, 567)(216, 568)(217, 569)(218, 570)(219, 571)(220, 572)(221, 573)(222, 574)(223, 575)(224, 576)(225, 577)(226, 578)(227, 579)(228, 580)(229, 581)(230, 582)(231, 583)(232, 584)(233, 585)(234, 586)(235, 587)(236, 588)(237, 589)(238, 590)(239, 591)(240, 592)(241, 593)(242, 594)(243, 595)(244, 596)(245, 597)(246, 598)(247, 599)(248, 600)(249, 601)(250, 602)(251, 603)(252, 604)(253, 605)(254, 606)(255, 607)(256, 608)(257, 609)(258, 610)(259, 611)(260, 612)(261, 613)(262, 614)(263, 615)(264, 616)(265, 617)(266, 618)(267, 619)(268, 620)(269, 621)(270, 622)(271, 623)(272, 624)(273, 625)(274, 626)(275, 627)(276, 628)(277, 629)(278, 630)(279, 631)(280, 632)(281, 633)(282, 634)(283, 635)(284, 636)(285, 637)(286, 638)(287, 639)(288, 640)(289, 641)(290, 642)(291, 643)(292, 644)(293, 645)(294, 646)(295, 647)(296, 648)(297, 649)(298, 650)(299, 651)(300, 652)(301, 653)(302, 654)(303, 655)(304, 656)(305, 657)(306, 658)(307, 659)(308, 660)(309, 661)(310, 662)(311, 663)(312, 664)(313, 665)(314, 666)(315, 667)(316, 668)(317, 669)(318, 670)(319, 671)(320, 672)(321, 673)(322, 674)(323, 675)(324, 676)(325, 677)(326, 678)(327, 679)(328, 680)(329, 681)(330, 682)(331, 683)(332, 684)(333, 685)(334, 686)(335, 687)(336, 688)(337, 689)(338, 690)(339, 691)(340, 692)(341, 693)(342, 694)(343, 695)(344, 696)(345, 697)(346, 698)(347, 699)(348, 700)(349, 701)(350, 702)(351, 703)(352, 704) local type(s) :: { ( 4^4 ), ( 4^8 ) } Outer automorphisms :: reflexible Dual of E23.1169 Graph:: simple bipartite v = 132 e = 352 f = 176 degree seq :: [ 4^88, 8^44 ] E23.1172 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 4}) Quotient :: dipole Aut^+ = D8 x D22 (small group id <176, 31>) Aut = C2 x D8 x D22 (small group id <352, 177>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^2, Y1^4, (R * Y2)^2, (R * Y3)^2, (Y3 * Y2)^2, (Y3 * Y1^-1)^2, (R * Y1)^2, (Y1^-1 * Y2 * Y1^-1)^2, Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 177, 2, 178, 6, 182, 5, 181)(3, 179, 9, 185, 14, 190, 11, 187)(4, 180, 12, 188, 15, 191, 8, 184)(7, 183, 16, 192, 13, 189, 18, 194)(10, 186, 21, 197, 24, 200, 20, 196)(17, 193, 27, 203, 23, 199, 26, 202)(19, 195, 29, 205, 22, 198, 31, 207)(25, 201, 33, 209, 28, 204, 35, 211)(30, 206, 39, 215, 32, 208, 38, 214)(34, 210, 43, 219, 36, 212, 42, 218)(37, 213, 45, 221, 40, 216, 47, 223)(41, 217, 49, 225, 44, 220, 51, 227)(46, 222, 55, 231, 48, 224, 54, 230)(50, 226, 59, 235, 52, 228, 58, 234)(53, 229, 61, 237, 56, 232, 63, 239)(57, 233, 65, 241, 60, 236, 67, 243)(62, 238, 71, 247, 64, 240, 70, 246)(66, 242, 110, 286, 68, 244, 109, 285)(69, 245, 113, 289, 72, 248, 115, 291)(73, 249, 117, 293, 76, 252, 119, 295)(74, 250, 120, 296, 82, 258, 122, 298)(75, 251, 123, 299, 83, 259, 125, 301)(77, 253, 127, 303, 81, 257, 129, 305)(78, 254, 130, 306, 80, 256, 132, 308)(79, 255, 133, 309, 88, 264, 135, 311)(84, 260, 140, 316, 87, 263, 142, 318)(85, 261, 143, 319, 86, 262, 145, 321)(89, 265, 149, 325, 90, 266, 151, 327)(91, 267, 153, 329, 92, 268, 155, 331)(93, 269, 157, 333, 94, 270, 159, 335)(95, 271, 161, 337, 96, 272, 163, 339)(97, 273, 165, 341, 98, 274, 167, 343)(99, 275, 169, 345, 100, 276, 171, 347)(101, 277, 173, 349, 102, 278, 175, 351)(103, 279, 166, 342, 104, 280, 168, 344)(105, 281, 164, 340, 106, 282, 162, 338)(107, 283, 174, 350, 108, 284, 176, 352)(111, 287, 172, 348, 112, 288, 170, 346)(114, 290, 152, 328, 116, 292, 150, 326)(118, 294, 146, 322, 126, 302, 144, 320)(121, 297, 137, 313, 138, 314, 128, 304)(124, 300, 154, 330, 139, 315, 156, 332)(131, 307, 158, 334, 136, 312, 160, 336)(134, 310, 141, 317, 148, 324, 147, 323)(353, 529, 355, 531)(354, 530, 359, 535)(356, 532, 362, 538)(357, 533, 365, 541)(358, 534, 366, 542)(360, 536, 369, 545)(361, 537, 371, 547)(363, 539, 374, 550)(364, 540, 375, 551)(367, 543, 376, 552)(368, 544, 377, 553)(370, 546, 380, 556)(372, 548, 382, 558)(373, 549, 384, 560)(378, 554, 386, 562)(379, 555, 388, 564)(381, 557, 389, 565)(383, 559, 392, 568)(385, 561, 393, 569)(387, 563, 396, 572)(390, 566, 398, 574)(391, 567, 400, 576)(394, 570, 402, 578)(395, 571, 404, 580)(397, 573, 405, 581)(399, 575, 408, 584)(401, 577, 409, 585)(403, 579, 412, 588)(406, 582, 414, 590)(407, 583, 416, 592)(410, 586, 418, 594)(411, 587, 420, 596)(413, 589, 421, 597)(415, 591, 424, 600)(417, 593, 428, 604)(419, 595, 425, 601)(422, 598, 432, 608)(423, 599, 430, 606)(426, 602, 467, 643)(427, 603, 461, 637)(429, 605, 469, 645)(431, 607, 482, 658)(433, 609, 471, 647)(434, 610, 465, 641)(435, 611, 462, 638)(436, 612, 477, 653)(437, 613, 472, 648)(438, 614, 474, 650)(439, 615, 475, 651)(440, 616, 484, 660)(441, 617, 479, 655)(442, 618, 481, 657)(443, 619, 487, 663)(444, 620, 485, 661)(445, 621, 494, 670)(446, 622, 492, 668)(447, 623, 495, 671)(448, 624, 497, 673)(449, 625, 501, 677)(450, 626, 503, 679)(451, 627, 507, 683)(452, 628, 505, 681)(453, 629, 511, 687)(454, 630, 509, 685)(455, 631, 513, 689)(456, 632, 515, 691)(457, 633, 517, 693)(458, 634, 519, 695)(459, 635, 523, 699)(460, 636, 521, 697)(463, 639, 527, 703)(464, 640, 525, 701)(466, 642, 518, 694)(468, 644, 520, 696)(470, 646, 514, 690)(473, 649, 502, 678)(476, 652, 522, 698)(478, 654, 516, 692)(480, 656, 498, 674)(483, 659, 526, 702)(486, 662, 510, 686)(488, 664, 528, 704)(489, 665, 496, 672)(490, 666, 504, 680)(491, 667, 524, 700)(493, 669, 508, 684)(499, 675, 506, 682)(500, 676, 512, 688) L = (1, 356)(2, 360)(3, 362)(4, 353)(5, 364)(6, 367)(7, 369)(8, 354)(9, 372)(10, 355)(11, 373)(12, 357)(13, 375)(14, 376)(15, 358)(16, 378)(17, 359)(18, 379)(19, 382)(20, 361)(21, 363)(22, 384)(23, 365)(24, 366)(25, 386)(26, 368)(27, 370)(28, 388)(29, 390)(30, 371)(31, 391)(32, 374)(33, 394)(34, 377)(35, 395)(36, 380)(37, 398)(38, 381)(39, 383)(40, 400)(41, 402)(42, 385)(43, 387)(44, 404)(45, 406)(46, 389)(47, 407)(48, 392)(49, 410)(50, 393)(51, 411)(52, 396)(53, 414)(54, 397)(55, 399)(56, 416)(57, 418)(58, 401)(59, 403)(60, 420)(61, 422)(62, 405)(63, 423)(64, 408)(65, 461)(66, 409)(67, 462)(68, 412)(69, 432)(70, 413)(71, 415)(72, 430)(73, 435)(74, 440)(75, 428)(76, 427)(77, 439)(78, 424)(79, 434)(80, 421)(81, 436)(82, 431)(83, 425)(84, 433)(85, 444)(86, 443)(87, 429)(88, 426)(89, 446)(90, 445)(91, 438)(92, 437)(93, 442)(94, 441)(95, 452)(96, 451)(97, 454)(98, 453)(99, 448)(100, 447)(101, 450)(102, 449)(103, 460)(104, 459)(105, 464)(106, 463)(107, 456)(108, 455)(109, 417)(110, 419)(111, 458)(112, 457)(113, 482)(114, 483)(115, 484)(116, 488)(117, 475)(118, 476)(119, 477)(120, 485)(121, 486)(122, 487)(123, 469)(124, 470)(125, 471)(126, 491)(127, 492)(128, 493)(129, 494)(130, 465)(131, 466)(132, 467)(133, 472)(134, 473)(135, 474)(136, 468)(137, 499)(138, 500)(139, 478)(140, 479)(141, 480)(142, 481)(143, 505)(144, 506)(145, 507)(146, 508)(147, 489)(148, 490)(149, 509)(150, 510)(151, 511)(152, 512)(153, 495)(154, 496)(155, 497)(156, 498)(157, 501)(158, 502)(159, 503)(160, 504)(161, 521)(162, 522)(163, 523)(164, 524)(165, 525)(166, 526)(167, 527)(168, 528)(169, 513)(170, 514)(171, 515)(172, 516)(173, 517)(174, 518)(175, 519)(176, 520)(177, 529)(178, 530)(179, 531)(180, 532)(181, 533)(182, 534)(183, 535)(184, 536)(185, 537)(186, 538)(187, 539)(188, 540)(189, 541)(190, 542)(191, 543)(192, 544)(193, 545)(194, 546)(195, 547)(196, 548)(197, 549)(198, 550)(199, 551)(200, 552)(201, 553)(202, 554)(203, 555)(204, 556)(205, 557)(206, 558)(207, 559)(208, 560)(209, 561)(210, 562)(211, 563)(212, 564)(213, 565)(214, 566)(215, 567)(216, 568)(217, 569)(218, 570)(219, 571)(220, 572)(221, 573)(222, 574)(223, 575)(224, 576)(225, 577)(226, 578)(227, 579)(228, 580)(229, 581)(230, 582)(231, 583)(232, 584)(233, 585)(234, 586)(235, 587)(236, 588)(237, 589)(238, 590)(239, 591)(240, 592)(241, 593)(242, 594)(243, 595)(244, 596)(245, 597)(246, 598)(247, 599)(248, 600)(249, 601)(250, 602)(251, 603)(252, 604)(253, 605)(254, 606)(255, 607)(256, 608)(257, 609)(258, 610)(259, 611)(260, 612)(261, 613)(262, 614)(263, 615)(264, 616)(265, 617)(266, 618)(267, 619)(268, 620)(269, 621)(270, 622)(271, 623)(272, 624)(273, 625)(274, 626)(275, 627)(276, 628)(277, 629)(278, 630)(279, 631)(280, 632)(281, 633)(282, 634)(283, 635)(284, 636)(285, 637)(286, 638)(287, 639)(288, 640)(289, 641)(290, 642)(291, 643)(292, 644)(293, 645)(294, 646)(295, 647)(296, 648)(297, 649)(298, 650)(299, 651)(300, 652)(301, 653)(302, 654)(303, 655)(304, 656)(305, 657)(306, 658)(307, 659)(308, 660)(309, 661)(310, 662)(311, 663)(312, 664)(313, 665)(314, 666)(315, 667)(316, 668)(317, 669)(318, 670)(319, 671)(320, 672)(321, 673)(322, 674)(323, 675)(324, 676)(325, 677)(326, 678)(327, 679)(328, 680)(329, 681)(330, 682)(331, 683)(332, 684)(333, 685)(334, 686)(335, 687)(336, 688)(337, 689)(338, 690)(339, 691)(340, 692)(341, 693)(342, 694)(343, 695)(344, 696)(345, 697)(346, 698)(347, 699)(348, 700)(349, 701)(350, 702)(351, 703)(352, 704) local type(s) :: { ( 4^4 ), ( 4^8 ) } Outer automorphisms :: reflexible Dual of E23.1167 Graph:: simple bipartite v = 132 e = 352 f = 176 degree seq :: [ 4^88, 8^44 ] E23.1173 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 4}) Quotient :: dipole Aut^+ = D8 x D22 (small group id <176, 31>) Aut = C2 x D8 x D22 (small group id <352, 177>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y3^-2 * Y1^2, Y3^2 * Y1^2, Y1^4, (R * Y3)^2, (Y3 * Y2)^2, (Y3^-1, Y1^-1), (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y1^-1 * Y2 * Y1^-1)^2, Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 177, 2, 178, 7, 183, 5, 181)(3, 179, 11, 187, 16, 192, 13, 189)(4, 180, 9, 185, 6, 182, 10, 186)(8, 184, 17, 193, 15, 191, 19, 195)(12, 188, 22, 198, 14, 190, 23, 199)(18, 194, 26, 202, 20, 196, 27, 203)(21, 197, 29, 205, 24, 200, 31, 207)(25, 201, 33, 209, 28, 204, 35, 211)(30, 206, 38, 214, 32, 208, 39, 215)(34, 210, 42, 218, 36, 212, 43, 219)(37, 213, 45, 221, 40, 216, 47, 223)(41, 217, 49, 225, 44, 220, 51, 227)(46, 222, 54, 230, 48, 224, 55, 231)(50, 226, 58, 234, 52, 228, 59, 235)(53, 229, 61, 237, 56, 232, 63, 239)(57, 233, 65, 241, 60, 236, 67, 243)(62, 238, 70, 246, 64, 240, 71, 247)(66, 242, 91, 267, 68, 244, 90, 266)(69, 245, 74, 250, 72, 248, 77, 253)(73, 249, 113, 289, 79, 255, 115, 291)(75, 251, 122, 298, 86, 262, 124, 300)(76, 252, 125, 301, 78, 254, 127, 303)(80, 256, 129, 305, 85, 261, 121, 297)(81, 257, 117, 293, 82, 258, 119, 295)(83, 259, 132, 308, 84, 260, 131, 307)(87, 263, 126, 302, 88, 264, 128, 304)(89, 265, 136, 312, 92, 268, 123, 299)(93, 269, 135, 311, 94, 270, 130, 306)(95, 271, 133, 309, 96, 272, 134, 310)(97, 273, 137, 313, 98, 274, 138, 314)(99, 275, 140, 316, 100, 276, 139, 315)(101, 277, 142, 318, 102, 278, 141, 317)(103, 279, 143, 319, 104, 280, 144, 320)(105, 281, 145, 321, 106, 282, 146, 322)(107, 283, 148, 324, 108, 284, 147, 323)(109, 285, 150, 326, 110, 286, 149, 325)(111, 287, 151, 327, 112, 288, 152, 328)(114, 290, 153, 329, 116, 292, 154, 330)(118, 294, 156, 332, 120, 296, 155, 331)(157, 333, 161, 337, 158, 334, 163, 339)(159, 335, 167, 343, 160, 336, 165, 341)(162, 338, 171, 347, 164, 340, 173, 349)(166, 342, 169, 345, 168, 344, 170, 346)(172, 348, 176, 352, 174, 350, 175, 351)(353, 529, 355, 531)(354, 530, 360, 536)(356, 532, 366, 542)(357, 533, 367, 543)(358, 534, 364, 540)(359, 535, 368, 544)(361, 537, 372, 548)(362, 538, 370, 546)(363, 539, 373, 549)(365, 541, 376, 552)(369, 545, 377, 553)(371, 547, 380, 556)(374, 550, 384, 560)(375, 551, 382, 558)(378, 554, 388, 564)(379, 555, 386, 562)(381, 557, 389, 565)(383, 559, 392, 568)(385, 561, 393, 569)(387, 563, 396, 572)(390, 566, 400, 576)(391, 567, 398, 574)(394, 570, 404, 580)(395, 571, 402, 578)(397, 573, 405, 581)(399, 575, 408, 584)(401, 577, 409, 585)(403, 579, 412, 588)(406, 582, 416, 592)(407, 583, 414, 590)(410, 586, 420, 596)(411, 587, 418, 594)(413, 589, 421, 597)(415, 591, 424, 600)(417, 593, 465, 641)(419, 595, 467, 643)(422, 598, 471, 647)(423, 599, 469, 645)(425, 601, 473, 649)(426, 602, 474, 650)(427, 603, 475, 651)(428, 604, 478, 654)(429, 605, 476, 652)(430, 606, 480, 656)(431, 607, 481, 657)(432, 608, 482, 658)(433, 609, 483, 659)(434, 610, 484, 660)(435, 611, 485, 661)(436, 612, 486, 662)(437, 613, 487, 663)(438, 614, 488, 664)(439, 615, 489, 665)(440, 616, 490, 666)(441, 617, 491, 667)(442, 618, 479, 655)(443, 619, 477, 653)(444, 620, 492, 668)(445, 621, 493, 669)(446, 622, 494, 670)(447, 623, 495, 671)(448, 624, 496, 672)(449, 625, 497, 673)(450, 626, 498, 674)(451, 627, 499, 675)(452, 628, 500, 676)(453, 629, 501, 677)(454, 630, 502, 678)(455, 631, 503, 679)(456, 632, 504, 680)(457, 633, 505, 681)(458, 634, 506, 682)(459, 635, 507, 683)(460, 636, 508, 684)(461, 637, 509, 685)(462, 638, 510, 686)(463, 639, 511, 687)(464, 640, 512, 688)(466, 642, 514, 690)(468, 644, 516, 692)(470, 646, 518, 694)(472, 648, 520, 696)(513, 689, 522, 698)(515, 691, 521, 697)(517, 693, 524, 700)(519, 695, 526, 702)(523, 699, 528, 704)(525, 701, 527, 703) L = (1, 356)(2, 361)(3, 364)(4, 359)(5, 362)(6, 353)(7, 358)(8, 370)(9, 357)(10, 354)(11, 374)(12, 368)(13, 375)(14, 355)(15, 372)(16, 366)(17, 378)(18, 367)(19, 379)(20, 360)(21, 382)(22, 365)(23, 363)(24, 384)(25, 386)(26, 371)(27, 369)(28, 388)(29, 390)(30, 376)(31, 391)(32, 373)(33, 394)(34, 380)(35, 395)(36, 377)(37, 398)(38, 383)(39, 381)(40, 400)(41, 402)(42, 387)(43, 385)(44, 404)(45, 406)(46, 392)(47, 407)(48, 389)(49, 410)(50, 396)(51, 411)(52, 393)(53, 414)(54, 399)(55, 397)(56, 416)(57, 418)(58, 403)(59, 401)(60, 420)(61, 422)(62, 408)(63, 423)(64, 405)(65, 443)(66, 412)(67, 442)(68, 409)(69, 469)(70, 415)(71, 413)(72, 471)(73, 430)(74, 434)(75, 436)(76, 425)(77, 433)(78, 431)(79, 428)(80, 440)(81, 426)(82, 429)(83, 427)(84, 438)(85, 439)(86, 435)(87, 432)(88, 437)(89, 448)(90, 417)(91, 419)(92, 447)(93, 450)(94, 449)(95, 441)(96, 444)(97, 445)(98, 446)(99, 456)(100, 455)(101, 458)(102, 457)(103, 451)(104, 452)(105, 453)(106, 454)(107, 464)(108, 463)(109, 468)(110, 466)(111, 459)(112, 460)(113, 479)(114, 461)(115, 477)(116, 462)(117, 424)(118, 519)(119, 421)(120, 517)(121, 478)(122, 483)(123, 485)(124, 484)(125, 465)(126, 481)(127, 467)(128, 473)(129, 480)(130, 489)(131, 476)(132, 474)(133, 488)(134, 475)(135, 490)(136, 486)(137, 487)(138, 482)(139, 495)(140, 496)(141, 497)(142, 498)(143, 492)(144, 491)(145, 494)(146, 493)(147, 503)(148, 504)(149, 505)(150, 506)(151, 500)(152, 499)(153, 502)(154, 501)(155, 511)(156, 512)(157, 514)(158, 516)(159, 508)(160, 507)(161, 523)(162, 510)(163, 525)(164, 509)(165, 470)(166, 524)(167, 472)(168, 526)(169, 528)(170, 527)(171, 515)(172, 520)(173, 513)(174, 518)(175, 521)(176, 522)(177, 529)(178, 530)(179, 531)(180, 532)(181, 533)(182, 534)(183, 535)(184, 536)(185, 537)(186, 538)(187, 539)(188, 540)(189, 541)(190, 542)(191, 543)(192, 544)(193, 545)(194, 546)(195, 547)(196, 548)(197, 549)(198, 550)(199, 551)(200, 552)(201, 553)(202, 554)(203, 555)(204, 556)(205, 557)(206, 558)(207, 559)(208, 560)(209, 561)(210, 562)(211, 563)(212, 564)(213, 565)(214, 566)(215, 567)(216, 568)(217, 569)(218, 570)(219, 571)(220, 572)(221, 573)(222, 574)(223, 575)(224, 576)(225, 577)(226, 578)(227, 579)(228, 580)(229, 581)(230, 582)(231, 583)(232, 584)(233, 585)(234, 586)(235, 587)(236, 588)(237, 589)(238, 590)(239, 591)(240, 592)(241, 593)(242, 594)(243, 595)(244, 596)(245, 597)(246, 598)(247, 599)(248, 600)(249, 601)(250, 602)(251, 603)(252, 604)(253, 605)(254, 606)(255, 607)(256, 608)(257, 609)(258, 610)(259, 611)(260, 612)(261, 613)(262, 614)(263, 615)(264, 616)(265, 617)(266, 618)(267, 619)(268, 620)(269, 621)(270, 622)(271, 623)(272, 624)(273, 625)(274, 626)(275, 627)(276, 628)(277, 629)(278, 630)(279, 631)(280, 632)(281, 633)(282, 634)(283, 635)(284, 636)(285, 637)(286, 638)(287, 639)(288, 640)(289, 641)(290, 642)(291, 643)(292, 644)(293, 645)(294, 646)(295, 647)(296, 648)(297, 649)(298, 650)(299, 651)(300, 652)(301, 653)(302, 654)(303, 655)(304, 656)(305, 657)(306, 658)(307, 659)(308, 660)(309, 661)(310, 662)(311, 663)(312, 664)(313, 665)(314, 666)(315, 667)(316, 668)(317, 669)(318, 670)(319, 671)(320, 672)(321, 673)(322, 674)(323, 675)(324, 676)(325, 677)(326, 678)(327, 679)(328, 680)(329, 681)(330, 682)(331, 683)(332, 684)(333, 685)(334, 686)(335, 687)(336, 688)(337, 689)(338, 690)(339, 691)(340, 692)(341, 693)(342, 694)(343, 695)(344, 696)(345, 697)(346, 698)(347, 699)(348, 700)(349, 701)(350, 702)(351, 703)(352, 704) local type(s) :: { ( 4^4 ), ( 4^8 ) } Outer automorphisms :: reflexible Dual of E23.1168 Graph:: simple bipartite v = 132 e = 352 f = 176 degree seq :: [ 4^88, 8^44 ] E23.1174 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 2, 2, 4}) Quotient :: dipole Aut^+ = (C4 x D22) : C2 (small group id <176, 34>) Aut = (D8 x D22) : C2 (small group id <352, 184>) |r| :: 2 Presentation :: [ R^2, Y2^2, Y1^-1 * Y3^2 * Y1^-1, Y3^2 * Y1^2, (Y1^-1 * Y3^-1)^2, (Y3 * Y2)^2, (Y3^-1, Y1^-1), (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y1^-1 * Y2 * Y3^2 * Y2 * Y1^-1, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 * Y2 * Y1^-1 ] Map:: polytopal non-degenerate R = (1, 177, 2, 178, 7, 183, 5, 181)(3, 179, 11, 187, 16, 192, 13, 189)(4, 180, 9, 185, 6, 182, 10, 186)(8, 184, 17, 193, 15, 191, 19, 195)(12, 188, 22, 198, 14, 190, 23, 199)(18, 194, 26, 202, 20, 196, 27, 203)(21, 197, 29, 205, 24, 200, 31, 207)(25, 201, 33, 209, 28, 204, 35, 211)(30, 206, 38, 214, 32, 208, 39, 215)(34, 210, 42, 218, 36, 212, 43, 219)(37, 213, 45, 221, 40, 216, 47, 223)(41, 217, 49, 225, 44, 220, 51, 227)(46, 222, 54, 230, 48, 224, 55, 231)(50, 226, 58, 234, 52, 228, 59, 235)(53, 229, 61, 237, 56, 232, 63, 239)(57, 233, 65, 241, 60, 236, 67, 243)(62, 238, 70, 246, 64, 240, 71, 247)(66, 242, 117, 293, 68, 244, 119, 295)(69, 245, 121, 297, 72, 248, 123, 299)(73, 249, 125, 301, 79, 255, 128, 304)(74, 250, 129, 305, 77, 253, 132, 308)(75, 251, 133, 309, 88, 264, 135, 311)(76, 252, 136, 312, 78, 254, 139, 315)(80, 256, 146, 322, 87, 263, 148, 324)(81, 257, 149, 325, 82, 258, 151, 327)(83, 259, 126, 302, 85, 261, 144, 320)(84, 260, 154, 330, 86, 262, 156, 332)(89, 265, 130, 306, 91, 267, 140, 316)(90, 266, 162, 338, 92, 268, 164, 340)(93, 269, 167, 343, 96, 272, 169, 345)(94, 270, 142, 318, 95, 271, 137, 313)(97, 273, 173, 349, 98, 274, 175, 351)(99, 275, 176, 352, 100, 276, 174, 350)(101, 277, 168, 344, 102, 278, 172, 348)(103, 279, 166, 342, 104, 280, 163, 339)(105, 281, 155, 331, 106, 282, 158, 334)(107, 283, 147, 323, 108, 284, 159, 335)(109, 285, 160, 336, 110, 286, 134, 310)(111, 287, 138, 314, 112, 288, 143, 319)(113, 289, 150, 326, 114, 290, 152, 328)(115, 291, 145, 321, 116, 292, 127, 303)(118, 294, 141, 317, 120, 296, 131, 307)(122, 298, 170, 346, 124, 300, 171, 347)(153, 329, 161, 337, 157, 333, 165, 341)(353, 529, 355, 531)(354, 530, 360, 536)(356, 532, 366, 542)(357, 533, 367, 543)(358, 534, 364, 540)(359, 535, 368, 544)(361, 537, 372, 548)(362, 538, 370, 546)(363, 539, 373, 549)(365, 541, 376, 552)(369, 545, 377, 553)(371, 547, 380, 556)(374, 550, 384, 560)(375, 551, 382, 558)(378, 554, 388, 564)(379, 555, 386, 562)(381, 557, 389, 565)(383, 559, 392, 568)(385, 561, 393, 569)(387, 563, 396, 572)(390, 566, 400, 576)(391, 567, 398, 574)(394, 570, 404, 580)(395, 571, 402, 578)(397, 573, 405, 581)(399, 575, 408, 584)(401, 577, 409, 585)(403, 579, 412, 588)(406, 582, 416, 592)(407, 583, 414, 590)(410, 586, 420, 596)(411, 587, 418, 594)(413, 589, 421, 597)(415, 591, 424, 600)(417, 593, 446, 622)(419, 595, 447, 623)(422, 598, 443, 619)(423, 599, 441, 617)(425, 601, 478, 654)(426, 602, 482, 658)(427, 603, 481, 657)(428, 604, 489, 665)(429, 605, 492, 668)(430, 606, 494, 670)(431, 607, 496, 672)(432, 608, 480, 656)(433, 609, 473, 649)(434, 610, 475, 651)(435, 611, 469, 645)(436, 612, 503, 679)(437, 613, 471, 647)(438, 614, 501, 677)(439, 615, 477, 653)(440, 616, 484, 660)(442, 618, 488, 664)(444, 620, 491, 667)(445, 621, 487, 663)(448, 624, 485, 661)(449, 625, 500, 676)(450, 626, 498, 674)(451, 627, 506, 682)(452, 628, 508, 684)(453, 629, 514, 690)(454, 630, 516, 692)(455, 631, 521, 697)(456, 632, 519, 695)(457, 633, 527, 703)(458, 634, 525, 701)(459, 635, 528, 704)(460, 636, 526, 702)(461, 637, 520, 696)(462, 638, 524, 700)(463, 639, 515, 691)(464, 640, 518, 694)(465, 641, 510, 686)(466, 642, 507, 683)(467, 643, 499, 675)(468, 644, 511, 687)(470, 646, 512, 688)(472, 648, 486, 662)(474, 650, 495, 671)(476, 652, 490, 666)(479, 655, 517, 693)(483, 659, 505, 681)(493, 669, 509, 685)(497, 673, 513, 689)(502, 678, 523, 699)(504, 680, 522, 698) L = (1, 356)(2, 361)(3, 364)(4, 359)(5, 362)(6, 353)(7, 358)(8, 370)(9, 357)(10, 354)(11, 374)(12, 368)(13, 375)(14, 355)(15, 372)(16, 366)(17, 378)(18, 367)(19, 379)(20, 360)(21, 382)(22, 365)(23, 363)(24, 384)(25, 386)(26, 371)(27, 369)(28, 388)(29, 390)(30, 376)(31, 391)(32, 373)(33, 394)(34, 380)(35, 395)(36, 377)(37, 398)(38, 383)(39, 381)(40, 400)(41, 402)(42, 387)(43, 385)(44, 404)(45, 406)(46, 392)(47, 407)(48, 389)(49, 410)(50, 396)(51, 411)(52, 393)(53, 414)(54, 399)(55, 397)(56, 416)(57, 418)(58, 403)(59, 401)(60, 420)(61, 422)(62, 408)(63, 423)(64, 405)(65, 469)(66, 412)(67, 471)(68, 409)(69, 441)(70, 415)(71, 413)(72, 443)(73, 428)(74, 433)(75, 436)(76, 431)(77, 434)(78, 425)(79, 430)(80, 442)(81, 429)(82, 426)(83, 446)(84, 440)(85, 447)(86, 427)(87, 444)(88, 438)(89, 424)(90, 439)(91, 421)(92, 432)(93, 451)(94, 437)(95, 435)(96, 452)(97, 453)(98, 454)(99, 448)(100, 445)(101, 450)(102, 449)(103, 459)(104, 460)(105, 461)(106, 462)(107, 456)(108, 455)(109, 458)(110, 457)(111, 467)(112, 468)(113, 470)(114, 472)(115, 464)(116, 463)(117, 419)(118, 466)(119, 417)(120, 465)(121, 482)(122, 513)(123, 492)(124, 517)(125, 488)(126, 494)(127, 490)(128, 491)(129, 501)(130, 475)(131, 502)(132, 503)(133, 506)(134, 507)(135, 508)(136, 480)(137, 478)(138, 497)(139, 477)(140, 473)(141, 504)(142, 496)(143, 479)(144, 489)(145, 495)(146, 514)(147, 515)(148, 516)(149, 484)(150, 493)(151, 481)(152, 483)(153, 522)(154, 487)(155, 512)(156, 485)(157, 523)(158, 486)(159, 518)(160, 510)(161, 476)(162, 500)(163, 511)(164, 498)(165, 474)(166, 499)(167, 528)(168, 527)(169, 526)(170, 509)(171, 505)(172, 525)(173, 520)(174, 519)(175, 524)(176, 521)(177, 529)(178, 530)(179, 531)(180, 532)(181, 533)(182, 534)(183, 535)(184, 536)(185, 537)(186, 538)(187, 539)(188, 540)(189, 541)(190, 542)(191, 543)(192, 544)(193, 545)(194, 546)(195, 547)(196, 548)(197, 549)(198, 550)(199, 551)(200, 552)(201, 553)(202, 554)(203, 555)(204, 556)(205, 557)(206, 558)(207, 559)(208, 560)(209, 561)(210, 562)(211, 563)(212, 564)(213, 565)(214, 566)(215, 567)(216, 568)(217, 569)(218, 570)(219, 571)(220, 572)(221, 573)(222, 574)(223, 575)(224, 576)(225, 577)(226, 578)(227, 579)(228, 580)(229, 581)(230, 582)(231, 583)(232, 584)(233, 585)(234, 586)(235, 587)(236, 588)(237, 589)(238, 590)(239, 591)(240, 592)(241, 593)(242, 594)(243, 595)(244, 596)(245, 597)(246, 598)(247, 599)(248, 600)(249, 601)(250, 602)(251, 603)(252, 604)(253, 605)(254, 606)(255, 607)(256, 608)(257, 609)(258, 610)(259, 611)(260, 612)(261, 613)(262, 614)(263, 615)(264, 616)(265, 617)(266, 618)(267, 619)(268, 620)(269, 621)(270, 622)(271, 623)(272, 624)(273, 625)(274, 626)(275, 627)(276, 628)(277, 629)(278, 630)(279, 631)(280, 632)(281, 633)(282, 634)(283, 635)(284, 636)(285, 637)(286, 638)(287, 639)(288, 640)(289, 641)(290, 642)(291, 643)(292, 644)(293, 645)(294, 646)(295, 647)(296, 648)(297, 649)(298, 650)(299, 651)(300, 652)(301, 653)(302, 654)(303, 655)(304, 656)(305, 657)(306, 658)(307, 659)(308, 660)(309, 661)(310, 662)(311, 663)(312, 664)(313, 665)(314, 666)(315, 667)(316, 668)(317, 669)(318, 670)(319, 671)(320, 672)(321, 673)(322, 674)(323, 675)(324, 676)(325, 677)(326, 678)(327, 679)(328, 680)(329, 681)(330, 682)(331, 683)(332, 684)(333, 685)(334, 686)(335, 687)(336, 688)(337, 689)(338, 690)(339, 691)(340, 692)(341, 693)(342, 694)(343, 695)(344, 696)(345, 697)(346, 698)(347, 699)(348, 700)(349, 701)(350, 702)(351, 703)(352, 704) local type(s) :: { ( 4^4 ), ( 4^8 ) } Outer automorphisms :: reflexible Dual of E23.1170 Graph:: simple bipartite v = 132 e = 352 f = 176 degree seq :: [ 4^88, 8^44 ] E23.1175 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 4, 92}) Quotient :: regular Aut^+ = C4 x D46 (small group id <184, 4>) Aut = D8 x D46 (small group id <368, 31>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-2 * T2)^2, (T1 * T2)^4, T1^43 * T2 * T1^-3 * T2 ] Map:: non-degenerate R = (1, 2, 5, 11, 20, 29, 37, 45, 53, 61, 71, 75, 80, 85, 89, 93, 97, 102, 139, 147, 151, 155, 159, 163, 167, 172, 179, 183, 145, 138, 133, 128, 124, 120, 116, 111, 108, 107, 105, 66, 58, 50, 42, 34, 26, 16, 23, 17, 24, 32, 40, 48, 56, 64, 72, 76, 73, 77, 81, 86, 90, 94, 98, 103, 140, 148, 152, 156, 160, 164, 168, 173, 180, 181, 174, 169, 143, 136, 131, 127, 123, 119, 115, 68, 60, 52, 44, 36, 28, 19, 10, 4)(3, 7, 15, 25, 33, 41, 49, 57, 65, 69, 78, 74, 87, 84, 95, 92, 104, 100, 137, 146, 149, 154, 157, 162, 165, 171, 175, 184, 178, 141, 135, 129, 126, 121, 118, 112, 110, 101, 63, 54, 47, 38, 31, 21, 14, 6, 13, 9, 18, 27, 35, 43, 51, 59, 67, 82, 70, 83, 79, 91, 88, 99, 96, 132, 106, 144, 150, 153, 158, 161, 166, 170, 176, 182, 177, 142, 134, 130, 125, 122, 117, 114, 109, 113, 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, 101)(63, 72)(67, 105)(68, 82)(69, 107)(70, 108)(71, 109)(73, 110)(74, 111)(75, 112)(76, 113)(77, 114)(78, 115)(79, 116)(80, 117)(81, 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, 133)(97, 134)(98, 135)(99, 136)(100, 138)(102, 141)(103, 142)(104, 143)(106, 145)(132, 169)(137, 174)(139, 177)(140, 178)(144, 181)(146, 183)(147, 184)(148, 182)(149, 180)(150, 179)(151, 176)(152, 175)(153, 173)(154, 172)(155, 171)(156, 170)(157, 168)(158, 167)(159, 166)(160, 165)(161, 164)(162, 163) local type(s) :: { ( 4^92 ) } Outer automorphisms :: reflexible Dual of E23.1176 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 2 e = 92 f = 46 degree seq :: [ 92^2 ] E23.1176 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 4, 92}) Quotient :: regular Aut^+ = C4 x D46 (small group id <184, 4>) Aut = D8 x D46 (small group id <368, 31>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^4, (T1^-1 * T2 * T1^-1)^2, T2 * T1^-1 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 ] Map:: non-degenerate R = (1, 2, 5, 4)(3, 7, 10, 8)(6, 11, 9, 12)(13, 17, 14, 18)(15, 19, 16, 20)(21, 25, 22, 26)(23, 27, 24, 28)(29, 33, 30, 34)(31, 35, 32, 36)(37, 42, 38, 39)(40, 57, 41, 59)(43, 67, 44, 61)(45, 65, 46, 63)(47, 71, 48, 69)(49, 75, 50, 73)(51, 79, 52, 77)(53, 83, 54, 81)(55, 87, 56, 85)(58, 91, 60, 89)(62, 93, 68, 95)(64, 98, 66, 97)(70, 101, 72, 102)(74, 104, 76, 105)(78, 109, 80, 110)(82, 113, 84, 114)(86, 117, 88, 118)(90, 121, 92, 122)(94, 125, 96, 126)(99, 129, 100, 130)(103, 134, 108, 133)(106, 137, 107, 138)(111, 142, 112, 141)(115, 145, 116, 144)(119, 150, 120, 149)(123, 154, 124, 153)(127, 158, 128, 157)(131, 162, 132, 161)(135, 166, 136, 165)(139, 170, 140, 169)(143, 173, 148, 174)(146, 178, 147, 177)(151, 181, 152, 182)(155, 183, 156, 184)(159, 180, 160, 179)(163, 175, 164, 176)(167, 171, 168, 172) L = (1, 3)(2, 6)(4, 9)(5, 10)(7, 13)(8, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19, 23)(20, 24)(25, 29)(26, 30)(27, 31)(28, 32)(33, 37)(34, 38)(35, 57)(36, 59)(39, 61)(40, 63)(41, 65)(42, 67)(43, 69)(44, 71)(45, 73)(46, 75)(47, 77)(48, 79)(49, 81)(50, 83)(51, 85)(52, 87)(53, 89)(54, 91)(55, 93)(56, 95)(58, 98)(60, 97)(62, 102)(64, 105)(66, 104)(68, 101)(70, 110)(72, 109)(74, 114)(76, 113)(78, 118)(80, 117)(82, 122)(84, 121)(86, 126)(88, 125)(90, 130)(92, 129)(94, 134)(96, 133)(99, 137)(100, 138)(103, 141)(106, 144)(107, 145)(108, 142)(111, 149)(112, 150)(115, 153)(116, 154)(119, 157)(120, 158)(123, 161)(124, 162)(127, 165)(128, 166)(131, 169)(132, 170)(135, 173)(136, 174)(139, 178)(140, 177)(143, 182)(146, 184)(147, 183)(148, 181)(151, 179)(152, 180)(155, 176)(156, 175)(159, 172)(160, 171)(163, 167)(164, 168) local type(s) :: { ( 92^4 ) } Outer automorphisms :: reflexible Dual of E23.1175 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 46 e = 92 f = 2 degree seq :: [ 4^46 ] E23.1177 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 92}) Quotient :: edge Aut^+ = C4 x D46 (small group id <184, 4>) Aut = D8 x D46 (small group id <368, 31>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T1)^2, (F * T2)^2, T2^4, (T2^-1 * T1 * T2^-1)^2, T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 ] Map:: R = (1, 3, 8, 4)(2, 5, 11, 6)(7, 13, 9, 14)(10, 15, 12, 16)(17, 21, 18, 22)(19, 23, 20, 24)(25, 29, 26, 30)(27, 31, 28, 32)(33, 37, 34, 38)(35, 44, 36, 39)(40, 57, 41, 59)(42, 68, 43, 61)(45, 65, 46, 63)(47, 70, 48, 67)(49, 75, 50, 73)(51, 79, 52, 77)(53, 83, 54, 81)(55, 87, 56, 85)(58, 91, 60, 89)(62, 93, 72, 95)(64, 98, 66, 97)(69, 101, 71, 102)(74, 104, 76, 105)(78, 108, 80, 109)(82, 113, 84, 114)(86, 117, 88, 118)(90, 121, 92, 122)(94, 125, 96, 126)(99, 129, 100, 130)(103, 134, 112, 133)(106, 137, 107, 138)(110, 142, 111, 141)(115, 145, 116, 144)(119, 149, 120, 148)(123, 154, 124, 153)(127, 158, 128, 157)(131, 162, 132, 161)(135, 166, 136, 165)(139, 170, 140, 169)(143, 173, 152, 174)(146, 178, 147, 177)(150, 181, 151, 182)(155, 183, 156, 184)(159, 180, 160, 179)(163, 175, 164, 176)(167, 171, 168, 172)(185, 186)(187, 191)(188, 193)(189, 194)(190, 196)(192, 195)(197, 201)(198, 202)(199, 203)(200, 204)(205, 209)(206, 210)(207, 211)(208, 212)(213, 217)(214, 218)(215, 219)(216, 220)(221, 241)(222, 243)(223, 245)(224, 247)(225, 249)(226, 251)(227, 254)(228, 252)(229, 257)(230, 259)(231, 261)(232, 263)(233, 265)(234, 267)(235, 269)(236, 271)(237, 273)(238, 275)(239, 277)(240, 279)(242, 282)(244, 281)(246, 286)(248, 289)(250, 288)(253, 293)(255, 292)(256, 285)(258, 298)(260, 297)(262, 302)(264, 301)(266, 306)(268, 305)(270, 310)(272, 309)(274, 314)(276, 313)(278, 318)(280, 317)(283, 321)(284, 322)(287, 325)(290, 328)(291, 329)(294, 332)(295, 333)(296, 326)(299, 337)(300, 338)(303, 341)(304, 342)(307, 345)(308, 346)(311, 349)(312, 350)(315, 353)(316, 354)(319, 357)(320, 358)(323, 362)(324, 361)(327, 366)(330, 368)(331, 367)(334, 363)(335, 364)(336, 365)(339, 360)(340, 359)(343, 356)(344, 355)(347, 351)(348, 352) L = (1, 185)(2, 186)(3, 187)(4, 188)(5, 189)(6, 190)(7, 191)(8, 192)(9, 193)(10, 194)(11, 195)(12, 196)(13, 197)(14, 198)(15, 199)(16, 200)(17, 201)(18, 202)(19, 203)(20, 204)(21, 205)(22, 206)(23, 207)(24, 208)(25, 209)(26, 210)(27, 211)(28, 212)(29, 213)(30, 214)(31, 215)(32, 216)(33, 217)(34, 218)(35, 219)(36, 220)(37, 221)(38, 222)(39, 223)(40, 224)(41, 225)(42, 226)(43, 227)(44, 228)(45, 229)(46, 230)(47, 231)(48, 232)(49, 233)(50, 234)(51, 235)(52, 236)(53, 237)(54, 238)(55, 239)(56, 240)(57, 241)(58, 242)(59, 243)(60, 244)(61, 245)(62, 246)(63, 247)(64, 248)(65, 249)(66, 250)(67, 251)(68, 252)(69, 253)(70, 254)(71, 255)(72, 256)(73, 257)(74, 258)(75, 259)(76, 260)(77, 261)(78, 262)(79, 263)(80, 264)(81, 265)(82, 266)(83, 267)(84, 268)(85, 269)(86, 270)(87, 271)(88, 272)(89, 273)(90, 274)(91, 275)(92, 276)(93, 277)(94, 278)(95, 279)(96, 280)(97, 281)(98, 282)(99, 283)(100, 284)(101, 285)(102, 286)(103, 287)(104, 288)(105, 289)(106, 290)(107, 291)(108, 292)(109, 293)(110, 294)(111, 295)(112, 296)(113, 297)(114, 298)(115, 299)(116, 300)(117, 301)(118, 302)(119, 303)(120, 304)(121, 305)(122, 306)(123, 307)(124, 308)(125, 309)(126, 310)(127, 311)(128, 312)(129, 313)(130, 314)(131, 315)(132, 316)(133, 317)(134, 318)(135, 319)(136, 320)(137, 321)(138, 322)(139, 323)(140, 324)(141, 325)(142, 326)(143, 327)(144, 328)(145, 329)(146, 330)(147, 331)(148, 332)(149, 333)(150, 334)(151, 335)(152, 336)(153, 337)(154, 338)(155, 339)(156, 340)(157, 341)(158, 342)(159, 343)(160, 344)(161, 345)(162, 346)(163, 347)(164, 348)(165, 349)(166, 350)(167, 351)(168, 352)(169, 353)(170, 354)(171, 355)(172, 356)(173, 357)(174, 358)(175, 359)(176, 360)(177, 361)(178, 362)(179, 363)(180, 364)(181, 365)(182, 366)(183, 367)(184, 368) local type(s) :: { ( 184, 184 ), ( 184^4 ) } Outer automorphisms :: reflexible Dual of E23.1181 Transitivity :: ET+ Graph:: simple bipartite v = 138 e = 184 f = 2 degree seq :: [ 2^92, 4^46 ] E23.1178 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 92}) Quotient :: edge Aut^+ = C4 x D46 (small group id <184, 4>) Aut = D8 x D46 (small group id <368, 31>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1 * T1^-1)^2, (T2 * T1^-1)^2, T1^-1 * T2^-46 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 3, 10, 18, 26, 34, 42, 50, 58, 66, 87, 75, 72, 76, 85, 91, 99, 102, 107, 110, 116, 168, 183, 181, 174, 169, 162, 157, 153, 149, 145, 140, 133, 125, 119, 123, 131, 139, 114, 62, 54, 46, 38, 30, 22, 14, 6, 13, 21, 29, 37, 45, 53, 61, 97, 93, 83, 79, 70, 77, 84, 92, 98, 103, 106, 111, 115, 166, 184, 180, 175, 171, 164, 159, 154, 150, 146, 141, 134, 126, 120, 124, 132, 68, 60, 52, 44, 36, 28, 20, 12, 5)(2, 7, 15, 23, 31, 39, 47, 55, 63, 95, 78, 81, 69, 82, 80, 96, 94, 105, 104, 113, 112, 163, 182, 176, 173, 178, 165, 160, 155, 151, 147, 142, 137, 129, 121, 127, 135, 117, 65, 57, 49, 41, 33, 25, 17, 9, 4, 11, 19, 27, 35, 43, 51, 59, 67, 86, 89, 71, 74, 73, 90, 88, 101, 100, 109, 108, 158, 118, 170, 177, 172, 179, 167, 161, 156, 152, 148, 143, 138, 130, 122, 128, 136, 144, 64, 56, 48, 40, 32, 24, 16, 8)(185, 186, 190, 188)(187, 193, 197, 192)(189, 195, 198, 191)(194, 200, 205, 201)(196, 199, 206, 203)(202, 209, 213, 208)(204, 211, 214, 207)(210, 216, 221, 217)(212, 215, 222, 219)(218, 225, 229, 224)(220, 227, 230, 223)(226, 232, 237, 233)(228, 231, 238, 235)(234, 241, 245, 240)(236, 243, 246, 239)(242, 248, 281, 249)(244, 247, 298, 251)(250, 301, 277, 328)(252, 270, 323, 279)(253, 303, 258, 304)(254, 305, 256, 306)(255, 307, 265, 308)(257, 309, 266, 310)(259, 311, 263, 312)(260, 313, 261, 314)(262, 315, 273, 316)(264, 317, 274, 318)(267, 319, 271, 320)(268, 321, 269, 322)(272, 324, 280, 325)(275, 326, 276, 327)(278, 329, 285, 330)(282, 331, 283, 332)(284, 333, 289, 334)(286, 335, 287, 336)(288, 337, 293, 338)(290, 339, 291, 340)(292, 341, 297, 343)(294, 344, 295, 345)(296, 346, 342, 348)(299, 349, 300, 351)(302, 353, 347, 355)(350, 363, 352, 362)(354, 359, 366, 358)(356, 368, 357, 367)(360, 364, 361, 365) L = (1, 185)(2, 186)(3, 187)(4, 188)(5, 189)(6, 190)(7, 191)(8, 192)(9, 193)(10, 194)(11, 195)(12, 196)(13, 197)(14, 198)(15, 199)(16, 200)(17, 201)(18, 202)(19, 203)(20, 204)(21, 205)(22, 206)(23, 207)(24, 208)(25, 209)(26, 210)(27, 211)(28, 212)(29, 213)(30, 214)(31, 215)(32, 216)(33, 217)(34, 218)(35, 219)(36, 220)(37, 221)(38, 222)(39, 223)(40, 224)(41, 225)(42, 226)(43, 227)(44, 228)(45, 229)(46, 230)(47, 231)(48, 232)(49, 233)(50, 234)(51, 235)(52, 236)(53, 237)(54, 238)(55, 239)(56, 240)(57, 241)(58, 242)(59, 243)(60, 244)(61, 245)(62, 246)(63, 247)(64, 248)(65, 249)(66, 250)(67, 251)(68, 252)(69, 253)(70, 254)(71, 255)(72, 256)(73, 257)(74, 258)(75, 259)(76, 260)(77, 261)(78, 262)(79, 263)(80, 264)(81, 265)(82, 266)(83, 267)(84, 268)(85, 269)(86, 270)(87, 271)(88, 272)(89, 273)(90, 274)(91, 275)(92, 276)(93, 277)(94, 278)(95, 279)(96, 280)(97, 281)(98, 282)(99, 283)(100, 284)(101, 285)(102, 286)(103, 287)(104, 288)(105, 289)(106, 290)(107, 291)(108, 292)(109, 293)(110, 294)(111, 295)(112, 296)(113, 297)(114, 298)(115, 299)(116, 300)(117, 301)(118, 302)(119, 303)(120, 304)(121, 305)(122, 306)(123, 307)(124, 308)(125, 309)(126, 310)(127, 311)(128, 312)(129, 313)(130, 314)(131, 315)(132, 316)(133, 317)(134, 318)(135, 319)(136, 320)(137, 321)(138, 322)(139, 323)(140, 324)(141, 325)(142, 326)(143, 327)(144, 328)(145, 329)(146, 330)(147, 331)(148, 332)(149, 333)(150, 334)(151, 335)(152, 336)(153, 337)(154, 338)(155, 339)(156, 340)(157, 341)(158, 342)(159, 343)(160, 344)(161, 345)(162, 346)(163, 347)(164, 348)(165, 349)(166, 350)(167, 351)(168, 352)(169, 353)(170, 354)(171, 355)(172, 356)(173, 357)(174, 358)(175, 359)(176, 360)(177, 361)(178, 362)(179, 363)(180, 364)(181, 365)(182, 366)(183, 367)(184, 368) local type(s) :: { ( 4^4 ), ( 4^92 ) } Outer automorphisms :: reflexible Dual of E23.1182 Transitivity :: ET+ Graph:: bipartite v = 48 e = 184 f = 92 degree seq :: [ 4^46, 92^2 ] E23.1179 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 92}) Quotient :: edge Aut^+ = C4 x D46 (small group id <184, 4>) Aut = D8 x D46 (small group id <368, 31>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-2 * T2)^2, (T2 * T1)^4, T1^43 * T2 * T1^-3 * T2 ] 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, 113)(63, 103)(67, 117)(68, 88)(69, 119)(70, 121)(71, 123)(72, 125)(73, 127)(74, 129)(75, 131)(76, 133)(77, 135)(78, 137)(79, 139)(80, 141)(81, 143)(82, 145)(83, 147)(84, 149)(85, 151)(86, 153)(87, 155)(89, 158)(90, 160)(91, 162)(92, 164)(93, 166)(94, 168)(95, 170)(96, 172)(97, 174)(98, 176)(99, 178)(100, 179)(101, 180)(102, 171)(104, 183)(105, 165)(106, 184)(107, 181)(108, 156)(109, 154)(110, 175)(111, 140)(112, 173)(114, 132)(115, 169)(116, 163)(118, 128)(120, 146)(122, 159)(124, 167)(126, 134)(130, 150)(136, 177)(138, 144)(142, 161)(148, 182)(152, 157)(185, 186, 189, 195, 204, 213, 221, 229, 237, 245, 262, 256, 253, 254, 257, 263, 271, 279, 284, 289, 293, 298, 322, 310, 304, 306, 312, 324, 340, 355, 362, 348, 337, 315, 327, 317, 329, 342, 301, 250, 242, 234, 226, 218, 210, 200, 207, 201, 208, 216, 224, 232, 240, 248, 287, 282, 277, 268, 274, 269, 275, 280, 285, 290, 294, 299, 366, 361, 351, 334, 345, 336, 347, 357, 365, 367, 358, 352, 331, 319, 307, 313, 325, 252, 244, 236, 228, 220, 212, 203, 194, 188)(187, 191, 199, 209, 217, 225, 233, 241, 249, 273, 264, 260, 255, 259, 267, 276, 281, 286, 291, 295, 300, 343, 326, 318, 308, 316, 332, 349, 359, 354, 364, 323, 346, 305, 344, 309, 350, 297, 247, 238, 231, 222, 215, 205, 198, 190, 197, 193, 202, 211, 219, 227, 235, 243, 251, 272, 266, 258, 265, 261, 270, 278, 283, 288, 292, 296, 302, 341, 330, 314, 328, 320, 338, 353, 363, 368, 339, 356, 311, 335, 303, 333, 321, 360, 246, 239, 230, 223, 214, 206, 196, 192) L = (1, 185)(2, 186)(3, 187)(4, 188)(5, 189)(6, 190)(7, 191)(8, 192)(9, 193)(10, 194)(11, 195)(12, 196)(13, 197)(14, 198)(15, 199)(16, 200)(17, 201)(18, 202)(19, 203)(20, 204)(21, 205)(22, 206)(23, 207)(24, 208)(25, 209)(26, 210)(27, 211)(28, 212)(29, 213)(30, 214)(31, 215)(32, 216)(33, 217)(34, 218)(35, 219)(36, 220)(37, 221)(38, 222)(39, 223)(40, 224)(41, 225)(42, 226)(43, 227)(44, 228)(45, 229)(46, 230)(47, 231)(48, 232)(49, 233)(50, 234)(51, 235)(52, 236)(53, 237)(54, 238)(55, 239)(56, 240)(57, 241)(58, 242)(59, 243)(60, 244)(61, 245)(62, 246)(63, 247)(64, 248)(65, 249)(66, 250)(67, 251)(68, 252)(69, 253)(70, 254)(71, 255)(72, 256)(73, 257)(74, 258)(75, 259)(76, 260)(77, 261)(78, 262)(79, 263)(80, 264)(81, 265)(82, 266)(83, 267)(84, 268)(85, 269)(86, 270)(87, 271)(88, 272)(89, 273)(90, 274)(91, 275)(92, 276)(93, 277)(94, 278)(95, 279)(96, 280)(97, 281)(98, 282)(99, 283)(100, 284)(101, 285)(102, 286)(103, 287)(104, 288)(105, 289)(106, 290)(107, 291)(108, 292)(109, 293)(110, 294)(111, 295)(112, 296)(113, 297)(114, 298)(115, 299)(116, 300)(117, 301)(118, 302)(119, 303)(120, 304)(121, 305)(122, 306)(123, 307)(124, 308)(125, 309)(126, 310)(127, 311)(128, 312)(129, 313)(130, 314)(131, 315)(132, 316)(133, 317)(134, 318)(135, 319)(136, 320)(137, 321)(138, 322)(139, 323)(140, 324)(141, 325)(142, 326)(143, 327)(144, 328)(145, 329)(146, 330)(147, 331)(148, 332)(149, 333)(150, 334)(151, 335)(152, 336)(153, 337)(154, 338)(155, 339)(156, 340)(157, 341)(158, 342)(159, 343)(160, 344)(161, 345)(162, 346)(163, 347)(164, 348)(165, 349)(166, 350)(167, 351)(168, 352)(169, 353)(170, 354)(171, 355)(172, 356)(173, 357)(174, 358)(175, 359)(176, 360)(177, 361)(178, 362)(179, 363)(180, 364)(181, 365)(182, 366)(183, 367)(184, 368) local type(s) :: { ( 8, 8 ), ( 8^92 ) } Outer automorphisms :: reflexible Dual of E23.1180 Transitivity :: ET+ Graph:: simple bipartite v = 94 e = 184 f = 46 degree seq :: [ 2^92, 92^2 ] E23.1180 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 92}) Quotient :: loop Aut^+ = C4 x D46 (small group id <184, 4>) Aut = D8 x D46 (small group id <368, 31>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T1)^2, (F * T2)^2, T2^4, (T2^-1 * T1 * T2^-1)^2, T2^-1 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 * T2^-1 * T1 ] Map:: R = (1, 185, 3, 187, 8, 192, 4, 188)(2, 186, 5, 189, 11, 195, 6, 190)(7, 191, 13, 197, 9, 193, 14, 198)(10, 194, 15, 199, 12, 196, 16, 200)(17, 201, 21, 205, 18, 202, 22, 206)(19, 203, 23, 207, 20, 204, 24, 208)(25, 209, 29, 213, 26, 210, 30, 214)(27, 211, 31, 215, 28, 212, 32, 216)(33, 217, 37, 221, 34, 218, 38, 222)(35, 219, 42, 226, 36, 220, 41, 225)(39, 223, 62, 246, 44, 228, 61, 245)(40, 224, 65, 249, 47, 231, 66, 250)(43, 227, 68, 252, 45, 229, 63, 247)(46, 230, 71, 255, 48, 232, 64, 248)(49, 233, 69, 253, 50, 234, 67, 251)(51, 235, 72, 256, 52, 236, 70, 254)(53, 237, 74, 258, 54, 238, 73, 257)(55, 239, 76, 260, 56, 240, 75, 259)(57, 241, 78, 262, 58, 242, 77, 261)(59, 243, 80, 264, 60, 244, 79, 263)(81, 265, 85, 269, 82, 266, 86, 270)(83, 267, 90, 274, 84, 268, 89, 273)(87, 271, 110, 294, 92, 276, 109, 293)(88, 272, 113, 297, 95, 279, 114, 298)(91, 275, 116, 300, 93, 277, 111, 295)(94, 278, 119, 303, 96, 280, 112, 296)(97, 281, 117, 301, 98, 282, 115, 299)(99, 283, 120, 304, 100, 284, 118, 302)(101, 285, 122, 306, 102, 286, 121, 305)(103, 287, 124, 308, 104, 288, 123, 307)(105, 289, 126, 310, 106, 290, 125, 309)(107, 291, 128, 312, 108, 292, 127, 311)(129, 313, 133, 317, 130, 314, 134, 318)(131, 315, 138, 322, 132, 316, 137, 321)(135, 319, 158, 342, 140, 324, 157, 341)(136, 320, 161, 345, 143, 327, 162, 346)(139, 323, 164, 348, 141, 325, 159, 343)(142, 326, 167, 351, 144, 328, 160, 344)(145, 329, 165, 349, 146, 330, 163, 347)(147, 331, 168, 352, 148, 332, 166, 350)(149, 333, 170, 354, 150, 334, 169, 353)(151, 335, 172, 356, 152, 336, 171, 355)(153, 337, 174, 358, 154, 338, 173, 357)(155, 339, 176, 360, 156, 340, 175, 359)(177, 361, 181, 365, 178, 362, 182, 366)(179, 363, 184, 368, 180, 364, 183, 367) L = (1, 186)(2, 185)(3, 191)(4, 193)(5, 194)(6, 196)(7, 187)(8, 195)(9, 188)(10, 189)(11, 192)(12, 190)(13, 201)(14, 202)(15, 203)(16, 204)(17, 197)(18, 198)(19, 199)(20, 200)(21, 209)(22, 210)(23, 211)(24, 212)(25, 205)(26, 206)(27, 207)(28, 208)(29, 217)(30, 218)(31, 219)(32, 220)(33, 213)(34, 214)(35, 215)(36, 216)(37, 245)(38, 246)(39, 247)(40, 248)(41, 249)(42, 250)(43, 251)(44, 252)(45, 253)(46, 254)(47, 255)(48, 256)(49, 257)(50, 258)(51, 259)(52, 260)(53, 261)(54, 262)(55, 263)(56, 264)(57, 265)(58, 266)(59, 267)(60, 268)(61, 221)(62, 222)(63, 223)(64, 224)(65, 225)(66, 226)(67, 227)(68, 228)(69, 229)(70, 230)(71, 231)(72, 232)(73, 233)(74, 234)(75, 235)(76, 236)(77, 237)(78, 238)(79, 239)(80, 240)(81, 241)(82, 242)(83, 243)(84, 244)(85, 293)(86, 294)(87, 295)(88, 296)(89, 297)(90, 298)(91, 299)(92, 300)(93, 301)(94, 302)(95, 303)(96, 304)(97, 305)(98, 306)(99, 307)(100, 308)(101, 309)(102, 310)(103, 311)(104, 312)(105, 313)(106, 314)(107, 315)(108, 316)(109, 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, 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, 317)(158, 318)(159, 319)(160, 320)(161, 321)(162, 322)(163, 323)(164, 324)(165, 325)(166, 326)(167, 327)(168, 328)(169, 329)(170, 330)(171, 331)(172, 332)(173, 333)(174, 334)(175, 335)(176, 336)(177, 337)(178, 338)(179, 339)(180, 340)(181, 368)(182, 367)(183, 366)(184, 365) local type(s) :: { ( 2, 92, 2, 92, 2, 92, 2, 92 ) } Outer automorphisms :: reflexible Dual of E23.1179 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 46 e = 184 f = 94 degree seq :: [ 8^46 ] E23.1181 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 92}) Quotient :: loop Aut^+ = C4 x D46 (small group id <184, 4>) Aut = D8 x D46 (small group id <368, 31>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1 * T1^-1)^2, (T2 * T1^-1)^2, T1^-1 * T2^-46 * T1^-1 ] Map:: R = (1, 185, 3, 187, 10, 194, 18, 202, 26, 210, 34, 218, 42, 226, 50, 234, 58, 242, 66, 250, 122, 306, 155, 339, 141, 325, 128, 312, 144, 328, 158, 342, 175, 359, 179, 363, 170, 354, 154, 338, 138, 322, 153, 337, 169, 353, 178, 362, 183, 367, 184, 368, 118, 302, 113, 297, 109, 293, 104, 288, 97, 281, 90, 274, 82, 266, 74, 258, 81, 265, 89, 273, 96, 280, 103, 287, 108, 292, 62, 246, 54, 238, 46, 230, 38, 222, 30, 214, 22, 206, 14, 198, 6, 190, 13, 197, 21, 205, 29, 213, 37, 221, 45, 229, 53, 237, 61, 245, 117, 301, 181, 365, 171, 355, 157, 341, 139, 323, 130, 314, 142, 326, 160, 344, 173, 357, 167, 351, 151, 335, 136, 320, 126, 310, 132, 316, 147, 331, 163, 347, 124, 308, 116, 300, 112, 296, 107, 291, 102, 286, 95, 279, 88, 272, 80, 264, 73, 257, 69, 253, 71, 255, 78, 262, 86, 270, 68, 252, 60, 244, 52, 236, 44, 228, 36, 220, 28, 212, 20, 204, 12, 196, 5, 189)(2, 186, 7, 191, 15, 199, 23, 207, 31, 215, 39, 223, 47, 231, 55, 239, 63, 247, 119, 303, 162, 346, 148, 332, 131, 315, 127, 311, 135, 319, 152, 336, 166, 350, 176, 360, 161, 345, 145, 329, 134, 318, 149, 333, 165, 349, 177, 361, 182, 366, 121, 305, 115, 299, 111, 295, 106, 290, 100, 284, 93, 277, 85, 269, 77, 261, 72, 256, 79, 263, 87, 271, 94, 278, 101, 285, 65, 249, 57, 241, 49, 233, 41, 225, 33, 217, 25, 209, 17, 201, 9, 193, 4, 188, 11, 195, 19, 203, 27, 211, 35, 219, 43, 227, 51, 235, 59, 243, 67, 251, 123, 307, 164, 348, 146, 330, 133, 317, 125, 309, 137, 321, 150, 334, 168, 352, 174, 358, 159, 343, 143, 327, 129, 313, 140, 324, 156, 340, 172, 356, 180, 364, 120, 304, 114, 298, 110, 294, 105, 289, 99, 283, 92, 276, 84, 268, 76, 260, 70, 254, 75, 259, 83, 267, 91, 275, 98, 282, 64, 248, 56, 240, 48, 232, 40, 224, 32, 216, 24, 208, 16, 200, 8, 192) L = (1, 186)(2, 190)(3, 193)(4, 185)(5, 195)(6, 188)(7, 189)(8, 187)(9, 197)(10, 200)(11, 198)(12, 199)(13, 192)(14, 191)(15, 206)(16, 205)(17, 194)(18, 209)(19, 196)(20, 211)(21, 201)(22, 203)(23, 204)(24, 202)(25, 213)(26, 216)(27, 214)(28, 215)(29, 208)(30, 207)(31, 222)(32, 221)(33, 210)(34, 225)(35, 212)(36, 227)(37, 217)(38, 219)(39, 220)(40, 218)(41, 229)(42, 232)(43, 230)(44, 231)(45, 224)(46, 223)(47, 238)(48, 237)(49, 226)(50, 241)(51, 228)(52, 243)(53, 233)(54, 235)(55, 236)(56, 234)(57, 245)(58, 248)(59, 246)(60, 247)(61, 240)(62, 239)(63, 292)(64, 301)(65, 242)(66, 285)(67, 244)(68, 307)(69, 309)(70, 312)(71, 315)(72, 314)(73, 319)(74, 311)(75, 323)(76, 326)(77, 328)(78, 330)(79, 325)(80, 334)(81, 317)(82, 321)(83, 339)(84, 342)(85, 344)(86, 346)(87, 341)(88, 350)(89, 332)(90, 336)(91, 355)(92, 357)(93, 359)(94, 306)(95, 358)(96, 348)(97, 352)(98, 250)(99, 363)(100, 351)(101, 365)(102, 345)(103, 303)(104, 360)(105, 335)(106, 354)(107, 327)(108, 251)(109, 343)(110, 338)(111, 320)(112, 318)(113, 329)(114, 310)(115, 322)(116, 324)(117, 249)(118, 313)(119, 252)(120, 337)(121, 316)(122, 275)(123, 287)(124, 349)(125, 258)(126, 299)(127, 253)(128, 256)(129, 296)(130, 254)(131, 265)(132, 304)(133, 255)(134, 302)(135, 266)(136, 294)(137, 257)(138, 298)(139, 263)(140, 368)(141, 259)(142, 261)(143, 297)(144, 260)(145, 291)(146, 273)(147, 366)(148, 262)(149, 300)(150, 274)(151, 290)(152, 264)(153, 305)(154, 295)(155, 271)(156, 308)(157, 267)(158, 269)(159, 286)(160, 268)(161, 293)(162, 280)(163, 356)(164, 270)(165, 367)(166, 281)(167, 283)(168, 272)(169, 364)(170, 289)(171, 278)(172, 362)(173, 277)(174, 288)(175, 276)(176, 279)(177, 347)(178, 361)(179, 284)(180, 331)(181, 282)(182, 353)(183, 340)(184, 333) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) } Outer automorphisms :: reflexible Dual of E23.1177 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 2 e = 184 f = 138 degree seq :: [ 184^2 ] E23.1182 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 92}) Quotient :: loop Aut^+ = C4 x D46 (small group id <184, 4>) Aut = D8 x D46 (small group id <368, 31>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-2 * T2)^2, (T2 * T1)^4, T1^43 * T2 * T1^-3 * T2 ] Map:: polytopal non-degenerate R = (1, 185, 3, 187)(2, 186, 6, 190)(4, 188, 9, 193)(5, 189, 12, 196)(7, 191, 16, 200)(8, 192, 17, 201)(10, 194, 15, 199)(11, 195, 21, 205)(13, 197, 23, 207)(14, 198, 24, 208)(18, 202, 26, 210)(19, 203, 27, 211)(20, 204, 30, 214)(22, 206, 32, 216)(25, 209, 34, 218)(28, 212, 33, 217)(29, 213, 38, 222)(31, 215, 40, 224)(35, 219, 42, 226)(36, 220, 43, 227)(37, 221, 46, 230)(39, 223, 48, 232)(41, 225, 50, 234)(44, 228, 49, 233)(45, 229, 54, 238)(47, 231, 56, 240)(51, 235, 58, 242)(52, 236, 59, 243)(53, 237, 62, 246)(55, 239, 64, 248)(57, 241, 66, 250)(60, 244, 65, 249)(61, 245, 93, 277)(63, 247, 115, 299)(67, 251, 102, 286)(68, 252, 119, 303)(69, 253, 121, 305)(70, 254, 123, 307)(71, 255, 125, 309)(72, 256, 127, 311)(73, 257, 129, 313)(74, 258, 131, 315)(75, 259, 133, 317)(76, 260, 135, 319)(77, 261, 137, 321)(78, 262, 139, 323)(79, 263, 141, 325)(80, 264, 143, 327)(81, 265, 145, 329)(82, 266, 113, 297)(83, 267, 148, 332)(84, 268, 150, 334)(85, 269, 152, 336)(86, 270, 154, 338)(87, 271, 156, 340)(88, 272, 158, 342)(89, 273, 160, 344)(90, 274, 162, 346)(91, 275, 164, 348)(92, 276, 166, 350)(94, 278, 169, 353)(95, 279, 171, 355)(96, 280, 173, 357)(97, 281, 117, 301)(98, 282, 176, 360)(99, 283, 178, 362)(100, 284, 180, 364)(101, 285, 179, 363)(103, 287, 183, 367)(104, 288, 174, 358)(105, 289, 184, 368)(106, 290, 170, 354)(107, 291, 181, 365)(108, 292, 159, 343)(109, 293, 177, 361)(110, 294, 155, 339)(111, 295, 172, 356)(112, 296, 146, 330)(114, 298, 167, 351)(116, 300, 140, 324)(118, 302, 157, 341)(120, 304, 136, 320)(122, 306, 153, 337)(124, 308, 134, 318)(126, 310, 163, 347)(128, 312, 165, 349)(130, 314, 144, 328)(132, 316, 175, 359)(138, 322, 151, 335)(142, 326, 182, 366)(147, 331, 161, 345)(149, 333, 168, 352) L = (1, 186)(2, 189)(3, 191)(4, 185)(5, 195)(6, 197)(7, 199)(8, 187)(9, 202)(10, 188)(11, 204)(12, 192)(13, 193)(14, 190)(15, 209)(16, 207)(17, 208)(18, 211)(19, 194)(20, 213)(21, 198)(22, 196)(23, 201)(24, 216)(25, 217)(26, 200)(27, 219)(28, 203)(29, 221)(30, 206)(31, 205)(32, 224)(33, 225)(34, 210)(35, 227)(36, 212)(37, 229)(38, 215)(39, 214)(40, 232)(41, 233)(42, 218)(43, 235)(44, 220)(45, 237)(46, 223)(47, 222)(48, 240)(49, 241)(50, 226)(51, 243)(52, 228)(53, 245)(54, 231)(55, 230)(56, 248)(57, 249)(58, 234)(59, 251)(60, 236)(61, 297)(62, 239)(63, 238)(64, 299)(65, 301)(66, 242)(67, 303)(68, 244)(69, 254)(70, 257)(71, 259)(72, 253)(73, 252)(74, 264)(75, 266)(76, 255)(77, 269)(78, 256)(79, 260)(80, 261)(81, 258)(82, 275)(83, 273)(84, 274)(85, 277)(86, 262)(87, 265)(88, 263)(89, 268)(90, 281)(91, 246)(92, 267)(93, 247)(94, 270)(95, 272)(96, 271)(97, 286)(98, 276)(99, 278)(100, 280)(101, 279)(102, 250)(103, 282)(104, 283)(105, 285)(106, 284)(107, 287)(108, 288)(109, 290)(110, 289)(111, 291)(112, 292)(113, 321)(114, 294)(115, 348)(116, 293)(117, 313)(118, 295)(119, 346)(120, 296)(121, 332)(122, 308)(123, 344)(124, 314)(125, 315)(126, 318)(127, 350)(128, 306)(129, 334)(130, 304)(131, 325)(132, 328)(133, 327)(134, 331)(135, 329)(136, 310)(137, 309)(138, 337)(139, 360)(140, 312)(141, 340)(142, 320)(143, 319)(144, 322)(145, 342)(146, 316)(147, 349)(148, 323)(149, 345)(150, 305)(151, 347)(152, 317)(153, 352)(154, 367)(155, 324)(156, 355)(157, 330)(158, 357)(159, 326)(160, 311)(161, 335)(162, 307)(163, 359)(164, 336)(165, 298)(166, 338)(167, 333)(168, 300)(169, 365)(170, 339)(171, 364)(172, 343)(173, 363)(174, 341)(175, 366)(176, 353)(177, 351)(178, 356)(179, 354)(180, 368)(181, 358)(182, 302)(183, 362)(184, 361) local type(s) :: { ( 4, 92, 4, 92 ) } Outer automorphisms :: reflexible Dual of E23.1178 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 92 e = 184 f = 48 degree seq :: [ 4^92 ] E23.1183 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 92}) Quotient :: dipole Aut^+ = C4 x D46 (small group id <184, 4>) Aut = D8 x D46 (small group id <368, 31>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, Y2^4, (R * Y2 * Y3^-1)^2, (Y2^-1 * Y1 * Y2^-1)^2, (Y2^-1 * R * Y2^-1)^2, Y2^-1 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1, (Y3 * Y2^-1)^92 ] Map:: R = (1, 185, 2, 186)(3, 187, 7, 191)(4, 188, 9, 193)(5, 189, 10, 194)(6, 190, 12, 196)(8, 192, 11, 195)(13, 197, 17, 201)(14, 198, 18, 202)(15, 199, 19, 203)(16, 200, 20, 204)(21, 205, 25, 209)(22, 206, 26, 210)(23, 207, 27, 211)(24, 208, 28, 212)(29, 213, 33, 217)(30, 214, 34, 218)(31, 215, 35, 219)(32, 216, 36, 220)(37, 221, 65, 249)(38, 222, 67, 251)(39, 223, 69, 253)(40, 224, 73, 257)(41, 225, 77, 261)(42, 226, 80, 264)(43, 227, 82, 266)(44, 228, 85, 269)(45, 229, 70, 254)(46, 230, 83, 267)(47, 231, 72, 256)(48, 232, 74, 258)(49, 233, 78, 262)(50, 234, 76, 260)(51, 235, 95, 279)(52, 236, 97, 281)(53, 237, 99, 283)(54, 238, 101, 285)(55, 239, 87, 271)(56, 240, 89, 273)(57, 241, 105, 289)(58, 242, 107, 291)(59, 243, 109, 293)(60, 244, 111, 295)(61, 245, 113, 297)(62, 246, 115, 299)(63, 247, 117, 301)(64, 248, 119, 303)(66, 250, 122, 306)(68, 252, 121, 305)(71, 255, 127, 311)(75, 259, 132, 316)(79, 263, 136, 320)(81, 265, 135, 319)(84, 268, 140, 324)(86, 270, 139, 323)(88, 272, 128, 312)(90, 274, 125, 309)(91, 275, 126, 310)(92, 276, 133, 317)(93, 277, 130, 314)(94, 278, 131, 315)(96, 280, 152, 336)(98, 282, 151, 335)(100, 284, 156, 340)(102, 286, 155, 339)(103, 287, 144, 328)(104, 288, 143, 327)(106, 290, 162, 346)(108, 292, 161, 345)(110, 294, 166, 350)(112, 296, 165, 349)(114, 298, 170, 354)(116, 300, 169, 353)(118, 302, 174, 358)(120, 304, 173, 357)(123, 307, 177, 361)(124, 308, 178, 362)(129, 313, 171, 355)(134, 318, 175, 359)(137, 321, 168, 352)(138, 322, 167, 351)(141, 325, 164, 348)(142, 326, 163, 347)(145, 329, 179, 363)(146, 330, 172, 356)(147, 331, 180, 364)(148, 332, 181, 365)(149, 333, 176, 360)(150, 334, 182, 366)(153, 337, 157, 341)(154, 338, 158, 342)(159, 343, 183, 367)(160, 344, 184, 368)(369, 553, 371, 555, 376, 560, 372, 556)(370, 554, 373, 557, 379, 563, 374, 558)(375, 559, 381, 565, 377, 561, 382, 566)(378, 562, 383, 567, 380, 564, 384, 568)(385, 569, 389, 573, 386, 570, 390, 574)(387, 571, 391, 575, 388, 572, 392, 576)(393, 577, 397, 581, 394, 578, 398, 582)(395, 579, 399, 583, 396, 580, 400, 584)(401, 585, 405, 589, 402, 586, 406, 590)(403, 587, 423, 607, 404, 588, 424, 608)(407, 591, 438, 622, 414, 598, 440, 624)(408, 592, 442, 626, 417, 601, 444, 628)(409, 593, 446, 630, 410, 594, 441, 625)(411, 595, 451, 635, 412, 596, 437, 621)(413, 597, 455, 639, 415, 599, 457, 641)(416, 600, 433, 617, 418, 602, 435, 619)(419, 603, 448, 632, 420, 604, 445, 629)(421, 605, 453, 637, 422, 606, 450, 634)(425, 609, 465, 649, 426, 610, 463, 647)(427, 611, 469, 653, 428, 612, 467, 651)(429, 613, 475, 659, 430, 614, 473, 657)(431, 615, 479, 663, 432, 616, 477, 661)(434, 618, 483, 667, 436, 620, 481, 665)(439, 623, 496, 680, 458, 642, 494, 678)(443, 627, 501, 685, 461, 645, 499, 683)(447, 631, 498, 682, 449, 633, 500, 684)(452, 636, 493, 677, 454, 638, 495, 679)(456, 640, 512, 696, 459, 643, 511, 695)(460, 644, 490, 674, 462, 646, 489, 673)(464, 648, 503, 687, 466, 650, 504, 688)(468, 652, 507, 691, 470, 654, 508, 692)(471, 655, 487, 671, 472, 656, 485, 669)(474, 658, 519, 703, 476, 660, 520, 704)(478, 662, 523, 707, 480, 664, 524, 708)(482, 666, 529, 713, 484, 668, 530, 714)(486, 670, 533, 717, 488, 672, 534, 718)(491, 675, 537, 721, 492, 676, 538, 722)(497, 681, 547, 731, 514, 698, 548, 732)(502, 686, 549, 733, 517, 701, 550, 734)(505, 689, 544, 728, 506, 690, 543, 727)(509, 693, 540, 724, 510, 694, 539, 723)(513, 697, 551, 735, 515, 699, 552, 736)(516, 700, 545, 729, 518, 702, 546, 730)(521, 705, 535, 719, 522, 706, 536, 720)(525, 709, 531, 715, 526, 710, 532, 716)(527, 711, 541, 725, 528, 712, 542, 726) L = (1, 370)(2, 369)(3, 375)(4, 377)(5, 378)(6, 380)(7, 371)(8, 379)(9, 372)(10, 373)(11, 376)(12, 374)(13, 385)(14, 386)(15, 387)(16, 388)(17, 381)(18, 382)(19, 383)(20, 384)(21, 393)(22, 394)(23, 395)(24, 396)(25, 389)(26, 390)(27, 391)(28, 392)(29, 401)(30, 402)(31, 403)(32, 404)(33, 397)(34, 398)(35, 399)(36, 400)(37, 433)(38, 435)(39, 437)(40, 441)(41, 445)(42, 448)(43, 450)(44, 453)(45, 438)(46, 451)(47, 440)(48, 442)(49, 446)(50, 444)(51, 463)(52, 465)(53, 467)(54, 469)(55, 455)(56, 457)(57, 473)(58, 475)(59, 477)(60, 479)(61, 481)(62, 483)(63, 485)(64, 487)(65, 405)(66, 490)(67, 406)(68, 489)(69, 407)(70, 413)(71, 495)(72, 415)(73, 408)(74, 416)(75, 500)(76, 418)(77, 409)(78, 417)(79, 504)(80, 410)(81, 503)(82, 411)(83, 414)(84, 508)(85, 412)(86, 507)(87, 423)(88, 496)(89, 424)(90, 493)(91, 494)(92, 501)(93, 498)(94, 499)(95, 419)(96, 520)(97, 420)(98, 519)(99, 421)(100, 524)(101, 422)(102, 523)(103, 512)(104, 511)(105, 425)(106, 530)(107, 426)(108, 529)(109, 427)(110, 534)(111, 428)(112, 533)(113, 429)(114, 538)(115, 430)(116, 537)(117, 431)(118, 542)(119, 432)(120, 541)(121, 436)(122, 434)(123, 545)(124, 546)(125, 458)(126, 459)(127, 439)(128, 456)(129, 539)(130, 461)(131, 462)(132, 443)(133, 460)(134, 543)(135, 449)(136, 447)(137, 536)(138, 535)(139, 454)(140, 452)(141, 532)(142, 531)(143, 472)(144, 471)(145, 547)(146, 540)(147, 548)(148, 549)(149, 544)(150, 550)(151, 466)(152, 464)(153, 525)(154, 526)(155, 470)(156, 468)(157, 521)(158, 522)(159, 551)(160, 552)(161, 476)(162, 474)(163, 510)(164, 509)(165, 480)(166, 478)(167, 506)(168, 505)(169, 484)(170, 482)(171, 497)(172, 514)(173, 488)(174, 486)(175, 502)(176, 517)(177, 491)(178, 492)(179, 513)(180, 515)(181, 516)(182, 518)(183, 527)(184, 528)(185, 553)(186, 554)(187, 555)(188, 556)(189, 557)(190, 558)(191, 559)(192, 560)(193, 561)(194, 562)(195, 563)(196, 564)(197, 565)(198, 566)(199, 567)(200, 568)(201, 569)(202, 570)(203, 571)(204, 572)(205, 573)(206, 574)(207, 575)(208, 576)(209, 577)(210, 578)(211, 579)(212, 580)(213, 581)(214, 582)(215, 583)(216, 584)(217, 585)(218, 586)(219, 587)(220, 588)(221, 589)(222, 590)(223, 591)(224, 592)(225, 593)(226, 594)(227, 595)(228, 596)(229, 597)(230, 598)(231, 599)(232, 600)(233, 601)(234, 602)(235, 603)(236, 604)(237, 605)(238, 606)(239, 607)(240, 608)(241, 609)(242, 610)(243, 611)(244, 612)(245, 613)(246, 614)(247, 615)(248, 616)(249, 617)(250, 618)(251, 619)(252, 620)(253, 621)(254, 622)(255, 623)(256, 624)(257, 625)(258, 626)(259, 627)(260, 628)(261, 629)(262, 630)(263, 631)(264, 632)(265, 633)(266, 634)(267, 635)(268, 636)(269, 637)(270, 638)(271, 639)(272, 640)(273, 641)(274, 642)(275, 643)(276, 644)(277, 645)(278, 646)(279, 647)(280, 648)(281, 649)(282, 650)(283, 651)(284, 652)(285, 653)(286, 654)(287, 655)(288, 656)(289, 657)(290, 658)(291, 659)(292, 660)(293, 661)(294, 662)(295, 663)(296, 664)(297, 665)(298, 666)(299, 667)(300, 668)(301, 669)(302, 670)(303, 671)(304, 672)(305, 673)(306, 674)(307, 675)(308, 676)(309, 677)(310, 678)(311, 679)(312, 680)(313, 681)(314, 682)(315, 683)(316, 684)(317, 685)(318, 686)(319, 687)(320, 688)(321, 689)(322, 690)(323, 691)(324, 692)(325, 693)(326, 694)(327, 695)(328, 696)(329, 697)(330, 698)(331, 699)(332, 700)(333, 701)(334, 702)(335, 703)(336, 704)(337, 705)(338, 706)(339, 707)(340, 708)(341, 709)(342, 710)(343, 711)(344, 712)(345, 713)(346, 714)(347, 715)(348, 716)(349, 717)(350, 718)(351, 719)(352, 720)(353, 721)(354, 722)(355, 723)(356, 724)(357, 725)(358, 726)(359, 727)(360, 728)(361, 729)(362, 730)(363, 731)(364, 732)(365, 733)(366, 734)(367, 735)(368, 736) local type(s) :: { ( 2, 184, 2, 184 ), ( 2, 184, 2, 184, 2, 184, 2, 184 ) } Outer automorphisms :: reflexible Dual of E23.1186 Graph:: bipartite v = 138 e = 368 f = 186 degree seq :: [ 4^92, 8^46 ] E23.1184 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 92}) Quotient :: dipole Aut^+ = C4 x D46 (small group id <184, 4>) Aut = D8 x D46 (small group id <368, 31>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y2 * Y1)^2, (Y2 * Y1^-1)^2, (Y3^-1 * Y1^-1)^2, Y1^4, Y2^45 * Y1 * Y2^-1 * Y1^-1 ] Map:: R = (1, 185, 2, 186, 6, 190, 4, 188)(3, 187, 9, 193, 13, 197, 8, 192)(5, 189, 11, 195, 14, 198, 7, 191)(10, 194, 16, 200, 21, 205, 17, 201)(12, 196, 15, 199, 22, 206, 19, 203)(18, 202, 25, 209, 29, 213, 24, 208)(20, 204, 27, 211, 30, 214, 23, 207)(26, 210, 32, 216, 37, 221, 33, 217)(28, 212, 31, 215, 38, 222, 35, 219)(34, 218, 41, 225, 45, 229, 40, 224)(36, 220, 43, 227, 46, 230, 39, 223)(42, 226, 48, 232, 53, 237, 49, 233)(44, 228, 47, 231, 54, 238, 51, 235)(50, 234, 57, 241, 61, 245, 56, 240)(52, 236, 59, 243, 62, 246, 55, 239)(58, 242, 64, 248, 101, 285, 65, 249)(60, 244, 63, 247, 74, 258, 67, 251)(66, 250, 72, 256, 109, 293, 69, 253)(68, 252, 107, 291, 70, 254, 103, 287)(71, 255, 105, 289, 77, 261, 110, 294)(73, 257, 111, 295, 76, 260, 112, 296)(75, 259, 113, 297, 81, 265, 114, 298)(78, 262, 115, 299, 80, 264, 116, 300)(79, 263, 117, 301, 85, 269, 118, 302)(82, 266, 119, 303, 84, 268, 120, 304)(83, 267, 121, 305, 89, 273, 122, 306)(86, 270, 123, 307, 88, 272, 124, 308)(87, 271, 125, 309, 93, 277, 126, 310)(90, 274, 127, 311, 92, 276, 128, 312)(91, 275, 129, 313, 97, 281, 130, 314)(94, 278, 131, 315, 96, 280, 132, 316)(95, 279, 133, 317, 102, 286, 134, 318)(98, 282, 136, 320, 100, 284, 137, 321)(99, 283, 138, 322, 135, 319, 139, 323)(104, 288, 142, 326, 108, 292, 143, 327)(106, 290, 146, 330, 140, 324, 147, 331)(141, 325, 177, 361, 144, 328, 178, 362)(145, 329, 181, 365, 148, 332, 182, 366)(149, 333, 184, 368, 150, 334, 183, 367)(151, 335, 180, 364, 152, 336, 179, 363)(153, 337, 175, 359, 154, 338, 176, 360)(155, 339, 173, 357, 156, 340, 174, 358)(157, 341, 172, 356, 158, 342, 171, 355)(159, 343, 170, 354, 160, 344, 169, 353)(161, 345, 167, 351, 162, 346, 168, 352)(163, 347, 165, 349, 164, 348, 166, 350)(369, 553, 371, 555, 378, 562, 386, 570, 394, 578, 402, 586, 410, 594, 418, 602, 426, 610, 434, 618, 473, 657, 481, 665, 485, 669, 489, 673, 493, 677, 497, 681, 501, 685, 506, 690, 514, 698, 549, 733, 548, 732, 541, 725, 538, 722, 533, 717, 530, 714, 525, 709, 522, 706, 517, 701, 512, 696, 472, 656, 468, 652, 462, 646, 460, 644, 454, 638, 452, 636, 446, 630, 444, 628, 438, 622, 442, 626, 430, 614, 422, 606, 414, 598, 406, 590, 398, 582, 390, 574, 382, 566, 374, 558, 381, 565, 389, 573, 397, 581, 405, 589, 413, 597, 421, 605, 429, 613, 469, 653, 477, 661, 478, 662, 482, 666, 486, 670, 490, 674, 494, 678, 498, 682, 502, 686, 507, 691, 515, 699, 550, 734, 547, 731, 542, 726, 537, 721, 534, 718, 529, 713, 526, 710, 521, 705, 518, 702, 509, 693, 476, 660, 466, 650, 464, 648, 458, 642, 456, 640, 450, 634, 448, 632, 441, 625, 436, 620, 428, 612, 420, 604, 412, 596, 404, 588, 396, 580, 388, 572, 380, 564, 373, 557)(370, 554, 375, 559, 383, 567, 391, 575, 399, 583, 407, 591, 415, 599, 423, 607, 431, 615, 471, 655, 479, 663, 483, 667, 487, 671, 491, 675, 495, 679, 499, 683, 504, 688, 510, 694, 545, 729, 552, 736, 543, 727, 540, 724, 535, 719, 532, 716, 527, 711, 524, 708, 519, 703, 516, 700, 474, 658, 503, 687, 463, 647, 465, 649, 455, 639, 457, 641, 447, 631, 449, 633, 439, 623, 440, 624, 433, 617, 425, 609, 417, 601, 409, 593, 401, 585, 393, 577, 385, 569, 377, 561, 372, 556, 379, 563, 387, 571, 395, 579, 403, 587, 411, 595, 419, 603, 427, 611, 435, 619, 475, 659, 480, 664, 484, 668, 488, 672, 492, 676, 496, 680, 500, 684, 505, 689, 511, 695, 546, 730, 551, 735, 544, 728, 539, 723, 536, 720, 531, 715, 528, 712, 523, 707, 520, 704, 513, 697, 508, 692, 467, 651, 470, 654, 459, 643, 461, 645, 451, 635, 453, 637, 443, 627, 445, 629, 437, 621, 432, 616, 424, 608, 416, 600, 408, 592, 400, 584, 392, 576, 384, 568, 376, 560) L = (1, 371)(2, 375)(3, 378)(4, 379)(5, 369)(6, 381)(7, 383)(8, 370)(9, 372)(10, 386)(11, 387)(12, 373)(13, 389)(14, 374)(15, 391)(16, 376)(17, 377)(18, 394)(19, 395)(20, 380)(21, 397)(22, 382)(23, 399)(24, 384)(25, 385)(26, 402)(27, 403)(28, 388)(29, 405)(30, 390)(31, 407)(32, 392)(33, 393)(34, 410)(35, 411)(36, 396)(37, 413)(38, 398)(39, 415)(40, 400)(41, 401)(42, 418)(43, 419)(44, 404)(45, 421)(46, 406)(47, 423)(48, 408)(49, 409)(50, 426)(51, 427)(52, 412)(53, 429)(54, 414)(55, 431)(56, 416)(57, 417)(58, 434)(59, 435)(60, 420)(61, 469)(62, 422)(63, 471)(64, 424)(65, 425)(66, 473)(67, 475)(68, 428)(69, 432)(70, 442)(71, 440)(72, 433)(73, 436)(74, 430)(75, 445)(76, 438)(77, 437)(78, 444)(79, 449)(80, 441)(81, 439)(82, 448)(83, 453)(84, 446)(85, 443)(86, 452)(87, 457)(88, 450)(89, 447)(90, 456)(91, 461)(92, 454)(93, 451)(94, 460)(95, 465)(96, 458)(97, 455)(98, 464)(99, 470)(100, 462)(101, 477)(102, 459)(103, 479)(104, 468)(105, 481)(106, 503)(107, 480)(108, 466)(109, 478)(110, 482)(111, 483)(112, 484)(113, 485)(114, 486)(115, 487)(116, 488)(117, 489)(118, 490)(119, 491)(120, 492)(121, 493)(122, 494)(123, 495)(124, 496)(125, 497)(126, 498)(127, 499)(128, 500)(129, 501)(130, 502)(131, 504)(132, 505)(133, 506)(134, 507)(135, 463)(136, 510)(137, 511)(138, 514)(139, 515)(140, 467)(141, 476)(142, 545)(143, 546)(144, 472)(145, 508)(146, 549)(147, 550)(148, 474)(149, 512)(150, 509)(151, 516)(152, 513)(153, 518)(154, 517)(155, 520)(156, 519)(157, 522)(158, 521)(159, 524)(160, 523)(161, 526)(162, 525)(163, 528)(164, 527)(165, 530)(166, 529)(167, 532)(168, 531)(169, 534)(170, 533)(171, 536)(172, 535)(173, 538)(174, 537)(175, 540)(176, 539)(177, 552)(178, 551)(179, 542)(180, 541)(181, 548)(182, 547)(183, 544)(184, 543)(185, 553)(186, 554)(187, 555)(188, 556)(189, 557)(190, 558)(191, 559)(192, 560)(193, 561)(194, 562)(195, 563)(196, 564)(197, 565)(198, 566)(199, 567)(200, 568)(201, 569)(202, 570)(203, 571)(204, 572)(205, 573)(206, 574)(207, 575)(208, 576)(209, 577)(210, 578)(211, 579)(212, 580)(213, 581)(214, 582)(215, 583)(216, 584)(217, 585)(218, 586)(219, 587)(220, 588)(221, 589)(222, 590)(223, 591)(224, 592)(225, 593)(226, 594)(227, 595)(228, 596)(229, 597)(230, 598)(231, 599)(232, 600)(233, 601)(234, 602)(235, 603)(236, 604)(237, 605)(238, 606)(239, 607)(240, 608)(241, 609)(242, 610)(243, 611)(244, 612)(245, 613)(246, 614)(247, 615)(248, 616)(249, 617)(250, 618)(251, 619)(252, 620)(253, 621)(254, 622)(255, 623)(256, 624)(257, 625)(258, 626)(259, 627)(260, 628)(261, 629)(262, 630)(263, 631)(264, 632)(265, 633)(266, 634)(267, 635)(268, 636)(269, 637)(270, 638)(271, 639)(272, 640)(273, 641)(274, 642)(275, 643)(276, 644)(277, 645)(278, 646)(279, 647)(280, 648)(281, 649)(282, 650)(283, 651)(284, 652)(285, 653)(286, 654)(287, 655)(288, 656)(289, 657)(290, 658)(291, 659)(292, 660)(293, 661)(294, 662)(295, 663)(296, 664)(297, 665)(298, 666)(299, 667)(300, 668)(301, 669)(302, 670)(303, 671)(304, 672)(305, 673)(306, 674)(307, 675)(308, 676)(309, 677)(310, 678)(311, 679)(312, 680)(313, 681)(314, 682)(315, 683)(316, 684)(317, 685)(318, 686)(319, 687)(320, 688)(321, 689)(322, 690)(323, 691)(324, 692)(325, 693)(326, 694)(327, 695)(328, 696)(329, 697)(330, 698)(331, 699)(332, 700)(333, 701)(334, 702)(335, 703)(336, 704)(337, 705)(338, 706)(339, 707)(340, 708)(341, 709)(342, 710)(343, 711)(344, 712)(345, 713)(346, 714)(347, 715)(348, 716)(349, 717)(350, 718)(351, 719)(352, 720)(353, 721)(354, 722)(355, 723)(356, 724)(357, 725)(358, 726)(359, 727)(360, 728)(361, 729)(362, 730)(363, 731)(364, 732)(365, 733)(366, 734)(367, 735)(368, 736) local type(s) :: { ( 2, 4, 2, 4, 2, 4, 2, 4 ), ( 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4, 2, 4 ) } Outer automorphisms :: reflexible Dual of E23.1185 Graph:: bipartite v = 48 e = 368 f = 276 degree seq :: [ 8^46, 184^2 ] E23.1185 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 92}) Quotient :: dipole Aut^+ = C4 x D46 (small group id <184, 4>) Aut = D8 x D46 (small group id <368, 31>) |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, Y3^43 * Y2 * Y3^-1 * Y2 * Y3^2, (Y3^-1 * Y1^-1)^92 ] Map:: polytopal R = (1, 185)(2, 186)(3, 187)(4, 188)(5, 189)(6, 190)(7, 191)(8, 192)(9, 193)(10, 194)(11, 195)(12, 196)(13, 197)(14, 198)(15, 199)(16, 200)(17, 201)(18, 202)(19, 203)(20, 204)(21, 205)(22, 206)(23, 207)(24, 208)(25, 209)(26, 210)(27, 211)(28, 212)(29, 213)(30, 214)(31, 215)(32, 216)(33, 217)(34, 218)(35, 219)(36, 220)(37, 221)(38, 222)(39, 223)(40, 224)(41, 225)(42, 226)(43, 227)(44, 228)(45, 229)(46, 230)(47, 231)(48, 232)(49, 233)(50, 234)(51, 235)(52, 236)(53, 237)(54, 238)(55, 239)(56, 240)(57, 241)(58, 242)(59, 243)(60, 244)(61, 245)(62, 246)(63, 247)(64, 248)(65, 249)(66, 250)(67, 251)(68, 252)(69, 253)(70, 254)(71, 255)(72, 256)(73, 257)(74, 258)(75, 259)(76, 260)(77, 261)(78, 262)(79, 263)(80, 264)(81, 265)(82, 266)(83, 267)(84, 268)(85, 269)(86, 270)(87, 271)(88, 272)(89, 273)(90, 274)(91, 275)(92, 276)(93, 277)(94, 278)(95, 279)(96, 280)(97, 281)(98, 282)(99, 283)(100, 284)(101, 285)(102, 286)(103, 287)(104, 288)(105, 289)(106, 290)(107, 291)(108, 292)(109, 293)(110, 294)(111, 295)(112, 296)(113, 297)(114, 298)(115, 299)(116, 300)(117, 301)(118, 302)(119, 303)(120, 304)(121, 305)(122, 306)(123, 307)(124, 308)(125, 309)(126, 310)(127, 311)(128, 312)(129, 313)(130, 314)(131, 315)(132, 316)(133, 317)(134, 318)(135, 319)(136, 320)(137, 321)(138, 322)(139, 323)(140, 324)(141, 325)(142, 326)(143, 327)(144, 328)(145, 329)(146, 330)(147, 331)(148, 332)(149, 333)(150, 334)(151, 335)(152, 336)(153, 337)(154, 338)(155, 339)(156, 340)(157, 341)(158, 342)(159, 343)(160, 344)(161, 345)(162, 346)(163, 347)(164, 348)(165, 349)(166, 350)(167, 351)(168, 352)(169, 353)(170, 354)(171, 355)(172, 356)(173, 357)(174, 358)(175, 359)(176, 360)(177, 361)(178, 362)(179, 363)(180, 364)(181, 365)(182, 366)(183, 367)(184, 368)(369, 553, 370, 554)(371, 555, 375, 559)(372, 556, 377, 561)(373, 557, 379, 563)(374, 558, 381, 565)(376, 560, 382, 566)(378, 562, 380, 564)(383, 567, 388, 572)(384, 568, 391, 575)(385, 569, 393, 577)(386, 570, 389, 573)(387, 571, 395, 579)(390, 574, 397, 581)(392, 576, 399, 583)(394, 578, 400, 584)(396, 580, 398, 582)(401, 585, 407, 591)(402, 586, 409, 593)(403, 587, 405, 589)(404, 588, 411, 595)(406, 590, 413, 597)(408, 592, 415, 599)(410, 594, 416, 600)(412, 596, 414, 598)(417, 601, 423, 607)(418, 602, 425, 609)(419, 603, 421, 605)(420, 604, 427, 611)(422, 606, 429, 613)(424, 608, 431, 615)(426, 610, 432, 616)(428, 612, 430, 614)(433, 617, 471, 655)(434, 618, 437, 621)(435, 619, 441, 625)(436, 620, 475, 659)(438, 622, 469, 653)(439, 623, 473, 657)(440, 624, 477, 661)(442, 626, 478, 662)(443, 627, 479, 663)(444, 628, 480, 664)(445, 629, 481, 665)(446, 630, 482, 666)(447, 631, 483, 667)(448, 632, 484, 668)(449, 633, 485, 669)(450, 634, 486, 670)(451, 635, 487, 671)(452, 636, 488, 672)(453, 637, 489, 673)(454, 638, 490, 674)(455, 639, 491, 675)(456, 640, 492, 676)(457, 641, 493, 677)(458, 642, 494, 678)(459, 643, 495, 679)(460, 644, 496, 680)(461, 645, 497, 681)(462, 646, 498, 682)(463, 647, 499, 683)(464, 648, 501, 685)(465, 649, 502, 686)(466, 650, 503, 687)(467, 651, 504, 688)(468, 652, 506, 690)(470, 654, 509, 693)(472, 656, 510, 694)(474, 658, 513, 697)(476, 660, 514, 698)(500, 684, 539, 723)(505, 689, 544, 728)(507, 691, 545, 729)(508, 692, 546, 730)(511, 695, 549, 733)(512, 696, 550, 734)(515, 699, 551, 735)(516, 700, 552, 736)(517, 701, 548, 732)(518, 702, 547, 731)(519, 703, 543, 727)(520, 704, 542, 726)(521, 705, 540, 724)(522, 706, 541, 725)(523, 707, 537, 721)(524, 708, 538, 722)(525, 709, 536, 720)(526, 710, 535, 719)(527, 711, 534, 718)(528, 712, 533, 717)(529, 713, 531, 715)(530, 714, 532, 716) L = (1, 371)(2, 373)(3, 376)(4, 369)(5, 380)(6, 370)(7, 383)(8, 385)(9, 386)(10, 372)(11, 388)(12, 390)(13, 391)(14, 374)(15, 377)(16, 375)(17, 394)(18, 395)(19, 378)(20, 381)(21, 379)(22, 398)(23, 399)(24, 382)(25, 384)(26, 402)(27, 403)(28, 387)(29, 389)(30, 406)(31, 407)(32, 392)(33, 393)(34, 410)(35, 411)(36, 396)(37, 397)(38, 414)(39, 415)(40, 400)(41, 401)(42, 418)(43, 419)(44, 404)(45, 405)(46, 422)(47, 423)(48, 408)(49, 409)(50, 426)(51, 427)(52, 412)(53, 413)(54, 430)(55, 431)(56, 416)(57, 417)(58, 434)(59, 435)(60, 420)(61, 421)(62, 469)(63, 471)(64, 424)(65, 425)(66, 473)(67, 475)(68, 428)(69, 433)(70, 441)(71, 448)(72, 436)(73, 429)(74, 445)(75, 438)(76, 443)(77, 437)(78, 450)(79, 440)(80, 432)(81, 447)(82, 439)(83, 454)(84, 444)(85, 452)(86, 442)(87, 458)(88, 449)(89, 456)(90, 446)(91, 462)(92, 453)(93, 460)(94, 451)(95, 466)(96, 457)(97, 464)(98, 455)(99, 472)(100, 461)(101, 477)(102, 468)(103, 484)(104, 459)(105, 478)(106, 500)(107, 479)(108, 465)(109, 480)(110, 482)(111, 483)(112, 485)(113, 486)(114, 487)(115, 488)(116, 481)(117, 489)(118, 490)(119, 491)(120, 492)(121, 493)(122, 494)(123, 495)(124, 496)(125, 497)(126, 498)(127, 499)(128, 501)(129, 502)(130, 503)(131, 504)(132, 463)(133, 506)(134, 509)(135, 510)(136, 513)(137, 467)(138, 514)(139, 476)(140, 470)(141, 545)(142, 539)(143, 505)(144, 474)(145, 549)(146, 546)(147, 508)(148, 507)(149, 512)(150, 511)(151, 516)(152, 515)(153, 518)(154, 517)(155, 520)(156, 519)(157, 522)(158, 521)(159, 524)(160, 523)(161, 526)(162, 525)(163, 528)(164, 527)(165, 530)(166, 529)(167, 532)(168, 531)(169, 534)(170, 533)(171, 544)(172, 536)(173, 535)(174, 538)(175, 537)(176, 550)(177, 551)(178, 552)(179, 541)(180, 540)(181, 548)(182, 547)(183, 543)(184, 542)(185, 553)(186, 554)(187, 555)(188, 556)(189, 557)(190, 558)(191, 559)(192, 560)(193, 561)(194, 562)(195, 563)(196, 564)(197, 565)(198, 566)(199, 567)(200, 568)(201, 569)(202, 570)(203, 571)(204, 572)(205, 573)(206, 574)(207, 575)(208, 576)(209, 577)(210, 578)(211, 579)(212, 580)(213, 581)(214, 582)(215, 583)(216, 584)(217, 585)(218, 586)(219, 587)(220, 588)(221, 589)(222, 590)(223, 591)(224, 592)(225, 593)(226, 594)(227, 595)(228, 596)(229, 597)(230, 598)(231, 599)(232, 600)(233, 601)(234, 602)(235, 603)(236, 604)(237, 605)(238, 606)(239, 607)(240, 608)(241, 609)(242, 610)(243, 611)(244, 612)(245, 613)(246, 614)(247, 615)(248, 616)(249, 617)(250, 618)(251, 619)(252, 620)(253, 621)(254, 622)(255, 623)(256, 624)(257, 625)(258, 626)(259, 627)(260, 628)(261, 629)(262, 630)(263, 631)(264, 632)(265, 633)(266, 634)(267, 635)(268, 636)(269, 637)(270, 638)(271, 639)(272, 640)(273, 641)(274, 642)(275, 643)(276, 644)(277, 645)(278, 646)(279, 647)(280, 648)(281, 649)(282, 650)(283, 651)(284, 652)(285, 653)(286, 654)(287, 655)(288, 656)(289, 657)(290, 658)(291, 659)(292, 660)(293, 661)(294, 662)(295, 663)(296, 664)(297, 665)(298, 666)(299, 667)(300, 668)(301, 669)(302, 670)(303, 671)(304, 672)(305, 673)(306, 674)(307, 675)(308, 676)(309, 677)(310, 678)(311, 679)(312, 680)(313, 681)(314, 682)(315, 683)(316, 684)(317, 685)(318, 686)(319, 687)(320, 688)(321, 689)(322, 690)(323, 691)(324, 692)(325, 693)(326, 694)(327, 695)(328, 696)(329, 697)(330, 698)(331, 699)(332, 700)(333, 701)(334, 702)(335, 703)(336, 704)(337, 705)(338, 706)(339, 707)(340, 708)(341, 709)(342, 710)(343, 711)(344, 712)(345, 713)(346, 714)(347, 715)(348, 716)(349, 717)(350, 718)(351, 719)(352, 720)(353, 721)(354, 722)(355, 723)(356, 724)(357, 725)(358, 726)(359, 727)(360, 728)(361, 729)(362, 730)(363, 731)(364, 732)(365, 733)(366, 734)(367, 735)(368, 736) local type(s) :: { ( 8, 184 ), ( 8, 184, 8, 184 ) } Outer automorphisms :: reflexible Dual of E23.1184 Graph:: simple bipartite v = 276 e = 368 f = 48 degree seq :: [ 2^184, 4^92 ] E23.1186 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 92}) Quotient :: dipole Aut^+ = C4 x D46 (small group id <184, 4>) Aut = D8 x D46 (small group id <368, 31>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, (R * Y2 * Y3)^2, (Y3 * Y1^-2)^2, (Y3 * Y1)^4, Y1^-2 * Y3 * Y1^21 * Y3 * Y1^-23 ] Map:: R = (1, 185, 2, 186, 5, 189, 11, 195, 20, 204, 29, 213, 37, 221, 45, 229, 53, 237, 61, 245, 78, 262, 74, 258, 79, 263, 85, 269, 90, 274, 94, 278, 98, 282, 102, 286, 107, 291, 149, 333, 154, 338, 156, 340, 159, 343, 164, 348, 169, 353, 173, 357, 177, 361, 153, 337, 146, 330, 141, 325, 136, 320, 132, 316, 128, 312, 123, 307, 118, 302, 114, 298, 111, 295, 112, 296, 109, 293, 66, 250, 58, 242, 50, 234, 42, 226, 34, 218, 26, 210, 16, 200, 23, 207, 17, 201, 24, 208, 32, 216, 40, 224, 48, 232, 56, 240, 64, 248, 80, 264, 75, 259, 71, 255, 73, 257, 77, 261, 84, 268, 89, 273, 93, 277, 97, 281, 101, 285, 106, 290, 147, 331, 160, 344, 157, 341, 161, 345, 165, 349, 170, 354, 174, 358, 178, 362, 182, 366, 180, 364, 151, 335, 144, 328, 139, 323, 135, 319, 131, 315, 127, 311, 122, 306, 126, 310, 68, 252, 60, 244, 52, 236, 44, 228, 36, 220, 28, 212, 19, 203, 10, 194, 4, 188)(3, 187, 7, 191, 15, 199, 25, 209, 33, 217, 41, 225, 49, 233, 57, 241, 65, 249, 70, 254, 86, 270, 72, 256, 87, 271, 83, 267, 95, 279, 92, 276, 103, 287, 100, 284, 140, 324, 110, 294, 152, 336, 162, 346, 158, 342, 171, 355, 168, 352, 179, 363, 176, 360, 184, 368, 148, 332, 143, 327, 137, 321, 134, 318, 129, 313, 125, 309, 119, 303, 116, 300, 113, 297, 105, 289, 63, 247, 54, 238, 47, 231, 38, 222, 31, 215, 21, 205, 14, 198, 6, 190, 13, 197, 9, 193, 18, 202, 27, 211, 35, 219, 43, 227, 51, 235, 59, 243, 67, 251, 82, 266, 69, 253, 81, 265, 76, 260, 91, 275, 88, 272, 99, 283, 96, 280, 108, 292, 104, 288, 145, 329, 166, 350, 155, 339, 167, 351, 163, 347, 175, 359, 172, 356, 183, 367, 181, 365, 150, 334, 142, 326, 138, 322, 133, 317, 130, 314, 124, 308, 121, 305, 115, 299, 120, 304, 117, 301, 62, 246, 55, 239, 46, 230, 39, 223, 30, 214, 22, 206, 12, 196, 8, 192)(369, 553)(370, 554)(371, 555)(372, 556)(373, 557)(374, 558)(375, 559)(376, 560)(377, 561)(378, 562)(379, 563)(380, 564)(381, 565)(382, 566)(383, 567)(384, 568)(385, 569)(386, 570)(387, 571)(388, 572)(389, 573)(390, 574)(391, 575)(392, 576)(393, 577)(394, 578)(395, 579)(396, 580)(397, 581)(398, 582)(399, 583)(400, 584)(401, 585)(402, 586)(403, 587)(404, 588)(405, 589)(406, 590)(407, 591)(408, 592)(409, 593)(410, 594)(411, 595)(412, 596)(413, 597)(414, 598)(415, 599)(416, 600)(417, 601)(418, 602)(419, 603)(420, 604)(421, 605)(422, 606)(423, 607)(424, 608)(425, 609)(426, 610)(427, 611)(428, 612)(429, 613)(430, 614)(431, 615)(432, 616)(433, 617)(434, 618)(435, 619)(436, 620)(437, 621)(438, 622)(439, 623)(440, 624)(441, 625)(442, 626)(443, 627)(444, 628)(445, 629)(446, 630)(447, 631)(448, 632)(449, 633)(450, 634)(451, 635)(452, 636)(453, 637)(454, 638)(455, 639)(456, 640)(457, 641)(458, 642)(459, 643)(460, 644)(461, 645)(462, 646)(463, 647)(464, 648)(465, 649)(466, 650)(467, 651)(468, 652)(469, 653)(470, 654)(471, 655)(472, 656)(473, 657)(474, 658)(475, 659)(476, 660)(477, 661)(478, 662)(479, 663)(480, 664)(481, 665)(482, 666)(483, 667)(484, 668)(485, 669)(486, 670)(487, 671)(488, 672)(489, 673)(490, 674)(491, 675)(492, 676)(493, 677)(494, 678)(495, 679)(496, 680)(497, 681)(498, 682)(499, 683)(500, 684)(501, 685)(502, 686)(503, 687)(504, 688)(505, 689)(506, 690)(507, 691)(508, 692)(509, 693)(510, 694)(511, 695)(512, 696)(513, 697)(514, 698)(515, 699)(516, 700)(517, 701)(518, 702)(519, 703)(520, 704)(521, 705)(522, 706)(523, 707)(524, 708)(525, 709)(526, 710)(527, 711)(528, 712)(529, 713)(530, 714)(531, 715)(532, 716)(533, 717)(534, 718)(535, 719)(536, 720)(537, 721)(538, 722)(539, 723)(540, 724)(541, 725)(542, 726)(543, 727)(544, 728)(545, 729)(546, 730)(547, 731)(548, 732)(549, 733)(550, 734)(551, 735)(552, 736) L = (1, 371)(2, 374)(3, 369)(4, 377)(5, 380)(6, 370)(7, 384)(8, 385)(9, 372)(10, 383)(11, 389)(12, 373)(13, 391)(14, 392)(15, 378)(16, 375)(17, 376)(18, 394)(19, 395)(20, 398)(21, 379)(22, 400)(23, 381)(24, 382)(25, 402)(26, 386)(27, 387)(28, 401)(29, 406)(30, 388)(31, 408)(32, 390)(33, 396)(34, 393)(35, 410)(36, 411)(37, 414)(38, 397)(39, 416)(40, 399)(41, 418)(42, 403)(43, 404)(44, 417)(45, 422)(46, 405)(47, 424)(48, 407)(49, 412)(50, 409)(51, 426)(52, 427)(53, 430)(54, 413)(55, 432)(56, 415)(57, 434)(58, 419)(59, 420)(60, 433)(61, 473)(62, 421)(63, 448)(64, 423)(65, 428)(66, 425)(67, 477)(68, 450)(69, 479)(70, 480)(71, 481)(72, 482)(73, 483)(74, 484)(75, 485)(76, 486)(77, 487)(78, 488)(79, 489)(80, 431)(81, 490)(82, 436)(83, 491)(84, 492)(85, 493)(86, 494)(87, 495)(88, 496)(89, 497)(90, 498)(91, 499)(92, 500)(93, 501)(94, 502)(95, 503)(96, 504)(97, 505)(98, 506)(99, 507)(100, 509)(101, 510)(102, 511)(103, 512)(104, 514)(105, 429)(106, 516)(107, 518)(108, 519)(109, 435)(110, 521)(111, 437)(112, 438)(113, 439)(114, 440)(115, 441)(116, 442)(117, 443)(118, 444)(119, 445)(120, 446)(121, 447)(122, 449)(123, 451)(124, 452)(125, 453)(126, 454)(127, 455)(128, 456)(129, 457)(130, 458)(131, 459)(132, 460)(133, 461)(134, 462)(135, 463)(136, 464)(137, 465)(138, 466)(139, 467)(140, 548)(141, 468)(142, 469)(143, 470)(144, 471)(145, 550)(146, 472)(147, 549)(148, 474)(149, 552)(150, 475)(151, 476)(152, 546)(153, 478)(154, 551)(155, 542)(156, 547)(157, 540)(158, 538)(159, 543)(160, 544)(161, 536)(162, 541)(163, 533)(164, 539)(165, 531)(166, 545)(167, 537)(168, 529)(169, 535)(170, 526)(171, 532)(172, 525)(173, 530)(174, 523)(175, 527)(176, 528)(177, 534)(178, 520)(179, 524)(180, 508)(181, 515)(182, 513)(183, 522)(184, 517)(185, 553)(186, 554)(187, 555)(188, 556)(189, 557)(190, 558)(191, 559)(192, 560)(193, 561)(194, 562)(195, 563)(196, 564)(197, 565)(198, 566)(199, 567)(200, 568)(201, 569)(202, 570)(203, 571)(204, 572)(205, 573)(206, 574)(207, 575)(208, 576)(209, 577)(210, 578)(211, 579)(212, 580)(213, 581)(214, 582)(215, 583)(216, 584)(217, 585)(218, 586)(219, 587)(220, 588)(221, 589)(222, 590)(223, 591)(224, 592)(225, 593)(226, 594)(227, 595)(228, 596)(229, 597)(230, 598)(231, 599)(232, 600)(233, 601)(234, 602)(235, 603)(236, 604)(237, 605)(238, 606)(239, 607)(240, 608)(241, 609)(242, 610)(243, 611)(244, 612)(245, 613)(246, 614)(247, 615)(248, 616)(249, 617)(250, 618)(251, 619)(252, 620)(253, 621)(254, 622)(255, 623)(256, 624)(257, 625)(258, 626)(259, 627)(260, 628)(261, 629)(262, 630)(263, 631)(264, 632)(265, 633)(266, 634)(267, 635)(268, 636)(269, 637)(270, 638)(271, 639)(272, 640)(273, 641)(274, 642)(275, 643)(276, 644)(277, 645)(278, 646)(279, 647)(280, 648)(281, 649)(282, 650)(283, 651)(284, 652)(285, 653)(286, 654)(287, 655)(288, 656)(289, 657)(290, 658)(291, 659)(292, 660)(293, 661)(294, 662)(295, 663)(296, 664)(297, 665)(298, 666)(299, 667)(300, 668)(301, 669)(302, 670)(303, 671)(304, 672)(305, 673)(306, 674)(307, 675)(308, 676)(309, 677)(310, 678)(311, 679)(312, 680)(313, 681)(314, 682)(315, 683)(316, 684)(317, 685)(318, 686)(319, 687)(320, 688)(321, 689)(322, 690)(323, 691)(324, 692)(325, 693)(326, 694)(327, 695)(328, 696)(329, 697)(330, 698)(331, 699)(332, 700)(333, 701)(334, 702)(335, 703)(336, 704)(337, 705)(338, 706)(339, 707)(340, 708)(341, 709)(342, 710)(343, 711)(344, 712)(345, 713)(346, 714)(347, 715)(348, 716)(349, 717)(350, 718)(351, 719)(352, 720)(353, 721)(354, 722)(355, 723)(356, 724)(357, 725)(358, 726)(359, 727)(360, 728)(361, 729)(362, 730)(363, 731)(364, 732)(365, 733)(366, 734)(367, 735)(368, 736) local type(s) :: { ( 4, 8 ), ( 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8 ) } Outer automorphisms :: reflexible Dual of E23.1183 Graph:: simple bipartite v = 186 e = 368 f = 138 degree seq :: [ 2^184, 184^2 ] E23.1187 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 92}) Quotient :: dipole Aut^+ = C4 x D46 (small group id <184, 4>) Aut = D8 x D46 (small group id <368, 31>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y2^2 * Y1)^2, (Y3 * Y2^-1)^4, Y2^41 * Y1 * Y2^-5 * Y1 ] Map:: R = (1, 185, 2, 186)(3, 187, 7, 191)(4, 188, 9, 193)(5, 189, 11, 195)(6, 190, 13, 197)(8, 192, 14, 198)(10, 194, 12, 196)(15, 199, 20, 204)(16, 200, 23, 207)(17, 201, 25, 209)(18, 202, 21, 205)(19, 203, 27, 211)(22, 206, 29, 213)(24, 208, 31, 215)(26, 210, 32, 216)(28, 212, 30, 214)(33, 217, 39, 223)(34, 218, 41, 225)(35, 219, 37, 221)(36, 220, 43, 227)(38, 222, 45, 229)(40, 224, 47, 231)(42, 226, 48, 232)(44, 228, 46, 230)(49, 233, 55, 239)(50, 234, 57, 241)(51, 235, 53, 237)(52, 236, 59, 243)(54, 238, 61, 245)(56, 240, 63, 247)(58, 242, 64, 248)(60, 244, 62, 246)(65, 249, 74, 258)(66, 250, 104, 288)(67, 251, 105, 289)(68, 252, 69, 253)(70, 254, 107, 291)(71, 255, 108, 292)(72, 256, 109, 293)(73, 257, 110, 294)(75, 259, 111, 295)(76, 260, 112, 296)(77, 261, 113, 297)(78, 262, 114, 298)(79, 263, 115, 299)(80, 264, 116, 300)(81, 265, 117, 301)(82, 266, 118, 302)(83, 267, 119, 303)(84, 268, 120, 304)(85, 269, 121, 305)(86, 270, 122, 306)(87, 271, 123, 307)(88, 272, 124, 308)(89, 273, 125, 309)(90, 274, 126, 310)(91, 275, 127, 311)(92, 276, 128, 312)(93, 277, 129, 313)(94, 278, 130, 314)(95, 279, 131, 315)(96, 280, 132, 316)(97, 281, 134, 318)(98, 282, 135, 319)(99, 283, 136, 320)(100, 284, 137, 321)(101, 285, 139, 323)(102, 286, 140, 324)(103, 287, 142, 326)(106, 290, 144, 328)(133, 317, 171, 355)(138, 322, 176, 360)(141, 325, 180, 364)(143, 327, 178, 362)(145, 329, 184, 368)(146, 330, 182, 366)(147, 331, 181, 365)(148, 332, 183, 367)(149, 333, 179, 363)(150, 334, 177, 361)(151, 335, 175, 359)(152, 336, 174, 358)(153, 337, 172, 356)(154, 338, 173, 357)(155, 339, 169, 353)(156, 340, 170, 354)(157, 341, 168, 352)(158, 342, 167, 351)(159, 343, 166, 350)(160, 344, 165, 349)(161, 345, 163, 347)(162, 346, 164, 348)(369, 553, 371, 555, 376, 560, 385, 569, 394, 578, 402, 586, 410, 594, 418, 602, 426, 610, 434, 618, 440, 624, 446, 630, 450, 634, 455, 639, 458, 642, 463, 647, 466, 650, 471, 655, 511, 695, 516, 700, 519, 703, 524, 708, 527, 711, 532, 716, 535, 719, 541, 725, 545, 729, 552, 736, 544, 728, 539, 723, 507, 691, 502, 686, 497, 681, 493, 677, 489, 673, 485, 669, 480, 664, 484, 668, 473, 657, 429, 613, 421, 605, 413, 597, 405, 589, 397, 581, 389, 573, 379, 563, 388, 572, 381, 565, 391, 575, 399, 583, 407, 591, 415, 599, 423, 607, 431, 615, 442, 626, 438, 622, 441, 625, 445, 629, 451, 635, 454, 638, 459, 643, 462, 646, 467, 651, 470, 654, 509, 693, 515, 699, 520, 704, 523, 707, 528, 712, 531, 715, 536, 720, 540, 724, 547, 731, 550, 734, 512, 696, 505, 689, 500, 684, 496, 680, 492, 676, 488, 672, 483, 667, 479, 663, 476, 660, 436, 620, 428, 612, 420, 604, 412, 596, 404, 588, 396, 580, 387, 571, 378, 562, 372, 556)(370, 554, 373, 557, 380, 564, 390, 574, 398, 582, 406, 590, 414, 598, 422, 606, 430, 614, 448, 632, 439, 623, 449, 633, 447, 631, 457, 641, 456, 640, 465, 649, 464, 648, 501, 685, 474, 658, 513, 697, 517, 701, 522, 706, 525, 709, 530, 714, 533, 717, 538, 722, 542, 726, 551, 735, 548, 732, 510, 694, 504, 688, 499, 683, 495, 679, 491, 675, 487, 671, 482, 666, 478, 662, 472, 656, 433, 617, 425, 609, 417, 601, 409, 593, 401, 585, 393, 577, 384, 568, 375, 559, 383, 567, 377, 561, 386, 570, 395, 579, 403, 587, 411, 595, 419, 603, 427, 611, 435, 619, 437, 621, 444, 628, 443, 627, 453, 637, 452, 636, 461, 645, 460, 644, 469, 653, 468, 652, 506, 690, 514, 698, 518, 702, 521, 705, 526, 710, 529, 713, 534, 718, 537, 721, 543, 727, 549, 733, 546, 730, 508, 692, 503, 687, 498, 682, 494, 678, 490, 674, 486, 670, 481, 665, 477, 661, 475, 659, 432, 616, 424, 608, 416, 600, 408, 592, 400, 584, 392, 576, 382, 566, 374, 558) L = (1, 370)(2, 369)(3, 375)(4, 377)(5, 379)(6, 381)(7, 371)(8, 382)(9, 372)(10, 380)(11, 373)(12, 378)(13, 374)(14, 376)(15, 388)(16, 391)(17, 393)(18, 389)(19, 395)(20, 383)(21, 386)(22, 397)(23, 384)(24, 399)(25, 385)(26, 400)(27, 387)(28, 398)(29, 390)(30, 396)(31, 392)(32, 394)(33, 407)(34, 409)(35, 405)(36, 411)(37, 403)(38, 413)(39, 401)(40, 415)(41, 402)(42, 416)(43, 404)(44, 414)(45, 406)(46, 412)(47, 408)(48, 410)(49, 423)(50, 425)(51, 421)(52, 427)(53, 419)(54, 429)(55, 417)(56, 431)(57, 418)(58, 432)(59, 420)(60, 430)(61, 422)(62, 428)(63, 424)(64, 426)(65, 442)(66, 472)(67, 473)(68, 437)(69, 436)(70, 475)(71, 476)(72, 477)(73, 478)(74, 433)(75, 479)(76, 480)(77, 481)(78, 482)(79, 483)(80, 484)(81, 485)(82, 486)(83, 487)(84, 488)(85, 489)(86, 490)(87, 491)(88, 492)(89, 493)(90, 494)(91, 495)(92, 496)(93, 497)(94, 498)(95, 499)(96, 500)(97, 502)(98, 503)(99, 504)(100, 505)(101, 507)(102, 508)(103, 510)(104, 434)(105, 435)(106, 512)(107, 438)(108, 439)(109, 440)(110, 441)(111, 443)(112, 444)(113, 445)(114, 446)(115, 447)(116, 448)(117, 449)(118, 450)(119, 451)(120, 452)(121, 453)(122, 454)(123, 455)(124, 456)(125, 457)(126, 458)(127, 459)(128, 460)(129, 461)(130, 462)(131, 463)(132, 464)(133, 539)(134, 465)(135, 466)(136, 467)(137, 468)(138, 544)(139, 469)(140, 470)(141, 548)(142, 471)(143, 546)(144, 474)(145, 552)(146, 550)(147, 549)(148, 551)(149, 547)(150, 545)(151, 543)(152, 542)(153, 540)(154, 541)(155, 537)(156, 538)(157, 536)(158, 535)(159, 534)(160, 533)(161, 531)(162, 532)(163, 529)(164, 530)(165, 528)(166, 527)(167, 526)(168, 525)(169, 523)(170, 524)(171, 501)(172, 521)(173, 522)(174, 520)(175, 519)(176, 506)(177, 518)(178, 511)(179, 517)(180, 509)(181, 515)(182, 514)(183, 516)(184, 513)(185, 553)(186, 554)(187, 555)(188, 556)(189, 557)(190, 558)(191, 559)(192, 560)(193, 561)(194, 562)(195, 563)(196, 564)(197, 565)(198, 566)(199, 567)(200, 568)(201, 569)(202, 570)(203, 571)(204, 572)(205, 573)(206, 574)(207, 575)(208, 576)(209, 577)(210, 578)(211, 579)(212, 580)(213, 581)(214, 582)(215, 583)(216, 584)(217, 585)(218, 586)(219, 587)(220, 588)(221, 589)(222, 590)(223, 591)(224, 592)(225, 593)(226, 594)(227, 595)(228, 596)(229, 597)(230, 598)(231, 599)(232, 600)(233, 601)(234, 602)(235, 603)(236, 604)(237, 605)(238, 606)(239, 607)(240, 608)(241, 609)(242, 610)(243, 611)(244, 612)(245, 613)(246, 614)(247, 615)(248, 616)(249, 617)(250, 618)(251, 619)(252, 620)(253, 621)(254, 622)(255, 623)(256, 624)(257, 625)(258, 626)(259, 627)(260, 628)(261, 629)(262, 630)(263, 631)(264, 632)(265, 633)(266, 634)(267, 635)(268, 636)(269, 637)(270, 638)(271, 639)(272, 640)(273, 641)(274, 642)(275, 643)(276, 644)(277, 645)(278, 646)(279, 647)(280, 648)(281, 649)(282, 650)(283, 651)(284, 652)(285, 653)(286, 654)(287, 655)(288, 656)(289, 657)(290, 658)(291, 659)(292, 660)(293, 661)(294, 662)(295, 663)(296, 664)(297, 665)(298, 666)(299, 667)(300, 668)(301, 669)(302, 670)(303, 671)(304, 672)(305, 673)(306, 674)(307, 675)(308, 676)(309, 677)(310, 678)(311, 679)(312, 680)(313, 681)(314, 682)(315, 683)(316, 684)(317, 685)(318, 686)(319, 687)(320, 688)(321, 689)(322, 690)(323, 691)(324, 692)(325, 693)(326, 694)(327, 695)(328, 696)(329, 697)(330, 698)(331, 699)(332, 700)(333, 701)(334, 702)(335, 703)(336, 704)(337, 705)(338, 706)(339, 707)(340, 708)(341, 709)(342, 710)(343, 711)(344, 712)(345, 713)(346, 714)(347, 715)(348, 716)(349, 717)(350, 718)(351, 719)(352, 720)(353, 721)(354, 722)(355, 723)(356, 724)(357, 725)(358, 726)(359, 727)(360, 728)(361, 729)(362, 730)(363, 731)(364, 732)(365, 733)(366, 734)(367, 735)(368, 736) local type(s) :: { ( 2, 8, 2, 8 ), ( 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8, 2, 8 ) } Outer automorphisms :: reflexible Dual of E23.1188 Graph:: bipartite v = 94 e = 368 f = 230 degree seq :: [ 4^92, 184^2 ] E23.1188 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 92}) Quotient :: dipole Aut^+ = C4 x D46 (small group id <184, 4>) Aut = D8 x D46 (small group id <368, 31>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y1^-1)^2, (Y3^-1 * Y1^-1)^2, Y1^4, (R * Y2 * Y3^-1)^2, Y3^45 * Y1 * Y3^-1 * Y1^-1, (Y3 * Y2^-1)^92 ] Map:: R = (1, 185, 2, 186, 6, 190, 4, 188)(3, 187, 9, 193, 13, 197, 8, 192)(5, 189, 11, 195, 14, 198, 7, 191)(10, 194, 16, 200, 21, 205, 17, 201)(12, 196, 15, 199, 22, 206, 19, 203)(18, 202, 25, 209, 29, 213, 24, 208)(20, 204, 27, 211, 30, 214, 23, 207)(26, 210, 32, 216, 37, 221, 33, 217)(28, 212, 31, 215, 38, 222, 35, 219)(34, 218, 41, 225, 45, 229, 40, 224)(36, 220, 43, 227, 46, 230, 39, 223)(42, 226, 48, 232, 53, 237, 49, 233)(44, 228, 47, 231, 54, 238, 51, 235)(50, 234, 57, 241, 61, 245, 56, 240)(52, 236, 59, 243, 62, 246, 55, 239)(58, 242, 64, 248, 69, 253, 65, 249)(60, 244, 63, 247, 98, 282, 67, 251)(66, 250, 100, 284, 70, 254, 104, 288)(68, 252, 71, 255, 106, 290, 73, 257)(72, 256, 108, 292, 77, 261, 110, 294)(74, 258, 112, 296, 76, 260, 114, 298)(75, 259, 115, 299, 81, 265, 117, 301)(78, 262, 120, 304, 80, 264, 122, 306)(79, 263, 123, 307, 85, 269, 125, 309)(82, 266, 128, 312, 84, 268, 130, 314)(83, 267, 131, 315, 89, 273, 133, 317)(86, 270, 136, 320, 88, 272, 138, 322)(87, 271, 139, 323, 93, 277, 141, 325)(90, 274, 144, 328, 92, 276, 146, 330)(91, 275, 147, 331, 97, 281, 149, 333)(94, 278, 152, 336, 96, 280, 154, 338)(95, 279, 155, 339, 103, 287, 157, 341)(99, 283, 160, 344, 102, 286, 162, 346)(101, 285, 163, 347, 105, 289, 165, 349)(107, 291, 169, 353, 111, 295, 171, 355)(109, 293, 172, 356, 119, 303, 174, 358)(113, 297, 176, 360, 118, 302, 178, 362)(116, 300, 179, 363, 127, 311, 181, 365)(121, 305, 180, 364, 126, 310, 184, 368)(124, 308, 177, 361, 135, 319, 182, 366)(129, 313, 183, 367, 134, 318, 173, 357)(132, 316, 175, 359, 143, 327, 170, 354)(137, 321, 168, 352, 142, 326, 164, 348)(140, 324, 166, 350, 151, 335, 161, 345)(145, 329, 156, 340, 150, 334, 167, 351)(148, 332, 153, 337, 159, 343, 158, 342)(369, 553)(370, 554)(371, 555)(372, 556)(373, 557)(374, 558)(375, 559)(376, 560)(377, 561)(378, 562)(379, 563)(380, 564)(381, 565)(382, 566)(383, 567)(384, 568)(385, 569)(386, 570)(387, 571)(388, 572)(389, 573)(390, 574)(391, 575)(392, 576)(393, 577)(394, 578)(395, 579)(396, 580)(397, 581)(398, 582)(399, 583)(400, 584)(401, 585)(402, 586)(403, 587)(404, 588)(405, 589)(406, 590)(407, 591)(408, 592)(409, 593)(410, 594)(411, 595)(412, 596)(413, 597)(414, 598)(415, 599)(416, 600)(417, 601)(418, 602)(419, 603)(420, 604)(421, 605)(422, 606)(423, 607)(424, 608)(425, 609)(426, 610)(427, 611)(428, 612)(429, 613)(430, 614)(431, 615)(432, 616)(433, 617)(434, 618)(435, 619)(436, 620)(437, 621)(438, 622)(439, 623)(440, 624)(441, 625)(442, 626)(443, 627)(444, 628)(445, 629)(446, 630)(447, 631)(448, 632)(449, 633)(450, 634)(451, 635)(452, 636)(453, 637)(454, 638)(455, 639)(456, 640)(457, 641)(458, 642)(459, 643)(460, 644)(461, 645)(462, 646)(463, 647)(464, 648)(465, 649)(466, 650)(467, 651)(468, 652)(469, 653)(470, 654)(471, 655)(472, 656)(473, 657)(474, 658)(475, 659)(476, 660)(477, 661)(478, 662)(479, 663)(480, 664)(481, 665)(482, 666)(483, 667)(484, 668)(485, 669)(486, 670)(487, 671)(488, 672)(489, 673)(490, 674)(491, 675)(492, 676)(493, 677)(494, 678)(495, 679)(496, 680)(497, 681)(498, 682)(499, 683)(500, 684)(501, 685)(502, 686)(503, 687)(504, 688)(505, 689)(506, 690)(507, 691)(508, 692)(509, 693)(510, 694)(511, 695)(512, 696)(513, 697)(514, 698)(515, 699)(516, 700)(517, 701)(518, 702)(519, 703)(520, 704)(521, 705)(522, 706)(523, 707)(524, 708)(525, 709)(526, 710)(527, 711)(528, 712)(529, 713)(530, 714)(531, 715)(532, 716)(533, 717)(534, 718)(535, 719)(536, 720)(537, 721)(538, 722)(539, 723)(540, 724)(541, 725)(542, 726)(543, 727)(544, 728)(545, 729)(546, 730)(547, 731)(548, 732)(549, 733)(550, 734)(551, 735)(552, 736) L = (1, 371)(2, 375)(3, 378)(4, 379)(5, 369)(6, 381)(7, 383)(8, 370)(9, 372)(10, 386)(11, 387)(12, 373)(13, 389)(14, 374)(15, 391)(16, 376)(17, 377)(18, 394)(19, 395)(20, 380)(21, 397)(22, 382)(23, 399)(24, 384)(25, 385)(26, 402)(27, 403)(28, 388)(29, 405)(30, 390)(31, 407)(32, 392)(33, 393)(34, 410)(35, 411)(36, 396)(37, 413)(38, 398)(39, 415)(40, 400)(41, 401)(42, 418)(43, 419)(44, 404)(45, 421)(46, 406)(47, 423)(48, 408)(49, 409)(50, 426)(51, 427)(52, 412)(53, 429)(54, 414)(55, 431)(56, 416)(57, 417)(58, 434)(59, 435)(60, 420)(61, 437)(62, 422)(63, 441)(64, 424)(65, 425)(66, 445)(67, 439)(68, 428)(69, 438)(70, 440)(71, 442)(72, 443)(73, 444)(74, 446)(75, 447)(76, 448)(77, 449)(78, 450)(79, 451)(80, 452)(81, 453)(82, 454)(83, 455)(84, 456)(85, 457)(86, 458)(87, 459)(88, 460)(89, 461)(90, 462)(91, 463)(92, 464)(93, 465)(94, 467)(95, 469)(96, 470)(97, 471)(98, 430)(99, 479)(100, 433)(101, 487)(102, 475)(103, 473)(104, 432)(105, 477)(106, 466)(107, 481)(108, 468)(109, 484)(110, 472)(111, 486)(112, 436)(113, 489)(114, 474)(115, 478)(116, 492)(117, 476)(118, 494)(119, 495)(120, 482)(121, 497)(122, 480)(123, 485)(124, 500)(125, 483)(126, 502)(127, 503)(128, 490)(129, 505)(130, 488)(131, 493)(132, 508)(133, 491)(134, 510)(135, 511)(136, 498)(137, 513)(138, 496)(139, 501)(140, 516)(141, 499)(142, 518)(143, 519)(144, 506)(145, 521)(146, 504)(147, 509)(148, 524)(149, 507)(150, 526)(151, 527)(152, 514)(153, 529)(154, 512)(155, 517)(156, 532)(157, 515)(158, 534)(159, 535)(160, 522)(161, 543)(162, 520)(163, 525)(164, 551)(165, 523)(166, 538)(167, 536)(168, 541)(169, 528)(170, 545)(171, 530)(172, 531)(173, 548)(174, 533)(175, 550)(176, 539)(177, 549)(178, 537)(179, 542)(180, 546)(181, 540)(182, 547)(183, 552)(184, 544)(185, 553)(186, 554)(187, 555)(188, 556)(189, 557)(190, 558)(191, 559)(192, 560)(193, 561)(194, 562)(195, 563)(196, 564)(197, 565)(198, 566)(199, 567)(200, 568)(201, 569)(202, 570)(203, 571)(204, 572)(205, 573)(206, 574)(207, 575)(208, 576)(209, 577)(210, 578)(211, 579)(212, 580)(213, 581)(214, 582)(215, 583)(216, 584)(217, 585)(218, 586)(219, 587)(220, 588)(221, 589)(222, 590)(223, 591)(224, 592)(225, 593)(226, 594)(227, 595)(228, 596)(229, 597)(230, 598)(231, 599)(232, 600)(233, 601)(234, 602)(235, 603)(236, 604)(237, 605)(238, 606)(239, 607)(240, 608)(241, 609)(242, 610)(243, 611)(244, 612)(245, 613)(246, 614)(247, 615)(248, 616)(249, 617)(250, 618)(251, 619)(252, 620)(253, 621)(254, 622)(255, 623)(256, 624)(257, 625)(258, 626)(259, 627)(260, 628)(261, 629)(262, 630)(263, 631)(264, 632)(265, 633)(266, 634)(267, 635)(268, 636)(269, 637)(270, 638)(271, 639)(272, 640)(273, 641)(274, 642)(275, 643)(276, 644)(277, 645)(278, 646)(279, 647)(280, 648)(281, 649)(282, 650)(283, 651)(284, 652)(285, 653)(286, 654)(287, 655)(288, 656)(289, 657)(290, 658)(291, 659)(292, 660)(293, 661)(294, 662)(295, 663)(296, 664)(297, 665)(298, 666)(299, 667)(300, 668)(301, 669)(302, 670)(303, 671)(304, 672)(305, 673)(306, 674)(307, 675)(308, 676)(309, 677)(310, 678)(311, 679)(312, 680)(313, 681)(314, 682)(315, 683)(316, 684)(317, 685)(318, 686)(319, 687)(320, 688)(321, 689)(322, 690)(323, 691)(324, 692)(325, 693)(326, 694)(327, 695)(328, 696)(329, 697)(330, 698)(331, 699)(332, 700)(333, 701)(334, 702)(335, 703)(336, 704)(337, 705)(338, 706)(339, 707)(340, 708)(341, 709)(342, 710)(343, 711)(344, 712)(345, 713)(346, 714)(347, 715)(348, 716)(349, 717)(350, 718)(351, 719)(352, 720)(353, 721)(354, 722)(355, 723)(356, 724)(357, 725)(358, 726)(359, 727)(360, 728)(361, 729)(362, 730)(363, 731)(364, 732)(365, 733)(366, 734)(367, 735)(368, 736) local type(s) :: { ( 4, 184 ), ( 4, 184, 4, 184, 4, 184, 4, 184 ) } Outer automorphisms :: reflexible Dual of E23.1187 Graph:: simple bipartite v = 230 e = 368 f = 94 degree seq :: [ 2^184, 8^46 ] E23.1189 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 4, 48}) Quotient :: regular Aut^+ = $<192, 68>$ (small group id <192, 68>) Aut = $<384, 1684>$ (small group id <384, 1684>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-2 * T2)^2, (T1 * T2)^4, T1^48 ] Map:: polytopal non-degenerate R = (1, 2, 5, 11, 20, 29, 37, 45, 53, 61, 113, 133, 144, 135, 146, 160, 175, 183, 188, 180, 172, 156, 140, 128, 122, 124, 130, 141, 157, 118, 111, 107, 103, 99, 94, 84, 91, 85, 92, 68, 60, 52, 44, 36, 28, 19, 10, 4)(3, 7, 15, 25, 33, 41, 49, 57, 65, 117, 164, 123, 162, 127, 167, 155, 185, 179, 190, 184, 174, 161, 143, 136, 126, 134, 149, 166, 116, 109, 106, 101, 98, 89, 82, 74, 81, 77, 86, 95, 62, 55, 46, 39, 30, 22, 12, 8)(6, 13, 9, 18, 27, 35, 43, 51, 59, 67, 119, 129, 152, 121, 150, 139, 177, 171, 191, 187, 182, 176, 159, 147, 132, 145, 138, 154, 170, 114, 110, 105, 102, 97, 90, 80, 76, 71, 75, 83, 93, 63, 54, 47, 38, 31, 21, 14)(16, 23, 17, 24, 32, 40, 48, 56, 64, 115, 169, 148, 137, 125, 131, 142, 158, 173, 181, 189, 192, 186, 178, 168, 151, 163, 153, 165, 120, 112, 108, 104, 100, 96, 87, 78, 72, 69, 70, 73, 79, 88, 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, 93)(63, 115)(67, 88)(68, 119)(69, 121)(70, 123)(71, 125)(72, 127)(73, 129)(74, 131)(75, 133)(76, 135)(77, 137)(78, 139)(79, 117)(80, 142)(81, 144)(82, 146)(83, 148)(84, 150)(85, 152)(86, 113)(87, 155)(89, 158)(90, 160)(91, 162)(92, 164)(94, 167)(95, 169)(96, 171)(97, 173)(98, 175)(99, 177)(100, 179)(101, 181)(102, 183)(103, 185)(104, 187)(105, 189)(106, 188)(107, 191)(108, 184)(109, 192)(110, 180)(111, 190)(112, 176)(114, 186)(116, 172)(118, 182)(120, 161)(122, 126)(124, 132)(128, 138)(130, 143)(134, 151)(136, 153)(140, 149)(141, 159)(145, 163)(147, 165)(154, 168)(156, 170)(157, 174)(166, 178) local type(s) :: { ( 4^48 ) } Outer automorphisms :: reflexible Dual of E23.1190 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 4 e = 96 f = 48 degree seq :: [ 48^4 ] E23.1190 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 4, 48}) Quotient :: regular Aut^+ = $<192, 68>$ (small group id <192, 68>) Aut = $<384, 1684>$ (small group id <384, 1684>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, T1^4, (T1^-1 * T2 * T1^-1)^2, (T1 * T2)^48 ] Map:: polytopal non-degenerate R = (1, 2, 5, 4)(3, 7, 10, 8)(6, 11, 9, 12)(13, 17, 14, 18)(15, 19, 16, 20)(21, 25, 22, 26)(23, 27, 24, 28)(29, 33, 30, 34)(31, 35, 32, 36)(37, 49, 38, 50)(39, 67, 43, 69)(40, 70, 42, 72)(41, 71, 48, 74)(44, 75, 47, 68)(45, 63, 46, 64)(51, 78, 52, 73)(53, 77, 54, 76)(55, 80, 56, 79)(57, 82, 58, 81)(59, 84, 60, 83)(61, 86, 62, 85)(65, 88, 66, 87)(89, 91, 90, 92)(93, 99, 94, 100)(95, 119, 96, 120)(97, 123, 98, 124)(101, 127, 102, 128)(103, 129, 104, 130)(105, 126, 106, 125)(107, 132, 108, 131)(109, 134, 110, 133)(111, 136, 112, 135)(113, 138, 114, 137)(115, 140, 116, 139)(117, 142, 118, 141)(121, 144, 122, 143)(145, 147, 146, 148)(149, 155, 150, 156)(151, 175, 152, 176)(153, 179, 154, 180)(157, 183, 158, 184)(159, 185, 160, 186)(161, 182, 162, 181)(163, 188, 164, 187)(165, 190, 166, 189)(167, 192, 168, 191)(169, 177, 170, 178)(171, 173, 172, 174) L = (1, 3)(2, 6)(4, 9)(5, 10)(7, 13)(8, 14)(11, 15)(12, 16)(17, 21)(18, 22)(19, 23)(20, 24)(25, 29)(26, 30)(27, 31)(28, 32)(33, 37)(34, 38)(35, 63)(36, 64)(39, 68)(40, 71)(41, 73)(42, 74)(43, 75)(44, 76)(45, 67)(46, 69)(47, 77)(48, 78)(49, 70)(50, 72)(51, 79)(52, 80)(53, 81)(54, 82)(55, 83)(56, 84)(57, 85)(58, 86)(59, 87)(60, 88)(61, 89)(62, 90)(65, 93)(66, 94)(91, 119)(92, 120)(95, 123)(96, 124)(97, 125)(98, 126)(99, 127)(100, 128)(101, 129)(102, 130)(103, 131)(104, 132)(105, 133)(106, 134)(107, 135)(108, 136)(109, 137)(110, 138)(111, 139)(112, 140)(113, 141)(114, 142)(115, 143)(116, 144)(117, 145)(118, 146)(121, 149)(122, 150)(147, 175)(148, 176)(151, 179)(152, 180)(153, 181)(154, 182)(155, 183)(156, 184)(157, 185)(158, 186)(159, 187)(160, 188)(161, 189)(162, 190)(163, 191)(164, 192)(165, 178)(166, 177)(167, 174)(168, 173)(169, 171)(170, 172) local type(s) :: { ( 48^4 ) } Outer automorphisms :: reflexible Dual of E23.1189 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 48 e = 96 f = 4 degree seq :: [ 4^48 ] E23.1191 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 48}) Quotient :: edge Aut^+ = $<192, 68>$ (small group id <192, 68>) Aut = $<384, 1684>$ (small group id <384, 1684>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T1)^2, (F * T2)^2, T2^4, (T2^-1 * T1 * T2^-1)^2, (T2 * T1)^48 ] Map:: polytopal R = (1, 3, 8, 4)(2, 5, 11, 6)(7, 13, 9, 14)(10, 15, 12, 16)(17, 21, 18, 22)(19, 23, 20, 24)(25, 29, 26, 30)(27, 31, 28, 32)(33, 37, 34, 38)(35, 61, 36, 63)(39, 66, 46, 68)(40, 70, 49, 72)(41, 73, 42, 69)(43, 76, 44, 65)(45, 79, 47, 81)(48, 84, 50, 86)(51, 89, 52, 91)(53, 93, 54, 95)(55, 97, 56, 99)(57, 101, 58, 103)(59, 105, 60, 107)(62, 109, 64, 111)(67, 114, 82, 116)(71, 118, 87, 120)(74, 121, 75, 117)(77, 124, 78, 113)(80, 127, 83, 129)(85, 132, 88, 134)(90, 137, 92, 139)(94, 141, 96, 143)(98, 145, 100, 147)(102, 149, 104, 151)(106, 153, 108, 155)(110, 157, 112, 159)(115, 162, 130, 164)(119, 166, 135, 168)(122, 169, 123, 165)(125, 172, 126, 161)(128, 175, 131, 177)(133, 180, 136, 182)(138, 185, 140, 187)(142, 189, 144, 191)(146, 190, 148, 192)(150, 186, 152, 188)(154, 184, 156, 181)(158, 179, 160, 176)(163, 170, 178, 171)(167, 173, 183, 174)(193, 194)(195, 199)(196, 201)(197, 202)(198, 204)(200, 203)(205, 209)(206, 210)(207, 211)(208, 212)(213, 217)(214, 218)(215, 219)(216, 220)(221, 225)(222, 226)(223, 227)(224, 228)(229, 236)(230, 235)(231, 257)(232, 261)(233, 255)(234, 253)(237, 258)(238, 268)(239, 260)(240, 262)(241, 265)(242, 264)(243, 271)(244, 273)(245, 276)(246, 278)(247, 281)(248, 283)(249, 285)(250, 287)(251, 289)(252, 291)(254, 293)(256, 295)(259, 305)(263, 309)(266, 303)(267, 301)(269, 299)(270, 297)(272, 306)(274, 316)(275, 308)(277, 310)(279, 313)(280, 312)(282, 319)(284, 321)(286, 324)(288, 326)(290, 329)(292, 331)(294, 333)(296, 335)(298, 337)(300, 339)(302, 341)(304, 343)(307, 353)(311, 357)(314, 351)(315, 349)(317, 347)(318, 345)(320, 354)(322, 364)(323, 356)(325, 358)(327, 361)(328, 360)(330, 367)(332, 369)(334, 372)(336, 374)(338, 377)(340, 379)(342, 381)(344, 383)(346, 382)(348, 384)(350, 378)(352, 380)(355, 359)(362, 368)(363, 371)(365, 373)(366, 376)(370, 375) L = (1, 193)(2, 194)(3, 195)(4, 196)(5, 197)(6, 198)(7, 199)(8, 200)(9, 201)(10, 202)(11, 203)(12, 204)(13, 205)(14, 206)(15, 207)(16, 208)(17, 209)(18, 210)(19, 211)(20, 212)(21, 213)(22, 214)(23, 215)(24, 216)(25, 217)(26, 218)(27, 219)(28, 220)(29, 221)(30, 222)(31, 223)(32, 224)(33, 225)(34, 226)(35, 227)(36, 228)(37, 229)(38, 230)(39, 231)(40, 232)(41, 233)(42, 234)(43, 235)(44, 236)(45, 237)(46, 238)(47, 239)(48, 240)(49, 241)(50, 242)(51, 243)(52, 244)(53, 245)(54, 246)(55, 247)(56, 248)(57, 249)(58, 250)(59, 251)(60, 252)(61, 253)(62, 254)(63, 255)(64, 256)(65, 257)(66, 258)(67, 259)(68, 260)(69, 261)(70, 262)(71, 263)(72, 264)(73, 265)(74, 266)(75, 267)(76, 268)(77, 269)(78, 270)(79, 271)(80, 272)(81, 273)(82, 274)(83, 275)(84, 276)(85, 277)(86, 278)(87, 279)(88, 280)(89, 281)(90, 282)(91, 283)(92, 284)(93, 285)(94, 286)(95, 287)(96, 288)(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) :: { ( 96, 96 ), ( 96^4 ) } Outer automorphisms :: reflexible Dual of E23.1195 Transitivity :: ET+ Graph:: simple bipartite v = 144 e = 192 f = 4 degree seq :: [ 2^96, 4^48 ] E23.1192 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 48}) Quotient :: edge Aut^+ = $<192, 68>$ (small group id <192, 68>) Aut = $<384, 1684>$ (small group id <384, 1684>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1 * T1^-1)^2, (T2 * T1^-1)^2, T2^48 ] Map:: polytopal non-degenerate R = (1, 3, 10, 18, 26, 34, 42, 50, 58, 66, 105, 113, 117, 121, 125, 129, 133, 138, 146, 181, 187, 191, 179, 174, 169, 166, 161, 158, 153, 150, 141, 108, 98, 96, 90, 88, 82, 80, 73, 68, 60, 52, 44, 36, 28, 20, 12, 5)(2, 7, 15, 23, 31, 39, 47, 55, 63, 103, 111, 115, 119, 123, 127, 131, 136, 142, 177, 185, 189, 183, 176, 171, 168, 163, 160, 155, 152, 145, 140, 99, 102, 91, 93, 83, 85, 75, 77, 69, 64, 56, 48, 40, 32, 24, 16, 8)(4, 11, 19, 27, 35, 43, 51, 59, 67, 107, 112, 116, 120, 124, 128, 132, 137, 143, 178, 186, 190, 184, 175, 172, 167, 164, 159, 156, 151, 148, 106, 135, 95, 97, 87, 89, 79, 81, 71, 72, 65, 57, 49, 41, 33, 25, 17, 9)(6, 13, 21, 29, 37, 45, 53, 61, 101, 109, 110, 114, 118, 122, 126, 130, 134, 139, 147, 182, 188, 192, 180, 173, 170, 165, 162, 157, 154, 149, 144, 104, 100, 94, 92, 86, 84, 78, 76, 70, 74, 62, 54, 46, 38, 30, 22, 14)(193, 194, 198, 196)(195, 201, 205, 200)(197, 203, 206, 199)(202, 208, 213, 209)(204, 207, 214, 211)(210, 217, 221, 216)(212, 219, 222, 215)(218, 224, 229, 225)(220, 223, 230, 227)(226, 233, 237, 232)(228, 235, 238, 231)(234, 240, 245, 241)(236, 239, 246, 243)(242, 249, 253, 248)(244, 251, 254, 247)(250, 256, 293, 257)(252, 255, 266, 259)(258, 264, 301, 261)(260, 299, 262, 295)(263, 297, 269, 302)(265, 303, 268, 304)(267, 305, 273, 306)(270, 307, 272, 308)(271, 309, 277, 310)(274, 311, 276, 312)(275, 313, 281, 314)(278, 315, 280, 316)(279, 317, 285, 318)(282, 319, 284, 320)(283, 321, 289, 322)(286, 323, 288, 324)(287, 325, 294, 326)(290, 328, 292, 329)(291, 330, 327, 331)(296, 334, 300, 335)(298, 338, 332, 339)(333, 369, 336, 370)(337, 373, 340, 374)(341, 377, 342, 378)(343, 379, 344, 380)(345, 381, 346, 382)(347, 383, 348, 384)(349, 375, 350, 376)(351, 371, 352, 372)(353, 368, 354, 367)(355, 366, 356, 365)(357, 363, 358, 364)(359, 361, 360, 362) L = (1, 193)(2, 194)(3, 195)(4, 196)(5, 197)(6, 198)(7, 199)(8, 200)(9, 201)(10, 202)(11, 203)(12, 204)(13, 205)(14, 206)(15, 207)(16, 208)(17, 209)(18, 210)(19, 211)(20, 212)(21, 213)(22, 214)(23, 215)(24, 216)(25, 217)(26, 218)(27, 219)(28, 220)(29, 221)(30, 222)(31, 223)(32, 224)(33, 225)(34, 226)(35, 227)(36, 228)(37, 229)(38, 230)(39, 231)(40, 232)(41, 233)(42, 234)(43, 235)(44, 236)(45, 237)(46, 238)(47, 239)(48, 240)(49, 241)(50, 242)(51, 243)(52, 244)(53, 245)(54, 246)(55, 247)(56, 248)(57, 249)(58, 250)(59, 251)(60, 252)(61, 253)(62, 254)(63, 255)(64, 256)(65, 257)(66, 258)(67, 259)(68, 260)(69, 261)(70, 262)(71, 263)(72, 264)(73, 265)(74, 266)(75, 267)(76, 268)(77, 269)(78, 270)(79, 271)(80, 272)(81, 273)(82, 274)(83, 275)(84, 276)(85, 277)(86, 278)(87, 279)(88, 280)(89, 281)(90, 282)(91, 283)(92, 284)(93, 285)(94, 286)(95, 287)(96, 288)(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) :: { ( 4^4 ), ( 4^48 ) } Outer automorphisms :: reflexible Dual of E23.1196 Transitivity :: ET+ Graph:: simple bipartite v = 52 e = 192 f = 96 degree seq :: [ 4^48, 48^4 ] E23.1193 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 48}) Quotient :: edge Aut^+ = $<192, 68>$ (small group id <192, 68>) Aut = $<384, 1684>$ (small group id <384, 1684>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-2 * T2)^2, (T2 * T1)^4, T1^48 ] 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, 72)(63, 99)(67, 69)(68, 103)(70, 101)(71, 107)(73, 110)(74, 112)(75, 97)(76, 115)(77, 117)(78, 119)(79, 121)(80, 123)(81, 125)(82, 127)(83, 129)(84, 131)(85, 133)(86, 135)(87, 137)(88, 139)(89, 141)(90, 143)(91, 145)(92, 147)(93, 149)(94, 151)(95, 153)(96, 155)(98, 158)(100, 160)(102, 163)(104, 165)(105, 167)(106, 162)(108, 170)(109, 172)(111, 174)(113, 176)(114, 157)(116, 179)(118, 181)(120, 183)(122, 185)(124, 187)(126, 189)(128, 188)(130, 191)(132, 184)(134, 192)(136, 180)(138, 190)(140, 178)(142, 186)(144, 175)(146, 182)(148, 173)(150, 166)(152, 169)(154, 177)(156, 159)(161, 168)(164, 171)(193, 194, 197, 203, 212, 221, 229, 237, 245, 253, 289, 311, 319, 327, 335, 343, 352, 362, 368, 373, 381, 384, 378, 358, 348, 340, 332, 324, 316, 308, 303, 298, 297, 294, 287, 283, 279, 275, 271, 260, 252, 244, 236, 228, 220, 211, 202, 196)(195, 199, 207, 217, 225, 233, 241, 249, 257, 293, 313, 307, 329, 323, 345, 339, 359, 357, 366, 383, 379, 374, 370, 363, 351, 344, 334, 328, 318, 312, 305, 301, 292, 285, 282, 277, 274, 269, 267, 263, 254, 247, 238, 231, 222, 214, 204, 200)(198, 205, 201, 210, 219, 227, 235, 243, 251, 259, 295, 302, 321, 315, 337, 331, 355, 347, 354, 377, 371, 382, 376, 369, 365, 353, 342, 336, 326, 320, 310, 306, 300, 290, 286, 281, 278, 273, 270, 266, 264, 255, 246, 239, 230, 223, 213, 206)(208, 215, 209, 216, 224, 232, 240, 248, 256, 291, 299, 304, 309, 317, 325, 333, 341, 350, 364, 349, 375, 380, 372, 367, 361, 360, 356, 346, 338, 330, 322, 314, 296, 288, 284, 280, 276, 272, 268, 265, 262, 261, 258, 250, 242, 234, 226, 218) L = (1, 193)(2, 194)(3, 195)(4, 196)(5, 197)(6, 198)(7, 199)(8, 200)(9, 201)(10, 202)(11, 203)(12, 204)(13, 205)(14, 206)(15, 207)(16, 208)(17, 209)(18, 210)(19, 211)(20, 212)(21, 213)(22, 214)(23, 215)(24, 216)(25, 217)(26, 218)(27, 219)(28, 220)(29, 221)(30, 222)(31, 223)(32, 224)(33, 225)(34, 226)(35, 227)(36, 228)(37, 229)(38, 230)(39, 231)(40, 232)(41, 233)(42, 234)(43, 235)(44, 236)(45, 237)(46, 238)(47, 239)(48, 240)(49, 241)(50, 242)(51, 243)(52, 244)(53, 245)(54, 246)(55, 247)(56, 248)(57, 249)(58, 250)(59, 251)(60, 252)(61, 253)(62, 254)(63, 255)(64, 256)(65, 257)(66, 258)(67, 259)(68, 260)(69, 261)(70, 262)(71, 263)(72, 264)(73, 265)(74, 266)(75, 267)(76, 268)(77, 269)(78, 270)(79, 271)(80, 272)(81, 273)(82, 274)(83, 275)(84, 276)(85, 277)(86, 278)(87, 279)(88, 280)(89, 281)(90, 282)(91, 283)(92, 284)(93, 285)(94, 286)(95, 287)(96, 288)(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, 8 ), ( 8^48 ) } Outer automorphisms :: reflexible Dual of E23.1194 Transitivity :: ET+ Graph:: simple bipartite v = 100 e = 192 f = 48 degree seq :: [ 2^96, 48^4 ] E23.1194 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 48}) Quotient :: loop Aut^+ = $<192, 68>$ (small group id <192, 68>) Aut = $<384, 1684>$ (small group id <384, 1684>) |r| :: 2 Presentation :: [ T1^2, F^2, (F * T1)^2, (F * T2)^2, T2^4, (T2^-1 * T1 * T2^-1)^2, (T2 * T1)^48 ] Map:: R = (1, 193, 3, 195, 8, 200, 4, 196)(2, 194, 5, 197, 11, 203, 6, 198)(7, 199, 13, 205, 9, 201, 14, 206)(10, 202, 15, 207, 12, 204, 16, 208)(17, 209, 21, 213, 18, 210, 22, 214)(19, 211, 23, 215, 20, 212, 24, 216)(25, 217, 29, 221, 26, 218, 30, 222)(27, 219, 31, 223, 28, 220, 32, 224)(33, 225, 37, 229, 34, 226, 38, 230)(35, 227, 57, 249, 36, 228, 59, 251)(39, 231, 61, 253, 42, 234, 63, 255)(40, 232, 64, 256, 45, 237, 66, 258)(41, 233, 67, 259, 43, 235, 69, 261)(44, 236, 72, 264, 46, 238, 74, 266)(47, 239, 77, 269, 48, 240, 79, 271)(49, 241, 81, 273, 50, 242, 83, 275)(51, 243, 85, 277, 52, 244, 87, 279)(53, 245, 89, 281, 54, 246, 91, 283)(55, 247, 93, 285, 56, 248, 95, 287)(58, 250, 98, 290, 60, 252, 97, 289)(62, 254, 102, 294, 70, 262, 101, 293)(65, 257, 105, 297, 75, 267, 104, 296)(68, 260, 108, 300, 71, 263, 107, 299)(73, 265, 113, 305, 76, 268, 112, 304)(78, 270, 118, 310, 80, 272, 117, 309)(82, 274, 122, 314, 84, 276, 121, 313)(86, 278, 126, 318, 88, 280, 125, 317)(90, 282, 130, 322, 92, 284, 129, 321)(94, 286, 134, 326, 96, 288, 133, 325)(99, 291, 137, 329, 100, 292, 138, 330)(103, 295, 141, 333, 110, 302, 142, 334)(106, 298, 144, 336, 115, 307, 145, 337)(109, 301, 147, 339, 111, 303, 148, 340)(114, 306, 152, 344, 116, 308, 153, 345)(119, 311, 157, 349, 120, 312, 158, 350)(123, 315, 161, 353, 124, 316, 162, 354)(127, 319, 165, 357, 128, 320, 166, 358)(131, 323, 169, 361, 132, 324, 170, 362)(135, 327, 173, 365, 136, 328, 174, 366)(139, 331, 178, 370, 140, 332, 177, 369)(143, 335, 182, 374, 150, 342, 181, 373)(146, 338, 185, 377, 155, 347, 184, 376)(149, 341, 188, 380, 151, 343, 187, 379)(154, 346, 189, 381, 156, 348, 191, 383)(159, 351, 192, 384, 160, 352, 186, 378)(163, 355, 190, 382, 164, 356, 183, 375)(167, 359, 179, 371, 168, 360, 180, 372)(171, 363, 175, 367, 172, 364, 176, 368) 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, 227)(32, 228)(33, 221)(34, 222)(35, 223)(36, 224)(37, 231)(38, 234)(39, 229)(40, 249)(41, 253)(42, 230)(43, 255)(44, 256)(45, 251)(46, 258)(47, 259)(48, 261)(49, 264)(50, 266)(51, 269)(52, 271)(53, 273)(54, 275)(55, 277)(56, 279)(57, 232)(58, 281)(59, 237)(60, 283)(61, 233)(62, 285)(63, 235)(64, 236)(65, 290)(66, 238)(67, 239)(68, 294)(69, 240)(70, 287)(71, 293)(72, 241)(73, 297)(74, 242)(75, 289)(76, 296)(77, 243)(78, 300)(79, 244)(80, 299)(81, 245)(82, 305)(83, 246)(84, 304)(85, 247)(86, 310)(87, 248)(88, 309)(89, 250)(90, 314)(91, 252)(92, 313)(93, 254)(94, 318)(95, 262)(96, 317)(97, 267)(98, 257)(99, 322)(100, 321)(101, 263)(102, 260)(103, 326)(104, 268)(105, 265)(106, 329)(107, 272)(108, 270)(109, 333)(110, 325)(111, 334)(112, 276)(113, 274)(114, 336)(115, 330)(116, 337)(117, 280)(118, 278)(119, 339)(120, 340)(121, 284)(122, 282)(123, 344)(124, 345)(125, 288)(126, 286)(127, 349)(128, 350)(129, 292)(130, 291)(131, 353)(132, 354)(133, 302)(134, 295)(135, 357)(136, 358)(137, 298)(138, 307)(139, 361)(140, 362)(141, 301)(142, 303)(143, 365)(144, 306)(145, 308)(146, 370)(147, 311)(148, 312)(149, 374)(150, 366)(151, 373)(152, 315)(153, 316)(154, 377)(155, 369)(156, 376)(157, 319)(158, 320)(159, 380)(160, 379)(161, 323)(162, 324)(163, 381)(164, 383)(165, 327)(166, 328)(167, 384)(168, 378)(169, 331)(170, 332)(171, 382)(172, 375)(173, 335)(174, 342)(175, 371)(176, 372)(177, 347)(178, 338)(179, 367)(180, 368)(181, 343)(182, 341)(183, 364)(184, 348)(185, 346)(186, 360)(187, 352)(188, 351)(189, 355)(190, 363)(191, 356)(192, 359) local type(s) :: { ( 2, 48, 2, 48, 2, 48, 2, 48 ) } Outer automorphisms :: reflexible Dual of E23.1193 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 48 e = 192 f = 100 degree seq :: [ 8^48 ] E23.1195 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 48}) Quotient :: loop Aut^+ = $<192, 68>$ (small group id <192, 68>) Aut = $<384, 1684>$ (small group id <384, 1684>) |r| :: 2 Presentation :: [ F^2, (F * T2)^2, (F * T1)^2, T1^4, (T2^-1 * T1^-1)^2, (T2 * T1^-1)^2, T2^48 ] Map:: R = (1, 193, 3, 195, 10, 202, 18, 210, 26, 218, 34, 226, 42, 234, 50, 242, 58, 250, 66, 258, 91, 283, 87, 279, 75, 267, 72, 264, 76, 268, 85, 277, 92, 284, 101, 293, 105, 297, 111, 303, 114, 306, 120, 312, 176, 368, 192, 384, 188, 380, 185, 377, 177, 369, 170, 362, 165, 357, 161, 353, 157, 349, 152, 344, 145, 337, 137, 329, 129, 321, 123, 315, 127, 319, 135, 327, 143, 335, 68, 260, 60, 252, 52, 244, 44, 236, 36, 228, 28, 220, 20, 212, 12, 204, 5, 197)(2, 194, 7, 199, 15, 207, 23, 215, 31, 223, 39, 231, 47, 239, 55, 247, 63, 255, 94, 286, 97, 289, 78, 270, 81, 273, 69, 261, 82, 274, 80, 272, 98, 290, 96, 288, 109, 301, 108, 300, 117, 309, 116, 308, 171, 363, 190, 382, 187, 379, 182, 374, 181, 373, 173, 365, 168, 360, 163, 355, 159, 351, 155, 347, 149, 341, 141, 333, 133, 325, 125, 317, 131, 323, 139, 331, 147, 339, 154, 346, 64, 256, 56, 248, 48, 240, 40, 232, 32, 224, 24, 216, 16, 208, 8, 200)(4, 196, 11, 203, 19, 211, 27, 219, 35, 227, 43, 235, 51, 243, 59, 251, 67, 259, 103, 295, 86, 278, 89, 281, 71, 263, 74, 266, 73, 265, 90, 282, 88, 280, 104, 296, 102, 294, 113, 305, 112, 304, 166, 358, 122, 314, 178, 370, 186, 378, 183, 375, 180, 372, 175, 367, 169, 361, 164, 356, 160, 352, 156, 348, 150, 342, 142, 334, 134, 326, 126, 318, 132, 324, 140, 332, 148, 340, 121, 313, 65, 257, 57, 249, 49, 241, 41, 233, 33, 225, 25, 217, 17, 209, 9, 201)(6, 198, 13, 205, 21, 213, 29, 221, 37, 229, 45, 237, 53, 245, 61, 253, 107, 299, 99, 291, 95, 287, 83, 275, 79, 271, 70, 262, 77, 269, 84, 276, 93, 285, 100, 292, 106, 298, 110, 302, 115, 307, 119, 311, 174, 366, 191, 383, 189, 381, 184, 376, 179, 371, 172, 364, 167, 359, 162, 354, 158, 350, 153, 345, 146, 338, 138, 330, 130, 322, 124, 316, 128, 320, 136, 328, 144, 336, 151, 343, 118, 310, 62, 254, 54, 246, 46, 238, 38, 230, 30, 222, 22, 214, 14, 206) L = (1, 194)(2, 198)(3, 201)(4, 193)(5, 203)(6, 196)(7, 197)(8, 195)(9, 205)(10, 208)(11, 206)(12, 207)(13, 200)(14, 199)(15, 214)(16, 213)(17, 202)(18, 217)(19, 204)(20, 219)(21, 209)(22, 211)(23, 212)(24, 210)(25, 221)(26, 224)(27, 222)(28, 223)(29, 216)(30, 215)(31, 230)(32, 229)(33, 218)(34, 233)(35, 220)(36, 235)(37, 225)(38, 227)(39, 228)(40, 226)(41, 237)(42, 240)(43, 238)(44, 239)(45, 232)(46, 231)(47, 246)(48, 245)(49, 234)(50, 249)(51, 236)(52, 251)(53, 241)(54, 243)(55, 244)(56, 242)(57, 253)(58, 256)(59, 254)(60, 255)(61, 248)(62, 247)(63, 310)(64, 299)(65, 250)(66, 313)(67, 252)(68, 295)(69, 315)(70, 317)(71, 319)(72, 318)(73, 321)(74, 316)(75, 323)(76, 325)(77, 326)(78, 327)(79, 324)(80, 329)(81, 320)(82, 322)(83, 331)(84, 333)(85, 334)(86, 335)(87, 332)(88, 337)(89, 328)(90, 330)(91, 339)(92, 341)(93, 342)(94, 260)(95, 340)(96, 344)(97, 336)(98, 338)(99, 346)(100, 347)(101, 348)(102, 349)(103, 343)(104, 345)(105, 351)(106, 352)(107, 257)(108, 353)(109, 350)(110, 355)(111, 356)(112, 357)(113, 354)(114, 360)(115, 361)(116, 362)(117, 359)(118, 259)(119, 365)(120, 367)(121, 291)(122, 369)(123, 266)(124, 261)(125, 264)(126, 262)(127, 273)(128, 263)(129, 274)(130, 265)(131, 271)(132, 267)(133, 269)(134, 268)(135, 281)(136, 270)(137, 282)(138, 272)(139, 279)(140, 275)(141, 277)(142, 276)(143, 289)(144, 278)(145, 290)(146, 280)(147, 287)(148, 283)(149, 285)(150, 284)(151, 286)(152, 296)(153, 288)(154, 258)(155, 293)(156, 292)(157, 301)(158, 294)(159, 298)(160, 297)(161, 305)(162, 300)(163, 303)(164, 302)(165, 309)(166, 364)(167, 304)(168, 307)(169, 306)(170, 358)(171, 371)(172, 308)(173, 312)(174, 372)(175, 311)(176, 373)(177, 363)(178, 376)(179, 314)(180, 368)(181, 366)(182, 384)(183, 383)(184, 382)(185, 370)(186, 380)(187, 381)(188, 379)(189, 378)(190, 377)(191, 374)(192, 375) 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 E23.1191 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 4 e = 192 f = 144 degree seq :: [ 96^4 ] E23.1196 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 48}) Quotient :: loop Aut^+ = $<192, 68>$ (small group id <192, 68>) Aut = $<384, 1684>$ (small group id <384, 1684>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T1^-2 * T2)^2, (T2 * T1)^4, T1^48 ] Map:: polytopal non-degenerate R = (1, 193, 3, 195)(2, 194, 6, 198)(4, 196, 9, 201)(5, 197, 12, 204)(7, 199, 16, 208)(8, 200, 17, 209)(10, 202, 15, 207)(11, 203, 21, 213)(13, 205, 23, 215)(14, 206, 24, 216)(18, 210, 26, 218)(19, 211, 27, 219)(20, 212, 30, 222)(22, 214, 32, 224)(25, 217, 34, 226)(28, 220, 33, 225)(29, 221, 38, 230)(31, 223, 40, 232)(35, 227, 42, 234)(36, 228, 43, 235)(37, 229, 46, 238)(39, 231, 48, 240)(41, 233, 50, 242)(44, 236, 49, 241)(45, 237, 54, 246)(47, 239, 56, 248)(51, 243, 58, 250)(52, 244, 59, 251)(53, 245, 62, 254)(55, 247, 64, 256)(57, 249, 66, 258)(60, 252, 65, 257)(61, 253, 105, 297)(63, 255, 87, 279)(67, 259, 109, 301)(68, 260, 73, 265)(69, 261, 111, 303)(70, 262, 113, 305)(71, 263, 115, 307)(72, 264, 117, 309)(74, 266, 120, 312)(75, 267, 122, 314)(76, 268, 124, 316)(77, 269, 126, 318)(78, 270, 128, 320)(79, 271, 130, 322)(80, 272, 132, 324)(81, 273, 134, 326)(82, 274, 136, 328)(83, 275, 138, 330)(84, 276, 140, 332)(85, 277, 142, 334)(86, 278, 144, 336)(88, 280, 147, 339)(89, 281, 149, 341)(90, 282, 151, 343)(91, 283, 153, 345)(92, 284, 155, 347)(93, 285, 157, 349)(94, 286, 159, 351)(95, 287, 161, 353)(96, 288, 163, 355)(97, 289, 165, 357)(98, 290, 167, 359)(99, 291, 169, 361)(100, 292, 171, 363)(101, 293, 173, 365)(102, 294, 175, 367)(103, 295, 177, 369)(104, 296, 179, 371)(106, 298, 181, 373)(107, 299, 183, 375)(108, 300, 185, 377)(110, 302, 187, 379)(112, 304, 186, 378)(114, 306, 180, 372)(116, 308, 174, 366)(118, 310, 170, 362)(119, 311, 182, 374)(121, 313, 184, 376)(123, 315, 189, 381)(125, 317, 166, 358)(127, 319, 164, 356)(129, 321, 191, 383)(131, 323, 158, 350)(133, 325, 190, 382)(135, 327, 178, 370)(137, 329, 176, 368)(139, 331, 154, 346)(141, 333, 188, 380)(143, 335, 172, 364)(145, 337, 168, 360)(146, 338, 192, 384)(148, 340, 150, 342)(152, 344, 162, 354)(156, 348, 160, 352) L = (1, 194)(2, 197)(3, 199)(4, 193)(5, 203)(6, 205)(7, 207)(8, 195)(9, 210)(10, 196)(11, 212)(12, 200)(13, 201)(14, 198)(15, 217)(16, 215)(17, 216)(18, 219)(19, 202)(20, 221)(21, 206)(22, 204)(23, 209)(24, 224)(25, 225)(26, 208)(27, 227)(28, 211)(29, 229)(30, 214)(31, 213)(32, 232)(33, 233)(34, 218)(35, 235)(36, 220)(37, 237)(38, 223)(39, 222)(40, 240)(41, 241)(42, 226)(43, 243)(44, 228)(45, 245)(46, 231)(47, 230)(48, 248)(49, 249)(50, 234)(51, 251)(52, 236)(53, 253)(54, 239)(55, 238)(56, 256)(57, 257)(58, 242)(59, 259)(60, 244)(61, 261)(62, 247)(63, 246)(64, 279)(65, 267)(66, 250)(67, 265)(68, 252)(69, 262)(70, 264)(71, 266)(72, 269)(73, 270)(74, 271)(75, 263)(76, 274)(77, 275)(78, 268)(79, 278)(80, 276)(81, 277)(82, 280)(83, 281)(84, 273)(85, 282)(86, 283)(87, 272)(88, 284)(89, 285)(90, 286)(91, 287)(92, 288)(93, 289)(94, 290)(95, 291)(96, 292)(97, 293)(98, 294)(99, 295)(100, 296)(101, 298)(102, 299)(103, 300)(104, 302)(105, 255)(106, 304)(107, 338)(108, 315)(109, 258)(110, 311)(111, 324)(112, 306)(113, 332)(114, 310)(115, 260)(116, 313)(117, 326)(118, 319)(119, 321)(120, 320)(121, 323)(122, 301)(123, 308)(124, 307)(125, 329)(126, 334)(127, 331)(128, 314)(129, 317)(130, 316)(131, 337)(132, 254)(133, 333)(134, 303)(135, 335)(136, 312)(137, 340)(138, 343)(139, 342)(140, 297)(141, 327)(142, 305)(143, 344)(144, 328)(145, 346)(146, 325)(147, 322)(148, 348)(149, 351)(150, 350)(151, 309)(152, 352)(153, 339)(154, 354)(155, 336)(156, 356)(157, 359)(158, 358)(159, 318)(160, 360)(161, 347)(162, 362)(163, 345)(164, 364)(165, 367)(166, 366)(167, 330)(168, 368)(169, 355)(170, 370)(171, 353)(172, 372)(173, 375)(174, 374)(175, 341)(176, 376)(177, 363)(178, 378)(179, 361)(180, 380)(181, 384)(182, 377)(183, 349)(184, 383)(185, 371)(186, 382)(187, 369)(188, 373)(189, 379)(190, 365)(191, 381)(192, 357) local type(s) :: { ( 4, 48, 4, 48 ) } Outer automorphisms :: reflexible Dual of E23.1192 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 96 e = 192 f = 52 degree seq :: [ 4^96 ] E23.1197 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 48}) Quotient :: dipole Aut^+ = $<192, 68>$ (small group id <192, 68>) Aut = $<384, 1684>$ (small group id <384, 1684>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, Y2^4, (R * Y2 * Y3^-1)^2, (Y2^-1 * Y1 * Y2^-1)^2, (Y3 * Y2^-1)^48 ] Map:: R = (1, 193, 2, 194)(3, 195, 7, 199)(4, 196, 9, 201)(5, 197, 10, 202)(6, 198, 12, 204)(8, 200, 11, 203)(13, 205, 17, 209)(14, 206, 18, 210)(15, 207, 19, 211)(16, 208, 20, 212)(21, 213, 25, 217)(22, 214, 26, 218)(23, 215, 27, 219)(24, 216, 28, 220)(29, 221, 33, 225)(30, 222, 34, 226)(31, 223, 35, 227)(32, 224, 36, 228)(37, 229, 58, 250)(38, 230, 57, 249)(39, 231, 71, 263)(40, 232, 74, 266)(41, 233, 75, 267)(42, 234, 76, 268)(43, 235, 72, 264)(44, 236, 73, 265)(45, 237, 81, 273)(46, 238, 82, 274)(47, 239, 83, 275)(48, 240, 84, 276)(49, 241, 85, 277)(50, 242, 86, 278)(51, 243, 77, 269)(52, 244, 78, 270)(53, 245, 79, 271)(54, 246, 80, 272)(55, 247, 68, 260)(56, 248, 67, 259)(59, 251, 87, 279)(60, 252, 88, 280)(61, 253, 89, 281)(62, 254, 90, 282)(63, 255, 91, 283)(64, 256, 92, 284)(65, 257, 93, 285)(66, 258, 94, 286)(69, 261, 95, 287)(70, 262, 96, 288)(97, 289, 99, 291)(98, 290, 100, 292)(101, 293, 117, 309)(102, 294, 118, 310)(103, 295, 135, 327)(104, 296, 138, 330)(105, 297, 136, 328)(106, 298, 137, 329)(107, 299, 141, 333)(108, 300, 144, 336)(109, 301, 142, 334)(110, 302, 143, 335)(111, 303, 145, 337)(112, 304, 146, 338)(113, 305, 139, 331)(114, 306, 140, 332)(115, 307, 131, 323)(116, 308, 132, 324)(119, 311, 147, 339)(120, 312, 148, 340)(121, 313, 149, 341)(122, 314, 150, 342)(123, 315, 151, 343)(124, 316, 152, 344)(125, 317, 153, 345)(126, 318, 154, 346)(127, 319, 155, 347)(128, 320, 156, 348)(129, 321, 157, 349)(130, 322, 158, 350)(133, 325, 159, 351)(134, 326, 160, 352)(161, 353, 163, 355)(162, 354, 164, 356)(165, 357, 174, 366)(166, 358, 173, 365)(167, 359, 192, 384)(168, 360, 191, 383)(169, 361, 187, 379)(170, 362, 188, 380)(171, 363, 184, 376)(172, 364, 183, 375)(175, 367, 189, 381)(176, 368, 190, 382)(177, 369, 186, 378)(178, 370, 185, 377)(179, 371, 181, 373)(180, 372, 182, 374)(385, 577, 387, 579, 392, 584, 388, 580)(386, 578, 389, 581, 395, 587, 390, 582)(391, 583, 397, 589, 393, 585, 398, 590)(394, 586, 399, 591, 396, 588, 400, 592)(401, 593, 405, 597, 402, 594, 406, 598)(403, 595, 407, 599, 404, 596, 408, 600)(409, 601, 413, 605, 410, 602, 414, 606)(411, 603, 415, 607, 412, 604, 416, 608)(417, 609, 421, 613, 418, 610, 422, 614)(419, 611, 451, 643, 420, 612, 452, 644)(423, 615, 456, 648, 430, 622, 457, 649)(424, 616, 459, 651, 433, 625, 460, 652)(425, 617, 461, 653, 426, 618, 462, 654)(427, 619, 463, 655, 428, 620, 464, 656)(429, 621, 466, 658, 431, 623, 455, 647)(432, 624, 469, 661, 434, 626, 458, 650)(435, 627, 471, 663, 436, 628, 472, 664)(437, 629, 473, 665, 438, 630, 474, 666)(439, 631, 467, 659, 440, 632, 465, 657)(441, 633, 470, 662, 442, 634, 468, 660)(443, 635, 475, 667, 444, 636, 476, 668)(445, 637, 477, 669, 446, 638, 478, 670)(447, 639, 479, 671, 448, 640, 480, 672)(449, 641, 481, 673, 450, 642, 482, 674)(453, 645, 485, 677, 454, 646, 486, 678)(483, 675, 515, 707, 484, 676, 516, 708)(487, 679, 520, 712, 488, 680, 521, 713)(489, 681, 523, 715, 490, 682, 524, 716)(491, 683, 526, 718, 492, 684, 527, 719)(493, 685, 529, 721, 494, 686, 530, 722)(495, 687, 531, 723, 496, 688, 532, 724)(497, 689, 533, 725, 498, 690, 534, 726)(499, 691, 522, 714, 500, 692, 519, 711)(501, 693, 528, 720, 502, 694, 525, 717)(503, 695, 535, 727, 504, 696, 536, 728)(505, 697, 537, 729, 506, 698, 538, 730)(507, 699, 539, 731, 508, 700, 540, 732)(509, 701, 541, 733, 510, 702, 542, 734)(511, 703, 543, 735, 512, 704, 544, 736)(513, 705, 545, 737, 514, 706, 546, 738)(517, 709, 549, 741, 518, 710, 550, 742)(547, 739, 575, 767, 548, 740, 576, 768)(551, 743, 571, 763, 552, 744, 572, 764)(553, 745, 568, 760, 554, 746, 567, 759)(555, 747, 563, 755, 556, 748, 564, 756)(557, 749, 573, 765, 558, 750, 574, 766)(559, 751, 570, 762, 560, 752, 569, 761)(561, 753, 565, 757, 562, 754, 566, 758) L = (1, 386)(2, 385)(3, 391)(4, 393)(5, 394)(6, 396)(7, 387)(8, 395)(9, 388)(10, 389)(11, 392)(12, 390)(13, 401)(14, 402)(15, 403)(16, 404)(17, 397)(18, 398)(19, 399)(20, 400)(21, 409)(22, 410)(23, 411)(24, 412)(25, 405)(26, 406)(27, 407)(28, 408)(29, 417)(30, 418)(31, 419)(32, 420)(33, 413)(34, 414)(35, 415)(36, 416)(37, 442)(38, 441)(39, 455)(40, 458)(41, 459)(42, 460)(43, 456)(44, 457)(45, 465)(46, 466)(47, 467)(48, 468)(49, 469)(50, 470)(51, 461)(52, 462)(53, 463)(54, 464)(55, 452)(56, 451)(57, 422)(58, 421)(59, 471)(60, 472)(61, 473)(62, 474)(63, 475)(64, 476)(65, 477)(66, 478)(67, 440)(68, 439)(69, 479)(70, 480)(71, 423)(72, 427)(73, 428)(74, 424)(75, 425)(76, 426)(77, 435)(78, 436)(79, 437)(80, 438)(81, 429)(82, 430)(83, 431)(84, 432)(85, 433)(86, 434)(87, 443)(88, 444)(89, 445)(90, 446)(91, 447)(92, 448)(93, 449)(94, 450)(95, 453)(96, 454)(97, 483)(98, 484)(99, 481)(100, 482)(101, 501)(102, 502)(103, 519)(104, 522)(105, 520)(106, 521)(107, 525)(108, 528)(109, 526)(110, 527)(111, 529)(112, 530)(113, 523)(114, 524)(115, 515)(116, 516)(117, 485)(118, 486)(119, 531)(120, 532)(121, 533)(122, 534)(123, 535)(124, 536)(125, 537)(126, 538)(127, 539)(128, 540)(129, 541)(130, 542)(131, 499)(132, 500)(133, 543)(134, 544)(135, 487)(136, 489)(137, 490)(138, 488)(139, 497)(140, 498)(141, 491)(142, 493)(143, 494)(144, 492)(145, 495)(146, 496)(147, 503)(148, 504)(149, 505)(150, 506)(151, 507)(152, 508)(153, 509)(154, 510)(155, 511)(156, 512)(157, 513)(158, 514)(159, 517)(160, 518)(161, 547)(162, 548)(163, 545)(164, 546)(165, 558)(166, 557)(167, 576)(168, 575)(169, 571)(170, 572)(171, 568)(172, 567)(173, 550)(174, 549)(175, 573)(176, 574)(177, 570)(178, 569)(179, 565)(180, 566)(181, 563)(182, 564)(183, 556)(184, 555)(185, 562)(186, 561)(187, 553)(188, 554)(189, 559)(190, 560)(191, 552)(192, 551)(193, 577)(194, 578)(195, 579)(196, 580)(197, 581)(198, 582)(199, 583)(200, 584)(201, 585)(202, 586)(203, 587)(204, 588)(205, 589)(206, 590)(207, 591)(208, 592)(209, 593)(210, 594)(211, 595)(212, 596)(213, 597)(214, 598)(215, 599)(216, 600)(217, 601)(218, 602)(219, 603)(220, 604)(221, 605)(222, 606)(223, 607)(224, 608)(225, 609)(226, 610)(227, 611)(228, 612)(229, 613)(230, 614)(231, 615)(232, 616)(233, 617)(234, 618)(235, 619)(236, 620)(237, 621)(238, 622)(239, 623)(240, 624)(241, 625)(242, 626)(243, 627)(244, 628)(245, 629)(246, 630)(247, 631)(248, 632)(249, 633)(250, 634)(251, 635)(252, 636)(253, 637)(254, 638)(255, 639)(256, 640)(257, 641)(258, 642)(259, 643)(260, 644)(261, 645)(262, 646)(263, 647)(264, 648)(265, 649)(266, 650)(267, 651)(268, 652)(269, 653)(270, 654)(271, 655)(272, 656)(273, 657)(274, 658)(275, 659)(276, 660)(277, 661)(278, 662)(279, 663)(280, 664)(281, 665)(282, 666)(283, 667)(284, 668)(285, 669)(286, 670)(287, 671)(288, 672)(289, 673)(290, 674)(291, 675)(292, 676)(293, 677)(294, 678)(295, 679)(296, 680)(297, 681)(298, 682)(299, 683)(300, 684)(301, 685)(302, 686)(303, 687)(304, 688)(305, 689)(306, 690)(307, 691)(308, 692)(309, 693)(310, 694)(311, 695)(312, 696)(313, 697)(314, 698)(315, 699)(316, 700)(317, 701)(318, 702)(319, 703)(320, 704)(321, 705)(322, 706)(323, 707)(324, 708)(325, 709)(326, 710)(327, 711)(328, 712)(329, 713)(330, 714)(331, 715)(332, 716)(333, 717)(334, 718)(335, 719)(336, 720)(337, 721)(338, 722)(339, 723)(340, 724)(341, 725)(342, 726)(343, 727)(344, 728)(345, 729)(346, 730)(347, 731)(348, 732)(349, 733)(350, 734)(351, 735)(352, 736)(353, 737)(354, 738)(355, 739)(356, 740)(357, 741)(358, 742)(359, 743)(360, 744)(361, 745)(362, 746)(363, 747)(364, 748)(365, 749)(366, 750)(367, 751)(368, 752)(369, 753)(370, 754)(371, 755)(372, 756)(373, 757)(374, 758)(375, 759)(376, 760)(377, 761)(378, 762)(379, 763)(380, 764)(381, 765)(382, 766)(383, 767)(384, 768) local type(s) :: { ( 2, 96, 2, 96 ), ( 2, 96, 2, 96, 2, 96, 2, 96 ) } Outer automorphisms :: reflexible Dual of E23.1200 Graph:: bipartite v = 144 e = 384 f = 196 degree seq :: [ 4^96, 8^48 ] E23.1198 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 48}) Quotient :: dipole Aut^+ = $<192, 68>$ (small group id <192, 68>) Aut = $<384, 1684>$ (small group id <384, 1684>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, (R * Y1)^2, (R * Y3)^2, (Y2 * Y1)^2, (Y3^-1 * Y1^-1)^2, (Y2^-1 * Y1)^2, Y1^4, Y2^48 ] Map:: R = (1, 193, 2, 194, 6, 198, 4, 196)(3, 195, 9, 201, 13, 205, 8, 200)(5, 197, 11, 203, 14, 206, 7, 199)(10, 202, 16, 208, 21, 213, 17, 209)(12, 204, 15, 207, 22, 214, 19, 211)(18, 210, 25, 217, 29, 221, 24, 216)(20, 212, 27, 219, 30, 222, 23, 215)(26, 218, 32, 224, 37, 229, 33, 225)(28, 220, 31, 223, 38, 230, 35, 227)(34, 226, 41, 233, 45, 237, 40, 232)(36, 228, 43, 235, 46, 238, 39, 231)(42, 234, 48, 240, 53, 245, 49, 241)(44, 236, 47, 239, 54, 246, 51, 243)(50, 242, 57, 249, 61, 253, 56, 248)(52, 244, 59, 251, 62, 254, 55, 247)(58, 250, 64, 256, 89, 281, 65, 257)(60, 252, 63, 255, 110, 302, 67, 259)(66, 258, 113, 305, 85, 277, 132, 324)(68, 260, 78, 270, 127, 319, 87, 279)(69, 261, 115, 307, 74, 266, 116, 308)(70, 262, 117, 309, 72, 264, 118, 310)(71, 263, 119, 311, 81, 273, 120, 312)(73, 265, 121, 313, 82, 274, 122, 314)(75, 267, 123, 315, 79, 271, 124, 316)(76, 268, 125, 317, 77, 269, 126, 318)(80, 272, 128, 320, 88, 280, 129, 321)(83, 275, 130, 322, 84, 276, 131, 323)(86, 278, 133, 325, 93, 285, 134, 326)(90, 282, 135, 327, 91, 283, 136, 328)(92, 284, 137, 329, 97, 289, 138, 330)(94, 286, 139, 331, 95, 287, 140, 332)(96, 288, 141, 333, 101, 293, 142, 334)(98, 290, 143, 335, 99, 291, 144, 336)(100, 292, 145, 337, 105, 297, 146, 338)(102, 294, 147, 339, 103, 295, 148, 340)(104, 296, 149, 341, 109, 301, 151, 343)(106, 298, 152, 344, 107, 299, 153, 345)(108, 300, 154, 346, 150, 342, 156, 348)(111, 303, 157, 349, 112, 304, 159, 351)(114, 306, 161, 353, 155, 347, 163, 355)(158, 350, 192, 384, 160, 352, 191, 383)(162, 354, 190, 382, 168, 360, 189, 381)(164, 356, 185, 377, 165, 357, 186, 378)(166, 358, 184, 376, 167, 359, 183, 375)(169, 361, 182, 374, 170, 362, 181, 373)(171, 363, 187, 379, 172, 364, 188, 380)(173, 365, 179, 371, 174, 366, 180, 372)(175, 367, 177, 369, 176, 368, 178, 370)(385, 577, 387, 579, 394, 586, 402, 594, 410, 602, 418, 610, 426, 618, 434, 626, 442, 634, 450, 642, 463, 655, 454, 646, 461, 653, 467, 659, 475, 667, 478, 670, 483, 675, 486, 678, 491, 683, 495, 687, 542, 734, 556, 748, 550, 742, 558, 750, 561, 753, 566, 758, 569, 761, 574, 766, 547, 739, 540, 732, 535, 727, 530, 722, 526, 718, 522, 714, 518, 710, 513, 705, 506, 698, 500, 692, 504, 696, 452, 644, 444, 636, 436, 628, 428, 620, 420, 612, 412, 604, 404, 596, 396, 588, 389, 581)(386, 578, 391, 583, 399, 591, 407, 599, 415, 607, 423, 615, 431, 623, 439, 631, 447, 639, 471, 663, 455, 647, 458, 650, 457, 649, 472, 664, 470, 662, 481, 673, 480, 672, 489, 681, 488, 680, 534, 726, 498, 690, 546, 738, 549, 741, 553, 745, 560, 752, 563, 755, 568, 760, 571, 763, 576, 768, 543, 735, 537, 729, 532, 724, 528, 720, 524, 716, 520, 712, 515, 707, 510, 702, 502, 694, 508, 700, 516, 708, 448, 640, 440, 632, 432, 624, 424, 616, 416, 608, 408, 600, 400, 592, 392, 584)(388, 580, 395, 587, 403, 595, 411, 603, 419, 611, 427, 619, 435, 627, 443, 635, 451, 643, 462, 654, 465, 657, 453, 645, 466, 658, 464, 656, 477, 669, 476, 668, 485, 677, 484, 676, 493, 685, 492, 684, 539, 731, 552, 744, 548, 740, 554, 746, 559, 751, 564, 756, 567, 759, 572, 764, 575, 767, 541, 733, 536, 728, 531, 723, 527, 719, 523, 715, 519, 711, 514, 706, 509, 701, 501, 693, 507, 699, 497, 689, 449, 641, 441, 633, 433, 625, 425, 617, 417, 609, 409, 601, 401, 593, 393, 585)(390, 582, 397, 589, 405, 597, 413, 605, 421, 613, 429, 621, 437, 629, 445, 637, 473, 665, 469, 661, 459, 651, 456, 648, 460, 652, 468, 660, 474, 666, 479, 671, 482, 674, 487, 679, 490, 682, 496, 688, 544, 736, 555, 747, 551, 743, 557, 749, 562, 754, 565, 757, 570, 762, 573, 765, 545, 737, 538, 730, 533, 725, 529, 721, 525, 717, 521, 713, 517, 709, 512, 704, 505, 697, 499, 691, 503, 695, 511, 703, 494, 686, 446, 638, 438, 630, 430, 622, 422, 614, 414, 606, 406, 598, 398, 590) L = (1, 387)(2, 391)(3, 394)(4, 395)(5, 385)(6, 397)(7, 399)(8, 386)(9, 388)(10, 402)(11, 403)(12, 389)(13, 405)(14, 390)(15, 407)(16, 392)(17, 393)(18, 410)(19, 411)(20, 396)(21, 413)(22, 398)(23, 415)(24, 400)(25, 401)(26, 418)(27, 419)(28, 404)(29, 421)(30, 406)(31, 423)(32, 408)(33, 409)(34, 426)(35, 427)(36, 412)(37, 429)(38, 414)(39, 431)(40, 416)(41, 417)(42, 434)(43, 435)(44, 420)(45, 437)(46, 422)(47, 439)(48, 424)(49, 425)(50, 442)(51, 443)(52, 428)(53, 445)(54, 430)(55, 447)(56, 432)(57, 433)(58, 450)(59, 451)(60, 436)(61, 473)(62, 438)(63, 471)(64, 440)(65, 441)(66, 463)(67, 462)(68, 444)(69, 466)(70, 461)(71, 458)(72, 460)(73, 472)(74, 457)(75, 456)(76, 468)(77, 467)(78, 465)(79, 454)(80, 477)(81, 453)(82, 464)(83, 475)(84, 474)(85, 459)(86, 481)(87, 455)(88, 470)(89, 469)(90, 479)(91, 478)(92, 485)(93, 476)(94, 483)(95, 482)(96, 489)(97, 480)(98, 487)(99, 486)(100, 493)(101, 484)(102, 491)(103, 490)(104, 534)(105, 488)(106, 496)(107, 495)(108, 539)(109, 492)(110, 446)(111, 542)(112, 544)(113, 449)(114, 546)(115, 503)(116, 504)(117, 507)(118, 508)(119, 511)(120, 452)(121, 499)(122, 500)(123, 497)(124, 516)(125, 501)(126, 502)(127, 494)(128, 505)(129, 506)(130, 509)(131, 510)(132, 448)(133, 512)(134, 513)(135, 514)(136, 515)(137, 517)(138, 518)(139, 519)(140, 520)(141, 521)(142, 522)(143, 523)(144, 524)(145, 525)(146, 526)(147, 527)(148, 528)(149, 529)(150, 498)(151, 530)(152, 531)(153, 532)(154, 533)(155, 552)(156, 535)(157, 536)(158, 556)(159, 537)(160, 555)(161, 538)(162, 549)(163, 540)(164, 554)(165, 553)(166, 558)(167, 557)(168, 548)(169, 560)(170, 559)(171, 551)(172, 550)(173, 562)(174, 561)(175, 564)(176, 563)(177, 566)(178, 565)(179, 568)(180, 567)(181, 570)(182, 569)(183, 572)(184, 571)(185, 574)(186, 573)(187, 576)(188, 575)(189, 545)(190, 547)(191, 541)(192, 543)(193, 577)(194, 578)(195, 579)(196, 580)(197, 581)(198, 582)(199, 583)(200, 584)(201, 585)(202, 586)(203, 587)(204, 588)(205, 589)(206, 590)(207, 591)(208, 592)(209, 593)(210, 594)(211, 595)(212, 596)(213, 597)(214, 598)(215, 599)(216, 600)(217, 601)(218, 602)(219, 603)(220, 604)(221, 605)(222, 606)(223, 607)(224, 608)(225, 609)(226, 610)(227, 611)(228, 612)(229, 613)(230, 614)(231, 615)(232, 616)(233, 617)(234, 618)(235, 619)(236, 620)(237, 621)(238, 622)(239, 623)(240, 624)(241, 625)(242, 626)(243, 627)(244, 628)(245, 629)(246, 630)(247, 631)(248, 632)(249, 633)(250, 634)(251, 635)(252, 636)(253, 637)(254, 638)(255, 639)(256, 640)(257, 641)(258, 642)(259, 643)(260, 644)(261, 645)(262, 646)(263, 647)(264, 648)(265, 649)(266, 650)(267, 651)(268, 652)(269, 653)(270, 654)(271, 655)(272, 656)(273, 657)(274, 658)(275, 659)(276, 660)(277, 661)(278, 662)(279, 663)(280, 664)(281, 665)(282, 666)(283, 667)(284, 668)(285, 669)(286, 670)(287, 671)(288, 672)(289, 673)(290, 674)(291, 675)(292, 676)(293, 677)(294, 678)(295, 679)(296, 680)(297, 681)(298, 682)(299, 683)(300, 684)(301, 685)(302, 686)(303, 687)(304, 688)(305, 689)(306, 690)(307, 691)(308, 692)(309, 693)(310, 694)(311, 695)(312, 696)(313, 697)(314, 698)(315, 699)(316, 700)(317, 701)(318, 702)(319, 703)(320, 704)(321, 705)(322, 706)(323, 707)(324, 708)(325, 709)(326, 710)(327, 711)(328, 712)(329, 713)(330, 714)(331, 715)(332, 716)(333, 717)(334, 718)(335, 719)(336, 720)(337, 721)(338, 722)(339, 723)(340, 724)(341, 725)(342, 726)(343, 727)(344, 728)(345, 729)(346, 730)(347, 731)(348, 732)(349, 733)(350, 734)(351, 735)(352, 736)(353, 737)(354, 738)(355, 739)(356, 740)(357, 741)(358, 742)(359, 743)(360, 744)(361, 745)(362, 746)(363, 747)(364, 748)(365, 749)(366, 750)(367, 751)(368, 752)(369, 753)(370, 754)(371, 755)(372, 756)(373, 757)(374, 758)(375, 759)(376, 760)(377, 761)(378, 762)(379, 763)(380, 764)(381, 765)(382, 766)(383, 767)(384, 768) 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 E23.1199 Graph:: bipartite v = 52 e = 384 f = 288 degree seq :: [ 8^48, 96^4 ] E23.1199 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 48}) Quotient :: dipole Aut^+ = $<192, 68>$ (small group id <192, 68>) Aut = $<384, 1684>$ (small group id <384, 1684>) |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, Y3^22 * Y2 * Y3^-26 * Y2, (Y3^-1 * Y1^-1)^48 ] Map:: polytopal R = (1, 193)(2, 194)(3, 195)(4, 196)(5, 197)(6, 198)(7, 199)(8, 200)(9, 201)(10, 202)(11, 203)(12, 204)(13, 205)(14, 206)(15, 207)(16, 208)(17, 209)(18, 210)(19, 211)(20, 212)(21, 213)(22, 214)(23, 215)(24, 216)(25, 217)(26, 218)(27, 219)(28, 220)(29, 221)(30, 222)(31, 223)(32, 224)(33, 225)(34, 226)(35, 227)(36, 228)(37, 229)(38, 230)(39, 231)(40, 232)(41, 233)(42, 234)(43, 235)(44, 236)(45, 237)(46, 238)(47, 239)(48, 240)(49, 241)(50, 242)(51, 243)(52, 244)(53, 245)(54, 246)(55, 247)(56, 248)(57, 249)(58, 250)(59, 251)(60, 252)(61, 253)(62, 254)(63, 255)(64, 256)(65, 257)(66, 258)(67, 259)(68, 260)(69, 261)(70, 262)(71, 263)(72, 264)(73, 265)(74, 266)(75, 267)(76, 268)(77, 269)(78, 270)(79, 271)(80, 272)(81, 273)(82, 274)(83, 275)(84, 276)(85, 277)(86, 278)(87, 279)(88, 280)(89, 281)(90, 282)(91, 283)(92, 284)(93, 285)(94, 286)(95, 287)(96, 288)(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)(385, 577, 386, 578)(387, 579, 391, 583)(388, 580, 393, 585)(389, 581, 395, 587)(390, 582, 397, 589)(392, 584, 398, 590)(394, 586, 396, 588)(399, 591, 404, 596)(400, 592, 407, 599)(401, 593, 409, 601)(402, 594, 405, 597)(403, 595, 411, 603)(406, 598, 413, 605)(408, 600, 415, 607)(410, 602, 416, 608)(412, 604, 414, 606)(417, 609, 423, 615)(418, 610, 425, 617)(419, 611, 421, 613)(420, 612, 427, 619)(422, 614, 429, 621)(424, 616, 431, 623)(426, 618, 432, 624)(428, 620, 430, 622)(433, 625, 439, 631)(434, 626, 441, 633)(435, 627, 437, 629)(436, 628, 443, 635)(438, 630, 445, 637)(440, 632, 447, 639)(442, 634, 448, 640)(444, 636, 446, 638)(449, 641, 503, 695)(450, 642, 482, 674)(451, 643, 486, 678)(452, 644, 507, 699)(453, 645, 509, 701)(454, 646, 511, 703)(455, 647, 513, 705)(456, 648, 515, 707)(457, 649, 517, 709)(458, 650, 519, 711)(459, 651, 521, 713)(460, 652, 523, 715)(461, 653, 525, 717)(462, 654, 527, 719)(463, 655, 529, 721)(464, 656, 531, 723)(465, 657, 533, 725)(466, 658, 535, 727)(467, 659, 537, 729)(468, 660, 539, 731)(469, 661, 541, 733)(470, 662, 543, 735)(471, 663, 545, 737)(472, 664, 547, 739)(473, 665, 549, 741)(474, 666, 551, 743)(475, 667, 553, 745)(476, 668, 555, 747)(477, 669, 557, 749)(478, 670, 502, 694)(479, 671, 506, 698)(480, 672, 561, 753)(481, 673, 563, 755)(483, 675, 566, 758)(484, 676, 568, 760)(485, 677, 570, 762)(487, 679, 573, 765)(488, 680, 571, 763)(489, 681, 575, 767)(490, 682, 576, 768)(491, 683, 562, 754)(492, 684, 556, 748)(493, 685, 569, 761)(494, 686, 546, 738)(495, 687, 564, 756)(496, 688, 540, 732)(497, 689, 558, 750)(498, 690, 550, 742)(499, 691, 528, 720)(500, 692, 520, 712)(501, 693, 536, 728)(504, 696, 516, 708)(505, 697, 530, 722)(508, 700, 538, 730)(510, 702, 565, 757)(512, 704, 559, 751)(514, 706, 560, 752)(518, 710, 567, 759)(522, 714, 572, 764)(524, 716, 532, 724)(526, 718, 542, 734)(534, 726, 552, 744)(544, 736, 554, 746)(548, 740, 574, 766) L = (1, 387)(2, 389)(3, 392)(4, 385)(5, 396)(6, 386)(7, 399)(8, 401)(9, 402)(10, 388)(11, 404)(12, 406)(13, 407)(14, 390)(15, 393)(16, 391)(17, 410)(18, 411)(19, 394)(20, 397)(21, 395)(22, 414)(23, 415)(24, 398)(25, 400)(26, 418)(27, 419)(28, 403)(29, 405)(30, 422)(31, 423)(32, 408)(33, 409)(34, 426)(35, 427)(36, 412)(37, 413)(38, 430)(39, 431)(40, 416)(41, 417)(42, 434)(43, 435)(44, 420)(45, 421)(46, 438)(47, 439)(48, 424)(49, 425)(50, 442)(51, 443)(52, 428)(53, 429)(54, 446)(55, 447)(56, 432)(57, 433)(58, 450)(59, 451)(60, 436)(61, 437)(62, 502)(63, 503)(64, 440)(65, 441)(66, 506)(67, 507)(68, 444)(69, 455)(70, 457)(71, 460)(72, 453)(73, 464)(74, 454)(75, 467)(76, 469)(77, 470)(78, 456)(79, 472)(80, 474)(81, 475)(82, 458)(83, 461)(84, 459)(85, 478)(86, 479)(87, 462)(88, 465)(89, 463)(90, 482)(91, 483)(92, 466)(93, 468)(94, 486)(95, 487)(96, 471)(97, 473)(98, 449)(99, 452)(100, 476)(101, 477)(102, 445)(103, 448)(104, 480)(105, 481)(106, 484)(107, 485)(108, 488)(109, 489)(110, 490)(111, 491)(112, 492)(113, 493)(114, 494)(115, 495)(116, 496)(117, 497)(118, 566)(119, 573)(120, 498)(121, 499)(122, 531)(123, 541)(124, 500)(125, 529)(126, 514)(127, 521)(128, 518)(129, 547)(130, 524)(131, 549)(132, 510)(133, 537)(134, 532)(135, 539)(136, 512)(137, 535)(138, 538)(139, 533)(140, 542)(141, 511)(142, 544)(143, 563)(144, 516)(145, 527)(146, 548)(147, 525)(148, 552)(149, 509)(150, 554)(151, 557)(152, 520)(153, 519)(154, 526)(155, 555)(156, 522)(157, 553)(158, 559)(159, 517)(160, 560)(161, 575)(162, 528)(163, 515)(164, 534)(165, 545)(166, 530)(167, 543)(168, 565)(169, 513)(170, 567)(171, 570)(172, 536)(173, 568)(174, 540)(175, 572)(176, 574)(177, 569)(178, 546)(179, 561)(180, 550)(181, 505)(182, 523)(183, 508)(184, 562)(185, 556)(186, 576)(187, 558)(188, 501)(189, 551)(190, 504)(191, 571)(192, 564)(193, 577)(194, 578)(195, 579)(196, 580)(197, 581)(198, 582)(199, 583)(200, 584)(201, 585)(202, 586)(203, 587)(204, 588)(205, 589)(206, 590)(207, 591)(208, 592)(209, 593)(210, 594)(211, 595)(212, 596)(213, 597)(214, 598)(215, 599)(216, 600)(217, 601)(218, 602)(219, 603)(220, 604)(221, 605)(222, 606)(223, 607)(224, 608)(225, 609)(226, 610)(227, 611)(228, 612)(229, 613)(230, 614)(231, 615)(232, 616)(233, 617)(234, 618)(235, 619)(236, 620)(237, 621)(238, 622)(239, 623)(240, 624)(241, 625)(242, 626)(243, 627)(244, 628)(245, 629)(246, 630)(247, 631)(248, 632)(249, 633)(250, 634)(251, 635)(252, 636)(253, 637)(254, 638)(255, 639)(256, 640)(257, 641)(258, 642)(259, 643)(260, 644)(261, 645)(262, 646)(263, 647)(264, 648)(265, 649)(266, 650)(267, 651)(268, 652)(269, 653)(270, 654)(271, 655)(272, 656)(273, 657)(274, 658)(275, 659)(276, 660)(277, 661)(278, 662)(279, 663)(280, 664)(281, 665)(282, 666)(283, 667)(284, 668)(285, 669)(286, 670)(287, 671)(288, 672)(289, 673)(290, 674)(291, 675)(292, 676)(293, 677)(294, 678)(295, 679)(296, 680)(297, 681)(298, 682)(299, 683)(300, 684)(301, 685)(302, 686)(303, 687)(304, 688)(305, 689)(306, 690)(307, 691)(308, 692)(309, 693)(310, 694)(311, 695)(312, 696)(313, 697)(314, 698)(315, 699)(316, 700)(317, 701)(318, 702)(319, 703)(320, 704)(321, 705)(322, 706)(323, 707)(324, 708)(325, 709)(326, 710)(327, 711)(328, 712)(329, 713)(330, 714)(331, 715)(332, 716)(333, 717)(334, 718)(335, 719)(336, 720)(337, 721)(338, 722)(339, 723)(340, 724)(341, 725)(342, 726)(343, 727)(344, 728)(345, 729)(346, 730)(347, 731)(348, 732)(349, 733)(350, 734)(351, 735)(352, 736)(353, 737)(354, 738)(355, 739)(356, 740)(357, 741)(358, 742)(359, 743)(360, 744)(361, 745)(362, 746)(363, 747)(364, 748)(365, 749)(366, 750)(367, 751)(368, 752)(369, 753)(370, 754)(371, 755)(372, 756)(373, 757)(374, 758)(375, 759)(376, 760)(377, 761)(378, 762)(379, 763)(380, 764)(381, 765)(382, 766)(383, 767)(384, 768) local type(s) :: { ( 8, 96 ), ( 8, 96, 8, 96 ) } Outer automorphisms :: reflexible Dual of E23.1198 Graph:: simple bipartite v = 288 e = 384 f = 52 degree seq :: [ 2^192, 4^96 ] E23.1200 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 48}) Quotient :: dipole Aut^+ = $<192, 68>$ (small group id <192, 68>) Aut = $<384, 1684>$ (small group id <384, 1684>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3 * Y2^-1)^2, (R * Y2 * Y3^-1)^2, Y3 * Y1^-2 * Y3^-1 * Y1^-2, (Y3^-1 * Y1)^4, Y1^48 ] Map:: polytopal R = (1, 193, 2, 194, 5, 197, 11, 203, 20, 212, 29, 221, 37, 229, 45, 237, 53, 245, 61, 253, 121, 313, 162, 354, 154, 346, 144, 336, 151, 343, 145, 337, 152, 344, 160, 352, 166, 358, 171, 363, 176, 368, 182, 374, 187, 379, 189, 381, 190, 382, 183, 375, 128, 320, 119, 311, 116, 308, 108, 300, 103, 295, 93, 285, 86, 278, 75, 267, 81, 273, 76, 268, 82, 274, 90, 282, 99, 291, 68, 260, 60, 252, 52, 244, 44, 236, 36, 228, 28, 220, 19, 211, 10, 202, 4, 196)(3, 195, 7, 199, 15, 207, 25, 217, 33, 225, 41, 233, 49, 241, 57, 249, 65, 257, 125, 317, 159, 351, 149, 341, 142, 334, 134, 326, 141, 333, 137, 329, 146, 338, 155, 347, 163, 355, 168, 360, 173, 365, 178, 370, 186, 378, 192, 384, 181, 373, 122, 314, 170, 362, 111, 303, 118, 310, 97, 289, 107, 299, 79, 271, 92, 284, 70, 262, 91, 283, 72, 264, 94, 286, 87, 279, 109, 301, 104, 296, 62, 254, 55, 247, 46, 238, 39, 231, 30, 222, 22, 214, 12, 204, 8, 200)(6, 198, 13, 205, 9, 201, 18, 210, 27, 219, 35, 227, 43, 235, 51, 243, 59, 251, 67, 259, 127, 319, 158, 350, 150, 342, 140, 332, 136, 328, 131, 323, 135, 327, 143, 335, 153, 345, 161, 353, 167, 359, 172, 364, 177, 369, 184, 376, 188, 380, 179, 371, 175, 367, 117, 309, 124, 316, 105, 297, 113, 305, 88, 280, 100, 292, 73, 265, 85, 277, 69, 261, 84, 276, 78, 270, 102, 294, 96, 288, 115, 307, 63, 255, 54, 246, 47, 239, 38, 230, 31, 223, 21, 213, 14, 206)(16, 208, 23, 215, 17, 209, 24, 216, 32, 224, 40, 232, 48, 240, 56, 248, 64, 256, 123, 315, 164, 356, 156, 348, 147, 339, 138, 330, 132, 324, 129, 321, 130, 322, 133, 325, 139, 331, 148, 340, 157, 349, 165, 357, 169, 361, 174, 366, 180, 372, 191, 383, 185, 377, 126, 318, 120, 312, 114, 306, 110, 302, 101, 293, 95, 287, 83, 275, 77, 269, 71, 263, 74, 266, 80, 272, 89, 281, 98, 290, 106, 298, 112, 304, 66, 258, 58, 250, 50, 242, 42, 234, 34, 226, 26, 218)(385, 577)(386, 578)(387, 579)(388, 580)(389, 581)(390, 582)(391, 583)(392, 584)(393, 585)(394, 586)(395, 587)(396, 588)(397, 589)(398, 590)(399, 591)(400, 592)(401, 593)(402, 594)(403, 595)(404, 596)(405, 597)(406, 598)(407, 599)(408, 600)(409, 601)(410, 602)(411, 603)(412, 604)(413, 605)(414, 606)(415, 607)(416, 608)(417, 609)(418, 610)(419, 611)(420, 612)(421, 613)(422, 614)(423, 615)(424, 616)(425, 617)(426, 618)(427, 619)(428, 620)(429, 621)(430, 622)(431, 623)(432, 624)(433, 625)(434, 626)(435, 627)(436, 628)(437, 629)(438, 630)(439, 631)(440, 632)(441, 633)(442, 634)(443, 635)(444, 636)(445, 637)(446, 638)(447, 639)(448, 640)(449, 641)(450, 642)(451, 643)(452, 644)(453, 645)(454, 646)(455, 647)(456, 648)(457, 649)(458, 650)(459, 651)(460, 652)(461, 653)(462, 654)(463, 655)(464, 656)(465, 657)(466, 658)(467, 659)(468, 660)(469, 661)(470, 662)(471, 663)(472, 664)(473, 665)(474, 666)(475, 667)(476, 668)(477, 669)(478, 670)(479, 671)(480, 672)(481, 673)(482, 674)(483, 675)(484, 676)(485, 677)(486, 678)(487, 679)(488, 680)(489, 681)(490, 682)(491, 683)(492, 684)(493, 685)(494, 686)(495, 687)(496, 688)(497, 689)(498, 690)(499, 691)(500, 692)(501, 693)(502, 694)(503, 695)(504, 696)(505, 697)(506, 698)(507, 699)(508, 700)(509, 701)(510, 702)(511, 703)(512, 704)(513, 705)(514, 706)(515, 707)(516, 708)(517, 709)(518, 710)(519, 711)(520, 712)(521, 713)(522, 714)(523, 715)(524, 716)(525, 717)(526, 718)(527, 719)(528, 720)(529, 721)(530, 722)(531, 723)(532, 724)(533, 725)(534, 726)(535, 727)(536, 728)(537, 729)(538, 730)(539, 731)(540, 732)(541, 733)(542, 734)(543, 735)(544, 736)(545, 737)(546, 738)(547, 739)(548, 740)(549, 741)(550, 742)(551, 743)(552, 744)(553, 745)(554, 746)(555, 747)(556, 748)(557, 749)(558, 750)(559, 751)(560, 752)(561, 753)(562, 754)(563, 755)(564, 756)(565, 757)(566, 758)(567, 759)(568, 760)(569, 761)(570, 762)(571, 763)(572, 764)(573, 765)(574, 766)(575, 767)(576, 768) L = (1, 387)(2, 390)(3, 385)(4, 393)(5, 396)(6, 386)(7, 400)(8, 401)(9, 388)(10, 399)(11, 405)(12, 389)(13, 407)(14, 408)(15, 394)(16, 391)(17, 392)(18, 410)(19, 411)(20, 414)(21, 395)(22, 416)(23, 397)(24, 398)(25, 418)(26, 402)(27, 403)(28, 417)(29, 422)(30, 404)(31, 424)(32, 406)(33, 412)(34, 409)(35, 426)(36, 427)(37, 430)(38, 413)(39, 432)(40, 415)(41, 434)(42, 419)(43, 420)(44, 433)(45, 438)(46, 421)(47, 440)(48, 423)(49, 428)(50, 425)(51, 442)(52, 443)(53, 446)(54, 429)(55, 448)(56, 431)(57, 450)(58, 435)(59, 436)(60, 449)(61, 499)(62, 437)(63, 507)(64, 439)(65, 444)(66, 441)(67, 496)(68, 511)(69, 513)(70, 514)(71, 515)(72, 516)(73, 517)(74, 518)(75, 519)(76, 520)(77, 521)(78, 522)(79, 523)(80, 524)(81, 525)(82, 526)(83, 527)(84, 528)(85, 529)(86, 530)(87, 531)(88, 532)(89, 533)(90, 534)(91, 535)(92, 536)(93, 537)(94, 538)(95, 539)(96, 540)(97, 541)(98, 542)(99, 543)(100, 544)(101, 545)(102, 546)(103, 547)(104, 548)(105, 549)(106, 509)(107, 550)(108, 551)(109, 505)(110, 552)(111, 553)(112, 451)(113, 555)(114, 556)(115, 445)(116, 557)(117, 558)(118, 560)(119, 561)(120, 562)(121, 493)(122, 564)(123, 447)(124, 566)(125, 490)(126, 568)(127, 452)(128, 570)(129, 453)(130, 454)(131, 455)(132, 456)(133, 457)(134, 458)(135, 459)(136, 460)(137, 461)(138, 462)(139, 463)(140, 464)(141, 465)(142, 466)(143, 467)(144, 468)(145, 469)(146, 470)(147, 471)(148, 472)(149, 473)(150, 474)(151, 475)(152, 476)(153, 477)(154, 478)(155, 479)(156, 480)(157, 481)(158, 482)(159, 483)(160, 484)(161, 485)(162, 486)(163, 487)(164, 488)(165, 489)(166, 491)(167, 492)(168, 494)(169, 495)(170, 571)(171, 497)(172, 498)(173, 500)(174, 501)(175, 573)(176, 502)(177, 503)(178, 504)(179, 575)(180, 506)(181, 574)(182, 508)(183, 572)(184, 510)(185, 576)(186, 512)(187, 554)(188, 567)(189, 559)(190, 565)(191, 563)(192, 569)(193, 577)(194, 578)(195, 579)(196, 580)(197, 581)(198, 582)(199, 583)(200, 584)(201, 585)(202, 586)(203, 587)(204, 588)(205, 589)(206, 590)(207, 591)(208, 592)(209, 593)(210, 594)(211, 595)(212, 596)(213, 597)(214, 598)(215, 599)(216, 600)(217, 601)(218, 602)(219, 603)(220, 604)(221, 605)(222, 606)(223, 607)(224, 608)(225, 609)(226, 610)(227, 611)(228, 612)(229, 613)(230, 614)(231, 615)(232, 616)(233, 617)(234, 618)(235, 619)(236, 620)(237, 621)(238, 622)(239, 623)(240, 624)(241, 625)(242, 626)(243, 627)(244, 628)(245, 629)(246, 630)(247, 631)(248, 632)(249, 633)(250, 634)(251, 635)(252, 636)(253, 637)(254, 638)(255, 639)(256, 640)(257, 641)(258, 642)(259, 643)(260, 644)(261, 645)(262, 646)(263, 647)(264, 648)(265, 649)(266, 650)(267, 651)(268, 652)(269, 653)(270, 654)(271, 655)(272, 656)(273, 657)(274, 658)(275, 659)(276, 660)(277, 661)(278, 662)(279, 663)(280, 664)(281, 665)(282, 666)(283, 667)(284, 668)(285, 669)(286, 670)(287, 671)(288, 672)(289, 673)(290, 674)(291, 675)(292, 676)(293, 677)(294, 678)(295, 679)(296, 680)(297, 681)(298, 682)(299, 683)(300, 684)(301, 685)(302, 686)(303, 687)(304, 688)(305, 689)(306, 690)(307, 691)(308, 692)(309, 693)(310, 694)(311, 695)(312, 696)(313, 697)(314, 698)(315, 699)(316, 700)(317, 701)(318, 702)(319, 703)(320, 704)(321, 705)(322, 706)(323, 707)(324, 708)(325, 709)(326, 710)(327, 711)(328, 712)(329, 713)(330, 714)(331, 715)(332, 716)(333, 717)(334, 718)(335, 719)(336, 720)(337, 721)(338, 722)(339, 723)(340, 724)(341, 725)(342, 726)(343, 727)(344, 728)(345, 729)(346, 730)(347, 731)(348, 732)(349, 733)(350, 734)(351, 735)(352, 736)(353, 737)(354, 738)(355, 739)(356, 740)(357, 741)(358, 742)(359, 743)(360, 744)(361, 745)(362, 746)(363, 747)(364, 748)(365, 749)(366, 750)(367, 751)(368, 752)(369, 753)(370, 754)(371, 755)(372, 756)(373, 757)(374, 758)(375, 759)(376, 760)(377, 761)(378, 762)(379, 763)(380, 764)(381, 765)(382, 766)(383, 767)(384, 768) 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 E23.1197 Graph:: simple bipartite v = 196 e = 384 f = 144 degree seq :: [ 2^192, 96^4 ] E23.1201 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 48}) Quotient :: dipole Aut^+ = $<192, 68>$ (small group id <192, 68>) Aut = $<384, 1684>$ (small group id <384, 1684>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y2^-1 * Y1 * Y2^-1)^2, (Y3 * Y2^-1)^4, Y2^48 ] Map:: R = (1, 193, 2, 194)(3, 195, 7, 199)(4, 196, 9, 201)(5, 197, 11, 203)(6, 198, 13, 205)(8, 200, 14, 206)(10, 202, 12, 204)(15, 207, 20, 212)(16, 208, 23, 215)(17, 209, 25, 217)(18, 210, 21, 213)(19, 211, 27, 219)(22, 214, 29, 221)(24, 216, 31, 223)(26, 218, 32, 224)(28, 220, 30, 222)(33, 225, 39, 231)(34, 226, 41, 233)(35, 227, 37, 229)(36, 228, 43, 235)(38, 230, 45, 237)(40, 232, 47, 239)(42, 234, 48, 240)(44, 236, 46, 238)(49, 241, 55, 247)(50, 242, 57, 249)(51, 243, 53, 245)(52, 244, 59, 251)(54, 246, 61, 253)(56, 248, 63, 255)(58, 250, 64, 256)(60, 252, 62, 254)(65, 257, 92, 284)(66, 258, 111, 303)(67, 259, 113, 305)(68, 260, 83, 275)(69, 261, 115, 307)(70, 262, 117, 309)(71, 263, 119, 311)(72, 264, 121, 313)(73, 265, 123, 315)(74, 266, 125, 317)(75, 267, 127, 319)(76, 268, 129, 321)(77, 269, 131, 323)(78, 270, 133, 325)(79, 271, 135, 327)(80, 272, 137, 329)(81, 273, 139, 331)(82, 274, 141, 333)(84, 276, 144, 336)(85, 277, 146, 338)(86, 278, 148, 340)(87, 279, 150, 342)(88, 280, 152, 344)(89, 281, 154, 346)(90, 282, 156, 348)(91, 283, 158, 350)(93, 285, 161, 353)(94, 286, 163, 355)(95, 287, 165, 357)(96, 288, 167, 359)(97, 289, 169, 361)(98, 290, 171, 363)(99, 291, 173, 365)(100, 292, 175, 367)(101, 293, 177, 369)(102, 294, 179, 371)(103, 295, 181, 373)(104, 296, 183, 375)(105, 297, 185, 377)(106, 298, 187, 379)(107, 299, 189, 381)(108, 300, 190, 382)(109, 301, 191, 383)(110, 302, 192, 384)(112, 304, 178, 370)(114, 306, 182, 374)(116, 308, 162, 354)(118, 310, 157, 349)(120, 312, 159, 351)(122, 314, 176, 368)(124, 316, 164, 356)(126, 318, 180, 372)(128, 320, 166, 358)(130, 322, 136, 328)(132, 324, 145, 337)(134, 326, 170, 362)(138, 330, 153, 345)(140, 332, 174, 366)(142, 334, 172, 364)(143, 335, 188, 380)(147, 339, 155, 347)(149, 341, 168, 360)(151, 343, 184, 376)(160, 352, 186, 378)(385, 577, 387, 579, 392, 584, 401, 593, 410, 602, 418, 610, 426, 618, 434, 626, 442, 634, 450, 642, 456, 648, 453, 645, 455, 647, 460, 652, 468, 660, 474, 666, 479, 671, 483, 675, 487, 679, 491, 683, 496, 688, 506, 698, 500, 692, 504, 696, 514, 706, 529, 721, 541, 733, 550, 742, 558, 750, 566, 758, 569, 761, 567, 759, 553, 745, 551, 743, 536, 728, 530, 722, 507, 699, 525, 717, 509, 701, 452, 644, 444, 636, 436, 628, 428, 620, 420, 612, 412, 604, 403, 595, 394, 586, 388, 580)(386, 578, 389, 581, 396, 588, 406, 598, 414, 606, 422, 614, 430, 622, 438, 630, 446, 638, 465, 657, 458, 650, 454, 646, 457, 649, 463, 655, 472, 664, 477, 669, 481, 673, 485, 677, 489, 681, 493, 685, 524, 716, 510, 702, 502, 694, 508, 700, 520, 712, 537, 729, 546, 738, 554, 746, 562, 754, 570, 762, 565, 757, 571, 763, 549, 741, 555, 747, 528, 720, 538, 730, 503, 695, 532, 724, 505, 697, 534, 726, 448, 640, 440, 632, 432, 624, 424, 616, 416, 608, 408, 600, 398, 590, 390, 582)(391, 583, 399, 591, 393, 585, 402, 594, 411, 603, 419, 611, 427, 619, 435, 627, 443, 635, 451, 643, 467, 659, 459, 651, 466, 658, 461, 653, 469, 661, 475, 667, 480, 672, 484, 676, 488, 680, 492, 684, 498, 690, 527, 719, 512, 704, 526, 718, 516, 708, 531, 723, 543, 735, 552, 744, 560, 752, 568, 760, 573, 765, 576, 768, 557, 749, 563, 755, 540, 732, 547, 739, 513, 705, 521, 713, 499, 691, 517, 709, 495, 687, 449, 641, 441, 633, 433, 625, 425, 617, 417, 609, 409, 601, 400, 592)(395, 587, 404, 596, 397, 589, 407, 599, 415, 607, 423, 615, 431, 623, 439, 631, 447, 639, 476, 668, 471, 663, 462, 654, 470, 662, 464, 656, 473, 665, 478, 670, 482, 674, 486, 678, 490, 682, 494, 686, 544, 736, 535, 727, 518, 710, 533, 725, 522, 714, 539, 731, 548, 740, 556, 748, 564, 756, 572, 764, 575, 767, 574, 766, 561, 753, 559, 751, 545, 737, 542, 734, 519, 711, 515, 707, 501, 693, 511, 703, 523, 715, 497, 689, 445, 637, 437, 629, 429, 621, 421, 613, 413, 605, 405, 597) L = (1, 386)(2, 385)(3, 391)(4, 393)(5, 395)(6, 397)(7, 387)(8, 398)(9, 388)(10, 396)(11, 389)(12, 394)(13, 390)(14, 392)(15, 404)(16, 407)(17, 409)(18, 405)(19, 411)(20, 399)(21, 402)(22, 413)(23, 400)(24, 415)(25, 401)(26, 416)(27, 403)(28, 414)(29, 406)(30, 412)(31, 408)(32, 410)(33, 423)(34, 425)(35, 421)(36, 427)(37, 419)(38, 429)(39, 417)(40, 431)(41, 418)(42, 432)(43, 420)(44, 430)(45, 422)(46, 428)(47, 424)(48, 426)(49, 439)(50, 441)(51, 437)(52, 443)(53, 435)(54, 445)(55, 433)(56, 447)(57, 434)(58, 448)(59, 436)(60, 446)(61, 438)(62, 444)(63, 440)(64, 442)(65, 476)(66, 495)(67, 497)(68, 467)(69, 499)(70, 501)(71, 503)(72, 505)(73, 507)(74, 509)(75, 511)(76, 513)(77, 515)(78, 517)(79, 519)(80, 521)(81, 523)(82, 525)(83, 452)(84, 528)(85, 530)(86, 532)(87, 534)(88, 536)(89, 538)(90, 540)(91, 542)(92, 449)(93, 545)(94, 547)(95, 549)(96, 551)(97, 553)(98, 555)(99, 557)(100, 559)(101, 561)(102, 563)(103, 565)(104, 567)(105, 569)(106, 571)(107, 573)(108, 574)(109, 575)(110, 576)(111, 450)(112, 562)(113, 451)(114, 566)(115, 453)(116, 546)(117, 454)(118, 541)(119, 455)(120, 543)(121, 456)(122, 560)(123, 457)(124, 548)(125, 458)(126, 564)(127, 459)(128, 550)(129, 460)(130, 520)(131, 461)(132, 529)(133, 462)(134, 554)(135, 463)(136, 514)(137, 464)(138, 537)(139, 465)(140, 558)(141, 466)(142, 556)(143, 572)(144, 468)(145, 516)(146, 469)(147, 539)(148, 470)(149, 552)(150, 471)(151, 568)(152, 472)(153, 522)(154, 473)(155, 531)(156, 474)(157, 502)(158, 475)(159, 504)(160, 570)(161, 477)(162, 500)(163, 478)(164, 508)(165, 479)(166, 512)(167, 480)(168, 533)(169, 481)(170, 518)(171, 482)(172, 526)(173, 483)(174, 524)(175, 484)(176, 506)(177, 485)(178, 496)(179, 486)(180, 510)(181, 487)(182, 498)(183, 488)(184, 535)(185, 489)(186, 544)(187, 490)(188, 527)(189, 491)(190, 492)(191, 493)(192, 494)(193, 577)(194, 578)(195, 579)(196, 580)(197, 581)(198, 582)(199, 583)(200, 584)(201, 585)(202, 586)(203, 587)(204, 588)(205, 589)(206, 590)(207, 591)(208, 592)(209, 593)(210, 594)(211, 595)(212, 596)(213, 597)(214, 598)(215, 599)(216, 600)(217, 601)(218, 602)(219, 603)(220, 604)(221, 605)(222, 606)(223, 607)(224, 608)(225, 609)(226, 610)(227, 611)(228, 612)(229, 613)(230, 614)(231, 615)(232, 616)(233, 617)(234, 618)(235, 619)(236, 620)(237, 621)(238, 622)(239, 623)(240, 624)(241, 625)(242, 626)(243, 627)(244, 628)(245, 629)(246, 630)(247, 631)(248, 632)(249, 633)(250, 634)(251, 635)(252, 636)(253, 637)(254, 638)(255, 639)(256, 640)(257, 641)(258, 642)(259, 643)(260, 644)(261, 645)(262, 646)(263, 647)(264, 648)(265, 649)(266, 650)(267, 651)(268, 652)(269, 653)(270, 654)(271, 655)(272, 656)(273, 657)(274, 658)(275, 659)(276, 660)(277, 661)(278, 662)(279, 663)(280, 664)(281, 665)(282, 666)(283, 667)(284, 668)(285, 669)(286, 670)(287, 671)(288, 672)(289, 673)(290, 674)(291, 675)(292, 676)(293, 677)(294, 678)(295, 679)(296, 680)(297, 681)(298, 682)(299, 683)(300, 684)(301, 685)(302, 686)(303, 687)(304, 688)(305, 689)(306, 690)(307, 691)(308, 692)(309, 693)(310, 694)(311, 695)(312, 696)(313, 697)(314, 698)(315, 699)(316, 700)(317, 701)(318, 702)(319, 703)(320, 704)(321, 705)(322, 706)(323, 707)(324, 708)(325, 709)(326, 710)(327, 711)(328, 712)(329, 713)(330, 714)(331, 715)(332, 716)(333, 717)(334, 718)(335, 719)(336, 720)(337, 721)(338, 722)(339, 723)(340, 724)(341, 725)(342, 726)(343, 727)(344, 728)(345, 729)(346, 730)(347, 731)(348, 732)(349, 733)(350, 734)(351, 735)(352, 736)(353, 737)(354, 738)(355, 739)(356, 740)(357, 741)(358, 742)(359, 743)(360, 744)(361, 745)(362, 746)(363, 747)(364, 748)(365, 749)(366, 750)(367, 751)(368, 752)(369, 753)(370, 754)(371, 755)(372, 756)(373, 757)(374, 758)(375, 759)(376, 760)(377, 761)(378, 762)(379, 763)(380, 764)(381, 765)(382, 766)(383, 767)(384, 768) 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 E23.1202 Graph:: bipartite v = 100 e = 384 f = 240 degree seq :: [ 4^96, 96^4 ] E23.1202 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 48}) Quotient :: dipole Aut^+ = $<192, 68>$ (small group id <192, 68>) Aut = $<384, 1684>$ (small group id <384, 1684>) |r| :: 2 Presentation :: [ Y2, R^2, (R * Y3)^2, (R * Y1)^2, (Y3^-1 * Y1^-1)^2, Y1^4, (Y3 * Y1^-1)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2^-1)^48 ] Map:: polytopal R = (1, 193, 2, 194, 6, 198, 4, 196)(3, 195, 9, 201, 13, 205, 8, 200)(5, 197, 11, 203, 14, 206, 7, 199)(10, 202, 16, 208, 21, 213, 17, 209)(12, 204, 15, 207, 22, 214, 19, 211)(18, 210, 25, 217, 29, 221, 24, 216)(20, 212, 27, 219, 30, 222, 23, 215)(26, 218, 32, 224, 37, 229, 33, 225)(28, 220, 31, 223, 38, 230, 35, 227)(34, 226, 41, 233, 45, 237, 40, 232)(36, 228, 43, 235, 46, 238, 39, 231)(42, 234, 48, 240, 53, 245, 49, 241)(44, 236, 47, 239, 54, 246, 51, 243)(50, 242, 57, 249, 61, 253, 56, 248)(52, 244, 59, 251, 62, 254, 55, 247)(58, 250, 64, 256, 81, 273, 65, 257)(60, 252, 63, 255, 106, 298, 67, 259)(66, 258, 109, 301, 77, 269, 120, 312)(68, 260, 71, 263, 115, 307, 79, 271)(69, 261, 111, 303, 74, 266, 112, 304)(70, 262, 113, 305, 72, 264, 114, 306)(73, 265, 116, 308, 80, 272, 117, 309)(75, 267, 118, 310, 76, 268, 119, 311)(78, 270, 121, 313, 85, 277, 122, 314)(82, 274, 123, 315, 83, 275, 124, 316)(84, 276, 125, 317, 89, 281, 126, 318)(86, 278, 127, 319, 87, 279, 128, 320)(88, 280, 129, 321, 93, 285, 130, 322)(90, 282, 131, 323, 91, 283, 132, 324)(92, 284, 133, 325, 97, 289, 134, 326)(94, 286, 135, 327, 95, 287, 136, 328)(96, 288, 137, 329, 101, 293, 138, 330)(98, 290, 139, 331, 99, 291, 140, 332)(100, 292, 141, 333, 105, 297, 143, 335)(102, 294, 144, 336, 103, 295, 145, 337)(104, 296, 146, 338, 142, 334, 148, 340)(107, 299, 149, 341, 108, 300, 151, 343)(110, 302, 153, 345, 147, 339, 155, 347)(150, 342, 192, 384, 152, 344, 190, 382)(154, 346, 189, 381, 156, 348, 191, 383)(157, 349, 188, 380, 158, 350, 187, 379)(159, 351, 186, 378, 160, 352, 185, 377)(161, 353, 183, 375, 162, 354, 184, 376)(163, 355, 181, 373, 164, 356, 182, 374)(165, 357, 180, 372, 166, 358, 179, 371)(167, 359, 178, 370, 168, 360, 177, 369)(169, 361, 175, 367, 170, 362, 176, 368)(171, 363, 173, 365, 172, 364, 174, 366)(385, 577)(386, 578)(387, 579)(388, 580)(389, 581)(390, 582)(391, 583)(392, 584)(393, 585)(394, 586)(395, 587)(396, 588)(397, 589)(398, 590)(399, 591)(400, 592)(401, 593)(402, 594)(403, 595)(404, 596)(405, 597)(406, 598)(407, 599)(408, 600)(409, 601)(410, 602)(411, 603)(412, 604)(413, 605)(414, 606)(415, 607)(416, 608)(417, 609)(418, 610)(419, 611)(420, 612)(421, 613)(422, 614)(423, 615)(424, 616)(425, 617)(426, 618)(427, 619)(428, 620)(429, 621)(430, 622)(431, 623)(432, 624)(433, 625)(434, 626)(435, 627)(436, 628)(437, 629)(438, 630)(439, 631)(440, 632)(441, 633)(442, 634)(443, 635)(444, 636)(445, 637)(446, 638)(447, 639)(448, 640)(449, 641)(450, 642)(451, 643)(452, 644)(453, 645)(454, 646)(455, 647)(456, 648)(457, 649)(458, 650)(459, 651)(460, 652)(461, 653)(462, 654)(463, 655)(464, 656)(465, 657)(466, 658)(467, 659)(468, 660)(469, 661)(470, 662)(471, 663)(472, 664)(473, 665)(474, 666)(475, 667)(476, 668)(477, 669)(478, 670)(479, 671)(480, 672)(481, 673)(482, 674)(483, 675)(484, 676)(485, 677)(486, 678)(487, 679)(488, 680)(489, 681)(490, 682)(491, 683)(492, 684)(493, 685)(494, 686)(495, 687)(496, 688)(497, 689)(498, 690)(499, 691)(500, 692)(501, 693)(502, 694)(503, 695)(504, 696)(505, 697)(506, 698)(507, 699)(508, 700)(509, 701)(510, 702)(511, 703)(512, 704)(513, 705)(514, 706)(515, 707)(516, 708)(517, 709)(518, 710)(519, 711)(520, 712)(521, 713)(522, 714)(523, 715)(524, 716)(525, 717)(526, 718)(527, 719)(528, 720)(529, 721)(530, 722)(531, 723)(532, 724)(533, 725)(534, 726)(535, 727)(536, 728)(537, 729)(538, 730)(539, 731)(540, 732)(541, 733)(542, 734)(543, 735)(544, 736)(545, 737)(546, 738)(547, 739)(548, 740)(549, 741)(550, 742)(551, 743)(552, 744)(553, 745)(554, 746)(555, 747)(556, 748)(557, 749)(558, 750)(559, 751)(560, 752)(561, 753)(562, 754)(563, 755)(564, 756)(565, 757)(566, 758)(567, 759)(568, 760)(569, 761)(570, 762)(571, 763)(572, 764)(573, 765)(574, 766)(575, 767)(576, 768) L = (1, 387)(2, 391)(3, 394)(4, 395)(5, 385)(6, 397)(7, 399)(8, 386)(9, 388)(10, 402)(11, 403)(12, 389)(13, 405)(14, 390)(15, 407)(16, 392)(17, 393)(18, 410)(19, 411)(20, 396)(21, 413)(22, 398)(23, 415)(24, 400)(25, 401)(26, 418)(27, 419)(28, 404)(29, 421)(30, 406)(31, 423)(32, 408)(33, 409)(34, 426)(35, 427)(36, 412)(37, 429)(38, 414)(39, 431)(40, 416)(41, 417)(42, 434)(43, 435)(44, 420)(45, 437)(46, 422)(47, 439)(48, 424)(49, 425)(50, 442)(51, 443)(52, 428)(53, 445)(54, 430)(55, 447)(56, 432)(57, 433)(58, 450)(59, 451)(60, 436)(61, 465)(62, 438)(63, 463)(64, 440)(65, 441)(66, 456)(67, 455)(68, 444)(69, 464)(70, 460)(71, 458)(72, 459)(73, 469)(74, 457)(75, 467)(76, 466)(77, 454)(78, 473)(79, 453)(80, 462)(81, 461)(82, 471)(83, 470)(84, 477)(85, 468)(86, 475)(87, 474)(88, 481)(89, 472)(90, 479)(91, 478)(92, 485)(93, 476)(94, 483)(95, 482)(96, 489)(97, 480)(98, 487)(99, 486)(100, 526)(101, 484)(102, 492)(103, 491)(104, 531)(105, 488)(106, 446)(107, 534)(108, 536)(109, 449)(110, 538)(111, 499)(112, 452)(113, 493)(114, 504)(115, 490)(116, 495)(117, 496)(118, 497)(119, 498)(120, 448)(121, 500)(122, 501)(123, 502)(124, 503)(125, 505)(126, 506)(127, 507)(128, 508)(129, 509)(130, 510)(131, 511)(132, 512)(133, 513)(134, 514)(135, 515)(136, 516)(137, 517)(138, 518)(139, 519)(140, 520)(141, 521)(142, 494)(143, 522)(144, 523)(145, 524)(146, 525)(147, 540)(148, 527)(149, 528)(150, 542)(151, 529)(152, 541)(153, 530)(154, 544)(155, 532)(156, 543)(157, 546)(158, 545)(159, 548)(160, 547)(161, 550)(162, 549)(163, 552)(164, 551)(165, 554)(166, 553)(167, 556)(168, 555)(169, 558)(170, 557)(171, 560)(172, 559)(173, 562)(174, 561)(175, 564)(176, 563)(177, 566)(178, 565)(179, 568)(180, 567)(181, 570)(182, 569)(183, 572)(184, 571)(185, 575)(186, 573)(187, 574)(188, 576)(189, 539)(190, 533)(191, 537)(192, 535)(193, 577)(194, 578)(195, 579)(196, 580)(197, 581)(198, 582)(199, 583)(200, 584)(201, 585)(202, 586)(203, 587)(204, 588)(205, 589)(206, 590)(207, 591)(208, 592)(209, 593)(210, 594)(211, 595)(212, 596)(213, 597)(214, 598)(215, 599)(216, 600)(217, 601)(218, 602)(219, 603)(220, 604)(221, 605)(222, 606)(223, 607)(224, 608)(225, 609)(226, 610)(227, 611)(228, 612)(229, 613)(230, 614)(231, 615)(232, 616)(233, 617)(234, 618)(235, 619)(236, 620)(237, 621)(238, 622)(239, 623)(240, 624)(241, 625)(242, 626)(243, 627)(244, 628)(245, 629)(246, 630)(247, 631)(248, 632)(249, 633)(250, 634)(251, 635)(252, 636)(253, 637)(254, 638)(255, 639)(256, 640)(257, 641)(258, 642)(259, 643)(260, 644)(261, 645)(262, 646)(263, 647)(264, 648)(265, 649)(266, 650)(267, 651)(268, 652)(269, 653)(270, 654)(271, 655)(272, 656)(273, 657)(274, 658)(275, 659)(276, 660)(277, 661)(278, 662)(279, 663)(280, 664)(281, 665)(282, 666)(283, 667)(284, 668)(285, 669)(286, 670)(287, 671)(288, 672)(289, 673)(290, 674)(291, 675)(292, 676)(293, 677)(294, 678)(295, 679)(296, 680)(297, 681)(298, 682)(299, 683)(300, 684)(301, 685)(302, 686)(303, 687)(304, 688)(305, 689)(306, 690)(307, 691)(308, 692)(309, 693)(310, 694)(311, 695)(312, 696)(313, 697)(314, 698)(315, 699)(316, 700)(317, 701)(318, 702)(319, 703)(320, 704)(321, 705)(322, 706)(323, 707)(324, 708)(325, 709)(326, 710)(327, 711)(328, 712)(329, 713)(330, 714)(331, 715)(332, 716)(333, 717)(334, 718)(335, 719)(336, 720)(337, 721)(338, 722)(339, 723)(340, 724)(341, 725)(342, 726)(343, 727)(344, 728)(345, 729)(346, 730)(347, 731)(348, 732)(349, 733)(350, 734)(351, 735)(352, 736)(353, 737)(354, 738)(355, 739)(356, 740)(357, 741)(358, 742)(359, 743)(360, 744)(361, 745)(362, 746)(363, 747)(364, 748)(365, 749)(366, 750)(367, 751)(368, 752)(369, 753)(370, 754)(371, 755)(372, 756)(373, 757)(374, 758)(375, 759)(376, 760)(377, 761)(378, 762)(379, 763)(380, 764)(381, 765)(382, 766)(383, 767)(384, 768) local type(s) :: { ( 4, 96 ), ( 4, 96, 4, 96, 4, 96, 4, 96 ) } Outer automorphisms :: reflexible Dual of E23.1201 Graph:: simple bipartite v = 240 e = 384 f = 100 degree seq :: [ 2^192, 8^48 ] E23.1203 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 4, 48}) Quotient :: regular Aut^+ = $<192, 77>$ (small group id <192, 77>) Aut = $<384, 1696>$ (small group id <384, 1696>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1)^4, T2 * T1 * T2 * T1^3 * T2 * T1 * T2 * T1^-1, (T1^3 * T2 * T1)^2, T1^14 * T2 * T1^-10 * T2 ] Map:: polytopal non-degenerate R = (1, 2, 5, 11, 23, 45, 68, 85, 101, 117, 133, 149, 165, 181, 174, 160, 143, 127, 110, 96, 79, 61, 32, 54, 73, 63, 36, 57, 75, 91, 107, 123, 139, 155, 171, 187, 180, 164, 148, 132, 116, 100, 84, 67, 44, 22, 10, 4)(3, 7, 15, 31, 59, 77, 93, 109, 125, 141, 157, 173, 185, 167, 150, 140, 121, 103, 86, 76, 52, 26, 12, 25, 49, 42, 21, 41, 65, 82, 98, 114, 130, 146, 162, 178, 182, 172, 153, 135, 118, 108, 89, 70, 46, 37, 18, 8)(6, 13, 27, 53, 43, 66, 83, 99, 115, 131, 147, 163, 179, 183, 166, 156, 137, 119, 102, 92, 72, 48, 24, 47, 40, 20, 9, 19, 38, 64, 81, 97, 113, 129, 145, 161, 177, 188, 169, 151, 134, 124, 105, 87, 69, 58, 30, 14)(16, 33, 50, 29, 56, 71, 90, 104, 122, 136, 154, 168, 186, 191, 189, 176, 159, 142, 126, 112, 95, 78, 60, 39, 55, 28, 17, 35, 51, 74, 88, 106, 120, 138, 152, 170, 184, 192, 190, 175, 158, 144, 128, 111, 94, 80, 62, 34) L = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 36)(19, 39)(20, 33)(22, 43)(23, 46)(25, 50)(26, 51)(27, 54)(30, 57)(31, 60)(34, 53)(35, 47)(37, 56)(38, 61)(40, 63)(41, 62)(42, 55)(44, 59)(45, 69)(48, 71)(49, 73)(52, 75)(58, 74)(64, 80)(65, 79)(66, 78)(67, 81)(68, 86)(70, 88)(72, 91)(76, 90)(77, 94)(82, 95)(83, 96)(84, 98)(85, 102)(87, 104)(89, 107)(92, 106)(93, 110)(97, 112)(99, 111)(100, 115)(101, 118)(103, 120)(105, 123)(108, 122)(109, 126)(113, 127)(114, 128)(116, 125)(117, 134)(119, 136)(121, 139)(124, 138)(129, 144)(130, 143)(131, 142)(132, 145)(133, 150)(135, 152)(137, 155)(140, 154)(141, 158)(146, 159)(147, 160)(148, 162)(149, 166)(151, 168)(153, 171)(156, 170)(157, 174)(161, 176)(163, 175)(164, 179)(165, 182)(167, 184)(169, 187)(172, 186)(173, 189)(177, 181)(178, 190)(180, 185)(183, 191)(188, 192) local type(s) :: { ( 4^48 ) } Outer automorphisms :: reflexible Dual of E23.1204 Transitivity :: ET+ VT+ AT+ REG+ Graph:: bipartite v = 4 e = 96 f = 48 degree seq :: [ 48^4 ] E23.1204 :: Family: { 1 } :: Oriented family(ies): { E1b } Signature :: (0; {2, 4, 48}) Quotient :: regular Aut^+ = $<192, 77>$ (small group id <192, 77>) Aut = $<384, 1696>$ (small group id <384, 1696>) |r| :: 2 Presentation :: [ T2^2, F^2, T1^4, (F * T1)^2, (F * T2)^2, T1^-1 * T2 * T1^-1 * T2 * T1^-2 * T2 * T1 * T2 * T1^-1, T2 * T1^-1 * T2 * T1 * T2 * T1^-1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1 * T2 * T1^-1, (T1 * T2 * T1^-1 * T2 * T1 * T2)^16 ] Map:: polytopal non-degenerate R = (1, 2, 5, 4)(3, 7, 13, 8)(6, 11, 20, 12)(9, 16, 28, 17)(10, 18, 31, 19)(14, 24, 32, 25)(15, 26, 33, 27)(21, 35, 29, 36)(22, 37, 30, 38)(23, 34, 44, 39)(40, 49, 42, 50)(41, 51, 43, 52)(45, 53, 47, 54)(46, 55, 48, 56)(57, 65, 59, 66)(58, 67, 60, 68)(61, 69, 63, 70)(62, 71, 64, 72)(73, 80, 75, 100)(74, 77, 76, 89)(78, 119, 94, 115)(79, 117, 99, 113)(81, 129, 87, 132)(82, 121, 88, 127)(83, 135, 85, 138)(84, 123, 86, 125)(90, 145, 92, 147)(91, 130, 93, 133)(95, 141, 97, 143)(96, 136, 98, 139)(101, 154, 103, 156)(102, 150, 104, 152)(105, 163, 107, 165)(106, 159, 108, 161)(109, 173, 111, 175)(110, 169, 112, 171)(114, 181, 118, 183)(116, 177, 120, 179)(122, 191, 128, 189)(124, 188, 126, 186)(131, 180, 134, 178)(137, 176, 140, 174)(142, 172, 144, 170)(146, 184, 148, 182)(149, 187, 168, 185)(151, 166, 153, 164)(155, 162, 157, 160)(158, 192, 167, 190) 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, 113)(70, 115)(71, 117)(72, 119)(77, 121)(78, 123)(79, 125)(80, 127)(81, 130)(82, 133)(83, 136)(84, 139)(85, 141)(86, 143)(87, 145)(88, 147)(89, 129)(90, 150)(91, 152)(92, 154)(93, 156)(94, 135)(95, 159)(96, 161)(97, 163)(98, 165)(99, 138)(100, 132)(101, 169)(102, 171)(103, 173)(104, 175)(105, 177)(106, 179)(107, 181)(108, 183)(109, 185)(110, 187)(111, 189)(112, 191)(114, 190)(116, 192)(118, 186)(120, 188)(122, 178)(124, 174)(126, 170)(128, 182)(131, 164)(134, 160)(137, 157)(140, 153)(142, 155)(144, 151)(146, 166)(148, 162)(149, 180)(158, 176)(167, 172)(168, 184) local type(s) :: { ( 48^4 ) } Outer automorphisms :: reflexible Dual of E23.1203 Transitivity :: ET+ VT+ AT+ REG+ Graph:: simple bipartite v = 48 e = 96 f = 4 degree seq :: [ 4^48 ] E23.1205 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 48}) Quotient :: edge Aut^+ = $<192, 77>$ (small group id <192, 77>) Aut = $<384, 1696>$ (small group id <384, 1696>) |r| :: 2 Presentation :: [ T1^2, F^2, T2^4, (F * T1)^2, (F * T2)^2, T2^-1 * T1 * T2^-1 * T1 * T2^-2 * T1 * T2 * T1 * T2^-1, T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2 ] Map:: polytopal R = (1, 3, 8, 4)(2, 5, 11, 6)(7, 13, 24, 14)(9, 16, 29, 17)(10, 18, 32, 19)(12, 21, 37, 22)(15, 26, 43, 27)(20, 34, 48, 35)(23, 39, 28, 40)(25, 41, 30, 42)(31, 44, 36, 45)(33, 46, 38, 47)(49, 57, 51, 58)(50, 59, 52, 60)(53, 61, 55, 62)(54, 63, 56, 64)(65, 73, 67, 74)(66, 75, 68, 76)(69, 129, 71, 133)(70, 131, 72, 135)(77, 138, 96, 140)(78, 142, 91, 144)(79, 146, 110, 141)(80, 149, 111, 151)(81, 153, 102, 137)(82, 156, 103, 158)(83, 160, 85, 162)(84, 163, 116, 159)(86, 161, 88, 167)(87, 168, 115, 166)(89, 148, 92, 145)(90, 172, 93, 174)(94, 155, 97, 152)(95, 179, 98, 181)(99, 175, 101, 186)(100, 170, 105, 185)(104, 143, 106, 169)(107, 182, 109, 190)(108, 165, 113, 189)(112, 139, 114, 164)(117, 191, 118, 192)(119, 147, 120, 150)(121, 187, 122, 188)(123, 154, 124, 157)(125, 176, 126, 177)(127, 171, 128, 173)(130, 183, 132, 184)(134, 178, 136, 180)(193, 194)(195, 199)(196, 201)(197, 202)(198, 204)(200, 207)(203, 212)(205, 215)(206, 217)(208, 220)(209, 222)(210, 223)(211, 225)(213, 228)(214, 230)(216, 226)(218, 224)(219, 229)(221, 227)(231, 241)(232, 242)(233, 243)(234, 244)(235, 240)(236, 245)(237, 246)(238, 247)(239, 248)(249, 257)(250, 258)(251, 259)(252, 260)(253, 261)(254, 262)(255, 263)(256, 264)(265, 287)(266, 286)(267, 290)(268, 289)(269, 329)(270, 333)(271, 337)(272, 340)(273, 344)(274, 347)(275, 351)(276, 345)(277, 332)(278, 358)(279, 338)(280, 336)(281, 325)(282, 321)(283, 343)(284, 327)(285, 323)(288, 350)(291, 377)(292, 355)(293, 354)(294, 373)(295, 371)(296, 362)(297, 330)(298, 352)(299, 381)(300, 360)(301, 359)(302, 366)(303, 364)(304, 357)(305, 334)(306, 353)(307, 341)(308, 348)(309, 361)(310, 378)(311, 335)(312, 367)(313, 356)(314, 382)(315, 331)(316, 374)(317, 342)(318, 384)(319, 339)(320, 383)(322, 349)(324, 380)(326, 346)(328, 379)(363, 376)(365, 372)(368, 375)(369, 370) L = (1, 193)(2, 194)(3, 195)(4, 196)(5, 197)(6, 198)(7, 199)(8, 200)(9, 201)(10, 202)(11, 203)(12, 204)(13, 205)(14, 206)(15, 207)(16, 208)(17, 209)(18, 210)(19, 211)(20, 212)(21, 213)(22, 214)(23, 215)(24, 216)(25, 217)(26, 218)(27, 219)(28, 220)(29, 221)(30, 222)(31, 223)(32, 224)(33, 225)(34, 226)(35, 227)(36, 228)(37, 229)(38, 230)(39, 231)(40, 232)(41, 233)(42, 234)(43, 235)(44, 236)(45, 237)(46, 238)(47, 239)(48, 240)(49, 241)(50, 242)(51, 243)(52, 244)(53, 245)(54, 246)(55, 247)(56, 248)(57, 249)(58, 250)(59, 251)(60, 252)(61, 253)(62, 254)(63, 255)(64, 256)(65, 257)(66, 258)(67, 259)(68, 260)(69, 261)(70, 262)(71, 263)(72, 264)(73, 265)(74, 266)(75, 267)(76, 268)(77, 269)(78, 270)(79, 271)(80, 272)(81, 273)(82, 274)(83, 275)(84, 276)(85, 277)(86, 278)(87, 279)(88, 280)(89, 281)(90, 282)(91, 283)(92, 284)(93, 285)(94, 286)(95, 287)(96, 288)(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) :: { ( 96, 96 ), ( 96^4 ) } Outer automorphisms :: reflexible Dual of E23.1209 Transitivity :: ET+ Graph:: simple bipartite v = 144 e = 192 f = 4 degree seq :: [ 2^96, 4^48 ] E23.1206 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 48}) Quotient :: edge Aut^+ = $<192, 77>$ (small group id <192, 77>) Aut = $<384, 1696>$ (small group id <384, 1696>) |r| :: 2 Presentation :: [ F^2, T1^4, (T2^-1 * T1^-1)^2, (F * T2)^2, (F * T1)^2, T1^-1 * T2^-1 * T1 * T2^-2 * T1 * T2^-1 * T1^-1, (T2^-3 * T1)^2, (T2 * T1^-1)^4, T2 * T1^-1 * T2^-23 * T1^-1 ] Map:: polytopal non-degenerate R = (1, 3, 10, 24, 48, 64, 80, 96, 112, 128, 144, 160, 176, 184, 168, 152, 136, 120, 104, 88, 72, 56, 39, 28, 42, 19, 41, 58, 74, 90, 106, 122, 138, 154, 170, 186, 180, 164, 148, 132, 116, 100, 84, 68, 52, 32, 14, 5)(2, 7, 17, 38, 57, 73, 89, 105, 121, 137, 153, 169, 185, 174, 158, 142, 126, 110, 94, 78, 62, 46, 23, 11, 26, 35, 31, 51, 67, 83, 99, 115, 131, 147, 163, 179, 188, 172, 156, 140, 124, 108, 92, 76, 60, 44, 20, 8)(4, 12, 27, 49, 65, 81, 97, 113, 129, 145, 161, 177, 190, 175, 159, 143, 127, 111, 95, 79, 63, 47, 25, 34, 30, 13, 29, 50, 66, 82, 98, 114, 130, 146, 162, 178, 189, 173, 157, 141, 125, 109, 93, 77, 61, 45, 22, 9)(6, 15, 33, 53, 69, 85, 101, 117, 133, 149, 165, 181, 191, 183, 167, 151, 135, 119, 103, 87, 71, 55, 37, 18, 40, 21, 43, 59, 75, 91, 107, 123, 139, 155, 171, 187, 192, 182, 166, 150, 134, 118, 102, 86, 70, 54, 36, 16)(193, 194, 198, 196)(195, 201, 213, 203)(197, 205, 210, 199)(200, 211, 226, 207)(202, 215, 225, 217)(204, 208, 227, 220)(206, 223, 228, 221)(209, 229, 219, 231)(212, 235, 214, 233)(216, 239, 251, 236)(218, 232, 222, 234)(224, 241, 247, 243)(230, 248, 242, 246)(237, 245, 238, 250)(240, 252, 261, 253)(244, 249, 262, 257)(254, 267, 255, 266)(256, 269, 283, 270)(258, 264, 259, 263)(260, 274, 279, 265)(268, 282, 271, 277)(272, 286, 293, 287)(273, 278, 275, 280)(276, 291, 294, 290)(281, 295, 289, 296)(284, 299, 285, 298)(288, 303, 315, 300)(292, 305, 311, 307)(297, 312, 306, 310)(301, 309, 302, 314)(304, 316, 325, 317)(308, 313, 326, 321)(318, 331, 319, 330)(320, 333, 347, 334)(322, 328, 323, 327)(324, 338, 343, 329)(332, 346, 335, 341)(336, 350, 357, 351)(337, 342, 339, 344)(340, 355, 358, 354)(345, 359, 353, 360)(348, 363, 349, 362)(352, 367, 379, 364)(356, 369, 375, 371)(361, 376, 370, 374)(365, 373, 366, 378)(368, 380, 383, 381)(372, 377, 384, 382) L = (1, 193)(2, 194)(3, 195)(4, 196)(5, 197)(6, 198)(7, 199)(8, 200)(9, 201)(10, 202)(11, 203)(12, 204)(13, 205)(14, 206)(15, 207)(16, 208)(17, 209)(18, 210)(19, 211)(20, 212)(21, 213)(22, 214)(23, 215)(24, 216)(25, 217)(26, 218)(27, 219)(28, 220)(29, 221)(30, 222)(31, 223)(32, 224)(33, 225)(34, 226)(35, 227)(36, 228)(37, 229)(38, 230)(39, 231)(40, 232)(41, 233)(42, 234)(43, 235)(44, 236)(45, 237)(46, 238)(47, 239)(48, 240)(49, 241)(50, 242)(51, 243)(52, 244)(53, 245)(54, 246)(55, 247)(56, 248)(57, 249)(58, 250)(59, 251)(60, 252)(61, 253)(62, 254)(63, 255)(64, 256)(65, 257)(66, 258)(67, 259)(68, 260)(69, 261)(70, 262)(71, 263)(72, 264)(73, 265)(74, 266)(75, 267)(76, 268)(77, 269)(78, 270)(79, 271)(80, 272)(81, 273)(82, 274)(83, 275)(84, 276)(85, 277)(86, 278)(87, 279)(88, 280)(89, 281)(90, 282)(91, 283)(92, 284)(93, 285)(94, 286)(95, 287)(96, 288)(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) :: { ( 4^4 ), ( 4^48 ) } Outer automorphisms :: reflexible Dual of E23.1210 Transitivity :: ET+ Graph:: simple bipartite v = 52 e = 192 f = 96 degree seq :: [ 4^48, 48^4 ] E23.1207 :: Family: { 2 } :: Oriented family(ies): { E3b } Signature :: (0; {2, 4, 48}) Quotient :: edge Aut^+ = $<192, 77>$ (small group id <192, 77>) Aut = $<384, 1696>$ (small group id <384, 1696>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-1)^4, T2 * T1^2 * T2 * T1^-1 * T2 * T1^-2 * T2 * T1, (T2 * T1^-4)^2, T1^18 * T2 * T1^-6 * T2 ] Map:: polytopal R = (1, 3)(2, 6)(4, 9)(5, 12)(7, 16)(8, 17)(10, 21)(11, 24)(13, 28)(14, 29)(15, 32)(18, 36)(19, 39)(20, 33)(22, 43)(23, 46)(25, 50)(26, 51)(27, 54)(30, 57)(31, 60)(34, 53)(35, 47)(37, 56)(38, 61)(40, 63)(41, 62)(42, 55)(44, 59)(45, 69)(48, 71)(49, 73)(52, 75)(58, 74)(64, 80)(65, 79)(66, 78)(67, 81)(68, 86)(70, 88)(72, 91)(76, 90)(77, 94)(82, 95)(83, 96)(84, 98)(85, 102)(87, 104)(89, 107)(92, 106)(93, 110)(97, 112)(99, 111)(100, 115)(101, 118)(103, 120)(105, 123)(108, 122)(109, 126)(113, 127)(114, 128)(116, 125)(117, 134)(119, 136)(121, 139)(124, 138)(129, 144)(130, 143)(131, 142)(132, 145)(133, 150)(135, 152)(137, 155)(140, 154)(141, 158)(146, 159)(147, 160)(148, 162)(149, 166)(151, 168)(153, 171)(156, 170)(157, 174)(161, 176)(163, 175)(164, 179)(165, 182)(167, 184)(169, 187)(172, 186)(173, 189)(177, 181)(178, 190)(180, 185)(183, 191)(188, 192)(193, 194, 197, 203, 215, 237, 260, 277, 293, 309, 325, 341, 357, 373, 366, 352, 335, 319, 302, 288, 271, 253, 224, 246, 265, 255, 228, 249, 267, 283, 299, 315, 331, 347, 363, 379, 372, 356, 340, 324, 308, 292, 276, 259, 236, 214, 202, 196)(195, 199, 207, 223, 251, 269, 285, 301, 317, 333, 349, 365, 377, 359, 342, 332, 313, 295, 278, 268, 244, 218, 204, 217, 241, 234, 213, 233, 257, 274, 290, 306, 322, 338, 354, 370, 374, 364, 345, 327, 310, 300, 281, 262, 238, 229, 210, 200)(198, 205, 219, 245, 235, 258, 275, 291, 307, 323, 339, 355, 371, 375, 358, 348, 329, 311, 294, 284, 264, 240, 216, 239, 232, 212, 201, 211, 230, 256, 273, 289, 305, 321, 337, 353, 369, 380, 361, 343, 326, 316, 297, 279, 261, 250, 222, 206)(208, 225, 242, 221, 248, 263, 282, 296, 314, 328, 346, 360, 378, 383, 381, 368, 351, 334, 318, 304, 287, 270, 252, 231, 247, 220, 209, 227, 243, 266, 280, 298, 312, 330, 344, 362, 376, 384, 382, 367, 350, 336, 320, 303, 286, 272, 254, 226) L = (1, 193)(2, 194)(3, 195)(4, 196)(5, 197)(6, 198)(7, 199)(8, 200)(9, 201)(10, 202)(11, 203)(12, 204)(13, 205)(14, 206)(15, 207)(16, 208)(17, 209)(18, 210)(19, 211)(20, 212)(21, 213)(22, 214)(23, 215)(24, 216)(25, 217)(26, 218)(27, 219)(28, 220)(29, 221)(30, 222)(31, 223)(32, 224)(33, 225)(34, 226)(35, 227)(36, 228)(37, 229)(38, 230)(39, 231)(40, 232)(41, 233)(42, 234)(43, 235)(44, 236)(45, 237)(46, 238)(47, 239)(48, 240)(49, 241)(50, 242)(51, 243)(52, 244)(53, 245)(54, 246)(55, 247)(56, 248)(57, 249)(58, 250)(59, 251)(60, 252)(61, 253)(62, 254)(63, 255)(64, 256)(65, 257)(66, 258)(67, 259)(68, 260)(69, 261)(70, 262)(71, 263)(72, 264)(73, 265)(74, 266)(75, 267)(76, 268)(77, 269)(78, 270)(79, 271)(80, 272)(81, 273)(82, 274)(83, 275)(84, 276)(85, 277)(86, 278)(87, 279)(88, 280)(89, 281)(90, 282)(91, 283)(92, 284)(93, 285)(94, 286)(95, 287)(96, 288)(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, 8 ), ( 8^48 ) } Outer automorphisms :: reflexible Dual of E23.1208 Transitivity :: ET+ Graph:: simple bipartite v = 100 e = 192 f = 48 degree seq :: [ 2^96, 48^4 ] E23.1208 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 48}) Quotient :: loop Aut^+ = $<192, 77>$ (small group id <192, 77>) Aut = $<384, 1696>$ (small group id <384, 1696>) |r| :: 2 Presentation :: [ T1^2, F^2, T2^4, (F * T1)^2, (F * T2)^2, T2^-1 * T1 * T2^-1 * T1 * T2^-2 * T1 * T2 * T1 * T2^-1, T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2 * T1 * T2^-1 * T1 * T2 * T1 * T2^-1 * T1 * T2 ] Map:: R = (1, 193, 3, 195, 8, 200, 4, 196)(2, 194, 5, 197, 11, 203, 6, 198)(7, 199, 13, 205, 24, 216, 14, 206)(9, 201, 16, 208, 29, 221, 17, 209)(10, 202, 18, 210, 32, 224, 19, 211)(12, 204, 21, 213, 37, 229, 22, 214)(15, 207, 26, 218, 43, 235, 27, 219)(20, 212, 34, 226, 48, 240, 35, 227)(23, 215, 39, 231, 28, 220, 40, 232)(25, 217, 41, 233, 30, 222, 42, 234)(31, 223, 44, 236, 36, 228, 45, 237)(33, 225, 46, 238, 38, 230, 47, 239)(49, 241, 57, 249, 51, 243, 58, 250)(50, 242, 59, 251, 52, 244, 60, 252)(53, 245, 61, 253, 55, 247, 62, 254)(54, 246, 63, 255, 56, 248, 64, 256)(65, 257, 73, 265, 67, 259, 74, 266)(66, 258, 75, 267, 68, 260, 76, 268)(69, 261, 117, 309, 71, 263, 119, 311)(70, 262, 118, 310, 72, 264, 120, 312)(77, 269, 125, 317, 83, 275, 126, 318)(78, 270, 127, 319, 84, 276, 128, 320)(79, 271, 129, 321, 80, 272, 130, 322)(81, 273, 132, 324, 82, 274, 133, 325)(85, 277, 135, 327, 86, 278, 136, 328)(87, 279, 131, 323, 103, 295, 138, 330)(88, 280, 139, 331, 89, 281, 140, 332)(90, 282, 142, 334, 91, 283, 143, 335)(92, 284, 134, 326, 108, 300, 145, 337)(93, 285, 146, 338, 94, 286, 147, 339)(95, 287, 144, 336, 96, 288, 148, 340)(97, 289, 137, 329, 98, 290, 141, 333)(99, 291, 149, 341, 100, 292, 150, 342)(101, 293, 151, 343, 102, 294, 152, 344)(104, 296, 153, 345, 105, 297, 154, 346)(106, 298, 155, 347, 107, 299, 156, 348)(109, 301, 157, 349, 110, 302, 158, 350)(111, 303, 159, 351, 112, 304, 160, 352)(113, 305, 161, 353, 114, 306, 162, 354)(115, 307, 163, 355, 116, 308, 164, 356)(121, 313, 169, 361, 122, 314, 170, 362)(123, 315, 171, 363, 124, 316, 172, 364)(165, 357, 190, 382, 167, 359, 192, 384)(166, 358, 189, 381, 168, 360, 191, 383)(173, 365, 184, 376, 175, 367, 182, 374)(174, 366, 183, 375, 176, 368, 181, 373)(177, 369, 188, 380, 179, 371, 186, 378)(178, 370, 187, 379, 180, 372, 185, 377) L = (1, 194)(2, 193)(3, 199)(4, 201)(5, 202)(6, 204)(7, 195)(8, 207)(9, 196)(10, 197)(11, 212)(12, 198)(13, 215)(14, 217)(15, 200)(16, 220)(17, 222)(18, 223)(19, 225)(20, 203)(21, 228)(22, 230)(23, 205)(24, 226)(25, 206)(26, 224)(27, 229)(28, 208)(29, 227)(30, 209)(31, 210)(32, 218)(33, 211)(34, 216)(35, 221)(36, 213)(37, 219)(38, 214)(39, 241)(40, 242)(41, 243)(42, 244)(43, 240)(44, 245)(45, 246)(46, 247)(47, 248)(48, 235)(49, 231)(50, 232)(51, 233)(52, 234)(53, 236)(54, 237)(55, 238)(56, 239)(57, 257)(58, 258)(59, 259)(60, 260)(61, 261)(62, 262)(63, 263)(64, 264)(65, 249)(66, 250)(67, 251)(68, 252)(69, 253)(70, 254)(71, 255)(72, 256)(73, 295)(74, 276)(75, 279)(76, 270)(77, 312)(78, 268)(79, 319)(80, 323)(81, 317)(82, 326)(83, 311)(84, 266)(85, 321)(86, 329)(87, 267)(88, 322)(89, 333)(90, 324)(91, 336)(92, 310)(93, 325)(94, 340)(95, 318)(96, 337)(97, 320)(98, 330)(99, 327)(100, 331)(101, 328)(102, 332)(103, 265)(104, 334)(105, 338)(106, 335)(107, 339)(108, 309)(109, 341)(110, 343)(111, 342)(112, 344)(113, 345)(114, 347)(115, 346)(116, 348)(117, 300)(118, 284)(119, 275)(120, 269)(121, 349)(122, 351)(123, 350)(124, 352)(125, 273)(126, 287)(127, 271)(128, 289)(129, 277)(130, 280)(131, 272)(132, 282)(133, 285)(134, 274)(135, 291)(136, 293)(137, 278)(138, 290)(139, 292)(140, 294)(141, 281)(142, 296)(143, 298)(144, 283)(145, 288)(146, 297)(147, 299)(148, 286)(149, 301)(150, 303)(151, 302)(152, 304)(153, 305)(154, 307)(155, 306)(156, 308)(157, 313)(158, 315)(159, 314)(160, 316)(161, 357)(162, 358)(163, 359)(164, 360)(165, 353)(166, 354)(167, 355)(168, 356)(169, 372)(170, 371)(171, 370)(172, 369)(173, 383)(174, 381)(175, 384)(176, 382)(177, 364)(178, 363)(179, 362)(180, 361)(181, 380)(182, 378)(183, 379)(184, 377)(185, 376)(186, 374)(187, 375)(188, 373)(189, 366)(190, 368)(191, 365)(192, 367) local type(s) :: { ( 2, 48, 2, 48, 2, 48, 2, 48 ) } Outer automorphisms :: reflexible Dual of E23.1207 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 48 e = 192 f = 100 degree seq :: [ 8^48 ] E23.1209 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 48}) Quotient :: loop Aut^+ = $<192, 77>$ (small group id <192, 77>) Aut = $<384, 1696>$ (small group id <384, 1696>) |r| :: 2 Presentation :: [ F^2, T1^4, (T2^-1 * T1^-1)^2, (F * T2)^2, (F * T1)^2, T1^-1 * T2^-1 * T1 * T2^-2 * T1 * T2^-1 * T1^-1, (T2^-3 * T1)^2, (T2 * T1^-1)^4, T2 * T1^-1 * T2^-23 * T1^-1 ] Map:: R = (1, 193, 3, 195, 10, 202, 24, 216, 48, 240, 64, 256, 80, 272, 96, 288, 112, 304, 128, 320, 144, 336, 160, 352, 176, 368, 184, 376, 168, 360, 152, 344, 136, 328, 120, 312, 104, 296, 88, 280, 72, 264, 56, 248, 39, 231, 28, 220, 42, 234, 19, 211, 41, 233, 58, 250, 74, 266, 90, 282, 106, 298, 122, 314, 138, 330, 154, 346, 170, 362, 186, 378, 180, 372, 164, 356, 148, 340, 132, 324, 116, 308, 100, 292, 84, 276, 68, 260, 52, 244, 32, 224, 14, 206, 5, 197)(2, 194, 7, 199, 17, 209, 38, 230, 57, 249, 73, 265, 89, 281, 105, 297, 121, 313, 137, 329, 153, 345, 169, 361, 185, 377, 174, 366, 158, 350, 142, 334, 126, 318, 110, 302, 94, 286, 78, 270, 62, 254, 46, 238, 23, 215, 11, 203, 26, 218, 35, 227, 31, 223, 51, 243, 67, 259, 83, 275, 99, 291, 115, 307, 131, 323, 147, 339, 163, 355, 179, 371, 188, 380, 172, 364, 156, 348, 140, 332, 124, 316, 108, 300, 92, 284, 76, 268, 60, 252, 44, 236, 20, 212, 8, 200)(4, 196, 12, 204, 27, 219, 49, 241, 65, 257, 81, 273, 97, 289, 113, 305, 129, 321, 145, 337, 161, 353, 177, 369, 190, 382, 175, 367, 159, 351, 143, 335, 127, 319, 111, 303, 95, 287, 79, 271, 63, 255, 47, 239, 25, 217, 34, 226, 30, 222, 13, 205, 29, 221, 50, 242, 66, 258, 82, 274, 98, 290, 114, 306, 130, 322, 146, 338, 162, 354, 178, 370, 189, 381, 173, 365, 157, 349, 141, 333, 125, 317, 109, 301, 93, 285, 77, 269, 61, 253, 45, 237, 22, 214, 9, 201)(6, 198, 15, 207, 33, 225, 53, 245, 69, 261, 85, 277, 101, 293, 117, 309, 133, 325, 149, 341, 165, 357, 181, 373, 191, 383, 183, 375, 167, 359, 151, 343, 135, 327, 119, 311, 103, 295, 87, 279, 71, 263, 55, 247, 37, 229, 18, 210, 40, 232, 21, 213, 43, 235, 59, 251, 75, 267, 91, 283, 107, 299, 123, 315, 139, 331, 155, 347, 171, 363, 187, 379, 192, 384, 182, 374, 166, 358, 150, 342, 134, 326, 118, 310, 102, 294, 86, 278, 70, 262, 54, 246, 36, 228, 16, 208) L = (1, 194)(2, 198)(3, 201)(4, 193)(5, 205)(6, 196)(7, 197)(8, 211)(9, 213)(10, 215)(11, 195)(12, 208)(13, 210)(14, 223)(15, 200)(16, 227)(17, 229)(18, 199)(19, 226)(20, 235)(21, 203)(22, 233)(23, 225)(24, 239)(25, 202)(26, 232)(27, 231)(28, 204)(29, 206)(30, 234)(31, 228)(32, 241)(33, 217)(34, 207)(35, 220)(36, 221)(37, 219)(38, 248)(39, 209)(40, 222)(41, 212)(42, 218)(43, 214)(44, 216)(45, 245)(46, 250)(47, 251)(48, 252)(49, 247)(50, 246)(51, 224)(52, 249)(53, 238)(54, 230)(55, 243)(56, 242)(57, 262)(58, 237)(59, 236)(60, 261)(61, 240)(62, 267)(63, 266)(64, 269)(65, 244)(66, 264)(67, 263)(68, 274)(69, 253)(70, 257)(71, 258)(72, 259)(73, 260)(74, 254)(75, 255)(76, 282)(77, 283)(78, 256)(79, 277)(80, 286)(81, 278)(82, 279)(83, 280)(84, 291)(85, 268)(86, 275)(87, 265)(88, 273)(89, 295)(90, 271)(91, 270)(92, 299)(93, 298)(94, 293)(95, 272)(96, 303)(97, 296)(98, 276)(99, 294)(100, 305)(101, 287)(102, 290)(103, 289)(104, 281)(105, 312)(106, 284)(107, 285)(108, 288)(109, 309)(110, 314)(111, 315)(112, 316)(113, 311)(114, 310)(115, 292)(116, 313)(117, 302)(118, 297)(119, 307)(120, 306)(121, 326)(122, 301)(123, 300)(124, 325)(125, 304)(126, 331)(127, 330)(128, 333)(129, 308)(130, 328)(131, 327)(132, 338)(133, 317)(134, 321)(135, 322)(136, 323)(137, 324)(138, 318)(139, 319)(140, 346)(141, 347)(142, 320)(143, 341)(144, 350)(145, 342)(146, 343)(147, 344)(148, 355)(149, 332)(150, 339)(151, 329)(152, 337)(153, 359)(154, 335)(155, 334)(156, 363)(157, 362)(158, 357)(159, 336)(160, 367)(161, 360)(162, 340)(163, 358)(164, 369)(165, 351)(166, 354)(167, 353)(168, 345)(169, 376)(170, 348)(171, 349)(172, 352)(173, 373)(174, 378)(175, 379)(176, 380)(177, 375)(178, 374)(179, 356)(180, 377)(181, 366)(182, 361)(183, 371)(184, 370)(185, 384)(186, 365)(187, 364)(188, 383)(189, 368)(190, 372)(191, 381)(192, 382) 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 E23.1205 Transitivity :: ET+ VT+ AT Graph:: bipartite v = 4 e = 192 f = 144 degree seq :: [ 96^4 ] E23.1210 :: Family: { 2* } :: Oriented family(ies): { E3*b } Signature :: (0; {2, 4, 48}) Quotient :: loop Aut^+ = $<192, 77>$ (small group id <192, 77>) Aut = $<384, 1696>$ (small group id <384, 1696>) |r| :: 2 Presentation :: [ T2^2, F^2, (F * T1)^2, (F * T2)^2, (T2 * T1^-1)^4, T2 * T1^2 * T2 * T1^-1 * T2 * T1^-2 * T2 * T1, (T2 * T1^-4)^2, T1^18 * T2 * T1^-6 * T2 ] Map:: polytopal non-degenerate R = (1, 193, 3, 195)(2, 194, 6, 198)(4, 196, 9, 201)(5, 197, 12, 204)(7, 199, 16, 208)(8, 200, 17, 209)(10, 202, 21, 213)(11, 203, 24, 216)(13, 205, 28, 220)(14, 206, 29, 221)(15, 207, 32, 224)(18, 210, 36, 228)(19, 211, 39, 231)(20, 212, 33, 225)(22, 214, 43, 235)(23, 215, 46, 238)(25, 217, 50, 242)(26, 218, 51, 243)(27, 219, 54, 246)(30, 222, 57, 249)(31, 223, 60, 252)(34, 226, 53, 245)(35, 227, 47, 239)(37, 229, 56, 248)(38, 230, 61, 253)(40, 232, 63, 255)(41, 233, 62, 254)(42, 234, 55, 247)(44, 236, 59, 251)(45, 237, 69, 261)(48, 240, 71, 263)(49, 241, 73, 265)(52, 244, 75, 267)(58, 250, 74, 266)(64, 256, 80, 272)(65, 257, 79, 271)(66, 258, 78, 270)(67, 259, 81, 273)(68, 260, 86, 278)(70, 262, 88, 280)(72, 264, 91, 283)(76, 268, 90, 282)(77, 269, 94, 286)(82, 274, 95, 287)(83, 275, 96, 288)(84, 276, 98, 290)(85, 277, 102, 294)(87, 279, 104, 296)(89, 281, 107, 299)(92, 284, 106, 298)(93, 285, 110, 302)(97, 289, 112, 304)(99, 291, 111, 303)(100, 292, 115, 307)(101, 293, 118, 310)(103, 295, 120, 312)(105, 297, 123, 315)(108, 300, 122, 314)(109, 301, 126, 318)(113, 305, 127, 319)(114, 306, 128, 320)(116, 308, 125, 317)(117, 309, 134, 326)(119, 311, 136, 328)(121, 313, 139, 331)(124, 316, 138, 330)(129, 321, 144, 336)(130, 322, 143, 335)(131, 323, 142, 334)(132, 324, 145, 337)(133, 325, 150, 342)(135, 327, 152, 344)(137, 329, 155, 347)(140, 332, 154, 346)(141, 333, 158, 350)(146, 338, 159, 351)(147, 339, 160, 352)(148, 340, 162, 354)(149, 341, 166, 358)(151, 343, 168, 360)(153, 345, 171, 363)(156, 348, 170, 362)(157, 349, 174, 366)(161, 353, 176, 368)(163, 355, 175, 367)(164, 356, 179, 371)(165, 357, 182, 374)(167, 359, 184, 376)(169, 361, 187, 379)(172, 364, 186, 378)(173, 365, 189, 381)(177, 369, 181, 373)(178, 370, 190, 382)(180, 372, 185, 377)(183, 375, 191, 383)(188, 380, 192, 384) L = (1, 194)(2, 197)(3, 199)(4, 193)(5, 203)(6, 205)(7, 207)(8, 195)(9, 211)(10, 196)(11, 215)(12, 217)(13, 219)(14, 198)(15, 223)(16, 225)(17, 227)(18, 200)(19, 230)(20, 201)(21, 233)(22, 202)(23, 237)(24, 239)(25, 241)(26, 204)(27, 245)(28, 209)(29, 248)(30, 206)(31, 251)(32, 246)(33, 242)(34, 208)(35, 243)(36, 249)(37, 210)(38, 256)(39, 247)(40, 212)(41, 257)(42, 213)(43, 258)(44, 214)(45, 260)(46, 229)(47, 232)(48, 216)(49, 234)(50, 221)(51, 266)(52, 218)(53, 235)(54, 265)(55, 220)(56, 263)(57, 267)(58, 222)(59, 269)(60, 231)(61, 224)(62, 226)(63, 228)(64, 273)(65, 274)(66, 275)(67, 236)(68, 277)(69, 250)(70, 238)(71, 282)(72, 240)(73, 255)(74, 280)(75, 283)(76, 244)(77, 285)(78, 252)(79, 253)(80, 254)(81, 289)(82, 290)(83, 291)(84, 259)(85, 293)(86, 268)(87, 261)(88, 298)(89, 262)(90, 296)(91, 299)(92, 264)(93, 301)(94, 272)(95, 270)(96, 271)(97, 305)(98, 306)(99, 307)(100, 276)(101, 309)(102, 284)(103, 278)(104, 314)(105, 279)(106, 312)(107, 315)(108, 281)(109, 317)(110, 288)(111, 286)(112, 287)(113, 321)(114, 322)(115, 323)(116, 292)(117, 325)(118, 300)(119, 294)(120, 330)(121, 295)(122, 328)(123, 331)(124, 297)(125, 333)(126, 304)(127, 302)(128, 303)(129, 337)(130, 338)(131, 339)(132, 308)(133, 341)(134, 316)(135, 310)(136, 346)(137, 311)(138, 344)(139, 347)(140, 313)(141, 349)(142, 318)(143, 319)(144, 320)(145, 353)(146, 354)(147, 355)(148, 324)(149, 357)(150, 332)(151, 326)(152, 362)(153, 327)(154, 360)(155, 363)(156, 329)(157, 365)(158, 336)(159, 334)(160, 335)(161, 369)(162, 370)(163, 371)(164, 340)(165, 373)(166, 348)(167, 342)(168, 378)(169, 343)(170, 376)(171, 379)(172, 345)(173, 377)(174, 352)(175, 350)(176, 351)(177, 380)(178, 374)(179, 375)(180, 356)(181, 366)(182, 364)(183, 358)(184, 384)(185, 359)(186, 383)(187, 372)(188, 361)(189, 368)(190, 367)(191, 381)(192, 382) local type(s) :: { ( 4, 48, 4, 48 ) } Outer automorphisms :: reflexible Dual of E23.1206 Transitivity :: ET+ VT+ AT Graph:: simple bipartite v = 96 e = 192 f = 52 degree seq :: [ 4^96 ] E23.1211 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 48}) Quotient :: dipole Aut^+ = $<192, 77>$ (small group id <192, 77>) Aut = $<384, 1696>$ (small group id <384, 1696>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, Y2^4, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, R * Y2^-2 * R * Y1 * Y2^-2 * Y1, Y2^-1 * Y1 * Y2 * R * Y2^2 * R * Y2^-1 * Y1 * Y2^-1, Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1 * Y2^-1 * Y1, (Y3 * Y2^-1)^48 ] Map:: R = (1, 193, 2, 194)(3, 195, 7, 199)(4, 196, 9, 201)(5, 197, 10, 202)(6, 198, 12, 204)(8, 200, 15, 207)(11, 203, 20, 212)(13, 205, 23, 215)(14, 206, 25, 217)(16, 208, 28, 220)(17, 209, 30, 222)(18, 210, 31, 223)(19, 211, 33, 225)(21, 213, 36, 228)(22, 214, 38, 230)(24, 216, 34, 226)(26, 218, 32, 224)(27, 219, 37, 229)(29, 221, 35, 227)(39, 231, 49, 241)(40, 232, 50, 242)(41, 233, 51, 243)(42, 234, 52, 244)(43, 235, 48, 240)(44, 236, 53, 245)(45, 237, 54, 246)(46, 238, 55, 247)(47, 239, 56, 248)(57, 249, 65, 257)(58, 250, 66, 258)(59, 251, 67, 259)(60, 252, 68, 260)(61, 253, 69, 261)(62, 254, 70, 262)(63, 255, 71, 263)(64, 256, 72, 264)(73, 265, 84, 276)(74, 266, 103, 295)(75, 267, 78, 270)(76, 268, 87, 279)(77, 269, 118, 310)(79, 271, 129, 321)(80, 272, 128, 320)(81, 273, 132, 324)(82, 274, 126, 318)(83, 275, 117, 309)(85, 277, 135, 327)(86, 278, 131, 323)(88, 280, 139, 331)(89, 281, 130, 322)(90, 282, 142, 334)(91, 283, 134, 326)(92, 284, 120, 312)(93, 285, 146, 338)(94, 286, 133, 325)(95, 287, 145, 337)(96, 288, 125, 317)(97, 289, 138, 330)(98, 290, 127, 319)(99, 291, 141, 333)(100, 292, 137, 329)(101, 293, 140, 332)(102, 294, 136, 328)(104, 296, 148, 340)(105, 297, 144, 336)(106, 298, 147, 339)(107, 299, 143, 335)(108, 300, 119, 311)(109, 301, 152, 344)(110, 302, 150, 342)(111, 303, 151, 343)(112, 304, 149, 341)(113, 305, 156, 348)(114, 306, 154, 346)(115, 307, 155, 347)(116, 308, 153, 345)(121, 313, 160, 352)(122, 314, 158, 350)(123, 315, 159, 351)(124, 316, 157, 349)(161, 353, 168, 360)(162, 354, 167, 359)(163, 355, 166, 358)(164, 356, 165, 357)(169, 361, 178, 370)(170, 362, 177, 369)(171, 363, 180, 372)(172, 364, 179, 371)(173, 365, 191, 383)(174, 366, 189, 381)(175, 367, 192, 384)(176, 368, 190, 382)(181, 373, 188, 380)(182, 374, 186, 378)(183, 375, 187, 379)(184, 376, 185, 377)(385, 577, 387, 579, 392, 584, 388, 580)(386, 578, 389, 581, 395, 587, 390, 582)(391, 583, 397, 589, 408, 600, 398, 590)(393, 585, 400, 592, 413, 605, 401, 593)(394, 586, 402, 594, 416, 608, 403, 595)(396, 588, 405, 597, 421, 613, 406, 598)(399, 591, 410, 602, 427, 619, 411, 603)(404, 596, 418, 610, 432, 624, 419, 611)(407, 599, 423, 615, 412, 604, 424, 616)(409, 601, 425, 617, 414, 606, 426, 618)(415, 607, 428, 620, 420, 612, 429, 621)(417, 609, 430, 622, 422, 614, 431, 623)(433, 625, 441, 633, 435, 627, 442, 634)(434, 626, 443, 635, 436, 628, 444, 636)(437, 629, 445, 637, 439, 631, 446, 638)(438, 630, 447, 639, 440, 632, 448, 640)(449, 641, 457, 649, 451, 643, 458, 650)(450, 642, 459, 651, 452, 644, 460, 652)(453, 645, 501, 693, 455, 647, 503, 695)(454, 646, 502, 694, 456, 648, 504, 696)(461, 653, 509, 701, 467, 659, 510, 702)(462, 654, 511, 703, 468, 660, 512, 704)(463, 655, 514, 706, 464, 656, 515, 707)(465, 657, 517, 709, 466, 658, 518, 710)(469, 661, 520, 712, 470, 662, 521, 713)(471, 663, 522, 714, 487, 679, 513, 705)(472, 664, 524, 716, 473, 665, 525, 717)(474, 666, 527, 719, 475, 667, 528, 720)(476, 668, 529, 721, 492, 684, 516, 708)(477, 669, 531, 723, 478, 670, 532, 724)(479, 671, 530, 722, 480, 672, 526, 718)(481, 673, 523, 715, 482, 674, 519, 711)(483, 675, 533, 725, 484, 676, 534, 726)(485, 677, 535, 727, 486, 678, 536, 728)(488, 680, 537, 729, 489, 681, 538, 730)(490, 682, 539, 731, 491, 683, 540, 732)(493, 685, 541, 733, 494, 686, 542, 734)(495, 687, 543, 735, 496, 688, 544, 736)(497, 689, 545, 737, 498, 690, 546, 738)(499, 691, 547, 739, 500, 692, 548, 740)(505, 697, 553, 745, 506, 698, 554, 746)(507, 699, 555, 747, 508, 700, 556, 748)(549, 741, 573, 765, 551, 743, 575, 767)(550, 742, 574, 766, 552, 744, 576, 768)(557, 749, 568, 760, 559, 751, 566, 758)(558, 750, 567, 759, 560, 752, 565, 757)(561, 753, 572, 764, 563, 755, 570, 762)(562, 754, 571, 763, 564, 756, 569, 761) L = (1, 386)(2, 385)(3, 391)(4, 393)(5, 394)(6, 396)(7, 387)(8, 399)(9, 388)(10, 389)(11, 404)(12, 390)(13, 407)(14, 409)(15, 392)(16, 412)(17, 414)(18, 415)(19, 417)(20, 395)(21, 420)(22, 422)(23, 397)(24, 418)(25, 398)(26, 416)(27, 421)(28, 400)(29, 419)(30, 401)(31, 402)(32, 410)(33, 403)(34, 408)(35, 413)(36, 405)(37, 411)(38, 406)(39, 433)(40, 434)(41, 435)(42, 436)(43, 432)(44, 437)(45, 438)(46, 439)(47, 440)(48, 427)(49, 423)(50, 424)(51, 425)(52, 426)(53, 428)(54, 429)(55, 430)(56, 431)(57, 449)(58, 450)(59, 451)(60, 452)(61, 453)(62, 454)(63, 455)(64, 456)(65, 441)(66, 442)(67, 443)(68, 444)(69, 445)(70, 446)(71, 447)(72, 448)(73, 468)(74, 487)(75, 462)(76, 471)(77, 502)(78, 459)(79, 513)(80, 512)(81, 516)(82, 510)(83, 501)(84, 457)(85, 519)(86, 515)(87, 460)(88, 523)(89, 514)(90, 526)(91, 518)(92, 504)(93, 530)(94, 517)(95, 529)(96, 509)(97, 522)(98, 511)(99, 525)(100, 521)(101, 524)(102, 520)(103, 458)(104, 532)(105, 528)(106, 531)(107, 527)(108, 503)(109, 536)(110, 534)(111, 535)(112, 533)(113, 540)(114, 538)(115, 539)(116, 537)(117, 467)(118, 461)(119, 492)(120, 476)(121, 544)(122, 542)(123, 543)(124, 541)(125, 480)(126, 466)(127, 482)(128, 464)(129, 463)(130, 473)(131, 470)(132, 465)(133, 478)(134, 475)(135, 469)(136, 486)(137, 484)(138, 481)(139, 472)(140, 485)(141, 483)(142, 474)(143, 491)(144, 489)(145, 479)(146, 477)(147, 490)(148, 488)(149, 496)(150, 494)(151, 495)(152, 493)(153, 500)(154, 498)(155, 499)(156, 497)(157, 508)(158, 506)(159, 507)(160, 505)(161, 552)(162, 551)(163, 550)(164, 549)(165, 548)(166, 547)(167, 546)(168, 545)(169, 562)(170, 561)(171, 564)(172, 563)(173, 575)(174, 573)(175, 576)(176, 574)(177, 554)(178, 553)(179, 556)(180, 555)(181, 572)(182, 570)(183, 571)(184, 569)(185, 568)(186, 566)(187, 567)(188, 565)(189, 558)(190, 560)(191, 557)(192, 559)(193, 577)(194, 578)(195, 579)(196, 580)(197, 581)(198, 582)(199, 583)(200, 584)(201, 585)(202, 586)(203, 587)(204, 588)(205, 589)(206, 590)(207, 591)(208, 592)(209, 593)(210, 594)(211, 595)(212, 596)(213, 597)(214, 598)(215, 599)(216, 600)(217, 601)(218, 602)(219, 603)(220, 604)(221, 605)(222, 606)(223, 607)(224, 608)(225, 609)(226, 610)(227, 611)(228, 612)(229, 613)(230, 614)(231, 615)(232, 616)(233, 617)(234, 618)(235, 619)(236, 620)(237, 621)(238, 622)(239, 623)(240, 624)(241, 625)(242, 626)(243, 627)(244, 628)(245, 629)(246, 630)(247, 631)(248, 632)(249, 633)(250, 634)(251, 635)(252, 636)(253, 637)(254, 638)(255, 639)(256, 640)(257, 641)(258, 642)(259, 643)(260, 644)(261, 645)(262, 646)(263, 647)(264, 648)(265, 649)(266, 650)(267, 651)(268, 652)(269, 653)(270, 654)(271, 655)(272, 656)(273, 657)(274, 658)(275, 659)(276, 660)(277, 661)(278, 662)(279, 663)(280, 664)(281, 665)(282, 666)(283, 667)(284, 668)(285, 669)(286, 670)(287, 671)(288, 672)(289, 673)(290, 674)(291, 675)(292, 676)(293, 677)(294, 678)(295, 679)(296, 680)(297, 681)(298, 682)(299, 683)(300, 684)(301, 685)(302, 686)(303, 687)(304, 688)(305, 689)(306, 690)(307, 691)(308, 692)(309, 693)(310, 694)(311, 695)(312, 696)(313, 697)(314, 698)(315, 699)(316, 700)(317, 701)(318, 702)(319, 703)(320, 704)(321, 705)(322, 706)(323, 707)(324, 708)(325, 709)(326, 710)(327, 711)(328, 712)(329, 713)(330, 714)(331, 715)(332, 716)(333, 717)(334, 718)(335, 719)(336, 720)(337, 721)(338, 722)(339, 723)(340, 724)(341, 725)(342, 726)(343, 727)(344, 728)(345, 729)(346, 730)(347, 731)(348, 732)(349, 733)(350, 734)(351, 735)(352, 736)(353, 737)(354, 738)(355, 739)(356, 740)(357, 741)(358, 742)(359, 743)(360, 744)(361, 745)(362, 746)(363, 747)(364, 748)(365, 749)(366, 750)(367, 751)(368, 752)(369, 753)(370, 754)(371, 755)(372, 756)(373, 757)(374, 758)(375, 759)(376, 760)(377, 761)(378, 762)(379, 763)(380, 764)(381, 765)(382, 766)(383, 767)(384, 768) local type(s) :: { ( 2, 96, 2, 96 ), ( 2, 96, 2, 96, 2, 96, 2, 96 ) } Outer automorphisms :: reflexible Dual of E23.1214 Graph:: bipartite v = 144 e = 384 f = 196 degree seq :: [ 4^96, 8^48 ] E23.1212 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 48}) Quotient :: dipole Aut^+ = $<192, 77>$ (small group id <192, 77>) Aut = $<384, 1696>$ (small group id <384, 1696>) |r| :: 2 Presentation :: [ R^2, Y2 * Y3^-1, Y1^4, (R * Y1)^2, (Y2^-1 * Y1^-1)^2, (R * Y3)^2, (Y3^-1 * Y1^-1)^2, Y2^-1 * Y1 * Y2 * Y1^-1 * Y2^2 * Y1^2, Y2^2 * Y1^-1 * Y2 * Y1^-2 * Y2 * Y1^-1, (Y2 * Y1^-1)^4, Y2 * Y1 * Y2^-22 * Y1^-1 * Y2 ] Map:: R = (1, 193, 2, 194, 6, 198, 4, 196)(3, 195, 9, 201, 21, 213, 11, 203)(5, 197, 13, 205, 18, 210, 7, 199)(8, 200, 19, 211, 34, 226, 15, 207)(10, 202, 23, 215, 33, 225, 25, 217)(12, 204, 16, 208, 35, 227, 28, 220)(14, 206, 31, 223, 36, 228, 29, 221)(17, 209, 37, 229, 27, 219, 39, 231)(20, 212, 43, 235, 22, 214, 41, 233)(24, 216, 47, 239, 59, 251, 44, 236)(26, 218, 40, 232, 30, 222, 42, 234)(32, 224, 49, 241, 55, 247, 51, 243)(38, 230, 56, 248, 50, 242, 54, 246)(45, 237, 53, 245, 46, 238, 58, 250)(48, 240, 60, 252, 69, 261, 61, 253)(52, 244, 57, 249, 70, 262, 65, 257)(62, 254, 75, 267, 63, 255, 74, 266)(64, 256, 77, 269, 91, 283, 78, 270)(66, 258, 72, 264, 67, 259, 71, 263)(68, 260, 82, 274, 87, 279, 73, 265)(76, 268, 90, 282, 79, 271, 85, 277)(80, 272, 94, 286, 101, 293, 95, 287)(81, 273, 86, 278, 83, 275, 88, 280)(84, 276, 99, 291, 102, 294, 98, 290)(89, 281, 103, 295, 97, 289, 104, 296)(92, 284, 107, 299, 93, 285, 106, 298)(96, 288, 111, 303, 123, 315, 108, 300)(100, 292, 113, 305, 119, 311, 115, 307)(105, 297, 120, 312, 114, 306, 118, 310)(109, 301, 117, 309, 110, 302, 122, 314)(112, 304, 124, 316, 133, 325, 125, 317)(116, 308, 121, 313, 134, 326, 129, 321)(126, 318, 139, 331, 127, 319, 138, 330)(128, 320, 141, 333, 155, 347, 142, 334)(130, 322, 136, 328, 131, 323, 135, 327)(132, 324, 146, 338, 151, 343, 137, 329)(140, 332, 154, 346, 143, 335, 149, 341)(144, 336, 158, 350, 165, 357, 159, 351)(145, 337, 150, 342, 147, 339, 152, 344)(148, 340, 163, 355, 166, 358, 162, 354)(153, 345, 167, 359, 161, 353, 168, 360)(156, 348, 171, 363, 157, 349, 170, 362)(160, 352, 175, 367, 187, 379, 172, 364)(164, 356, 177, 369, 183, 375, 179, 371)(169, 361, 184, 376, 178, 370, 182, 374)(173, 365, 181, 373, 174, 366, 186, 378)(176, 368, 188, 380, 191, 383, 189, 381)(180, 372, 185, 377, 192, 384, 190, 382)(385, 577, 387, 579, 394, 586, 408, 600, 432, 624, 448, 640, 464, 656, 480, 672, 496, 688, 512, 704, 528, 720, 544, 736, 560, 752, 568, 760, 552, 744, 536, 728, 520, 712, 504, 696, 488, 680, 472, 664, 456, 648, 440, 632, 423, 615, 412, 604, 426, 618, 403, 595, 425, 617, 442, 634, 458, 650, 474, 666, 490, 682, 506, 698, 522, 714, 538, 730, 554, 746, 570, 762, 564, 756, 548, 740, 532, 724, 516, 708, 500, 692, 484, 676, 468, 660, 452, 644, 436, 628, 416, 608, 398, 590, 389, 581)(386, 578, 391, 583, 401, 593, 422, 614, 441, 633, 457, 649, 473, 665, 489, 681, 505, 697, 521, 713, 537, 729, 553, 745, 569, 761, 558, 750, 542, 734, 526, 718, 510, 702, 494, 686, 478, 670, 462, 654, 446, 638, 430, 622, 407, 599, 395, 587, 410, 602, 419, 611, 415, 607, 435, 627, 451, 643, 467, 659, 483, 675, 499, 691, 515, 707, 531, 723, 547, 739, 563, 755, 572, 764, 556, 748, 540, 732, 524, 716, 508, 700, 492, 684, 476, 668, 460, 652, 444, 636, 428, 620, 404, 596, 392, 584)(388, 580, 396, 588, 411, 603, 433, 625, 449, 641, 465, 657, 481, 673, 497, 689, 513, 705, 529, 721, 545, 737, 561, 753, 574, 766, 559, 751, 543, 735, 527, 719, 511, 703, 495, 687, 479, 671, 463, 655, 447, 639, 431, 623, 409, 601, 418, 610, 414, 606, 397, 589, 413, 605, 434, 626, 450, 642, 466, 658, 482, 674, 498, 690, 514, 706, 530, 722, 546, 738, 562, 754, 573, 765, 557, 749, 541, 733, 525, 717, 509, 701, 493, 685, 477, 669, 461, 653, 445, 637, 429, 621, 406, 598, 393, 585)(390, 582, 399, 591, 417, 609, 437, 629, 453, 645, 469, 661, 485, 677, 501, 693, 517, 709, 533, 725, 549, 741, 565, 757, 575, 767, 567, 759, 551, 743, 535, 727, 519, 711, 503, 695, 487, 679, 471, 663, 455, 647, 439, 631, 421, 613, 402, 594, 424, 616, 405, 597, 427, 619, 443, 635, 459, 651, 475, 667, 491, 683, 507, 699, 523, 715, 539, 731, 555, 747, 571, 763, 576, 768, 566, 758, 550, 742, 534, 726, 518, 710, 502, 694, 486, 678, 470, 662, 454, 646, 438, 630, 420, 612, 400, 592) L = (1, 387)(2, 391)(3, 394)(4, 396)(5, 385)(6, 399)(7, 401)(8, 386)(9, 388)(10, 408)(11, 410)(12, 411)(13, 413)(14, 389)(15, 417)(16, 390)(17, 422)(18, 424)(19, 425)(20, 392)(21, 427)(22, 393)(23, 395)(24, 432)(25, 418)(26, 419)(27, 433)(28, 426)(29, 434)(30, 397)(31, 435)(32, 398)(33, 437)(34, 414)(35, 415)(36, 400)(37, 402)(38, 441)(39, 412)(40, 405)(41, 442)(42, 403)(43, 443)(44, 404)(45, 406)(46, 407)(47, 409)(48, 448)(49, 449)(50, 450)(51, 451)(52, 416)(53, 453)(54, 420)(55, 421)(56, 423)(57, 457)(58, 458)(59, 459)(60, 428)(61, 429)(62, 430)(63, 431)(64, 464)(65, 465)(66, 466)(67, 467)(68, 436)(69, 469)(70, 438)(71, 439)(72, 440)(73, 473)(74, 474)(75, 475)(76, 444)(77, 445)(78, 446)(79, 447)(80, 480)(81, 481)(82, 482)(83, 483)(84, 452)(85, 485)(86, 454)(87, 455)(88, 456)(89, 489)(90, 490)(91, 491)(92, 460)(93, 461)(94, 462)(95, 463)(96, 496)(97, 497)(98, 498)(99, 499)(100, 468)(101, 501)(102, 470)(103, 471)(104, 472)(105, 505)(106, 506)(107, 507)(108, 476)(109, 477)(110, 478)(111, 479)(112, 512)(113, 513)(114, 514)(115, 515)(116, 484)(117, 517)(118, 486)(119, 487)(120, 488)(121, 521)(122, 522)(123, 523)(124, 492)(125, 493)(126, 494)(127, 495)(128, 528)(129, 529)(130, 530)(131, 531)(132, 500)(133, 533)(134, 502)(135, 503)(136, 504)(137, 537)(138, 538)(139, 539)(140, 508)(141, 509)(142, 510)(143, 511)(144, 544)(145, 545)(146, 546)(147, 547)(148, 516)(149, 549)(150, 518)(151, 519)(152, 520)(153, 553)(154, 554)(155, 555)(156, 524)(157, 525)(158, 526)(159, 527)(160, 560)(161, 561)(162, 562)(163, 563)(164, 532)(165, 565)(166, 534)(167, 535)(168, 536)(169, 569)(170, 570)(171, 571)(172, 540)(173, 541)(174, 542)(175, 543)(176, 568)(177, 574)(178, 573)(179, 572)(180, 548)(181, 575)(182, 550)(183, 551)(184, 552)(185, 558)(186, 564)(187, 576)(188, 556)(189, 557)(190, 559)(191, 567)(192, 566)(193, 577)(194, 578)(195, 579)(196, 580)(197, 581)(198, 582)(199, 583)(200, 584)(201, 585)(202, 586)(203, 587)(204, 588)(205, 589)(206, 590)(207, 591)(208, 592)(209, 593)(210, 594)(211, 595)(212, 596)(213, 597)(214, 598)(215, 599)(216, 600)(217, 601)(218, 602)(219, 603)(220, 604)(221, 605)(222, 606)(223, 607)(224, 608)(225, 609)(226, 610)(227, 611)(228, 612)(229, 613)(230, 614)(231, 615)(232, 616)(233, 617)(234, 618)(235, 619)(236, 620)(237, 621)(238, 622)(239, 623)(240, 624)(241, 625)(242, 626)(243, 627)(244, 628)(245, 629)(246, 630)(247, 631)(248, 632)(249, 633)(250, 634)(251, 635)(252, 636)(253, 637)(254, 638)(255, 639)(256, 640)(257, 641)(258, 642)(259, 643)(260, 644)(261, 645)(262, 646)(263, 647)(264, 648)(265, 649)(266, 650)(267, 651)(268, 652)(269, 653)(270, 654)(271, 655)(272, 656)(273, 657)(274, 658)(275, 659)(276, 660)(277, 661)(278, 662)(279, 663)(280, 664)(281, 665)(282, 666)(283, 667)(284, 668)(285, 669)(286, 670)(287, 671)(288, 672)(289, 673)(290, 674)(291, 675)(292, 676)(293, 677)(294, 678)(295, 679)(296, 680)(297, 681)(298, 682)(299, 683)(300, 684)(301, 685)(302, 686)(303, 687)(304, 688)(305, 689)(306, 690)(307, 691)(308, 692)(309, 693)(310, 694)(311, 695)(312, 696)(313, 697)(314, 698)(315, 699)(316, 700)(317, 701)(318, 702)(319, 703)(320, 704)(321, 705)(322, 706)(323, 707)(324, 708)(325, 709)(326, 710)(327, 711)(328, 712)(329, 713)(330, 714)(331, 715)(332, 716)(333, 717)(334, 718)(335, 719)(336, 720)(337, 721)(338, 722)(339, 723)(340, 724)(341, 725)(342, 726)(343, 727)(344, 728)(345, 729)(346, 730)(347, 731)(348, 732)(349, 733)(350, 734)(351, 735)(352, 736)(353, 737)(354, 738)(355, 739)(356, 740)(357, 741)(358, 742)(359, 743)(360, 744)(361, 745)(362, 746)(363, 747)(364, 748)(365, 749)(366, 750)(367, 751)(368, 752)(369, 753)(370, 754)(371, 755)(372, 756)(373, 757)(374, 758)(375, 759)(376, 760)(377, 761)(378, 762)(379, 763)(380, 764)(381, 765)(382, 766)(383, 767)(384, 768) 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 E23.1213 Graph:: bipartite v = 52 e = 384 f = 288 degree seq :: [ 8^48, 96^4 ] E23.1213 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 48}) Quotient :: dipole Aut^+ = $<192, 77>$ (small group id <192, 77>) Aut = $<384, 1696>$ (small group id <384, 1696>) |r| :: 2 Presentation :: [ Y1, Y2^2, R^2, (R * Y3)^2, (R * Y1)^2, (R * Y2 * Y3^-1)^2, (Y3 * Y2)^4, Y3^-3 * Y2 * Y3^-1 * Y2 * Y3 * Y2 * Y3^-1 * Y2, Y3^2 * Y2 * Y3^-22 * Y2, (Y3^-1 * Y1^-1)^48 ] Map:: polytopal R = (1, 193)(2, 194)(3, 195)(4, 196)(5, 197)(6, 198)(7, 199)(8, 200)(9, 201)(10, 202)(11, 203)(12, 204)(13, 205)(14, 206)(15, 207)(16, 208)(17, 209)(18, 210)(19, 211)(20, 212)(21, 213)(22, 214)(23, 215)(24, 216)(25, 217)(26, 218)(27, 219)(28, 220)(29, 221)(30, 222)(31, 223)(32, 224)(33, 225)(34, 226)(35, 227)(36, 228)(37, 229)(38, 230)(39, 231)(40, 232)(41, 233)(42, 234)(43, 235)(44, 236)(45, 237)(46, 238)(47, 239)(48, 240)(49, 241)(50, 242)(51, 243)(52, 244)(53, 245)(54, 246)(55, 247)(56, 248)(57, 249)(58, 250)(59, 251)(60, 252)(61, 253)(62, 254)(63, 255)(64, 256)(65, 257)(66, 258)(67, 259)(68, 260)(69, 261)(70, 262)(71, 263)(72, 264)(73, 265)(74, 266)(75, 267)(76, 268)(77, 269)(78, 270)(79, 271)(80, 272)(81, 273)(82, 274)(83, 275)(84, 276)(85, 277)(86, 278)(87, 279)(88, 280)(89, 281)(90, 282)(91, 283)(92, 284)(93, 285)(94, 286)(95, 287)(96, 288)(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)(385, 577, 386, 578)(387, 579, 391, 583)(388, 580, 393, 585)(389, 581, 395, 587)(390, 582, 397, 589)(392, 584, 401, 593)(394, 586, 405, 597)(396, 588, 409, 601)(398, 590, 413, 605)(399, 591, 412, 604)(400, 592, 416, 608)(402, 594, 420, 612)(403, 595, 422, 614)(404, 596, 407, 599)(406, 598, 427, 619)(408, 600, 430, 622)(410, 602, 434, 626)(411, 603, 436, 628)(414, 606, 441, 633)(415, 607, 432, 624)(417, 609, 439, 631)(418, 610, 429, 621)(419, 611, 437, 629)(421, 613, 442, 634)(423, 615, 433, 625)(424, 616, 440, 632)(425, 617, 431, 623)(426, 618, 438, 630)(428, 620, 435, 627)(443, 635, 457, 649)(444, 636, 453, 645)(445, 637, 458, 650)(446, 638, 459, 651)(447, 639, 461, 653)(448, 640, 452, 644)(449, 641, 454, 646)(450, 642, 455, 647)(451, 643, 465, 657)(456, 648, 469, 661)(460, 652, 473, 665)(462, 654, 475, 667)(463, 655, 474, 666)(464, 656, 478, 670)(466, 658, 471, 663)(467, 659, 470, 662)(468, 660, 482, 674)(472, 664, 486, 678)(476, 668, 490, 682)(477, 669, 491, 683)(479, 671, 489, 681)(480, 672, 495, 687)(481, 673, 487, 679)(483, 675, 485, 677)(484, 676, 499, 691)(488, 680, 503, 695)(492, 684, 507, 699)(493, 685, 506, 698)(494, 686, 505, 697)(496, 688, 508, 700)(497, 689, 502, 694)(498, 690, 501, 693)(500, 692, 504, 696)(509, 701, 521, 713)(510, 702, 522, 714)(511, 703, 523, 715)(512, 704, 525, 717)(513, 705, 517, 709)(514, 706, 518, 710)(515, 707, 519, 711)(516, 708, 529, 721)(520, 712, 533, 725)(524, 716, 537, 729)(526, 718, 539, 731)(527, 719, 538, 730)(528, 720, 542, 734)(530, 722, 535, 727)(531, 723, 534, 726)(532, 724, 546, 738)(536, 728, 550, 742)(540, 732, 554, 746)(541, 733, 555, 747)(543, 735, 553, 745)(544, 736, 559, 751)(545, 737, 551, 743)(547, 739, 549, 741)(548, 740, 563, 755)(552, 744, 567, 759)(556, 748, 571, 763)(557, 749, 570, 762)(558, 750, 569, 761)(560, 752, 572, 764)(561, 753, 566, 758)(562, 754, 565, 757)(564, 756, 568, 760)(573, 765, 575, 767)(574, 766, 576, 768) L = (1, 387)(2, 389)(3, 392)(4, 385)(5, 396)(6, 386)(7, 399)(8, 402)(9, 403)(10, 388)(11, 407)(12, 410)(13, 411)(14, 390)(15, 415)(16, 391)(17, 418)(18, 421)(19, 423)(20, 393)(21, 425)(22, 394)(23, 429)(24, 395)(25, 432)(26, 435)(27, 437)(28, 397)(29, 439)(30, 398)(31, 430)(32, 441)(33, 400)(34, 444)(35, 401)(36, 436)(37, 447)(38, 438)(39, 448)(40, 404)(41, 449)(42, 405)(43, 450)(44, 406)(45, 416)(46, 427)(47, 408)(48, 453)(49, 409)(50, 422)(51, 456)(52, 424)(53, 457)(54, 412)(55, 458)(56, 413)(57, 459)(58, 414)(59, 417)(60, 426)(61, 419)(62, 420)(63, 464)(64, 465)(65, 466)(66, 467)(67, 428)(68, 431)(69, 440)(70, 433)(71, 434)(72, 472)(73, 473)(74, 474)(75, 475)(76, 442)(77, 443)(78, 445)(79, 446)(80, 480)(81, 481)(82, 482)(83, 483)(84, 451)(85, 452)(86, 454)(87, 455)(88, 488)(89, 489)(90, 490)(91, 491)(92, 460)(93, 461)(94, 462)(95, 463)(96, 496)(97, 497)(98, 498)(99, 499)(100, 468)(101, 469)(102, 470)(103, 471)(104, 504)(105, 505)(106, 506)(107, 507)(108, 476)(109, 477)(110, 478)(111, 479)(112, 512)(113, 513)(114, 514)(115, 515)(116, 484)(117, 485)(118, 486)(119, 487)(120, 520)(121, 521)(122, 522)(123, 523)(124, 492)(125, 493)(126, 494)(127, 495)(128, 528)(129, 529)(130, 530)(131, 531)(132, 500)(133, 501)(134, 502)(135, 503)(136, 536)(137, 537)(138, 538)(139, 539)(140, 508)(141, 509)(142, 510)(143, 511)(144, 544)(145, 545)(146, 546)(147, 547)(148, 516)(149, 517)(150, 518)(151, 519)(152, 552)(153, 553)(154, 554)(155, 555)(156, 524)(157, 525)(158, 526)(159, 527)(160, 560)(161, 561)(162, 562)(163, 563)(164, 532)(165, 533)(166, 534)(167, 535)(168, 568)(169, 569)(170, 570)(171, 571)(172, 540)(173, 541)(174, 542)(175, 543)(176, 566)(177, 573)(178, 572)(179, 574)(180, 548)(181, 549)(182, 550)(183, 551)(184, 558)(185, 575)(186, 564)(187, 576)(188, 556)(189, 557)(190, 559)(191, 565)(192, 567)(193, 577)(194, 578)(195, 579)(196, 580)(197, 581)(198, 582)(199, 583)(200, 584)(201, 585)(202, 586)(203, 587)(204, 588)(205, 589)(206, 590)(207, 591)(208, 592)(209, 593)(210, 594)(211, 595)(212, 596)(213, 597)(214, 598)(215, 599)(216, 600)(217, 601)(218, 602)(219, 603)(220, 604)(221, 605)(222, 606)(223, 607)(224, 608)(225, 609)(226, 610)(227, 611)(228, 612)(229, 613)(230, 614)(231, 615)(232, 616)(233, 617)(234, 618)(235, 619)(236, 620)(237, 621)(238, 622)(239, 623)(240, 624)(241, 625)(242, 626)(243, 627)(244, 628)(245, 629)(246, 630)(247, 631)(248, 632)(249, 633)(250, 634)(251, 635)(252, 636)(253, 637)(254, 638)(255, 639)(256, 640)(257, 641)(258, 642)(259, 643)(260, 644)(261, 645)(262, 646)(263, 647)(264, 648)(265, 649)(266, 650)(267, 651)(268, 652)(269, 653)(270, 654)(271, 655)(272, 656)(273, 657)(274, 658)(275, 659)(276, 660)(277, 661)(278, 662)(279, 663)(280, 664)(281, 665)(282, 666)(283, 667)(284, 668)(285, 669)(286, 670)(287, 671)(288, 672)(289, 673)(290, 674)(291, 675)(292, 676)(293, 677)(294, 678)(295, 679)(296, 680)(297, 681)(298, 682)(299, 683)(300, 684)(301, 685)(302, 686)(303, 687)(304, 688)(305, 689)(306, 690)(307, 691)(308, 692)(309, 693)(310, 694)(311, 695)(312, 696)(313, 697)(314, 698)(315, 699)(316, 700)(317, 701)(318, 702)(319, 703)(320, 704)(321, 705)(322, 706)(323, 707)(324, 708)(325, 709)(326, 710)(327, 711)(328, 712)(329, 713)(330, 714)(331, 715)(332, 716)(333, 717)(334, 718)(335, 719)(336, 720)(337, 721)(338, 722)(339, 723)(340, 724)(341, 725)(342, 726)(343, 727)(344, 728)(345, 729)(346, 730)(347, 731)(348, 732)(349, 733)(350, 734)(351, 735)(352, 736)(353, 737)(354, 738)(355, 739)(356, 740)(357, 741)(358, 742)(359, 743)(360, 744)(361, 745)(362, 746)(363, 747)(364, 748)(365, 749)(366, 750)(367, 751)(368, 752)(369, 753)(370, 754)(371, 755)(372, 756)(373, 757)(374, 758)(375, 759)(376, 760)(377, 761)(378, 762)(379, 763)(380, 764)(381, 765)(382, 766)(383, 767)(384, 768) local type(s) :: { ( 8, 96 ), ( 8, 96, 8, 96 ) } Outer automorphisms :: reflexible Dual of E23.1212 Graph:: simple bipartite v = 288 e = 384 f = 52 degree seq :: [ 2^192, 4^96 ] E23.1214 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 48}) Quotient :: dipole Aut^+ = $<192, 77>$ (small group id <192, 77>) Aut = $<384, 1696>$ (small group id <384, 1696>) |r| :: 2 Presentation :: [ Y2, R^2, Y3^2, R * Y2 * R * Y2^-1, (R * Y1)^2, (R * Y3)^2, (Y3 * Y2^-1)^2, (Y3 * Y1^-1)^4, Y1 * Y3 * Y1^-1 * Y3 * Y1 * Y3 * Y1^3 * Y3, (Y3 * Y1^-4)^2, Y1^-4 * Y3 * Y1^10 * Y3 * Y1^-10 ] Map:: polytopal R = (1, 193, 2, 194, 5, 197, 11, 203, 23, 215, 45, 237, 68, 260, 85, 277, 101, 293, 117, 309, 133, 325, 149, 341, 165, 357, 181, 373, 174, 366, 160, 352, 143, 335, 127, 319, 110, 302, 96, 288, 79, 271, 61, 253, 32, 224, 54, 246, 73, 265, 63, 255, 36, 228, 57, 249, 75, 267, 91, 283, 107, 299, 123, 315, 139, 331, 155, 347, 171, 363, 187, 379, 180, 372, 164, 356, 148, 340, 132, 324, 116, 308, 100, 292, 84, 276, 67, 259, 44, 236, 22, 214, 10, 202, 4, 196)(3, 195, 7, 199, 15, 207, 31, 223, 59, 251, 77, 269, 93, 285, 109, 301, 125, 317, 141, 333, 157, 349, 173, 365, 185, 377, 167, 359, 150, 342, 140, 332, 121, 313, 103, 295, 86, 278, 76, 268, 52, 244, 26, 218, 12, 204, 25, 217, 49, 241, 42, 234, 21, 213, 41, 233, 65, 257, 82, 274, 98, 290, 114, 306, 130, 322, 146, 338, 162, 354, 178, 370, 182, 374, 172, 364, 153, 345, 135, 327, 118, 310, 108, 300, 89, 281, 70, 262, 46, 238, 37, 229, 18, 210, 8, 200)(6, 198, 13, 205, 27, 219, 53, 245, 43, 235, 66, 258, 83, 275, 99, 291, 115, 307, 131, 323, 147, 339, 163, 355, 179, 371, 183, 375, 166, 358, 156, 348, 137, 329, 119, 311, 102, 294, 92, 284, 72, 264, 48, 240, 24, 216, 47, 239, 40, 232, 20, 212, 9, 201, 19, 211, 38, 230, 64, 256, 81, 273, 97, 289, 113, 305, 129, 321, 145, 337, 161, 353, 177, 369, 188, 380, 169, 361, 151, 343, 134, 326, 124, 316, 105, 297, 87, 279, 69, 261, 58, 250, 30, 222, 14, 206)(16, 208, 33, 225, 50, 242, 29, 221, 56, 248, 71, 263, 90, 282, 104, 296, 122, 314, 136, 328, 154, 346, 168, 360, 186, 378, 191, 383, 189, 381, 176, 368, 159, 351, 142, 334, 126, 318, 112, 304, 95, 287, 78, 270, 60, 252, 39, 231, 55, 247, 28, 220, 17, 209, 35, 227, 51, 243, 74, 266, 88, 280, 106, 298, 120, 312, 138, 330, 152, 344, 170, 362, 184, 376, 192, 384, 190, 382, 175, 367, 158, 350, 144, 336, 128, 320, 111, 303, 94, 286, 80, 272, 62, 254, 34, 226)(385, 577)(386, 578)(387, 579)(388, 580)(389, 581)(390, 582)(391, 583)(392, 584)(393, 585)(394, 586)(395, 587)(396, 588)(397, 589)(398, 590)(399, 591)(400, 592)(401, 593)(402, 594)(403, 595)(404, 596)(405, 597)(406, 598)(407, 599)(408, 600)(409, 601)(410, 602)(411, 603)(412, 604)(413, 605)(414, 606)(415, 607)(416, 608)(417, 609)(418, 610)(419, 611)(420, 612)(421, 613)(422, 614)(423, 615)(424, 616)(425, 617)(426, 618)(427, 619)(428, 620)(429, 621)(430, 622)(431, 623)(432, 624)(433, 625)(434, 626)(435, 627)(436, 628)(437, 629)(438, 630)(439, 631)(440, 632)(441, 633)(442, 634)(443, 635)(444, 636)(445, 637)(446, 638)(447, 639)(448, 640)(449, 641)(450, 642)(451, 643)(452, 644)(453, 645)(454, 646)(455, 647)(456, 648)(457, 649)(458, 650)(459, 651)(460, 652)(461, 653)(462, 654)(463, 655)(464, 656)(465, 657)(466, 658)(467, 659)(468, 660)(469, 661)(470, 662)(471, 663)(472, 664)(473, 665)(474, 666)(475, 667)(476, 668)(477, 669)(478, 670)(479, 671)(480, 672)(481, 673)(482, 674)(483, 675)(484, 676)(485, 677)(486, 678)(487, 679)(488, 680)(489, 681)(490, 682)(491, 683)(492, 684)(493, 685)(494, 686)(495, 687)(496, 688)(497, 689)(498, 690)(499, 691)(500, 692)(501, 693)(502, 694)(503, 695)(504, 696)(505, 697)(506, 698)(507, 699)(508, 700)(509, 701)(510, 702)(511, 703)(512, 704)(513, 705)(514, 706)(515, 707)(516, 708)(517, 709)(518, 710)(519, 711)(520, 712)(521, 713)(522, 714)(523, 715)(524, 716)(525, 717)(526, 718)(527, 719)(528, 720)(529, 721)(530, 722)(531, 723)(532, 724)(533, 725)(534, 726)(535, 727)(536, 728)(537, 729)(538, 730)(539, 731)(540, 732)(541, 733)(542, 734)(543, 735)(544, 736)(545, 737)(546, 738)(547, 739)(548, 740)(549, 741)(550, 742)(551, 743)(552, 744)(553, 745)(554, 746)(555, 747)(556, 748)(557, 749)(558, 750)(559, 751)(560, 752)(561, 753)(562, 754)(563, 755)(564, 756)(565, 757)(566, 758)(567, 759)(568, 760)(569, 761)(570, 762)(571, 763)(572, 764)(573, 765)(574, 766)(575, 767)(576, 768) L = (1, 387)(2, 390)(3, 385)(4, 393)(5, 396)(6, 386)(7, 400)(8, 401)(9, 388)(10, 405)(11, 408)(12, 389)(13, 412)(14, 413)(15, 416)(16, 391)(17, 392)(18, 420)(19, 423)(20, 417)(21, 394)(22, 427)(23, 430)(24, 395)(25, 434)(26, 435)(27, 438)(28, 397)(29, 398)(30, 441)(31, 444)(32, 399)(33, 404)(34, 437)(35, 431)(36, 402)(37, 440)(38, 445)(39, 403)(40, 447)(41, 446)(42, 439)(43, 406)(44, 443)(45, 453)(46, 407)(47, 419)(48, 455)(49, 457)(50, 409)(51, 410)(52, 459)(53, 418)(54, 411)(55, 426)(56, 421)(57, 414)(58, 458)(59, 428)(60, 415)(61, 422)(62, 425)(63, 424)(64, 464)(65, 463)(66, 462)(67, 465)(68, 470)(69, 429)(70, 472)(71, 432)(72, 475)(73, 433)(74, 442)(75, 436)(76, 474)(77, 478)(78, 450)(79, 449)(80, 448)(81, 451)(82, 479)(83, 480)(84, 482)(85, 486)(86, 452)(87, 488)(88, 454)(89, 491)(90, 460)(91, 456)(92, 490)(93, 494)(94, 461)(95, 466)(96, 467)(97, 496)(98, 468)(99, 495)(100, 499)(101, 502)(102, 469)(103, 504)(104, 471)(105, 507)(106, 476)(107, 473)(108, 506)(109, 510)(110, 477)(111, 483)(112, 481)(113, 511)(114, 512)(115, 484)(116, 509)(117, 518)(118, 485)(119, 520)(120, 487)(121, 523)(122, 492)(123, 489)(124, 522)(125, 500)(126, 493)(127, 497)(128, 498)(129, 528)(130, 527)(131, 526)(132, 529)(133, 534)(134, 501)(135, 536)(136, 503)(137, 539)(138, 508)(139, 505)(140, 538)(141, 542)(142, 515)(143, 514)(144, 513)(145, 516)(146, 543)(147, 544)(148, 546)(149, 550)(150, 517)(151, 552)(152, 519)(153, 555)(154, 524)(155, 521)(156, 554)(157, 558)(158, 525)(159, 530)(160, 531)(161, 560)(162, 532)(163, 559)(164, 563)(165, 566)(166, 533)(167, 568)(168, 535)(169, 571)(170, 540)(171, 537)(172, 570)(173, 573)(174, 541)(175, 547)(176, 545)(177, 565)(178, 574)(179, 548)(180, 569)(181, 561)(182, 549)(183, 575)(184, 551)(185, 564)(186, 556)(187, 553)(188, 576)(189, 557)(190, 562)(191, 567)(192, 572)(193, 577)(194, 578)(195, 579)(196, 580)(197, 581)(198, 582)(199, 583)(200, 584)(201, 585)(202, 586)(203, 587)(204, 588)(205, 589)(206, 590)(207, 591)(208, 592)(209, 593)(210, 594)(211, 595)(212, 596)(213, 597)(214, 598)(215, 599)(216, 600)(217, 601)(218, 602)(219, 603)(220, 604)(221, 605)(222, 606)(223, 607)(224, 608)(225, 609)(226, 610)(227, 611)(228, 612)(229, 613)(230, 614)(231, 615)(232, 616)(233, 617)(234, 618)(235, 619)(236, 620)(237, 621)(238, 622)(239, 623)(240, 624)(241, 625)(242, 626)(243, 627)(244, 628)(245, 629)(246, 630)(247, 631)(248, 632)(249, 633)(250, 634)(251, 635)(252, 636)(253, 637)(254, 638)(255, 639)(256, 640)(257, 641)(258, 642)(259, 643)(260, 644)(261, 645)(262, 646)(263, 647)(264, 648)(265, 649)(266, 650)(267, 651)(268, 652)(269, 653)(270, 654)(271, 655)(272, 656)(273, 657)(274, 658)(275, 659)(276, 660)(277, 661)(278, 662)(279, 663)(280, 664)(281, 665)(282, 666)(283, 667)(284, 668)(285, 669)(286, 670)(287, 671)(288, 672)(289, 673)(290, 674)(291, 675)(292, 676)(293, 677)(294, 678)(295, 679)(296, 680)(297, 681)(298, 682)(299, 683)(300, 684)(301, 685)(302, 686)(303, 687)(304, 688)(305, 689)(306, 690)(307, 691)(308, 692)(309, 693)(310, 694)(311, 695)(312, 696)(313, 697)(314, 698)(315, 699)(316, 700)(317, 701)(318, 702)(319, 703)(320, 704)(321, 705)(322, 706)(323, 707)(324, 708)(325, 709)(326, 710)(327, 711)(328, 712)(329, 713)(330, 714)(331, 715)(332, 716)(333, 717)(334, 718)(335, 719)(336, 720)(337, 721)(338, 722)(339, 723)(340, 724)(341, 725)(342, 726)(343, 727)(344, 728)(345, 729)(346, 730)(347, 731)(348, 732)(349, 733)(350, 734)(351, 735)(352, 736)(353, 737)(354, 738)(355, 739)(356, 740)(357, 741)(358, 742)(359, 743)(360, 744)(361, 745)(362, 746)(363, 747)(364, 748)(365, 749)(366, 750)(367, 751)(368, 752)(369, 753)(370, 754)(371, 755)(372, 756)(373, 757)(374, 758)(375, 759)(376, 760)(377, 761)(378, 762)(379, 763)(380, 764)(381, 765)(382, 766)(383, 767)(384, 768) 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 E23.1211 Graph:: simple bipartite v = 196 e = 384 f = 144 degree seq :: [ 2^192, 96^4 ] E23.1215 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 48}) Quotient :: dipole Aut^+ = $<192, 77>$ (small group id <192, 77>) Aut = $<384, 1696>$ (small group id <384, 1696>) |r| :: 2 Presentation :: [ Y1^2, R^2, Y3^-1 * Y1, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, (Y2^-1 * Y1)^4, (Y3 * Y2^-1)^4, Y2^-1 * Y1 * Y2^2 * Y1 * Y2 * Y1 * Y2^-2 * Y1, (Y2^4 * Y1)^2, Y2^6 * Y1 * Y2^-18 * Y1 ] Map:: R = (1, 193, 2, 194)(3, 195, 7, 199)(4, 196, 9, 201)(5, 197, 11, 203)(6, 198, 13, 205)(8, 200, 17, 209)(10, 202, 21, 213)(12, 204, 25, 217)(14, 206, 29, 221)(15, 207, 28, 220)(16, 208, 32, 224)(18, 210, 36, 228)(19, 211, 38, 230)(20, 212, 23, 215)(22, 214, 43, 235)(24, 216, 46, 238)(26, 218, 50, 242)(27, 219, 52, 244)(30, 222, 57, 249)(31, 223, 48, 240)(33, 225, 55, 247)(34, 226, 45, 237)(35, 227, 53, 245)(37, 229, 58, 250)(39, 231, 49, 241)(40, 232, 56, 248)(41, 233, 47, 239)(42, 234, 54, 246)(44, 236, 51, 243)(59, 251, 73, 265)(60, 252, 69, 261)(61, 253, 74, 266)(62, 254, 75, 267)(63, 255, 77, 269)(64, 256, 68, 260)(65, 257, 70, 262)(66, 258, 71, 263)(67, 259, 81, 273)(72, 264, 85, 277)(76, 268, 89, 281)(78, 270, 91, 283)(79, 271, 90, 282)(80, 272, 94, 286)(82, 274, 87, 279)(83, 275, 86, 278)(84, 276, 98, 290)(88, 280, 102, 294)(92, 284, 106, 298)(93, 285, 107, 299)(95, 287, 105, 297)(96, 288, 111, 303)(97, 289, 103, 295)(99, 291, 101, 293)(100, 292, 115, 307)(104, 296, 119, 311)(108, 300, 123, 315)(109, 301, 122, 314)(110, 302, 121, 313)(112, 304, 124, 316)(113, 305, 118, 310)(114, 306, 117, 309)(116, 308, 120, 312)(125, 317, 137, 329)(126, 318, 138, 330)(127, 319, 139, 331)(128, 320, 141, 333)(129, 321, 133, 325)(130, 322, 134, 326)(131, 323, 135, 327)(132, 324, 145, 337)(136, 328, 149, 341)(140, 332, 153, 345)(142, 334, 155, 347)(143, 335, 154, 346)(144, 336, 158, 350)(146, 338, 151, 343)(147, 339, 150, 342)(148, 340, 162, 354)(152, 344, 166, 358)(156, 348, 170, 362)(157, 349, 171, 363)(159, 351, 169, 361)(160, 352, 175, 367)(161, 353, 167, 359)(163, 355, 165, 357)(164, 356, 179, 371)(168, 360, 183, 375)(172, 364, 187, 379)(173, 365, 186, 378)(174, 366, 185, 377)(176, 368, 188, 380)(177, 369, 182, 374)(178, 370, 181, 373)(180, 372, 184, 376)(189, 381, 191, 383)(190, 382, 192, 384)(385, 577, 387, 579, 392, 584, 402, 594, 421, 613, 447, 639, 464, 656, 480, 672, 496, 688, 512, 704, 528, 720, 544, 736, 560, 752, 566, 758, 550, 742, 534, 726, 518, 710, 502, 694, 486, 678, 470, 662, 454, 646, 433, 625, 409, 601, 432, 624, 453, 645, 440, 632, 413, 605, 439, 631, 458, 650, 474, 666, 490, 682, 506, 698, 522, 714, 538, 730, 554, 746, 570, 762, 564, 756, 548, 740, 532, 724, 516, 708, 500, 692, 484, 676, 468, 660, 451, 643, 428, 620, 406, 598, 394, 586, 388, 580)(386, 578, 389, 581, 396, 588, 410, 602, 435, 627, 456, 648, 472, 664, 488, 680, 504, 696, 520, 712, 536, 728, 552, 744, 568, 760, 558, 750, 542, 734, 526, 718, 510, 702, 494, 686, 478, 670, 462, 654, 445, 637, 419, 611, 401, 593, 418, 610, 444, 636, 426, 618, 405, 597, 425, 617, 449, 641, 466, 658, 482, 674, 498, 690, 514, 706, 530, 722, 546, 738, 562, 754, 572, 764, 556, 748, 540, 732, 524, 716, 508, 700, 492, 684, 476, 668, 460, 652, 442, 634, 414, 606, 398, 590, 390, 582)(391, 583, 399, 591, 415, 607, 430, 622, 427, 619, 450, 642, 467, 659, 483, 675, 499, 691, 515, 707, 531, 723, 547, 739, 563, 755, 574, 766, 559, 751, 543, 735, 527, 719, 511, 703, 495, 687, 479, 671, 463, 655, 446, 638, 420, 612, 436, 628, 424, 616, 404, 596, 393, 585, 403, 595, 423, 615, 448, 640, 465, 657, 481, 673, 497, 689, 513, 705, 529, 721, 545, 737, 561, 753, 573, 765, 557, 749, 541, 733, 525, 717, 509, 701, 493, 685, 477, 669, 461, 653, 443, 635, 417, 609, 400, 592)(395, 587, 407, 599, 429, 621, 416, 608, 441, 633, 459, 651, 475, 667, 491, 683, 507, 699, 523, 715, 539, 731, 555, 747, 571, 763, 576, 768, 567, 759, 551, 743, 535, 727, 519, 711, 503, 695, 487, 679, 471, 663, 455, 647, 434, 626, 422, 614, 438, 630, 412, 604, 397, 589, 411, 603, 437, 629, 457, 649, 473, 665, 489, 681, 505, 697, 521, 713, 537, 729, 553, 745, 569, 761, 575, 767, 565, 757, 549, 741, 533, 725, 517, 709, 501, 693, 485, 677, 469, 661, 452, 644, 431, 623, 408, 600) L = (1, 386)(2, 385)(3, 391)(4, 393)(5, 395)(6, 397)(7, 387)(8, 401)(9, 388)(10, 405)(11, 389)(12, 409)(13, 390)(14, 413)(15, 412)(16, 416)(17, 392)(18, 420)(19, 422)(20, 407)(21, 394)(22, 427)(23, 404)(24, 430)(25, 396)(26, 434)(27, 436)(28, 399)(29, 398)(30, 441)(31, 432)(32, 400)(33, 439)(34, 429)(35, 437)(36, 402)(37, 442)(38, 403)(39, 433)(40, 440)(41, 431)(42, 438)(43, 406)(44, 435)(45, 418)(46, 408)(47, 425)(48, 415)(49, 423)(50, 410)(51, 428)(52, 411)(53, 419)(54, 426)(55, 417)(56, 424)(57, 414)(58, 421)(59, 457)(60, 453)(61, 458)(62, 459)(63, 461)(64, 452)(65, 454)(66, 455)(67, 465)(68, 448)(69, 444)(70, 449)(71, 450)(72, 469)(73, 443)(74, 445)(75, 446)(76, 473)(77, 447)(78, 475)(79, 474)(80, 478)(81, 451)(82, 471)(83, 470)(84, 482)(85, 456)(86, 467)(87, 466)(88, 486)(89, 460)(90, 463)(91, 462)(92, 490)(93, 491)(94, 464)(95, 489)(96, 495)(97, 487)(98, 468)(99, 485)(100, 499)(101, 483)(102, 472)(103, 481)(104, 503)(105, 479)(106, 476)(107, 477)(108, 507)(109, 506)(110, 505)(111, 480)(112, 508)(113, 502)(114, 501)(115, 484)(116, 504)(117, 498)(118, 497)(119, 488)(120, 500)(121, 494)(122, 493)(123, 492)(124, 496)(125, 521)(126, 522)(127, 523)(128, 525)(129, 517)(130, 518)(131, 519)(132, 529)(133, 513)(134, 514)(135, 515)(136, 533)(137, 509)(138, 510)(139, 511)(140, 537)(141, 512)(142, 539)(143, 538)(144, 542)(145, 516)(146, 535)(147, 534)(148, 546)(149, 520)(150, 531)(151, 530)(152, 550)(153, 524)(154, 527)(155, 526)(156, 554)(157, 555)(158, 528)(159, 553)(160, 559)(161, 551)(162, 532)(163, 549)(164, 563)(165, 547)(166, 536)(167, 545)(168, 567)(169, 543)(170, 540)(171, 541)(172, 571)(173, 570)(174, 569)(175, 544)(176, 572)(177, 566)(178, 565)(179, 548)(180, 568)(181, 562)(182, 561)(183, 552)(184, 564)(185, 558)(186, 557)(187, 556)(188, 560)(189, 575)(190, 576)(191, 573)(192, 574)(193, 577)(194, 578)(195, 579)(196, 580)(197, 581)(198, 582)(199, 583)(200, 584)(201, 585)(202, 586)(203, 587)(204, 588)(205, 589)(206, 590)(207, 591)(208, 592)(209, 593)(210, 594)(211, 595)(212, 596)(213, 597)(214, 598)(215, 599)(216, 600)(217, 601)(218, 602)(219, 603)(220, 604)(221, 605)(222, 606)(223, 607)(224, 608)(225, 609)(226, 610)(227, 611)(228, 612)(229, 613)(230, 614)(231, 615)(232, 616)(233, 617)(234, 618)(235, 619)(236, 620)(237, 621)(238, 622)(239, 623)(240, 624)(241, 625)(242, 626)(243, 627)(244, 628)(245, 629)(246, 630)(247, 631)(248, 632)(249, 633)(250, 634)(251, 635)(252, 636)(253, 637)(254, 638)(255, 639)(256, 640)(257, 641)(258, 642)(259, 643)(260, 644)(261, 645)(262, 646)(263, 647)(264, 648)(265, 649)(266, 650)(267, 651)(268, 652)(269, 653)(270, 654)(271, 655)(272, 656)(273, 657)(274, 658)(275, 659)(276, 660)(277, 661)(278, 662)(279, 663)(280, 664)(281, 665)(282, 666)(283, 667)(284, 668)(285, 669)(286, 670)(287, 671)(288, 672)(289, 673)(290, 674)(291, 675)(292, 676)(293, 677)(294, 678)(295, 679)(296, 680)(297, 681)(298, 682)(299, 683)(300, 684)(301, 685)(302, 686)(303, 687)(304, 688)(305, 689)(306, 690)(307, 691)(308, 692)(309, 693)(310, 694)(311, 695)(312, 696)(313, 697)(314, 698)(315, 699)(316, 700)(317, 701)(318, 702)(319, 703)(320, 704)(321, 705)(322, 706)(323, 707)(324, 708)(325, 709)(326, 710)(327, 711)(328, 712)(329, 713)(330, 714)(331, 715)(332, 716)(333, 717)(334, 718)(335, 719)(336, 720)(337, 721)(338, 722)(339, 723)(340, 724)(341, 725)(342, 726)(343, 727)(344, 728)(345, 729)(346, 730)(347, 731)(348, 732)(349, 733)(350, 734)(351, 735)(352, 736)(353, 737)(354, 738)(355, 739)(356, 740)(357, 741)(358, 742)(359, 743)(360, 744)(361, 745)(362, 746)(363, 747)(364, 748)(365, 749)(366, 750)(367, 751)(368, 752)(369, 753)(370, 754)(371, 755)(372, 756)(373, 757)(374, 758)(375, 759)(376, 760)(377, 761)(378, 762)(379, 763)(380, 764)(381, 765)(382, 766)(383, 767)(384, 768) 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 E23.1216 Graph:: bipartite v = 100 e = 384 f = 240 degree seq :: [ 4^96, 96^4 ] E23.1216 :: Family: { 3 } :: Oriented family(ies): { E5a } Signature :: (0; {2, 4, 48}) Quotient :: dipole Aut^+ = $<192, 77>$ (small group id <192, 77>) Aut = $<384, 1696>$ (small group id <384, 1696>) |r| :: 2 Presentation :: [ Y2, R^2, (Y1^-1 * Y3^-1)^2, Y1^4, (R * Y1)^2, (R * Y3)^2, (R * Y2 * Y3^-1)^2, Y3^-1 * Y1 * Y3^-2 * Y1 * Y3^-1 * Y1^2, (Y3^3 * Y1^-1)^2, (Y3 * Y1^-1)^4, Y3 * Y1^-1 * Y3^-23 * Y1^-1, (Y3 * Y2^-1)^48 ] Map:: polytopal R = (1, 193, 2, 194, 6, 198, 4, 196)(3, 195, 9, 201, 21, 213, 11, 203)(5, 197, 13, 205, 18, 210, 7, 199)(8, 200, 19, 211, 34, 226, 15, 207)(10, 202, 23, 215, 33, 225, 25, 217)(12, 204, 16, 208, 35, 227, 28, 220)(14, 206, 31, 223, 36, 228, 29, 221)(17, 209, 37, 229, 27, 219, 39, 231)(20, 212, 43, 235, 22, 214, 41, 233)(24, 216, 47, 239, 59, 251, 44, 236)(26, 218, 40, 232, 30, 222, 42, 234)(32, 224, 49, 241, 55, 247, 51, 243)(38, 230, 56, 248, 50, 242, 54, 246)(45, 237, 53, 245, 46, 238, 58, 250)(48, 240, 60, 252, 69, 261, 61, 253)(52, 244, 57, 249, 70, 262, 65, 257)(62, 254, 75, 267, 63, 255, 74, 266)(64, 256, 77, 269, 91, 283, 78, 270)(66, 258, 72, 264, 67, 259, 71, 263)(68, 260, 82, 274, 87, 279, 73, 265)(76, 268, 90, 282, 79, 271, 85, 277)(80, 272, 94, 286, 101, 293, 95, 287)(81, 273, 86, 278, 83, 275, 88, 280)(84, 276, 99, 291, 102, 294, 98, 290)(89, 281, 103, 295, 97, 289, 104, 296)(92, 284, 107, 299, 93, 285, 106, 298)(96, 288, 111, 303, 123, 315, 108, 300)(100, 292, 113, 305, 119, 311, 115, 307)(105, 297, 120, 312, 114, 306, 118, 310)(109, 301, 117, 309, 110, 302, 122, 314)(112, 304, 124, 316, 133, 325, 125, 317)(116, 308, 121, 313, 134, 326, 129, 321)(126, 318, 139, 331, 127, 319, 138, 330)(128, 320, 141, 333, 155, 347, 142, 334)(130, 322, 136, 328, 131, 323, 135, 327)(132, 324, 146, 338, 151, 343, 137, 329)(140, 332, 154, 346, 143, 335, 149, 341)(144, 336, 158, 350, 165, 357, 159, 351)(145, 337, 150, 342, 147, 339, 152, 344)(148, 340, 163, 355, 166, 358, 162, 354)(153, 345, 167, 359, 161, 353, 168, 360)(156, 348, 171, 363, 157, 349, 170, 362)(160, 352, 175, 367, 187, 379, 172, 364)(164, 356, 177, 369, 183, 375, 179, 371)(169, 361, 184, 376, 178, 370, 182, 374)(173, 365, 181, 373, 174, 366, 186, 378)(176, 368, 188, 380, 191, 383, 189, 381)(180, 372, 185, 377, 192, 384, 190, 382)(385, 577)(386, 578)(387, 579)(388, 580)(389, 581)(390, 582)(391, 583)(392, 584)(393, 585)(394, 586)(395, 587)(396, 588)(397, 589)(398, 590)(399, 591)(400, 592)(401, 593)(402, 594)(403, 595)(404, 596)(405, 597)(406, 598)(407, 599)(408, 600)(409, 601)(410, 602)(411, 603)(412, 604)(413, 605)(414, 606)(415, 607)(416, 608)(417, 609)(418, 610)(419, 611)(420, 612)(421, 613)(422, 614)(423, 615)(424, 616)(425, 617)(426, 618)(427, 619)(428, 620)(429, 621)(430, 622)(431, 623)(432, 624)(433, 625)(434, 626)(435, 627)(436, 628)(437, 629)(438, 630)(439, 631)(440, 632)(441, 633)(442, 634)(443, 635)(444, 636)(445, 637)(446, 638)(447, 639)(448, 640)(449, 641)(450, 642)(451, 643)(452, 644)(453, 645)(454, 646)(455, 647)(456, 648)(457, 649)(458, 650)(459, 651)(460, 652)(461, 653)(462, 654)(463, 655)(464, 656)(465, 657)(466, 658)(467, 659)(468, 660)(469, 661)(470, 662)(471, 663)(472, 664)(473, 665)(474, 666)(475, 667)(476, 668)(477, 669)(478, 670)(479, 671)(480, 672)(481, 673)(482, 674)(483, 675)(484, 676)(485, 677)(486, 678)(487, 679)(488, 680)(489, 681)(490, 682)(491, 683)(492, 684)(493, 685)(494, 686)(495, 687)(496, 688)(497, 689)(498, 690)(499, 691)(500, 692)(501, 693)(502, 694)(503, 695)(504, 696)(505, 697)(506, 698)(507, 699)(508, 700)(509, 701)(510, 702)(511, 703)(512, 704)(513, 705)(514, 706)(515, 707)(516, 708)(517, 709)(518, 710)(519, 711)(520, 712)(521, 713)(522, 714)(523, 715)(524, 716)(525, 717)(526, 718)(527, 719)(528, 720)(529, 721)(530, 722)(531, 723)(532, 724)(533, 725)(534, 726)(535, 727)(536, 728)(537, 729)(538, 730)(539, 731)(540, 732)(541, 733)(542, 734)(543, 735)(544, 736)(545, 737)(546, 738)(547, 739)(548, 740)(549, 741)(550, 742)(551, 743)(552, 744)(553, 745)(554, 746)(555, 747)(556, 748)(557, 749)(558, 750)(559, 751)(560, 752)(561, 753)(562, 754)(563, 755)(564, 756)(565, 757)(566, 758)(567, 759)(568, 760)(569, 761)(570, 762)(571, 763)(572, 764)(573, 765)(574, 766)(575, 767)(576, 768) L = (1, 387)(2, 391)(3, 394)(4, 396)(5, 385)(6, 399)(7, 401)(8, 386)(9, 388)(10, 408)(11, 410)(12, 411)(13, 413)(14, 389)(15, 417)(16, 390)(17, 422)(18, 424)(19, 425)(20, 392)(21, 427)(22, 393)(23, 395)(24, 432)(25, 418)(26, 419)(27, 433)(28, 426)(29, 434)(30, 397)(31, 435)(32, 398)(33, 437)(34, 414)(35, 415)(36, 400)(37, 402)(38, 441)(39, 412)(40, 405)(41, 442)(42, 403)(43, 443)(44, 404)(45, 406)(46, 407)(47, 409)(48, 448)(49, 449)(50, 450)(51, 451)(52, 416)(53, 453)(54, 420)(55, 421)(56, 423)(57, 457)(58, 458)(59, 459)(60, 428)(61, 429)(62, 430)(63, 431)(64, 464)(65, 465)(66, 466)(67, 467)(68, 436)(69, 469)(70, 438)(71, 439)(72, 440)(73, 473)(74, 474)(75, 475)(76, 444)(77, 445)(78, 446)(79, 447)(80, 480)(81, 481)(82, 482)(83, 483)(84, 452)(85, 485)(86, 454)(87, 455)(88, 456)(89, 489)(90, 490)(91, 491)(92, 460)(93, 461)(94, 462)(95, 463)(96, 496)(97, 497)(98, 498)(99, 499)(100, 468)(101, 501)(102, 470)(103, 471)(104, 472)(105, 505)(106, 506)(107, 507)(108, 476)(109, 477)(110, 478)(111, 479)(112, 512)(113, 513)(114, 514)(115, 515)(116, 484)(117, 517)(118, 486)(119, 487)(120, 488)(121, 521)(122, 522)(123, 523)(124, 492)(125, 493)(126, 494)(127, 495)(128, 528)(129, 529)(130, 530)(131, 531)(132, 500)(133, 533)(134, 502)(135, 503)(136, 504)(137, 537)(138, 538)(139, 539)(140, 508)(141, 509)(142, 510)(143, 511)(144, 544)(145, 545)(146, 546)(147, 547)(148, 516)(149, 549)(150, 518)(151, 519)(152, 520)(153, 553)(154, 554)(155, 555)(156, 524)(157, 525)(158, 526)(159, 527)(160, 560)(161, 561)(162, 562)(163, 563)(164, 532)(165, 565)(166, 534)(167, 535)(168, 536)(169, 569)(170, 570)(171, 571)(172, 540)(173, 541)(174, 542)(175, 543)(176, 568)(177, 574)(178, 573)(179, 572)(180, 548)(181, 575)(182, 550)(183, 551)(184, 552)(185, 558)(186, 564)(187, 576)(188, 556)(189, 557)(190, 559)(191, 567)(192, 566)(193, 577)(194, 578)(195, 579)(196, 580)(197, 581)(198, 582)(199, 583)(200, 584)(201, 585)(202, 586)(203, 587)(204, 588)(205, 589)(206, 590)(207, 591)(208, 592)(209, 593)(210, 594)(211, 595)(212, 596)(213, 597)(214, 598)(215, 599)(216, 600)(217, 601)(218, 602)(219, 603)(220, 604)(221, 605)(222, 606)(223, 607)(224, 608)(225, 609)(226, 610)(227, 611)(228, 612)(229, 613)(230, 614)(231, 615)(232, 616)(233, 617)(234, 618)(235, 619)(236, 620)(237, 621)(238, 622)(239, 623)(240, 624)(241, 625)(242, 626)(243, 627)(244, 628)(245, 629)(246, 630)(247, 631)(248, 632)(249, 633)(250, 634)(251, 635)(252, 636)(253, 637)(254, 638)(255, 639)(256, 640)(257, 641)(258, 642)(259, 643)(260, 644)(261, 645)(262, 646)(263, 647)(264, 648)(265, 649)(266, 650)(267, 651)(268, 652)(269, 653)(270, 654)(271, 655)(272, 656)(273, 657)(274, 658)(275, 659)(276, 660)(277, 661)(278, 662)(279, 663)(280, 664)(281, 665)(282, 666)(283, 667)(284, 668)(285, 669)(286, 670)(287, 671)(288, 672)(289, 673)(290, 674)(291, 675)(292, 676)(293, 677)(294, 678)(295, 679)(296, 680)(297, 681)(298, 682)(299, 683)(300, 684)(301, 685)(302, 686)(303, 687)(304, 688)(305, 689)(306, 690)(307, 691)(308, 692)(309, 693)(310, 694)(311, 695)(312, 696)(313, 697)(314, 698)(315, 699)(316, 700)(317, 701)(318, 702)(319, 703)(320, 704)(321, 705)(322, 706)(323, 707)(324, 708)(325, 709)(326, 710)(327, 711)(328, 712)(329, 713)(330, 714)(331, 715)(332, 716)(333, 717)(334, 718)(335, 719)(336, 720)(337, 721)(338, 722)(339, 723)(340, 724)(341, 725)(342, 726)(343, 727)(344, 728)(345, 729)(346, 730)(347, 731)(348, 732)(349, 733)(350, 734)(351, 735)(352, 736)(353, 737)(354, 738)(355, 739)(356, 740)(357, 741)(358, 742)(359, 743)(360, 744)(361, 745)(362, 746)(363, 747)(364, 748)(365, 749)(366, 750)(367, 751)(368, 752)(369, 753)(370, 754)(371, 755)(372, 756)(373, 757)(374, 758)(375, 759)(376, 760)(377, 761)(378, 762)(379, 763)(380, 764)(381, 765)(382, 766)(383, 767)(384, 768) local type(s) :: { ( 4, 96 ), ( 4, 96, 4, 96, 4, 96, 4, 96 ) } Outer automorphisms :: reflexible Dual of E23.1215 Graph:: simple bipartite v = 240 e = 384 f = 100 degree seq :: [ 2^192, 8^48 ] ## Checksum: 1216 records. ## Written on: Sun Oct 20 11:42:53 CEST 2019